Finite Group Databasebeta

← #14913334

Subgroups — #14913334

Order 2816.

3374 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623158C211yesmaximal, characteristic
2C2×C4×#4343C211yesmaximal, characteristic, complemented
3C22×#66945C211yesmaximal, characteristic, complemented
4#13071656C211yesmaximal, characteristic, complemented
5#13071653C211yesmaximal, characteristic, complemented
6#13071648C211yesmaximal, characteristic, complemented
7#13071639C211yesmaximal, characteristic, complemented
8#13071632C211yesmaximal, characteristic, complemented
9#13071630C211yesmaximal, characteristic, complemented
10#13071625C211yesmaximal, characteristic, complemented
11#13071615C212yesmaximal, complemented
12#13071603C212yesmaximal, complemented
13#13071598C212yesmaximal, complemented
14#13071592C212yesmaximal, complemented
15#13071105C211yesmaximal, characteristic, complemented
16#13071097C211yesmaximal, characteristic, complemented
17#13071074C212yesmaximal, complemented
18#13071054C212yesmaximal, complemented
19#13071052C212yesmaximal, complemented
20C4×(C22⋊D11)⋊C4C212yesmaximal, complemented
21C4×#66945C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2360C211yesmaximal, characteristic, complemented
24C22×#4343C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic, complemented
28C22×C11×C4⋊C4C2211yescharacteristic
29C2×#66999C2211yescharacteristic
30C2×Q8×Dic11C2211yescharacteristic, complemented
31C2×#66983C2211yescharacteristic
32C2×C4×C22⋊D11C2212yes—
33C22×(C2×D11)⋊C4C2212yes—
34C22×C4⋊Dic11C2211yescharacteristic
35C22×C4×Dic11C2212yes—
36#10623158C4116yescomplemented
37C4×#4343—28no—
38C2×#66948C2211yescharacteristic
39C2×#66947C2212yes—
40C2×#66946C2212yes—
41C2×#66946C2212yes—
42C2×#66946C2211yescharacteristic, complemented
43C2×#66945—28no—
44C2×#66945C2211yescharacteristic
45C2×#66945C2211yescharacteristic
46C2×#66945C2211yescharacteristic
47C2×#66945C2212yes—
48C2×#66945C2212yes—
49C2×#66945C2211yescharacteristic
50C2×#66945C2211yescharacteristic
51C2×#66945C2212yescomplemented
52C2×#66935C2212yes—
53C2×(C22⋊D11)⋊C4C2212yes—
54C2×(C22⋊D11)⋊C4C2212yes—
55C2×C22⋊C4×D11C2211yescharacteristic
56C2×C22⋊C4×D11C2211yescharacteristic
57C2×C4×D44C2212yes—
58C2×C4×D44C2211yescharacteristic, complemented
59C2×C42×D11C2211yescharacteristic
60C2×C42×D11C2211yescharacteristic
61C2×C42×D11C2212yescomplemented
62C11×#391C2211yescharacteristic, complemented
63C11×#389C2211yescharacteristic, complemented
64C11×#389C2212yescomplemented
65C11×#387C2212yescomplemented
66C11×#385C2212yes—
67C4×C11×C4⋊C4C2211yescharacteristic, complemented
68C4×C11×C22⋊C4C2211yescharacteristic
69C4×C11×C22⋊C4C2212yes—
70#10622843C2211yescharacteristic, complemented
71#10622826C2212yes—
72C4×C22⋊Dic11C2211yescharacteristic
73#10622603C2212yes—
74#10622603C2212yescomplemented
75#10622603C2212yescomplemented
76#10622602C2212yes—
77#10622602C2212yescomplemented
78#10622601C2212yes—
79#10622601C2211yescharacteristic, complemented
80#10622598C2211yescharacteristic, complemented
81#10622598C2212yescomplemented
82#10622594C2212yescomplemented
83#10622591C2212yescomplemented
84C4⋊C4×Dic11C2211yescharacteristic, complemented
85C4⋊C4×Dic11C2211yescharacteristic, complemented
86C4⋊C4×Dic11C2212yescomplemented
87#10622586C2211yescharacteristic, complemented
88#10622571C2212yes—
89#10622563C2212yes—
90C22⋊C4×Dic11C2212yes—
91C22⋊C4×Dic11C2211yescharacteristic
92C22⋊C4×Dic11C2211yescharacteristic
93#10622553C2212yes—
