Finite Group Databasebeta

← #14914394

Subgroups — #14914394

Order 2816.

2186 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623059C211yesmaximal, characteristic
2#13071745C212yesmaximal, complemented
3#13071744C212yesmaximal, complemented
4#13071743C212yesmaximal, complemented
5#13071739C212yesmaximal, complemented
6#13071590C211yesmaximal, characteristic, complemented
7#13071587C211yesmaximal, characteristic, complemented
8#13071558C211yesmaximal, characteristic, complemented
9#13071549C211yesmaximal, characteristic, complemented
10#13071510C211yesmaximal, characteristic, complemented
11#13071476C211yesmaximal, characteristic, complemented
12#13071473C211yesmaximal, characteristic, complemented
13#13071304C212yesmaximal
14#13071293C212yesmaximal, complemented
15#13071266C211yesmaximal, characteristic, complemented
16#13071258C211yesmaximal, characteristic, complemented
17C4×#66942C212yesmaximal, complemented
18#13071157C212yesmaximal, complemented
19#13071013C211yesmaximal, characteristic, complemented
20#13070980C211yesmaximal, characteristic, complemented
21#13070975C211yesmaximal, characteristic, complemented
22C4×#66945C211yesmaximal, characteristic, complemented
23C11×#2347C211yesmaximal, characteristic, complemented
24C2×C11×#117C2211yescharacteristic
25C2×C4×C22⋊D11C2211yescharacteristic
26C2×C4×C22⋊D11C2211yescharacteristic
27#10623059C4116yescomplemented
28C2×#66951C2211yescharacteristic
29C2×#66949C2211yescharacteristic
30C2×#66947C2211yescharacteristic
31C2×#66945C2212yes—
32C2×#66942C2211yescharacteristic
33C2×#66940C2212yes—
34C2×#66938C2211yescharacteristic
35C2×#66937C2211yescharacteristic
36C2×#66936C2211yescharacteristic
37C2×(C22⋊D11)⋊C4C2212yes—
38C2×#66932C2211yescharacteristic
39C2×C4×D44C2211yescharacteristic
40C2×#66925C2211yescharacteristic
41C2×C42×D11C2211yescharacteristic
42C2×C4×Dic22C2211yescharacteristic
43C11×#389C2212yes—
44C11×#388C2212yes—
45C11×#388C2212yes—
46C11×#383C2211yescharacteristic
47C11×#383C2211yescharacteristic
48C11×#380C2211yescharacteristic
49C4×C11×C4⋊C4C2212yes—
50C4×C11×C4⋊C4C2211yescharacteristic
51C4×C11×C4⋊C4C2211yescharacteristic
52C4×C11×C22⋊C4C2211yescharacteristic
53#10622824C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55#10622603C2212yes—
56#10622603C2212yes—
57#10622603C2212yes—
58#10622603C2212yes—
59#10622603C2212yes—
60#10622594C2212yes—
61#10622594C2212yes—
62#10622591C2212yes—
63C4⋊C4×Dic11C2212yes—
64C4⋊C4×Dic11C2212yes—
65#10622585C2212yes—
66#10622585C2212yes—
67#10622571C2212yes—
68#10622570C2212yes—
69#10622570C2212yes—
70#10622563C2212yes—
71#10622558C2212yes—
72#10622557C2212yes—
73C22⋊C4×Dic11C2212yes—
74C22⋊C4×Dic11C2212yes—
75C22⋊C4×Dic11C2212yes—
76#10622553C2212yes—
