Finite Group Databasebeta

← #14914047

Subgroups — #14914047

Order 2816.

3534 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623158C211yesmaximal, characteristic
2C2×#10623105C211yesmaximal, characteristic, complemented
3C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
4#13071634C211yesmaximal, characteristic, complemented
5#13071632C211yesmaximal, characteristic, complemented
6#13071631C211yesmaximal, characteristic, complemented
7#13071630C211yesmaximal, characteristic, complemented
8#13071626C211yesmaximal, characteristic, complemented
9#13071625C211yesmaximal, characteristic, complemented
10#13071617C211yesmaximal, characteristic, complemented
11#13071540C212yesmaximal, complemented
12#13071539C212yesmaximal, complemented
13#13071517C212yesmaximal, complemented
14#13071514C212yesmaximal, complemented
15#13071289C212yesmaximal, complemented
16#13071280C212yesmaximal, complemented
17#13071238C211yesmaximal, characteristic, complemented
18#13071207C211yesmaximal, characteristic, complemented
19C4×#66935C212yesmaximal, complemented
20#13071117C212yesmaximal, complemented
21#13070997C211yesmaximal, characteristic, complemented
22#13070970C211yesmaximal, characteristic, complemented
23C11×#2360C211yesmaximal, characteristic, complemented
24C22×#4343C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C23×C4×D11C2212yes—
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic, complemented
29C22×C11×C4⋊C4C2211yescharacteristic
30C2×#66999C2211yescharacteristic
31C2×Q8×Dic11C2211yescharacteristic, complemented
32C2×#66983C2211yescharacteristic
33C2×C4×C22⋊D11C2212yes—
34C22×C4⋊Dic11C2211yescharacteristic
35C22×Dic11⋊C4C2212yes—
36#10623158C4116yescomplemented
37#10623105—28no—
38C2×#66948C2211yescharacteristic
39C2×#66947C2212yes—
40C2×#66946C2212yes—
41C2×#66946C2212yes—
42C2×#66946C2212yes—
43C2×#66946C2211yescharacteristic, complemented
44C2×#66945C2211yescharacteristic
45C2×C4⋊C4×D11—28no—
46C2×C4⋊C4×D11C2211yescharacteristic
47C2×C4⋊C4×D11C2211yescharacteristic
48C2×C4⋊C4×D11C2211yescharacteristic
49C2×C4⋊C4×D11C2212yes—
50C2×C4⋊C4×D11C2212yes—
51C2×C4⋊C4×D11C2211yescharacteristic
52C2×C4⋊C4×D11C2212yescomplemented
53C2×#66935C2212yes—
54C2×(C22⋊D11)⋊C4C2212yes—
55C2×(C22⋊D11)⋊C4C2212yes—
56C2×C4×D44C2212yes—
57C2×C4×D44C2212yes—
58C2×C4×D44C2211yescharacteristic, complemented
59C2×#66925C2211yescharacteristic
60C2×#66925C2211yescharacteristic
61C2×#66925C2212yescomplemented
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#10622603C2212yescomplemented
74#10622602C2212yes—
75#10622602C2212yes—
76#10622602C2212yescomplemented
77#10622602C2212yescomplemented
78#10622601C2211yescharacteristic, complemented
79#10622598C2211yescharacteristic, complemented
80#10622598C2212yescomplemented
81#10622594C2212yescomplemented
82#10622589C2212yescomplemented
83C4⋊C4×Dic11C2211yescharacteristic, complemented
84C4⋊C4×Dic11C2211yescharacteristic, complemented
85#10622586C2211yescharacteristic, complemented
86#10622585C2212yescomplemented
87#10622571C2212yes—
88#10622568C2211yescharacteristic
89#10622568C2211yescharacteristic
90#10622563C2212yes—
91#10622555C2211yescharacteristic
92#10622555C2211yescharacteristic
93C22⋊C4×Dic11C2212yes—
94#10622553C2212yescomplemented
95#10622552C2211yescharacteristic, complemented
96C4×(C2×D11)⋊C4C2211yescharacteristic
97C4×(C2×D11)⋊C4C2212yes—
98C4×(C2×D11)⋊C4C2211yescharacteristic
99C4×(C2×D11)⋊C4C2212yes—
100C4×C4⋊Dic11C2211yescharacteristic, complemented
