Finite Group Databasebeta

← #14914933

Subgroups — #14914933

Order 2816.

2946 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623206C211yesmaximal, characteristic
2C2×#10623077C211yesmaximal, characteristic
3C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
4#13071691C211yesmaximal, characteristic, complemented
5#13071689C211yesmaximal, characteristic, complemented
6#13071686C211yesmaximal, characteristic, complemented
7#13071674C211yesmaximal, characteristic, complemented
8#13071673C211yesmaximal, characteristic, complemented
9#13071672C211yesmaximal, characteristic, complemented
10#13071670C211yesmaximal, characteristic, complemented
11#13071646C212yesmaximal, complemented
12#13071640C212yesmaximal, complemented
13#13071622C212yesmaximal, complemented
14#13071616C212yesmaximal, complemented
15#13071286C212yesmaximal, complemented
16#13071283C212yesmaximal, complemented
17#13071199C211yesmaximal, characteristic, complemented
18#13071143C212yesmaximal, complemented
19C4×#66936C212yesmaximal, complemented
20#13071103C211yesmaximal, characteristic
21#13071096C211yesmaximal, characteristic, complemented
22#13070970C211yesmaximal, characteristic, complemented
23C11×#2367C211yesmaximal, characteristic, complemented
24C22×Q8×D11C2211yescharacteristic
25C22×#4341C2211yescharacteristic
26C2×C11×#124C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×Q8×Dic11C2211yescharacteristic
30C2×#66997C2211yescharacteristic
31C2×#66989C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic
33C2×C4×C22⋊D11C2212yes—
34C22×Dic11⋊C4C2212yes—
35#10623206C4116yescomplemented
36C4×Q8×D11—28no—
37#10623077—28no—
38C2×#66945C2211yescharacteristic
39C2×C4⋊C4×D11C2212yes—
40C2×C4⋊C4×D11C2211yescharacteristic
41C2×#66940C2212yes—
42C2×#66940C2211yescharacteristic
43C2×#66940C2211yescharacteristic
44C2×#66936C2212yes—
45C2×#66936C2212yes—
46C2×(C22⋊D11)⋊C4C2212yes—
47C2×#66931C2212yes—
48C2×#66931C2212yes—
49C2×#66930C2212yes—
50C2×#66925C2211yescharacteristic
51C2×#66925C2211yescharacteristic
52C2×C42×D11C2212yes—
53C2×C42×D11C2211yescharacteristic
54C2×#66922C2211yescharacteristic
55C2×C4×Dic22C2212yes—
56C2×C4×Dic22C2211yescharacteristic
57C2×C4×Dic22C2211yescharacteristic
58C11×#391C2211yescharacteristic
59C11×#390C2211yescharacteristic
60C11×#388C2212yes—
61C11×#388C2212yes—
62C11×#385C2212yes—
63C4×C11×C4⋊C4C2211yescharacteristic
64C4×C11×C4⋊C4C2211yescharacteristic
65C4×C11×C22⋊C4C2212yes—
66#10622843C2211yescharacteristic
67#10622834C2211yescharacteristic
68#10622823C2212yes—
69C4×C22⋊Dic11C2212yes—
70#10622602C2211yescharacteristic
71#10622602C2211yescharacteristic
72#10622591C2212yes—
73C4⋊C4×Dic11C2212yes—
74C4⋊C4×Dic11C2211yescharacteristic
75C4⋊C4×Dic11C2211yescharacteristic
76#10622587C2211yescharacteristic
77#10622587C2211yescharacteristic
78#10622586C2212yes—
79#10622585C2211yescharacteristic
80#10622585C2212yes—
81#10622585C2211yescharacteristic
82#10622569C2212yes—
83#10622569C2212yes—
84#10622564C2212yes—
85#10622564C2212yes—