77#10622553C2212yes—
78#10622552C2212yes—
79C4×(C2×D11)⋊C4C2212yes—
80C4×(C2×D11)⋊C4C2212yes—
81#10622550C2211yescharacteristic
82#10622549C2211yescharacteristic
83C4×C4⋊Dic11C2212yes—
84C4×C4⋊Dic11C2211yescharacteristic
85#10622545C2211yescharacteristic
86C4×Dic11⋊C4C2212yes—
87C4×Dic11⋊C4C2212yes—
88C4×Dic11⋊C4C2212yes—
89C4×Dic11⋊C4C2212yes—
90C4×Dic11⋊C4C2212yes—
91C42×Dic11C2212yes—
92#10622282C2212yes—
93#10622281C2212yes—
94#10622280C2211yescharacteristic
95#10622280C2212yes—
96#10622279C2212yes—
97#10622279C2212yes—
98#10622279C2211yescharacteristic
99#10622279C2211yescharacteristic
100#10622279C2211yescharacteristic
101#10622279C2212yes—
102#10622278C2212yes—
103#10622277C2211yescharacteristic
104#10622277C2211yescharacteristic
105#10622277C2211yescharacteristic
106D11×#95C2211yescharacteristic
107#10622268C2212yes—
108#10622268C2212yes—
109#10622266C2212yes—
110#10622266C2212yes—
111#10622265C2212yes—
112#10622264C2211yescharacteristic
113#10622263C2212yes—
114#10622263C2211yescharacteristic
115#10622262C2211yescharacteristic
116#10622262C2211yescharacteristic
117#10622262C2211yescharacteristic
118#10622261C2211yescharacteristic
119#10622261C2211yescharacteristic
120#10622261C2211yescharacteristic
121#10622261C2212yes—
122#10622260C2212yes—
123#10622259C2212yes—
124C23×C4×C11C2311yescharacteristic
125C22×C22⋊D11C2311yescharacteristic
126C22×C22⋊D11C2311yescharacteristic
127C23×Dic11C2312yes—
128C22×D44C2311yescharacteristic
129C22×C4×D11C2311yescharacteristic
130C22×C4×D11C2312yes—
131C22×C4×D11C2311yescharacteristic
132C22×C4×D11C2311yescharacteristic
133C22×C4×D11C2311yescharacteristic
134C22×Dic22C2311yescharacteristic
135C11×#117C2×C418yescomplemented
136C2×C11×C4⋊C4C2312yes—
137C2×C11×C4⋊C4C2312yes—
138C2×C11×C4⋊C4C2312yes—
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C22⋊C4C2312yes—
142C2×C11×C22⋊C4C2312yes—
143C2×C11×C22⋊C4C2311yescharacteristic
144C2×C11×C22⋊C4C2311yescharacteristic
145C2×C42×C11C2312yes—
146C2×C42×C11C2312yes—
147C2×C42×C11C2312yes—
148C2×C42×C11C2311yescharacteristic
149C2×C42×C11C2311yescharacteristic
150C2×C22⋊Dic11C2312yes—
151C2×C22⋊Dic11C2311yescharacteristic
152C2×C22⋊Dic11C2311yescharacteristic
153C4×C22⋊D11C2×C418yes—
154C4×C22⋊D11C2×C418yescomplemented
155C2×(C2×D11)⋊C4C2312yes—
156C2×(C2×D11)⋊C4C2312yes—
157C2×(C2×D11)⋊C4C2312yes—
158C2×(C2×D11)⋊C4C2312yes—
159C2×(C2×D11)⋊C4C2312yes—
160C2×(C2×D11)⋊C4C2312yes—
161C2×(C2×D11)⋊C4C2312yes—
162C2×(C2×D11)⋊C4C2311yescharacteristic
163C2×(C2×D11)⋊C4C2311yescharacteristic
164C2×(C2×D11)⋊C4C2311yescharacteristic
165C2×(C2×D11)⋊C4C2311yescharacteristic
166C2×(C2×D11)⋊C4C2311yescharacteristic
167C2×(C2×D11)⋊C4C2311yescharacteristic
168C2×C4⋊Dic11C2312yes—
169C2×C4⋊Dic11C2312yes—
