Finite Group Databasebeta

← #15622240

Subgroups — #15622240

Order 2816.

2180 conjugacy classes of subgroups.

The subgroup lattice has 1368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623222C211yesmaximal, characteristic, complemented
2C4×#41×D11C211yesmaximal, characteristic, complemented
3#13078792C212yesmaximal, complemented
4#13078759C212yesmaximal, complemented
5#13078732C212yesmaximal, complemented
6#13078730C212yesmaximal, complemented
7#13078701C212yesmaximal, complemented
8#13078668C212yesmaximal, complemented
9#13078641C212yesmaximal, complemented
10#13078639C212yesmaximal, complemented
11#13078566C211yesmaximal, characteristic, complemented
12#13078558C211yesmaximal, characteristic, complemented
13#13078434C211yesmaximal, characteristic, complemented
14#13078111C211yesmaximal, characteristic, complemented
15#13078110C211yesmaximal, characteristic, complemented
16#13077877C211yesmaximal, characteristic, complemented
17#13077869C211yesmaximal, characteristic
18#13077440C211yesmaximal, characteristic, complemented
19#13077434C211yesmaximal, characteristic, complemented
20#13077429C211yesmaximal, characteristic, complemented
21#13077423C211yesmaximal, characteristic, complemented
22#13077248C211yesmaximal, characteristic, complemented
23C11×#3080C211yesmaximal, characteristic, complemented
24C2×#41×D11C2211yescharacteristic
25C2×C11×#125C2211yescharacteristic, complemented
26C4×C11×#41C2211yescharacteristic
27#41×Dic11C2211yescharacteristic
28C2×#67004C2211yescharacteristic
29C2×#67002C2211yescharacteristic
30C2×#66962C2211yescharacteristic
31C2×#66961C2211yescharacteristic
32#10623222—21no—
33#10623222—21no—
34#10623222—21no—
35#10623222—21no—
36#10623222C2212yes—
37#10623222C2212yes—
38#10623222C2212yescomplemented
39#10623222C2212yescomplemented
40C4×#4343C2211yescharacteristic, complemented
41C4×#4343C2211yescharacteristic, complemented
42C4×Q8×D11C2211yescharacteristic, complemented
43C4×Q8×D11C2211yescharacteristic, complemented
44C4×D4×D11—21no—
45C4×D4×D11—21no—
46C4×D4×D11C2211yescharacteristic, complemented
47C4×D4×D11C2211yescharacteristic, complemented
48C4×#4341—21no—
49C4×#4341—21no—
50C4×#4341C2211yescharacteristic, complemented
51C4×#4341C2211yescharacteristic, complemented
52#10623053—21no—
53#10623053C2211yescharacteristic
54D11×#117—21no—
55D11×#117C2211yescharacteristic
56C2×#66951—21no—
57C2×#66950C2211yescharacteristic
58C2×#66948C2211yescharacteristic
59C2×#66947—21no—
60C2×#66946—21no—
61C2×#66946C2211yescharacteristic, complemented
62C2×#66945—21no—
63C2×#66940C2211yescharacteristic, complemented
64C2×#66928C2211yescharacteristic, complemented
65C4×#4339—21no—
66C4×#4339C2211yescharacteristic
67C2×C42×D11—21no—
68C2×C42×D11C2211yescharacteristic
69C11×#479C2212yescomplemented
70C11×#479C2212yescomplemented
71C11×#478C2212yescomplemented
72C11×#478C2212yescomplemented
73C11×#428C2211yescharacteristic, complemented
74C11×#428C2211yescharacteristic, complemented
75C11×#423C2211yescharacteristic, complemented
76C11×#417C2211yescharacteristic
77C11×#417C2211yescharacteristic
78#10622744C2211yescharacteristic, complemented
79#10622739C2211yescharacteristic
80#10622739C2211yescharacteristic
81#10622733C2211yescharacteristic, complemented
82M16×Dic11C2211yescharacteristic, complemented
83M16×Dic11C2211yescharacteristic, complemented
84#10622679C2212yescomplemented
85#10622679C2212yescomplemented
86#10622676C2212yescomplemented
87#10622676C2212yescomplemented
88#10622641C2212yescomplemented
89#10622641C2212yescomplemented
90#10622629C2212yescomplemented
91#10622629C2212yescomplemented
92#10622617C2211yescharacteristic, complemented
93#10622614C2211yescharacteristic, complemented
94#10622579C2211yescharacteristic
95#10622579C2211yescharacteristic
96#10622577C2211yescharacteristic, complemented
97#10622577C2211yescharacteristic, complemented
98#10622537C2211yescharacteristic, complemented
99#10622502C2212yescomplemented
100#10622502C2212yescomplemented
101#10622501C2212yescomplemented
102#10622498C2212yescomplemented
103#10622497C2212yescomplemented
