Finite Group Databasebeta

← #14922687

Subgroups — #14922687

Order 2816.

2522 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623219C211yesmaximal, characteristic, complemented
2C2×C4×#4341C211yesmaximal, characteristic
3#13072490C211yesmaximal, characteristic, complemented
4#13072477C211yesmaximal, characteristic, complemented
5#13072473C211yesmaximal, characteristic, complemented
6#13072469C211yesmaximal, characteristic, complemented
7#13072460C211yesmaximal, characteristic, complemented
8#13072456C211yesmaximal, characteristic, complemented
9#13072453C211yesmaximal, characteristic, complemented
10#13072447C212yesmaximal, complemented
11#13072435C212yesmaximal, complemented
12#13072428C212yesmaximal, complemented
13#13072424C212yesmaximal, complemented
14#13071891C212yesmaximal, complemented
15#13071885C212yesmaximal, complemented
16#13071148C212yesmaximal, complemented
17#13071144C212yesmaximal, complemented
18#13071103C211yesmaximal, characteristic
19#13071103C211yesmaximal, characteristic
20#13071097C211yesmaximal, characteristic, complemented
21#13071097C211yesmaximal, characteristic, complemented
22C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2454C211yesmaximal, characteristic, complemented
24C22×#4341C2211yescharacteristic
25C2×C11×#125C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×D4×Dic11C2211yescharacteristic
28C2×C4×C22⋊D11C2212yes—
29C2×#66977C2212yes—
30C22×C4×Dic11C2212yes—
31#10623219—28no—
32C4×#4341—28no—
33C2×#66949C2212yes—
34C2×#66949C2212yes—
35C2×#66945C2211yescharacteristic
36C2×#66945C2211yescharacteristic
37C2×#66945C2211yescharacteristic
38C2×C4⋊C4×D11C2211yescharacteristic
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×#66941C2211yescharacteristic
41C2×#66941C2211yescharacteristic
42C2×#66940C2212yes—
43C2×#66940C2212yes—
44C2×#66940C2211yescharacteristic
45C2×(C22⋊D11)⋊C4C2212yes—
46C2×#66931C2212yes—
47C2×#66930C2212yes—
48C2×C42×D11C2211yescharacteristic
49C2×C42×D11C2211yescharacteristic
50C2×C42×D11C2211yescharacteristic
51C2×#66923C2211yescharacteristic
52C2×C4×Dic22C2211yescharacteristic
53C11×#399C2212yes—
54C11×#396C2212yes—
55C11×#390C2211yescharacteristic
56C11×#390C2211yescharacteristic
57C11×#389C2211yescharacteristic
58C11×#389C2211yescharacteristic
59C11×#385C2212yes—
60C11×#380C2212yes—
61C4×C11×C4⋊C4C2211yescharacteristic
62#10622834C2211yescharacteristic
63#10622834C2211yescharacteristic
64#10622823C2212yes—
65#10622602C2212yes—
66#10622602C2212yes—
67#10622598C2211yescharacteristic
68#10622598C2211yescharacteristic
69#10622597C2212yes—
70#10622596C2212yes—
71#10622595C2212yes—
72#10622593C2212yes—
73#10622593C2212yes—
74#10622592C2212yes—
75#10622591C2212yes—
76C4⋊C4×Dic11C2211yescharacteristic
77C4⋊C4×Dic11C2212yes—
78C4⋊C4×Dic11C2212yes—
79C4⋊C4×Dic11C2211yescharacteristic
80#10622587C2212yes—
81#10622587C2211yescharacteristic
82#10622587C2211yescharacteristic
