Finite Group Databasebeta

← #15618030

Subgroups — #15618030

Order 2816.

2734 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623306C211yesmaximal, characteristic
2C4×#67043C211yesmaximal, characteristic, complemented
3C4×#67037C211yesmaximal, characteristic, complemented
4#13077487C211yesmaximal, characteristic, complemented
5#13077486C212yesmaximal, complemented
6#13077478C211yesmaximal, characteristic, complemented
7#13077470C212yesmaximal, complemented
8#13077457C211yesmaximal, characteristic, complemented
9#13077452C212yesmaximal, complemented
10#13077449C211yesmaximal, characteristic, complemented
11#13077441C212yesmaximal, complemented
12C4×#66962C211yesmaximal, characteristic, complemented
13#13077438C212yesmaximal, complemented
14#13077427C212yesmaximal, complemented
15#13077414C211yesmaximal, characteristic, complemented
16#13077413C212yesmaximal, complemented
17C2×#10622631C211yesmaximal, characteristic, complemented
18D11×#440C212yesmaximal, complemented
19#13077215C211yesmaximal, characteristic, complemented
20#13077147C211yesmaximal, characteristic, complemented
21#13077141C211yesmaximal, characteristic, complemented
22#13077045C211yesmaximal, characteristic, complemented
23C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
24C2×#67043C2211yescharacteristic
25C2×#67037C2211yescharacteristic
26C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
27C4×C11×#41C2211yescharacteristic, complemented
28C2×C4×D4×C11C2211yescharacteristic
29#10623358C2211yescharacteristic, complemented
30C2×#67003C2211yescharacteristic
31#10623329C2211yescharacteristic
32C22×#4324C2211yescharacteristic
33C2×C4×C22⋊D11—22no—
34#10623306C4116yescomplemented
35C2×#66968C2212yes—
36C2×SD16×D11C2212yes—
37C2×#66965C2212yes—
38C2×#66964C2212yes—
39C2×#66962C2211yescharacteristic
40C2×#66960C2211yescharacteristic
41C2×#66960C2211yescharacteristic
42#10623103C2212yescomplemented
43C4×Q8×D11C2212yescomplemented
44#10623077—22no—
45#10623077—21no—
46#10623077C2212yes—
47#10623077C2212yescomplemented
48#10623076—21no—
49#10623076C2212yes—
50C4×D4×D11—21no—
51C4×D4×D11C2212yes—
52C4×#4341—22no—
53C4×#4341—21no—
54C4×#4341C2212yes—
55C4×#4341C2212yescomplemented
56#10623054—21no—
57#10623054C2211yescharacteristic
58#10623047—21no—
59#10623047C2211yescharacteristic, complemented
60#10623035C2211yescharacteristic
61#10623035C2211yescharacteristic
62#10623017—22no—
63C4×#4339—21no—
64C4×#4339C2211yescharacteristic
65C4×#4339C2211yescharacteristic
66C2×C4×Dic22—21no—
67C2×C4×Dic22C2211yescharacteristic, complemented
68C11×#442C2212yescomplemented
69C11×#440C2212yescomplemented
70C4×C11×SD16C2212yescomplemented
71C4×C11×D8C2212yescomplemented
72C11×#428C2211yescharacteristic, complemented
73C11×#418C2211yescharacteristic
74C11×#417C2211yescharacteristic, complemented
75C4×C11×M16C2211yescharacteristic, complemented
76#10622846C2211yescharacteristic, complemented
77C2×#66896C2211yescharacteristic
78#10622777C2212yescomplemented
79SD16×Dic11C2212yescomplemented
80#10622765C2212yescomplemented
81D8×Dic11C2212yescomplemented
82#10622746C2211yescharacteristic
83#10622735C2211yescharacteristic, complemented
84#10622735C2211yescharacteristic, complemented
85#10622734C2211yescharacteristic, complemented
86#10622733C2211yescharacteristic, complemented
87#10622643C2211yescharacteristic, complemented
88#10622643C2211yescharacteristic, complemented
89#10622639C2211yescharacteristic, complemented
90#10622639C2211yescharacteristic, complemented
91#10622631C2212yescomplemented
92#10622631C2212yescomplemented
93#10622631C2212yescomplemented
94#10622631C2212yescomplemented
95#10622631C2211yescharacteristic, complemented
96#10622631C2211yescharacteristic, complemented
97#10622627C2211yescharacteristic, complemented
98#10622627C2211yescharacteristic, complemented
99#10622615C2211yescharacteristic
