Finite Group Databasebeta

← #15618023

Subgroups — #15618023

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×#10623293C211yesmaximal, characteristic
2C4×#67040C211yesmaximal, characteristic, complemented
3C4×#67037C211yesmaximal, characteristic, complemented
4#13077490C211yesmaximal, characteristic, complemented
5#13077488C212yesmaximal, complemented
6#13077476C211yesmaximal, characteristic, complemented
7#13077472C212yesmaximal, complemented
8#13077456C212yesmaximal, complemented
9#13077453C211yesmaximal, characteristic, complemented
10#13077447C212yesmaximal, complemented
11#13077442C211yesmaximal, characteristic, complemented
12#13077438C212yesmaximal, complemented
13C4×#66995C211yesmaximal, characteristic, complemented
14C4×#66985C211yesmaximal, characteristic, complemented
15#13077421C212yesmaximal, complemented
16#13077418C211yesmaximal, characteristic, complemented
17#13077411C212yesmaximal, complemented
18D11×#440C212yesmaximal, complemented
19#13077212C211yesmaximal, characteristic, complemented
20#13077144C211yesmaximal, characteristic, complemented
21#13077137C211yesmaximal, characteristic, complemented
22#13077041C211yesmaximal, characteristic, complemented
23C2×C11×#440C211yesmaximal, characteristic, complemented
24C2×#67040C2211yescharacteristic
25C2×#67037C2211yescharacteristic
26C22×C11×SD16C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic, complemented
28C2×C4×D4×C11C2211yescharacteristic
29#10623343C2211yescharacteristic, complemented
30C2×#66995C2211yescharacteristic
31#10623329C2211yescharacteristic
32C2×#66985C2211yescharacteristic
33C2×C4×C22⋊D11—22no—
34#10623293C4116yescomplemented
35C2×#66969C2212yes—
36C2×#66968C2212yes—
37C2×#66967C2212yes—
38C2×SD16×D11C2212yes—
39C2×#66957C2211yescharacteristic
40C2×#66954C2211yescharacteristic
41C2×#66954C2211yescharacteristic
42#10623105—21no—
43#10623105C2212yescomplemented
44C4×#4343—21no—
45C4×#4343C2212yescomplemented
46#10623103—21no—
47#10623103C2212yescomplemented
48C4×Q8×D11—21no—
49C4×Q8×D11C2212yescomplemented
50#10623077—21no—
51#10623077C2212yes—
52#10623076—21no—
53#10623076C2212yes—
54C4×D4×D11—21no—
55C4×D4×D11C2212yes—
56C4×#4341—21no—
57C4×#4341C2212yes—
58#10623035—22no—
59#10623035C2211yescharacteristic
60#10623035C2211yescharacteristic
61#10623035C2211yescharacteristic
62#10623035C2211yescharacteristic, complemented
63#10623017—22no—
64C4×#4339—22no—
65C4×#4339C2211yescharacteristic
66C4×#4339C2211yescharacteristic
67C4×#4339C2211yescharacteristic, complemented
68C11×#440C2212yescomplemented
69C11×#440C2212yescomplemented
70C11×#440C2212yescomplemented
71C11×#440C2212yescomplemented
72C2×C11×#107C2211yescharacteristic, complemented
73C2×C11×#103C2211yescharacteristic, complemented
74C2×C11×#102C2211yescharacteristic
75C2×C11×#97C2211yescharacteristic, complemented
76#10622838C2211yescharacteristic, complemented
77#10622828C2211yescharacteristic
78#10622777C2212yescomplemented
79#10622777C2212yescomplemented
80SD16×Dic11C2212yescomplemented
81SD16×Dic11C2212yescomplemented
82#10622726C2211yescharacteristic
83#10622726C2211yescharacteristic, complemented
84#10622719C2211yescharacteristic, complemented
85#10622714C2211yescharacteristic, complemented
86#10622714C2211yescharacteristic, complemented
87#10622643C2212yescomplemented
88C4×#4326C2212yescomplemented
89#10622639C2212yescomplemented
90C4×#4325C2212yescomplemented
91#10622631C2212yescomplemented
92C4×#4324C2212yescomplemented
93#10622627C2212yescomplemented
94C4×#4323C2212yescomplemented
95#10622579C2211yescharacteristic
96#10622579C2211yescharacteristic, complemented
97#10622577C2211yescharacteristic, complemented