104#10622495C2212yes—
105#10622486C2212yescomplemented
106#10622485C2212yescomplemented
107#10622482C2212yescomplemented
108#10622480C2212yescomplemented
109#10622479C2212yescomplemented
110#10622476C2212yes—
111#10622475C2212yescomplemented
112#10622466C2212yescomplemented
113#10622465C2212yescomplemented
114#10622465C2212yescomplemented
115#10622458C2212yescomplemented
116#10622458C2212yescomplemented
117#10622457C2212yescomplemented
118#10622457C2212yescomplemented
119#10622448C2212yescomplemented
120#10622448C2212yescomplemented
121#10622446C2212yescomplemented
122#10622446C2212yescomplemented
123#10622430C2212yescomplemented
124#10622424C2212yes—
125#10622423C2212yescomplemented
126#10622421C2212yescomplemented
127#10622419C2212yes—
128#10622403C2212yescomplemented
129#10622402C2212yescomplemented
130#10622401C2212yescomplemented
131#10622398C2212yescomplemented
132#10622396C2212yescomplemented
133#10622394C2212yes—
134#10622389C2212yescomplemented
135#10622386C2212yes—
136#10622371C2212yescomplemented
137#10622370C2212yescomplemented
138#10622369C2212yescomplemented
139C2×C11×#41C2311yescharacteristic
140#41×D11—24no—
141#41×D11—24no—
142C2×#4343C2311yescharacteristic
143C2×Q8×D11C2311yescharacteristic
144C2×#4341—21no—
145C2×#4341C2311yescharacteristic
146C2×D4×D11—21no—
147C2×D4×D11C2311yescharacteristic
148C2×#4339—21no—
149C2×#4339C2311yescharacteristic
150C22×D44—21no—
151C22×D44C2311yescharacteristic
152C22×C4×D11—21no—
153C22×C4×D11—21no—
154C22×C4×D11—21no—
155C22×C4×D11—21no—
156C22×C4×D11D411yescharacteristic
157C22×C4×D11D411yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×Dic22C2311yescharacteristic
160C2×C11×M16C2311yescharacteristic
161C2×C11×M16C2311yescharacteristic
162C11×#125—21no—
163C11×#125—21no—
164C11×#125C2312yes—
165C11×#125C2312yes—
166C4×Q8×C11C2311yescharacteristic
167C4×Q8×C11C2311yescharacteristic
168C4×D4×C11—21no—
169C4×D4×C11—21no—
170C4×D4×C11C2311yescharacteristic
171C4×D4×C11C2311yescharacteristic
172C11×#117—21no—
173C11×#117C2311yescharacteristic
174C2×C11×C4⋊C4—21no—
175C2×C11×C4⋊C4—21no—
176C2×C11×C4⋊C4C2311yescharacteristic
177C2×C11×C4⋊C4C2311yescharacteristic
178C2×C42×C11—21no—
179C2×C42×C11C2311yescharacteristic
180#67004—24no—
181#67002—24no—
182Q8×Dic11C2311yescharacteristic
183Q8×Dic11C2311yescharacteristic
184C2×#4326C2312yes—
185C2×#4325C2312yes—
186D4×Dic11—21no—
187D4×Dic11—21no—
188D4×Dic11C2311yescharacteristic
189D4×Dic11C2311yescharacteristic
190C2×#4324C2312yes—
191C2×#4323C2312yes—
192C4×C22⋊D11—21no—
193C4×C22⋊D11—21no—
194C4×C22⋊D11—21no—
195C4×C22⋊D11—21no—
196C4×C22⋊D11—21no—
197C4×C22⋊D11—21no—
198C2×(C2×D11)⋊C4—21no—
199C2×(C2×D11)⋊C4—21no—
200C2×(C2×D11)⋊C4—21no—
201C2×(C2×D11)⋊C4—21no—
202C2×(C2×D11)⋊C4—21no—
203#66979—21no—
204#66979C2311yescharacteristic
205C2×C4⋊Dic11—21no—
206C2×Dic11⋊C4—21no—
207C2×C4×Dic11—21no—
208C2×C4×Dic11—21no—
209C2×C4×Dic11—21no—
210C2×C4×Dic11—21no—
211C2×C4×Dic11D411yescharacteristic
212C2×C4×Dic11D411yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×#4318C2311yescharacteristic
215C2×#4318C2311yescharacteristic
216#66962—24no—
217#66961—24no—
218C2×Dic44C2312yes—
219C2×D88C2312yes—
220C2×#4314C2312yes—
221C2×#4314C2312yes—
222#66951—22no—
223#66951—22no—
224#66951—22no—
225#66951—22no—
226#66950—21no—
227#66950—21no—
228#66950C2312yes—
229#66950C2312yes—
230#66948—21no—
231#66948—21no—
232#66948C2312yes—
233#66948C2312yes—
234#66947—22no—
235#66947—22no—
236#66947—22no—
237#66947—22no—
238#66946—22no—
239#66946—22no—
240#66946—22no—
241#66946—22no—
242#66946—21no—
243#66946—21no—
244#66946—21no—
245#66946—21no—
246#66946C2311yescharacteristic
247#66946C2312yes—
248#66946C2311yescharacteristic
249#66946C2312yes—
250#66945—22no—
251#66945—22no—
252#66945—22no—
253#66945—22no—
254#66945—21no—
255#66945—21no—
256#66945C2311yescharacteristic
257#66945C2311yescharacteristic
258C4⋊C4×D11—21no—
259C4⋊C4×D11—21no—
260C4⋊C4×D11C2311yescharacteristic
261C4⋊C4×D11C2311yescharacteristic
262#66940—21no—
263#66940—21no—
264#66940—21no—
265#66940—21no—
266#66940C2311yescharacteristic
267#66940C2312yes—