100#10622611C2211yescharacteristic, complemented
101C2×#66874C2211yescharacteristic, complemented
102C2×#66871C2211yescharacteristic, complemented
103C2×#66867C2211yescharacteristic, complemented
104#10622502C2212yescomplemented
105#10622494C2212yescomplemented
106D11×#107C2212yescomplemented
107#10622486C2212yescomplemented
108#10622474C2212yescomplemented
109#10622473C2212yescomplemented
110#10622466C2212yescomplemented
111#10622465C2212yescomplemented
112#10622430C2212yescomplemented
113#10622415C2212yescomplemented
114D11×#103C2212yescomplemented
115#10622403C2212yescomplemented
116#10622385C2212yes—
117#10622385C2212yescomplemented
118#10622384C2212yes—
119#10622384C2212yescomplemented
120#10622383C2212yes—
121D11×#102C2212yes—
122#10622371C2212yescomplemented
123#10622371C2212yescomplemented
124#10622370C2212yescomplemented
125#10622370C2212yescomplemented
126#10622370C2212yescomplemented
127#10622369C2212yescomplemented
128#10622329C2212yescomplemented
129#10622323C2212yescomplemented
130#10622320C2212yescomplemented
131D11×#97C2212yescomplemented
132C4×Dic44C2212yescomplemented
133C4×#4314C2212yescomplemented
134#10622302C2212yescomplemented
135#10622302C2212yescomplemented
136C2×C11×#41C2311yescharacteristic
137C22×D4×C11C2311yescharacteristic
138C23×C4×C11—21no—
139C22×C22⋊D11—22no—
140#67043—24no—
141#67043C2×C418yescomplemented
142C2×Q8×D11C2312yes—
143#67037—24no—
144#67037C2×C418yescomplemented
145C2×#4341—22no—
146C2×#4341—21no—
147C2×#4341C2312yes—
148C2×#4341C2312yes—
149C2×D4×D11—21no—
150C2×D4×D11C2312yes—
151C2×#4339—21no—
152C2×#4339C2311yescharacteristic
153C2×#4339C2311yescharacteristic
154C22×C4×D11—22no—
155C22×Dic22—21no—
156C22×Dic22C2311yescharacteristic
157C11×AGL(1,ℤ/8)C2×C418yescomplemented
158C2×C11×SD16C2312yes—
159C2×C11×D8C2312yes—
160C2×C11×M16C2311yescharacteristic
161C2×C11×M16C2311yescharacteristic
162C4×Q8×C11C2311yescharacteristic
163C4×Q8×C11C2311yescharacteristic
164C4×D4×C11—21no—
165C4×D4×C11—21no—
166C4×D4×C11—21no—
167C4×D4×C11—21no—
168C4×D4×C11C2312yes—
169C4×D4×C11C2311yescharacteristic
170C4×D4×C11C2312yes—
171C4×D4×C11C2311yescharacteristic
172C11×#117—21no—
173C11×#117C2311yescharacteristic
174C2×C11×C4⋊C4C2311yescharacteristic
175C2×C11×C22⋊C4—21no—
176C2×C42×C11—21no—
177C2×C42×C11C2311yescharacteristic
178C2×C22⋊Dic11—22no—
179#67003C2×C418yescomplemented
180Q8×Dic11C2312yes—
181C2×#4326C2311yescharacteristic
182C2×#4325C2311yescharacteristic
183D4×Dic11—22no—
184D4×Dic11—21no—
185D4×Dic11—21no—
186D4×Dic11C2312yes—
187D4×Dic11C2312yes—
188D4×Dic11C2312yes—
189C2×#4324C2×C418yescomplemented
190C2×#4324C2312yes—
191C2×#4324C2311yescharacteristic
192C2×#4324C2312yes—
193C2×#4323C2311yescharacteristic
194C4×C22⋊D11—21no—
195C4×C22⋊D11—21no—
196C4×C22⋊D11—22no—
197C4×C22⋊D11—22no—
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⋊D11D412yes—
205C4×C22⋊D11D412yes—
206C2×(C2×D11)⋊C4—22no—
207#66979—21no—
208#66979C2311yescharacteristic
209#66979C2311yescharacteristic
210C2×C4⋊Dic11—21no—
211C2×C4⋊Dic11C2311yescharacteristic
212C2×Dic11⋊C4—21no—
213C2×Dic11⋊C4—22no—
214C2×Dic11⋊C4—22no—
215C2×C4×Dic11—21no—
216C2×C4×Dic11—22no—
217C2×C4×Dic11—22no—
218C22×C11⋊C8C2311yescharacteristic
219C22×C11⋊C8C2311yescharacteristic
220#66968C2×C4116yescomplemented
221SD16×D11C2×C4116yescomplemented
222#66965C2×C4116yescomplemented
223#66964C2×C4116yescomplemented
224#66962C2×C418yescomplemented
225#66960—24no—
226#66960C2×C418yescomplemented
227C2×Dic44C2312yes—
228C2×#4314C2312yes—
229C2×#4313C2312yes—
230C2×#4313C2312yes—
231C2×C8×D11C2312yes—
232C2×C8×D11C2312yes—
233#66946—21no—
234#66946C2312yes—
235#66945—22no—
236#66945—21no—
237#66945C2312yes—
238#66945C2312yes—
239C4⋊C4×D11—22no—
240C4⋊C4×D11—21no—
241C4⋊C4×D11C2312yes—
242C4⋊C4×D11C2312yes—
243#66940—21no—
244#66940—22no—
245#66940—22no—
246#66940C2312yes—