98#10622577C2211yescharacteristic, complemented
99C4×#4318C2211yescharacteristic, complemented
100#10622502C2212yescomplemented
101#10622502C2212yescomplemented
102#10622494C2212yescomplemented
103#10622494C2212yescomplemented
104#10622493C2212yescomplemented
105D11×#107C2212yescomplemented
106#10622486C2212yescomplemented
107#10622485C2212yescomplemented
108#10622430C2212yescomplemented
109#10622417C2212yescomplemented
110#10622416C2212yescomplemented
111#10622415C2212yescomplemented
112D11×#103C2212yescomplemented
113#10622403C2212yescomplemented
114#10622402C2212yescomplemented
115#10622401C2212yescomplemented
116#10622398C2212yescomplemented
117#10622385C2212yes—
118#10622384C2212yes—
119#10622383C2212yes—
120D11×#102C2212yes—
121#10622371C2212yescomplemented
122#10622370C2212yescomplemented
123#10622369C2212yescomplemented
124#10622329C2211yescharacteristic, complemented
125#10622329C2211yescharacteristic, complemented
126#10622324C2211yescharacteristic, complemented
127#10622324C2211yescharacteristic, complemented
128#10622323C2211yescharacteristic, complemented
129#10622323C2211yescharacteristic, complemented
130#10622323C2211yescharacteristic, complemented
131#10622323C2211yescharacteristic, complemented
132#10622321C2212yescomplemented
133#10622321C2212yescomplemented
134#10622320C2212yescomplemented
135D11×#97C2212yescomplemented
136C22×Q8×C11C2311yescharacteristic
137C22×D4×C11C2311yescharacteristic
138C23×C4×C11—21no—
139C22×C22⋊D11—22no—
140#67040—24no—
141#67040C2×C418yescomplemented
142C2×#4343—21no—
143C2×#4343C2312yes—
144C2×Q8×D11—21no—
145C2×Q8×D11C2312yes—
146#67037—24no—
147#67037C2×C418yescomplemented
148C2×#4341—21no—
149C2×#4341C2312yes—
150C2×D4×D11—21no—
151C2×D4×D11C2312yes—
152C2×#4339—22no—
153C2×#4339C2311yescharacteristic
154C2×#4339C2311yescharacteristic
155C2×#4339C2311yescharacteristic
156C22×C4×D11—22no—
157C2×C11×SD16C2×C418yescomplemented
158C2×C11×SD16C2312yes—
159C2×C11×SD16C2312yes—
160C22×C8×C11C2311yescharacteristic
161C22×C8×C11C2311yescharacteristic
162C4×Q8×C11—21no—
163C4×Q8×C11—21no—
164C4×Q8×C11C2312yes—
165C4×Q8×C11C2312yes—
166C4×D4×C11—21no—
167C4×D4×C11—21no—
168C4×D4×C11C2312yes—
169C4×D4×C11C2312yes—
170C2×C11×C4⋊C4—21no—
171C2×C11×C4⋊C4C2311yescharacteristic
172C2×C11×C4⋊C4C2311yescharacteristic
173C2×C11×C22⋊C4—21no—
174C2×C42×C11—21no—
175C2×C42×C11C2311yescharacteristic
176C2×C22⋊Dic11—22no—
177Q8×Dic11—21no—
178Q8×Dic11—21no—
179Q8×Dic11C2312yes—
180Q8×Dic11C2312yes—
181C2×#4326C2312yes—
182#66995C2×C418yescomplemented
183C2×#4325C2312yes—
184D4×Dic11—21no—
185D4×Dic11—21no—
186D4×Dic11C2312yes—
187D4×Dic11C2312yes—
188C2×#4324C2312yes—
189#66985C2×C418yescomplemented
190C2×#4323C2312yes—
191C4×C22⋊D11—21no—
192C4×C22⋊D11—21no—
193C4×C22⋊D11—21no—
194C4×C22⋊D11—21no—
195C4×C22⋊D11—22no—
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⋊D11D412yes—
204C4×C22⋊D11D412yes—
205C2×(C2×D11)⋊C4—22no—
206#66979—22no—
207#66979C2311yescharacteristic
208#66979C2311yescharacteristic
209#66979C2311yescharacteristic
210C2×Dic11⋊C4—22no—
211C2×C4×Dic11—22no—
212C2×#4318C2311yescharacteristic
213C2×#4318C2311yescharacteristic
214#66969C2×C4116yescomplemented
215#66968C2×C4116yescomplemented
216#66967C2×C4116yescomplemented
217SD16×D11C2×C4116yescomplemented
218C2×Dic44C2311yescharacteristic
219#66957C2×C418yescomplemented
220C2×D88C2311yescharacteristic
221C2×#4314C2311yescharacteristic
222C2×#4314C2311yescharacteristic
223#66954—24no—
224#66954C2×C418yescomplemented
225C2×#4313C2312yes—
226C2×#4313C2312yes—
227C2×C8×D11C2312yes—
228C2×C8×D11C2312yes—
229#66946—21no—
230#66946—21no—
231#66946—22no—
