Finite Group Databasebeta

← C2×#13072107 #14921898

Subgroups — C2×#13072107 #14921898

Order 2816.

3438 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C211yesmaximal, characteristic
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3#13072107C2116yesmaximal, direct product factor
4C2×#10622565C211yesmaximal, characteristic, complemented
5C2×#10622287C211yesmaximal, characteristic, complemented
6C2×#10622285C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622570C211yesmaximal, characteristic, complemented
9C2×#10622260C211yesmaximal, characteristic, complemented
10C2×#10622826C211yesmaximal, characteristic, complemented
11C2×#10622278C211yesmaximal, characteristic, complemented
12C2×#10622263C211yesmaximal, characteristic, complemented
13C2×#10622277C211yesmaximal, characteristic, complemented
14C2×#10622280C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#381C211yesmaximal, characteristic, complemented
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C2×C4×C22⋊D11—28no—
28C2×C4×C22⋊D11C2218yescomplemented
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×C4×Dic11C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C2×#66937—28no—
45C2×#66937C2218yes—
46C11×#381C2218yescomplemented
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2211yescharacteristic
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51#10622826C2218yescomplemented
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58#10622574C2218yescomplemented
59#10622570C2218yescomplemented
60#10622565C2218yescomplemented
61#10622287C2218yescomplemented
62#10622285C2218yescomplemented
63#10622280C2218yescomplemented
64#10622279C2218yescomplemented
65#10622278C2218yescomplemented
66#10622277C2218yescomplemented
67#10622263C2218yescomplemented
68#10622260C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C23×C4×C11—24no—
73C23×C4×C11—24no—
74C23×C4×C11—42no—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2314yes—
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—24no—
83C22×C22⋊D11—24no—
84C22×C22⋊D11—24no—
85C22×C22⋊D11—24no—
86C22×C22⋊D11—42no—
87C22×C22⋊D11D418yes—
88C22×C22⋊D11C2314yes—
89C22×C22⋊D11C2314yes—
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C22×D44—24no—
97C22×D44—24no—
98C22×D44—42no—
99C22×D44C2314yes—
100C22×C4×D11—24no—
101C22×C4×D11—24no—
102C22×C4×D11—24no—
103C22×C4×D11—24no—
104C22×C4×D11—24no—
105C22×C4×D11—42no—
106C22×C4×D11C2314yes—
107C22×C4×D11C2314yes—
108C2×C11×C22⋊C4—24no—
109C2×C11×C22⋊C4—42no—
110C2×C11×C22⋊C4C2314yes—
111C2×C11×C22⋊C4C2314yes—
112C2×C22⋊Dic11—24no—
113C2×C22⋊Dic11—42no—
114C2×C22⋊Dic11C2314yes—
115C2×C22⋊Dic11C2314yes—
116C4×C22⋊D11—232no—
117C2×(C2×D11)⋊C4—24no—
118C2×(C2×D11)⋊C4—24no—
119C2×(C2×D11)⋊C4—24no—
120C2×(C2×D11)⋊C4—24no—
121C2×(C2×D11)⋊C4—42no—
122C2×(C2×D11)⋊C4—42no—
123C2×(C2×D11)⋊C4—42no—
124C2×(C2×D11)⋊C4—42no—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×C4⋊Dic11—42no—
134C2×C4⋊Dic11C2314yes—
135C2×Dic11⋊C4—24no—
136C2×Dic11⋊C4—24no—
137C2×Dic11⋊C4—24no—
138C2×Dic11⋊C4—42no—
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×C4×Dic11—24no—
144C2×C4×Dic11—24no—
145C2×C4×Dic11C2314yes—
146C2×C4×Dic11C2314yes—