170C2×C4⋊Dic11C2311yescharacteristic
171C2×C4⋊Dic11C2311yescharacteristic
172C2×Dic11⋊C4C2312yes—
173C2×Dic11⋊C4C2312yes—
174C2×Dic11⋊C4C2312yes—
175C2×Dic11⋊C4C2312yes—
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2311yescharacteristic
178C2×Dic11⋊C4C2311yescharacteristic
179C2×Dic11⋊C4C2311yescharacteristic
180C2×Dic11⋊C4C2311yescharacteristic
181C2×Dic11⋊C4C2311yescharacteristic
182C2×Dic11⋊C4C2311yescharacteristic
183C2×C4×Dic11C2312yes—
184C2×C4×Dic11C2312yes—
185C2×C4×Dic11C2312yes—
186C2×C4×Dic11C2312yes—
187C2×C4×Dic11C2312yes—
188C2×C4×Dic11C2312yes—
189C2×C4×Dic11C2312yes—
190C2×C4×Dic11C2312yes—
191C2×C4×Dic11C2312yes—
192C2×C4×Dic11C2312yes—
193C2×C4×Dic11C2311yescharacteristic
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2312yes—
198#66951C2×C418yescomplemented
199#66949C2×C418yescomplemented
200#66947C2×C418yescomplemented
201#66945—28no—
202#66942C2×C418yescomplemented
203#66940—28no—
204#66938C2×C418yes—
205#66937C2×C418yes—
206#66936C2×C418yescomplemented
207(C22⋊D11)⋊C4—28no—
208#66932C2×C418yescomplemented
209C4×D44C2×C418yescomplemented
210#66925C2×C418yescomplemented
211C42×D11C2×C418yescomplemented
212C4×Dic22C2×C418yescomplemented
213C11×#95C2312yes—
214C11×#95C2312yes—
215C11×#95C2311yescharacteristic
216C11×#95C2311yescharacteristic
217C11×#95C2311yescharacteristic
218C11×#95C2312yes—
219C11×#95C2311yescharacteristic
220C11×#95C2312yes—
221C11⋊#95C2312yes—
222C11⋊#95C2312yes—
223C11⋊#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2311yescharacteristic
226C11⋊#95C2312yes—
227C11⋊#95C2311yescharacteristic
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2311yescharacteristic
234C11⋊#95C2311yescharacteristic
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241#34227—111nomaximal, Sylow
242C24×C11C2411yescharacteristic
243C23×D11C2411yescharacteristic
244C23×D11C2411yescharacteristic
245C22×C4×C11—42no—
246C22×C4×C11C22×C414yes—
247C22×C4×C11C2412yes—
248C22×C4×C11C2412yes—
249C22×C4×C11C2412yes—
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C22×C4×C11C2411yescharacteristic
255C22×C4×C11C2411yescharacteristic
256C22×C4×C11C2412yes—
257C2×C22⋊D11—24no—
258C2×C22⋊D11—41no—
259C2×C22⋊D11—41no—
260C2×C22⋊D11C22×C414yes—
261C2×C22⋊D11C22×C414yes—
262C22×Dic11—24no—
263C22×Dic11—42no—
264C22×Dic11—42no—
265C22×Dic11C2412yes—
266C22×Dic11C2412yes—
267C22×Dic11C2412yes—
268C22×Dic11C2411yescharacteristic
269C22×Dic11C2411yescharacteristic
270C22×Dic11C2411yescharacteristic
271C22×Dic11C2411yescharacteristic
272C22×Dic11C2411yescharacteristic
273C22×Dic11C2412yes—
274C22×Dic11C2411yescharacteristic
275C2×D44—41no—
276C2×D44—41no—
277C2×D44C22×C414yes—
278C2×C4×D11—24no—
279C2×C4×D11—24no—
280C2×C4×D11—41no—
