Finite Group Databasebeta

← #15618054

Subgroups — #15618054

Order 2816.

2818 conjugacy classes of subgroups.

The subgroup lattice has 1262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623305C211yesmaximal, characteristic
2C4×#67042C211yesmaximal, characteristic, complemented
3C4×#67037C211yesmaximal, characteristic, complemented
4#13077495C211yesmaximal, characteristic, complemented
5#13077494C212yesmaximal, complemented
6#13077464C211yesmaximal, characteristic, complemented
7#13077463C212yesmaximal, complemented
8#13077449C211yesmaximal, characteristic, complemented
9#13077446C211yesmaximal, characteristic, complemented
10#13077443C212yesmaximal, complemented
11#13077441C212yesmaximal, complemented
12C4×#66961C211yesmaximal, characteristic, complemented
13#13077427C212yesmaximal, complemented
14#13077421C212yesmaximal, complemented
15#13077414C211yesmaximal, characteristic, complemented
16#13077411C212yesmaximal, complemented
17C2×#10622627C211yesmaximal, characteristic, complemented
18D11×#442C212yesmaximal, complemented
19#13077210C211yesmaximal, characteristic, complemented
20#13077141C211yesmaximal, characteristic, complemented
21#13077140C211yesmaximal, characteristic, complemented
22#13077045C211yesmaximal, characteristic, complemented
23C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
24C2×#67042C2211yescharacteristic
25C2×#67037C2211yescharacteristic
26C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
27C4×C11×#41C2211yescharacteristic, complemented
28C2×C4×D4×C11C2211yescharacteristic, complemented
29#10623358C2211yescharacteristic, complemented
30C2×#67003C2211yescharacteristic
31#10623329C2211yescharacteristic, complemented
32C22×#4323C2211yescharacteristic
33C2×C4×C22⋊D11—22no—
34#10623305C4116yescomplemented
35C2×#66969C2212yes—
36C2×#66967C2212yes—
37C2×#66964C2212yes—
38C2×D8×D11C2212yes—
39C2×#66961C2211yescharacteristic
40C2×#66960C2211yescharacteristic
41C2×#66960C2211yescharacteristic
42#10623105C2212yescomplemented
43C4×#4343C2212yescomplemented
44#10623077—21no—
45#10623077C2212yescomplemented
46#10623076—22no—
47#10623076—21no—
48#10623076C2212yescomplemented
49#10623076C2212yescomplemented
50C4×D4×D11—22no—
51C4×D4×D11—21no—
52C4×D4×D11C2212yescomplemented
53C4×D4×D11C2212yescomplemented
54C4×#4341—21no—
55C4×#4341C2212yescomplemented
56#10623054—21no—
57#10623054C2211yescharacteristic
58#10623052—21no—
59#10623052C2211yescharacteristic, complemented
60#10623035C2211yescharacteristic
61#10623035C2211yescharacteristic, complemented
62#10623017—22no—
63C4×#4339—21no—
64C4×#4339C2211yescharacteristic
65C4×#4339C2211yescharacteristic, complemented
66C2×C4×D44—21no—
67C2×C4×D44C2211yescharacteristic, complemented
68C11×#442C2212yescomplemented
69C11×#440C2212yescomplemented
70C4×C11×SD16C2212yescomplemented
71C4×C11×D8C2212yescomplemented
72C11×#428C2211yescharacteristic, complemented
73C11×#418C2211yescharacteristic, complemented
74C11×#417C2211yescharacteristic, complemented
75C4×C11×M16C2211yescharacteristic, complemented
76#10622846C2211yescharacteristic, complemented
77C2×#66896C2211yescharacteristic, complemented
78#10622777C2212yescomplemented
79SD16×Dic11C2212yescomplemented
80#10622765C2212yescomplemented
81D8×Dic11C2212yescomplemented
82#10622746C2211yescharacteristic, complemented
83#10622744C2211yescharacteristic, complemented
84#10622735C2211yescharacteristic, complemented
85#10622735C2211yescharacteristic, complemented
86#10622734C2211yescharacteristic, complemented
87#10622643C2211yescharacteristic, complemented
88#10622643C2211yescharacteristic, complemented
89#10622639C2211yescharacteristic, complemented
90#10622639C2211yescharacteristic, complemented
91#10622631C2211yescharacteristic, complemented
92#10622631C2211yescharacteristic, complemented
93#10622627C2211yescharacteristic, complemented
94#10622627C2212yescomplemented
95#10622627C2212yescomplemented
96#10622627C2212yescomplemented
97#10622627C2212yescomplemented
98#10622627C2211yescharacteristic, complemented
99#10622615C2211yescharacteristic, complemented
100#10622611C2211yescharacteristic, complemented