247#66940C2312yes—
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—
258#66930—22no—
259#66930—22no—
260#66930—22no—
261#66930—22no—
262#66930—22no—
263C4×D44—21no—
264C4×D44D411yescharacteristic
265C4×D44D411yescharacteristic
266C4×D44C2311yescharacteristic
267C4×D44C2311yescharacteristic
268#66925—21no—
269#66925—22no—
270#66925C2312yes—
271C42×D11—22no—
272C42×D11—21no—
273C42×D11C2312yes—
274C4×Dic22—21no—
275C4×Dic22—21no—
276C4×Dic22—21no—
277C4×Dic22—21no—
278C4×Dic22—21no—
279C4×Dic22—22no—
280C4×Dic22—22no—
281C4×Dic22D411yescharacteristic
282C4×Dic22D411yescharacteristic
283C4×Dic22C2312yes—
284C4×Dic22C2312yes—
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#66882C2312yes—
303#66881C2312yes—
304#66880C2312yes—
305#66880C2312yes—
306#66880C2312yes—
307#66879C2312yes—
308#66879C2312yes—
309C8×Dic11C2312yes—
310C8×Dic11C2312yes—
311#66874C2312yes—
312#66874C2311yescharacteristic
313#66874C2312yes—
314#66874C2311yescharacteristic
315#66873C2311yescharacteristic
316#66873C2311yescharacteristic
317#66872C2311yescharacteristic
318#66872C2311yescharacteristic
319#66871C2311yescharacteristic
320#66871C2312yes—
321#66871C2312yes—
322#66871C2311yescharacteristic
323#66867C2311yescharacteristic
324#66867C2311yescharacteristic
325#66867C2311yescharacteristic
326#66867C2311yescharacteristic
327#60174—111nomaximal, Sylow
328C24×C11—21no—
329C23×D11—22no—
330C11×#41—22no—
331C11×#41C22×C414yescomplemented
332C2×Q8×C11C2411yescharacteristic
333C2×D4×C11—21no—
334C2×D4×C11—21no—
335C2×D4×C11—22no—
336C2×D4×C11C22×C414yes—
337C2×D4×C11C2411yescharacteristic
338C2×D4×C11C2412yes—
339C22×C4×C11—21no—
340C22×C4×C11—21no—
341C22×C4×C11—21no—
342C22×C4×C11—22no—
343C22×C4×C11—21no—
344C22×C4×C11—22no—
345C22×C4×C11—82no—
346C22×C4×C11C2×D411yescharacteristic
347C22×C4×C11C2×D411yescharacteristic
348C22×C4×C11C2411yescharacteristic
349C2×C22⋊D11—216no—
350C2×C22⋊D11—22no—
351C2×C22⋊D11—21no—
352C2×C22⋊D11—22no—
353C2×C22⋊D11—22no—
354C2×C22⋊D11C2×D412yes—
355C22×Dic11—22no—
356C22×Dic11—22no—
357C22×Dic11—22no—
358C22×Dic11—22no—
359C22×Dic11—22no—
360C22×Dic11—21no—
361C22×Dic11—21no—
362Q8×D11—24no—
363Q8×D11C22×C418yescomplemented
364#4341—216no—
365#4341—24no—
366#4341—24no—
367#4341—28no—
368#4341C22×C418yes—
369#4341C22×C418yescomplemented
370D4×D11—28no—
371D4×D11—24no—
372D4×D11C22×C418yes—
373#4339—28no—
374#4339—22no—
375#4339C22×C414yes—
376#4339C22×C414yes—
377#4339#4114yes—
378C2×D44C2×D411yescharacteristic
379C2×D44C2411yescharacteristic
380C2×C4×D11—22no—
381C2×C4×D11—22no—
382C2×C4×D11—22no—
383C2×C4×D11—22no—
384C2×C4×D11—21no—
385C2×C4×D11—21no—
386C2×C4×D11—21no—
387C2×C4×D11—84no—
388C2×C4×D11C2×D412yes—
389C2×C4×D11C2×D412yes—
390C2×C4×D11C2412yes—
391C2×Dic22—22no—
392C2×Dic22—28no—
393C2×Dic22—21no—
394C2×Dic22—22no—
395C2×Dic22C22×C414yescomplemented
396C2×Dic22C2×D411yescharacteristic
397C2×Dic22C2412yes—
398C2×Dic22C2411yescharacteristic
399C11×SD16C22×C418yescomplemented
400C11×D8C22×C418yescomplemented
401C11×M16—22no—
402C11×M16C22×C414yescomplemented
403C2×C8×C11C2412yes—
404C2×C8×C11C2412yes—
405C11×C4⋊C4—21no—
406C11×C4⋊C4—21no—
407C11×C4⋊C4—21no—
408C11×C4⋊C4C2412yes—
409C11×C4⋊C4C2411yescharacteristic
410C11×C4⋊C4C2411yescharacteristic
411C11×C22⋊C4—21no—
412C11×C22⋊C4—21no—
413C11×C22⋊C4—21no—
414C11×C22⋊C4—22no—
415C11×C22⋊C4—22no—
416C42×C11—21no—
417C42×C11—21no—
418C42×C11—21no—
419C42×C11C2×D411yescharacteristic
420C42×C11C2×D411yescharacteristic
421C42×C11C2411yescharacteristic
422C42×C11C2411yescharacteristic
423C22⋊Dic11—22no—
424C22⋊Dic11—22no—
425C22⋊Dic11—22no—
426C22⋊Dic11—21no—
427C22⋊Dic11C2×D412yes—
428#4326C22×C414yescomplemented
429#4325C22×C414yescomplemented
430#4324C22×C418yescomplemented
431#4324C22×C414yescomplemented
432#4324C22×C418yescomplemented
433#4323C22×C414yescomplemented
434(C2×D11)⋊C4—22no—