94#10622552C2212yes—
95#10622552C2211yescharacteristic, complemented
96C4×(C2×D11)⋊C4C2211yescharacteristic
97C4×(C2×D11)⋊C4C2211yescharacteristic
98C4×(C2×D11)⋊C4C2212yes—
99C4×(C2×D11)⋊C4C2212yescomplemented
100C4×C4⋊Dic11C2211yescharacteristic, complemented
101C4×Dic11⋊C4C2212yescomplemented
102C42×Dic11C2212yescomplemented
103#10622541C2211yescharacteristic, complemented
104#10622283C2212yes—
105#10622283C2212yescomplemented
106#10622283C2212yescomplemented
107#10622282C2212yes—
108#10622281C2212yes—
109#10622281C2212yescomplemented
110#10622279C2211yescharacteristic
111#10622279C2211yescharacteristic
112#10622279C2212yes—
113#10622279C2212yescomplemented
114#10622279C2212yescomplemented
115#10622279C2212yescomplemented
116#10622278C2212yes—
117#10622278C2212yes—
118#10622278C2212yes—
119#10622278C2212yes—
120D11×#95C2211yescharacteristic
121D11×#95C2211yescharacteristic
122#10622268C2212yescomplemented
123#10622262C2212yescomplemented
124#10622262C2212yescomplemented
125#10622261C2212yescomplemented
126C24×D11C2311yescharacteristic
127C22×Q8×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C23×C4×C11C2311yescharacteristic
130C22×C22⋊D11C2312yes—
131C23×Dic11C2312yes—
132C23×Dic11C2311yescharacteristic
133C2×#4343—24no—
134C2×#4343—24no—
135C2×#4343C2×C418yescomplemented
136C22×D44C2312yes—
137C22×D44C2311yescharacteristic
138C22×D44C2312yes—
139C22×C4×D11—24no—
140C22×C4×D11—24no—
141C22×C4×D11C2×C418yescomplemented
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×C4×D11C2312yes—
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C11×C22⋊Q8C2×C418yescomplemented
154C4×Q8×C11—24no—
155C2×C11×C4⋊C4—24no—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2312yes—
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C22⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2312yes—
169C2×C42×C11C2312yes—
170C2×C22⋊Dic11C2311yescharacteristic
171C2×C22⋊Dic11C2311yescharacteristic
172#66999C2×C418yescomplemented
173Q8×Dic11—24no—
174#66983C2×C418yescomplemented
175C4×C22⋊D11—28no—
176C2×(C2×D11)⋊C4—28no—
177C2×(C2×D11)⋊C4C2312yes—
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2311yescharacteristic
180C2×(C2×D11)⋊C4C2311yescharacteristic
181C2×(C2×D11)⋊C4C2311yescharacteristic
182C2×(C2×D11)⋊C4C2311yescharacteristic
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×C4⋊Dic11—24no—
196C2×C4⋊Dic11C2312yes—
197C2×C4⋊Dic11C2312yes—
198C2×C4⋊Dic11C2311yescharacteristic
199C2×C4⋊Dic11C2312yes—
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2311yescharacteristic
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×C4×Dic11—28no—
206C2×C4×Dic11C2311yescharacteristic
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221#66948C2×C418yescomplemented
222#66947C2×C4116yescomplemented
223#66946—24no—
224#66946—28no—
225#66946C2×C4116yescomplemented
226#66945—24no—
227#66945—24no—
228#66945—28no—
229#66945—24no—
230#66945—28no—
231#66945—28no—
232#66945C2×C418yescomplemented
233#66945D418yescomplemented
234#66935C2×C4116yescomplemented
235(C22⋊D11)⋊C4—28no—
236(C22⋊D11)⋊C4C2×C4116yescomplemented
237C22⋊C4×D11—24no—
238C22⋊C4×D11—24no—
239C4×D44—28no—
240C4×D44—24no—
241C42×D11—24no—
242C42×D11—24no—
243C42×D11—28no—
244C11×#95C2312yes—
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11×#95C2312yes—
248C11×#95C2311yescharacteristic
249C11×#95C2311yescharacteristic
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2312yes—