86#10622563C2212yes—
87#10622559C2212yes—
88#10622558C2212yes—
89#10622558C2212yes—
90#10622557C2212yes—
91#10622557C2212yes—
92C22⋊C4×Dic11C2212yes—
93C22⋊C4×Dic11C2212yes—
94C22⋊C4×Dic11C2212yes—
95C22⋊C4×Dic11C2212yes—
96C4×(C2×D11)⋊C4C2212yes—
97C4×C4⋊Dic11C2212yes—
98C4×C4⋊Dic11C2211yescharacteristic
99C4×C4⋊Dic11C2211yescharacteristic
100#10622546C2212yes—
101C4×Dic11⋊C4C2212yes—
102C4×Dic11⋊C4C2212yes—
103C4×Dic11⋊C4C2211yescharacteristic
104C4×Dic11⋊C4C2211yescharacteristic
105#10622542C2211yescharacteristic
106#10622542C2211yescharacteristic
107#10622541C2212yes—
108#10622281C2211yescharacteristic
109#10622281C2211yescharacteristic
110#10622279C2212yes—
111#10622277C2212yes—
112#10622277C2212yes—
113#10622268C2212yes—
114#10622267C2212yes—
115#10622267C2212yes—
116#10622266C2212yes—
117#10622266C2212yes—
118#10622265C2212yes—
119#10622262C2212yes—
120#10622262C2212yes—
121#10622260C2211yescharacteristic
122#10622260C2212yes—
123#10622260C2211yescharacteristic
124#10622259C2212yes—
125#10622259C2212yes—
126C22×Q8×C11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C22×C22⋊D11C2312yes—
130C23×Dic11C2312yes—
131C23×Dic11C2312yes—
132C2×Q8×D11—24no—
133C2×Q8×D11—24no—
134C2×Q8×D11C2×C418yescomplemented
135C2×#4341—24no—
136C2×#4341—24no—
137C2×#4341C2×C418yes—
138C22×C4×D11C2311yescharacteristic
139C22×C4×D11C2312yes—
140C22×C4×D11C2311yescharacteristic
141C22×C4×D11C2312yes—
142C22×C4×D11C2311yescharacteristic
143C22×Dic22C2311yescharacteristic
144C22×Dic22C2311yescharacteristic
145C22×Dic22C2312yes—
146C11×#124C2×C418yescomplemented
147C4×Q8×C11—24no—
148C4×D4×C11—24no—
149C2×C11×C4⋊C4C2312yes—
150C2×C11×C4⋊C4C2311yescharacteristic
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C4⋊C4C2311yescharacteristic
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×C11C2312yes—
161C2×C42×C11C2311yescharacteristic
162C2×C42×C11C2312yes—
163C2×C42×C11C2311yescharacteristic
164C2×C22⋊Dic11C2312yes—
165C2×C22⋊Dic11C2312yes—
166C2×C22⋊Dic11C2312yes—
167C2×C22⋊Dic11C2312yes—
168C2×C22⋊Dic11C2312yes—
169Q8×Dic11—24no—
170#66997C2×C418yescomplemented
171#66989C2×C418yescomplemented
172D4×Dic11—24no—
173C4×C22⋊D11—28no—
174C2×(C2×D11)⋊C4C2311yescharacteristic
175C2×(C2×D11)⋊C4C2311yescharacteristic
176C2×(C2×D11)⋊C4C2312yes—
177C2×(C2×D11)⋊C4C2311yescharacteristic
178C2×(C2×D11)⋊C4C2311yescharacteristic
179C2×C4⋊Dic11C2312yes—
180C2×C4⋊Dic11C2311yescharacteristic
181C2×C4⋊Dic11C2311yescharacteristic
182C2×C4⋊Dic11C2311yescharacteristic
183C2×C4⋊Dic11C2312yes—
184C2×C4⋊Dic11C2312yes—
185C2×C4⋊Dic11C2311yescharacteristic
186C2×Dic11⋊C4—28no—
187C2×Dic11⋊C4C2312yes—
188C2×Dic11⋊C4C2312yes—
189C2×Dic11⋊C4C2312yes—
190C2×Dic11⋊C4C2311yescharacteristic
191C2×Dic11⋊C4C2311yescharacteristic
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2311yescharacteristic
194C2×Dic11⋊C4C2311yescharacteristic
195C2×Dic11⋊C4C2311yescharacteristic
196C2×Dic11⋊C4C2311yescharacteristic
197C2×Dic11⋊C4C2311yescharacteristic
198C2×Dic11⋊C4C2311yescharacteristic