281C2×C4×D11—41no—
282C2×C4×D11—42no—
283C2×C4×D11—42no—
284C2×C4×D11—42no—
285C2×C4×D11—42no—
286C2×C4×D11C22×C414yes—
287C2×C4×D11C22×C414yes—
288C2×C4×D11C22×C414yes—
289C2×C4×D11C22×C414yes—
290C2×Dic22—24no—
291C2×Dic22C22×C414yes—
292C11×C4⋊C4—24no—
293C11×C4⋊C4—24no—
294C11×C4⋊C4—42no—
295C11×C4⋊C4C22×C414yes—
296C11×C4⋊C4C22×C414yes—
297C11×C22⋊C4—24no—
298C11×C22⋊C4—42no—
299C11×C22⋊C4C22×C414yes—
300C11×C22⋊C4C22×C414yes—
301C42×C11—42no—
302C42×C11—42no—
303C42×C11—42no—
304C42×C11C22×C414yes—
305C42×C11C22×C414yes—
306C22⋊Dic11—42no—
307C22⋊Dic11C22×C414yes—
308C22⋊Dic11C22×C414yes—
309(C2×D11)⋊C4—24no—
310(C2×D11)⋊C4—24no—
311(C2×D11)⋊C4—24no—
312(C2×D11)⋊C4—42no—
313(C2×D11)⋊C4—42no—
314(C2×D11)⋊C4—42no—
315(C2×D11)⋊C4—42no—
316(C2×D11)⋊C4C22×C414yes—
317(C2×D11)⋊C4C22×C414yes—
318(C2×D11)⋊C4C22×C414yes—
319(C2×D11)⋊C4C22×C414yes—
320(C2×D11)⋊C4C22×C414yes—
321(C2×D11)⋊C4C22×C414yes—
322C4⋊Dic11—24no—
323C4⋊Dic11—42no—
324C4⋊Dic11C22×C414yes—
325C4⋊Dic11C22×C414yes—
326Dic11⋊C4—24no—
327Dic11⋊C4—24no—
328Dic11⋊C4—24no—
329Dic11⋊C4—42no—
330Dic11⋊C4—42no—
331Dic11⋊C4C22×C414yes—
332Dic11⋊C4C22×C414yes—
333Dic11⋊C4C22×C414yes—
334Dic11⋊C4C22×C414yes—
335Dic11⋊C4C22×C414yes—
336Dic11⋊C4C22×C414yes—
337C4×Dic11—24no—
338C4×Dic11—24no—
339C4×Dic11—24no—
340C4×Dic11—42no—
341C4×Dic11—42no—
342C4×Dic11—42no—
343C4×Dic11—42no—
344C4×Dic11—42no—
345C4×Dic11—42no—
346C4×Dic11—42no—
347C4×Dic11C22×C414yes—
348C4×Dic11C22×C414yes—
349C4×Dic11C22×C414yes—
350C4×Dic11C22×C414yes—
351C4×Dic11#4118yes—
352C2×#529—111no—
353#2374—112no—
354#2374—112no—
355#2373—112no—
356#2373—112no—
357#2357—111no—
358#2357—111no—
359#2353—111no—
360#2353—111no—
361#2347—111no—
362#2347D1111yescharacteristic, complemented
363#2343—111no—
364#2343—111no—
365#2324—112no—
366#2323—112no—
367#2320—111no—
368#2319—111no—
369C4×#125—112no—
370C4×#124—112no—
371#2283—111no—
372#2276—111no—
373#2275—111no—
374C4×#117—111no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—21no—
378C23×C11—21no—
379C23×C11C23×C412yes—
380C23×C11C2511yescharacteristic
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—21no—
385C22×D11—22no—
386C22×D11—21no—
387C22×D11—21no—
388C22×D11—21no—
389C22×D11C23×C412yes—
390C22×D11C23×C412yes—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—21no—
395C2×C4×C11—22no—
396C2×C4×C11—21no—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—44no—
411C2×C4×C11C23×C412yes—
412C2×C4×C11C23×C412yes—
413C2×C4×C11C23×C412yes—
414C2×C4×C11C23×C412yes—
415C2×C4×C11C23×C412yes—
416C2×C4×C11C23×C412yes—
417C2×C4×C11C2×#4114yes—
418C22⋊D11—28no—
419C22⋊D11—44no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—21no—
423C2×Dic11—21no—