83#10622586C2212yes—
84#10622586C2211yescharacteristic
85#10622586C2211yescharacteristic
86#10622585C2212yes—
87#10622569C2212yes—
88#10622569C2212yes—
89#10622569C2212yes—
90#10622569C2212yes—
91#10622562C2212yes—
92#10622561C2212yes—
93#10622561C2212yes—
94#10622561C2212yes—
95#10622560C2212yes—
96#10622560C2212yes—
97#10622559C2212yes—
98#10622559C2212yes—
99#10622555C2212yes—
100C22⋊C4×Dic11C2212yes—
101C22⋊C4×Dic11C2212yes—
102C22⋊C4×Dic11C2212yes—
103C22⋊C4×Dic11C2212yes—
104C4×C4⋊Dic11C2211yescharacteristic
105C4×Dic11⋊C4C2211yescharacteristic
106C4×Dic11⋊C4C2211yescharacteristic
107#10622542C2211yescharacteristic
108#10622542C2211yescharacteristic
109#10622541C2211yescharacteristic
110#10622541C2211yescharacteristic
111#10622281C2212yes—
112#10622281C2212yes—
113D11×#95C2211yescharacteristic
114D11×#95C2211yescharacteristic
115#10622271C2212yes—
116#10622269C2212yes—
117#10622266C2212yes—
118#10622265C2212yes—
119#10622265C2212yes—
120#10622262C2212yes—
121#10622262C2211yescharacteristic
122#10622262C2211yescharacteristic
123#10622262C2212yes—
124#10622259C2212yes—
125C22×D4×C11C2311yescharacteristic
126C23×C4×C11C2312yes—
127C22×C22⋊D11C2312yes—
128C23×Dic11C2312yes—
129C23×Dic11C2312yes—
130C2×#4341—24no—
131C2×#4341—24no—
132C2×#4341Q818yescomplemented
133C22×C4×D11C2311yescharacteristic
134C22×C4×D11C2311yescharacteristic
135C22×C4×D11C2311yescharacteristic
136C22×C4×D11C2311yescharacteristic
137C22×C4×D11C2311yescharacteristic
138C22×C4×D11C2311yescharacteristic
139C22×C4×D11C2311yescharacteristic
140C22×Dic22C2312yes—
141C22×Dic22C2312yes—
142C22×Dic22C2311yescharacteristic
143C11×#125—24no—
144C4×D4×C11—24no—
145C2×C11×C4⋊C4C2312yes—
146C2×C11×C4⋊C4C2312yes—
147C2×C11×C4⋊C4C2311yescharacteristic
148C2×C11×C4⋊C4C2311yescharacteristic
149C2×C11×C4⋊C4C2311yescharacteristic
150C2×C11×C4⋊C4C2311yescharacteristic
151C2×C11×C4⋊C4C2312yes—
152C2×C11×C4⋊C4C2312yes—
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C22⋊C4C2312yes—
155C2×C11×C22⋊C4C2312yes—
156C2×C11×C22⋊C4C2312yes—
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C42×C11C2311yescharacteristic
160C2×C42×C11C2311yescharacteristic
161C2×C42×C11C2311yescharacteristic
162C2×C22⋊Dic11C2312yes—
163C2×C22⋊Dic11C2312yes—
164C2×C22⋊Dic11C2312yes—
165C2×C22⋊Dic11C2312yes—
166C2×C22⋊Dic11C2312yes—
167D4×Dic11—24no—
168C4×C22⋊D11—28no—
169C2×(C2×D11)⋊C4C2312yes—
170C2×(C2×D11)⋊C4C2312yes—
171C2×(C2×D11)⋊C4C2312yes—
172C2×C4⋊Dic11C2311yescharacteristic
173C2×C4⋊Dic11C2311yescharacteristic
174C2×C4⋊Dic11C2311yescharacteristic
175C2×C4⋊Dic11C2312yes—
176C2×C4⋊Dic11C2312yes—
177C2×C4⋊Dic11C2311yescharacteristic
178C2×C4⋊Dic11C2311yescharacteristic
179#66977—28no—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2312yes—
188C2×Dic11⋊C4C2311yescharacteristic
189C2×Dic11⋊C4C2311yescharacteristic
190C2×Dic11⋊C4C2311yescharacteristic
191C2×Dic11⋊C4C2312yes—