199C2×Dic11⋊C4C2312yes—
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2312yes—
202C2×C4×Dic11C2311yescharacteristic
203C2×C4×Dic11C2312yes—
204C2×C4×Dic11C2312yes—
205C2×C4×Dic11C2311yescharacteristic
206C2×C4×Dic11C2312yes—
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2312yes—
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2311yescharacteristic
216#66945—24no—
217C4⋊C4×D11—28no—
218C4⋊C4×D11D418yes—
219#66940—24no—
220#66940—24no—
221#66940—28no—
222#66936C2×C4116yescomplemented
223#66936C2×C4116yescomplemented
224(C22⋊D11)⋊C4—28no—
225#66931C2×C4116yescomplemented
226#66931C2×C4116yescomplemented
227#66930—28no—
228#66925—24no—
229#66925C2×C418yescomplemented
230C42×D11—24no—
231C42×D11—28no—
232#66922C2×C418yescomplemented
233C4×Dic22—24no—
234C4×Dic22—24no—
235C4×Dic22—28no—
236C11×#95C2312yes—
237C11×#95C2312yes—
238C11×#95C2311yescharacteristic
239C11×#95C2311yescharacteristic
240C11×#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2311yescharacteristic
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2311yescharacteristic
259C11⋊#95C2312yes—
260#34266—111nomaximal, Sylow
261C24×C11C2412yes—
262C23×D11C2411yescharacteristic
263C2×Q8×C11—22no—
264C2×Q8×C11—22no—
265C2×Q8×C11C22×C414yes—
266C2×D4×C11—22no—
267C2×D4×C11—22no—
268C2×D4×C11C22×C414yes—
269C22×C4×C11—24no—
270C22×C4×C11—42no—
271C22×C4×C11—42no—
272C22×C4×C11C2412yes—
273C22×C4×C11C2411yescharacteristic
274C22×C4×C11C2411yescharacteristic
275C22×C4×C11C2411yescharacteristic
276C22×C4×C11C2411yescharacteristic
277C22×C4×C11C2412yes—
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2412yes—
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2411yescharacteristic
282C2×C22⋊D11—24no—
283C2×C22⋊D11—24no—
284C2×C22⋊D11C22×C418yes—
285C22×Dic11—24no—
286C22×Dic11—24no—
287C22×Dic11—24no—
288C22×Dic11—42no—
289C22×Dic11—42no—
290C22×Dic11C22×C418yes—
291C22×Dic11C2412yes—
292C22×Dic11C2411yescharacteristic
293C22×Dic11C2411yescharacteristic
294C22×Dic11C2411yescharacteristic
295C22×Dic11C2411yescharacteristic
296C22×Dic11C2411yescharacteristic
297C22×Dic11C2412yes—
298C22×Dic11C2412yes—
299C22×Dic11C2412yes—
300C22×Dic11C2411yescharacteristic
301C22×Dic11C2411yescharacteristic
302Q8×D11—232no—
303#4341—232no—
304C2×C4×D11—22no—
305C2×C4×D11—22no—
306C2×C4×D11—24no—
307C2×C4×D11—22no—
308C2×C4×D11—24no—
309C2×C4×D11—22no—
310C2×C4×D11—42no—
311C2×C4×D11—42no—
312C2×C4×D11—41no—
313C2×C4×D11—41no—
314C2×C4×D11C22×C418yes—
315C2×C4×D11C22×C414yes—
316C2×C4×D11C2×D418yes—
317C2×C4×D11C2×D414yes—
318C2×C4×D11#4114yes—
319C2×Dic22—24no—
320C2×Dic22—24no—
321C2×Dic22—22no—
322C2×Dic22—22no—
323C2×Dic22—22no—
324C2×Dic22—22no—
325C2×Dic22C22×C414yes—
326C2×Dic22C22×C414yes—
327C2×Dic22C22×C418yes—
328C11×C4⋊C4—24no—
329C11×C4⋊C4—22no—
330C11×C4⋊C4—22no—
331C11×C4⋊C4—41no—
332C11×C4⋊C4C2×D414yes—
333C11×C22⋊C4—24no—
334C11×C22⋊C4—24no—
335C11×C22⋊C4—42no—
336C11×C22⋊C4C22×C418yes—
337C11×C22⋊C4C22×C418yes—
338C42×C11—24no—
339C42×C11—22no—
340C42×C11—22no—