268#66940C2311yescharacteristic
269#66940C2312yes—
270(C22⋊D11)⋊C4—21no—
271(C22⋊D11)⋊C4—21no—
272(C22⋊D11)⋊C4—21no—
273(C22⋊D11)⋊C4—21no—
274(C22⋊D11)⋊C4—21no—
275(C22⋊D11)⋊C4—21no—
276C22⋊C4×D11—21no—
277C22⋊C4×D11—21no—
278C22⋊C4×D11—21no—
279#66930—21no—
280#66930—21no—
281#66930—21no—
282#66928—21no—
283#66928—21no—
284#66928C2312yes—
285#66928C2312yes—
286C4×D44—21no—
287C4×D44—21no—
288C4×D44C2311yescharacteristic
289C4×D44C2311yescharacteristic
290#66925—21no—
291#66925—21no—
292#66925—21no—
293C42×D11—21no—
294C42×D11—21no—
295C42×D11—21no—
296C42×D11—21no—
297C42×D11—21no—
298C42×D11—21no—
299C42×D11—21no—
300C42×D11D411yescharacteristic
301C42×D11D411yescharacteristic
302C42×D11D411yescharacteristic
303C42×D11D411yescharacteristic
304C42×D11C2311yescharacteristic
305C42×D11C2311yescharacteristic
306C42×D11C2311yescharacteristic
307C42×D11C2311yescharacteristic
308C4×Dic22—21no—
309C4×Dic22—21no—
310C4×Dic22C2311yescharacteristic
311C4×Dic22C2311yescharacteristic
312C11×#107C2312yes—
313C11×#107C2312yes—
314C11×#106C2312yes—
315C11×#106C2312yes—
316C11×C4⋊C8C2312yes—
317C11×C4⋊C8C2312yes—
318C11×#103C2312yes—
319C11×#103C2312yes—
320C11×#102C2312yes—
321C11×#102C2312yes—
322#66885C2312yes—
323#66885C2312yes—
324(C2×D11)⋊C8C2312yes—
325(C2×D11)⋊C8C2312yes—
326(C2×D11)⋊C8C2312yes—
327(C2×D11)⋊C8C2312yes—
328#66880C2312yes—
329#66880C2312yes—
330#66879C2312yes—
331#66879C2312yes—
332C8×Dic11C2312yes—
333C8×Dic11C2312yes—
334#66874C2312yes—
335#66874C2312yes—
336#66874C2312yes—
337#66874C2312yes—
338#66873C2312yes—
339#66873C2312yes—
340#66873C2312yes—
341#66873C2312yes—
342#66872C2312yes—
343#66872C2312yes—
344#66871C2312yes—
345#66871C2312yes—
346C4⋊(C11⋊C8)C2312yes—
347C4⋊(C11⋊C8)C2312yes—
348#60563—111nomaximal, Sylow
349C23×D11—21no—
350C23×D11—21no—
351C23×D11C2×D411yescharacteristic
352C11×#41—22no—
353C11×#41#4114yes—
354C2×Q8×C11C2411yescharacteristic
355C2×D4×C11—21no—
356C2×D4×C11C2411yescharacteristic
357C22×C4×C11—21no—
358C22×C4×C11—21no—
359C22×C4×C11—21no—
360C22×C4×C11—21no—
361C22×C4×C11—21no—
362C22×C4×C11C2×D411yescharacteristic
363C22×C4×C11C2×D411yescharacteristic
364C22×C4×C11C2411yescharacteristic
365C2×C22⋊D11—21no—
366C2×C22⋊D11—21no—
367C2×C22⋊D11—21no—
368C22×Dic11—21no—
369C22×Dic11—21no—
370C22×Dic11—21no—
371C22×Dic11—21no—
372C22×Dic11C2×D411yescharacteristic
373C22×Dic11C2×D411yescharacteristic
374C22×Dic11C2×D411yescharacteristic
375#4343—22no—
376#4343—22no—
377Q8×D11—22no—
378Q8×D11—22no—
379#4341—28no—
380#4341—22no—
381#4341—22no—
382D4×D11—28no—
383D4×D11—22no—
384D4×D11—22no—
385#4339—28no—
386#4339—22no—
387#4339#4114yes—
388C2×D44—21no—
389C2×D44—22no—
390C2×D44—22no—
391C2×D44—21no—
392C2×D44—22no—
393C2×D44—22no—
394C2×D44—44no—
395C2×D44C2412yes—
396C2×D44C2411yescharacteristic
397C2×C4×D11—28no—
398C2×C4×D11—21no—
399C2×C4×D11—21no—
400C2×C4×D11—21no—
401C2×C4×D11—22no—
402C2×C4×D11—22no—
403C2×C4×D11—21no—
404C2×C4×D11—21no—
405C2×C4×D11—21no—
406C2×C4×D11—21no—
407C2×C4×D11—21no—
408C2×C4×D11—21no—
409C2×C4×D11—22no—
410C2×C4×D11—22no—
411C2×C4×D11—42no—
412C2×C4×D11—42no—
413C2×C4×D11—44no—
414C2×C4×D11—44no—
415C2×C4×D11—44no—
416C2×C4×D11C2×D411yescharacteristic
417C2×C4×D11C2×D411yescharacteristic
418C2×C4×D11C2×D411yescharacteristic
419C2×C4×D11C2×D411yescharacteristic
420C2×C4×D11C2×D411yescharacteristic
421C2×C4×D11C2×D411yescharacteristic
422C2×C4×D11C2×D411yescharacteristic
423C2×C4×D11C2×D411yescharacteristic
424C2×C4×D11C2×D411yescharacteristic
425C2×C4×D11C2×D411yescharacteristic
426C2×C4×D11C2411yescharacteristic
427C2×C4×D11C2411yescharacteristic
428C2×Dic22—21no—
429C2×Dic22—21no—
430C2×Dic22—22no—
431C2×Dic22—22no—
432C2×Dic22C2412yes—
433C2×Dic22C2411yescharacteristic
434C11×M16—22no—
435C11×M16—22no—
436C2×C8×C11C2412yes—
437C2×C8×C11C2412yes—
438C11×C4⋊C4—21no—
439C11×C4⋊C4—21no—
440C11×C4⋊C4—21no—
441C11×C4⋊C4—22no—
442C11×C4⋊C4—22no—
443C11×C4⋊C4—21no—
444C11×C4⋊C4—22no—
445C11×C4⋊C4—22no—
446C11×C4⋊C4C2412yes—
447C11×C4⋊C4C2412yes—
448C11×C4⋊C4C2411yescharacteristic
449C11×C4⋊C4C2411yescharacteristic
450C11×C22⋊C4—21no—