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2311yescharacteristic
194C2×C4×Dic11—28no—
195C2×C4×Dic11C2312yes—
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2311yescharacteristic
199C2×C4×Dic11C2311yescharacteristic
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2311yescharacteristic
203C2×C4×Dic11C2311yescharacteristic
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2312yes—
206C2×C4×Dic11C2312yes—
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2312yes—
209#66949—28no—
210#66949—28no—
211#66945—24no—
212#66945—24no—
213#66945D418yes—
214C4⋊C4×D11—24no—
215C4⋊C4×D11—24no—
216#66941—24no—
217#66941—24no—
218#66940—24no—
219#66940—28no—
220#66940—28no—
221(C22⋊D11)⋊C4—28no—
222#66931—28no—
223#66930—28no—
224C42×D11—24no—
225C42×D11—24no—
226C42×D11—24no—
227#66923—24no—
228C4×Dic22—24no—
229C11×#95C2312yes—
230C11×#95C2311yescharacteristic
231C11×#95C2312yes—
232C11×#95C2311yescharacteristic
233C11⋊#95C2311yescharacteristic
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2311yescharacteristic
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2311yescharacteristic
252C11⋊#95C2312yes—
253#34745—111nomaximal, Sylow
254C24×C11C2412yes—
255C23×D11C2411yescharacteristic
256C2×D4×C11—22no—
257C2×D4×C11—22no—
258C2×D4×C11C2×Q814yes—
259C22×C4×C11—24no—
260C22×C4×C11—24no—
261C22×C4×C11—42no—
262C22×C4×C11C2411yescharacteristic
263C22×C4×C11C2412yes—
264C22×C4×C11C2411yescharacteristic
265C22×C4×C11C2411yescharacteristic
266C22×C4×C11C2411yescharacteristic
267C22×C4×C11C2412yes—
268C22×C4×C11C2412yes—
269C22×C4×C11C2411yescharacteristic
270C22×C4×C11C2411yescharacteristic
271C22×C4×C11C2411yescharacteristic
272C2×C22⋊D11—24no—
273C2×C22⋊D11—24no—
274C2×C22⋊D11C2×Q818yes—
275C22×Dic11—24no—
276C22×Dic11—24no—
277C22×Dic11—24no—
278C22×Dic11—24no—
279C22×Dic11—42no—
280C22×Dic11C2×Q818yes—
281C22×Dic11C2411yescharacteristic
282C22×Dic11C2412yes—
283C22×Dic11C2411yescharacteristic
284C22×Dic11C2412yes—
285C22×Dic11C2412yes—
286C22×Dic11C2412yes—
287C22×Dic11C2411yescharacteristic
288C22×Dic11C2411yescharacteristic
289C22×Dic11C2411yescharacteristic
290C22×Dic11C2411yescharacteristic
291C22×Dic11C2411yescharacteristic
292#4341—232no—
293C2×C4×D11—22no—
294C2×C4×D11—22no—
295C2×C4×D11—22no—
296C2×C4×D11—22no—
297C2×C4×D11—22no—
298C2×C4×D11—22no—
299C2×C4×D11—22no—
300C2×C4×D11—22no—
301C2×C4×D11—22no—
302C2×C4×D11—22no—
303C2×C4×D11—22no—
304C2×C4×D11—22no—
305C2×C4×D11—41no—
306C2×C4×D11—41no—
307C2×C4×D11—41no—
308C2×C4×D11—41no—
309C2×C4×D11—41no—
310C2×C4×D11—41no—
311C2×C4×D11C2×D414yes—
312C2×C4×D11C2×Q814yes—
313C2×C4×D11#4114yes—
314C2×Dic22—24no—
315C2×Dic22—24no—
316C2×Dic22—24no—
317C2×Dic22—22no—
318C2×Dic22—24no—
319C2×Dic22—22no—
320C2×Dic22—42no—
321C2×Dic22—42no—
322C2×Dic22C2×Q814yes—
323C11×C4⋊C4—24no—
324C11×C4⋊C4—24no—
325C11×C4⋊C4—22no—
326C11×C4⋊C4—22no—
327C11×C4⋊C4—22no—
328C11×C4⋊C4—22no—