341C42×C11—42no—
342C42×C11C22×C414yes—
343C22⋊Dic11—24no—
344C22⋊Dic11—24no—
345C22⋊Dic11—42no—
346C22⋊Dic11C22×C418yes—
347C22⋊Dic11C22×C418yes—
348(C2×D11)⋊C4—22no—
349(C2×D11)⋊C4—22no—
350(C2×D11)⋊C4—24no—
351(C2×D11)⋊C4C22×C414yes—
352(C2×D11)⋊C4C22×C414yes—
353C4⋊Dic11—24no—
354C4⋊Dic11—22no—
355C4⋊Dic11—22no—
356C4⋊Dic11—41no—
357C4⋊Dic11C22×C418yes—
358C4⋊Dic11C22×C418yes—
359C4⋊Dic11C2×D414yes—
360Dic11⋊C4—24no—
361Dic11⋊C4—24no—
362Dic11⋊C4—22no—
363Dic11⋊C4—22no—
364Dic11⋊C4—22no—
365Dic11⋊C4—24no—
366Dic11⋊C4—24no—
367Dic11⋊C4—22no—
368Dic11⋊C4—41no—
369Dic11⋊C4—41no—
370Dic11⋊C4C22×C414yes—
371Dic11⋊C4C22×C414yes—
372Dic11⋊C4C22×C418yes—
373Dic11⋊C4C22×C418yes—
374Dic11⋊C4C2×D418yes—
375C4×Dic11—24no—
376C4×Dic11—22no—
377C4×Dic11—24no—
378C4×Dic11—22no—
379C4×Dic11—24no—
380C4×Dic11—24no—
381C4×Dic11—24no—
382C4×Dic11—22no—
383C4×Dic11—22no—
384C4×Dic11—24no—
385C4×Dic11—42no—
386C4×Dic11—42no—
387C4×Dic11—42no—
388C4×Dic11C22×C414yes—
389C2×#536—111no—
390C2×#520—111no—
391C22×C4×Q8—111no—
392#2367—111no—
393#2367—111no—
394#2367—111no—
395#2367D1111yescharacteristic, complemented
396#2365—111no—
397#2365—111no—
398#2365—111no—
399#2365—111no—
400#2362—112no—
401#2362—112no—
402#2360—112no—
403#2360—112no—
404#2322—112no—
405#2322—112no—
406#2310—111no—
407C4×#123—112no—
408C4×#123—112no—
409#2297—111no—
410#2296—111no—
411#2274—111no—
412C23×C11—22no—
413C23×C11—22no—
414C23×C11—22no—
415C23×C11—22no—
416C23×C11—22no—
417C23×C11—22no—
418C23×C11C23×C414yes—
419C23×C11C2511yescharacteristic
420C22×D11—21no—
421C22×D11—21no—
422C22×D11—21no—
423C22×D11—21no—
424C22×D11C23×C412yes—
425C22×D11C22×D412yes—
426C22×D11C2×#4112yes—
427Q8×C11—28no—
428D4×C11—28no—
429C2×C4×C11—21no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—21no—
433C2×C4×C11—21no—
434C2×C4×C11—21no—
435C2×C4×C11—21no—
436C2×C4×C11—22no—
437C2×C4×C11—21no—
438C2×C4×C11—22no—
439C2×C4×C11—21no—
440C2×C4×C11—21no—
441C2×C4×C11—21no—
442C2×C4×C11—22no—
443C2×C4×C11—21no—
444C2×C4×C11—22no—
445C2×C4×C11—21no—
446C2×C4×C11—22no—
447C2×C4×C11—21no—
448C2×C4×C11—21no—
449C2×C4×C11—21no—
450C2×C4×C11—21no—
451C2×C4×C11—84no—
452C2×C4×C11C23×C414yes—
453C2×C4×C11C23×C412yes—
454C2×C4×C11C23×C412yes—
455C2×C4×C11C23×C412yes—
456C2×C4×C11C22×D414yes—
457C2×C4×C11C22×D412yes—
458C2×C4×C11C2×#4112yes—
459C2×C4×C112−1+412yes—
460C22⋊D11—216no—
461C2×Dic11—21no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—21no—
467C2×Dic11—21no—
468C2×Dic11—21no—
469C2×Dic11—21no—
470C2×Dic11—21no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—216no—
474C2×Dic11—21no—
475C2×Dic11—21no—
476C2×Dic11—21no—
477C2×Dic11—22no—
478C2×Dic11—21no—
479C2×Dic11—21no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—21no—
483C2×Dic11—21no—
484C2×Dic11—21no—
485C2×Dic11—21no—
486C2×Dic11—84no—
487C2×Dic11C23×C412yes—
488C2×Dic11C23×C412yes—
489C2×Dic11C23×C414yes—
490C2×Dic11C23×C414yes—
491C2×Dic11C23×C412yes—
492C2×Dic11C22×D414yes—
493C2×Dic11C22×D412yes—
494C2×Dic11C2×#4112yes—