147#66937—232no—
148C11×#95C2314yes—
149C11×#95C2314yes—
150C11×#95C2314yes—
151C11×#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2420—111nomaximal, Sylow
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11C2×D414yes—
166C24×C11C2412yes—
167C24×C11C2411yescharacteristic
168C23×D11—22no—
169C23×D11—22no—
170C23×D11—22no—
171C23×D11—22no—
172C23×D11—22no—
173C23×D11—22no—
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11C2×D414yes—
181C23×D11#4114yes—
182C23×D11C2412yes—
183C23×D11C2412yes—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—28no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—28no—
203C22×C4×C11—44no—
204C22×C4×C11—416no—
205C22×C4×C11#4114yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C2×C22⋊D11—232no—
213C2×C22⋊D11—28no—
214C2×C22⋊D11—28no—
215C2×C22⋊D11—28no—
216C2×C22⋊D11—28no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11—416no—
219C2×C22⋊D11C2×D4116yes—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11C2×D414yes—
236C22×Dic11#4114yes—
237C22×Dic11#4114yes—
238C22×Dic11C2412yes—
239C22×Dic11C2412yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C2×D44—28no—
245C2×D44—28no—
246C2×D44—44no—
247C2×D44—416no—
248C2×C4×D11—28no—
249C2×C4×D11—28no—
250C2×C4×D11—28no—
251C2×C4×D11—28no—
252C2×C4×D11—28no—
253C2×C4×D11—44no—
254C2×C4×D11—416no—
255C2×C4×D11—416no—
256C11×C22⋊C4—28no—
257C11×C22⋊C4—44no—
258C22⋊Dic11—28no—
259C22⋊Dic11—44no—
260(C2×D11)⋊C4—28no—
261(C2×D11)⋊C4—28no—
262(C2×D11)⋊C4—28no—
263(C2×D11)⋊C4—28no—
264(C2×D11)⋊C4—44no—
265(C2×D11)⋊C4—44no—
266(C2×D11)⋊C4—44no—
267(C2×D11)⋊C4—44no—
268C4⋊Dic11—44no—
269Dic11⋊C4—28no—
270Dic11⋊C4—28no—
271Dic11⋊C4—28no—
272Dic11⋊C4—44no—
273C4×Dic11—28no—
274C4×Dic11—28no—
275C22×#121—111no—
276C22×C4×D4—111no—
277#2420—1116no—
278C2×#397—111no—
279C2×#397—111no—
280C2×#394—111no—
281C2×#394—111no—
282C2×#390—111no—
283C2×#389—111no—
284C2×#386—111no—
285C2×#386—111no—
286C2×#382—111no—
287C2×#381—111no—
288C2×#381D1111yescharacteristic, complemented
289C2×#380—111no—
290C2×C4×C22⋊C4—111no—
291C23×C11—28no—
292C23×C11—28no—
293C23×C11—28no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—44no—
301C23×C11—44no—
302C23×C11—44no—
303C23×C11—44no—
304C23×C11C22×D414yes—
305C23×C11C22×D412yes—
306C23×C11C2×#4112yes—
307C23×C11C2×#4112yes—
308C23×C11C2×#4112yes—
309C23×C11C2×#4112yes—
310C23×C11H(5,𝔽2)12yes—
311C23×C11H(5,𝔽2)12yes—
312C23×C11C2511yescharacteristic
313C22×D11—28no—
314C22×D11—28no—
315C22×D11—28no—
316C22×D11—28no—
317C22×D11—28no—
318C22×D11—28no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—44no—
332C22×D11—44no—
333C22×D11—44no—
334C22×D11—44no—
335C22×D11—44no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11—44no—
339C22×D11C22×D414yes—
340C22×D11C2×#4114yes—
341C2×C4×C11—28no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—416no—
360C2×C4×C11—44no—
361C2×C4×C11—44no—
362C2×C4×C11—44no—
363C2×C4×C11—44no—
364C2×C4×C11—44no—
365C2×C4×C11C2×#4114yes—
366C22⋊D11—232no—
367C22⋊D11—416no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—44no—
384C2×Dic11—44no—
385C2×Dic11—44no—
386C2×Dic11—44no—
387C2×Dic11—44no—
388C2×Dic11#123116yes—
