Finite Group Databasebeta

← #15622672

Subgroups — #15622672

Order 2816.

2084 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081817C211yesmaximal, characteristic, complemented
2#13078902C212yesmaximal, complemented
3#13078854C212yesmaximal, complemented
4#13078839C212yesmaximal, complemented
5#13078794C212yesmaximal, complemented
6#13078761C212yesmaximal, complemented
7#13078719C212yesmaximal, complemented
8#13078670C212yesmaximal, complemented
9#13078628C212yesmaximal, complemented
10#13078545C211yesmaximal, characteristic, complemented
11C2×#10622648C211yesmaximal, characteristic, complemented
12#13078474C211yesmaximal, characteristic, complemented
13#13078463C211yesmaximal, characteristic, complemented
14#13078151C211yesmaximal, characteristic, complemented
15#13078151C211yesmaximal, characteristic, complemented
16#13077866C211yesmaximal, characteristic, complemented
17#13077832C211yesmaximal, characteristic, complemented
18#13077497C211yesmaximal, characteristic, complemented
19#13077489C211yesmaximal, characteristic, complemented
20#13077448C211yesmaximal, characteristic, complemented
21#13077448C211yesmaximal, characteristic, complemented
22#13077274C211yesmaximal, characteristic, complemented
23C11×#3494C211yesmaximal, characteristic, complemented
24C22×#4339C2211yescharacteristic
25C11×#555—21no—
26C11×#553—21no—
27C11×#553—21no—
28C11×#551—22no—
29C11×#547—21no—
30C11×#546—22no—
31C11×#544C2211yescharacteristic, complemented
32C11×#542C2212yes—
33C11×#540C2212yes—
34C11×#535C2211yescharacteristic, complemented
35C11×#532C2212yescomplemented
36C11×#529C2212yescomplemented
37C11×#525C2211yescharacteristic
38C2×C11×#121C2211yescharacteristic
39C11×#520C2211yescharacteristic, complemented
40C11×#518C2211yescharacteristic, complemented
41C2×C11×#117C2211yescharacteristic
42C2×#67003C2211yescharacteristic
43C2×#67003C2211yescharacteristic
44C2×#66985C2211yescharacteristic
45C2×#66985C2211yescharacteristic
46C2×#66979C2211yescharacteristic
47#10623054C2211yescharacteristic
48#10623054C2211yescharacteristic
49#10623054C2211yescharacteristic
50#10623054C2211yescharacteristic
51#10623053—22no—
52#10623052C2212yescomplemented
53D11×#117—21no—
54D11×#117—21no—
55#10623047C2212yescomplemented
56#10623035—21no—
57#10623035—21no—
58#10623017—22no—
59C4×#4339C2212yescomplemented
60C4×#4339C2212yescomplemented
61#10622845C2211yescharacteristic, complemented
62#10622845C2211yescharacteristic, complemented
63C2×#66896C2211yescharacteristic, complemented
64C2×#66896C2211yescharacteristic, complemented
65#10622820C2211yescharacteristic
66C2×C22⋊(C11⋊C8)C2211yescharacteristic
67#10622707C2212yescomplemented
68#10622704C2212yescomplemented
69#10622700C2212yescomplemented
70#10622697C2212yescomplemented
71#10622688C2212yescomplemented
72#10622688C2212yescomplemented
73#10622685C2212yescomplemented
74#10622685C2212yescomplemented
75#10622679C2212yescomplemented
76#10622679C2212yescomplemented
77#10622676C2212yescomplemented
78#10622676C2212yescomplemented
79#10622670C2212yescomplemented
80#10622670C2212yescomplemented
81#10622667C2212yescomplemented
82#10622667C2212yescomplemented
83#10622663C2211yescharacteristic, complemented
84#10622660C2211yescharacteristic, complemented
85#10622660C2211yescharacteristic, complemented
86#10622659C2211yescharacteristic, complemented
87#10622658C2212yescomplemented
88#10622658C2212yescomplemented
89#10622653C2212yes—
90#10622653C2211yescharacteristic, complemented
91#10622650C2212yes—
92#10622650C2212yes—
93#10622650C2211yescharacteristic, complemented
94#10622650C2211yescharacteristic, complemented
95#10622649C2212yes—
96#10622649C2211yescharacteristic, complemented
97#10622648C2212yes—