451C11×C22⋊C4—21no—
452C11×C22⋊C4—21no—
453C42×C11—21no—
454C42×C11—21no—
455C42×C11—21no—
456C42×C11C2×D411yescharacteristic
457C42×C11C2×D411yescharacteristic
458C42×C11C2411yescharacteristic
459C42×C11C2411yescharacteristic
460C22⋊Dic11—21no—
461C22⋊Dic11—21no—
462C22⋊Dic11—21no—
463#4326—24no—
464#4325—24no—
465#4324—24no—
466#4323—24no—
467(C2×D11)⋊C4—21no—
468(C2×D11)⋊C4—21no—
469(C2×D11)⋊C4—22no—
470(C2×D11)⋊C4—22no—
471(C2×D11)⋊C4—22no—
472(C2×D11)⋊C4—22no—
473(C2×D11)⋊C4—21no—
474(C2×D11)⋊C4—21no—
475(C2×D11)⋊C4—22no—
476(C2×D11)⋊C4—22no—
477(C2×D11)⋊C4—21no—
478(C2×D11)⋊C4—21no—
479(C2×D11)⋊C4—22no—
480(C2×D11)⋊C4—22no—
481(C2×D11)⋊C4—22no—
482(C2×D11)⋊C4—22no—
483C4⋊Dic11—21no—
484C4⋊Dic11—21no—
485C4⋊Dic11—22no—
486C4⋊Dic11—22no—
487C4⋊Dic11C2411yescharacteristic
488C4⋊Dic11C2411yescharacteristic
489Dic11⋊C4—21no—
490Dic11⋊C4—21no—
491Dic11⋊C4—21no—
492Dic11⋊C4—21no—
493Dic11⋊C4—22no—
494Dic11⋊C4—22no—
495Dic11⋊C4—21no—
496Dic11⋊C4—21no—
497C4×Dic11—21no—
498C4×Dic11—21no—
499C4×Dic11—21no—
500C4×Dic11—21no—
501C4×Dic11—21no—
502C4×Dic11—21no—
503C4×Dic11—22no—
504C4×Dic11—22no—
505C4×Dic11—21no—
506C4×Dic11—21no—
507C4×Dic11—21no—
508C4×Dic11C2×D411yescharacteristic
509C4×Dic11C2×D411yescharacteristic
510C4×Dic11C2×D411yescharacteristic
511C4×Dic11C2×D411yescharacteristic
512C4×Dic11C2×D411yescharacteristic
513C4×Dic11C2×D411yescharacteristic
514C4×Dic11C2×D411yescharacteristic
515C4×Dic11C2×D411yescharacteristic
516C4×Dic11C2×D411yescharacteristic
517C4×Dic11C2×D411yescharacteristic
518C4×Dic11C2411yescharacteristic
519C4×Dic11C2411yescharacteristic
520#4318—22no—
521#4318—22no—
522C2×C11⋊C8C2412yes—
523C2×C11⋊C8C2412yes—
524Dic44—24no—
525D88—24no—
526#4314—24no—
527#4314—24no—
528C2×#529—111no—
529C2×C4×#41—111no—
530#3117—112no—
531#3114—112no—
532#3111—112no—
533#3111—112no—
534#3108—112no—
535#3105—112no—
536#3102—112no—
537#3102—112no—
538#3095—111no—
539#3094—111no—
540#3080—111no—
541#3080D1111yescharacteristic, complemented
542#3040—111no—
543#3040—111no—
544#3007—111no—
545#3006—111no—
546C4×#137—111no—
547C4×#137—111no—
548C4×AGL(1,ℤ/8)—111no—
549C4×AGL(1,ℤ/8)—111no—
550#2920—111no—
551C23×C11—21no—
552C23×C11C22×D411yescharacteristic
553C22×D11—24no—
554C22×D11—22no—
555C22×D11—21no—
556C22×D11—22no—
557C22×D11—22no—
558C22×D11—41no—
559C22×D11—42no—
560C22×D11—42no—
561C22×D11—42no—
562C22×D11—42no—
563C22×D11—42no—
564C22×D11C22×D411yescharacteristic
565C22×D11C22×D411yescharacteristic
566Q8×C11—21no—
567Q8×C11C2×#4112yes—
568D4×C11—24no—
569D4×C11—21no—
570D4×C11C2×#4112yes—
571C2×C4×C11—21no—
572C2×C4×C11—24no—
573C2×C4×C11—21no—
574C2×C4×C11—21no—
575C2×C4×C11—22no—
576C2×C4×C11—22no—
577C2×C4×C11—41no—
578C2×C4×C11—41no—
579C2×C4×C11—42no—
580C2×C4×C11—42no—
581C2×C4×C11—42no—
582C2×C4×C11—42no—
583C2×C4×C11C22×D411yescharacteristic
584C2×C4×C11C22×D411yescharacteristic
585C2×C4×C11C22×D411yescharacteristic
586C2×C4×C11C22×D411yescharacteristic
587C2×C4×C11C22×D411yescharacteristic
588C2×C4×C11C2×#4112yes—
589C2×C4×C11C2×#4112yes—
590C2×C4×C11C2511yescharacteristic
591C22⋊D11—24no—
592C22⋊D11—24no—
593C22⋊D11—24no—
594C2×Dic11—24no—
595C2×Dic11—22no—
596C2×Dic11—21no—
597C2×Dic11—22no—
598C2×Dic11—21no—
599C2×Dic11—21no—
600C2×Dic11—22no—
601C2×Dic11—41no—
602C2×Dic11—42no—
603C2×Dic11—42no—
604C2×Dic11—42no—
605C2×Dic11C22×D411yescharacteristic
606C2×Dic11C22×D411yescharacteristic
607C2×Dic11C22×D411yescharacteristic
608C2×Dic11C22×D411yescharacteristic
609C2×Dic11C22×D411yescharacteristic
610C2×Dic11C22×D411yescharacteristic
611D44—24no—
612D44—21no—
613D44—22no—
614D44—22no—
615D44—44no—
616D44—44no—
617D44—42no—
618D44C2×#4112yes—
619C4×D11—24no—
620C4×D11—24no—
621C4×D11—22no—
622C4×D11—22no—
623C4×D11—22no—
624C4×D11—24no—
625C4×D11—22no—
626C4×D11—21no—
627C4×D11—21no—
628C4×D11—21no—
629C4×D11—21no—
630C4×D11—22no—
631C4×D11—22no—
632C4×D11—41no—
633C4×D11—41no—
634C4×D11—41no—
635C4×D11—41no—
636C4×D11—42no—
637C4×D11—44no—
638C4×D11—42no—
639C4×D11—42no—
640C4×D11—42no—
641C4×D11—42no—
642C4×D11—42no—
643C4×D11—44no—
644Dic22—24no—
645Dic22—21no—