329C11×C4⋊C4—42no—
330C11×C4⋊C4—42no—
331C11×C4⋊C4C2×D414yes—
332C11×C22⋊C4—24no—
333C11×C22⋊C4—24no—
334C11×C22⋊C4—42no—
335C11×C22⋊C4—42no—
336C11×C22⋊C4—42no—
337C42×C11—22no—
338C42×C11—22no—
339C42×C11—22no—
340C22⋊Dic11—24no—
341C22⋊Dic11—24no—
342C22⋊Dic11—24no—
343C22⋊Dic11—24no—
344C22⋊Dic11—42no—
345(C2×D11)⋊C4—24no—
346(C2×D11)⋊C4—24no—
347(C2×D11)⋊C4C2×D418yes—
348C4⋊Dic11—22no—
349C4⋊Dic11—24no—
350C4⋊Dic11—22no—
351C4⋊Dic11—22no—
352C4⋊Dic11—42no—
353C4⋊Dic11C2×D414yes—
354C4⋊Dic11#4114yescomplemented
355Dic11⋊C4—24no—
356Dic11⋊C4—24no—
357Dic11⋊C4—24no—
358Dic11⋊C4—24no—
359Dic11⋊C4—24no—
360Dic11⋊C4—22no—
361Dic11⋊C4—22no—
362Dic11⋊C4—22no—
363Dic11⋊C4—24no—
364Dic11⋊C4—24no—
365Dic11⋊C4—24no—
366Dic11⋊C4—24no—
367Dic11⋊C4—42no—
368Dic11⋊C4#4114yescomplemented
369C4×Dic11—24no—
370C4×Dic11—22no—
371C4×Dic11—22no—
372C4×Dic11—22no—
373C4×Dic11—22no—
374C4×Dic11—24no—
375C4×Dic11—22no—
376C4×Dic11—22no—
377C4×Dic11—24no—
378C4×Dic11—22no—
379C4×Dic11—22no—
380C4×Dic11—24no—
381C4×Dic11—22no—
382C4×Dic11C2×D418yes—
383C2×#533—111no—
384C2×C4×#41—111no—
385#2454—111no—
386#2454D1111yescharacteristic, complemented
387#2453—111no—
388#2453—111no—
389#2452—111no—
390#2452—111no—
391#2451—111no—
392#2451—111no—
393#2450—112no—
394#2450—112no—
395#2449—112no—
396#2449—112no—
397#2396—112no—
398#2396—112no—
399C4×C22⋊Q8—112no—
400C4×C22⋊Q8—112no—
401#2297—111no—
402#2297—111no—
403#2296—111no—
404#2296—111no—
405C2×C4×C4⋊C4—111no—
406C23×C11—22no—
407C23×C11—22no—
408C23×C11—22no—
409C23×C11—22no—
410C23×C11—22no—
411C23×C11—22no—
412C23×C11C22×Q814yes—
413C23×C11C2511yescharacteristic
414C22×D11—21no—
415C22×D11—21no—
416C22×D11—21no—
417C22×D11—21no—
418C22×D11C22×D412yes—
419C22×D11C22×Q812yes—
420C22×D11C2×#4112yes—
421D4×C11—28no—
422C2×C4×C11—21no—
423C2×C4×C11—21no—
424C2×C4×C11—21no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—21no—
428C2×C4×C11—21no—
429C2×C4×C11—21no—
430C2×C4×C11—21no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—21no—
434C2×C4×C11—22no—
435C2×C4×C11—21no—
436C2×C4×C11—21no—
437C2×C4×C11—21no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—21no—
441C2×C4×C11—21no—
442C2×C4×C11—21no—
443C2×C4×C11—22no—
444C2×C4×C11—21no—
445C2×C4×C11—21no—
446C2×C4×C11—48no—
447C2×C4×C11C22×D414yes—
448C2×C4×C11C22×D412yes—
449C2×C4×C11C22×Q812yes—
450C2×C4×C11C2×#4112yes—
451C2×C4×C11C2×#4112yes—
452C2×C4×C11C2×#4112yes—
453C22⋊D11—216no—
454C2×Dic11—21no—
455C2×Dic11—21no—
456C2×Dic11—21no—
457C2×Dic11—22no—
458C2×Dic11—21no—
459C2×Dic11—21no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—21no—
464C2×Dic11—21no—
465C2×Dic11—21no—
466C2×Dic11—216no—
467C2×Dic11—21no—
468C2×Dic11—22no—
469C2×Dic11—21no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—21no—
474C2×Dic11—22no—
475C2×Dic11—21no—
476C2×Dic11—21no—
477C2×Dic11—22no—
478C2×Dic11—21no—
479C2×Dic11—48no—
480C2×Dic11C22×D414yes—