101C2×#66873C2211yescharacteristic, complemented
102C2×#66872C2211yescharacteristic, complemented
103C2×#66867C2211yescharacteristic, complemented
104#10622502C2212yescomplemented
105#10622494C2212yescomplemented
106#10622493C2212yescomplemented
107#10622485C2212yescomplemented
108#10622482C2212yescomplemented
109#10622474C2212yescomplemented
110D11×#106C2212yescomplemented
111#10622465C2212yescomplemented
112#10622417C2212yescomplemented
113#10622416C2212yescomplemented
114#10622402C2212yescomplemented
115#10622401C2212yescomplemented
116#10622398C2212yescomplemented
117#10622398C2212yescomplemented
118#10622398C2212yescomplemented
119#10622385C2212yescomplemented
120#10622384C2212yescomplemented
121#10622383C2212yescomplemented
122#10622383C2212yescomplemented
123D11×#102C2212yescomplemented
124D11×#102C2212yescomplemented
125#10622371C2212yescomplemented
126#10622369C2212yescomplemented
127#10622369C2212yescomplemented
128#10622324C2212yescomplemented
129#10622323C2212yescomplemented
130#10622320C2212yescomplemented
131D11×#97C2212yescomplemented
132C4×D88C2212yescomplemented
133C4×#4314C2212yescomplemented
134#10622302C2212yescomplemented
135#10622302C2212yescomplemented
136C2×C11×#41C2311yescharacteristic
137C22×D4×C11C2311yescharacteristic
138C23×C4×C11—21no—
139C22×C22⋊D11—22no—
140#67042—24no—
141#67042C2×C418yescomplemented
142C2×#4343C2312yes—
143#67037—24no—
144#67037C2×C418yescomplemented
145C2×#4341—21no—
146C2×#4341C2312yes—
147C2×D4×D11—22no—
148C2×D4×D11—21no—
149C2×D4×D11C2312yes—
150C2×D4×D11C2312yes—
151C2×#4339—21no—
152C2×#4339C2311yescharacteristic
153C2×#4339C2311yescharacteristic
154C22×D44—21no—
155C22×D44C2311yescharacteristic
156C22×C4×D11—21no—
157C22×C4×D11—22no—
158C22×C4×D11—22no—
159C11×AGL(1,ℤ/8)C2×C418yescomplemented
160C2×C11×SD16C2312yes—
161C2×C11×D8C2312yes—
162C2×C11×M16C2311yescharacteristic
163C2×C11×M16C2311yescharacteristic
164C4×Q8×C11C2311yescharacteristic
165C4×Q8×C11C2311yescharacteristic
166C4×D4×C11—21no—
167C4×D4×C11—21no—
168C4×D4×C11—21no—
169C4×D4×C11—21no—
170C4×D4×C11C2312yes—
171C4×D4×C11C2311yescharacteristic
172C4×D4×C11C2311yescharacteristic
173C4×D4×C11C2312yes—
174C11×#117—21no—
175C11×#117C2311yescharacteristic
176C2×C11×C4⋊C4C2311yescharacteristic
177C2×C11×C22⋊C4—21no—
178C2×C42×C11—21no—
179C2×C42×C11C2311yescharacteristic
180C2×C22⋊Dic11—22no—
181#67003C2×C418yescomplemented
182Q8×Dic11C2312yes—
183C2×#4326C2311yescharacteristic
184C2×#4325C2311yescharacteristic
185D4×Dic11—22no—
186D4×Dic11—21no—
187D4×Dic11—21no—
188D4×Dic11C2312yes—
189D4×Dic11C2312yes—
190D4×Dic11C2312yes—
191C2×#4324C2311yescharacteristic
192C2×#4323C2×C418yescomplemented
193C2×#4323C2311yescharacteristic
194C2×#4323C2312yes—
195C2×#4323C2312yes—
196C4×C22⋊D11—21no—
197C4×C22⋊D11—21no—
198C4×C22⋊D11—22no—
199C4×C22⋊D11—22no—
200C4×C22⋊D11—22no—
201C4×C22⋊D11—22no—
202C4×C22⋊D11—22no—
203C4×C22⋊D11—22no—
204C4×C22⋊D11—22no—
205C4×C22⋊D11—22no—
206C4×C22⋊D11D412yes—
207C4×C22⋊D11D412yes—
208C2×(C2×D11)⋊C4—21no—
209C2×(C2×D11)⋊C4—22no—
210C2×(C2×D11)⋊C4—22no—
211#66979—21no—
212#66979C2311yescharacteristic
213#66979C2311yescharacteristic
214C2×C4⋊Dic11—21no—
215C2×C4⋊Dic11C2311yescharacteristic
216C2×Dic11⋊C4—22no—
217C2×C4×Dic11—22no—
218C22×C11⋊C8C2311yescharacteristic
219C22×C11⋊C8C2311yescharacteristic
220#66969C2×C4116yescomplemented
221#66967C2×C4116yescomplemented
222#66964C2×C4116yescomplemented
223D8×D11C2×C4116yescomplemented
224#66961C2×C418yescomplemented
225#66960—24no—
226#66960C2×C418yescomplemented
227C2×D88C2312yes—
228C2×#4314C2312yes—
229C2×#4313C2312yes—
230C2×#4313C2312yes—
231C2×C8×D11C2312yes—
232C2×C8×D11C2312yes—
233#66946—21no—
234#66946—22no—
235#66946—22no—
236#66946C2312yes—
237#66946C2312yes—
238#66946C2312yes—
239#66945—21no—
240#66945—22no—
241#66945C2312yes—
242#66945C2312yes—
243C4⋊C4×D11—21no—
244C4⋊C4×D11—22no—
245C4⋊C4×D11C2312yes—
246C4⋊C4×D11C2312yes—
247#66940—21no—
248#66940C2312yes—
249(C22⋊D11)⋊C4—22no—
250(C22⋊D11)⋊C4—22no—
251(C22⋊D11)⋊C4—22no—
252(C22⋊D11)⋊C4—22no—
253(C22⋊D11)⋊C4—22no—
254(C22⋊D11)⋊C4—22no—
255(C22⋊D11)⋊C4—22no—