646Dic22—22no—
647Dic22—22no—
648Dic22—42no—
649Dic22C2×#4112yes—
650C8×C11—22no—
651C8×C11—22no—
652C11⋊C8—22no—
653C11⋊C8—22no—
654C22×#41—111no—
655C2×#137—111no—
656C2×#137—111no—
657C2×AGL(1,ℤ/8)—111no—
658C2×AGL(1,ℤ/8)—111no—
659#529—112no—
660#529—112no—
661#529—112no—
662#529—112no—
663#529—221no—
664#529—221no—
665#529—221no—
666#529—221no—
667C2×#126—221no—
668C2×#125C2×D1111yescharacteristic, complemented
669C2×#124—111no—
670C2×#123—221no—
671C2×C22⋊Q8—111no—
672C2×#121—111no—
673C4×#41—111no—
674C4×#41—111no—
675C4×#41—111no—
676C4×#41—111no—
677C4×#41—111no—
678C4×#41—111no—
679C4×#41—111no—
680C4×#41—221no—
681C4×#41—221no—
682C4×#41—221no—
683C4×#41—221no—
684C4×#41C2×D1111yescharacteristic
685C2×C4×Q8—111no—
686C2×C4×Q8—111no—
687C2×C4×Q8—111no—
688C2×C4×D4—111no—
689C2×C4×D4—111no—
690C2×C4×D4—111no—
691C2×C4×D4—221no—
692C2×C4×D4—221no—
693C2×C4×D4—221no—
694C2×#117—111no—
695C2×#117—221no—
696C2×#117—221no—
697C22×C42—111no—
698C22×C42—221no—
699#485—112no—
700#485—112no—
701#484—112no—
702#483—112no—
703#482—112no—
704#482—112no—
705#481—112no—
706#480—112no—
707#479—112no—
708#479—112no—
709#479C2×D1112yescomplemented
710#479C2×D1112yescomplemented
711#478—112no—
712#478—112no—
713#478C2×D1112yescomplemented
714#478C2×D1112yescomplemented
715#464—112no—
716#464—112no—
717#464—112no—
718#464—112no—
719#463—112no—
720#463—112no—
721#463—112no—
722#463—112no—
723#452—112no—
724#452—112no—
725#451—112no—
726#450—112no—
727#449—112no—
728#449—112no—
729#448—112no—
730#447—112no—
731#442—112no—
732#442—112no—
733#441—112no—
734#441—112no—
735#440—112no—
736#440—112no—
737#440—112no—
738#440—112no—
739C4×Q16—112no—
740C4×Q16—112no—
741C4×SD16—112no—
742C4×SD16—112no—
743C4×SD16—112no—
744C4×SD16—112no—
745C4×D8—112no—
746C4×D8—112no—
747#432—112no—
748#432—112no—
749#431—112no—
750#431—112no—
751#428—111no—
752#428—111no—
753#428C2×D1111yescharacteristic, complemented
754#428C2×D1111yescharacteristic, complemented
755#423—111no—
756#423C2×D1111yescharacteristic, complemented
757#419—111no—
758#419—111no—
759#418—111no—
760#418—111no—
761#417—111no—
762#417—111no—
763#417C2×D1111yescharacteristic
764#417C2×D1111yescharacteristic
765#407—111no—
766#407—111no—
767C4×M16—111no—
768C4×M16—111no—
769C22×C11—21no—
770C22×C11—21no—
771C22×C11—22no—
772C22×C11—41no—
773C22×C11—41no—
774C22×C11#52512yes—
775C22×C11C23×D411yescharacteristic
776C2×D11—21no—
777C2×D11—21no—
778C2×D11—22no—
779C2×D11—21no—
780C2×D11—21no—
781C2×D11—21no—
782C2×D11—44no—
783C2×D11—48no—
784C2×D11—41no—
785C2×D11—41no—
786C2×D11—42no—
787C2×D11—42no—
788C2×D11—42no—
789C2×D11—84no—
790C2×D11#57512yes—
791C4×C11—22no—
792C4×C11—21no—
793C4×C11—21no—
794C4×C11—21no—
795C4×C11—21no—
796C4×C11—41no—
797C4×C11—41no—
798C4×C11—42no—
799C4×C11—42no—
800C4×C11#52512yes—
801C4×C11C22×#4111yescharacteristic
802C4×C11C22×#4111yescharacteristic
803Dic11—21no—
804Dic11—22no—
805Dic11—21no—
806Dic11—21no—
807Dic11—21no—
808Dic11—21no—
809Dic11—42no—
810Dic11—41no—
811Dic11—41no—
812Dic11#57512yes—
813C2×#41—111no—
814C2×#41—111no—
815C2×#41—111no—
816C2×#41—221no—
817C2×#41—221no—
818C2×#41—224no—
819C2×#41—224no—
820C2×#41C22×D1111yescharacteristic
821C22×Q8—111no—
822C22×Q8—111no—
823C22×D4—111no—
824C22×D4—111no—
825C22×D4—221no—
826C22×D4—221no—
827C23×C4—111no—
828C23×C4—111no—
829C23×C4—111no—
830C23×C4—221no—
831C23×C4—221no—
832C23×C4—221no—
833C23×C4—221no—
834#137—224no—
835#137—224no—
836AGL(1,ℤ/8)—224no—
837AGL(1,ℤ/8)—224no—
838C2×Q16—112no—
839C2×Q16—112no—
840C2×SD16—112no—
841C2×SD16—112no—
842C2×SD16—112no—
843C2×SD16—112no—
844C2×D8—112no—
845C2×D8—112no—
846C2×M16—111no—
847C2×M16—111no—
848C2×M16C22×D1111yescharacteristic
849C2×M16C22×D1111yescharacteristic
850#126—222no—
851#126—222no—
852#126—222no—
853#126—222no—
854#125—21no—
855#125—21no—
856#125C22×D1112yes—
857#125C22×D1112yes—
858#124—112no—
859#124—112no—
860#124—221no—
861#124—221no—
862#123—222no—
863#123—222no—
864#123—222no—
865#123—222no—
866C22⋊Q8—112no—
867C22⋊Q8—112no—
868C22⋊Q8—221no—
869C22⋊Q8—221no—
870#121—112no—
871#121—112no—