424C2×Dic11—21no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—21no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—84no—
439C2×Dic11C23×C412yes—
440C2×Dic11C23×C412yes—
441C2×Dic11C23×C412yes—
442C2×Dic11C23×C412yes—
443C2×Dic11C23×C412yes—
444C2×Dic11C23×C412yes—
445C2×Dic11C2×#4114yes—
446C2×Dic11C2×#4114yes—
447D44—44no—
448C4×D11—28no—
449C4×D11—44no—
450C4×D11—44no—
451C4×D11—44no—
452C4×D11—84no—
453Dic22—28no—
454#529—1116no—
455C2×#126—111no—
456C2×#126—111no—
457C2×#125—111no—
458C2×#124—111no—
459C2×#123—111no—
460C2×#123—111no—
461C2×C22⋊Q8—111no—
462C2×#121—111no—
463C2×C4×Q8—112no—
464C2×C4×Q8—111no—
465C2×C4×D4—111no—
466C2×C4×D4—111no—
467C2×C4×D4—112no—
468C2×C4×D4—111no—
469C2×#117—112no—
470C2×#117—111no—
471C2×#117C2×D1111yescharacteristic
472C22×C42—111no—
473#391—112no—
474#390—112no—
475#390—112no—
476#390—112no—
477#389—112no—
478#389—112no—
479#389—112no—
480#389C2×D1112yes—
481#388—112no—
482#388—112no—
483#388—112no—
484#388—112no—
485#388—112no—
486#388—112no—
487#388—112no—
488#388—112no—
489#388—112no—
490#388—112no—
491#388C2×D1112yes—
492#388C2×D1112yes—
493#387—112no—
494#387—112no—
495#387—112no—
496#387—112no—
497#387—112no—
498#387—112no—
499#387—112no—
500#387—112no—
501#386—112no—
502#386—112no—
503#385—112no—
504#385—112no—
505#383—111no—
506#383—111no—
507#383C2×D1111yescharacteristic
508#383C2×D1111yescharacteristic
509#382—111no—
510#382—112no—
511#382—111no—
512#381—111no—
513#381—111no—
514#381—111no—
515#381—111no—
516#380—111no—
517#380—112no—
518#380C2×D1111yescharacteristic
519C4×C4⋊C4—112no—
520C4×C4⋊C4—112no—
521C4×C4⋊C4—112no—
522C4×C4⋊C4—112no—
523C4×C4⋊C4—112no—
524C4×C4⋊C4—112no—
525C4×C4⋊C4—112no—
526C4×C4⋊C4—111no—
527C4×C4⋊C4—112no—
528C4×C4⋊C4—111no—
529C4×C4⋊C4—111no—
530C4×C4⋊C4—111no—
531C4×C4⋊C4C2×D1112yes—
532C4×C4⋊C4C2×D1111yescharacteristic
533C4×C4⋊C4C2×D1111yescharacteristic
534C4×C22⋊C4—112no—
535C4×C22⋊C4—112no—
536C4×C22⋊C4—112no—
537C4×C22⋊C4—112no—
538C4×C22⋊C4—112no—
539C4×C22⋊C4—112no—
540C4×C22⋊C4—111no—
541C4×C22⋊C4—111no—
542C4×C22⋊C4—112no—
543C4×C22⋊C4—111no—
544C4×C22⋊C4—112no—
545C4×C22⋊C4C2×D1111yescharacteristic
546#376—111no—
547#376—111no—
548#376—111no—
549#376—112no—
550#376—111no—
551C2×#95—111no—
552C2×#95—111no—
553C43—112no—
554C22×C11—22no—
555C22×C11—22no—
556C22×C11—22no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11C24×C411yescharacteristic
560C22×C11C22×#4112yes—
561C22×C11#58512yes—
562C22×C11#58511yescharacteristic
563C22×C11#58511yescharacteristic
564C2×D11—22no—
565C2×D11—22no—
566C2×D11—22no—
567C2×D11—22no—
568C2×D11—22no—
569C2×D11—22no—
570C2×D11—42no—
571C2×D11—42no—
572C2×D11—42no—
573C2×D11—42no—
574C4×C11—22no—
575C4×C11—22no—
576C4×C11—22no—
577C4×C11—22no—
578C4×C11—22no—
579C4×C11—22no—