435(C2×D11)⋊C4—22no—
436(C2×D11)⋊C4—22no—
437(C2×D11)⋊C4—21no—
438(C2×D11)⋊C4—21no—
439(C2×D11)⋊C4C2×D412yes—
440(C2×D11)⋊C4C2×D412yes—
441C4⋊Dic11—22no—
442C4⋊Dic11—21no—
443C4⋊Dic11C2×D411yescharacteristic
444C4⋊Dic11C2×D411yescharacteristic
445C4⋊Dic11C2412yes—
446C4⋊Dic11C2411yescharacteristic
447C4⋊Dic11C2411yescharacteristic
448Dic11⋊C4—22no—
449Dic11⋊C4—22no—
450Dic11⋊C4—22no—
451Dic11⋊C4—22no—
452Dic11⋊C4—22no—
453Dic11⋊C4—22no—
454Dic11⋊C4—22no—
455Dic11⋊C4—21no—
456Dic11⋊C4—21no—
457Dic11⋊C4C2×D412yes—
458Dic11⋊C4C2×D412yes—
459C4×Dic11—22no—
460C4×Dic11—22no—
461C4×Dic11—22no—
462C4×Dic11—22no—
463C4×Dic11—22no—
464C4×Dic11—22no—
465C4×Dic11—22no—
466C4×Dic11—22no—
467C4×Dic11—21no—
468C4×Dic11—21no—
469C4×Dic11—21no—
470C4×Dic11C2×D412yes—
471C4×Dic11C2×D412yes—
472C4×Dic11C2412yes—
473C2×C11⋊C8—22no—
474C2×C11⋊C8C22×C414yescomplemented
475C2×C11⋊C8C2411yescharacteristic
476C2×C11⋊C8C2411yescharacteristic
477C2×C11⋊C8C2411yescharacteristic
478C2×C11⋊C8C2411yescharacteristic
479Dic44C22×C418yescomplemented
480#4314C22×C418yescomplemented
481#4313—24no—
482#4313C22×C418yescomplemented
483C8×D11—24no—
484C8×D11C22×C418yescomplemented
485C2×#577—111no—
486C4×2−1+4—111no—
487C4×H(5,𝔽2)—111no—
488#2951—112no—
489#2951—111no—
490#2949—112no—
491#2949—111no—
492#2947—112no—
493#2947—111no—
494#2946—112no—
495#2946—111no—
496C4×#137—112no—
497C4×#137—111no—
498C4×AGL(1,ℤ/8)—112no—
499C4×AGL(1,ℤ/8)D1111yescharacteristic, complemented
500#2943—112no—
501#2943—111no—
502C2×#440—112no—
503C2×#440—111no—
504#2913—111no—
505#2898—111no—
506#2897—111no—
507#2875—111no—
508C23×C11—21no—
509C23×C11—22no—
510C23×C11—24no—
511C23×C11—81no—
512C23×C11—81no—
513C23×C11C22×D411yescharacteristic
514C22×D11—21no—
515C22×D11—28no—
516C22×D11—82no—
517C22×D11—82no—
518C22×D11C22×D412yes—
519Q8×C11—21no—
520Q8×C11C23×C412yes—
521D4×C11—24no—
522D4×C11—24no—
523D4×C11—22no—
524D4×C11—21no—
525D4×C11C23×C412yes—
526D4×C11C23×C414yes—
527C2×C4×C11—21no—
528C2×C4×C11—24no—
529C2×C4×C11—21no—
530C2×C4×C11—21no—
531C2×C4×C11—22no—
532C2×C4×C11—41no—
533C2×C4×C11—41no—
534C2×C4×C11—44no—
535C2×C4×C11—42no—
536C2×C4×C11—81no—
537C2×C4×C11—82no—
538C2×C4×C11—81no—
539C2×C4×C11C23×C412yes—
540C2×C4×C11C22×D411yescharacteristic
541C2×C4×C11C22×D411yescharacteristic
542C2×C4×C11C22×D411yescharacteristic
543C2×C4×C11C22×D411yescharacteristic
544C2×C4×C11C22×D411yescharacteristic
545C2×C4×C11C2×#4112yes—
546C2×C4×C11C2511yescharacteristic
547C22⋊D11—24no—
548C22⋊D11—28no—
549C22⋊D11—28no—
550C22⋊D11—28no—
551C22⋊D11C4×D418yes—
552C2×Dic11—24no—
553C2×Dic11—22no—
554C2×Dic11—21no—
555C2×Dic11—28no—
556C2×Dic11—28no—
557C2×Dic11—22no—
558C2×Dic11—21no—
559C2×Dic11—21no—
560C2×Dic11—82no—
561C2×Dic11—82no—
562C2×Dic11—82no—
563C2×Dic11—81no—
564C2×Dic11C22×D412yes—
565C2×Dic11C22×D412yes—
566C2×Dic11C22×D412yes—
567D44—21no—
568D44C4×D414yes—
569D44C23×C412yes—
570C4×D11—28no—
571C4×D11—24no—
572C4×D11—42no—
573C4×D11—42no—
574C4×D11—42no—
575C4×D11—82no—
576C4×D11—81no—
577C4×D11—82no—
578C4×D11—82no—
579C4×D11C23×C414yes—
580C4×D11C2×#4114yes—
581Dic22—24no—
582Dic22—22no—
583Dic22—21no—
584Dic22—28no—
585Dic22C4×D414yes—
586Dic22C23×C414yes—
587Dic22C23×C412yes—
588C8×C11—22no—
589C8×C11C23×C414yes—
590C11⋊C8—21no—
591C11⋊C8—21no—
592C11⋊C8C23×C412yes—
593C11⋊C8C23×C412yes—
594C2×2−1+4—111no—
595C2×H(5,𝔽2)—111no—
596#577—1116no—
597C2×#137—112no—
598C2×#137—111no—
599C2×AGL(1,ℤ/8)—112no—
600C2×AGL(1,ℤ/8)C2×D1111yescharacteristic
601C2×#135—111no—
602C2×#135—112no—
603C22×SD16—111no—
604C22×SD16—112no—
605C2×#131—111no—
606C2×#131—111no—
607#520—111no—
608#520—111no—
609#520—111no—
610#520—112no—
611#520—112no—
612#520—111no—
613#520—221no—
614#520—222no—
615#520—221no—
616#519—112no—
617#519—111no—
618#519—221no—
619#518—111no—
620#518—112no—
621#518—222no—
622#518—221no—
623C4×#41—111no—