872#121—221no—
873#121—221no—
874C4×Q8—111no—
875C4×Q8—111no—
876C4×Q8—111no—
877C4×Q8—111no—
878C4×Q8—112no—
879C4×Q8—112no—
880C4×Q8—111no—
881C4×Q8—111no—
882C4×Q8—221no—
883C4×Q8—221no—
884C4×Q8—221no—
885C4×Q8—221no—
886C4×Q8—221no—
887C4×Q8—221no—
888C4×Q8C22×D1111yescharacteristic
889C4×Q8C22×D1111yescharacteristic
890C4×D4—21no—
891C4×D4—21no—
892C4×D4—111no—
893C4×D4—111no—
894C4×D4—111no—
895C4×D4—111no—
896C4×D4—112no—
897C4×D4—112no—
898C4×D4—111no—
899C4×D4—111no—
900C4×D4—221no—
901C4×D4—221no—
902C4×D4—221no—
903C4×D4—221no—
904C4×D4—221no—
905C4×D4—221no—
906C4×D4—221no—
907C4×D4—221no—
908C4×D4—221no—
909C4×D4—221no—
910C4×D4—221no—
911C4×D4—221no—
912C4×D4—221no—
913C4×D4—221no—
914C4×D4—222no—
915C4×D4—222no—
916C4×D4—222no—
917C4×D4—222no—
918C4×D4—221no—
919C4×D4—221no—
920C4×D4—221no—
921C4×D4—221no—
922C4×D4—221no—
923C4×D4—221no—
924C4×D4C22×D1111yescharacteristic
925C4×D4C22×D1111yescharacteristic
926#117—21no—
927#117—111no—
928#117—111no—
929#117—111no—
930#117—221no—
931#117—221no—
932#117—221no—
933#117—221no—
934#117—221no—
935#117—221no—
936#117—222no—
937#117—222no—
938#117—222no—
939#117—222no—
940#117—221no—
941#117—221no—
942#117—221no—
943#117C22×D1111yescharacteristic
944C2×C4⋊C4—21no—
945C2×C4⋊C4—21no—
946C2×C4⋊C4—111no—
947C2×C4⋊C4—111no—
948C2×C4⋊C4—221no—
949C2×C4⋊C4—221no—
950C2×C4⋊C4—221no—
951C2×C4⋊C4—221no—
952C2×C4⋊C4C22×D1111yescharacteristic
953C2×C4⋊C4C22×D1111yescharacteristic
954C2×C22⋊C4—221no—
955C2×C22⋊C4—221no—
956C2×C22⋊C4—221no—
957C2×C22⋊C4—221no—
958C2×C22⋊C4—221no—
959C2×C22⋊C4—221no—
960C2×C22⋊C4—221no—
961C2×C22⋊C4—221no—
962C2×C42—21no—
963C2×C42—111no—
964C2×C42—111no—
965C2×C42—111no—
966C2×C42—111no—
967C2×C42—111no—
968C2×C42—111no—
969C2×C42—111no—
970C2×C42—111no—
971C2×C42—111no—
972C2×C42—111no—
973C2×C42—111no—
974C2×C42—221no—
975C2×C42—221no—
976C2×C42—221no—
977C2×C42—221no—
978C2×C42—221no—
979C2×C42—221no—
980C2×C42—221no—
981C2×C42—221no—
982C2×C42—221no—
983C2×C42—221no—
984C2×C42—221no—
985C2×C42C22×D1111yescharacteristic
986#107—112no—
987#107—112no—
988#107C22×D1112yes—
989#107C22×D1112yes—
990#106—112no—
991#106—112no—
992#106C22×D1112yes—
993#106C22×D1112yes—
994C4⋊C8—112no—
995C4⋊C8—112no—
996C4⋊C8C22×D1112yes—
997C4⋊C8C22×D1112yes—
998#103—112no—
999#103—112no—
1000#103—112no—
1001#103—112no—
1002#103—112no—
1003#103—112no—
1004#103C22×D1112yes—
1005#103C22×D1112yes—
1006#102—112no—
1007#102—112no—
1008#102—112no—
1009#102—112no—
1010#102—112no—
1011#102—112no—
1012#102C22×D1112yes—
1013#102C22×D1112yes—
1014C22⋊C8—112no—
1015C22⋊C8—112no—
1016C22⋊C8—112no—
1017C22⋊C8—112no—
1018#97—112no—
1019#97—112no—
1020C4×C8—112no—
1021C4×C8—112no—
1022C2×C11—22no—
1023C2×C11—42no—
1024C2×C11C2×#52511yescharacteristic
1025C2×C11C2×#57511yescharacteristic
1026C2×C11C2×#57511yescharacteristic
1027D11—22no—
1028D11—41no—
1029D11—42no—
1030D11—82no—
1031C24—111no—
1032C24—221no—
1033C24—221no—
1034#41—22no—
1035#41—114no—
1036#41—228no—
1037#41—222no—
1038#41—228no—
1039#41—222no—
1040#41—222no—
1041#41—222no—
1042#41—222no—
1043#41#434314yes—
1044C2×Q8—111no—
1045C2×Q8—112no—
1046C2×Q8—221no—
1047C2×Q8—222no—
1048C2×Q8—222no—
1049C2×Q8—221no—
1050C2×Q8—222no—
1051C2×Q8—222no—
1052C2×Q8C23×D1111yescharacteristic
1053C2×D4—21no—
1054C2×D4—111no—
1055C2×D4—112no—
1056C2×D4—221no—
1057C2×D4—222no—
1058C2×D4—222no—
1059C2×D4—221no—
1060C2×D4—222no—
1061C2×D4—228no—
1062C2×D4—221no—
1063C2×D4—221no—
1064C2×D4—222no—
1065C2×D4—221no—
1066C2×D4—222no—
1067C2×D4—222no—
1068C2×D4—444no—
1069C2×D4C23×D1111yescharacteristic
1070C22×C4—21no—
1071C22×C4—21no—
1072C22×C4—21no—
1073C22×C4—21no—
1074C22×C4—21no—
1075C22×C4—111no—
1076C22×C4—111no—
1077C22×C4—111no—
1078C22×C4—111no—
1079C22×C4—111no—
1080C22×C4—111no—
1081C22×C4—111no—
1082C22×C4—111no—
1083C22×C4—111no—
1084C22×C4—111no—
1085C22×C4—111no—
1086C22×C4—111no—
1087C22×C4—111no—
1088C22×C4—111no—
1089C22×C4—111no—
1090C22×C4—221no—
1091C22×C4—221no—
1092C22×C4—221no—
1093C22×C4—222no—
1094C22×C4—222no—
1095C22×C4—221no—
1096C22×C4—228no—
1097C22×C4—221no—
1098C22×C4—221no—