232#66946—22no—
233#66946C2312yes—
234#66946C2312yes—
235#66945—22no—
236#66945—21no—
237#66945—21no—
238#66945—22no—
239#66945C2312yes—
240#66945C2312yes—
241C4⋊C4×D11—22no—
242C4⋊C4×D11—21no—
243C4⋊C4×D11—21no—
244C4⋊C4×D11—22no—
245C4⋊C4×D11C2312yes—
246C4⋊C4×D11C2312yes—
247#66940—21no—
248#66940—21no—
249#66940—22no—
250#66940—22no—
251#66940C2312yes—
252#66940C2312yes—
253(C22⋊D11)⋊C4—22no—
254(C22⋊D11)⋊C4—22no—
255(C22⋊D11)⋊C4—22no—
256(C22⋊D11)⋊C4—22no—
257C22⋊C4×D11—22no—
258C22⋊C4×D11—22no—
259#66930—22no—
260#66930—22no—
261C4×D44—22no—
262C4×D44—22no—
263C4×D44D411yescharacteristic
264C4×D44D411yescharacteristic
265C4×D44C2311yescharacteristic
266C4×D44C2311yescharacteristic
267C4×D44C2311yescharacteristic
268C4×D44C2311yescharacteristic
269#66925—21no—
270#66925—21no—
271#66925—22no—
272#66925—22no—
273#66925C2312yes—
274C42×D11—22no—
275C42×D11—21no—
276C42×D11—21no—
277C42×D11—22no—
278C42×D11C2312yes—
279C4×Dic22—22no—
280C4×Dic22—22no—
281C4×Dic22D411yescharacteristic
282C4×Dic22D411yescharacteristic
283C4×Dic22C2311yescharacteristic
284C4×Dic22C2311yescharacteristic
285C4×Dic22C2311yescharacteristic
286C4×Dic22C2311yescharacteristic
287C11×#107C2312yes—
288C11×#107C2312yes—
289C11×#103C2312yes—
290C11×#103C2312yes—
291C11×#102C2312yes—
292C11×#102C2312yes—
293C11×#97C2311yescharacteristic
294C11×#97C2311yescharacteristic
295C11×#97C2311yescharacteristic
296C11×#97C2311yescharacteristic
297#66899C2312yes—
298#66899C2312yes—
299#66896C2312yes—
300#66896C2312yes—
301#66885C2311yescharacteristic
302#66885C2311yescharacteristic
303#66885C2311yescharacteristic
304#66885C2311yescharacteristic
305#66882C2311yescharacteristic
306#66882C2311yescharacteristic
307#66881C2311yescharacteristic
308#66881C2311yescharacteristic
309#66880C2311yescharacteristic
310#66880C2311yescharacteristic
311#66880C2311yescharacteristic
312#66880C2311yescharacteristic
313#66879C2312yes—
314#66879C2312yes—
315C8×Dic11C2312yes—
316C8×Dic11C2312yes—
317#66874C2312yes—
318#66874C2312yes—
319#66873C2312yes—
320#66873C2312yes—
321#66872C2312yes—
322#66872C2312yes—
323#66871C2312yes—
324#66871C2312yes—
325#66867C2312yes—
326C4×C11⋊C8C2312yes—
327#60174—111nomaximal, Sylow
328C24×C11—21no—
329C23×D11—22no—
330C2×Q8×C11—21no—
331C2×Q8×C11—22no—
332C2×Q8×C11C22×C414yescomplemented
333C2×Q8×C11C2412yes—
334C2×D4×C11—21no—
335C2×D4×C11—22no—
336C2×D4×C11C22×C414yes—
337C2×D4×C11C2412yes—
338C22×C4×C11—21no—
339C22×C4×C11—21no—
340C22×C4×C11—21no—
341C22×C4×C11—22no—
342C22×C4×C11—22no—
343C22×C4×C11—82no—
344C22×C4×C11C2×D411yescharacteristic
345C22×C4×C11C2×D411yescharacteristic
346C22×C4×C11C2411yescharacteristic
347C2×C22⋊D11—216no—
348C2×C22⋊D11—22no—
349C2×C22⋊D11—21no—
350C2×C22⋊D11—21no—
351C2×C22⋊D11—22no—
352C2×C22⋊D11C2×D412yes—
353C22×Dic11—22no—
354C22×Dic11—22no—
355C22×Dic11—22no—
356#4343—28no—
357#4343—24no—
358#4343C22×C418yescomplemented
359Q8×D11—24no—
360Q8×D11—28no—
361Q8×D11C22×C418yescomplemented
362#4341—24no—
363#4341—28no—
364#4341C22×C418yes—
365D4×D11—28no—
366D4×D11—24no—
367D4×D11C22×C418yes—
368#4339—216no—
369#4339—22no—
370#4339—22no—
371#4339C22×C414yes—
372#4339C22×C414yes—
373#4339C22×C414yescomplemented
374#4339#4114yes—
375C2×D44—22no—
376C2×D44C2×D411yescharacteristic
377C2×D44C2411yescharacteristic
378C2×D44C2411yescharacteristic
379C2×C4×D11—22no—
380C2×C4×D11—22no—
381C2×C4×D11—22no—
382C2×C4×D11—22no—
383C2×C4×D11—22no—
384C2×C4×D11—22no—
385C2×C4×D11—21no—
386C2×C4×D11—21no—
387C2×C4×D11—21no—
388C2×C4×D11—21no—
389C2×C4×D11—21no—
390C2×C4×D11—21no—
391C2×C4×D11—84no—
392C2×C4×D11C2×D412yes—
393C2×C4×D11C2×D412yes—
394C2×C4×D11C2412yes—