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2312yes—
257C11⋊#95C2311yescharacteristic
258C11⋊#95C2311yescharacteristic
259C11⋊#95C2311yescharacteristic
260C11⋊#95C2311yescharacteristic
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264#34136—111nomaximal, Sylow
265C24×C11C2411yescharacteristic
266C23×D11—22no—
267C23×D11—22no—
268C23×D11—22no—
269C23×D11—22no—
270C23×D11—41no—
271C23×D11—41no—
272C23×D11C22×C414yes—
273C23×D11C2411yescharacteristic
274C23×D11C2412yes—
275C23×D11C2411yescharacteristic
276C2×Q8×C11—22no—
277C2×Q8×C11—22no—
278C2×Q8×C11C22×C414yes—
279C22×C4×C11—22no—
280C22×C4×C11—22no—
281C22×C4×C11—24no—
282C22×C4×C11—24no—
283C22×C4×C11—42no—
284C22×C4×C11C22×C414yes—
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2412yes—
288C22×C4×C11C2412yes—
289C22×C4×C11C2412yes—
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2412yes—
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C2×C22⋊D11—24no—
296C2×C22⋊D11—24no—
297C2×C22⋊D11C22×C418yes—
298C22×Dic11—22no—
299C22×Dic11—22no—
300C22×Dic11—24no—
301C22×Dic11—24no—
302C22×Dic11—42no—
303C22×Dic11C22×C414yes—
304C22×Dic11C2411yescharacteristic
305C22×Dic11C2412yes—
306C22×Dic11C2411yescharacteristic
307C22×Dic11C2411yescharacteristic
308C22×Dic11C2412yes—
309C22×Dic11C2412yes—
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2411yescharacteristic
313#4343—232no—
314C2×D44—24no—
315C2×D44—24no—
316C2×D44—22no—
317C2×D44—22no—
318C2×D44—42no—
319C2×D44—42no—
320C2×D44C22×C418yes—
321C2×D44C22×C414yes—
322C2×D44C22×C418yes—
323C2×C4×D11—24no—
324C2×C4×D11—22no—
325C2×C4×D11—22no—
326C2×C4×D11—24no—
327C2×C4×D11—232no—
328C2×C4×D11—24no—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11—24no—
332C2×C4×D11—22no—
333C2×C4×D11—22no—
334C2×C4×D11—22no—
335C2×C4×D11—22no—
336C2×C4×D11—22no—
337C2×C4×D11—22no—
338C2×C4×D11—22no—
339C2×C4×D11—24no—
340C2×C4×D11—22no—
341C2×C4×D11—22no—
342C2×C4×D11—22no—
343C2×C4×D11—24no—
344C2×C4×D11—41no—
345C2×C4×D11—42no—
346C2×C4×D11—41no—
347C2×C4×D11—42no—
348C2×C4×D11—41no—
349C2×C4×D11—41no—
350C2×C4×D11C22×C418yes—
351C2×C4×D11C22×C414yes—
352C2×C4×D11C22×C414yes—
353C2×C4×D11C22×C414yes—
354C2×C4×D11C22×C414yes—
355C2×C4×D11C2×D414yes—
356C2×C4×D11#4114yes—
357C11×C4⋊C4—24no—
358C11×C4⋊C4—22no—
359C11×C4⋊C4—24no—
360C11×C4⋊C4—42no—
361C11×C4⋊C4C22×C414yes—
362C11×C4⋊C4C22×C418yes—
363C11×C4⋊C4C2×D414yes—
364C11×C22⋊C4—22no—
365C11×C22⋊C4C22×C418yes—
366C11×C22⋊C4#4114yescomplemented
367C42×C11—24no—
368C42×C11—22no—
369C42×C11—22no—
370C42×C11—42no—
371C22⋊Dic11—22no—
372C22⋊Dic11#4114yescomplemented
373(C2×D11)⋊C4—24no—
374(C2×D11)⋊C4—24no—
375(C2×D11)⋊C4—22no—
376(C2×D11)⋊C4—22no—
377(C2×D11)⋊C4—24no—
378(C2×D11)⋊C4—24no—
379(C2×D11)⋊C4—24no—
380(C2×D11)⋊C4—24no—
381(C2×D11)⋊C4—22no—
382(C2×D11)⋊C4—22no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—42no—
385(C2×D11)⋊C4—42no—
386(C2×D11)⋊C4C22×C418yes—
387(C2×D11)⋊C4C22×C418yes—
388(C2×D11)⋊C4C22×C418yes—
389(C2×D11)⋊C4C22×C418yes—
390(C2×D11)⋊C4C2×D418yes—
391C4⋊Dic11—24no—
392C4⋊Dic11—24no—
393C4⋊Dic11—22no—
394C4⋊Dic11—42no—
395C4⋊Dic11C22×C414yes—
396C4⋊Dic11C2×D414yes—
397Dic11⋊C4—24no—
398Dic11⋊C4—24no—
399Dic11⋊C4C22×C418yes—
400C4×Dic11—22no—
401C4×Dic11—22no—
402C4×Dic11—24no—
403C4×Dic11—24no—
404C4×Dic11—24no—
405C4×Dic11—22no—
406C4×Dic11—22no—
407C4×Dic11—24no—
408C4×Dic11—22no—
409C4×Dic11—24no—
410C4×Dic11—22no—
411C4×Dic11—24no—
412C4×Dic11—42no—
413C4×Dic11C22×C418yes—
414C4×Dic11C2×D418yes—