101#10622546C2212yescomplemented
102C4×Dic11⋊C4C2212yescomplemented
103#10622541C2211yescharacteristic, complemented
104#10622283C2212yescomplemented
105#10622282C2212yescomplemented
106#10622281C2212yes—
107#10622281C2212yes—
108#10622281C2212yescomplemented
109#10622281C2212yescomplemented
110#10622280C2211yescharacteristic
111#10622280C2211yescharacteristic
112#10622280C2212yescomplemented
113#10622280C2212yescomplemented
114#10622279C2212yes—
115#10622279C2212yes—
116#10622278C2212yes—
117#10622278C2212yes—
118#10622278C2212yes—
119#10622278C2212yes—
120#10622277C2211yescharacteristic
121#10622277C2211yescharacteristic
122#10622265C2212yescomplemented
123#10622263C2212yescomplemented
124#10622262C2212yescomplemented
125#10622260C2212yescomplemented
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×D44C2312yes—
138C22×D44C2311yescharacteristic
139C22×C4×D11—24no—
140C22×C4×D11—24no—
141C22×C4×D11—28no—
142C22×C4×D11—44no—
143C22×C4×D11—44no—
144C22×C4×D11C2×C418yescomplemented
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2312yes—
151C22×C4×D11C2312yes—
152C22×C4×D11C2312yes—
153C22×C4×D11C2312yes—
154C22×C4×D11C2312yes—
155C22×C4×D11C2311yescharacteristic
156C11×C22⋊Q8C2×C418yescomplemented
157C4×Q8×C11—24no—
158C2×C11×C4⋊C4—24no—
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2312yes—
161C2×C11×C4⋊C4C2312yes—
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2312yes—
165C2×C11×C4⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2312yes—
169C2×C42×C11C2311yescharacteristic
170C2×C42×C11C2311yescharacteristic
171C2×C42×C11C2312yes—
172C2×C42×C11C2312yes—
173C2×C22⋊Dic11C2311yescharacteristic
174C2×C22⋊Dic11C2311yescharacteristic
175#66999C2×C418yescomplemented
176Q8×Dic11—24no—
177#66983C2×C418yescomplemented
178C4×C22⋊D11—44no—
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)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2311yescharacteristic
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×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×C4⋊Dic11—24no—
198C2×C4⋊Dic11C2312yes—
199C2×C4⋊Dic11C2312yes—
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2312yes—
202C2×C4⋊Dic11C2311yescharacteristic
203C2×C4⋊Dic11C2311yescharacteristic
204C2×Dic11⋊C4—28no—
205C2×Dic11⋊C4C2311yescharacteristic
206C2×Dic11⋊C4C2311yescharacteristic
207C2×Dic11⋊C4C2311yescharacteristic
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2312yes—
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2312yes—
222C2×C4×Dic11C2312yes—
223#66948C2×C418yescomplemented
224#66947C2×C4116yescomplemented
225#66946—28no—
226#66946—24no—
227#66946—44no—
228#66946C2×C4116yescomplemented
229#66945C2×C418yescomplemented
230C4⋊C4×D11—24no—
231C4⋊C4×D11—28no—
232C4⋊C4×D11—24no—
233C4⋊C4×D11—24no—
234C4⋊C4×D11—28no—
235C4⋊C4×D11—28no—
236C4⋊C4×D11D418yescomplemented
237#66935C2×C4116yescomplemented
238(C22⋊D11)⋊C4—44no—
239(C22⋊D11)⋊C4C2×C4116yescomplemented
240C4×D44—28no—
241C4×D44—24no—
242C4×D44—44no—
243#66925—24no—
244#66925—24no—
245#66925—28no—
246C11×#95C2312yes—
247C11×#95C2312yes—
248C11×#95C2312yes—
249C11×#95C2312yes—
250C11×#95C2311yescharacteristic
251C11×#95C2311yescharacteristic
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2311yescharacteristic
258C11⋊#95C2312yes—
259C11⋊#95C2311yescharacteristic
260C11⋊#95C2311yescharacteristic
261C11⋊#95C2311yescharacteristic
262C11⋊#95C2311yescharacteristic
263C11⋊#95C2312yes—
264C11⋊#95C2312yes—