495C2×Dic112−1+412yes—
496C4×D11—28no—
497C4×D11—216no—
498C4×D11—48no—
499C4×D11—44no—
500C4×D11C4×D4116yes—
501Dic22—28no—
502Dic22—28no—
503Dic22—216no—
504C22×#41—111no—
505C23×Q8—111no—
506#536—1116no—
507C2×C4⋊Q8—111no—
508C2×C4⋊Q8—111no—
509C2×#124—111no—
510C2×#124C2×D1111yescharacteristic
511C2×#123—112no—
512C2×#123—112no—
513C2×C22⋊Q8—112no—
514C2×C22⋊Q8—112no—
515#520—228no—
516C2×C4×Q8—111no—
517C2×C4×Q8—112no—
518C2×C4×Q8—111no—
519C2×C4×Q8—111no—
520C2×C4×Q8—112no—
521C2×C4×Q8—111no—
522C2×C4×Q8—111no—
523C2×C4×Q8—228no—
524C2×C4×Q8C2×D1111yescharacteristic
525C2×C4×D4—111no—
526C2×C4×D4—112no—
527C2×C4×D4—112no—
528C2×C4×D4C2×D1111yescharacteristic
529C2×#117—111no—
530C2×#117—112no—
531C2×#117—111no—
532C2×#117—111no—
533C22×C4⋊C4—111no—
534C22×C4⋊C4—112no—
535C22×C4⋊C4—112no—
536C22×C42—111no—
537C22×C42—112no—
538#391—111no—
539#391—111no—
540#391—111no—
541#391—111no—
542#391—111no—
543#391—112no—
544#391—112no—
545#391C2×D1111yescharacteristic
546#390—111no—
547#390C2×D1111yescharacteristic
548#389—112no—
549#389—112no—
550#389—111no—
551#389—111no—
552#389—112no—
553#389—112no—
554#389—111no—
555#389—111no—
556#388—112no—
557#388—112no—
558#388—112no—
559#388—112no—
560#388—112no—
561#388—112no—
562#388C2×D1112yes—
563#388C2×D1112yes—
564#387—112no—
565#387—112no—
566#387—112no—
567#387—112no—
568#387—112no—
569#387—112no—
570#387—112no—
571#387—112no—
572#386—112no—
573#386—112no—
574#385—112no—
575#385—111no—
576#385—111no—
577#385—112no—
578#385—112no—
579#385—111no—
580#385—111no—
581#385C2×D1112yes—
582#381—112no—
583#381—112no—
584C4×C4⋊C4—112no—
585C4×C4⋊C4—111no—
586C4×C4⋊C4—111no—
587C4×C4⋊C4—112no—
588C4×C4⋊C4—112no—
589C4×C4⋊C4—112no—
590C4×C4⋊C4—111no—
591C4×C4⋊C4—111no—
592C4×C4⋊C4—111no—
593C4×C4⋊C4—111no—
594C4×C4⋊C4—112no—
595C4×C4⋊C4—112no—
596C4×C4⋊C4C2×D1111yescharacteristic
597C4×C4⋊C4C2×D1111yescharacteristic
598C4×C22⋊C4—112no—
599C4×C22⋊C4—112no—
600C4×C22⋊C4—112no—
601C4×C22⋊C4—112no—
602C4×C22⋊C4—112no—
603C4×C22⋊C4—112no—
604C4×C22⋊C4—112no—
605C4×C22⋊C4C2×D1112yes—
606C22×C11—24no—
607C22×C11—24no—
608C22×C11—24no—
609C22×C11—42no—
610C22×C11—42no—
611C22×C11—42no—
612C22×C11—42no—
613C22×C11C24×C411yescharacteristic
614C22×C11C23×D411yescharacteristic
615C22×C11C22×#4111yescharacteristic
616C22×C11C2×2−1+411yescharacteristic
617C22×C11C2×2−1+411yescharacteristic
618C22×C11#58511yescharacteristic
619C22×C11#58511yescharacteristic
620C2×D11—22no—
621C2×D11—22no—
622C2×D11—22no—
623C2×D11—22no—
624C2×D11—22no—
625C2×D11—22no—
626C2×D11C2×C4×D414yes—
627C4×C11—24no—
628C4×C11—22no—
629C4×C11—22no—
630C4×C11—24no—
631C4×C11—22no—
632C4×C11—41no—
633C4×C11—41no—
634C4×C11—41no—
635C4×C11—42no—
636C4×C11C2×C4×D414yes—
637Dic11—24no—
638Dic11—24no—
639Dic11—22no—
640Dic11—22no—
641Dic11—24no—
642Dic11—22no—
643Dic11—41no—
644Dic11—41no—
645Dic11—41no—
646Dic11—42no—
647Dic11C2×C4×D414yes—
648C2×#41—118no—
649C2×#41—224no—
650C2×#41—224no—
651C22×Q8—118no—
652C22×Q8—112no—
653C22×Q8—111no—