395C2×Dic22—22no—
396C2×Dic22C2×D411yescharacteristic
397C2×Dic22C2411yescharacteristic
398C2×Dic22C2411yescharacteristic
399C11×SD16C22×C418yescomplemented
400C11×SD16C22×C418yescomplemented
401C2×C8×C11—22no—
402C2×C8×C11C22×C414yescomplemented
403C2×C8×C11C2411yescharacteristic
404C2×C8×C11C2411yescharacteristic
405C2×C8×C11C2411yescharacteristic
406C2×C8×C11C2411yescharacteristic
407C11×C4⋊C4—22no—
408C11×C4⋊C4—22no—
409C11×C4⋊C4—21no—
410C11×C4⋊C4—21no—
411C11×C4⋊C4C2412yes—
412C11×C4⋊C4C2412yes—
413C11×C22⋊C4—22no—
414C11×C22⋊C4—22no—
415C42×C11—22no—
416C42×C11—22no—
417C42×C11C2×D411yescharacteristic
418C42×C11C2×D411yescharacteristic
419C42×C11C2411yescharacteristic
420C42×C11C2411yescharacteristic
421C22⋊Dic11—22no—
422C22⋊Dic11—22no—
423C22⋊Dic11—21no—
424C22⋊Dic11—21no—
425C22⋊Dic11C2×D412yes—
426#4326C22×C418yescomplemented
427#4325C22×C418yescomplemented
428#4324C22×C418yescomplemented
429#4323C22×C418yescomplemented
430(C2×D11)⋊C4—22no—
431(C2×D11)⋊C4—22no—
432(C2×D11)⋊C4—22no—
433(C2×D11)⋊C4—22no—
434(C2×D11)⋊C4—21no—
435(C2×D11)⋊C4—21no—
436(C2×D11)⋊C4—21no—
437(C2×D11)⋊C4—21no—
438(C2×D11)⋊C4C2×D412yes—
439(C2×D11)⋊C4C2×D412yes—
440C4⋊Dic11—22no—
441C4⋊Dic11—22no—
442C4⋊Dic11C2×D411yescharacteristic
443C4⋊Dic11C2×D411yescharacteristic
444C4⋊Dic11C2411yescharacteristic
445C4⋊Dic11C2411yescharacteristic
446C4⋊Dic11C2411yescharacteristic
447C4⋊Dic11C2411yescharacteristic
448Dic11⋊C4—22no—
449Dic11⋊C4—22no—
450Dic11⋊C4—22no—
451Dic11⋊C4—22no—
452Dic11⋊C4—21no—
453Dic11⋊C4—21no—
454Dic11⋊C4—21no—
455Dic11⋊C4—21no—
456Dic11⋊C4C2×D412yes—
457Dic11⋊C4C2×D412yes—
458C4×Dic11—22no—
459C4×Dic11—22no—
460C4×Dic11—22no—
461C4×Dic11—22no—
462C4×Dic11—22no—
463C4×Dic11—22no—
464C4×Dic11—21no—
465C4×Dic11—21no—
466C4×Dic11—21no—
467C4×Dic11—21no—
468C4×Dic11—21no—
469C4×Dic11—21no—
470C4×Dic11C2×D412yes—
471C4×Dic11C2×D412yes—
472C4×Dic11C2412yes—
473#4318—22no—
474#4318C22×C414yescomplemented
475C2×C11⋊C8C2412yes—
476C2×C11⋊C8C2412yes—
477Dic44C22×C414yescomplemented
478D88C22×C414yescomplemented
479#4314C22×C414yescomplemented
480#4314C22×C414yescomplemented
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)—111no—
500#2943—112no—
501#2943—111no—
502C2×#440—112no—
503C2×#440D1111yescharacteristic, complemented
504#2913—111no—
505#2898—111no—
506#2897—111no—
507#2875—111no—
508C23×C11—22no—
509C23×C11—24no—
510C23×C11—81no—
511C23×C11—81no—
512C23×C11C22×D411yescharacteristic
513C22×D11—21no—
514C22×D11—21no—
515C22×D11—28no—
516C22×D11—82no—
517C22×D11—82no—
518C22×D11C22×D412yes—
519Q8×C11—24no—
520Q8×C11—22no—
521Q8×C11C23×C414yes—
522D4×C11—24no—
523D4×C11—22no—
524D4×C11C23×C414yes—
525C2×C4×C11—24no—
526C2×C4×C11—22no—
527C2×C4×C11—22no—
528C2×C4×C11—22no—
529C2×C4×C11—41no—
530C2×C4×C11—41no—
531C2×C4×C11—44no—
532C2×C4×C11—82no—
533C2×C4×C11—81no—
534C2×C4×C11—81no—
535C2×C4×C11C23×C412yes—
536C2×C4×C11C22×D411yescharacteristic
537C2×C4×C11C22×D411yescharacteristic
538C2×C4×C11C22×D411yescharacteristic
539C2×C4×C11C22×D411yescharacteristic
540C2×C4×C11C22×D411yescharacteristic
541C2×C4×C11C2×#4112yes—
542C2×C4×C11C2511yescharacteristic
543C22⋊D11—24no—
544C22⋊D11—24no—
545C22⋊D11—28no—
546C22⋊D11—28no—
547C22⋊D11C4×D418yes—
548C2×Dic11—21no—
549C2×Dic11—21no—
550C2×Dic11—28no—
551C2×Dic11—21no—
552C2×Dic11—21no—
553C2×Dic11—21no—
554C2×Dic11—21no—
555C2×Dic11—82no—
556C2×Dic11—82no—
557C2×Dic11C22×D412yes—
558C2×Dic11C22×D412yes—
559C2×Dic11C22×D412yes—
560D44—28no—
561D44—21no—
562D44—21no—
563D44C4×D414yes—
564D44C23×C412yes—
565D44C23×C412yes—
566C4×D11—28no—
567C4×D11—24no—
568C4×D11—24no—
569C4×D11—28no—
570C4×D11—42no—
571C4×D11—42no—