265C11⋊#95C2312yes—
266#34200—111nomaximal, Sylow
267C24×C11C2411yescharacteristic
268C23×D11—22no—
269C23×D11—22no—
270C23×D11—22no—
271C23×D11—22no—
272C23×D11—22no—
273C23×D11—22no—
274C23×D11C22×C414yes—
275C23×D11C2412yes—
276C23×D11C2411yescharacteristic
277C23×D11C2411yescharacteristic
278C2×Q8×C11—22no—
279C2×Q8×C11—22no—
280C2×Q8×C11C22×C414yescomplemented
281C22×C4×C11—22no—
282C22×C4×C11—22no—
283C22×C4×C11—24no—
284C22×C4×C11—24no—
285C22×C4×C11—42no—
286C22×C4×C11C22×C414yes—
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2412yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2412yes—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2412yes—
296C22×C4×C11C2411yescharacteristic
297C2×C22⋊D11—24no—
298C2×C22⋊D11—24no—
299C2×C22⋊D11C22×C418yes—
300C22×Dic11—22no—
301C22×Dic11—22no—
302C22×Dic11—24no—
303C22×Dic11—24no—
304C22×Dic11—42no—
305C22×Dic11C22×C414yes—
306C22×Dic11C2411yescharacteristic
307C22×Dic11C2411yescharacteristic
308C22×Dic11C2411yescharacteristic
309C22×Dic11C2412yes—
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2412yes—
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2412yes—
314C22×Dic11C2411yescharacteristic
315#4343—232no—
316C2×D44—24no—
317C2×D44—24no—
318C2×D44—24no—
319C2×D44—24no—
320C2×D44—22no—
321C2×D44—22no—
322C2×D44C22×C418yes—
323C2×D44C22×C418yes—
324C2×D44C22×C414yescomplemented
325C2×C4×D11—24no—
326C2×C4×D11—22no—
327C2×C4×D11—22no—
328C2×C4×D11—24no—
329C2×C4×D11—232no—
330C2×C4×D11—24no—
331C2×C4×D11—24no—
332C2×C4×D11—22no—
333C2×C4×D11—24no—
334C2×C4×D11—22no—
335C2×C4×D11—24no—
336C2×C4×D11—24no—
337C2×C4×D11—22no—
338C2×C4×D11—24no—
339C2×C4×D11—24no—
340C2×C4×D11—22no—
341C2×C4×D11—42no—
342C2×C4×D11—42no—
343C2×C4×D11—42no—
344C2×C4×D11—42no—
345C2×C4×D11—42no—
346C2×C4×D11—42no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11—42no—
350C2×C4×D11—42no—
351C2×C4×D11—432no—
352C2×C4×D11C22×C414yes—
353C2×C4×D11C22×C414yes—
354C2×C4×D11C22×C414yes—
355C2×C4×D11C22×C414yes—
356C2×C4×D11C22×C418yescomplemented
357C2×C4×D11C2×D418yes—
358C2×C4×D11C2×D414yes—
359C2×C4×D11#4114yes—
360C11×C4⋊C4—24no—
361C11×C4⋊C4—22no—
362C11×C4⋊C4—24no—
363C11×C4⋊C4—42no—
364C11×C4⋊C4C22×C414yescomplemented
365C11×C4⋊C4C22×C418yescomplemented
366C11×C4⋊C4C2×D414yes—
367C11×C22⋊C4—22no—
368C11×C22⋊C4—22no—
369C11×C22⋊C4C22×C418yes—
370C42×C11—24no—
371C42×C11—22no—
372C42×C11—22no—
373C42×C11—42no—
374C22⋊Dic11—22no—
375C22⋊Dic11—22no—
376(C2×D11)⋊C4—24no—
377(C2×D11)⋊C4—22no—
378(C2×D11)⋊C4—22no—
379(C2×D11)⋊C4—22no—
380(C2×D11)⋊C4—22no—
381(C2×D11)⋊C4—22no—
382(C2×D11)⋊C4—22no—
383(C2×D11)⋊C4—22no—
384(C2×D11)⋊C4—22no—
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—42no—
387(C2×D11)⋊C4—42no—
388(C2×D11)⋊C4—42no—
389(C2×D11)⋊C4—42no—
390(C2×D11)⋊C4C22×C418yes—
391(C2×D11)⋊C4C22×C418yes—
392(C2×D11)⋊C4C22×C418yescomplemented
393(C2×D11)⋊C4C22×C418yescomplemented
394C4⋊Dic11—24no—
395C4⋊Dic11—24no—
396C4⋊Dic11—22no—
397C4⋊Dic11—42no—
398C4⋊Dic11C22×C414yescomplemented
399C4⋊Dic11C2×D414yes—
400Dic11⋊C4—22no—
401Dic11⋊C4—22no—
402Dic11⋊C4—24no—
403Dic11⋊C4—24no—
404Dic11⋊C4—22no—
405Dic11⋊C4—22no—
406Dic11⋊C4—24no—
407Dic11⋊C4—42no—
408Dic11⋊C4—42no—
409Dic11⋊C4C22×C418yescomplemented
410Dic11⋊C4C2×D418yes—
411C4×Dic11—24no—
412C4×Dic11—22no—
413C4×Dic11—22no—
414C4×Dic11—42no—
415C4×Dic11—42no—
416C4×Dic11—42no—
417C4×Dic11C22×C418yescomplemented
418C2×#525—111no—
419C2×#520—111no—
420C23×C4⋊C4—111no—
421#2361—111no—
422#2361—111no—