256C22⋊C4×D11—22no—
257C22⋊C4×D11—22no—
258C22⋊C4×D11—22no—
259C22⋊C4×D11—22no—
260C22⋊C4×D11—22no—
261#66930—22no—
262#66930—22no—
263C4×D44—21no—
264C4×D44—22no—
265C4×D44—21no—
266C4×D44—21no—
267C4×D44—22no—
268C4×D44—21no—
269C4×D44—21no—
270C4×D44D411yescharacteristic
271C4×D44D411yescharacteristic
272C4×D44C2312yes—
273C4×D44C2312yes—
274C4×D44C2311yescharacteristic
275C4×D44C2311yescharacteristic
276#66925—21no—
277#66925—22no—
278#66925C2312yes—
279C42×D11—21no—
280C42×D11—22no—
281C42×D11C2312yes—
282C4×Dic22—21no—
283C4×Dic22D411yescharacteristic
284C4×Dic22D411yescharacteristic
285C4×Dic22C2311yescharacteristic
286C4×Dic22C2311yescharacteristic
287C11×#107C2312yes—
288C11×#106C2312yes—
289C11×#103C2312yes—
290C11×#102C2312yes—
291C11×#102C2312yes—
292C11×#102C2312yes—
293C11×#97C2312yes—
294C4×C8×C11C2312yes—
295#66899C2311yescharacteristic
296#66899C2311yescharacteristic
297#66896C2311yescharacteristic
298#66896C2312yes—
299#66896C2311yescharacteristic
300#66896C2312yes—
301#66885C2312yes—
302#66885C2312yes—
303#66885C2312yes—
304#66882C2312yes—
305#66881C2312yes—
306#66880C2312yes—
307#66879C2312yes—
308#66879C2312yes—
309C8×Dic11C2312yes—
310C8×Dic11C2312yes—
311#66874C2311yescharacteristic
312#66874C2311yescharacteristic
313#66873C2312yes—
314#66873C2311yescharacteristic
315#66873C2312yes—
316#66873C2311yescharacteristic
317#66872C2311yescharacteristic
318#66872C2312yes—
319#66872C2312yes—
320#66872C2311yescharacteristic
321#66871C2311yescharacteristic
322#66871C2311yescharacteristic
323#66867C2311yescharacteristic
324#66867C2311yescharacteristic
325#66867C2311yescharacteristic
326#66867C2311yescharacteristic
327#60176—111nomaximal, Sylow
328C24×C11—21no—
329C23×D11—21no—
330C23×D11—22no—
331C23×D11—22no—
332C11×#41—22no—
333C11×#41C22×C414yescomplemented
334C2×Q8×C11C2411yescharacteristic
335C2×D4×C11—21no—
336C2×D4×C11—21no—
337C2×D4×C11—22no—
338C2×D4×C11C22×C414yescomplemented
339C2×D4×C11C2412yes—
340C2×D4×C11C2411yescharacteristic
341C22×C4×C11—21no—
342C22×C4×C11—21no—
343C22×C4×C11—22no—
344C22×C4×C11—21no—
345C22×C4×C11—22no—
346C22×C4×C11—21no—
347C22×C4×C11—82no—
348C22×C4×C11C2×D411yescharacteristic
349C22×C4×C11C2×D411yescharacteristic
350C22×C4×C11C2411yescharacteristic
351C2×C22⋊D11—216no—
352C2×C22⋊D11—22no—
353C2×C22⋊D11—22no—
354C2×C22⋊D11—21no—
355C2×C22⋊D11—22no—
356C2×C22⋊D11C2×D412yes—
357C22×Dic11—22no—
358C22×Dic11—22no—
359C22×Dic11—22no—
360C22×Dic11—22no—
361C22×Dic11—21no—
362#4343—24no—
363#4343C22×C418yescomplemented
364#4341—24no—
365#4341—28no—
366#4341C22×C418yescomplemented
367D4×D11—216no—
368D4×D11—28no—
369D4×D11—24no—
370D4×D11—24no—
371D4×D11C22×C418yescomplemented
372D4×D11C22×C418yescomplemented
373#4339—28no—
374#4339—22no—
375#4339C22×C414yes—
376#4339C22×C414yescomplemented
377#4339#4114yes—
378C2×D44—28no—
379C2×D44—22no—
380C2×D44—21no—
381C2×D44—22no—
382C2×D44C22×C414yescomplemented
383C2×D44C2×D411yescharacteristic
384C2×D44C2412yes—
385C2×D44C2411yescharacteristic
386C2×C4×D11—22no—
387C2×C4×D11—22no—
388C2×C4×D11—22no—
389C2×C4×D11—22no—
390C2×C4×D11—22no—
391C2×C4×D11—22no—
392C2×C4×D11—21no—
393C2×C4×D11—22no—
394C2×C4×D11—21no—
395C2×C4×D11—21no—
396C2×C4×D11—22no—
397C2×C4×D11—82no—
398C2×C4×D11—84no—
399C2×C4×D11—84no—
400C2×C4×D11C2×D412yes—
401C2×C4×D11C2×D412yes—
402C2×C4×D11C2412yes—
403C2×Dic22C2×D411yescharacteristic
404C2×Dic22C2411yescharacteristic
405C11×SD16C22×C418yescomplemented
406C11×D8C22×C418yescomplemented
407C11×M16—22no—
408C11×M16C22×C414yescomplemented
409C2×C8×C11C2412yes—
410C2×C8×C11C2412yes—
411C11×C4⋊C4—21no—
412C11×C4⋊C4—21no—
413C11×C4⋊C4—21no—
414C11×C4⋊C4C2411yescharacteristic
415C11×C4⋊C4C2411yescharacteristic
416C11×C4⋊C4C2412yes—
417C11×C22⋊C4—21no—
418C11×C22⋊C4—22no—
419C11×C22⋊C4—22no—
420C11×C22⋊C4—21no—
421C11×C22⋊C4—21no—
422C42×C11—21no—
423C42×C11—21no—
424C42×C11—21no—
425C42×C11C2×D411yescharacteristic
426C42×C11C2×D411yescharacteristic
427C42×C11C2411yescharacteristic
428C42×C11C2411yescharacteristic
429C22⋊Dic11—22no—
430C22⋊Dic11—22no—
431C22⋊Dic11—22no—
432C22⋊Dic11—21no—