481C2×Dic11C22×D412yes—
482C2×Dic11C22×Q814yes—
483C2×Dic11C22×Q812yes—
484C2×Dic11C2×#4112yes—
485C2×Dic11C2×#4112yes—
486C2×Dic11C2×#4112yes—
487C2×Dic11C2×#4112yes—
488C2×Dic11C2×#4112yes—
489C4×D11—28no—
490C4×D11—44no—
491C4×D11—44no—
492C4×D11—44no—
493C4×D11—44no—
494C4×D11—44no—
495C4×D11C22⋊Q8116yescomplemented
496Dic22—28no—
497Dic22—48no—
498Dic22—48no—
499C22×#41—111no—
500#533—228no—
501C2×C4⋊Q8—111no—
502C2×C4⋊Q8—111no—
503C2×#125—111no—
504C2×#125C2×D1111yescharacteristic
505C2×C22⋊Q8—112no—
506C2×C22⋊Q8—112no—
507C2×C22⋊Q8—112no—
508C2×C22⋊Q8—112no—
509C4×#41—228no—
510C2×C4×Q8—112no—
511C2×C4×Q8—112no—
512C2×C4×Q8—111no—
513C2×C4×Q8—111no—
514C2×C4×D4—111no—
515C2×C4×D4—112no—
516C2×C4×D4—112no—
517C2×C4×D4C2×D1111yescharacteristic
518C2×#117—111no—
519C2×#117—111no—
520C2×#117—111no—
521C2×#117—112no—
522C22×C4⋊C4—111no—
523C22×C4⋊C4—111no—
524C22×C42—112no—
525C22×C42—111no—
526C22×C42—111no—
527C22×C42—111no—
528#400—112no—
529#400—112no—
530#399—112no—
531#399C2×D1112yes—
532#398—112no—
533#398—112no—
534#398—112no—
535#398—112no—
536#396—112no—
537#396—112no—
538#396—112no—
539#396C2×D1112yes—
540#395—112no—
541#395—112no—
542#393—112no—
543#393—112no—
544#391—112no—
545#391—111no—
546#391—111no—
547#391—111no—
548#391—111no—
549#391—112no—
550#390—111no—
551#390—111no—
552#390C2×D1111yescharacteristic
553#390C2×D1111yescharacteristic
554#389—112no—
555#389—112no—
556#389—111no—
557#389—111no—
558#389—111no—
559#389—111no—
560#389—111no—
561#389—111no—
562#389C2×D1111yescharacteristic
563#389C2×D1111yescharacteristic
564#387—112no—
565#387—112no—
566#387—112no—
567#387—112no—
568#386—112no—
569#386—112no—
570#386—112no—
571#386—112no—
572#385—112no—
573#385—112no—
574#385—112no—
575#385—112no—
576#385—112no—
577#385—112no—
578#385—112no—
579#385C2×D1112yes—
580#380—112no—
581#380C2×D1112yes—
582C4×C4⋊C4—111no—
583C4×C4⋊C4—112no—
584C4×C4⋊C4—112no—
585C4×C4⋊C4—111no—
586C4×C4⋊C4—111no—
587C4×C4⋊C4—111no—
588C4×C4⋊C4—111no—
589C4×C4⋊C4—111no—
590C4×C4⋊C4—112no—
591C4×C4⋊C4—111no—
592C4×C4⋊C4—112no—
593C4×C4⋊C4C2×D1111yescharacteristic
594C4×C22⋊C4—112no—
595C4×C22⋊C4—112no—
596C4×C22⋊C4—112no—
597C4×C22⋊C4—112no—
598C2×#95—111no—
599C2×#95—111no—
600C22×C11—24no—
601C22×C11—24no—
602C22×C11—24no—
603C22×C11—42no—
604C22×C11—42no—
605C22×C11—42no—
606C22×C11—42no—
607C22×C11C23×D411yescharacteristic
608C22×C11C23×Q811yescharacteristic
609C22×C11C22×#4111yescharacteristic
610C22×C11C22×#4111yescharacteristic
611C22×C11C22×#4111yescharacteristic
612C22×C11#58511yescharacteristic
613C22×C11#58511yescharacteristic
614C2×D11—22no—
615C2×D11—22no—
616C2×D11—22no—
617C2×D11—22no—
618C2×D11—22no—
619C2×D11—22no—
620C2×D11C2×C22⋊Q814yes—
621C4×C11—22no—
622C4×C11—22no—
623C4×C11—24no—
624C4×C11—42no—
625C4×C11—41no—
626C4×C11—42no—
627C4×C11—41no—
628C4×C11—41no—
629C4×C11—41no—
630C4×C11C2×C22⋊Q814yes—
631Dic11—24no—