98#10622648C2212yes—
99#10622648C2212yescomplemented
100#10622648C2212yescomplemented
101#10622648C2212yescomplemented
102#10622648C2212yescomplemented
103#10622643C2212yescomplemented
104C4×#4326C2212yescomplemented
105#10622639C2212yescomplemented
106C4×#4325C2212yescomplemented
107#10622631C2212yescomplemented
108#10622631C2212yescomplemented
109#10622631C2212yescomplemented
110C4×#4324C2212yescomplemented
111C4×#4324C2212yescomplemented
112C4×#4324C2212yescomplemented
113#10622627C2212yescomplemented
114#10622627C2212yescomplemented
115#10622627C2212yescomplemented
116C4×#4323C2212yescomplemented
117C4×#4323C2212yescomplemented
118C4×#4323C2212yescomplemented
119#10622615C2211yescharacteristic
120#10622615C2211yescharacteristic
121#10622613C2212yescomplemented
122#10622613C2212yescomplemented
123#10622612C2211yescharacteristic, complemented
124#10622612C2211yescharacteristic, complemented
125#10622610C2211yescharacteristic, complemented
126#10622610C2211yescharacteristic, complemented
127#10622608C2211yescharacteristic, complemented
128#10622608C2211yescharacteristic, complemented
129#10622579C2211yescharacteristic
130#10622579C2211yescharacteristic
131C2×#66872C2211yescharacteristic, complemented
132C2×#66871C2211yescharacteristic, complemented
133#10622539C2212yescomplemented
134#10622538C2212yescomplemented
135C2×C11×#41—22no—
136C2×C11×#41C2311yescharacteristic
137C22×D4×C11—21no—
138C22×D4×C11C2311yescharacteristic
139C23×C4×C11C2311yescharacteristic
140C22×C22⋊D11—21no—
141C2×#4339—21no—
142C2×#4339—21no—
143C2×#4339—24no—
144C2×#4339—24no—
145C2×#4339C2311yescharacteristic
146C2×#4339C2311yescharacteristic
147C2×#4339C2311yescharacteristic
148C2×#4339C2311yescharacteristic
149C22×D44C2311yescharacteristic
150C22×C4×D11—21no—
151C22×Dic22C2311yescharacteristic
152C11×C4⋊Q8—21no—
153C11×C4⋊Q8C2312yes—
154C11×#127C2312yes—
155C11×#126—22no—
156C11×#126—22no—
157C11×#125—21no—
158C11×#125C2312yes—
159C11×#124—22no—
160C11×#124—22no—
161C11×#124C2312yes—
162C11×#123—21no—
163C11×#123—22no—
164C11×#123—22no—
165C11×#123—22no—
166C11×#123—22no—
167C11×C22⋊Q8—22no—
168C11×C22⋊Q8—22no—
169C11×C22⋊Q8C2311yescharacteristic
170C11×C22⋊Q8C2311yescharacteristic
171C11×#121—21no—
172C11×#121—21no—
173C11×#121—22no—
174C11×#121—21no—
175C11×#121—21no—
176C11×#121—22no—
177C11×#121—22no—
178C11×#121C2312yes—
179C11×#121C2312yes—
180C11×#121C2311yescharacteristic
181C11×#121C2311yescharacteristic
182C11×#120—21no—
183C11×#120—22no—
184C4×Q8×C11C2312yes—
185C4×D4×C11—21no—
186C4×D4×C11—21no—
187C4×D4×C11—22no—
188C4×D4×C11—21no—
189C4×D4×C11—21no—
190C4×D4×C11—22no—
191C4×D4×C11—22no—
192C4×D4×C11C2312yes—
193C4×D4×C11C2312yes—
194C4×D4×C11C2312yes—
195C11×#117—21no—
196C11×#117—22no—
197C11×#117D411yescharacteristic
198C11×#117D411yescharacteristic
199C11×#117D412yes—
200C11×#117C2311yescharacteristic
201C11×#117C2312yes—
202C11×#117C2311yescharacteristic
203C11×#117C2311yescharacteristic
204C2×C11×C4⋊C4—21no—
205C2×C11×C4⋊C4D411yescharacteristic
206C2×C11×C4⋊C4D411yescharacteristic
207C2×C11×C4⋊C4C2311yescharacteristic
208C2×C11×C22⋊C4—21no—
209C2×C11×C22⋊C4—22no—
210C2×C11×C22⋊C4D412yes—
211C2×C42×C11C2312yes—
212C2×C22⋊Dic11—21no—
213#67003—24no—
214#67003—24no—
215C2×#4326C2311yescharacteristic
216C2×#4326C2311yescharacteristic
217C2×#4325C2311yescharacteristic
218C2×#4325C2311yescharacteristic
219C2×#4324C2312yes—
220C2×#4324C2312yes—
221C2×#4324C2311yescharacteristic
222C2×#4324C2311yescharacteristic
223#66985—24no—
224#66985—24no—
225C2×#4323C2312yes—
226C2×#4323C2312yes—
227C2×#4323C2311yescharacteristic
228C2×#4323C2311yescharacteristic
229C4×C22⋊D11—22no—
230C4×C22⋊D11—22no—
231C4×C22⋊D11—22no—
232C4×C22⋊D11—22no—
233#66979—21no—