580C4×C11—24no—
581C4×C11—42no—
582C4×C11—42no—
583C4×C11—42no—
584Dic11—22no—
585Dic11—22no—
586Dic11—22no—
587Dic11—22no—
588Dic11—22no—
589Dic11—24no—
590Dic11—42no—
591Dic11—42no—
592Dic11—42no—
593Dic11C4×#4114yes—
594C22×Q8—111no—
595C22×D4—111no—
596C22×D4—111no—
597C22×D4—111no—
598C23×C4—111no—
599C23×C4—111no—
600C23×C4—111no—
601C23×C4—111no—
602C23×C4—112no—
603C23×C4—112no—
604C23×C4C22×D1111yescharacteristic
605#126—118no—
606#126—118no—
607#125—118no—
608#124—118no—
609#123—118no—
610#123—118no—
611C22⋊Q8—118no—
612#121—118no—
613C4×Q8—118no—
614C4×Q8—228no—
615C4×D4—118no—
616C4×D4—118no—
617C4×D4—118no—
618C4×D4—228no—
619#117—118no—
620#117—228no—
621#117C4×D1118yescomplemented
622C2×C4⋊C4—111no—
623C2×C4⋊C4—111no—
624C2×C4⋊C4—111no—
625C2×C4⋊C4—111no—
626C2×C4⋊C4—111no—
627C2×C4⋊C4—111no—
628C2×C4⋊C4—111no—
629C2×C4⋊C4—111no—
630C2×C4⋊C4—112no—
631C2×C4⋊C4—112no—
632C2×C4⋊C4—112no—
633C2×C4⋊C4—112no—
634C2×C4⋊C4—112no—
635C2×C4⋊C4—112no—
636C2×C4⋊C4—112no—
637C2×C4⋊C4C22×D1112yes—
638C2×C4⋊C4C22×D1112yes—
639C2×C4⋊C4C22×D1112yes—
640C2×C4⋊C4C22×D1111yescharacteristic
641C2×C4⋊C4C22×D1111yescharacteristic
642C2×C22⋊C4—111no—
643C2×C22⋊C4—111no—
644C2×C22⋊C4—111no—
645C2×C22⋊C4—111no—
646C2×C22⋊C4—111no—
647C2×C22⋊C4—111no—
648C2×C22⋊C4—111no—
649C2×C22⋊C4—111no—
650C2×C22⋊C4—112no—
651C2×C22⋊C4—112no—
652C2×C22⋊C4—112no—
653C2×C22⋊C4—112no—
654C2×C22⋊C4—112no—
655C2×C22⋊C4—112no—
656C2×C22⋊C4—112no—
657C2×C22⋊C4—112no—
658C2×C22⋊C4C22×D1112yes—
659C2×C22⋊C4C22×D1112yes—
660C2×C22⋊C4C22×D1111yescharacteristic
661C2×C22⋊C4C22×D1111yescharacteristic
662C2×C42—112no—
663C2×C42—111no—
664C2×C42—111no—
665C2×C42—111no—
666C2×C42—111no—
667C2×C42—118no—
668C2×C42—112no—
669C2×C42—112no—
670C2×C42—112no—
671C2×C42—112no—
672C2×C42—112no—
673C2×C42—112no—
674C2×C42—112no—
675C2×C42—112no—
676C2×C42—112no—
677C2×C42—112no—
678C2×C42C22×D1112yes—
679C2×C42C22×D1112yes—
680C2×C42C22×D1112yes—
681C2×C42C22×D1111yescharacteristic
682C2×C42C22×D1111yescharacteristic
683#95—111no—
684#95—111no—
685#95—112no—
686#95—112no—
687#95—112no—
688#95—111no—
689#95—112no—
690#95—112no—
691#95—112no—
692#95—111no—
693#95—112no—
694#95—112no—
695#95—112no—
696#95—112no—
697#95—112no—
698#95—112no—
699#95—112no—
700#95—112no—
701#95—112no—
702#95—112no—
703#95C22×D1111yescharacteristic
704#95C22×D1111yescharacteristic
705#95C22×D1111yescharacteristic
706#95C22×D1111yescharacteristic
707#95C22×D1112yes—
708#95C22×D1112yes—
709#95C22×D1112yes—
710#95C22×D1112yes—
711C2×C11—42no—
712C2×C11C2×C4×#4111yescharacteristic
713C2×C11#342811yescharacteristic
714C2×C11#342811yescharacteristic
715C2×C11#351012yes—
716C2×C11#351212yes—
717D11—42no—
718D11—42no—
719C24—111no—
