Finite Group Databasebeta

← C2×#13072363 #14921509

Subgroups — C2×#13072363 #14921509

Order 2816.

3546 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66991C211yesmaximal, characteristic
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3#13072363C2116yesmaximal, direct product factor
4C2×#10622273C211yesmaximal, characteristic, complemented
5C2×#10622565C211yesmaximal, characteristic, complemented
6C2×#10622566C211yesmaximal, characteristic, complemented
7C2×#10622835C211yesmaximal, characteristic, complemented
8C2×#10622564C211yesmaximal, characteristic, complemented
9C2×#10622268C211yesmaximal, characteristic, complemented
10C2×#10622569C211yesmaximal, characteristic, complemented
11C2×#10622569C211yesmaximal, characteristic, complemented
12C2×#10622569C211yesmaximal, characteristic, complemented
13C2×#10622281C211yesmaximal, characteristic, complemented
14C2×#10622824C211yesmaximal, characteristic, complemented
15C2×D11×#95C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C2×#66991—28no—
34C2×#66991C2218yes—
35C2×C4×C22⋊D11—28no—
36C2×C4×C22⋊D11C2218yescomplemented
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×C4⋊Dic11C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C11×#386C2218yescomplemented
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47#10622835C2218yescomplemented
48#10622824C2218yescomplemented
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59#10622569C2218yescomplemented
60#10622569C2218yescomplemented
61#10622569C2218yescomplemented
62#10622566C2218yescomplemented
63#10622565C2218yescomplemented
64#10622564C2218yescomplemented
65#10622281C2218yescomplemented
66D11×#95C2218yescomplemented
67#10622273C2218yescomplemented
68#10622268C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C22×D4×C11—24no—
73C22×D4×C11—24no—
74C22×D4×C11—42no—
75C22×D4×C11C2314yes—
76C23×C4×C11—24no—
77C23×C4×C11—24no—
78C23×C4×C11—42no—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2314yes—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C22×C22⋊D11—24no—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11D418yes—
91C22×C22⋊D11C2314yes—
92C22×C22⋊D11C2314yes—
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
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×D11—42no—
107C22×C4×D11—42no—
108C22×C4×D11—42no—
109C22×C4×D11C2314yes—
110C22×C4×D11C2314yes—
111C22×C4×D11C2314yes—
112C2×C11×C22⋊C4—24no—
113C2×C11×C22⋊C4—42no—
114C2×C11×C22⋊C4—42no—
115C2×C11×C22⋊C4C2314yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C11×C22⋊C4C2314yes—
118C2×C22⋊Dic11—24no—
119C2×C22⋊Dic11—24no—
120C2×C22⋊Dic11—24no—
121C2×C22⋊Dic11—42no—
122C2×C22⋊Dic11—42no—
123C2×C22⋊Dic11—42no—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130#66991—232no—
131C4×C22⋊D11—232no—
132C2×(C2×D11)⋊C4—24no—
133C2×(C2×D11)⋊C4—24no—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×C4⋊Dic11—24no—
137C2×C4⋊Dic11—42no—
138C2×C4⋊Dic11C2314yes—
139C2×C4⋊Dic11C2314yes—
140C2×Dic11⋊C4—24no—
141C2×Dic11⋊C4—24no—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×C4×Dic11—24no—
145C2×C4×Dic11C2314yes—
146C11×#95C2314yes—
147C11×#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2444—111nomaximal, Sylow
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11C2×D414yes—
173C24×C11C2412yes—
174C24×C11C2412yes—
175C24×C11C2411yescharacteristic
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11C2×D414yes—
181C23×D11#4114yes—
182C23×D11#4114yes—
183C23×D11C2412yes—