234#66979—21no—
235#66979C2312yes—
236#66979C2312yes—
237C2×C4⋊Dic11C2311yescharacteristic
238C2×C4⋊Dic11C2311yescharacteristic
239C2×C4×Dic11—21no—
240C2×#4318C2311yescharacteristic
241C2×#4318C2311yescharacteristic
242C22×C11⋊C8C2311yescharacteristic
243C22×C11⋊C8C2311yescharacteristic
244#66946—22no—
245#66946—22no—
246#66945—21no—
247#66945—21no—
248#66945—21no—
249#66945—21no—
250C4⋊C4×D11—21no—
251C4⋊C4×D11—21no—
252C4⋊C4×D11—21no—
253C4⋊C4×D11—21no—
254#66940—22no—
255#66940—22no—
256(C22⋊D11)⋊C4—22no—
257(C22⋊D11)⋊C4—22no—
258(C22⋊D11)⋊C4—22no—
259(C22⋊D11)⋊C4—22no—
260C22⋊C4×D11—22no—
261C22⋊C4×D11—22no—
262#66930—22no—
263#66930—22no—
264C4×D44C2312yes—
265C4×D44C2312yes—
266C4×D44C2312yes—
267C4×D44C2312yes—
268#66925—22no—
269#66925—22no—
270C42×D11—22no—
271C42×D11—22no—
272C4×Dic22C2312yes—
273C4×Dic22C2312yes—
274C4×Dic22C2312yes—
275C4×Dic22C2312yes—
276#66899C2312yes—
277#66899C2312yes—
278#66896C2312yes—
279#66896C2312yes—
280#66896C2312yes—
281#66896C2312yes—
282#66896C2312yes—
283#66896C2312yes—
284C22⋊(C11⋊C8)C2311yescharacteristic
285C22⋊(C11⋊C8)C2312yes—
286C22⋊(C11⋊C8)C2311yescharacteristic
287C22⋊(C11⋊C8)C2311yescharacteristic
288C22⋊(C11⋊C8)C2311yescharacteristic
289C22⋊(C11⋊C8)C2312yes—
290#66874C2312yes—
291#66874C2312yes—
292#66874C2311yescharacteristic
293#66874C2311yescharacteristic
294#66874C2311yescharacteristic
295#66874C2311yescharacteristic
296#66873C2312yes—
297#66873C2312yes—
298#66873C2311yescharacteristic
299#66873C2311yescharacteristic
300#66873C2311yescharacteristic
301#66873C2311yescharacteristic
302#66872C2312yes—
303#66872C2312yes—
304#66872C2312yes—
305#66872C2312yes—
306#66871C2312yes—
307#66871C2312yes—
308#66871C2312yes—
309#66871C2312yes—
310C4⋊(C11⋊C8)C2312yes—
311C4⋊(C11⋊C8)C2312yes—
312C4⋊(C11⋊C8)C2312yes—
313C4⋊(C11⋊C8)C2312yes—
314#66867C2312yes—
315#66867C2312yes—
316C4×C11⋊C8C2312yes—
317C4×C11⋊C8C2312yes—
318#60587—111nomaximal, Sylow
319C24×C11—21no—
320C24×C11C2×D411yescharacteristic
321C23×D11—21no—
322C11×#41—22no—
323C11×#41—22no—
324C11×#41—84no—
325C2×Q8×C11—22no—
326C2×Q8×C11C2411yescharacteristic
327C2×D4×C11—21no—
328C2×D4×C11—21no—
329C2×D4×C11—22no—
330C2×D4×C11—21no—
331C2×D4×C11—22no—
332C2×D4×C11—21no—
333C2×D4×C11—22no—
334C2×D4×C11—22no—
335C2×D4×C11—22no—
336C2×D4×C11—22no—
337C2×D4×C11—82no—
338C2×D4×C11C2412yes—
339C2×D4×C11C2411yescharacteristic
340C22×C4×C11—22no—
341C22×C4×C11—22no—
342C22×C4×C11—21no—
343C22×C4×C11—21no—
344C22×C4×C11—22no—
345C22×C4×C11—22no—
346C22×C4×C11—22no—
347C22×C4×C11C2×D411yescharacteristic
348C22×C4×C11C2×D411yescharacteristic
349C22×C4×C11C2×D411yescharacteristic
350C22×C4×C11C2×D412yes—
351C22×C4×C11C2×D412yes—
352C22×C4×C11C2411yescharacteristic
353C22×C4×C11C2411yescharacteristic
354C22×C4×C11C2411yescharacteristic
355C2×C22⋊D11—28no—
356C2×C22⋊D11—21no—
357C2×C22⋊D11—21no—
358C2×C22⋊D11—21no—
359C2×C22⋊D11—21no—
360C22×Dic11—21no—
361C22×Dic11—21no—
362C22×Dic11—21no—
363#4339—28no—
364#4339—28no—
365#4339—22no—
366#4339—22no—
367#4339—22no—
368#4339—22no—
369#4339—22no—
370#4339—22no—
371#4339#4114yescomplemented
372#4339#4114yescomplemented
373C2×D44—22no—
374C2×D44—22no—
375C2×D44—21no—
376C2×D44C2411yescharacteristic
377C2×D44C2411yescharacteristic
378C2×C4×D11—28no—
379C2×C4×D11—21no—
380C2×C4×D11—21no—
381C2×C4×D11—21no—
382C2×C4×D11—21no—
383C2×C4×D11—22no—
384C2×C4×D11—22no—
385C2×C4×D11—22no—
386C2×C4×D11—22no—
387C2×Dic22—22no—
388C2×Dic22—22no—
389C2×Dic22—21no—
390C2×Dic22C2411yescharacteristic
391C2×Dic22C2411yescharacteristic
392C11×C4⋊C4—21no—
393C11×C4⋊C4—22no—
394C11×C4⋊C4—21no—
395C11×C4⋊C4—22no—
396C11×C4⋊C4—22no—
397C11×C4⋊C4—22no—
398C11×C4⋊C4—21no—
399C11×C4⋊C4C2×D412yes—
400C11×C4⋊C4C2×D412yes—