433C22⋊Dic11C2×D412yes—
434#4326C22×C414yescomplemented
435#4325C22×C414yescomplemented
436#4324C22×C414yescomplemented
437#4323C22×C414yescomplemented
438#4323C22×C418yescomplemented
439#4323C22×C418yescomplemented
440(C2×D11)⋊C4—22no—
441(C2×D11)⋊C4—22no—
442(C2×D11)⋊C4—22no—
443(C2×D11)⋊C4—22no—
444(C2×D11)⋊C4—22no—
445(C2×D11)⋊C4—22no—
446(C2×D11)⋊C4—21no—
447(C2×D11)⋊C4—21no—
448(C2×D11)⋊C4—22no—
449(C2×D11)⋊C4C2×D412yes—
450(C2×D11)⋊C4C2×D412yes—
451C4⋊Dic11—22no—
452C4⋊Dic11—21no—
453C4⋊Dic11C2×D411yescharacteristic
454C4⋊Dic11C2×D411yescharacteristic
455C4⋊Dic11C2411yescharacteristic
456C4⋊Dic11C2411yescharacteristic
457C4⋊Dic11C2412yes—
458Dic11⋊C4—22no—
459Dic11⋊C4—22no—
460Dic11⋊C4—22no—
461Dic11⋊C4—21no—
462Dic11⋊C4—21no—
463Dic11⋊C4C2×D412yes—
464Dic11⋊C4C2×D412yes—
465C4×Dic11—22no—
466C4×Dic11—22no—
467C4×Dic11—22no—
468C4×Dic11—22no—
469C4×Dic11—21no—
470C4×Dic11—21no—
471C4×Dic11—21no—
472C4×Dic11C2×D412yes—
473C4×Dic11C2×D412yes—
474C4×Dic11C2412yes—
475C2×C11⋊C8—22no—
476C2×C11⋊C8C22×C414yescomplemented
477C2×C11⋊C8C2411yescharacteristic
478C2×C11⋊C8C2411yescharacteristic
479C2×C11⋊C8C2411yescharacteristic
480C2×C11⋊C8C2411yescharacteristic
481D88C22×C418yescomplemented
482#4314C22×C418yescomplemented
483#4313—24no—
484#4313C22×C418yescomplemented
485C8×D11—24no—
486C8×D11C22×C418yescomplemented
487C2×#576—111no—
488C4×H(5,𝔽2)—111no—
489C4×H(5,𝔽2)—111no—
490#2952—112no—
491#2952—111no—
492#2948—112no—
493#2948—111no—
494#2946—112no—
495#2946—112no—
496#2946—111no—
497#2946—111no—
498C4×AGL(1,ℤ/8)—112no—
499C4×AGL(1,ℤ/8)—112no—
500C4×AGL(1,ℤ/8)—111no—
501C4×AGL(1,ℤ/8)D1111yescharacteristic, complemented
502#2943—112no—
503#2943—111no—
504C2×#442—112no—
505C2×#442—111no—
506#2912—111no—
507#2897—111no—
508#2897—111no—
509#2875—111no—
510C23×C11—22no—
511C23×C11—21no—
512C23×C11—24no—
513C23×C11—81no—
514C23×C11—81no—
515C23×C11C22×D411yescharacteristic
516C22×D11—22no—
517C22×D11—21no—
518C22×D11—24no—
519C22×D11—28no—
520C22×D11—28no—
521C22×D11—82no—
522C22×D11—82no—
523C22×D11—82no—
524C22×D11—82no—
525C22×D11—81no—
526C22×D11—81no—
527C22×D11C22×D412yes—
528Q8×C11—21no—
529Q8×C11C23×C412yes—
530D4×C11—24no—
531D4×C11—24no—
532D4×C11—21no—
533D4×C11—22no—
534D4×C11C23×C414yes—
535D4×C11C23×C412yes—
536C2×C4×C11—21no—
537C2×C4×C11—24no—
538C2×C4×C11—22no—
539C2×C4×C11—21no—
540C2×C4×C11—21no—
541C2×C4×C11—41no—
542C2×C4×C11—41no—
543C2×C4×C11—42no—
544C2×C4×C11—44no—
545C2×C4×C11—81no—
546C2×C4×C11—82no—
547C2×C4×C11—81no—
548C2×C4×C11C23×C412yes—
549C2×C4×C11C22×D411yescharacteristic
550C2×C4×C11C22×D411yescharacteristic
551C2×C4×C11C22×D411yescharacteristic
552C2×C4×C11C22×D411yescharacteristic
553C2×C4×C11C22×D411yescharacteristic
554C2×C4×C11C2×#4112yes—
555C2×C4×C11C2511yescharacteristic
556C22⋊D11—24no—
557C22⋊D11—28no—
558C22⋊D11—28no—
559C22⋊D11—28no—
560C22⋊D11C4×D418yes—
561C2×Dic11—21no—
562C2×Dic11—28no—
563C2×Dic11—21no—
564C2×Dic11—21no—
565C2×Dic11—22no—
566C2×Dic11—82no—
567C2×Dic11—82no—
568C2×Dic11—82no—
569C2×Dic11—81no—
570C2×Dic11C22×D412yes—
571C2×Dic11C22×D412yes—
572C2×Dic11C22×D412yes—
573D44—28no—
574D44—24no—
575D44—22no—
576D44—21no—
577D44C4×D414yes—
578D44C23×C414yes—
579D44C23×C412yes—
580C4×D11—24no—
581C4×D11—28no—
582C4×D11—42no—
583C4×D11—42no—
584C4×D11—42no—
585C4×D11—44no—
586C4×D11—82no—
587C4×D11—82no—
588C4×D11—82no—
589C4×D11—81no—
590C4×D11—82no—
591C4×D11—82no—
592C4×D11—82no—
593C4×D11C23×C414yes—
594C4×D11C2×#4114yes—
595Dic22—21no—
596Dic22C4×D414yes—
597Dic22C23×C412yes—
598C8×C11—22no—
599C8×C11C23×C414yes—
600C11⋊C8—21no—
601C11⋊C8—21no—
602C11⋊C8C23×C412yes—
603C11⋊C8C23×C412yes—
604C2×H(5,𝔽2)—111no—
605C2×H(5,𝔽2)—111no—
606#576—1116no—
607C2×AGL(1,ℤ/8)—112no—
608C2×AGL(1,ℤ/8)—112no—
609C2×AGL(1,ℤ/8)—111no—
610C2×AGL(1,ℤ/8)C2×D1111yescharacteristic
611C2×#135—111no—
612C2×#135—112no—
613C22×D8—111no—
614C22×D8—112no—
615C2×#131—111no—
616C2×#131—111no—
617#520—111no—
618#520—111no—
619#520—111no—
620#520—112no—
621#520—112no—
622#520—111no—
623#520—221no—
624#520—221no—
625#518—111no—
626#518—112no—
627#518—112no—
628#518—111no—
629#518—222no—