572C4×D11—42no—
573C4×D11—42no—
574C4×D11—82no—
575C4×D11—82no—
576C4×D11—81no—
577C4×D11—81no—
578C4×D11—82no—
579C4×D11—82no—
580C4×D11C23×C414yes—
581C4×D11C2×#4114yes—
582Dic22—21no—
583Dic22—21no—
584Dic22—28no—
585Dic22C4×D414yes—
586Dic22C23×C412yes—
587Dic22C23×C412yes—
588C8×C11—21no—
589C8×C11—21no—
590C8×C11C23×C412yes—
591C8×C11C23×C412yes—
592C11⋊C8—22no—
593C11⋊C8C23×C414yes—
594C2×2−1+4—111no—
595C2×H(5,𝔽2)—111no—
596#577—1116no—
597C2×#137—111no—
598C2×#137—112no—
599C2×AGL(1,ℤ/8)—111no—
600C2×AGL(1,ℤ/8)—112no—
601C2×#135—112no—
602C2×#135—111no—
603C22×SD16—112no—
604C22×SD16C2×D1111yescharacteristic
605C2×#131—111no—
606C2×#131—111no—
607#520—111no—
608#520—111no—
609#520—112no—
610#520—112no—
611#520—111no—
612#520—111no—
613#520—222no—
614#520—221no—
615#520—221no—
616#519—111no—
617#519—112no—
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—111no—
628C4×#41—222no—
629C4×#41—221no—
630C4×#41—221no—
631C2×C4×Q8—112no—
632C2×C4×Q8—221no—
633C2×C4×Q8C2×D1111yescharacteristic, complemented
634C2×C4×D4—112no—
635C2×C4×D4—221no—
636C2×C4×D4—222no—
637C2×C4×D4C2×D1111yescharacteristic
638#442—112no—
639#442—112no—
640#442—111no—
641#442—111no—
642#441—112no—
643#441—112no—
644#441—111no—
645#441—111no—
646#440—112no—
647#440—112no—
648#440—112no—
649#440—112no—
650#440—112no—
651#440—112no—
652#440—112no—
653#440—112no—
654#440—111no—
655#440—111no—
656#440—111no—
657#440—111no—
658#440C2×D1112yescomplemented
659#440C2×D1112yescomplemented
660#440C2×D1112yescomplemented
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×SD16—112no—
671C4×D8—112no—
672C4×D8—112no—
673C4×D8—112no—
674#428—111no—
675#428—111no—
676#428—112no—
677#428—112no—
678#427—111no—
679#427—112no—
680C2×#107—112no—
681C2×#107C2×D1111yescharacteristic, complemented
682#419—111no—
683#419—112no—
684#418—111no—
685#418—112no—
686#417—111no—
687#417—111no—
688#417—112no—
689#417—112no—
690#416—111no—
691#416—111no—
692#416—112no—
693#416—112no—
694C2×#103—112no—
695C2×#103C2×D1111yescharacteristic, complemented
696C2×#102—112no—
697C2×#102C2×D1111yescharacteristic
698#405—111no—
699#405—111no—
700#405—112no—
701#405—112no—
702C4×M16—111no—
703C4×M16—112no—
704C2×#97—112no—
705C2×#97C2×D1111yescharacteristic, complemented
706C22×C11—21no—
707C22×C11—21no—
708C22×C11—24no—
709C22×C11—42no—
710C22×C11—42no—
711C22×C11—84no—
712C22×C11C2×C4×D412yes—
713C22×C11C23×D411yescharacteristic
714C2×D11—22no—
715C2×D11—22no—
716C2×D11—22no—
717C2×D11—22no—
718C2×D11—41no—
719C2×D11—41no—
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—24no—
729C4×C11—42no—
730C4×C11—42no—
731C4×C11C2×C4×D412yes—
732C4×C11C24×C411yescharacteristic
733C4×C11C22×#4111yescharacteristic
734Dic11—22no—
735Dic11—22no—
736Dic11—22no—
737Dic11—22no—
738Dic11—41no—
739Dic11—41no—
740Dic11—41no—
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—111no—
752C2×#41—222no—
753C2×#41—221no—
754C2×#41—221no—
755C22×Q8—112no—
756C22×Q8—221no—
757C22×Q8C22×D1111yescharacteristic
758C22×D4—112no—
759C22×D4—221no—
760C22×D4—222no—
761C22×D4C22×D1111yescharacteristic
762C23×C4—21no—
763C23×C4—222no—
764#137—118no—
765#137—1116no—
766AGL(1,ℤ/8)—118no—
767AGL(1,ℤ/8)—1116no—
768#135—1116no—
769#135—118no—
770C2×Q16—112no—
771C2×Q16—111no—
772C2×SD16—112no—
773C2×SD16—112no—
774C2×SD16—1116no—
775C2×SD16—111no—
776C2×SD16—111no—
777C2×SD16C4×D1118yescomplemented
778C2×SD16C22×D1112yes—
779C2×SD16C22×D1112yes—
780C2×D8—112no—
781C2×D8—111no—
782#131—118no—
783#131—224no—
784C2×M16—111no—
785C2×M16—111no—
786C2×M16—112no—
787C2×M16—112no—
788C22×C8—112no—
789C22×C8—112no—
790C22×C8C22×D1111yescharacteristic