654C22×Q8—111no—
655C22×Q8—224no—
656C22×Q8—224no—
657C22×Q8C22×D1111yescharacteristic
658C22×D4—112no—
659C22×D4C22×D1111yescharacteristic
660C23×C4—111no—
661C23×C4—112no—
662C23×C4—112no—
663C23×C4—112no—
664C23×C4—112no—
665C23×C4—111no—
666C23×C4—111no—
667C23×C4C22×D1112yes—
668C4⋊Q8—118no—
669C4⋊Q8—118no—
670#124—118no—
671#124C4×D1118yescomplemented
672#123—1116no—
673#123—1116no—
674C22⋊Q8—1116no—
675C22⋊Q8—1116no—
676C4×Q8—24no—
677C4×Q8—228no—
678C4×Q8—224no—
679C4×Q8—224no—
680C4×Q8—228no—
681C4×Q8—224no—
682C4×Q8—224no—
683C4×Q8—224no—
684C4×D4—24no—
685C4×D4—228no—
686C4×D4—224no—
687C4×D4—228no—
688#117—118no—
689#117—224no—
690#117—228no—
691#117—224no—
692C2×C4⋊C4—112no—
693C2×C4⋊C4—111no—
694C2×C4⋊C4—111no—
695C2×C4⋊C4—111no—
696C2×C4⋊C4—112no—
697C2×C4⋊C4—112no—
698C2×C4⋊C4—112no—
699C2×C4⋊C4—112no—
700C2×C4⋊C4—118no—
701C2×C4⋊C4—111no—
702C2×C4⋊C4—112no—
703C2×C4⋊C4—112no—
704C2×C4⋊C4—112no—
705C2×C4⋊C4—112no—
706C2×C4⋊C4—112no—
707C2×C4⋊C4—111no—
708C2×C4⋊C4—111no—
709C2×C4⋊C4—111no—
710C2×C4⋊C4—111no—
711C2×C4⋊C4—111no—
712C2×C4⋊C4—111no—
713C2×C4⋊C4—111no—
714C2×C4⋊C4—111no—
715C2×C4⋊C4—228no—
716C2×C4⋊C4—228no—
717C2×C4⋊C4C22×D1112yes—
718C2×C4⋊C4C22×D1111yescharacteristic
719C2×C4⋊C4C22×D1111yescharacteristic
720C2×C4⋊C4C22×D1111yescharacteristic
721C2×C4⋊C4C22×D1111yescharacteristic
722C2×C22⋊C4—112no—
723C2×C22⋊C4—112no—
724C2×C22⋊C4—111no—
725C2×C22⋊C4—111no—
726C2×C22⋊C4—112no—
727C2×C22⋊C4—112no—
728C2×C22⋊C4—111no—
729C2×C22⋊C4—111no—
730C2×C22⋊C4—112no—
731C2×C22⋊C4—112no—
732C2×C22⋊C4C22×D1112yes—
733C2×C22⋊C4C22×D1112yes—
734C2×C22⋊C4C22×D1112yes—
735C2×C22⋊C4C22×D1112yes—
736C2×C22⋊C4C22×D1112yes—
737C2×C42—111no—
738C2×C42—112no—
739C2×C42—112no—
740C2×C42—111no—
741C2×C42—112no—
742C2×C42—111no—
743C2×C42—111no—
744C2×C42—112no—
745C2×C42—112no—
746C2×C42—112no—
747C2×C42—111no—
748C2×C42—112no—
749C2×C42—112no—
750C2×C42—112no—
751C2×C42—224no—
752C2×C42—228no—
753C2×C42C22×D1111yescharacteristic
754C2×C42C22×D1112yes—
755C2×C42C22×D1111yescharacteristic
756C2×C42C22×D1112yes—
757C2×C42C22×D1111yescharacteristic
758#95—111no—
759#95—111no—
760#95—111no—
761#95—112no—
762#95—112no—
763#95—112no—
764#95—112no—
765#95—112no—
766#95—112no—
767#95—112no—
768#95—112no—
769#95—112no—
770#95—112no—
771#95—112no—
772#95—112no—
773#95—112no—
774#95—111no—
775#95—111no—
776#95—111no—
777#95C22×D1112yes—
778#95C22×D1111yescharacteristic
779#95C22×D1112yes—
780#95C22×D1112yes—
781#95C22×D1111yescharacteristic
782C2×C11—44no—
783C2×C11C22×C4×D411yescharacteristic
784C2×C11C4×2−1+411yescharacteristic
785C2×C11C4×2−1+411yescharacteristic
786C2×C11#348511yescharacteristic
787C2×C11#348611yescharacteristic
788C2×C11#350711yescharacteristic
789C2×C11#350711yescharacteristic
790D11—24no—
791C24—111no—
792C24C23×D1112yes—
793#41—2232no—
794C2×Q8—22no—
795C2×Q8—22no—
796C2×Q8—118no—
797C2×Q8—114no—
798C2×Q8—114no—
799C2×Q8—224no—
800C2×Q8—224no—
801C2×Q8—2232no—
802C2×Q8—222no—
803C2×Q8—222no—
804C2×Q8—222no—
805C2×Q8—222no—