632Dic11—22no—
633Dic11—22no—
634Dic11—22no—
635Dic11—24no—
636Dic11—22no—
637Dic11—42no—
638Dic11—41no—
639Dic11—42no—
640Dic11—41no—
641Dic11C2×C22⋊Q814yes—
642C2×#41—118no—
643C2×#41—224no—
644C2×#41—224no—
645C22×Q8—111no—
646C22×Q8—112no—
647C22×Q8—112no—
648C22×D4—112no—
649C22×D4C22×D1111yescharacteristic
650C23×C4—111no—
651C23×C4—112no—
652C23×C4—112no—
653C23×C4—111no—
654C23×C4—111no—
655C23×C4—111no—
656C23×C4—111no—
657C23×C4—111no—
658C23×C4—111no—
659C23×C4C22×D1112yes—
660C4⋊Q8—224no—
661C4⋊Q8—224no—
662#125—24no—
663#125—224no—
664C22⋊Q8—228no—
665C22⋊Q8—228no—
666C22⋊Q8—228no—
667C22⋊Q8—228no—
668C4×Q8—224no—
669C4×Q8—228no—
670C4×Q8—228no—
671C4×Q8—224no—
672C4×D4—24no—
673C4×D4—228no—
674C4×D4—228no—
675C4×D4—224no—
676#117—118no—
677#117—228no—
678#117—224no—
679#117—224no—
680C2×C4⋊C4—111no—
681C2×C4⋊C4—111no—
682C2×C4⋊C4—111no—
683C2×C4⋊C4—111no—
684C2×C4⋊C4—111no—
685C2×C4⋊C4—111no—
686C2×C4⋊C4—111no—
687C2×C4⋊C4—112no—
688C2×C4⋊C4—112no—
689C2×C4⋊C4—111no—
690C2×C4⋊C4—111no—
691C2×C4⋊C4—112no—
692C2×C4⋊C4—112no—
693C2×C4⋊C4—112no—
694C2×C4⋊C4—112no—
695C2×C4⋊C4—112no—
696C2×C4⋊C4—112no—
697C2×C4⋊C4—112no—
698C2×C4⋊C4—112no—
699C2×C4⋊C4—112no—
700C2×C4⋊C4—112no—
701C2×C4⋊C4—224no—
702C2×C4⋊C4—224no—
703C2×C4⋊C4C22×D1111yescharacteristic
704C2×C4⋊C4C22×D1111yescharacteristic
705C2×C4⋊C4C22×D1111yescharacteristic
706C2×C4⋊C4C22×D1111yescharacteristic
707C2×C4⋊C4C22×D1112yes—
708C2×C4⋊C4C22×D1112yes—
709C2×C4⋊C4C22×D1112yes—
710C2×C4⋊C4C22×D1112yes—
711C2×C4⋊C4C22×D1111yescharacteristic
712C2×C22⋊C4—112no—
713C2×C22⋊C4—112no—
714C2×C22⋊C4—112no—
715C2×C22⋊C4—112no—
716C2×C22⋊C4—112no—
717C2×C22⋊C4—112no—
718C2×C22⋊C4—112no—
719C2×C22⋊C4—112no—
720C2×C22⋊C4C22×D1112yes—
721C2×C22⋊C4C22×D1112yes—
722C2×C22⋊C4C22×D1112yes—
723C2×C22⋊C4C22×D1112yes—
724C2×C22⋊C4C22×D1112yes—
725C2×C42—112no—
726C2×C42—111no—
727C2×C42—112no—
728C2×C42—112no—
729C2×C42—111no—
730C2×C42—112no—
731C2×C42—112no—
732C2×C42—111no—
733C2×C42—111no—
734C2×C42—111no—
735C2×C42—111no—
736C2×C42—111no—
737C2×C42—111no—
738C2×C42—111no—
739C2×C42—224no—
740C2×C42—224no—
741C2×C42—224no—
742C2×C42—228no—
743C2×C42C22×D1111yescharacteristic
744C2×C42C22×D1111yescharacteristic
745C2×C42C22×D1111yescharacteristic
746#95—111no—
747#95—111no—
748#95—111no—
749#95—111no—
750#95—111no—
751#95—111no—
752#95—112no—
753#95—112no—
754#95—112no—
755#95—112no—
756#95—112no—
757#95—112no—
758#95—112no—
759#95—112no—
760#95—112no—
761#95—112no—
762#95—112no—
763#95—112no—
764#95—112no—
765#95—112no—
766#95C22×D1111yescharacteristic
767#95C22×D1111yescharacteristic
768#95C22×D1112yes—
769#95C22×D1112yes—
770C2×C11—44no—
771C2×C11C22×C22⋊Q811yescharacteristic
772C2×C11#344411yescharacteristic
773C2×C11#345511yescharacteristic
774C2×C11D4×#4111yescharacteristic
775C2×C11D4×#4111yescharacteristic
776C2×C11Q8×#4111yescharacteristic
777C2×C11Q8×#4111yescharacteristic