791C22×C8C22×D1111yescharacteristic
792C4×Q8—21no—
793C4×Q8—21no—
794C4×Q8—111no—
795C4×Q8—111no—
796C4×Q8—112no—
797C4×Q8—112no—
798C4×Q8—112no—
799C4×Q8—112no—
800C4×Q8—111no—
801C4×Q8—111no—
802C4×Q8—111no—
803C4×Q8—111no—
804C4×Q8—222no—
805C4×Q8—222no—
806C4×Q8—222no—
807C4×Q8—222no—
808C4×Q8—221no—
809C4×Q8—221no—
810C4×Q8—221no—
811C4×Q8—221no—
812C4×Q8C22×D1112yes—
813C4×Q8C22×D1112yes—
814C4×D4—21no—
815C4×D4—21no—
816C4×D4—112no—
817C4×D4—112no—
818C4×D4—112no—
819C4×D4—112no—
820C4×D4—112no—
821C4×D4—112no—
822C4×D4—111no—
823C4×D4—111no—
824C4×D4—111no—
825C4×D4—111no—
826C4×D4—111no—
827C4×D4—111no—
828C4×D4—222no—
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—221no—
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×D4—221no—
851C4×D4—221no—
852C4×D4C22×D1112yes—
853C4×D4C22×D1112yes—
854#117—111no—
855#117—112no—
856#117—111no—
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#117—221no—
871C2×C4⋊C4—21no—
872C2×C4⋊C4—112no—
873C2×C4⋊C4—112no—
874C2×C4⋊C4—221no—
875C2×C4⋊C4—222no—
876C2×C4⋊C4—221no—
877C2×C4⋊C4—222no—
878C2×C4⋊C4—222no—
879C2×C4⋊C4C22×D1111yescharacteristic
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—111no—
895#107—111no—
896#107—112no—
897#107—112no—
898#107C22×D1112yes—
899#107C22×D1112yes—
900#106—111no—
901#106—111no—
902#106—112no—
903#106—112no—
904#103—112no—
905#103—112no—
906#103—111no—
907#103—111no—
908#103—111no—
909#103—111no—
910#103—112no—
911#103—112no—
912#103C22×D1112yes—
913#103C22×D1112yes—
914#102—112no—
915#102—112no—
916#102—111no—
917#102—111no—
918#102—111no—
919#102—111no—
920#102—112no—
921#102—112no—
922#102C22×D1112yes—
923#102C22×D1112yes—
924#97—112no—
925#97—112no—
926#97—112no—
927#97C22×D1111yescharacteristic
928#97C22×D1111yescharacteristic
929#97C22×D1111yescharacteristic
930#97C22×D1111yescharacteristic
931C4×C8—112no—
932C4×C8—112no—
933C4×C8—112no—
934C2×C11—22no—
935C2×C11—44no—
936C2×C11C22×C4×D411yescharacteristic
937C2×C11#358511yescharacteristic
938C2×C11#358611yescharacteristic
939D11—24no—
940D11—42no—
941D11—42no—
942C24—21no—
943C24—222no—
944#41—114no—
945#41—114no—
946#41—118no—
947#41—118no—
948#41—114no—
949#41—114no—
950#41—2216no—
951#41—224no—
952#41—224no—
953#41—228no—
954#41—228no—
955#41—222no—
956#41—222no—
957C2×Q8—21no—
958C2×Q8—22no—
959C2×Q8—111no—
960C2×Q8—118no—
961C2×Q8—111no—
962C2×Q8—111no—
963C2×Q8—222no—
964C2×Q8—224no—
965C2×Q8—228no—
966C2×Q8C2×C4×D1114yescomplemented
967C2×Q8C23×D1112yes—
968C2×D4—21no—
969C2×D4—22no—
970C2×D4—112no—
971C2×D4—118no—
972C2×D4—111no—
973C2×D4—111no—
974C2×D4—111no—
975C2×D4—222no—
976C2×D4—224no—
977C2×D4—222no—
978C2×D4—228no—
979C2×D4—2216no—
980C2×D4—222no—
981C2×D4—221no—
982C2×D4—221no—
983C2×D4C2×C4×D1114yes—
984C2×D4C23×D1112yes—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—22no—
989C22×C4—22no—
990C22×C4—82no—
991C22×C4—112no—
992C22×C4—112no—
993C22×C4—112no—
994C22×C4—222no—
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—221no—
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—118no—
1014Q16—114no—
1015SD16—118no—
1016SD16—118no—
1017SD16—114no—
1018SD16—114no—
1019SD16C2×C4×D1118yescomplemented
1020SD16C2×C4×D1118yescomplemented
1021D8—118no—
1022D8—114no—
1023M16—114no—
1024M16—118no—
1025M16—224no—
1026M16—222no—
1027C2×C8—22no—
1028C2×C8—112no—
1029C2×C8—118no—
1030C2×C8—112no—
1031C2×C8—224no—
1032C2×C8C2×C4×D1114yescomplemented
1033C2×C8C23×D1111yescharacteristic
1034C2×C8C23×D1111yescharacteristic
1035C2×C8C23×D1111yescharacteristic
1036C2×C8C23×D1111yescharacteristic
1037C4⋊C4—22no—
1038C4⋊C4—22no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—112no—
1042C4⋊C4—111no—