389C2×Dic11C22×D414yes—
390C2×Dic11C2×#4114yes—
391C2×Dic11C2×#4114yes—
392D44—416no—
393C4×D11—416no—
394C4×D11—416no—
395C23×D4—111no—
396C23×D4—111no—
397C23×D4—111no—
398C24×C4—111no—
399C24×C4—111no—
400C24×C4C2×D1111yescharacteristic
401C2×#121—118no—
402C2×#121—228no—
403C2×C4×D4—118no—
404C2×C4×D4—228no—
405C22×C4⋊C4—111no—
406C22×C4⋊C4—111no—
407C22×C4⋊C4—111no—
408C22×C4⋊C4—111no—
409C22×C4⋊C4—111no—
410C22×C22⋊C4—111no—
411C22×C22⋊C4—111no—
412C22×C22⋊C4—111no—
413C22×C22⋊C4—111no—
414C22×C22⋊C4—111no—
415C22×C22⋊C4—111no—
416C22×C22⋊C4—111no—
417C22×C22⋊C4—111no—
418C22×C22⋊C4—111no—
419C22×C22⋊C4—111no—
420C22×C22⋊C4C2×D1111yescharacteristic
421C22×C22⋊C4C2×D1111yescharacteristic
422C22×C42—111no—
423C22×C42—111no—
424#397—118no—
425#397—118no—
426#394—118no—
427#394—118no—
428#390—118no—
429#389—118no—
430#386—118no—
431#386—118no—
432#382—118no—
433#381—118no—
434#381C2×D1118yescomplemented
435#380—118no—
436C4×C22⋊C4—118no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95C2×D1111yescharacteristic
444C2×#95C2×D1111yescharacteristic
445C2×#95C2×D1111yescharacteristic
446C2×#95C2×D1111yescharacteristic
447C22×C11—24no—
448C22×C11—24no—
449C22×C11—24no—
450C22×C11—42no—
451C22×C11—416no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11C2×#12314yes—
456C22×C11#52914yes—
457C22×C11#54014yes—
458C22×C11#54614yes—
459C22×C11#54614yes—
460C22×C11#55314yes—
461C22×C11#55514yes—
462C22×C11C23×D411yescharacteristic
463C22×C11C22×#4111yescharacteristic
464C22×C11C22×#4111yescharacteristic
465C22×C11C22×#4111yescharacteristic
466C22×C11C22×#4111yescharacteristic
467C22×C11C2×H(5,𝔽2)11yescharacteristic
468C22×C11C2×H(5,𝔽2)11yescharacteristic
469C2×D11—24no—
470C2×D11—24no—
471C2×D11—24no—
472C2×D11—24no—
473C2×D11—24no—
474C2×D11—24no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—416no—
478C2×D11—416no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—42no—
485C4×C11—24no—
486C4×C11—42no—
487C4×C11—42no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11—42no—
491Dic11—42no—
492Dic11—42no—
493Dic11—42no—
494Dic11—42no—
495Dic11—42no—
496Dic11C2×#12318yes—
497C25—111no—
498C25—111no—
499C25C22×D1111yescharacteristic
500C22×D4—118no—
501C22×D4—114no—
502C22×D4—114no—
503C22×D4—114no—
504C22×D4—224no—
505C22×D4—224no—
506C22×D4—224no—
507C22×D4—224no—
508C22×D4—224no—
509C22×D4—224no—
510C22×D4—442no—
511C22×D4—442no—
512C23×C4—24no—
513C23×C4—24no—
514C23×C4—42no—
515C23×C4—111no—
516C23×C4—111no—
517C23×C4—111no—
518C23×C4—111no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—114no—
522C23×C4—114no—
523C23×C4—224no—
524C23×C4—224no—
525C23×C4—224no—
526C23×C4—224no—
527C23×C4—224no—
528C23×C4—442no—
529C23×C4C22×D1111yescharacteristic
530C23×C4C22×D1111yescharacteristic
531C23×C4C22×D1111yescharacteristic
532C23×C4C22×D1111yescharacteristic
533C23×C4C22×D1111yescharacteristic
534C23×C4C22×D1114yes—
535C23×C4C22×D1111yescharacteristic
536#121—2232no—
537C4×D4—2232no—
538C2×C4⋊C4—114no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—114no—
541C2×C4⋊C4—114no—
542C2×C4⋊C4—114no—
543C2×C4⋊C4—224no—
544C2×C4⋊C4—224no—
545C2×C4⋊C4—224no—
546C2×C4⋊C4—442no—