401C11×C4⋊C4C2×D411yescharacteristic
402C11×C4⋊C4C2×D411yescharacteristic
403C11×C4⋊C4C2×D411yescharacteristic
404C11×C4⋊C4C2×D411yescharacteristic
405C11×C4⋊C4C2412yes—
406C11×C4⋊C4C2411yescharacteristic
407C11×C4⋊C4C2411yescharacteristic
408C11×C22⋊C4—21no—
409C11×C22⋊C4—21no—
410C11×C22⋊C4—21no—
411C11×C22⋊C4—22no—
412C11×C22⋊C4—22no—
413C11×C22⋊C4—22no—
414C11×C22⋊C4—22no—
415C11×C22⋊C4—22no—
416C11×C22⋊C4—22no—
417C11×C22⋊C4—21no—
418C11×C22⋊C4—22no—
419C11×C22⋊C4—21no—
420C11×C22⋊C4C2×D412yes—
421C11×C22⋊C4C2×D412yes—
422C11×C22⋊C4C2×D412yes—
423C11×C22⋊C4C2×D412yes—
424C42×C11—22no—
425C42×C11—21no—
426C42×C11C2×D412yes—
427C42×C11C2×D412yes—
428C42×C11C2412yes—
429C42×C11C2412yes—
430C22⋊Dic11—22no—
431C22⋊Dic11—22no—
432#4326—22no—
433#4326—22no—
434#4325—22no—
435#4325—22no—
436#4324—24no—
437#4324—24no—
438#4324—22no—
439#4324—22no—
440#4323—24no—
441#4323—24no—
442#4323—22no—
443#4323—22no—
444(C2×D11)⋊C4—22no—
445(C2×D11)⋊C4—22no—
446(C2×D11)⋊C4—22no—
447(C2×D11)⋊C4—22no—
448C4⋊Dic11—21no—
449C4⋊Dic11—21no—
450C4⋊Dic11C2412yes—
451C4⋊Dic11C2412yes—
452Dic11⋊C4—22no—
453Dic11⋊C4—22no—
454Dic11⋊C4—22no—
455Dic11⋊C4—22no—
456C4×Dic11—22no—
457C4×Dic11—22no—
458C4×Dic11—22no—
459C4×Dic11—22no—
460C4×Dic11—22no—
461C4×Dic11—22no—
462#4318—22no—
463#4318—22no—
464C2×C11⋊C8—22no—
465C2×C11⋊C8—22no—
466C2×C11⋊C8C2411yescharacteristic
467C2×C11⋊C8C2411yescharacteristic
468C2×C11⋊C8C2412yes—
469C2×C11⋊C8C2412yes—
470C2×C11⋊C8C2411yescharacteristic
471C2×C11⋊C8C2411yescharacteristic
472#3494D1111yescharacteristic, complemented
473#3428—111no—
474#3126—112no—
475#3122—112no—
476#3121—112no—
477#3118—112no—
478#3115—112no—
479#3111—112no—
480#3106—112no—
481#3102—112no—
482#3093—111no—
483C2×#482—111no—
484#3084—111no—
485#3083—111no—
486#3045—111no—
487#3045—111no—
488#3006—111no—
489#3002—111no—
490#2952—111no—
491#2951—111no—
492#2946—111no—
493#2946—111no—
494#2924—111no—
495C23×C11—22no—
496C23×C11—22no—
497C23×C11—21no—
498C23×C11—41no—
499C23×C11—41no—
500C23×C11—42no—
501C23×C11—81no—
502C23×C11—81no—
503C23×C11C22×D411yescharacteristic
504C23×C11C22×D411yescharacteristic
505C23×C11C22×D411yescharacteristic
506C22×D11—21no—
507C22×D11—21no—
508C22×D11—24no—
509C22×D11—81no—
510C22×D11—81no—
511Q8×C11—21no—
512Q8×C11—21no—
513Q8×C11—82no—
514D4×C11—22no—
515D4×C11—22no—
516D4×C11—21no—
517D4×C11—21no—
518D4×C11—44no—
519D4×C11—42no—
520D4×C11—42no—
521D4×C11—42no—
522D4×C11—82no—
523D4×C11—82no—
524D4×C11—81no—
525D4×C11—82no—
526C2×C4×C11—22no—
527C2×C4×C11—22no—
528C2×C4×C11—22no—
529C2×C4×C11—21no—
530C2×C4×C11—21no—
531C2×C4×C11—21no—
532C2×C4×C11—21no—
533C2×C4×C11—21no—
534C2×C4×C11—21no—
535C2×C4×C11—21no—
536C2×C4×C11—22no—
537C2×C4×C11—42no—
538C2×C4×C11—42no—
539C2×C4×C11—42no—
540C2×C4×C11—82no—
541C2×C4×C11—82no—
542C2×C4×C11—82no—
543C2×C4×C11—81no—
544C2×C4×C11C22×D411yescharacteristic
545C2×C4×C11C22×D411yescharacteristic
546C2×C4×C11C22×D412yes—
547C2×C4×C11C22×D412yes—
548C2×C4×C11C22×D412yes—
549C2×C4×C11C22×D412yes—
550C2×C4×C11C22×D411yescharacteristic
551C2×C4×C11C2×#4112yes—
552C2×C4×C11C2×#4112yes—
553C2×C4×C11C2511yescharacteristic
554C22⋊D11—24no—
555C22⋊D11—24no—
556C22⋊D11—24no—
557C22⋊D11—24no—
558C2×Dic11—24no—
559C2×Dic11—21no—
560C2×Dic11—21no—
561C2×Dic11—22no—
562C2×Dic11—22no—
563C2×Dic11—81no—
564C2×Dic11—81no—
565D44—24no—
566D44—21no—
567D44—21no—
568D44C2×#4112yes—
569D44C2×#4112yes—
570C4×D11—24no—
571C4×D11—24no—
572C4×D11—24no—
573C4×D11—24no—
574C4×D11—82no—
575C4×D11—82no—
576C4×D11—82no—
577C4×D11—82no—
578Dic22—24no—
579Dic22—21no—
580Dic22—21no—
581Dic22C2×#4112yes—
582Dic22C2×#4112yes—
583C11⋊C8—21no—
584C11⋊C8—21no—
585C11⋊C8—21no—
586C11⋊C8—21no—
587C11⋊C8—22no—