423#2361—111no—
424#2361—111no—
425#2360—111no—
426#2360—111no—
427#2360—111no—
428#2360D1111yescharacteristic, complemented
429#2352—112no—
430#2352—112no—
431D4×C4⋊C4—112no—
432D4×C4⋊C4—112no—
433#2322—112no—
434#2322—112no—
435#2317—111no—
436#2311—111no—
437C4×#120—112no—
438C4×#120—112no—
439#2280—111no—
440#2274—111no—
441C23×C11—21no—
442C23×C11—21no—
443C23×C11—21no—
444C23×C11—21no—
445C23×C11C23×C412yes—
446C23×C11H(5,𝔽2)12yes—
447C23×C112−1+412yes—
448C23×C11C2511yescharacteristic
449C22×D11—28no—
450C22×D11—28no—
451C22×D11—28no—
452C22×D11—28no—
453C22×D11—28no—
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—21no—
461C22×D11—21no—
462C22×D11—28no—
463C22×D11—28no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11C23×C414yes—
471C22×D11C23×C412yes—
472C22×D11C23×C412yes—
473C22×D11C22×D412yes—
474C22×D11C2×#4112yes—
475C22×D11H(5,𝔽2)12yes—
476C22×D112−1+412yes—
477Q8×C11—28no—
478C2×C4×C11—22no—
479C2×C4×C11—21no—
480C2×C4×C11—21no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—28no—
487C2×C4×C11—22no—
488C2×C4×C11—21no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—22no—
495C2×C4×C11—21no—
496C2×C4×C11—21no—
497C2×C4×C11—22no—
498C2×C4×C11—21no—
499C2×C4×C11—21no—
500C2×C4×C11—21no—
501C2×C4×C11—21no—
502C2×C4×C11—48no—
503C2×C4×C11C23×C414yes—
504C2×C4×C11C23×C414yes—
505C2×C4×C11C23×C412yes—
506C2×C4×C11C23×C412yes—
507C2×C4×C11C22×D414yes—
508C2×C4×C11C22×D412yes—
509C2×C4×C11C2×#4112yes—
510C22⋊D11—216no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—28no—
518C2×Dic11—21no—
519C2×Dic11—21no—
520C2×Dic11—22no—
521C2×Dic11—21no—
522C2×Dic11—21no—
523C2×Dic11—21no—
524C2×Dic11—21no—
525C2×Dic11—21no—
526C2×Dic11—22no—
527C2×Dic11—21no—
528C2×Dic11—22no—
529C2×Dic11—21no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—21no—
533C2×Dic11—48no—
534C2×Dic11C23×C414yes—
535C2×Dic11C23×C412yes—
536C2×Dic11C23×C412yes—
537C2×Dic11C22×D414yes—
538C2×Dic11C22×D412yes—
539C2×Dic11C2×#4112yes—
540D44—216no—
541D44—216no—
542D44—28no—
543C4×D11—28no—
544C4×D11—28no—
545C4×D11—28no—
546C4×D11—216no—
547C4×D11—48no—
548C4×D11—48no—
549C4×D11—48no—
550C4×D11—48no—
551C4×D11—84no—
552C4×D11—84no—
553C4×D11C4×D4116yescomplemented
554C22×#41—111no—
555C24×C4—111no—
556C24×C4—112no—
557#525—1116no—
558C2×#123—112no—
559C2×C22⋊Q8—111no—
560C2×C22⋊Q8C2×D1111yescharacteristic
561C2×#121—111no—
562C2×#121—111no—
563C2×#120—112no—
564#520—228no—
565C2×C4×Q8—111no—
566C2×C4×Q8C2×D1111yescharacteristic, complemented
567C2×C4×D4—112no—
568C2×C4×D4—112no—
569C2×C4×D4—112no—
570C2×C4×D4—111no—
571C2×C4×D4—112no—
572C2×C4×D4—112no—
573C2×C4×D4—112no—
574C2×C4×D4—112no—
575C2×C4×D4—111no—
576C2×C4×D4—112no—
577C2×#117—111no—
578C2×#117—111no—
579C2×#117—111no—
580C2×#117—112no—
581C22×C4⋊C4—111no—
582C22×C4⋊C4—112no—
583C22×C4⋊C4—111no—
584C22×C4⋊C4—111no—
585C22×C4⋊C4—112no—
586C22×C4⋊C4—112no—
587C22×C4⋊C4—112no—
588C22×C4⋊C4—111no—
589C22×C4⋊C4—111no—
590C22×C4⋊C4—228no—
591C22×C4⋊C4C2×D1111yescharacteristic
592#391—111no—
593#391C2×D1111yescharacteristic, complemented
594#390—111no—
595#390—111no—
596#389—111no—
597#389—111no—
598#389—112no—
599#389—112no—
600#389—111no—
601#389—112no—
602#389C2×D1111yescharacteristic, complemented
603#389C2×D1112yescomplemented
604#388—112no—
605#388—112no—
606#388—112no—
607#388—112no—
608#387—112no—
609#387—112no—
610#387—112no—
611#387C2×D1112yescomplemented
612#386—112no—
613#386—112no—
614#386—112no—
615#386—112no—