778D11—24no—
779C24—111no—
780C24C23×D1112yes—
781#41—2232no—
782C2×Q8—114no—
783C2×Q8—224no—
784C2×Q8—224no—
785C2×Q8—224no—
786C2×Q8—222no—
787C2×Q8—224no—
788C2×Q8—222no—
789C2×Q8—442no—
790C2×Q8—442no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—118no—
794C2×D4—224no—
795C2×D4—224no—
796C2×D4Q8×D1114yes—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—42no—
800C22×C4—111no—
801C22×C4—114no—
802C22×C4—114no—
803C22×C4—114no—
804C22×C4—118no—
805C22×C4—112no—
806C22×C4—111no—
807C22×C4—111no—
808C22×C4—111no—
809C22×C4—111no—
810C22×C4—112no—
811C22×C4—111no—
812C22×C4—112no—
813C22×C4—111no—
814C22×C4—112no—
815C22×C4—222no—
816C22×C4—222no—
817C22×C4—222no—
818C22×C4—222no—
819C22×C4—222no—
820C22×C4—222no—
821C22×C4—222no—
822C22×C4—222no—
823C22×C4—222no—
824C22×C4—222no—
825C22×C4—224no—
826C22×C4—224no—
827C22×C4—224no—
828C22×C4—224no—
829C22×C4—222no—
830C22×C4—222no—
831C22×C4—441no—
832C22×C4—441no—
833C22×C4—441no—
834C22×C4—441no—
835C22×C4—441no—
836C22×C4—441no—
837C22×C4—442no—
838C22×C4C23×D1111yescharacteristic
839C22×C4C23×D1112yes—
840C22×C4C23×D1111yescharacteristic
841C22×C4C23×D1111yescharacteristic
842C22×C4C23×D1111yescharacteristic
843C22×C4C23×D1112yes—
844C22×C4C23×D1112yes—
845C22×C4C23×D1111yescharacteristic
846C22×C4C23×D1111yescharacteristic
847C22×C4C23×D1111yescharacteristic
848C4⋊C4—22no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4—114no—
857C4⋊C4—114no—
858C4⋊C4—114no—
859C4⋊C4—222no—
860C4⋊C4—222no—
861C4⋊C4—222no—
862C4⋊C4—222no—
863C4⋊C4—224no—
864C4⋊C4—224no—
865C4⋊C4—224no—
866C4⋊C4—224no—
867C4⋊C4—224no—
868C4⋊C4—224no—
869C4⋊C4—224no—
870C4⋊C4—222no—
871C4⋊C4—224no—
872C4⋊C4—222no—
873C4⋊C4—224no—
874C4⋊C4—224no—
875C4⋊C4—442no—
876C4⋊C4—442no—
877C4⋊C4D4×D1114yes—
878C22⋊C4—24no—
879C22⋊C4—24no—
880C22⋊C4—42no—
881C22⋊C4—42no—
882C22⋊C4—42no—
883C22⋊C4—118no—
884C22⋊C4—224no—
885C22⋊C4—224no—
886C22⋊C4—224no—
887C22⋊C4—224no—
888C22⋊C4—224no—
889C22⋊C4—224no—
890C22⋊C4—442no—
891C42—22no—
892C42—22no—
893C42—22no—
894C42—118no—
895C42—222no—
896C42—222no—
897C42—224no—
898C42—222no—
899C42—222no—
900C42—222no—
901C42—222no—
902C42—224no—
903C42—224no—
904C42—224no—
905C42—222no—
906C42—222no—
907C42—222no—
908C11#3474511yescharacteristic, complemented, Sylow
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—112no—
916C23—112no—
917C23—112no—
918C23—221no—
919C23—221no—
920C23—221no—
921C23—221no—
922C23C2×Q8×D1114yes—
923C23C24×D1111yescharacteristic
924Q8—228no—
925Q8—448no—
926Q8—448no—
927D4—28no—
928D4—2216no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—22no—
939C2×C4—21no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—48no—
954C2×C4—112no—
955C2×C4—112no—
956C2×C4—112no—
957C2×C4—1116no—
958C2×C4—114no—
959C2×C4—114no—
960C2×C4—112no—
961C2×C4—112no—
962C2×C4—112no—
963C2×C4—112no—
964C2×C4—228no—
965C2×C4—2216no—
966C2×C4—221no—
967C2×C4—222no—