588C11⋊C8—22no—
589C22×#41—111no—
590C2×AGL(1,ℤ/8)—111no—
591C2×AGL(1,ℤ/8)—111no—
592C2×#135—111no—
593C2×#135—111no—
594#555—21no—
595#553—21no—
596#553—21no—
597#551—22no—
598#547—21no—
599#546—22no—
600#544C2×D1111yescharacteristic, complemented
601#542C2×D1112yes—
602#540C2×D1112yes—
603#535C2×D1111yescharacteristic, complemented
604#532C2×D1112yescomplemented
605#529C2×D1112yescomplemented
606#525C2×D1111yescharacteristic
607C2×#121C2×D1111yescharacteristic
608#520—111no—
609#520—111no—
610#520—111no—
611#520—111no—
612#520—221no—
613#520—221no—
614#520C2×D1111yescharacteristic, complemented
615#519—112no—
616#518—112no—
617#518—222no—
618#518C2×D1111yescharacteristic, complemented
619C4×#41—112no—
620C4×#41—112no—
621C4×#41—222no—
622C2×#117—111no—
623C2×#117—221no—
624C2×#117—221no—
625C2×#117C2×D1111yescharacteristic
626#485—112no—
627#485—112no—
628#482—112no—
629#482—112no—
630#482—112no—
631#482—112no—
632#482—112no—
633#482—112no—
634#479—112no—
635#479—112no—
636#478—112no—
637#478—112no—
638#477—112no—
639#476—112no—
640#475—112no—
641#474—112no—
642#464—112no—
643#464—112no—
644#463—112no—
645#463—112no—
646#460—112no—
647#460—112no—
648#459—112no—
649#459—112no—
650#452—111no—
651#452—111no—
652#451—111no—
653#450—111no—
654#449—112no—
655#449—111no—
656#449—112no—
657#449—111no—
658#448—112no—
659#448—111no—
660#447—112no—
661#447—111no—
662#442—112no—
663#442—112no—
664#442—112no—
665#441—112no—
666#440—112no—
667#440—112no—
668#440—112no—
669#440—112no—
670C4×Q16—112no—
671C4×SD16—112no—
672C4×SD16—112no—
673C4×SD16—112no—
674C4×SD16—112no—
675C4×D8—112no—
676C4×D8—112no—
677C4×D8—112no—
678#433—112no—
679#433—112no—
680#432—112no—
681#431—112no—
682#428—111no—
683#428—111no—
684C2×#107—111no—
685C2×#106—111no—
686#424—111no—
687#424—111no—
688#417—111no—
689#417—111no—
690#417—111no—
691#417—111no—
692#416—111no—
693#416—111no—
694C2×#102—111no—
695C2×#102—111no—
696#407—111no—
697C2×C22⋊C8—111no—
698#405—111no—
699#405—111no—
700C22×C11—21no—
701C22×C11—21no—
702C22×C11—21no—
703C22×C11—21no—
704C22×C11—21no—
705C22×C11—21no—
706C22×C11—21no—
707C22×C11—21no—
708C22×C11—42no—
709C22×C11—41no—
710C22×C11—41no—
711C22×C11—42no—
712C22×C11—41no—
713C22×C11—42no—
714C22×C11—82no—
715C22×C11—162no—
716C22×C11#52512yes—
717C22×C11C23×D411yescharacteristic
718C2×D11—22no—
719C2×D11—22no—
720C2×D11—41no—
721C2×D11—41no—
722C2×D11—41no—
723C2×D11—41no—
724C2×D11—84no—
725C4×C11—22no—
726C4×C11—22no—
727C4×C11—22no—
728C4×C11—22no—
729C4×C11—21no—
730C4×C11—21no—
731C4×C11—41no—
732C4×C11—42no—
733C4×C11—41no—
734C4×C11—41no—
735C4×C11#52512yes—
736C4×C11C22×#4111yescharacteristic
737C4×C11C22×#4111yescharacteristic
738Dic11—22no—
739Dic11—22no—
740Dic11—42no—
741Dic11—42no—
742C2×#41—22no—
743C2×#41—111no—
744C2×#41—111no—
745C2×#41—111no—
746C2×#41—111no—
747C2×#41—224no—
748C2×#41—224no—
749C2×#41—221no—
750C2×#41—221no—
751C2×#41C22×D1111yescharacteristic
752C22×Q8—111no—
753C22×D4—21no—
754C22×D4—111no—
755C22×D4—221no—
756C22×D4C22×D1111yescharacteristic
757C23×C4—221no—
758C23×C4C22×D1111yescharacteristic
759AGL(1,ℤ/8)—224no—
760AGL(1,ℤ/8)—224no—
761#135—224no—
762#135—224no—
763C2×Q16—111no—
764C2×Q16—111no—
765C2×SD16—111no—
766C2×SD16—111no—
767C2×SD16—111no—
768C2×SD16—111no—
769C2×SD16—112no—
770C2×SD16—112no—
771C2×D8—111no—
772C2×D8—111no—
773C2×D8—112no—
774C2×D8—112no—
775C2×M16—111no—
776C2×M16—111no—
777C22×C8—111no—
778C22×C8—111no—
779C4⋊Q8—21no—
780C4⋊Q8C22×D1112yes—
781#127C22×D1112yes—
782#126—22no—
783#126—22no—
784#125—21no—
785#125C22×D1112yes—
786#124—22no—
787#124—22no—
788#124C22×D1112yes—
789#123—21no—
790#123—22no—
791#123—22no—
792#123—22no—
793#123—22no—
794C22⋊Q8—22no—
795C22⋊Q8—22no—