547C2×C4⋊C4—442no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—114no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—114no—
557C2×C22⋊C4—114no—
558C2×C22⋊C4—114no—
559C2×C22⋊C4—114no—
560C2×C22⋊C4—224no—
561C2×C22⋊C4—224no—
562C2×C22⋊C4—224no—
563C2×C22⋊C4—224no—
564C2×C22⋊C4—224no—
565C2×C22⋊C4—442no—
566C2×C22⋊C4—442no—
567C2×C22⋊C4—442no—
568C2×C22⋊C4—442no—
569C2×C22⋊C4—442no—
570C2×C22⋊C4C22×D1114yes—
571C2×C22⋊C4C22×D1114yes—
572C2×C42—114no—
573C2×C42—114no—
574C2×C42—224no—
575C2×C42—224no—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—114no—
580#95—114no—
581#95—114no—
582#95C22×D1114yes—
583#95C22×D1114yes—
584#95C22×D1114yes—
585#95C22×D1114yes—
586C2×C11—44no—
587C2×C11#242018yescomplemented
588C2×C11C22×#12311yescharacteristic
589C2×C11C2×#52911yescharacteristic
590C2×C11C2×#54011yescharacteristic
591C2×C11C2×#54611yescharacteristic
592C2×C11C2×#54611yescharacteristic
593C2×C11C2×#55311yescharacteristic
594C2×C11C2×#55511yescharacteristic
595D11—44no—
596D11—44no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—114no—
604C24—114no—
605C24—112no—
606C24—112no—
607C24—222no—
608C24—222no—
609C24—222no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24—222no—
616C24—222no—
617C24—222no—
618C24—222no—
619C24D4×D1114yes—
620C24C23×D1112yes—
621C24C23×D1111yescharacteristic
622C2×D4—1116no—
623C2×D4—228no—
624C2×D4—228no—
625C2×D4—2232no—
626C2×D4—228no—
627C2×D4—228no—
628C2×D4—228no—
629C2×D4—228no—
630C2×D4—444no—
631C2×D4—4416no—
632C2×D4—444no—
633C2×D4—4416no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—28no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—28no—
653C22×C4—44no—
654C22×C4—416no—
655C22×C4—114no—
656C22×C4—114no—
657C22×C4—114no—
658C22×C4—112no—
659C22×C4—112no—
660C22×C4—112no—
661C22×C4—112no—
662C22×C4—112no—
663C22×C4—112no—
664C22×C4—228no—
665C22×C4—228no—
666C22×C4—228no—
667C22×C4—228no—
668C22×C4—222no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—222no—
674C22×C4—222no—
675C22×C4—222no—
676C22×C4—222no—
677C22×C4—222no—
678C22×C4—222no—
679C22×C4—222no—
680C22×C4—222no—
681C22×C4—222no—
682C22×C4—222no—
683C22×C4—228no—
684C22×C4—444no—
685C22×C4—4416no—
686C22×C4—4416no—
687C22×C4#433914yes—
688C22×C4C23×D1112yes—
689C22×C4C23×D1112yes—
690C22×C4C23×D1112yes—
691C22×C4C23×D1112yes—
692C22×C4C23×D1112yes—
693C22×C4C23×D1112yes—
694C4⋊C4—228no—
695C4⋊C4—228no—
696C4⋊C4—228no—
697C4⋊C4—444no—
698C4⋊C4—444no—
699C22⋊C4—28no—
700C22⋊C4—44no—
701C22⋊C4—228no—
702C22⋊C4—228no—
703C22⋊C4—228no—
704C22⋊C4—228no—
705C22⋊C4—228no—
706C22⋊C4—444no—
707C22⋊C4—444no—
708C22⋊C4—444no—
709C22⋊C4—444no—
710C22⋊C4—444no—
711C42—228no—
712C42—228no—
713C11C2×#242011yescharacteristic, complemented, Sylow
714C23—28no—
715C23—28no—
716C23—28no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—114no—
728C23—114no—
729C23—228no—
730C23—228no—
731C23—228no—
732C23—228no—
733C23—228no—
734C23—222no—
735C23—222no—
736C23—222no—
737C23—222no—
738C23—222no—
739C23—228no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—222no—
744C23—222no—
745C23—222no—
746C23—222no—
747C23—444no—
748C23—444no—
749C23—444no—
750C23—444no—
751C23—444no—
752C23—444no—
753C23—444no—