806C2×Q8C2×C4×D1114yes—
807C2×D4—22no—
808C2×D4—22no—
809C2×D4—118no—
810C2×D4—224no—
811C2×D4—224no—
812C2×D4C2×C4×D1114yes—
813C22×C4—24no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—111no—
817C22×C4—114no—
818C22×C4—114no—
819C22×C4—114no—
820C22×C4—118no—
821C22×C4—111no—
822C22×C4—111no—
823C22×C4—111no—
824C22×C4—112no—
825C22×C4—112no—
826C22×C4—112no—
827C22×C4—118no—
828C22×C4—118no—
829C22×C4—112no—
830C22×C4—111no—
831C22×C4—111no—
832C22×C4—111no—
833C22×C4—222no—
834C22×C4—222no—
835C22×C4—224no—
836C22×C4—224no—
837C22×C4—222no—
838C22×C4—224no—
839C22×C4—224no—
840C22×C4—224no—
841C22×C4—222no—
842C22×C4—442no—
843C22×C4—442no—
844C22×C4—441no—
845C22×C4—441no—
846C22×C4—442no—
847C22×C4—442no—
848C22×C4C23×D1112yes—
849C22×C4C23×D1111yescharacteristic
850C22×C4C23×D1111yescharacteristic
851C22×C4C23×D1111yescharacteristic
852C22×C4C23×D1111yescharacteristic
853C22×C4C23×D1112yes—
854C22×C4C23×D1111yescharacteristic
855C22×C4C23×D1112yes—
856C22×C4C23×D1111yescharacteristic
857C22×C4C23×D1111yescharacteristic
858C4⋊C4—24no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—41no—
862C4⋊C4—114no—
863C4⋊C4—114no—
864C4⋊C4—118no—
865C4⋊C4—118no—
866C4⋊C4—118no—
867C4⋊C4—118no—
868C4⋊C4—118no—
869C4⋊C4—114no—
870C4⋊C4—222no—
871C4⋊C4—224no—
872C4⋊C4—224no—
873C4⋊C4—224no—
874C4⋊C4—222no—
875C4⋊C4—222no—
876C4⋊C4—222no—
877C4⋊C4—224no—
878C4⋊C4—224no—
879C4⋊C4—222no—
880C4⋊C4—222no—
881C4⋊C4—441no—
882C4⋊C4—441no—
883C4⋊C4—441no—
884C4⋊C4D4×D1114yes—
885C22⋊C4—24no—
886C22⋊C4—24no—
887C22⋊C4—42no—
888C22⋊C4—118no—
889C22⋊C4—118no—
890C22⋊C4—114no—
891C22⋊C4—114no—
892C22⋊C4—222no—
893C22⋊C4—222no—
894C22⋊C4—224no—
895C22⋊C4—224no—
896C22⋊C4—224no—
897C22⋊C4—442no—
898C22⋊C4C2×C4×D1118yes—
899C22⋊C4C2×C4×D1118yes—
900C42—24no—
901C42—22no—
902C42—22no—
903C42—42no—
904C42—114no—
905C42—222no—
906C42—224no—
907C42—224no—
908C42—222no—
909C42—224no—
910C42—224no—
911C42—224no—
912C42—222no—
913C42—224no—
914C42—222no—
915C42—442no—
916C42—442no—
917C42—442no—
918C42C2×C4×D1114yes—
919C11#3426611yescharacteristic, complemented, Sylow
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—112no—
927C23—112no—
928C23—112no—
929C23—221no—
930C23—221no—
931C23—221no—
932C23—221no—
933C23C22×C4×D1114yes—
934C23C24×D1111yescharacteristic
935Q8—28no—
936Q8—2216no—
937Q8—228no—
938Q8—228no—
939D4—28no—
940D4—2216no—
941C2×C4—21no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—22no—
947C2×C4—21no—
948C2×C4—22no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—22no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—84no—
964C2×C4—112no—
965C2×C4—112no—
966C2×C4—112no—
967C2×C4—1116no—
968C2×C4—112no—
969C2×C4—112no—
970C2×C4—114no—
971C2×C4—114no—
972C2×C4—114no—
973C2×C4—112no—
974C2×C4—2216no—
975C2×C4—228no—
976C2×C4—2216no—
977C2×C4—221no—
978C2×C4—222no—
979C2×C4—222no—
980C2×C4—222no—
981C2×C4—222no—
982C2×C4—221no—
983C2×C4—221no—
984C2×C4—221no—
985C2×C4—222no—
986C2×C4—221no—
987C2×C4—222no—
988C2×C4—221no—