1099C22×C4—221no—
1100C22×C4—221no—
1101C22×C4—221no—
1102C22×C4—221no—
1103C22×C4—222no—
1104C22×C4—222no—
1105C22×C4—221no—
1106C22×C4—221no—
1107C22×C4—221no—
1108C22×C4—442no—
1109C22×C4—442no—
1110C22×C4—444no—
1111C22×C4—444no—
1112C22×C4—444no—
1113C22×C4D4×D1111yescharacteristic
1114C22×C4D4×D1111yescharacteristic
1115C22×C4C23×D1111yescharacteristic
1116Q16—224no—
1117Q16—224no—
1118SD16—224no—
1119SD16—224no—
1120SD16—224no—
1121SD16—224no—
1122D8—224no—
1123D8—224no—
1124M16—22no—
1125M16—22no—
1126M16—222no—
1127M16—222no—
1128C2×C8—112no—
1129C2×C8—112no—
1130C2×C8C23×D1112yes—
1131C2×C8C23×D1112yes—
1132C4⋊C4—22no—
1133C4⋊C4—22no—
1134C4⋊C4—22no—
1135C4⋊C4—22no—
1136C4⋊C4—21no—
1137C4⋊C4—21no—
1138C4⋊C4—21no—
1139C4⋊C4—21no—
1140C4⋊C4—111no—
1141C4⋊C4—111no—
1142C4⋊C4—221no—
1143C4⋊C4—221no—
1144C4⋊C4—221no—
1145C4⋊C4—221no—
1146C4⋊C4—221no—
1147C4⋊C4—221no—
1148C4⋊C4—222no—
1149C4⋊C4—222no—
1150C4⋊C4—222no—
1151C4⋊C4—222no—
1152C4⋊C4—221no—
1153C4⋊C4—221no—
1154C4⋊C4C23×D1111yescharacteristic
1155C4⋊C4C23×D1111yescharacteristic
1156C4⋊C4C23×D1112yes—
1157C4⋊C4C23×D1112yes—
1158C22⋊C4—21no—
1159C22⋊C4—21no—
1160C22⋊C4—21no—
1161C22⋊C4—221no—
1162C22⋊C4—221no—
1163C22⋊C4—222no—
1164C22⋊C4—222no—
1165C22⋊C4—222no—
1166C22⋊C4—222no—
1167C22⋊C4—221no—
1168C22⋊C4—221no—
1169C22⋊C4—222no—
1170C22⋊C4—222no—
1171C22⋊C4—221no—
1172C22⋊C4—221no—
1173C22⋊C4—221no—
1174C22⋊C4—221no—
1175C22⋊C4—221no—
1176C22⋊C4—222no—
1177C22⋊C4—222no—
1178C22⋊C4—222no—
1179C22⋊C4—222no—
1180C42—21no—
1181C42—21no—
1182C42—21no—
1183C42—111no—
1184C42—111no—
1185C42—111no—
1186C42—111no—
1187C42—111no—
1188C42—111no—
1189C42—111no—
1190C42—111no—
1191C42—111no—
1192C42—111no—
1193C42—111no—
1194C42—111no—
1195C42—221no—
1196C42—221no—
1197C42—221no—
1198C42—221no—
1199C42—221no—
1200C42—221no—
1201C42—222no—
1202C42—222no—
1203C42—221no—
1204C42—221no—
1205C42—221no—
1206C42D4×D1111yescharacteristic
1207C42D4×D1111yescharacteristic
1208C42C23×D1111yescharacteristic
1209C42C23×D1111yescharacteristic
1210C11#6056311yescharacteristic, complemented, Sylow
1211C23—21no—
1212C23—111no—
1213C23—111no—
1214C23—222no—
1215C23—224no—
1216C23—222no—
1217C23—221no—
1218C23—222no—
1219C23—441no—
1220C23—442no—
1221C23—442no—
1222C23—442no—
1223C23—442no—
1224C23—442no—
1225C23C2×D4×D1111yescharacteristic
1226Q8—21no—
1227Q8—112no—
1228Q8—224no—
1229Q8—221no—
1230Q8—222no—
1231Q8—222no—
1232Q8—442no—
1233Q8C2×#434312yes—
1234D4—24no—
1235D4—21no—
1236D4—112no—
1237D4—224no—
1238D4—224no—
1239D4—224no—
1240D4—224no—
1241D4—221no—
1242D4—222no—
1243D4—222no—
1244D4—444no—
1245D4—444no—
1246D4—442no—
1247D4C2×#434312yes—
1248C2×C4—21no—
1249C2×C4—24no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—42no—
1257C2×C4—42no—
1258C2×C4—42no—
1259C2×C4—42no—
1260C2×C4—111no—
1261C2×C4—111no—
1262C2×C4—111no—
1263C2×C4—111no—
1264C2×C4—111no—
1265C2×C4—111no—
1266C2×C4—222no—
1267C2×C4—222no—
1268C2×C4—222no—
1269C2×C4—222no—
1270C2×C4—224no—
1271C2×C4—224no—
1272C2×C4—222no—
1273C2×C4—224no—
1274C2×C4—222no—
1275C2×C4—221no—
1276C2×C4—222no—
1277C2×C4—222no—
1278C2×C4—224no—
1279C2×C4—221no—
1280C2×C4—221no—
1281C2×C4—221no—
1282C2×C4—221no—
1283C2×C4—221no—
1284C2×C4—221no—
1285C2×C4—222no—
1286C2×C4—441no—
1287C2×C4—441no—
1288C2×C4—441no—
1289C2×C4—441no—
1290C2×C4—442no—
1291C2×C4—442no—
1292C2×C4—442no—
1293C2×C4—444no—
1294C2×C4—442no—
1295C2×C4—444no—
1296C2×C4—442no—
1297C2×C4—442no—
1298C2×C4—442no—
1299C2×C4—441no—
1300C2×C4—442no—
1301C2×C4—442no—
1302C2×C4C2×D4×D1111yescharacteristic
1303C2×C4C2×D4×D1111yescharacteristic
1304C2×C4C2×D4×D1111yescharacteristic
1305C2×C4C2×D4×D1111yescharacteristic
1306C2×C4C2×D4×D1111yescharacteristic
1307C2×C4C2×#434312yes—
1308C2×C4#41×D1112yes—
1309C2×C4C24×D1111yescharacteristic
1310C8—22no—
1311C8—22no—
1312C8—222no—
1313C8—222no—
1314C22—21no—
1315C22—21no—
1316C22—22no—
1317C22—41no—
1318C22—41no—
1319C22—112no—
1320C22—221no—
1321C22—221no—
1322C22—222no—
1323C22—221no—
1324C22—221no—
1325C22—221no—
1326C22—444no—
1327C22—448no—
1328C22—441no—
1329C22—441no—
1330C22—442no—