616#386—112no—
617#386—112no—
618#385—112no—
619#385—112no—
620#385—112no—
621#385—112no—
622#385—112no—
623#385—112no—
624#385—112no—
625#385—112no—
626#385—112no—
627#385C2×D1112yes—
628#384—112no—
629#382—112no—
630#381—111no—
631#381—111no—
632#380—111no—
633#380—111no—
634#380—112no—
635#380—112no—
636#380—111no—
637#380—111no—
638#379—111no—
639#379—111no—
640C4×C4⋊C4—111no—
641C4×C4⋊C4—111no—
642C4×C4⋊C4—112no—
643C4×C4⋊C4—111no—
644C4×C4⋊C4—112no—
645C4×C4⋊C4C2×D1111yescharacteristic, complemented
646C4×C22⋊C4—111no—
647C4×C22⋊C4—112no—
648C4×C22⋊C4—112no—
649C4×C22⋊C4—112no—
650C4×C22⋊C4—111no—
651C4×C22⋊C4—111no—
652C4×C22⋊C4—112no—
653C4×C22⋊C4—112no—
654C4×C22⋊C4C2×D1112yes—
655C4×C22⋊C4C2×D1111yescharacteristic
656C22×C11—22no—
657C22×C11—22no—
658C22×C11—22no—
659C22×C11—22no—
660C22×C11—22no—
661C22×C11—22no—
662C22×C11#52014yescomplemented
663C22×C11C24×C411yescharacteristic
664C22×C11C23×D411yescharacteristic
665C22×C11C22×#4111yescharacteristic
666C22×C11C2×H(5,𝔽2)11yescharacteristic
667C22×C11C2×H(5,𝔽2)11yescharacteristic
668C22×C11C2×2−1+411yescharacteristic
669C22×C11C2×2−1+411yescharacteristic
670C2×D11—232no—
671C2×D11—22no—
672C2×D11—22no—
673C2×D11—22no—
674C2×D11—22no—
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—22no—
678C2×D11—22no—
679C2×D11—22no—
680C2×D11—22no—
681C2×D11—22no—
682C2×D11—22no—
683C2×D11—24no—
684C2×D11—24no—
685C2×D11—24no—
686C2×D11—42no—
687C2×D11—42no—
688C2×D11—42no—
689C2×D11—42no—
690C2×D11C2×C4×D414yes—
691C2×D11#52014yescomplemented
692C4×C11—22no—
693C4×C11—24no—
694C4×C11—24no—
695C4×C11—24no—
696C4×C11—42no—
697C4×C11—41no—
698C4×C11—41no—
699C4×C11—41no—
700C4×C11—41no—
701C4×C11C2×C4×D414yes—
702Dic11—22no—
703Dic11—24no—
704Dic11—24no—
705Dic11—42no—
706Dic11—41no—
707Dic11—41no—
708Dic11—41no—
709Dic11—41no—
710Dic11C2×C4×D414yes—
711C25—111no—
712C2×#41—118no—
713C2×#41—224no—
714C2×#41—224no—
715C22×Q8C22×D1111yescharacteristic
716C22×D4—112no—
717C22×D4—112no—
718C22×D4—112no—
719C22×D4—111no—
720C23×C4—111no—
721C23×C4—111no—
722C23×C4—118no—
723C23×C4—111no—
724C23×C4—111no—
725C23×C4—111no—
726C23×C4—112no—
727C23×C4—112no—
728C23×C4—112no—
729C23×C4—112no—
730C23×C4—112no—
731C23×C4—112no—
732C23×C4—112no—
733C23×C4—112no—
734C23×C4—224no—
735C23×C4—224no—
736C23×C4—228no—
737C23×C4—444no—
738C23×C4—444no—
739C23×C4C22×D1112yes—
740C23×C4C22×D1111yescharacteristic
741#123—1116no—
742C22⋊Q8—118no—
743C22⋊Q8C4×D1118yescomplemented
744#121—118no—
745#121—118no—
746#120—1116no—
747C4×Q8—24no—
748C4×Q8—224no—
749C4×D4—1116no—
750C4×D4—1116no—
751C4×D4—224no—
752C4×D4—228no—
753C4×D4—228no—
754C4×D4—224no—
755C4×D4—444no—
756C4×D4—444no—
757C4×D4—444no—
758C4×D4—444no—
759#117—118no—
760#117—228no—
761#117—224no—
762#117—224no—
763C2×C4⋊C4—24no—
764C2×C4⋊C4—112no—
765C2×C4⋊C4—111no—
766C2×C4⋊C4—111no—
767C2×C4⋊C4—112no—
768C2×C4⋊C4—118no—
769C2×C4⋊C4—112no—
770C2×C4⋊C4—112no—
771C2×C4⋊C4—112no—
772C2×C4⋊C4—112no—
773C2×C4⋊C4—111no—
774C2×C4⋊C4—111no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4—228no—
783C2×C4⋊C4—224no—
784C2×C4⋊C4—228no—
785C2×C4⋊C4—224no—
786C2×C4⋊C4—228no—
787C2×C4⋊C4—228no—
788C2×C4⋊C4—224no—
789C2×C4⋊C4—224no—
790C2×C4⋊C4C22×D1112yes—
791C2×C4⋊C4C22×D1111yescharacteristic
792C2×C4⋊C4C22×D1112yes—
793C2×C4⋊C4C22×D1112yes—
794C2×C4⋊C4C22×D1111yescharacteristic
795C2×C4⋊C4C22×D1112yes—
796C2×C4⋊C4C22×D1111yescharacteristic
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—111no—