720C24—111no—
721C24C23×D1111yescharacteristic
722C2×Q8—114no—
723C2×Q8—224no—
724C2×D4—114no—
725C2×D4—114no—
726C2×D4—114no—
727C2×D4—224no—
728C2×D4—441no—
729C2×D4—441no—
730C2×D4—441no—
731C2×D4—441no—
732C22×C4—42no—
733C22×C4—111no—
734C22×C4—112no—
735C22×C4—111no—
736C22×C4—111no—
737C22×C4—111no—
738C22×C4—111no—
739C22×C4—111no—
740C22×C4—114no—
741C22×C4—114no—
742C22×C4—114no—
743C22×C4—114no—
744C22×C4—112no—
745C22×C4—112no—
746C22×C4—112no—
747C22×C4—224no—
748C22×C4—224no—
749C22×C4—224no—
750C22×C4—442no—
751C22×C4—442no—
752C22×C4—441no—
753C22×C4—441no—
754C22×C4—442no—
755C22×C4—442no—
756C22×C4—442no—
757C22×C4—442no—
758C22×C4C2×C4×D1114yes—
759C22×C4C23×D1112yes—
760C22×C4C23×D1112yes—
761C22×C4C23×D1112yes—
762C22×C4C23×D1111yescharacteristic
763C22×C4C23×D1111yescharacteristic
764C22×C4C23×D1111yescharacteristic
765C22×C4C23×D1111yescharacteristic
766C22×C4C23×D1111yescharacteristic
767C22×C4C23×D1111yescharacteristic
768C22×C4C23×D1112yes—
769C4⋊C4—24no—
770C4⋊C4—24no—
771C4⋊C4—42no—
772C4⋊C4—114no—
773C4⋊C4—114no—
774C4⋊C4—114no—
775C4⋊C4—114no—
776C4⋊C4—114no—
777C4⋊C4—114no—
778C4⋊C4—114no—
779C4⋊C4—114no—
780C4⋊C4—224no—
781C4⋊C4—224no—
782C4⋊C4—224no—
783C4⋊C4—224no—
784C4⋊C4—442no—
785C4⋊C4—442no—
786C4⋊C4—442no—
787C4⋊C4C2×C4×D1114yes—
788C4⋊C4C2×C4×D1114yes—
789C22⋊C4—24no—
790C22⋊C4—42no—
791C22⋊C4—114no—
792C22⋊C4—114no—
793C22⋊C4—114no—
794C22⋊C4—114no—
795C22⋊C4—114no—
796C22⋊C4—114no—
797C22⋊C4—114no—
798C22⋊C4—114no—
799C22⋊C4—224no—
800C22⋊C4—224no—
801C22⋊C4—224no—
802C22⋊C4—442no—
803C22⋊C4—442no—
804C22⋊C4—442no—
805C22⋊C4—442no—
806C22⋊C4—442no—
807C22⋊C4C2×C4×D1114yes—
808C22⋊C4C2×C4×D1114yes—
809C42—42no—
810C42—42no—
811C42—42no—
812C42—114no—
813C42—114no—
814C42—114no—
815C42—114no—
816C42—118no—
817C42—224no—
818C42—224no—
819C42—224no—
820C42—442no—
821C42—442no—
822C42—442no—
823C42—442no—
824C42—442no—
825C42—442no—
826C42—442no—
827C42C2×C4×D1114yes—
828C42C2×C4×D1114yes—
829C11#3422711yescharacteristic, complemented, Sylow
830C23—22no—
831C23—22no—
832C23—21no—
833C23—21no—
834C23—112no—
835C23—112no—
836C23—222no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—221no—
841C23—221no—
842C23—221no—
843C23—221no—
844C23C22×C4×D1112yes—
845C23C24×D1111yescharacteristic
846Q8—228no—
847D4—228no—
848D4—444no—
849D4—444no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—44no—
870C2×C4—112no—
871C2×C4—114no—
872C2×C4—112no—
873C2×C4—112no—
874C2×C4—112no—
875C2×C4—112no—
876C2×C4—112no—
877C2×C4—114no—
878C2×C4—228no—
879C2×C4—222no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—221no—
884C2×C4—221no—
885C2×C4—221no—
886C2×C4—222no—
887C2×C4—221no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—222no—