630#518—221no—
631#518—222no—
632#518—221no—
633C4×#41—111no—
634C4×#41—112no—
635C4×#41—112no—
636C4×#41—111no—
637C4×#41—221no—
638C4×#41—221no—
639C4×#41C2×D1111yescharacteristic, complemented
640C2×C4×D4—112no—
641C2×C4×D4—112no—
642C2×C4×D4—111no—
643C2×C4×D4—221no—
644C2×C4×D4—222no—
645C2×C4×D4—221no—
646C2×C4×D4—222no—
647C2×C4×D4C2×D1111yescharacteristic, complemented
648#442—112no—
649#442—111no—
650#442—112no—
651#442—112no—
652#442—112no—
653#442—112no—
654#442—111no—
655#442—112no—
656#442—112no—
657#442—112no—
658#442—112no—
659#442—112no—
660#442C2×D1112yescomplemented
661#441—111no—
662#441—111no—
663#441—112no—
664#440—112no—
665#440—111no—
666#440—111no—
667#440—111no—
668#440—111no—
669#440—112no—
670#440—112no—
671#440C2×D1112yescomplemented
672C4×SD16—112no—
673C4×SD16—112no—
674C4×SD16—112no—
675C4×SD16—112no—
676C4×SD16—112no—
677C4×SD16C2×D1112yescomplemented
678C4×D8—112no—
679C4×D8—112no—
680C4×D8—112no—
681C4×D8—112no—
682C4×D8—112no—
683C4×D8C2×D1112yescomplemented
684#428—111no—
685#428—112no—
686#428—112no—
687#428C2×D1111yescharacteristic, complemented
688#427—111no—
689#427—112no—
690C2×#106—111no—
691C2×#106—112no—
692#418—111no—
693#418—112no—
694#418—112no—
695#418C2×D1111yescharacteristic, complemented
696#417—111no—
697#417—112no—
698#417—112no—
699#417C2×D1111yescharacteristic, complemented
700#416—111no—
701#416—111no—
702#416—112no—
703#416—112no—
704C2×#102—111no—
705C2×#102—111no—
706C2×#102—112no—
707C2×#102—112no—
708#405—111no—
709#405—111no—
710#405—112no—
711#405—112no—
712C4×M16—112no—
713C4×M16C2×D1111yescharacteristic, complemented
714C2×#97—111no—
715C2×#97—112no—
716C22×C11—21no—
717C22×C11—21no—
718C22×C11—22no—
719C22×C11—24no—
720C22×C11—42no—
721C22×C11—41no—
722C22×C11—41no—
723C22×C11—42no—
724C22×C11—84no—
725C22×C11C2×C4×D412yes—
726C22×C11C23×D411yescharacteristic
727C2×D11—22no—
728C2×D11—22no—
729C2×D11—24no—
730C2×D11—22no—
731C2×D11—41no—
732C2×D11—42no—
733C2×D11—42no—
734C2×D11—41no—
735C2×D11—88no—
736C2×D11—88no—
737C2×D11—84no—
738C2×D11C2×C4×D414yes—
739C4×C11—21no—
740C4×C11—21no—
741C4×C11—21no—
742C4×C11—21no—
743C4×C11—22no—
744C4×C11—42no—
745C4×C11—41no—
746C4×C11—41no—
747C4×C11C2×C4×D412yes—
748C4×C11C24×C411yescharacteristic
749C4×C11C22×#4111yescharacteristic
750Dic11—22no—
751Dic11—22no—
752Dic11—22no—
753Dic11—41no—
754Dic11—42no—
755Dic11—41no—
756Dic11C2×C4×D414yes—
757H(5,𝔽2)—118no—
758H(5,𝔽2)—118no—
759H(5,𝔽2)—224no—
760H(5,𝔽2)—224no—
761C2×#41—111no—
762C2×#41—112no—
763C2×#41—112no—
764C2×#41—111no—
765C2×#41—221no—
766C2×#41—221no—
767C2×#41C22×D1111yescharacteristic
768C22×D4—112no—
769C22×D4—112no—
770C22×D4—111no—
771C22×D4—221no—
772C22×D4—222no—
773C22×D4—221no—
774C22×D4—222no—
775C22×D4C22×D1111yescharacteristic
776C23×C4—21no—
777C23×C4—222no—
778C23×C4—222no—
779C23×C4—221no—
780AGL(1,ℤ/8)—1116no—
781AGL(1,ℤ/8)—1116no—
782AGL(1,ℤ/8)—118no—
783AGL(1,ℤ/8)C4×D1118yescomplemented
784#135—118no—
785#135—1116no—
786C2×Q16—111no—
787C2×SD16—111no—
788C2×SD16—111no—
789C2×SD16—112no—
790C2×SD16C22×D1112yes—
791C2×D8—118no—
792C2×D8—112no—
793C2×D8—111no—
794C2×D8—112no—
795C2×D8—1116no—
796C2×D8—112no—
797C2×D8C22×D1112yes—
798#131—118no—
799#131—224no—
800C2×M16—112no—
801C2×M16—112no—
802C2×M16C22×D1111yescharacteristic
803C2×M16C22×D1111yescharacteristic
804C22×C8—111no—
805C22×C8—112no—
806C22×C8—111no—
807C22×C8—112no—
808C4×Q8—111no—
809C4×Q8—111no—
810C4×Q8—112no—
811C4×Q8—112no—
812C4×Q8—111no—
813C4×Q8—111no—
814C4×Q8—221no—
815C4×Q8—221no—
816C4×Q8C22×D1111yescharacteristic
817C4×Q8C22×D1111yescharacteristic
818C4×D4—21no—
819C4×D4—21no—
820C4×D4—21no—
821C4×D4—21no—
822C4×D4—112no—
823C4×D4—112no—
824C4×D4—112no—
825C4×D4—112no—
826C4×D4—112no—
827C4×D4—112no—
828C4×D4—112no—
829C4×D4—112no—
830C4×D4—111no—
831C4×D4—111no—
832C4×D4—111no—
833C4×D4—112no—
834C4×D4—112no—
835C4×D4—111no—
836C4×D4—222no—
837C4×D4—221no—
838C4×D4—221no—
839C4×D4—222no—
840C4×D4—221no—
841C4×D4—222no—
842C4×D4—222no—
843C4×D4—222no—
844C4×D4—222no—
845C4×D4—222no—
846C4×D4—222no—
847C4×D4—222no—
848C4×D4—222no—
849C4×D4—222no—