415C2×#525—111no—
416C2×C4×#41—111no—
417C22×#117—111no—
418#2363—111no—
419#2363—111no—
420#2362—111no—
421#2362—111no—
422#2361—111no—
423#2361—111no—
424#2360—111no—
425#2360D1111yescharacteristic, complemented
426#2359—112no—
427#2359—112no—
428#2358—112no—
429#2358—112no—
430#2297—111no—
431#2296—111no—
432#2293—112no—
433#2290—112no—
434#2290—112no—
435C42×D4—112no—
436C4×#117—111no—
437C2×C4×C22⋊C4—111no—
438C23×C11—21no—
439C23×C11—21no—
440C23×C11—21no—
441C23×C11—21no—
442C23×C11C23×C412yes—
443C23×C11C2×#4112yes—
444C23×C11C2×#4112yes—
445C23×C11C2511yescharacteristic
446C22×D11—21no—
447C22×D11—21no—
448C22×D11—21no—
449C22×D11—21no—
450C22×D11—28no—
451C22×D11—21no—
452C22×D11—22no—
453C22×D11—21no—
454C22×D11—21no—
455C22×D11—22no—
456C22×D11—22no—
457C22×D11—21no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—28no—
464C22×D11—44no—
465C22×D11—44no—
466C22×D11—44no—
467C22×D11—44no—
468C22×D11—44no—
469C22×D11C23×C412yes—
470C22×D11C23×C414yes—
471C22×D11C23×C412yes—
472C22×D11C22×D412yes—
473C22×D11C2×#4112yes—
474Q8×C11—28no—
475C2×C4×C11—22no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—21no—
479C2×C4×C11—22no—
480C2×C4×C11—21no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—21no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—21no—
487C2×C4×C11—28no—
488C2×C4×C11—22no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—22no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—22no—
496C2×C4×C11—21no—
497C2×C4×C11—48no—
498C2×C4×C11C23×C414yes—
499C2×C4×C11C23×C414yes—
500C2×C4×C11C23×C412yes—
501C2×C4×C11C23×C412yes—
502C2×C4×C11C22×D414yes—
503C2×C4×C11C22×D412yes—
504C2×C4×C11C2×#4112yes—
505C2×C4×C11C2×#4112yes—
506C2×C4×C11C2×#4112yes—
507C22⋊D11—216no—
508C2×Dic11—21no—
509C2×Dic11—21no—
510C2×Dic11—21no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—22no—
517C2×Dic11—21no—
518C2×Dic11—28no—
519C2×Dic11—21no—
520C2×Dic11—22no—
521C2×Dic11—21no—
522C2×Dic11—22no—
523C2×Dic11—21no—
524C2×Dic11—21no—
525C2×Dic11—21no—
526C2×Dic11—22no—
527C2×Dic11—21no—
528C2×Dic11—48no—
529C2×Dic11C23×C414yes—
530C2×Dic11C23×C412yes—
531C2×Dic11C23×C412yes—
532C2×Dic11C22×D414yes—
533C2×Dic11C22×D412yes—
534C2×Dic11C2×#4112yes—
535C2×Dic11C2×#4112yes—
536C2×Dic11C2×#4112yes—
537D44—216no—
538D44—28no—
539D44—48no—
540C4×D11—28no—
541C4×D11—28no—
542C4×D11—28no—
543C4×D11—216no—
544C4×D11—48no—
545C4×D11—48no—
546C4×D11—44no—
547C4×D11—44no—
548C4×D11—44no—
549C4×D11—44no—
550C4×D11C4×D4116yescomplemented
551C22×#41—111no—
552C24×C4—111no—
553#525—1116no—
554C2×#123—112no—
555C2×C22⋊Q8—111no—
556C2×C22⋊Q8C2×D1111yescharacteristic
557C2×#121—111no—
558C2×#121—111no—
559C2×#120—112no—
560C4×#41—228no—
561C2×C4×Q8—111no—
562C2×C4×Q8C2×D1111yescharacteristic, complemented
563C2×C4×D4—112no—
564C2×C4×D4—112no—
565C2×C4×D4—112no—
566C2×C4×D4—111no—
567C2×C4×D4—112no—
568C2×C4×D4—112no—
569C2×C4×D4—112no—
570C2×C4×D4—111no—
571C2×#117—111no—
572C2×#117—111no—
573C2×#117—112no—
574C2×#117—111no—
575C2×#117—111no—
576C2×#117—112no—
577C2×#117—111no—
578C2×#117—112no—
579C2×#117—228no—
580C22×C4⋊C4—111no—
581C22×C4⋊C4C2×D1111yescharacteristic
582C22×C22⋊C4—112no—
583C22×C22⋊C4—111no—
584C22×C22⋊C4—111no—
585C22×C42—112no—
586C22×C42—111no—
587C22×C42—111no—
588C22×C42—112no—
589#391—111no—
590#391C2×D1111yescharacteristic, complemented
591#390—112no—
592#390—111no—
593#390—112no—
594#390—111no—
595#389—112no—
596#389—111no—
597#389—111no—