754C23—444no—
755C23C2×#433912yes—
756C23C2×D4×D1114yes—
757C23C2×D4×D1112yes—
758C23#6703712yes—
759C23#41×D1112yes—
760C23#41×D1112yes—
761C23#41×D1112yes—
762C23#6704212yes—
763C23C24×D1111yescharacteristic
764D4—2232no—
765D4—4416no—
766D4—4416no—
767C2×C4—28no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—416no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—1116no—
792C2×C4—114no—
793C2×C4—114no—
794C2×C4—114no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—4416no—
811C2×C4—4416no—
812C2×C4—444no—
813C2×C4—444no—
814C2×C4—444no—
815C2×C4—444no—
816C2×C4—444no—
817C2×C4C2×#433914yes—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—416no—
826C22—224no—
827C22—224no—
828C22—224no—
829C22—224no—
830C22—224no—
831C22—224no—
832C22—442no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—442no—
838C22—442no—
839C22—4416no—
840C22—4416no—
841C22—442no—
842C22#1062302114yes—
843C22#1062305914yes—
844C22#1062306314yes—
845C22D11×#12314yes—
846C22#1062318514yes—
847C22#1062319214yes—
848C22#1062319414yes—
849C22C22×#433911yescharacteristic
850C22C22×D4×D1111yescharacteristic
851C22C2×#6703711yescharacteristic
852C22C2×#41×D1111yescharacteristic
853C22C2×#41×D1111yescharacteristic
854C22C2×#41×D1111yescharacteristic
855C22C2×#6704211yescharacteristic
856C4—24no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—118no—
863C4—442no—
864C4—442no—
865C4—442no—
866C4—442no—
867C4—442no—
868C2—44no—
869C2—444no—
870C2—444no—
871C2#1307210718yesdirect product factor
872C2C2×D11×#12311yescharacteristic
873C2C2×#1062305911yescharacteristic
874C2C2×#1062319411yescharacteristic
875C2C2×#1062302111yescharacteristic
876C2C2×#1062318511yescharacteristic
877C2C2×#1062319211yescharacteristic
878C2C2×#1062306311yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#381C2
socleC24×C11C24
prime radicalC22×#66937C2
hypercenterC2×#381D11
hypocenterC11C2×#2420
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D11C2semidirect
3. #13072107C2direct (N × H)
4. C2×#10622565C2semidirect
5. C2×#10622287C2semidirect
6. C2×#10622285C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622570C2semidirect
9. C2×#10622260C2semidirect
10. C2×#10622826C2semidirect
11. C2×#10622278C2semidirect
12. C2×#10622263C2semidirect
13. C2×#10622277C2semidirect
14. C2×#10622280C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#381C2semidirect
28. C2×C4×C22⋊D11C22semidirect
46. C11×#381C22semidirect
51. #10622826C22semidirect
58. #10622574C22semidirect
59. #10622570C22semidirect
60. #10622565C22semidirect
61. #10622287C22semidirect
62. #10622285C22semidirect
63. #10622280C22semidirect
64. #10622279C22semidirect
65. #10622278C22semidirect
66. #10622277C22semidirect
67. #10622263C22semidirect
68. #10622260C22semidirect
288. C2×#381D11semidirect
434. #381C2×D11semidirect
587. C2×C11#2420semidirect
713. C11C2×#2420semidirect
871. C2#13072107direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669372
C22×C4×C22⋊D112
#130721072
C2×#106225652
C2×#106222872
C2×#106222852
C2×#106225742
C2×#106225702
C2×#106222602
C2×#106228262
C2×#106222782
C2×#106222632
C2×#106222772
C2×#106222802
C2×#106222792
C2×C11×#3812
C2×#242011