989C2×C4—221no—
990C2×C4—221no—
991C2×C4—221no—
992C2×C4—222no—
993C2×C4—221no—
994C2×C4—222no—
995C2×C4—221no—
996C2×C4—221no—
997C2×C4—221no—
998C2×C4—221no—
999C2×C4—222no—
1000C2×C4—221no—
1001C2×C4—448no—
1002C2×C4—444no—
1003C2×C4—884no—
1004C2×C4C22×C4×D1112yes—
1005C2×C4C22×C4×D1112yes—
1006C2×C4C22×C4×D1114yes—
1007C2×C4C22×C4×D1112yes—
1008C2×C4C2×D4×D1114yes—
1009C2×C4C2×D4×D1112yes—
1010C2×C4#41×D1112yes—
1011C2×C4#6704312yes—
1012C22—24no—
1013C22—24no—
1014C22—24no—
1015C22—42no—
1016C22—42no—
1017C22—42no—
1018C22—42no—
1019C22—114no—
1020C22—222no—
1021C22—222no—
1022C22—222no—
1023C22—222no—
1024C22—222no—
1025C22—222no—
1026C22C23×C4×D1111yescharacteristic
1027C22C22×D4×D1111yescharacteristic
1028C22C2×#41×D1111yescharacteristic
1029C22C2×#6704311yescharacteristic
1030C22#1062345311yescharacteristic
1031C22#1062345511yescharacteristic
1032C22D11×2−1+411yescharacteristic
1033C4—24no—
1034C4—22no—
1035C4—24no—
1036C4—22no—
1037C4—22no—
1038C4—42no—
1039C4—41no—
1040C4—41no—
1041C4—41no—
1042C4—114no—
1043C4—224no—
1044C4—222no—
1045C4—224no—
1046C4—224no—
1047C4—222no—
1048C4—222no—
1049C4—442no—
1050C4—441no—
1051C4—441no—
1052C4—441no—
1053C4C4×D4×D1114yes—
1054C2—44no—
1055C2—224no—
1056C2C2×C4×D4×D1111yescharacteristic
1057C2C4×#6704311yescharacteristic
1058C2#1308182711yescharacteristic
1059C2#1308225311yescharacteristic
1060C2#1308226211yescharacteristic
1061C2#1308247311yescharacteristic
1062C2#1308247711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2367C2
socle, cosocleC23×C11C25
prime radicalC22×#4341C22
hypercenter#2367D11
hypocenterC11#34266
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2367

Complements

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

NH ≅ G/Ntype
3. C2×C4×Q8×D11C2semidirect
4. #13071691C2semidirect
5. #13071689C2semidirect
6. #13071686C2semidirect
7. #13071674C2semidirect
8. #13071673C2semidirect
9. #13071672C2semidirect
10. #13071670C2semidirect
11. #13071646C2semidirect
12. #13071640C2semidirect
13. #13071622C2semidirect
14. #13071616C2semidirect
15. #13071286C2semidirect
16. #13071283C2semidirect
17. #13071199C2semidirect
18. #13071143C2semidirect
19. C4×#66936C2semidirect
21. #13071096C2semidirect
22. #13070970C2semidirect
23. C11×#2367C2semidirect
35. #10623206C4semidirect
134. C2×Q8×D11C2×C4semidirect
146. C11×#124C2×C4semidirect
170. #66997C2×C4semidirect
171. #66989C2×C4semidirect
222. #66936C2×C4semidirect
223. #66936C2×C4semidirect
225. #66931C2×C4semidirect
226. #66931C2×C4semidirect
229. #66925C2×C4semidirect
232. #66922C2×C4semidirect
395. #2367D11semidirect
671. #124C4×D11semidirect
919. C11#34266semidirect

Maximal subgroups

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

subgroupindex
C2×#106232062
C2×#106230772
C2×C4×Q8×D112
#130716912
#130716892
#130716862
#130716742
#130716732
#130716722
#130716702
#130716462
#130716402
#130716222
#130716162
#130712862
#130712832
#130711992
#130711432
C4×#669362
#130711032
#130710962
#130709702
C11×#23672
#3426611