598#389—111no—
599#389C2×D1112yescomplemented
600#389C2×D1111yescharacteristic, complemented
601#388—112no—
602#388—112no—
603#388—112no—
604#388—112no—
605#388—112no—
606#388—112no—
607#388—112no—
608#388—112no—
609#387—112no—
610#387—112no—
611#387—112no—
612#387C2×D1112yescomplemented
613#386—112no—
614#386—112no—
615#386—112no—
616#386—112no—
617#386—112no—
618#386—112no—
619#385—112no—
620#385—112no—
621#385—112no—
622#385—112no—
623#385—112no—
624#385C2×D1112yes—
625C4×C4⋊C4—111no—
626C4×C4⋊C4—111no—
627C4×C4⋊C4—112no—
628C4×C4⋊C4—112no—
629C4×C4⋊C4—111no—
630C4×C4⋊C4—112no—
631C4×C4⋊C4—112no—
632C4×C4⋊C4C2×D1111yescharacteristic, complemented
633C4×C22⋊C4—111no—
634C4×C22⋊C4—112no—
635C4×C22⋊C4—111no—
636C4×C22⋊C4—111no—
637C4×C22⋊C4—112no—
638C4×C22⋊C4—112no—
639C4×C22⋊C4—111no—
640C4×C22⋊C4—111no—
641C4×C22⋊C4—112no—
642C4×C22⋊C4—112no—
643C4×C22⋊C4—111no—
644C4×C22⋊C4—111no—
645C4×C22⋊C4—112no—
646C4×C22⋊C4—112no—
647C4×C22⋊C4C2×D1112yes—
648C4×C22⋊C4C2×D1111yescharacteristic
649#376—112no—
650C2×#95—111no—
651C2×#95—111no—
652C43—112no—
653C22×C11—22no—
654C22×C11—22no—
655C22×C11—22no—
656C22×C11—22no—
657C22×C11—22no—
658C22×C11—22no—
659C22×C11C4×#4114yescomplemented
660C22×C11C24×C411yescharacteristic
661C22×C11C23×D411yescharacteristic
662C22×C11C22×#4111yescharacteristic
663C22×C11C22×#4111yescharacteristic
664C22×C11C22×#4111yescharacteristic
665C22×C11#58511yescharacteristic
666C22×C11#58511yescharacteristic
667C2×D11—22no—
668C2×D11—22no—
669C2×D11—22no—
670C2×D11—22no—
671C2×D11—22no—
672C2×D11—22no—
673C2×D11—22no—
674C2×D11—24no—
675C2×D11—22no—
676C2×D11—24no—
677C2×D11—22no—
678C2×D11—24no—
679C2×D11—416no—
680C2×D11—41no—
681C2×D11—41no—
682C2×D11—42no—
683C2×D11—42no—
684C2×D11—42no—
685C2×D11—42no—
686C2×D11—41no—
687C2×D11—41no—
688C2×D11C2×C4×D414yes—
689C4×C11—22no—
690C4×C11—24no—
691C4×C11—24no—
692C4×C11—24no—
693C4×C11—22no—
694C4×C11—22no—
695C4×C11—42no—
696C4×C11—41no—
697C4×C11—41no—
698C4×C11C2×C4×D414yes—
699Dic11—22no—
700Dic11—24no—
701Dic11—22no—
702Dic11—24no—
703Dic11—22no—
704Dic11—41no—
705Dic11—42no—
706Dic11—41no—
707Dic11C2×C4×D414yes—
708C25—111no—
709C2×#41—118no—
710C2×#41—224no—
711C2×#41—224no—
712C22×Q8C22×D1111yescharacteristic
713C22×D4—112no—
714C22×D4—112no—
715C22×D4—111no—
716C22×D4—112no—
717C23×C4—111no—
718C23×C4—111no—
719C23×C4—118no—
720C23×C4—111no—
721C23×C4—111no—
722C23×C4—111no—
723C23×C4—112no—
724C23×C4—112no—
725C23×C4—111no—
726C23×C4—111no—
727C23×C4—111no—
728C23×C4—111no—
729C23×C4—112no—
730C23×C4—112no—
731C23×C4—224no—
732C23×C4—224no—
733C23×C4C22×D1112yes—
734C23×C4C22×D1111yescharacteristic
735#123—1116no—
736C22⋊Q8—118no—
737C22⋊Q8C4×D1118yescomplemented
738#121—118no—
739#121—118no—
740#120—1116no—
741C4×Q8—24no—
742C4×Q8—224no—
743C4×D4—1116no—
744C4×D4—1116no—
745C4×D4—228no—
746C4×D4—224no—
747C4×D4—228no—
748C4×D4—228no—
749C4×D4—224no—
750C4×D4—228no—
751#117—118no—
752#117—118no—
753#117—228no—
754#117—228no—
755#117—228no—
756#117—224no—
757#117—224no—
758#117—224no—
759C2×C4⋊C4—24no—
760C2×C4⋊C4—111no—
761C2×C4⋊C4—111no—
762C2×C4⋊C4—112no—
763C2×C4⋊C4—112no—
764C2×C4⋊C4—111no—
765C2×C4⋊C4—112no—
766C2×C4⋊C4—112no—
767C2×C4⋊C4—112no—
768C2×C4⋊C4—112no—
769C2×C4⋊C4—224no—
770C2×C4⋊C4C22×D1112yes—
771C2×C4⋊C4C22×D1111yescharacteristic
772C2×C4⋊C4C22×D1112yes—
773C2×C4⋊C4C22×D1112yes—
774C2×C4⋊C4C22×D1111yescharacteristic
775C2×C4⋊C4C22×D1112yes—
776C2×C4⋊C4C22×D1111yescharacteristic