796C22⋊Q8C22×D1111yescharacteristic
797C22⋊Q8C22×D1111yescharacteristic
798#121—21no—
799#121—21no—
800#121—22no—
801#121—21no—
802#121—21no—
803#121—22no—
804#121—22no—
805#121C22×D1112yes—
806#121C22×D1112yes—
807#121C22×D1111yescharacteristic
808#121C22×D1111yescharacteristic
809#120—21no—
810#120—22no—
811C4×Q8—112no—
812C4×Q8—112no—
813C4×Q8—112no—
814C4×Q8—112no—
815C4×Q8—222no—
816C4×Q8—222no—
817C4×Q8C22×D1112yes—
818C4×D4—21no—
819C4×D4—21no—
820C4×D4—22no—
821C4×D4—21no—
822C4×D4—21no—
823C4×D4—22no—
824C4×D4—22no—
825C4×D4—112no—
826C4×D4—112no—
827C4×D4—112no—
828C4×D4—112no—
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×D4C22×D1112yes—
840C4×D4C22×D1112yes—
841C4×D4C22×D1112yes—
842#117—21no—
843#117—22no—
844#117—112no—
845#117—112no—
846#117—221no—
847#117—221no—
848#117—221no—
849#117—221no—
850#117—221no—
851#117—221no—
852#117—222no—
853#117—222no—
854#117—222no—
855#117—222no—
856#117C22⋊D1111yescharacteristic
857#117C22⋊D1111yescharacteristic
858#117C22⋊D1112yes—
859#117C22×D1111yescharacteristic
860#117C22×D1112yes—
861#117C22×D1111yescharacteristic
862#117C22×D1111yescharacteristic
863C2×C4⋊C4—21no—
864C2×C4⋊C4—111no—
865C2×C4⋊C4—111no—
866C2×C4⋊C4—221no—
867C2×C4⋊C4—221no—
868C2×C4⋊C4—221no—
869C2×C4⋊C4—221no—
870C2×C4⋊C4C22⋊D1111yescharacteristic
871C2×C4⋊C4C22⋊D1111yescharacteristic
872C2×C4⋊C4C22×D1111yescharacteristic
873C2×C22⋊C4—21no—
874C2×C22⋊C4—22no—
875C2×C22⋊C4—221no—
876C2×C22⋊C4—222no—
877C2×C22⋊C4—222no—
878C2×C22⋊C4C22⋊D1112yes—
879C2×C42—221no—
880C2×C42—222no—
881C2×C42—222no—
882C2×C42C22×D1112yes—
883#107—112no—
884#107—112no—
885#107—112no—
886#107—112no—
887#106—112no—
888#106—112no—
889#106—112no—
890#106—112no—
891C4⋊C8—112no—
892C4⋊C8—112no—
893C4⋊C8—112no—
894C4⋊C8—112no—
895#103—112no—
896#103—112no—
897#103—111no—
898#103—111no—
899#103—111no—
900#103—111no—
901#103—112no—
902#103—112no—
903#102—112no—
904#102—112no—
905#102—112no—
906#102—112no—
907#102—112no—
908#102—112no—
909#102—111no—
910#102—111no—
911#102—111no—
912#102—111no—
913#102—112no—
914#102—112no—
915C22⋊C8—111no—
916C22⋊C8—111no—
917C22⋊C8—111no—
918C22⋊C8—111no—
919C22⋊C8—112no—
920C22⋊C8—112no—
921#97—112no—
922#97—112no—
923C4×C8—112no—
924C4×C8—112no—
925C2×C11—22no—
926C2×C11—41no—
927C2×C11—41no—
928C2×C11—81no—
929C2×C11—82no—
930C2×C11C2×#52511yescharacteristic
931C2×C11#358411yescharacteristic
932C2×C11#358511yescharacteristic
933D11—42no—
934D11—42no—
935C24—21no—
936C24—221no—
937C24C2×C22⋊D1111yescharacteristic
938#41—22no—
939#41—22no—
940#41—84no—
941#41—114no—
942#41—114no—
943#41—222no—
944#41—222no—
945#41—222no—
946#41—222no—
947#41—228no—
948#41—228no—
949#41—222no—
950#41—222no—
951C2×Q8—22no—
952C2×Q8—111no—
953C2×Q8—111no—
954C2×Q8—222no—
955C2×Q8—222no—
956C2×Q8—221no—
957C2×Q8C23×D1111yescharacteristic
958C2×D4—21no—
959C2×D4—21no—
960C2×D4—22no—
961C2×D4—21no—
962C2×D4—22no—
963C2×D4—22no—
964C2×D4—22no—
965C2×D4—21no—
966C2×D4—22no—
967C2×D4—22no—
968C2×D4—82no—
969C2×D4—111no—
970C2×D4—111no—
971C2×D4—222no—
972C2×D4—222no—
973C2×D4—228no—
974C2×D4—221no—
975C2×D4—221no—
976C2×D4—221no—
977C2×D4—221no—
978C2×D4—221no—
979C2×D4C23×D1112yes—
980C2×D4C23×D1111yescharacteristic
981C22×C4—22no—
982C22×C4—22no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—22no—
986C22×C4—22no—
987C22×C4—22no—
988C22×C4—228no—
989C22×C4—221no—
990C22×C4—221no—
991C22×C4—221no—
992C22×C4—221no—
993C22×C4—221no—
994C22×C4—221no—
995C22×C4—221no—
996C22×C4—222no—
997C22×C4—222no—
998C22×C4—222no—
999C22×C4—222no—
1000C22×C4C2×C22⋊D1111yescharacteristic
1001C22×C4C2×C22⋊D1111yescharacteristic
1002C22×C4C2×C22⋊D1111yescharacteristic
1003C22×C4C2×C22⋊D1112yes—
1004C22×C4C2×C22⋊D1112yes—