892C2×C4—222no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—444no—
898C2×C4—444no—
899C2×C4—444no—
900C2×C4—884no—
901C2×C4—884no—
902C2×C4C22×C4×D1112yes—
903C2×C4C22×C4×D1112yes—
904C2×C4C22×C4×D1112yes—
905C2×C4C22×C4×D1112yes—
906C2×C4C22×C4×D1112yes—
907C2×C4C22×C4×D1112yes—
908C2×C4#41×D1114yes—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—42no—
913C22—42no—
914C22—222no—
915C22—222no—
916C22—222no—
917C22—222no—
918C22—222no—
919C22—222no—
920C22—442no—
921C22—442no—
922C22—442no—
923C22—442no—
924C22C23×C4×D1111yescharacteristic
925C22C2×#41×D1112yes—
926C22#1062345312yes—
927C22#1062345511yescharacteristic
928C22#1062345711yescharacteristic
929C4—24no—
930C4—22no—
931C4—22no—
932C4—22no—
933C4—22no—
934C4—22no—
935C4—22no—
936C4—42no—
937C4—42no—
938C4—42no—
939C4—114no—
940C4—224no—
941C4—222no—
942C4—222no—
943C4—222no—
944C4—222no—
945C4—222no—
946C4—442no—
947C4—442no—
948C4—442no—
949C2—42no—
950C2—442no—
951C2—442no—
952C2C4×#41×D1111yescharacteristic
953C2#1308181611yescharacteristic
954C2#1308181711yescharacteristic
955C2#1308250612yes—
956C2#1308253212yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2347C2
socle, cosocleC23×C11C25
prime radicalC2×#66937C22
hypercenter#2347D11
hypocenterC11#34227
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2347

Complements

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

NH ≅ G/Ntype
2. #13071745C2semidirect
3. #13071744C2semidirect
4. #13071743C2semidirect
5. #13071739C2semidirect
6. #13071590C2semidirect
7. #13071587C2semidirect
8. #13071558C2semidirect
9. #13071549C2semidirect
10. #13071510C2semidirect
11. #13071476C2semidirect
12. #13071473C2semidirect
14. #13071293C2semidirect
15. #13071266C2semidirect
16. #13071258C2semidirect
17. C4×#66942C2semidirect
18. #13071157C2semidirect
19. #13071013C2semidirect
20. #13070980C2semidirect
21. #13070975C2semidirect
22. C4×#66945C2semidirect
23. C11×#2347C2semidirect
27. #10623059C4semidirect
135. C11×#117C2×C4semidirect
154. C4×C22⋊D11C2×C4semidirect
198. #66951C2×C4semidirect
199. #66949C2×C4semidirect
200. #66947C2×C4semidirect
202. #66942C2×C4semidirect
206. #66936C2×C4semidirect
208. #66932C2×C4semidirect
209. C4×D44C2×C4semidirect
210. #66925C2×C4semidirect
211. C42×D11C2×C4semidirect
212. C4×Dic22C2×C4semidirect
362. #2347D11semidirect
621. #117C4×D11semidirect
829. C11#34227semidirect

Maximal subgroups

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

subgroupindex
C2×#106230592
#130717452
#130717442
#130717432
#130717392
#130715902
#130715872
#130715582
#130715492
#130715102
#130714762
#130714732
#130713042
#130712932
#130712662
#130712582
C4×#669422
#130711572
#130710132
#130709802
#130709752
C4×#669452
C11×#23472
#3422711