777C2×C22⋊C4—111no—
778C2×C22⋊C4—112no—
779C2×C22⋊C4—112no—
780C2×C22⋊C4—112no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—111no—
788C2×C22⋊C4—111no—
789C2×C22⋊C4—111no—
790C2×C22⋊C4—111no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—224no—
798C2×C22⋊C4—228no—
799C2×C22⋊C4—224no—
800C2×C22⋊C4C22×D1111yescharacteristic
801C2×C22⋊C4C22×D1112yes—
802C2×C22⋊C4C22×D1111yescharacteristic
803C2×C42—112no—
804C2×C42—112no—
805C2×C42—111no—
806C2×C42—112no—
807C2×C42—112no—
808C2×C42—112no—
809C2×C42—111no—
810C2×C42—112no—
811C2×C42—112no—
812C2×C42—112no—
813C2×C42—111no—
814C2×C42—111no—
815C2×C42—111no—
816C2×C42—111no—
817C2×C42—112no—
818C2×C42—228no—
819C2×C42—224no—
820C2×C42—224no—
821C2×C42—228no—
822C2×C42C22×D1111yescharacteristic
823C2×C42C22×D1112yes—
824C2×C42C22×D1111yescharacteristic
825C2×C42C22×D1112yes—
826#95—111no—
827#95—111no—
828#95—111no—
829#95—111no—
830#95—111no—
831#95—111no—
832#95—112no—
833#95—112no—
834#95—112no—
835#95—112no—
836#95—112no—
837#95—112no—
838#95—112no—
839#95—112no—
840#95C22×D1111yescharacteristic
841#95C22×D1111yescharacteristic
842#95C22×D1112yes—
843#95C22×D1112yes—
844#95C22×D1112yes—
845#95C22×D1112yes—
846C2×C11—24no—
847C2×C11C22×C4×D411yescharacteristic
848C2×C11C2×C4×#4111yescharacteristic
849C2×C11#342811yescharacteristic
850C2×C11D4×#4111yescharacteristic
851C2×C11D4×#4111yescharacteristic
852C2×C11#347511yescharacteristic
853C2×C11#347511yescharacteristic
854D11—24no—
855D11—44no—
856D11—42no—
857C24—111no—
858C24—111no—
859C24—112no—
860C24—114no—
861C24—222no—
862C24—222no—
863C24—222no—
864C24—222no—
865C24—441no—
866C24—441no—
867C24C23×D1111yescharacteristic
868#41—2232no—
869C2×Q8—22no—
870C2×Q8—22no—
871C2×Q8C2×C4×D1114yes—
872C2×D4—118no—
873C2×D4—118no—
874C2×D4—114no—
875C2×D4—118no—
876C2×D4—224no—
877C2×D4—224no—
878C2×D4—224no—
879C2×D4—224no—
880C2×D4—222no—
881C2×D4—222no—
882C2×D4—442no—
883C2×D4—442no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—24no—
887C22×C4—24no—
888C22×C4—42no—
889C22×C4—111no—
890C22×C4—114no—
891C22×C4—114no—
892C22×C4—114no—
893C22×C4—114no—
894C22×C4—111no—
895C22×C4—111no—
896C22×C4—111no—
897C22×C4—112no—
898C22×C4—112no—
899C22×C4—114no—
900C22×C4—118no—
901C22×C4—114no—
902C22×C4—114no—
903C22×C4—111no—
904C22×C4—111no—
905C22×C4—112no—
906C22×C4—224no—
907C22×C4—222no—
908C22×C4—222no—
909C22×C4—2232no—
910C22×C4—224no—
911C22×C4—224no—
912C22×C4—222no—
913C22×C4—222no—
914C22×C4—224no—
915C22×C4—222no—
916C22×C4—222no—
917C22×C4—222no—
918C22×C4—222no—
919C22×C4—222no—
920C22×C4—222no—
921C22×C4—222no—
922C22×C4—222no—
923C22×C4—224no—
924C22×C4—222no—
925C22×C4—222no—
926C22×C4—224no—
927C22×C4—224no—
928C22×C4—222no—
929C22×C4—222no—
930C22×C4—224no—
931C22×C4—441no—
932C22×C4—442no—
933C22×C4—442no—
934C22×C4—441no—
935C22×C4—441no—
936C22×C4—441no—
937C22×C4—442no—
938C22×C4C2×C4×D1114yes—
939C22×C4C23×D1111yescharacteristic
940C22×C4C23×D1111yescharacteristic
941C22×C4C23×D1112yes—
942C22×C4C23×D1112yes—
943C22×C4C23×D1112yes—
944C22×C4C23×D1111yescharacteristic
945C22×C4C23×D1112yes—
946C22×C4C23×D1111yescharacteristic
947C22×C4C23×D1111yescharacteristic
948C22×C4C23×D1111yescharacteristic
949C4⋊C4—24no—
950C4⋊C4—22no—
951C4⋊C4—24no—
952C4⋊C4—42no—
953C4⋊C4—114no—
954C4⋊C4—118no—
955C4⋊C4—114no—
956C4⋊C4—224no—
957C4⋊C4—224no—
958C4⋊C4—224no—
959C4⋊C4—222no—
960C4⋊C4—224no—
961C4⋊C4—442no—
962C4⋊C4C2×C4×D1114yes—
963C4⋊C4C2×C4×D1118yes—