1005C22×C4C23×D1111yescharacteristic
1006C22×C4C23×D1111yescharacteristic
1007C22×C4C23×D1111yescharacteristic
1008Q16—222no—
1009Q16—222no—
1010SD16—222no—
1011SD16—222no—
1012SD16—224no—
1013SD16—224no—
1014SD16—222no—
1015SD16—222no—
1016D8—222no—
1017D8—222no—
1018D8—224no—
1019D8—224no—
1020M16—222no—
1021M16—222no—
1022C2×C8—111no—
1023C2×C8—111no—
1024C2×C8—112no—
1025C2×C8—112no—
1026C2×C8—111no—
1027C2×C8—111no—
1028C2×C8—222no—
1029C2×C8—222no—
1030C4⋊C4—21no—
1031C4⋊C4—22no—
1032C4⋊C4—21no—
1033C4⋊C4—22no—
1034C4⋊C4—22no—
1035C4⋊C4—22no—
1036C4⋊C4—21no—
1037C4⋊C4—112no—
1038C4⋊C4—112no—
1039C4⋊C4—221no—
1040C4⋊C4—221no—
1041C4⋊C4—222no—
1042C4⋊C4—222no—
1043C4⋊C4—222no—
1044C4⋊C4—222no—
1045C4⋊C4C2×C22⋊D1111yescharacteristic
1046C4⋊C4C2×C22⋊D1111yescharacteristic
1047C4⋊C4C2×C22⋊D1111yescharacteristic
1048C4⋊C4C2×C22⋊D1111yescharacteristic
1049C4⋊C4C2×C22⋊D1112yes—
1050C4⋊C4C2×C22⋊D1112yes—
1051C4⋊C4C23×D1112yes—
1052C4⋊C4C23×D1111yescharacteristic
1053C4⋊C4C23×D1111yescharacteristic
1054C22⋊C4—21no—
1055C22⋊C4—21no—
1056C22⋊C4—21no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—22no—
1063C22⋊C4—21no—
1064C22⋊C4—22no—
1065C22⋊C4—21no—
1066C22⋊C4—222no—
1067C22⋊C4—222no—
1068C22⋊C4—222no—
1069C22⋊C4—222no—
1070C22⋊C4—222no—
1071C22⋊C4—222no—
1072C22⋊C4C2×C22⋊D1112yes—
1073C22⋊C4C2×C22⋊D1112yes—
1074C22⋊C4C2×C22⋊D1112yes—
1075C22⋊C4C2×C22⋊D1112yes—
1076C42—22no—
1077C42—21no—
1078C42—222no—
1079C42—222no—
1080C42—222no—
1081C42—222no—
1082C42—222no—
1083C42—222no—
1084C42C2×C22⋊D1112yes—
1085C42C2×C22⋊D1112yes—
1086C42C23×D1112yes—
1087C42C23×D1112yes—
1088C11#6058711yescharacteristic, complemented, Sylow
1089C23—22no—
1090C23—22no—
1091C23—21no—
1092C23—41no—
1093C23—41no—
1094C23—42no—
1095C23—81no—
1096C23—81no—
1097C23—224no—
1098C23—221no—
1099C23—221no—
1100C23—881no—
1101C23—881no—
1102C23C22×C22⋊D1111yescharacteristic
1103C23C22×C22⋊D1111yescharacteristic
1104C23C22×C22⋊D1111yescharacteristic
1105Q8—21no—
1106Q8—21no—
1107Q8—82no—
1108Q8—112no—
1109Q8—112no—
1110Q8—224no—
1111Q8—221no—
1112Q8—221no—
1113D4—22no—
1114D4—22no—
1115D4—21no—
1116D4—21no—
1117D4—44no—
1118D4—42no—
1119D4—42no—
1120D4—42no—
1121D4—82no—
1122D4—82no—
1123D4—81no—
1124D4—82no—
1125D4—112no—
1126D4—112no—
1127D4—224no—
1128D4—224no—
1129D4—224no—
1130D4—224no—
1131D4—224no—
1132D4—221no—
1133D4—221no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—22no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—82no—
1149C2×C4—82no—
1150C2×C4—82no—
1151C2×C4—81no—
1152C2×C4—224no—
1153C2×C4—224no—
1154C2×C4—224no—
1155C2×C4—221no—
1156C2×C4—221no—
1157C2×C4—224no—
1158C2×C4—224no—
1159C2×C4—222no—
1160C2×C4—222no—
1161C2×C4—882no—
1162C2×C4—882no—
1163C2×C4—882no—
1164C2×C4—882no—
1165C2×C4—881no—
1166C2×C4—881no—
1167C2×C4#41×D1112yes—
1168C2×C4#41×D1112yes—
1169C2×C4C22×C22⋊D1112yes—
1170C2×C4C22×C22⋊D1111yescharacteristic
1171C2×C4C22×C22⋊D1111yescharacteristic
1172C2×C4C22×C22⋊D1112yes—
1173C2×C4C22×C22⋊D1112yes—
1174C2×C4C22×C22⋊D1112yes—
1175C2×C4C22×C22⋊D1111yescharacteristic
1176C2×C4C24×D1111yescharacteristic
1177C8—221no—
1178C8—221no—
1179C8—221no—
1180C8—221no—
1181C8—222no—
1182C8—222no—
1183C22—21no—
1184C22—21no—
1185C22—21no—
1186C22—21no—
1187C22—21no—
1188C22—21no—
1189C22—21no—
1190C22—21no—
1191C22—41no—
1192C22—42no—
1193C22—42no—
1194C22—41no—
1195C22—41no—
1196C22—42no—
1197C22—82no—
1198C22—162no—
1199C22—222no—
1200C22—222no—
1201C22—441no—
1202C22—441no—
1203C22—441no—
1204C22—441no—
1205C22—884no—
1206C22#1062335912yes—
1207C22C23×C22⋊D1111yescharacteristic
1208C4—22no—
1209C4—22no—
1210C4—22no—
1211C4—22no—
1212C4—21no—
1213C4—21no—
1214C4—42no—
1215C4—41no—
1216C4—41no—
1217C4—41no—
1218C4—222no—
1219C4—222no—