624C4×#41—112no—
625C4×#41—112no—
626C4×#41—111no—
627C4×#41—221no—
628C4×#41—222no—
629C4×#41—221no—
630C4×#41C2×D1111yescharacteristic, complemented
631C2×C4×Q8—112no—
632C2×C4×Q8—111no—
633C2×C4×Q8—221no—
634C2×C4×D4—112no—
635C2×C4×D4—221no—
636C2×C4×D4—222no—
637C2×C4×D4C2×D1111yescharacteristic
638#442—112no—
639#442—111no—
640#442—111no—
641#442C2×D1112yescomplemented
642#441—111no—
643#441—111no—
644#441—112no—
645#441—112no—
646#440—112no—
647#440—111no—
648#440—111no—
649#440—112no—
650#440—112no—
651#440—112no—
652#440—112no—
653#440—111no—
654#440—111no—
655#440—112no—
656#440—112no—
657#440—112no—
658#440—112no—
659#440—112no—
660#440—112no—
661#440C2×D1112yescomplemented
662C4×Q16—112no—
663C4×Q16—112no—
664C4×Q16—112no—
665C4×SD16—112no—
666C4×SD16—112no—
667C4×SD16—112no—
668C4×SD16—112no—
669C4×SD16—112no—
670C4×SD16C2×D1112yescomplemented
671C4×D8—112no—
672C4×D8—112no—
673C4×D8C2×D1112yescomplemented
674#428—111no—
675#428—112no—
676#428—112no—
677#428C2×D1111yescharacteristic, complemented
678#427—111no—
679#427—112no—
680C2×#107—111no—
681C2×#107—112no—
682#419—111no—
683#419—112no—
684#418—112no—
685#418C2×D1111yescharacteristic
686#417—111no—
687#417—112no—
688#417—112no—
689#417C2×D1111yescharacteristic, complemented
690#416—111no—
691#416—111no—
692#416—112no—
693#416—112no—
694C2×#103—111no—
695C2×#103—112no—
696C2×#102—111no—
697C2×#102—112no—
698#405—111no—
699#405—111no—
700#405—112no—
701#405—112no—
702C4×M16—112no—
703C4×M16C2×D1111yescharacteristic, complemented
704C2×#97—111no—
705C2×#97—112no—
706C22×C11—21no—
707C22×C11—21no—
708C22×C11—22no—
709C22×C11—24no—
710C22×C11—42no—
711C22×C11—41no—
712C22×C11—41no—
713C22×C11—42no—
714C22×C11—84no—
715C22×C11C2×C4×D412yes—
716C22×C11C23×D411yescharacteristic
717C2×D11—22no—
718C2×D11—22no—
719C2×D11—22no—
720C2×D11—41no—
721C2×D11—41no—
722C2×D11—88no—
723C2×D11C2×C4×D414yes—
724C4×C11—21no—
725C4×C11—21no—
726C4×C11—21no—
727C4×C11—21no—
728C4×C11—22no—
729C4×C11—42no—
730C4×C11—41no—
731C4×C11—41no—
732C4×C11C2×C4×D412yes—
733C4×C11C24×C411yescharacteristic
734C4×C11C22×#4111yescharacteristic
735Dic11—22no—
736Dic11—22no—
737Dic11—24no—
738Dic11—22no—
739Dic11—41no—
740Dic11—42no—
741Dic11—41no—
742Dic11C2×C4×D414yes—
7432−1+4—118no—
7442−1+4—224no—
745H(5,𝔽2)—118no—
746H(5,𝔽2)—224no—
747C2×#41—111no—
748C2×#41—112no—
749C2×#41—112no—
750C2×#41—111no—
751C2×#41—221no—
752C2×#41—222no—
753C2×#41—221no—
754C2×#41C22×D1111yescharacteristic
755C22×Q8—112no—
756C22×Q8—111no—
757C22×Q8—221no—
758C22×D4—112no—
759C22×D4—221no—
760C22×D4—222no—
761C22×D4C22×D1111yescharacteristic
762C23×C4—21no—
763C23×C4—222no—
764#137—1116no—
765#137—118no—
766AGL(1,ℤ/8)—1116no—
767AGL(1,ℤ/8)C4×D1118yescomplemented
768#135—118no—
769#135—1116no—
770C2×Q16—111no—
771C2×Q16—112no—
772C2×SD16—111no—
773C2×SD16—118no—
774C2×SD16—112no—
775C2×SD16—112no—
776C2×SD16—111no—
777C2×SD16—1116no—
778C2×SD16—112no—
779C2×SD16C22×D1112yes—
780C2×D8—111no—
781C2×D8C22×D1112yes—
782#131—118no—
783#131—224no—
784C2×M16—112no—
785C2×M16—112no—
786C2×M16C22×D1111yescharacteristic
787C2×M16C22×D1111yescharacteristic
788C22×C8—111no—
789C22×C8—112no—
790C22×C8—111no—
791C22×C8—112no—
792C4×Q8—111no—
793C4×Q8—111no—
794C4×Q8—112no—
795C4×Q8—112no—
796C4×Q8—112no—
797C4×Q8—112no—
798C4×Q8—112no—
799C4×Q8—112no—
800C4×Q8—111no—
801C4×Q8—111no—
802C4×Q8—222no—
803C4×Q8—221no—
804C4×Q8—222no—
805C4×Q8—221no—
806C4×Q8—221no—
807C4×Q8—222no—
808C4×Q8—222no—
809C4×Q8—221no—
810C4×Q8—221no—
811C4×Q8—221no—
812C4×Q8C22×D1111yescharacteristic
813C4×Q8C22×D1111yescharacteristic
814C4×D4—21no—
815C4×D4—21no—
816C4×D4—21no—
817C4×D4—21no—
818C4×D4—112no—
819C4×D4—112no—
820C4×D4—112no—
821C4×D4—112no—
822C4×D4—112no—
823C4×D4—112no—
824C4×D4—111no—
825C4×D4—111no—
826C4×D4—111no—
827C4×D4—111no—
828C4×D4—221no—
829C4×D4—222no—