850C4×D4—222no—
851C4×D4—222no—
852C4×D4—222no—
853C4×D4—222no—
854C4×D4—222no—
855C4×D4—221no—
856C4×D4—222no—
857C4×D4—222no—
858C4×D4—221no—
859C4×D4—221no—
860C4×D4—222no—
861C4×D4—222no—
862C4×D4—221no—
863C4×D4—221no—
864C4×D4—221no—
865C4×D4—221no—
866C4×D4C22×D1111yescharacteristic
867C4×D4C22×D1112yes—
868C4×D4C22×D1112yes—
869C4×D4C22×D1111yescharacteristic
870#117—21no—
871#117—111no—
872#117—112no—
873#117—111no—
874#117—112no—
875#117—112no—
876#117—222no—
877#117—222no—
878#117—222no—
879#117—222no—
880#117—221no—
881#117—221no—
882#117—221no—
883#117C22×D1111yescharacteristic
884C2×C4⋊C4—111no—
885C2×C4⋊C4—112no—
886C2×C4⋊C4—112no—
887C2×C4⋊C4—222no—
888C2×C4⋊C4—221no—
889C2×C4⋊C4—222no—
890C2×C4⋊C4—221no—
891C2×C4⋊C4C22×D1111yescharacteristic
892C2×C22⋊C4—21no—
893C2×C22⋊C4—222no—
894C2×C22⋊C4—222no—
895C2×C22⋊C4—222no—
896C2×C22⋊C4—222no—
897C2×C22⋊C4—222no—
898C2×C22⋊C4—222no—
899C2×C22⋊C4—222no—
900C2×C22⋊C4—222no—
901C2×C22⋊C4—221no—
902C2×C42—21no—
903C2×C42—112no—
904C2×C42—222no—
905C2×C42—222no—
906C2×C42—221no—
907C2×C42C22×D1111yescharacteristic
908#107—112no—
909#107—111no—
910#107—111no—
911#107C22×D1112yes—
912#106—112no—
913#106—112no—
914#106—111no—
915#106—112no—
916#106—111no—
917#106C22×D1112yes—
918#103—111no—
919#103—111no—
920#103—112no—
921#103—111no—
922#103—111no—
923#103C22×D1112yes—
924#102—112no—
925#102—111no—
926#102—112no—
927#102—111no—
928#102—112no—
929#102—112no—
930#102—112no—
931#102—112no—
932#102—111no—
933#102—112no—
934#102—111no—
935#102C22×D1112yes—
936#102C22×D1112yes—
937#102C22×D1112yes—
938#97—112no—
939#97—112no—
940#97—111no—
941#97—111no—
942#97—111no—
943#97—111no—
944#97C22×D1112yes—
945C4×C8—112no—
946C4×C8—112no—
947C4×C8C22×D1112yes—
948C2×C11—22no—
949C2×C11—42no—
950C2×C11—44no—
951C2×C11C22×C4×D411yescharacteristic
952C2×C11#358511yescharacteristic
953C2×C11#358511yescharacteristic
954D11—24no—
955D11—44no—
956D11—42no—
957C24—21no—
958C24—222no—
959C24—222no—
960C24—221no—
961#41—22no—
962#41—114no—
963#41—114no—
964#41—118no—
965#41—118no—
966#41—114no—
967#41—228no—
968#41—224no—
969#41—224no—
970#41—228no—
971#41—222no—
972#41C2×C4×D1114yescomplemented
973C2×Q8—111no—
974C2×Q8—111no—
975C2×Q8C23×D1111yescharacteristic
976C2×D4—21no—
977C2×D4—21no—
978C2×D4—22no—
979C2×D4—112no—
980C2×D4—118no—
981C2×D4—118no—
982C2×D4—114no—
983C2×D4—111no—
984C2×D4—111no—
985C2×D4—112no—
986C2×D4—228no—
987C2×D4—222no—
988C2×D4—224no—
989C2×D4—224no—
990C2×D4—222no—
991C2×D4—222no—
992C2×D4—2216no—
993C2×D4—228no—
994C2×D4—2216no—
995C2×D4—222no—
996C2×D4—221no—
997C2×D4—221no—
998C2×D4—222no—
999C2×D4C2×C4×D1114yescomplemented
1000C2×D4C23×D1112yes—
1001C2×D4C23×D1111yescharacteristic
1002C22×C4—21no—
1003C22×C4—21no—
1004C22×C4—21no—
1005C22×C4—22no—
1006C22×C4—21no—
1007C22×C4—22no—
1008C22×C4—82no—
1009C22×C4—112no—
1010C22×C4—112no—
1011C22×C4—112no—
1012C22×C4—222no—
1013C22×C4—222no—
1014C22×C4—222no—
1015C22×C4—222no—
1016C22×C4—222no—
1017C22×C4—222no—
1018C22×C4—222no—
1019C22×C4—222no—
1020C22×C4—222no—
1021C22×C4—222no—
1022C22×C4—221no—
1023C22×C4—221no—
1024C22×C4—222no—
1025C22×C4—221no—
1026C22×C4—221no—
1027C22×C4—222no—
1028C22×C4—882no—
1029C22×C4—884no—
1030C22×C4—884no—
1031C22×C4D4×D1111yescharacteristic
1032C22×C4D4×D1111yescharacteristic
1033C22×C4C23×D1111yescharacteristic
1034Q16—114no—
1035SD16—114no—
1036SD16—114no—
1037SD16—118no—
1038SD16C2×C4×D1118yescomplemented
1039D8—118no—
1040D8—114no—
1041D8—118no—
1042D8—118no—
1043D8C2×C4×D1118yescomplemented
1044M16—22no—
1045M16—118no—
1046M16—224no—
1047M16C2×C4×D1114yescomplemented
1048C2×C8—114no—
1049C2×C8—111no—
1050C2×C8—111no—
1051C2×C8—118no—
1052C2×C8—111no—
1053C2×C8—111no—
1054C2×C8—224no—
1055C2×C8—222no—
1056C2×C8C23×D1112yes—
1057C2×C8C23×D1112yes—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—112no—
1062C4⋊C4—112no—
1063C4⋊C4—111no—
1064C4⋊C4—111no—
1065C4⋊C4—112no—
1066C4⋊C4—111no—
1067C4⋊C4—111no—
1068C4⋊C4—222no—
1069C4⋊C4—222no—
1070C4⋊C4—222no—
1071C4⋊C4—222no—
1072C4⋊C4—221no—
1073C4⋊C4—221no—
1074C4⋊C4—221no—
1075C4⋊C4C23×D1112yes—
1076C4⋊C4C23×D1111yescharacteristic