964C4⋊C4D4×D1114yes—
965C22⋊C4—22no—
966C22⋊C4—114no—
967C22⋊C4—118no—
968C22⋊C4—118no—
969C22⋊C4—118no—
970C22⋊C4—118no—
971C22⋊C4—118no—
972C22⋊C4—224no—
973C22⋊C4—222no—
974C22⋊C4—222no—
975C22⋊C4—224no—
976C22⋊C4—224no—
977C22⋊C4—224no—
978C22⋊C4—222no—
979C22⋊C4—224no—
980C22⋊C4—224no—
981C22⋊C4—222no—
982C22⋊C4—222no—
983C22⋊C4—224no—
984C22⋊C4—442no—
985C22⋊C4—442no—
986C22⋊C4C2×C4×D1118yes—
987C22⋊C4#434314yescomplemented
988C42—24no—
989C42—22no—
990C42—22no—
991C42—42no—
992C42—118no—
993C42—118no—
994C42—222no—
995C42—222no—
996C42—224no—
997C42—224no—
998C42—224no—
999C42—222no—
1000C42—222no—
1001C42—224no—
1002C42—224no—
1003C42—222no—
1004C42—224no—
1005C42—222no—
1006C42—442no—
1007C11#3413611yescharacteristic, complemented, Sylow
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—112no—
1013C23—112no—
1014C23—112no—
1015C23—112no—
1016C23—114no—
1017C23—228no—
1018C23—221no—
1019C23—221no—
1020C23—221no—
1021C23—221no—
1022C23—228no—
1023C23—221no—
1024C23—222no—
1025C23—221no—
1026C23—222no—
1027C23—221no—
1028C23—222no—
1029C23—221no—
1030C23—222no—
1031C23—222no—
1032C23—221no—
1033C23—222no—
1034C23—221no—
1035C23—444no—
1036C23—444no—
1037C23—444no—
1038C23—444no—
1039C23—444no—
1040C23C22×C4×D1112yes—
1041C23C2×#434312yes—
1042C23#41×D1112yes—
1043C23C24×D1111yescharacteristic
1044Q8—28no—
1045D4—2216no—
1046D4—2216no—
1047D4—228no—
1048D4—448no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—21no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—21no—
1061C2×C4—28no—
1062C2×C4—21no—
1063C2×C4—22no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—48no—
1072C2×C4—112no—
1073C2×C4—112no—
1074C2×C4—112no—
1075C2×C4—1116no—
1076C2×C4—114no—
1077C2×C4—112no—
1078C2×C4—114no—
1079C2×C4—112no—
1080C2×C4—112no—
1081C2×C4—228no—
1082C2×C4—2216no—
1083C2×C4—228no—
1084C2×C4—228no—
1085C2×C4—221no—
1086C2×C4—221no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—221no—
1090C2×C4—222no—
1091C2×C4—221no—
1092C2×C4—221no—
1093C2×C4—221no—
1094C2×C4—222no—
1095C2×C4—228no—
1096C2×C4—222no—
1097C2×C4—221no—
1098C2×C4—221no—
1099C2×C4—221no—
1100C2×C4—222no—
1101C2×C4—221no—
1102C2×C4—221no—
1103C2×C4—222no—
1104C2×C4—221no—
1105C2×C4—448no—
1106C2×C4—448no—
1107C2×C4—444no—
1108C2×C4—444no—
1109C2×C4—444no—
1110C2×C4—444no—
1111C2×C4—448no—
1112C2×C4C22×C4×D1114yes—
1113C2×C4C22×C4×D1112yes—
1114C2×C4C22×C4×D1114yes—
1115C2×C4C22×C4×D1112yes—
1116C2×C4C2×D4×D1114yes—
1117C2×C4C2×D4×D1112yes—
1118C2×C4C2×#434312yes—
1119C2×C4C2×#434312yes—
1120C2×C4#41×D1112yes—
1121C22—22no—
1122C22—22no—
1123C22—22no—
1124C22—22no—
1125C22—22no—
1126C22—22no—
1127C22—114no—
1128C22—222no—
1129C22—222no—
1130C22—222no—
1131C22—222no—
1132C22—222no—
1133C22—222no—
1134C22—222no—
1135C22—224no—
1136C22—224no—
1137C22—222no—
1138C22—222no—
1139C22—224no—
1140C22—4416no—
1141C22—441no—
1142C22—442no—
1143C22—441no—
1144C22—442no—
1145C22—442no—
1146C22—441no—
1147C22—442no—
1148C22—441no—
1149C22C4×#434314yescomplemented
1150C22C23×C4×D1111yescharacteristic
1151C22C22×D4×D1111yescharacteristic
1152C22C22×#434311yescharacteristic
1153C22C2×#41×D1111yescharacteristic
1154C22C2×#41×D1111yescharacteristic
1155C22#1062345511yescharacteristic
1156C22#1062345711yescharacteristic
1157C4—22no—
1158C4—22no—
1159C4—24no—
1160C4—24no—
1161C4—24no—
1162C4—22no—
1163C4—41no—
1164C4—42no—
1165C4—41no—
1166C4—114no—
1167C4—222no—
1168C4—222no—
1169C4—224no—
1170C4—222no—
1171C4—224no—