802C2×C22⋊C4—111no—
803C2×C22⋊C4—111no—
804C2×C22⋊C4—111no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—111no—
808C2×C22⋊C4—111no—
809C2×C22⋊C4—111no—
810C2×C22⋊C4—111no—
811C2×C22⋊C4—111no—
812C2×C22⋊C4—111no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—112no—
817C2×C22⋊C4C22×D1111yescharacteristic
818C2×C22⋊C4C22×D1111yescharacteristic
819C2×C22⋊C4C22×D1112yes—
820C2×C42—112no—
821C2×C42—112no—
822C2×C42—111no—
823C2×C42—111no—
824C2×C42—112no—
825C2×C42—112no—
826C2×C42—112no—
827C2×C42C22×D1112yes—
828C2×C42C22×D1111yescharacteristic
829C2×C42C22×D1111yescharacteristic
830C2×C42C22×D1112yes—
831#95—112no—
832#95—112no—
833#95—112no—
834#95—111no—
835#95—111no—
836#95—111no—
837#95—111no—
838#95—111no—
839#95—111no—
840#95—112no—
841#95—112no—
842#95—112no—
843#95—112no—
844#95—112no—
845#95C22×D1112yes—
846#95C22×D1112yes—
847#95C22×D1111yescharacteristic
848#95C22×D1111yescharacteristic
849#95C22×D1112yes—
850#95C22×D1112yes—
851C2×C11—24no—
852C2×C11C22×C4×D411yescharacteristic
853C2×C11C2×#52011yescharacteristic
854C2×C11C2×#52011yescharacteristic
855C2×C11#348411yescharacteristic
856C2×C11#348611yescharacteristic
857C2×C11#349211yescharacteristic
858C2×C11#349211yescharacteristic
859D11—24no—
860D11—24no—
861D11—44no—
862C24—111no—
863C24—111no—
864C24—114no—
865C24—112no—
866C24—222no—
867C24—222no—
868C24—222no—
869C24—222no—
870C24—222no—
871C24—222no—
872C24C23×D1111yescharacteristic
873#41—2232no—
874C2×Q8—22no—
875C2×Q8—22no—
876C2×Q8C2×C4×D1114yescomplemented
877C2×D4—118no—
878C2×D4—118no—
879C2×D4—118no—
880C2×D4—114no—
881C2×D4—224no—
882C2×D4—224no—
883C2×D4—224no—
884C2×D4—224no—
885C2×D4—224no—
886C2×D4—224no—
887C2×D4—222no—
888C2×D4—222no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—24no—
892C22×C4—24no—
893C22×C4—42no—
894C22×C4—111no—
895C22×C4—114no—
896C22×C4—114no—
897C22×C4—114no—
898C22×C4—114no—
899C22×C4—112no—
900C22×C4—111no—
901C22×C4—112no—
902C22×C4—114no—
903C22×C4—118no—
904C22×C4—114no—
905C22×C4—114no—
906C22×C4—118no—
907C22×C4—111no—
908C22×C4—111no—
909C22×C4—111no—
910C22×C4—112no—
911C22×C4—111no—
912C22×C4—222no—
913C22×C4—224no—
914C22×C4—222no—
915C22×C4—2232no—
916C22×C4—224no—
917C22×C4—224no—
918C22×C4—224no—
919C22×C4—222no—
920C22×C4—222no—
921C22×C4—224no—
922C22×C4—224no—
923C22×C4—224no—
924C22×C4—222no—
925C22×C4—222no—
926C22×C4—224no—
927C22×C4—222no—
928C22×C4—222no—
929C22×C4—224no—
930C22×C4—224no—
931C22×C4—224no—
932C22×C4—442no—
933C22×C4—442no—
934C22×C4—442no—
935C22×C4—442no—
936C22×C4—442no—
937C22×C4—442no—
938C22×C4—442no—
939C22×C4—442no—
940C22×C4—442no—
941C22×C4—442no—
942C22×C4—4432no—
943C22×C4—442no—
944C22×C4C2×C4×D1114yes—
945C22×C4C23×D1111yescharacteristic
946C22×C4C23×D1111yescharacteristic
947C22×C4C23×D1111yescharacteristic
948C22×C4C23×D1112yes—
949C22×C4C23×D1111yescharacteristic
950C22×C4C23×D1112yes—
951C22×C4C23×D1112yes—
952C22×C4C23×D1111yescharacteristic
953C22×C4C23×D1112yes—
954C22×C4C23×D1111yescharacteristic
955C4⋊C4—24no—
956C4⋊C4—22no—
957C4⋊C4—24no—
958C4⋊C4—42no—
959C4⋊C4—114no—
960C4⋊C4—118no—
961C4⋊C4—118no—
962C4⋊C4—114no—
963C4⋊C4—224no—
964C4⋊C4—224no—
965C4⋊C4—224no—
966C4⋊C4—222no—
967C4⋊C4—224no—
968C4⋊C4—222no—
969C4⋊C4—222no—
970C4⋊C4—222no—
971C4⋊C4—224no—
972C4⋊C4—222no—
973C4⋊C4—442no—
974C4⋊C4—442no—
975C4⋊C4—442no—
976C4⋊C4C2×C4×D1114yescomplemented
977C4⋊C4C2×C4×D1118yescomplemented
978C4⋊C4D4×D1114yes—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—118no—