1077C4⋊C4C23×D1111yescharacteristic
1078C22⋊C4—21no—
1079C22⋊C4—22no—
1080C22⋊C4—22no—
1081C22⋊C4—21no—
1082C22⋊C4—21no—
1083C22⋊C4—112no—
1084C22⋊C4—112no—
1085C22⋊C4—112no—
1086C22⋊C4—222no—
1087C22⋊C4—222no—
1088C22⋊C4—222no—
1089C22⋊C4—222no—
1090C22⋊C4—222no—
1091C22⋊C4—222no—
1092C22⋊C4—222no—
1093C22⋊C4—222no—
1094C22⋊C4—221no—
1095C22⋊C4—221no—
1096C22⋊C4—221no—
1097C22⋊C4—222no—
1098C22⋊C4—222no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—112no—
1103C42—112no—
1104C42—112no—
1105C42—222no—
1106C42—222no—
1107C42—222no—
1108C42—222no—
1109C42—221no—
1110C42—221no—
1111C42—221no—
1112C42D4×D1111yescharacteristic
1113C42D4×D1111yescharacteristic
1114C42C23×D1111yescharacteristic
1115C42C23×D1111yescharacteristic
1116C11#6017611yescharacteristic, complemented, Sylow
1117C23—21no—
1118C23—22no—
1119C23—24no—
1120C23—81no—
1121C23—81no—
1122C23—112no—
1123C23—228no—
1124C23—228no—
1125C23—221no—
1126C23—222no—
1127C23—224no—
1128C23—881no—
1129C23—881no—
1130C23—882no—
1131C23—882no—
1132C23—882no—
1133C23—882no—
1134C23C2×D4×D1111yescharacteristic
1135Q8—21no—
1136Q8—114no—
1137Q8—112no—
1138Q8—221no—
1139Q8C22×C4×D1112yes—
1140D4—24no—
1141D4—24no—
1142D4—22no—
1143D4—21no—
1144D4—118no—
1145D4—114no—
1146D4—114no—
1147D4—112no—
1148D4—228no—
1149D4—228no—
1150D4—228no—
1151D4—228no—
1152D4—224no—
1153D4—224no—
1154D4—221no—
1155D4—222no—
1156D4C22×C4×D1114yes—
1157D4C22×C4×D1112yes—
1158C2×C4—21no—
1159C2×C4—24no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—22no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—44no—
1166C2×C4—42no—
1167C2×C4—81no—
1168C2×C4—82no—
1169C2×C4—81no—
1170C2×C4—112no—
1171C2×C4—114no—
1172C2×C4—114no—
1173C2×C4—112no—
1174C2×C4—112no—
1175C2×C4—228no—
1176C2×C4—228no—
1177C2×C4—221no—
1178C2×C4—224no—
1179C2×C4—221no—
1180C2×C4—221no—
1181C2×C4—222no—
1182C2×C4—442no—
1183C2×C4—442no—
1184C2×C4—442no—
1185C2×C4—444no—
1186C2×C4—882no—
1187C2×C4—881no—
1188C2×C4—882no—
1189C2×C4—882no—
1190C2×C4—882no—
1191C2×C4—882no—
1192C2×C4—882no—
1193C2×C4—882no—
1194C2×C4—882no—
1195C2×C4—882no—
1196C2×C4—881no—
1197C2×C4C22×C4×D1112yes—
1198C2×C4C2×D4×D1111yescharacteristic
1199C2×C4C2×D4×D1111yescharacteristic
1200C2×C4C2×D4×D1111yescharacteristic
1201C2×C4C2×D4×D1111yescharacteristic
1202C2×C4C2×D4×D1111yescharacteristic
1203C2×C4#41×D1112yes—
1204C2×C4C24×D1111yescharacteristic
1205C8—22no—
1206C8—112no—
1207C8—112no—
1208C8—221no—
1209C8—221no—
1210C8C22×C4×D1114yes—
1211C22—21no—
1212C22—21no—
1213C22—22no—
1214C22—24no—
1215C22—42no—
1216C22—41no—
1217C22—41no—
1218C22—42no—
1219C22—84no—
1220C22—114no—
1221C22—222no—
1222C22—222no—
1223C22—224no—
1224C22—222no—
1225C22—441no—
1226C22—442no—
1227C22—442no—
1228C22—441no—
1229C22—884no—
1230C22—888no—
1231C22—888no—
1232C22C4×D4×D1112yes—
1233C22C22×D4×D1111yescharacteristic
1234C4—21no—
1235C4—21no—
1236C4—21no—
1237C4—21no—
1238C4—22no—
1239C4—42no—
1240C4—41no—
1241C4—41no—
1242C4—114no—
1243C4—222no—
1244C4—222no—
1245C4—222no—
1246C4—441no—
1247C4—442no—
1248C4—441no—
1249C4C4×D4×D1112yes—
1250C4C23×C4×D1111yescharacteristic
1251C4C2×#41×D1111yescharacteristic
1252C2—22no—
1253C2—44no—
1254C2—42no—
1255C2—224no—
1256C2—442no—
1257C2—444no—
1258C2C2×C4×D4×D1111yescharacteristic
1259C2#1308339211yescharacteristic
1260C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC4×C11×AGL(1,ℤ/8)C2
socleC22×C11C23×D4
prime radicalC2×#10623305C2
cosocleC2×C4×C11C25
hypercenterC4×AGL(1,ℤ/8)D11
hypocenterC11#60176
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C4×#67042C2semidirect
3. C4×#67037C2semidirect
4. #13077495C2semidirect
5. #13077494C2semidirect
6. #13077464C2semidirect
7. #13077463C2semidirect
8. #13077449C2semidirect
9. #13077446C2semidirect
10. #13077443C2semidirect
11. #13077441C2semidirect
12. C4×#66961C2semidirect
13. #13077427C2semidirect
14. #13077421C2semidirect
15. #13077414C2semidirect
16. #13077411C2semidirect
17. C2×#10622627C2semidirect
18. D11×#442C2semidirect
19. #13077210C2semidirect
20. #13077141C2semidirect
21. #13077140C2semidirect
22. #13077045C2semidirect