830C4×D4—222no—
831C4×D4—222no—
832C4×D4—222no—
833C4×D4—222no—
834C4×D4—222no—
835C4×D4—222no—
836C4×D4—222no—
837C4×D4—222no—
838C4×D4—222no—
839C4×D4—222no—
840C4×D4—222no—
841C4×D4—221no—
842C4×D4—222no—
843C4×D4—221no—
844C4×D4—221no—
845C4×D4—222no—
846C4×D4—222no—
847C4×D4—222no—
848C4×D4—221no—
849C4×D4—221no—
850C4×D4C22×D1112yes—
851C4×D4C22×D1112yes—
852C4×D4C22×D1111yescharacteristic
853C4×D4C22×D1111yescharacteristic
854#117—21no—
855#117—111no—
856#117—112no—
857#117—111no—
858#117—112no—
859#117—112no—
860#117—222no—
861#117—222no—
862#117—222no—
863#117—222no—
864#117—222no—
865#117—222no—
866#117—222no—
867#117—221no—
868#117—221no—
869#117—221no—
870#117C22×D1111yescharacteristic
871C2×C4⋊C4—111no—
872C2×C4⋊C4—112no—
873C2×C4⋊C4—112no—
874C2×C4⋊C4—221no—
875C2×C4⋊C4—222no—
876C2×C4⋊C4—222no—
877C2×C4⋊C4—222no—
878C2×C4⋊C4—221no—
879C2×C4⋊C4—221no—
880C2×C4⋊C4C22×D1111yescharacteristic
881C2×C22⋊C4—21no—
882C2×C22⋊C4—222no—
883C2×C22⋊C4—222no—
884C2×C22⋊C4—222no—
885C2×C22⋊C4—222no—
886C2×C42—21no—
887C2×C42—112no—
888C2×C42—222no—
889C2×C42—222no—
890C2×C42—222no—
891C2×C42—221no—
892C2×C42—221no—
893C2×C42C22×D1111yescharacteristic
894#107—112no—
895#107—112no—
896#107—111no—
897#107—112no—
898#107—111no—
899#107C22×D1112yes—
900#106—112no—
901#106—111no—
902#106—111no—
903#106C22×D1112yes—
904#103—111no—
905#103—111no—
906#103—112no—
907#103—112no—
908#103—112no—
909#103—112no—
910#103—112no—
911#103—111no—
912#103—111no—
913#103C22×D1112yes—
914#102—112no—
915#102—112no—
916#102—111no—
917#102—111no—
918#102—112no—
919#102—111no—
920#102—111no—
921#102C22×D1112yes—
922#102C22×D1112yes—
923#102C22×D1112yes—
924#97—112no—
925#97—112no—
926#97—111no—
927#97—111no—
928#97—111no—
929#97—111no—
930#97C22×D1112yes—
931C4×C8—112no—
932C4×C8—112no—
933C4×C8C22×D1112yes—
934C2×C11—22no—
935C2×C11—44no—
936C2×C11—42no—
937C2×C11C22×C4×D411yescharacteristic
938C2×C11#358511yescharacteristic
939C2×C11#358611yescharacteristic
940D11—24no—
941D11—42no—
942C24—21no—
943C24—222no—
944#41—22no—
945#41—114no—
946#41—114no—
947#41—118no—
948#41—118no—
949#41—114no—
950#41—228no—
951#41—224no—
952#41—224no—
953#41—2216no—
954#41—228no—
955#41—222no—
956#41C2×C4×D1114yescomplemented
957C2×Q8—111no—
958C2×Q8—118no—
959C2×Q8—114no—
960C2×Q8—112no—
961C2×Q8—111no—
962C2×Q8—222no—
963C2×Q8—228no—
964C2×Q8—224no—
965C2×Q8—221no—
966C2×Q8—222no—
967C2×Q8C23×D1111yescharacteristic
968C2×D4—21no—
969C2×D4—21no—
970C2×D4—22no—
971C2×D4—112no—
972C2×D4—118no—
973C2×D4—111no—
974C2×D4—111no—
975C2×D4—224no—
976C2×D4—222no—
977C2×D4—228no—
978C2×D4—2216no—
979C2×D4—222no—
980C2×D4—222no—
981C2×D4—221no—
982C2×D4C2×C4×D1114yes—
983C2×D4C23×D1111yescharacteristic
984C2×D4C23×D1112yes—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—22no—
989C22×C4—21no—
990C22×C4—22no—
991C22×C4—82no—
992C22×C4—112no—
993C22×C4—112no—
994C22×C4—112no—
995C22×C4—222no—
996C22×C4—222no—
997C22×C4—222no—
998C22×C4—222no—
999C22×C4—222no—
1000C22×C4—222no—
1001C22×C4—222no—
1002C22×C4—222no—
1003C22×C4—222no—
1004C22×C4—221no—
1005C22×C4—221no—
1006C22×C4—221no—
1007C22×C4—221no—
1008C22×C4—221no—
1009C22×C4—884no—
1010C22×C4D4×D1111yescharacteristic
1011C22×C4D4×D1111yescharacteristic
1012C22×C4C23×D1111yescharacteristic
1013Q16—114no—
1014Q16—118no—
1015SD16—114no—
1016SD16—118no—
1017SD16—118no—
1018SD16—114no—
1019SD16—118no—
1020SD16C2×C4×D1118yescomplemented
1021D8—114no—
1022D8C2×C4×D1118yescomplemented
1023M16—22no—
1024M16—118no—
1025M16—224no—
1026M16C2×C4×D1114yescomplemented
1027C2×C8—114no—
1028C2×C8—111no—
1029C2×C8—111no—
1030C2×C8—118no—
1031C2×C8—111no—
1032C2×C8—111no—
1033C2×C8—224no—
1034C2×C8—222no—
1035C2×C8C23×D1112yes—
1036C2×C8C23×D1112yes—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—112no—
1041C4⋊C4—111no—
1042C4⋊C4—112no—
1043C4⋊C4—111no—
1044C4⋊C4—112no—