1220C4—442no—
1221C4—442no—
1222C4#1062335912yes—
1223C4C2×#41×D1111yescharacteristic
1224C4C2×#41×D1111yescharacteristic
1225C2—22no—
1226C2—41no—
1227C2—41no—
1228C2—82no—
1229C2—81no—
1230C2—442no—
1231C2—442no—
1232C2C2×#1062335911yescharacteristic
1233C2#1308338711yescharacteristic
1234C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3494C2
socleC22×C11C23×D4
hypercenter#3494D11
hypocenterC11#60587
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3494

Complements

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

NH ≅ G/Ntype
1. #13081817C2semidirect
2. #13078902C2semidirect
3. #13078854C2semidirect
4. #13078839C2semidirect
5. #13078794C2semidirect
6. #13078761C2semidirect
7. #13078719C2semidirect
8. #13078670C2semidirect
9. #13078628C2semidirect
10. #13078545C2semidirect
11. C2×#10622648C2semidirect
12. #13078474C2semidirect
13. #13078463C2semidirect
14. #13078151C2semidirect
15. #13078151C2semidirect
16. #13077866C2semidirect
17. #13077832C2semidirect
18. #13077497C2semidirect
19. #13077489C2semidirect
20. #13077448C2semidirect
21. #13077448C2semidirect
22. #13077274C2semidirect
23. C11×#3494C2semidirect
31. C11×#544C22semidirect
34. C11×#535C22semidirect
35. C11×#532C22semidirect
36. C11×#529C22semidirect
39. C11×#520C22semidirect
40. C11×#518C22semidirect
52. #10623052C22semidirect
55. #10623047C22semidirect
59. C4×#4339C22semidirect
60. C4×#4339C22semidirect
61. #10622845C22semidirect
62. #10622845C22semidirect
63. C2×#66896C22semidirect
64. C2×#66896C22semidirect
67. #10622707C22semidirect
68. #10622704C22semidirect
69. #10622700C22semidirect
70. #10622697C22semidirect
71. #10622688C22semidirect
72. #10622688C22semidirect
73. #10622685C22semidirect
74. #10622685C22semidirect
75. #10622679C22semidirect
76. #10622679C22semidirect
77. #10622676C22semidirect
78. #10622676C22semidirect
79. #10622670C22semidirect
80. #10622670C22semidirect
81. #10622667C22semidirect
82. #10622667C22semidirect
83. #10622663C22semidirect
84. #10622660C22semidirect
85. #10622660C22semidirect
86. #10622659C22semidirect
87. #10622658C22semidirect
88. #10622658C22semidirect
90. #10622653C22semidirect
93. #10622650C22semidirect
94. #10622650C22semidirect
96. #10622649C22semidirect
99. #10622648C22semidirect
100. #10622648C22semidirect
101. #10622648C22semidirect
102. #10622648C22semidirect
103. #10622643C22semidirect
104. C4×#4326C22semidirect
105. #10622639C22semidirect
106. C4×#4325C22semidirect
107. #10622631C22semidirect
108. #10622631C22semidirect
109. #10622631C22semidirect
110. C4×#4324C22semidirect
111. C4×#4324C22semidirect
112. C4×#4324C22semidirect
113. #10622627C22semidirect
114. #10622627C22semidirect
115. #10622627C22semidirect
116. C4×#4323C22semidirect
117. C4×#4323C22semidirect
118. C4×#4323C22semidirect
121. #10622613C22semidirect
122. #10622613C22semidirect
123. #10622612C22semidirect
124. #10622612C22semidirect
125. #10622610C22semidirect
126. #10622610C22semidirect
127. #10622608C22semidirect
128. #10622608C22semidirect
131. C2×#66872C22semidirect
132. C2×#66871C22semidirect
133. #10622539C22semidirect
134. #10622538C22semidirect
371. #4339#41semidirect
372. #4339#41semidirect
472. #3494D11semidirect
600. #544C2×D11semidirect
603. #535C2×D11semidirect
604. #532C2×D11semidirect
605. #529C2×D11semidirect
614. #520C2×D11semidirect
618. #518C2×D11semidirect
1088. C11#60587semidirect

Maximal subgroups

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

subgroupindex
#130818172
#130789022
#130788542
#130788392
#130787942
#130787612
#130787192
#130786702
#130786282
#130785452
C2×#106226482
#130784742
#130784632
#130781512
#130778662
#130778322
#130774972
#130774892
#130774482
#130772742
C11×#34942
#6058711