23. C4×C11×AGL(1,ℤ/8)C2semidirect
27. C4×C11×#41C22semidirect
28. C2×C4×D4×C11C22semidirect
29. #10623358C22semidirect
31. #10623329C22semidirect
34. #10623305C4semidirect
42. #10623105C22semidirect
43. C4×#4343C22semidirect
45. #10623077C22semidirect
48. #10623076C22semidirect
49. #10623076C22semidirect
52. C4×D4×D11C22semidirect
53. C4×D4×D11C22semidirect
55. C4×#4341C22semidirect
59. #10623052C22semidirect
61. #10623035C22semidirect
65. C4×#4339C22semidirect
67. C2×C4×D44C22semidirect
68. C11×#442C22semidirect
69. C11×#440C22semidirect
70. C4×C11×SD16C22semidirect
71. C4×C11×D8C22semidirect
72. C11×#428C22semidirect
73. C11×#418C22semidirect
74. C11×#417C22semidirect
75. C4×C11×M16C22semidirect
76. #10622846C22semidirect
77. C2×#66896C22semidirect
78. #10622777C22semidirect
79. SD16×Dic11C22semidirect
80. #10622765C22semidirect
81. D8×Dic11C22semidirect
82. #10622746C22semidirect
83. #10622744C22semidirect
84. #10622735C22semidirect
85. #10622735C22semidirect
86. #10622734C22semidirect
87. #10622643C22semidirect
88. #10622643C22semidirect
89. #10622639C22semidirect
90. #10622639C22semidirect
91. #10622631C22semidirect
92. #10622631C22semidirect
93. #10622627C22semidirect
94. #10622627C22semidirect
95. #10622627C22semidirect
96. #10622627C22semidirect
97. #10622627C22semidirect
98. #10622627C22semidirect
99. #10622615C22semidirect
100. #10622611C22semidirect
101. C2×#66873C22semidirect
102. C2×#66872C22semidirect
103. C2×#66867C22semidirect
104. #10622502C22semidirect
105. #10622494C22semidirect
106. #10622493C22semidirect
107. #10622485C22semidirect
108. #10622482C22semidirect
109. #10622474C22semidirect
110. D11×#106C22semidirect
111. #10622465C22semidirect
112. #10622417C22semidirect
113. #10622416C22semidirect
114. #10622402C22semidirect
115. #10622401C22semidirect
116. #10622398C22semidirect
117. #10622398C22semidirect
118. #10622398C22semidirect
119. #10622385C22semidirect
120. #10622384C22semidirect
121. #10622383C22semidirect
122. #10622383C22semidirect
123. D11×#102C22semidirect
124. D11×#102C22semidirect
125. #10622371C22semidirect
126. #10622369C22semidirect
127. #10622369C22semidirect
128. #10622324C22semidirect
129. #10622323C22semidirect
130. #10622320C22semidirect
131. D11×#97C22semidirect
132. C4×D88C22semidirect
133. C4×#4314C22semidirect
134. #10622302C22semidirect
135. #10622302C22semidirect
141. #67042C2×C4semidirect
144. #67037C2×C4semidirect
159. C11×AGL(1,ℤ/8)C2×C4semidirect
181. #67003C2×C4semidirect
192. C2×#4323C2×C4semidirect
220. #66969C2×C4semidirect
221. #66967C2×C4semidirect
222. #66964C2×C4semidirect
223. D8×D11C2×C4semidirect
224. #66961C2×C4semidirect
226. #66960C2×C4semidirect
333. C11×#41C22×C4semidirect
338. C2×D4×C11C22×C4semidirect
363. #4343C22×C4semidirect
366. #4341C22×C4semidirect
371. D4×D11C22×C4semidirect
372. D4×D11C22×C4semidirect
376. #4339C22×C4semidirect
382. C2×D44C22×C4semidirect
405. C11×SD16C22×C4semidirect
406. C11×D8C22×C4semidirect
408. C11×M16C22×C4semidirect
434. #4326C22×C4semidirect
435. #4325C22×C4semidirect
436. #4324C22×C4semidirect
437. #4323C22×C4semidirect
438. #4323C22×C4semidirect
439. #4323C22×C4semidirect
476. C2×C11⋊C8C22×C4semidirect
481. D88C22×C4semidirect
482. #4314C22×C4semidirect
484. #4313C22×C4semidirect
486. C8×D11C22×C4semidirect
501. C4×AGL(1,ℤ/8)D11semidirect
639. C4×#41C2×D11semidirect
647. C2×C4×D4C2×D11semidirect
660. #442C2×D11semidirect
671. #440C2×D11semidirect
677. C4×SD16C2×D11semidirect
683. C4×D8C2×D11semidirect
687. #428C2×D11semidirect
695. #418C2×D11semidirect
699. #417C2×D11semidirect
713. C4×M16C2×D11semidirect
783. AGL(1,ℤ/8)C4×D11semidirect
972. #41C2×C4×D11semidirect
999. C2×D4C2×C4×D11semidirect
1038. SD16C2×C4×D11semidirect
1043. D8C2×C4×D11semidirect
1047. M16C2×C4×D11semidirect
1116. C11#60176semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106233052
C4×#670422
C4×#670372
#130774952
#130774942
#130774642
#130774632
#130774492
#130774462
#130774432
#130774412
C4×#669612
#130774272
#130774212
#130774142
#130774112
C2×#106226272
D11×#4422
#130772102
#130771412
#130771402
#130770452
C4×C11×AGL(1,ℤ/8)2
#6017611