1331C22—442no—
1332C22—442no—
1333C22—884no—
1334C22#1062315812yes—
1335C22C22×D4×D1111yescharacteristic
1336C4—22no—
1337C4—21no—
1338C4—21no—
1339C4—21no—
1340C4—21no—
1341C4—41no—
1342C4—42no—
1343C4—41no—
1344C4—42no—
1345C4—112no—
1346C4—221no—
1347C4—221no—
1348C4—222no—
1349C4—221no—
1350C4—221no—
1351C4—221no—
1352C4—442no—
1353C4—441no—
1354C4—441no—
1355C4#1062315812yes—
1356C4C22×#434311yescharacteristic
1357C4C2×#41×D1111yescharacteristic
1358C2—22no—
1359C2—42no—
1360C2—222no—
1361C2—441no—
1362C2—442no—
1363C2—882no—
1364C2C2×#1062315811yescharacteristic
1365C2D11×#57511yescharacteristic
1366C2D11×#57511yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3080C2
socleC22×C11C23×D4
prime radical#13077869C2
hypercenter#3080D11
hypocenterC11#60563
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3080

Complements

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

NH ≅ G/Ntype
1. C2×#10623222C2semidirect
2. C4×#41×D11C2semidirect
3. #13078792C2semidirect
4. #13078759C2semidirect
5. #13078732C2semidirect
6. #13078730C2semidirect
7. #13078701C2semidirect
8. #13078668C2semidirect
9. #13078641C2semidirect
10. #13078639C2semidirect
11. #13078566C2semidirect
12. #13078558C2semidirect
13. #13078434C2semidirect
14. #13078111C2semidirect
15. #13078110C2semidirect
16. #13077877C2semidirect
18. #13077440C2semidirect
19. #13077434C2semidirect
20. #13077429C2semidirect
21. #13077423C2semidirect
22. #13077248C2semidirect
23. C11×#3080C2semidirect
25. C2×C11×#125C22semidirect
38. #10623222C22semidirect
39. #10623222C22semidirect
40. C4×#4343C22semidirect
41. C4×#4343C22semidirect
42. C4×Q8×D11C22semidirect
43. C4×Q8×D11C22semidirect
46. C4×D4×D11C22semidirect
47. C4×D4×D11C22semidirect
50. C4×#4341C22semidirect
51. C4×#4341C22semidirect
61. C2×#66946C22semidirect
63. C2×#66940C22semidirect
64. C2×#66928C22semidirect
69. C11×#479C22semidirect
70. C11×#479C22semidirect
71. C11×#478C22semidirect
72. C11×#478C22semidirect
73. C11×#428C22semidirect
74. C11×#428C22semidirect
75. C11×#423C22semidirect
78. #10622744C22semidirect
81. #10622733C22semidirect
82. M16×Dic11C22semidirect
83. M16×Dic11C22semidirect
84. #10622679C22semidirect
85. #10622679C22semidirect
86. #10622676C22semidirect
87. #10622676C22semidirect
88. #10622641C22semidirect
89. #10622641C22semidirect
90. #10622629C22semidirect
91. #10622629C22semidirect
92. #10622617C22semidirect
93. #10622614C22semidirect
96. #10622577C22semidirect
97. #10622577C22semidirect
98. #10622537C22semidirect
99. #10622502C22semidirect
100. #10622502C22semidirect
101. #10622501C22semidirect
102. #10622498C22semidirect
103. #10622497C22semidirect
105. #10622486C22semidirect
106. #10622485C22semidirect
107. #10622482C22semidirect
108. #10622480C22semidirect
109. #10622479C22semidirect
111. #10622475C22semidirect
112. #10622466C22semidirect
113. #10622465C22semidirect
114. #10622465C22semidirect
115. #10622458C22semidirect
116. #10622458C22semidirect
117. #10622457C22semidirect
118. #10622457C22semidirect
119. #10622448C22semidirect
120. #10622448C22semidirect
121. #10622446C22semidirect
122. #10622446C22semidirect
123. #10622430C22semidirect
125. #10622423C22semidirect
126. #10622421C22semidirect
128. #10622403C22semidirect
129. #10622402C22semidirect
130. #10622401C22semidirect
131. #10622398C22semidirect
132. #10622396C22semidirect
134. #10622389C22semidirect
136. #10622371C22semidirect
137. #10622370C22semidirect
138. #10622369C22semidirect
541. #3080D11semidirect
668. C2×#125C2×D11semidirect
709. #479C2×D11semidirect
710. #479C2×D11semidirect
713. #478C2×D11semidirect
714. #478C2×D11semidirect
753. #428C2×D11semidirect
754. #428C2×D11semidirect
756. #423C2×D11semidirect
1210. C11#60563semidirect

Maximal subgroups

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

subgroupindex
C2×#106232222
C4×#41×D112
#130787922
#130787592
#130787322
#130787302
#130787012
#130786682
#130786412
#130786392
#130785662
#130785582
#130784342
#130781112
#130781102
#130778772
#130778692
#130774402
#130774342
#130774292
#130774232
#130772482
C11×#30802
#6056311