1172C4—441no—
1173C4—441no—
1174C4—442no—
1175C4C4×D4×D1114yes—
1176C2—24no—
1177C2—224no—
1178C2—442no—
1179C2—444no—
1180C2C2×C4×D4×D1111yescharacteristic
1181C2C2×C4×#434311yescharacteristic
1182C2#1308181611yescharacteristic
1183C2#1308210011yescharacteristic
1184C2D4×#434311yescharacteristic
1185C2#1308216911yescharacteristic
1186C2#1308218211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2360C2
socle, cosocleC23×C11C25
prime radicalC2×#10623158C2
hypercenter#2360D11
hypocenterC11#34136
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2360

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4343C2semidirect
3. C22×#66945C2semidirect
4. #13071656C2semidirect
5. #13071653C2semidirect
6. #13071648C2semidirect
7. #13071639C2semidirect
8. #13071632C2semidirect
9. #13071630C2semidirect
10. #13071625C2semidirect
11. #13071615C2semidirect
12. #13071603C2semidirect
13. #13071598C2semidirect
14. #13071592C2semidirect
15. #13071105C2semidirect
16. #13071097C2semidirect
17. #13071074C2semidirect
18. #13071054C2semidirect
19. #13071052C2semidirect
20. C4×(C22⋊D11)⋊C4C2semidirect
21. C4×#66945C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2360C2semidirect
27. C2×C4×Q8×C11C22semidirect
30. C2×Q8×Dic11C22semidirect
36. #10623158C4semidirect
42. C2×#66946C22semidirect
51. C2×#66945C22semidirect
58. C2×C4×D44C22semidirect
61. C2×C42×D11C22semidirect
62. C11×#391C22semidirect
63. C11×#389C22semidirect
64. C11×#389C22semidirect
65. C11×#387C22semidirect
67. C4×C11×C4⋊C4C22semidirect
70. #10622843C22semidirect
74. #10622603C22semidirect
75. #10622603C22semidirect
77. #10622602C22semidirect
79. #10622601C22semidirect
80. #10622598C22semidirect
81. #10622598C22semidirect
82. #10622594C22semidirect
83. #10622591C22semidirect
84. C4⋊C4×Dic11C22semidirect
85. C4⋊C4×Dic11C22semidirect
86. C4⋊C4×Dic11C22semidirect
87. #10622586C22semidirect
95. #10622552C22semidirect
99. C4×(C2×D11)⋊C4C22semidirect
100. C4×C4⋊Dic11C22semidirect
101. C4×Dic11⋊C4C22semidirect
102. C42×Dic11C22semidirect
103. #10622541C22semidirect
105. #10622283C22semidirect
106. #10622283C22semidirect
109. #10622281C22semidirect
113. #10622279C22semidirect
114. #10622279C22semidirect
115. #10622279C22semidirect
122. #10622268C22semidirect
123. #10622262C22semidirect
124. #10622262C22semidirect
125. #10622261C22semidirect
135. C2×#4343C2×C4semidirect
141. C22×C4×D11C2×C4semidirect
153. C11×C22⋊Q8C2×C4semidirect
172. #66999C2×C4semidirect
174. #66983C2×C4semidirect
221. #66948C2×C4semidirect
222. #66947C2×C4semidirect
225. #66946C2×C4semidirect
232. #66945C2×C4semidirect
233. #66945D4semidirect
234. #66935C2×C4semidirect
236. (C22⋊D11)⋊C4C2×C4semidirect
366. C11×C22⋊C4#41semidirect
372. C22⋊Dic11#41semidirect
425. #2360D11semidirect
550. C4×D11C4×D4semidirect
562. C2×C4×Q8C2×D11semidirect
590. #391C2×D11semidirect
599. #389C2×D11semidirect
600. #389C2×D11semidirect
612. #387C2×D11semidirect
632. C4×C4⋊C4C2×D11semidirect
659. C22×C11C4×#41semidirect
737. C22⋊Q8C4×D11semidirect
987. C22⋊C4#4343semidirect
1007. C11#34136semidirect
1149. C22C4×#4343semidirect

Maximal subgroups

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

subgroupindex
C2×#106231582
C2×C4×#43432
C22×#669452
#130716562
#130716532
#130716482
#130716392
#130716322
#130716302
#130716252
#130716152
#130716032
#130715982
#130715922
#130711052
#130710972
#130710742
#130710542
#130710522
C4×(C22⋊D11)⋊C42
C4×#669452
C4×C22⋊C4×D112
C11×#23602
#3413611