1043C4⋊C4—112no—
1044C4⋊C4—111no—
1045C4⋊C4—111no—
1046C4⋊C4—111no—
1047C4⋊C4—111no—
1048C4⋊C4—111no—
1049C4⋊C4—222no—
1050C4⋊C4—222no—
1051C4⋊C4—222no—
1052C4⋊C4—222no—
1053C4⋊C4—222no—
1054C4⋊C4—222no—
1055C4⋊C4—221no—
1056C4⋊C4—221no—
1057C4⋊C4—221no—
1058C4⋊C4—221no—
1059C4⋊C4C23×D1112yes—
1060C4⋊C4C23×D1112yes—
1061C22⋊C4—22no—
1062C22⋊C4—22no—
1063C22⋊C4—112no—
1064C22⋊C4—112no—
1065C22⋊C4—112no—
1066C22⋊C4—222no—
1067C22⋊C4—222no—
1068C22⋊C4—222no—
1069C22⋊C4—222no—
1070C22⋊C4—222no—
1071C22⋊C4—222no—
1072C22⋊C4—221no—
1073C22⋊C4—221no—
1074C22⋊C4—221no—
1075C22⋊C4—221no—
1076C22⋊C4—221no—
1077C22⋊C4—221no—
1078C42—22no—
1079C42—22no—
1080C42—112no—
1081C42—112no—
1082C42—112no—
1083C42—222no—
1084C42—222no—
1085C42—222no—
1086C42—222no—
1087C42—222no—
1088C42—222no—
1089C42—221no—
1090C42—221no—
1091C42—221no—
1092C42—221no—
1093C42—221no—
1094C42—221no—
1095C42D4×D1111yescharacteristic
1096C42D4×D1111yescharacteristic
1097C42C23×D1111yescharacteristic
1098C42C23×D1111yescharacteristic
1099C11#6017411yescharacteristic, complemented, Sylow
1100C23—22no—
1101C23—24no—
1102C23—81no—
1103C23—81no—
1104C23—112no—
1105C23—228no—
1106C23—221no—
1107C23—221no—
1108C23—882no—
1109C23—882no—
1110C23C2×D4×D1111yescharacteristic
1111Q8—24no—
1112Q8—22no—
1113Q8—114no—
1114Q8—112no—
1115Q8—112no—
1116Q8—228no—
1117Q8—221no—
1118Q8—221no—
1119Q8C22×C4×D1114yes—
1120D4—24no—
1121D4—22no—
1122D4—118no—
1123D4—114no—
1124D4—112no—
1125D4—112no—
1126D4—228no—
1127D4—228no—
1128D4—228no—
1129D4—224no—
1130D4—224no—
1131D4—221no—
1132D4—221no—
1133D4C22×C4×D1114yes—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—44no—
1141C2×C4—82no—
1142C2×C4—81no—
1143C2×C4—81no—
1144C2×C4—112no—
1145C2×C4—114no—
1146C2×C4—114no—
1147C2×C4—112no—
1148C2×C4—112no—
1149C2×C4—228no—
1150C2×C4—228no—
1151C2×C4—228no—
1152C2×C4—221no—
1153C2×C4—221no—
1154C2×C4—224no—
1155C2×C4—224no—
1156C2×C4—221no—
1157C2×C4—221no—
1158C2×C4—221no—
1159C2×C4—221no—
1160C2×C4—442no—
1161C2×C4—442no—
1162C2×C4—442no—
1163C2×C4—442no—
1164C2×C4—881no—
1165C2×C4—881no—
1166C2×C4—882no—
1167C2×C4—882no—
1168C2×C4—882no—
1169C2×C4—882no—
1170C2×C4—882no—
1171C2×C4—882no—
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—21no—
1181C8—21no—
1182C8—114no—
1183C8—222no—
1184C8C22×C4×D1112yes—
1185C8C22×C4×D1112yes—
1186C22—21no—
1187C22—21no—
1188C22—24no—
1189C22—42no—
1190C22—42no—
1191C22—84no—
1192C22—114no—
1193C22—222no—
1194C22—222no—
1195C22—222no—
1196C22—222no—
1197C22—441no—
1198C22—441no—
1199C22—441no—
1200C22—441no—
1201C22—888no—
1202C22C4×D4×D1112yes—
1203C22C22×D4×D1111yescharacteristic
1204C4—21no—
1205C4—21no—
1206C4—21no—
1207C4—21no—
1208C4—24no—
1209C4—42no—
1210C4—42no—
1211C4—114no—
1212C4—222no—
1213C4—222no—
1214C4—222no—
1215C4—222no—
1216C4—441no—
1217C4—441no—
1218C4—441no—
1219C4—441no—
1220C4C4×D4×D1112yes—
1221C4C23×C4×D1111yescharacteristic
1222C4C2×#41×D1111yescharacteristic
1223C2—22no—
1224C2—44no—
1225C2—224no—
1226C2—442no—
1227C2—442no—
1228C2C2×C4×D4×D1111yescharacteristic
1229C2#1308339211yescharacteristic
1230C2#1308339911yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#440C2
socleC22×C11C23×D4
prime radicalC2×#10623293C2
cosocleC2×C4×C11C25
hypercenterC2×#440D11
hypocenterC11#60174
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C4×#67040C2semidirect
3. C4×#67037C2semidirect
4. #13077490C2semidirect
5. #13077488C2semidirect
6. #13077476C2semidirect
7. #13077472C2semidirect
8. #13077456C2semidirect
9. #13077453C2semidirect
10. #13077447C2semidirect
11. #13077442C2semidirect
12. #13077438C2semidirect
13. C4×#66995C2semidirect
14. C4×#66985C2semidirect