1045C4⋊C4—111no—
1046C4⋊C4—111no—
1047C4⋊C4—222no—
1048C4⋊C4—222no—
1049C4⋊C4—222no—
1050C4⋊C4—222no—
1051C4⋊C4—222no—
1052C4⋊C4—222no—
1053C4⋊C4—221no—
1054C4⋊C4—221no—
1055C4⋊C4—222no—
1056C4⋊C4—222no—
1057C4⋊C4—221no—
1058C4⋊C4C23×D1111yescharacteristic
1059C4⋊C4C23×D1111yescharacteristic
1060C4⋊C4C23×D1112yes—
1061C22⋊C4—21no—
1062C22⋊C4—22no—
1063C22⋊C4—22no—
1064C22⋊C4—21no—
1065C22⋊C4—21no—
1066C22⋊C4—112no—
1067C22⋊C4—112no—
1068C22⋊C4—112no—
1069C22⋊C4—222no—
1070C22⋊C4—222no—
1071C22⋊C4—222no—
1072C22⋊C4—222no—
1073C22⋊C4—222no—
1074C22⋊C4—222no—
1075C22⋊C4—221no—
1076C22⋊C4—221no—
1077C22⋊C4—221no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—112no—
1082C42—112no—
1083C42—112no—
1084C42—222no—
1085C42—222no—
1086C42—222no—
1087C42—222no—
1088C42—222no—
1089C42—222no—
1090C42—221no—
1091C42—222no—
1092C42—221no—
1093C42—221no—
1094C42—222no—
1095C42D4×D1111yescharacteristic
1096C42D4×D1111yescharacteristic
1097C42C23×D1111yescharacteristic
1098C42C23×D1111yescharacteristic
1099C11#6017411yescharacteristic, complemented, Sylow
1100C23—21no—
1101C23—22no—
1102C23—24no—
1103C23—81no—
1104C23—81no—
1105C23—112no—
1106C23—228no—
1107C23—221no—
1108C23—882no—
1109C23—882no—
1110C23C2×D4×D1111yescharacteristic
1111Q8—21no—
1112Q8—114no—
1113Q8—114no—
1114Q8—112no—
1115Q8—228no—
1116Q8—224no—
1117Q8—222no—
1118Q8—221no—
1119Q8C22×C4×D1112yes—
1120D4—24no—
1121D4—24no—
1122D4—22no—
1123D4—21no—
1124D4—118no—
1125D4—114no—
1126D4—112no—
1127D4—228no—
1128D4—228no—
1129D4—228no—
1130D4—224no—
1131D4—221no—
1132D4C22×C4×D1112yes—
1133D4C22×C4×D1114yes—
1134C2×C4—21no—
1135C2×C4—24no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—22no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—42no—
1142C2×C4—44no—
1143C2×C4—81no—
1144C2×C4—82no—
1145C2×C4—81no—
1146C2×C4—112no—
1147C2×C4—114no—
1148C2×C4—114no—
1149C2×C4—112no—
1150C2×C4—112no—
1151C2×C4—228no—
1152C2×C4—228no—
1153C2×C4—228no—
1154C2×C4—224no—
1155C2×C4—221no—
1156C2×C4—222no—
1157C2×C4—224no—
1158C2×C4—221no—
1159C2×C4—222no—
1160C2×C4—221no—
1161C2×C4—442no—
1162C2×C4—442no—
1163C2×C4—442no—
1164C2×C4—881no—
1165C2×C4—882no—
1166C2×C4—882no—
1167C2×C4—882no—
1168C2×C4—882no—
1169C2×C4—882no—
1170C2×C4—882no—
1171C2×C4—881no—
1172C2×C4C22×C4×D1112yes—
1173C2×C4C2×D4×D1111yescharacteristic
1174C2×C4C2×D4×D1111yescharacteristic
1175C2×C4C2×D4×D1111yescharacteristic
1176C2×C4C2×D4×D1111yescharacteristic
1177C2×C4C2×D4×D1111yescharacteristic
1178C2×C4#41×D1112yes—
1179C2×C4C24×D1111yescharacteristic
1180C8—22no—
1181C8—112no—
1182C8—112no—
1183C8—221no—
1184C8—221no—
1185C8C22×C4×D1114yes—
1186C22—21no—
1187C22—21no—
1188C22—22no—
1189C22—24no—
1190C22—42no—
1191C22—41no—
1192C22—41no—
1193C22—42no—
1194C22—84no—
1195C22—114no—
1196C22—222no—
1197C22—222no—
1198C22—222no—
1199C22—441no—
1200C22—441no—
1201C22—888no—
1202C22C4×D4×D1112yes—
1203C22C22×D4×D1111yescharacteristic
1204C4—21no—
1205C4—21no—
1206C4—21no—
1207C4—21no—
1208C4—22no—
1209C4—42no—
1210C4—41no—
1211C4—41no—
1212C4—114no—
1213C4—222no—
1214C4—222no—
1215C4—222no—
1216C4—224no—
1217C4—441no—
1218C4—442no—
1219C4—441no—
1220C4C4×D4×D1112yes—
1221C4C23×C4×D1111yescharacteristic
1222C4C2×#41×D1111yescharacteristic
1223C2—22no—
1224C2—44no—
1225C2—42no—
1226C2—224no—
1227C2—442no—
1228C2C2×C4×D4×D1111yescharacteristic
1229C2#1308339211yescharacteristic
1230C2#1308340011yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC4×C11×AGL(1,ℤ/8)C2
socleC22×C11C23×D4
prime radicalC2×#10623306C2
cosocleC2×C4×C11C25
hypercenterC4×AGL(1,ℤ/8)D11
hypocenterC11#60174
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×#67043C2semidirect
3. C4×#67037C2semidirect
4. #13077487C2semidirect
5. #13077486C2semidirect
6. #13077478C2semidirect
7. #13077470C2semidirect
8. #13077457C2semidirect
9. #13077452C2semidirect
10. #13077449C2semidirect