982C22⋊C4—118no—
983C22⋊C4—118no—
984C22⋊C4—118no—
985C22⋊C4—224no—
986C22⋊C4—222no—
987C22⋊C4—222no—
988C22⋊C4—222no—
989C22⋊C4—222no—
990C22⋊C4—222no—
991C22⋊C4—222no—
992C22⋊C4—222no—
993C22⋊C4—222no—
994C22⋊C4—222no—
995C22⋊C4—222no—
996C22⋊C4—224no—
997C22⋊C4—442no—
998C22⋊C4—442no—
999C22⋊C4—442no—
1000C22⋊C4—442no—
1001C22⋊C4C2×C4×D1118yes—
1002C42—24no—
1003C42—22no—
1004C42—22no—
1005C42—42no—
1006C42—118no—
1007C42—224no—
1008C42—222no—
1009C42—222no—
1010C42—442no—
1011C42—442no—
1012C42—442no—
1013C11#3420011yescharacteristic, complemented, Sylow
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—112no—
1019C23—112no—
1020C23—112no—
1021C23—112no—
1022C23—112no—
1023C23—112no—
1024C23—114no—
1025C23—228no—
1026C23—228no—
1027C23—228no—
1028C23—228no—
1029C23—228no—
1030C23—228no—
1031C23—228no—
1032C23—221no—
1033C23—221no—
1034C23—221no—
1035C23—221no—
1036C23—221no—
1037C23—221no—
1038C23—221no—
1039C23—221no—
1040C23—222no—
1041C23—222no—
1042C23—222no—
1043C23—222no—
1044C23—222no—
1045C23—222no—
1046C23C22×C4×D1112yes—
1047C23#6704012yes—
1048C23#6704212yes—
1049C23C24×D1111yescharacteristic
1050Q8—28no—
1051D4—2216no—
1052D4—2216no—
1053D4—2216no—
1054D4—228no—
1055C2×C4—22no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—28no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—48no—
1080C2×C4—112no—
1081C2×C4—112no—
1082C2×C4—112no—
1083C2×C4—1116no—
1084C2×C4—114no—
1085C2×C4—112no—
1086C2×C4—114no—
1087C2×C4—228no—
1088C2×C4—2216no—
1089C2×C4—228no—
1090C2×C4—228no—
1091C2×C4—221no—
1092C2×C4—222no—
1093C2×C4—221no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—228no—
1098C2×C4—221no—
1099C2×C4—221no—
1100C2×C4—222no—
1101C2×C4—221no—
1102C2×C4—221no—
1103C2×C4—221no—
1104C2×C4—221no—
1105C2×C4—221no—
1106C2×C4—221no—
1107C2×C4—222no—
1108C2×C4—221no—
1109C2×C4—221no—
1110C2×C4—222no—
1111C2×C4—221no—
1112C2×C4—221no—
1113C2×C4—448no—
1114C2×C4—448no—
1115C2×C4—448no—
1116C2×C4—448no—
1117C2×C4—448no—
1118C2×C4—884no—
1119C2×C4—884no—
1120C2×C4C22×C4×D1114yes—
1121C2×C4C22×C4×D1112yes—
1122C2×C4C22×C4×D1114yes—
1123C2×C4C22×C4×D1112yes—
1124C2×C4C2×D4×D1114yes—
1125C2×C4C2×D4×D1112yes—
1126C2×C4#41×D1112yes—
1127C22—22no—
1128C22—22no—
1129C22—22no—
1130C22—22no—
1131C22—22no—
1132C22—22no—
1133C22—114no—
1134C22—114no—
1135C22—2232no—
1136C22—222no—
1137C22—222no—
1138C22—222no—
1139C22—222no—
1140C22—222no—
1141C22—222no—
1142C22—222no—
1143C22—222no—
1144C22—222no—
1145C22—222no—
1146C22—222no—
1147C22—222no—
1148C22—224no—
1149C22—224no—
1150C22—224no—
1151C22—442no—
1152C22—442no—
1153C22—442no—
1154C22—442no—
1155C22#1062310514yescomplemented
1156C22C23×C4×D1111yescharacteristic
1157C22C22×D4×D1111yescharacteristic
1158C22C2×#6704011yescharacteristic
1159C22C2×#41×D1111yescharacteristic
1160C22C2×#6704211yescharacteristic
1161C22D11×H(5,𝔽2)11yescharacteristic
1162C22D11×2−1+411yescharacteristic
1163C4—24no—
1164C4—22no—
1165C4—24no—
1166C4—24no—
1167C4—42no—
1168C4—41no—
1169C4—41no—
1170C4—41no—
1171C4—41no—
1172C4—114no—
1173C4—224no—
1174C4—222no—
1175C4—224no—
1176C4—442no—
1177C4—441no—
1178C4—441no—
1179C4—441no—
1180C4—441no—
1181C4C4×D4×D1114yes—
1182C2—24no—
1183C2—224no—
1184C2—224no—
1185C2—444no—
1186C2C2×C4×D4×D1111yescharacteristic
1187C2D11×#52011yescharacteristic
1188C2C2×#1062310511yescharacteristic
1189C2#1308224611yescharacteristic
1190C2#1308226611yescharacteristic
1191C2#1308231611yescharacteristic