15. #13077421C2semidirect
16. #13077418C2semidirect
17. #13077411C2semidirect
18. D11×#440C2semidirect
19. #13077212C2semidirect
20. #13077144C2semidirect
21. #13077137C2semidirect
22. #13077041C2semidirect
23. C2×C11×#440C2semidirect
27. C2×C4×Q8×C11C22semidirect
29. #10623343C22semidirect
34. #10623293C4semidirect
43. #10623105C22semidirect
45. C4×#4343C22semidirect
47. #10623103C22semidirect
49. C4×Q8×D11C22semidirect
62. #10623035C22semidirect
67. C4×#4339C22semidirect
68. C11×#440C22semidirect
69. C11×#440C22semidirect
70. C11×#440C22semidirect
71. C11×#440C22semidirect
72. C2×C11×#107C22semidirect
73. C2×C11×#103C22semidirect
75. C2×C11×#97C22semidirect
76. #10622838C22semidirect
78. #10622777C22semidirect
79. #10622777C22semidirect
80. SD16×Dic11C22semidirect
81. SD16×Dic11C22semidirect
83. #10622726C22semidirect
84. #10622719C22semidirect
85. #10622714C22semidirect
86. #10622714C22semidirect
87. #10622643C22semidirect
88. C4×#4326C22semidirect
89. #10622639C22semidirect
90. C4×#4325C22semidirect
91. #10622631C22semidirect
92. C4×#4324C22semidirect
93. #10622627C22semidirect
94. C4×#4323C22semidirect
96. #10622579C22semidirect
97. #10622577C22semidirect
98. #10622577C22semidirect
99. C4×#4318C22semidirect
100. #10622502C22semidirect
101. #10622502C22semidirect
102. #10622494C22semidirect
103. #10622494C22semidirect
104. #10622493C22semidirect
105. D11×#107C22semidirect
106. #10622486C22semidirect
107. #10622485C22semidirect
108. #10622430C22semidirect
109. #10622417C22semidirect
110. #10622416C22semidirect
111. #10622415C22semidirect
112. D11×#103C22semidirect
113. #10622403C22semidirect
114. #10622402C22semidirect
115. #10622401C22semidirect
116. #10622398C22semidirect
121. #10622371C22semidirect
122. #10622370C22semidirect
123. #10622369C22semidirect
124. #10622329C22semidirect
125. #10622329C22semidirect
126. #10622324C22semidirect
127. #10622324C22semidirect
128. #10622323C22semidirect
129. #10622323C22semidirect
130. #10622323C22semidirect
131. #10622323C22semidirect
132. #10622321C22semidirect
133. #10622321C22semidirect
134. #10622320C22semidirect
135. D11×#97C22semidirect
141. #67040C2×C4semidirect
147. #67037C2×C4semidirect
157. C2×C11×SD16C2×C4semidirect
182. #66995C2×C4semidirect
189. #66985C2×C4semidirect
214. #66969C2×C4semidirect
215. #66968C2×C4semidirect
216. #66967C2×C4semidirect
217. SD16×D11C2×C4semidirect
219. #66957C2×C4semidirect
224. #66954C2×C4semidirect
332. C2×Q8×C11C22×C4semidirect
358. #4343C22×C4semidirect
361. Q8×D11C22×C4semidirect
373. #4339C22×C4semidirect
399. C11×SD16C22×C4semidirect
400. C11×SD16C22×C4semidirect
402. C2×C8×C11C22×C4semidirect
426. #4326C22×C4semidirect
427. #4325C22×C4semidirect
428. #4324C22×C4semidirect
429. #4323C22×C4semidirect
474. #4318C22×C4semidirect
477. Dic44C22×C4semidirect
478. D88C22×C4semidirect
479. #4314C22×C4semidirect
480. #4314C22×C4semidirect
482. #4313C22×C4semidirect
484. C8×D11C22×C4semidirect
503. C2×#440D11semidirect
633. C2×C4×Q8C2×D11semidirect
658. #440C2×D11semidirect
659. #440C2×D11semidirect
660. #440C2×D11semidirect
661. #440C2×D11semidirect
681. C2×#107C2×D11semidirect
695. C2×#103C2×D11semidirect
705. C2×#97C2×D11semidirect
777. C2×SD16C4×D11semidirect
966. C2×Q8C2×C4×D11semidirect
1019. SD16C2×C4×D11semidirect
1020. SD16C2×C4×D11semidirect
1032. C2×C8C2×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×#106232932
C4×#670402
C4×#670372
#130774902
#130774882
#130774762
#130774722
#130774562
#130774532
#130774472
#130774422
#130774382
C4×#669952
C4×#669852
#130774212
#130774182
#130774112
D11×#4402
#130772122
#130771442
#130771372
#130770412
C2×C11×#4402
#6017411