11. #13077441C2semidirect
12. C4×#66962C2semidirect
13. #13077438C2semidirect
14. #13077427C2semidirect
15. #13077414C2semidirect
16. #13077413C2semidirect
17. C2×#10622631C2semidirect
18. D11×#440C2semidirect
19. #13077215C2semidirect
20. #13077147C2semidirect
21. #13077141C2semidirect
22. #13077045C2semidirect
23. C4×C11×AGL(1,ℤ/8)C2semidirect
27. C4×C11×#41C22semidirect
29. #10623358C22semidirect
34. #10623306C4semidirect
42. #10623103C22semidirect
43. C4×Q8×D11C22semidirect
47. #10623077C22semidirect
55. C4×#4341C22semidirect
59. #10623047C22semidirect
67. C2×C4×Dic22C22semidirect
68. C11×#442C22semidirect
69. C11×#440C22semidirect
70. C4×C11×SD16C22semidirect
71. C4×C11×D8C22semidirect
72. C11×#428C22semidirect
74. C11×#417C22semidirect
75. C4×C11×M16C22semidirect
76. #10622846C22semidirect
78. #10622777C22semidirect
79. SD16×Dic11C22semidirect
80. #10622765C22semidirect
81. D8×Dic11C22semidirect
83. #10622735C22semidirect
84. #10622735C22semidirect
85. #10622734C22semidirect
86. #10622733C22semidirect
87. #10622643C22semidirect
88. #10622643C22semidirect
89. #10622639C22semidirect
90. #10622639C22semidirect
91. #10622631C22semidirect
92. #10622631C22semidirect
93. #10622631C22semidirect
94. #10622631C22semidirect
95. #10622631C22semidirect
96. #10622631C22semidirect
97. #10622627C22semidirect
98. #10622627C22semidirect
100. #10622611C22semidirect
101. C2×#66874C22semidirect
102. C2×#66871C22semidirect
103. C2×#66867C22semidirect
104. #10622502C22semidirect
105. #10622494C22semidirect
106. D11×#107C22semidirect
107. #10622486C22semidirect
108. #10622474C22semidirect
109. #10622473C22semidirect
110. #10622466C22semidirect
111. #10622465C22semidirect
112. #10622430C22semidirect
113. #10622415C22semidirect
114. D11×#103C22semidirect
115. #10622403C22semidirect
117. #10622385C22semidirect
119. #10622384C22semidirect
122. #10622371C22semidirect
123. #10622371C22semidirect
124. #10622370C22semidirect
125. #10622370C22semidirect
126. #10622370C22semidirect
127. #10622369C22semidirect
128. #10622329C22semidirect
129. #10622323C22semidirect
130. #10622320C22semidirect
131. D11×#97C22semidirect
132. C4×Dic44C22semidirect
133. C4×#4314C22semidirect
134. #10622302C22semidirect
135. #10622302C22semidirect
141. #67043C2×C4semidirect
144. #67037C2×C4semidirect
157. C11×AGL(1,ℤ/8)C2×C4semidirect
179. #67003C2×C4semidirect
189. C2×#4324C2×C4semidirect
220. #66968C2×C4semidirect
221. SD16×D11C2×C4semidirect
222. #66965C2×C4semidirect
223. #66964C2×C4semidirect
224. #66962C2×C4semidirect
226. #66960C2×C4semidirect
331. C11×#41C22×C4semidirect
363. Q8×D11C22×C4semidirect
369. #4341C22×C4semidirect
395. C2×Dic22C22×C4semidirect
399. C11×SD16C22×C4semidirect
400. C11×D8C22×C4semidirect
402. C11×M16C22×C4semidirect
428. #4326C22×C4semidirect
429. #4325C22×C4semidirect
430. #4324C22×C4semidirect
431. #4324C22×C4semidirect
432. #4324C22×C4semidirect
433. #4323C22×C4semidirect
474. C2×C11⋊C8C22×C4semidirect
479. Dic44C22×C4semidirect
480. #4314C22×C4semidirect
482. #4313C22×C4semidirect
484. C8×D11C22×C4semidirect
499. C4×AGL(1,ℤ/8)D11semidirect
630. C4×#41C2×D11semidirect
641. #442C2×D11semidirect
661. #440C2×D11semidirect
670. C4×SD16C2×D11semidirect
673. C4×D8C2×D11semidirect
677. #428C2×D11semidirect
689. #417C2×D11semidirect
703. C4×M16C2×D11semidirect
767. AGL(1,ℤ/8)C4×D11semidirect
956. #41C2×C4×D11semidirect
1020. SD16C2×C4×D11semidirect
1022. D8C2×C4×D11semidirect
1026. M16C2×C4×D11semidirect
1099. C11#60174semidirect

Maximal subgroups

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

subgroupindex
C2×#106233062
C4×#670432
C4×#670372
#130774872
#130774862
#130774782
#130774702
#130774572
#130774522
#130774492
#130774412
C4×#669622
#130774382
#130774272
#130774142
#130774132
C2×#106226312
D11×#4402
#130772152
#130771472
#130771412
#130770452
C4×C11×AGL(1,ℤ/8)2
#6017411