1192C2#1308232411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2360C2
socle, cosocleC23×C11C25
prime radicalC2×#10623158C2
hypercenter#2360D11
hypocenterC11#34200
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2360

Complements

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

NH ≅ G/Ntype
2. C2×#10623105C2semidirect
3. C22×C4⋊C4×D11C2semidirect
4. #13071634C2semidirect
5. #13071632C2semidirect
6. #13071631C2semidirect
7. #13071630C2semidirect
8. #13071626C2semidirect
9. #13071625C2semidirect
10. #13071617C2semidirect
11. #13071540C2semidirect
12. #13071539C2semidirect
13. #13071517C2semidirect
14. #13071514C2semidirect
15. #13071289C2semidirect
16. #13071280C2semidirect
17. #13071238C2semidirect
18. #13071207C2semidirect
19. C4×#66935C2semidirect
20. #13071117C2semidirect
21. #13070997C2semidirect
22. #13070970C2semidirect
23. C11×#2360C2semidirect
28. C2×C4×Q8×C11C22semidirect
31. C2×Q8×Dic11C22semidirect
36. #10623158C4semidirect
43. C2×#66946C22semidirect
52. C2×C4⋊C4×D11C22semidirect
58. C2×C4×D44C22semidirect
61. C2×#66925C22semidirect
62. C11×#391C22semidirect
63. C11×#389C22semidirect
64. C11×#389C22semidirect
65. C11×#387C22semidirect
67. C4×C11×C4⋊C4C22semidirect
70. #10622843C22semidirect
73. #10622603C22semidirect
76. #10622602C22semidirect
77. #10622602C22semidirect
78. #10622601C22semidirect
79. #10622598C22semidirect
80. #10622598C22semidirect
81. #10622594C22semidirect
82. #10622589C22semidirect
83. C4⋊C4×Dic11C22semidirect
84. C4⋊C4×Dic11C22semidirect
85. #10622586C22semidirect
86. #10622585C22semidirect
94. #10622553C22semidirect
95. #10622552C22semidirect
100. C4×C4⋊Dic11C22semidirect
101. #10622546C22semidirect
102. C4×Dic11⋊C4C22semidirect
103. #10622541C22semidirect
104. #10622283C22semidirect
105. #10622282C22semidirect
108. #10622281C22semidirect
109. #10622281C22semidirect
112. #10622280C22semidirect
113. #10622280C22semidirect
122. #10622265C22semidirect
123. #10622263C22semidirect
124. #10622262C22semidirect
125. #10622260C22semidirect
135. C2×#4343C2×C4semidirect
144. C22×C4×D11C2×C4semidirect
156. C11×C22⋊Q8C2×C4semidirect
175. #66999C2×C4semidirect
177. #66983C2×C4semidirect
223. #66948C2×C4semidirect
224. #66947C2×C4semidirect
228. #66946C2×C4semidirect
229. #66945C2×C4semidirect
236. C4⋊C4×D11D4semidirect
237. #66935C2×C4semidirect
239. (C22⋊D11)⋊C4C2×C4semidirect
280. C2×Q8×C11C22×C4semidirect
324. C2×D44C22×C4semidirect
356. C2×C4×D11C22×C4semidirect
364. C11×C4⋊C4C22×C4semidirect
365. C11×C4⋊C4C22×C4semidirect
392. (C2×D11)⋊C4C22×C4semidirect
393. (C2×D11)⋊C4C22×C4semidirect
398. C4⋊Dic11C22×C4semidirect
409. Dic11⋊C4C22×C4semidirect
417. C4×Dic11C22×C4semidirect
428. #2360D11semidirect
553. C4×D11C4×D4semidirect
566. C2×C4×Q8C2×D11semidirect
593. #391C2×D11semidirect
602. #389C2×D11semidirect
603. #389C2×D11semidirect
611. #387C2×D11semidirect
645. C4×C4⋊C4C2×D11semidirect
662. C22×C11#520semidirect
691. C2×D11#520semidirect
743. C22⋊Q8C4×D11semidirect
876. C2×Q8C2×C4×D11semidirect
976. C4⋊C4C2×C4×D11semidirect
977. C4⋊C4C2×C4×D11semidirect
1013. C11#34200semidirect
1155. C22#10623105semidirect

Maximal subgroups

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

subgroupindex
C2×#106231582
C2×#106231052
C22×C4⋊C4×D112
#130716342
#130716322
#130716312
#130716302
#130716262
#130716252
#130716172
#130715402
#130715392
#130715172
#130715142
#130712892
#130712802
#130712382
#130712072
C4×#669352
#130711172
#130709972
#130709702
C11×#23602
#3420011