968C2×C4—221no—
969C2×C4—221no—
970C2×C4—221no—
971C2×C4—221no—
972C2×C4—222no—
973C2×C4—222no—
974C2×C4—222no—
975C2×C4—221no—
976C2×C4—221no—
977C2×C4—221no—
978C2×C4—221no—
979C2×C4—222no—
980C2×C4—221no—
981C2×C4—222no—
982C2×C4—222no—
983C2×C4—222no—
984C2×C4—222no—
985C2×C4—221no—
986C2×C4—221no—
987C2×C4—222no—
988C2×C4—221no—
989C2×C4—221no—
990C2×C4—444no—
991C2×C4—444no—
992C2×C4—444no—
993C2×C4—444no—
994C2×C4—444no—
995C2×C4—448no—
996C2×C4C2×D4×D1114yes—
997C2×C4C2×D4×D1112yes—
998C2×C4C2×Q8×D1112yes—
999C2×C4#41×D1112yes—
1000C2×C4#41×D1112yes—
1001C2×C4#41×D1112yes—
1002C22—24no—
1003C22—24no—
1004C22—24no—
1005C22—42no—
1006C22—42no—
1007C22—42no—
1008C22—42no—
1009C22—114no—
1010C22—222no—
1011C22—222no—
1012C22—222no—
1013C22—222no—
1014C22—222no—
1015C22—222no—
1016C22C22×D4×D1111yescharacteristic
1017C22C22×Q8×D1111yescharacteristic
1018C22C2×#41×D1111yescharacteristic
1019C22C2×#41×D1111yescharacteristic
1020C22C2×#41×D1111yescharacteristic
1021C22#1062345511yescharacteristic
1022C22#1062345511yescharacteristic
1023C4—22no—
1024C4—22no—
1025C4—24no—
1026C4—41no—
1027C4—42no—
1028C4—41no—
1029C4—41no—
1030C4—41no—
1031C4—42no—
1032C4—114no—
1033C4—222no—
1034C4—224no—
1035C4—222no—
1036C4—222no—
1037C4—222no—
1038C4—224no—
1039C4—442no—
1040C4—441no—
1041C4—441no—
1042C4—442no—
1043C4D11×C22⋊Q814yes—
1044C2—44no—
1045C2—224no—
1046C2C2×D11×C22⋊Q811yescharacteristic
1047C2#1308191011yescharacteristic
1048C2#1308200011yescharacteristic
1049C2#1308210011yescharacteristic
1050C2#1308210611yescharacteristic
1051C2#1308219511yescharacteristic
1052C2#1308219511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2454C2
prime radicalC22×#4341C22
hypercenter#2454D11
hypocenterC11#34745
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2454

Complements

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

NH ≅ G/Ntype
1. C2×#10623219C2semidirect
3. #13072490C2semidirect
4. #13072477C2semidirect
5. #13072473C2semidirect
6. #13072469C2semidirect
7. #13072460C2semidirect
8. #13072456C2semidirect
9. #13072453C2semidirect
10. #13072447C2semidirect
11. #13072435C2semidirect
12. #13072428C2semidirect
13. #13072424C2semidirect
14. #13071891C2semidirect
15. #13071885C2semidirect
16. #13071148C2semidirect
17. #13071144C2semidirect
20. #13071097C2semidirect
21. #13071097C2semidirect
22. C4×C4⋊C4×D11C2semidirect
23. C11×#2454C2semidirect
132. C2×#4341Q8semidirect
354. C4⋊Dic11#41semidirect
368. Dic11⋊C4#41semidirect
386. #2454D11semidirect
495. C4×D11C22⋊Q8semidirect
908. C11#34745semidirect

Maximal subgroups

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

subgroupindex
C2×#106232192
C2×C4×#43412
#130724902
#130724772
#130724732
#130724692
#130724602
#130724562
#130724532
#130724472
#130724352
#130724282
#130724242
#130718912
#130718852
#130711482
#130711442
#130711032
#130710972
C4×C4⋊C4×D112
C11×#24542
#3474511