184C2×D4×C11—28no—
185C2×D4×C11—28no—
186C2×D4×C11—44no—
187C2×D4×C11—416no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—28no—
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×C11#4114yes—
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—28no—
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×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—22no—
238C22×Dic11—22no—
239C22×Dic11—22no—
240C22×Dic11C2×D414yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
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—44no—
255C2×C4×D11—44no—
256C2×C4×D11—44no—
257C2×C4×D11—416no—
258C2×C4×D11—416no—
259C2×C4×D11—416no—
260C11×C22⋊C4—28no—
261C11×C22⋊C4—44no—
262C11×C22⋊C4—44no—
263C22⋊Dic11—28no—
264C22⋊Dic11—28no—
265C22⋊Dic11—28no—
266C22⋊Dic11—44no—
267C22⋊Dic11—44no—
268C22⋊Dic11—44no—
269(C2×D11)⋊C4—28no—
270(C2×D11)⋊C4—28no—
271C4⋊Dic11—28no—
272C4⋊Dic11—44no—
273Dic11⋊C4—28no—
274Dic11⋊C4—28no—
275C4×Dic11—28no—
276C22×#121—111no—
277C22×C4×D4—111no—
278#2444—1116no—
279C2×#400—111no—
280C2×#397—111no—
281C2×#397—111no—
282C2×#394—111no—
283C2×#388—111no—
284C2×#387—111no—
285C2×#386—111no—
286C2×#386—111no—
287C2×#386—111no—
288C2×#386D1111yescharacteristic, complemented
289C2×#385—111no—
290C2×#381—111no—
291C22×#95—111no—
292C23×C11—28no—
293C23×C11—28no—
294C23×C11—28no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—44no—
309C23×C11—44no—
310C23×C11—44no—
311C23×C11—44no—
312C23×C11—44no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11—44no—
316C23×C11—44no—
317C23×C11—44no—
318C23×C11—44no—
319C23×C11C22×D414yes—
320C23×C11C22×D412yes—
321C23×C11C2×#4112yes—
322C23×C11C2×#4112yes—
323C23×C11C2×#4112yes—
324C23×C11C2×#4112yes—
325C23×C11H(5,𝔽2)12yes—
326C23×C11H(5,𝔽2)12yes—
327C23×C11C2511yescharacteristic
328C22×D11—28no—
329C22×D11—28no—
330C22×D11—28no—
331C22×D11—28no—
332C22×D11—28no—
333C22×D11—28no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11#123116yes—
339C22×D11C22×D414yes—
340C22×D11C2×#4114yes—
341C22×D11C2×#4114yes—
342D4×C11—416no—
343C2×C4×C11—28no—
344C2×C4×C11—28no—
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—416no—
359C2×C4×C11—44no—
360C2×C4×C11—44no—
361C2×C4×C11—44no—
362C2×C4×C11C2×#4114yes—
363C2×C4×C11C2×#4114yes—
364C22⋊D11—232no—
365C22⋊D11—416no—
366C2×Dic11—28no—
367C2×Dic11—22no—
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—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—44no—
388C2×Dic11—44no—
389C2×Dic11—44no—
390C2×Dic11—44no—
391C2×Dic11—44no—
392C2×Dic11—44no—
393C2×Dic11C22×D414yes—
394C4×D11—416no—
395C4×D11—416no—
396C4×D11—416no—
397C23×D4—111no—
398C23×D4—111no—
399C23×D4C2×D1111yescharacteristic
400C24×C4—111no—
401C24×C4—111no—
402C24×C4—111no—
403C24×C4C2×D1111yescharacteristic
404C2×#121—118no—
405C2×#121—228no—
406C2×C4×D4—118no—
407C2×C4×D4—228no—
408C22×C4⋊C4—111no—
409C22×C4⋊C4—111no—
410C22×C4⋊C4—111no—
411C22×C4⋊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×C22⋊C4C2×D1111yescharacteristic
423C22×C42—111no—
424#400—118no—
425#397—118no—
426#397—118no—
427#394—118no—
428#388—118no—
429#387—118no—
430#386—118no—
431#386—118no—
432#386—118no—
433#386C2×D1118yescomplemented
434#385—118no—
435#381—118no—
436C2×#95—111no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95—111no—
444C2×#95—111no—
445C2×#95—111no—
446C2×#95—118no—
447C2×#95C2×D1111yescharacteristic
448C2×#95C2×D1111yescharacteristic
449C22×C11—24no—
450C22×C11—24no—
451C22×C11—24no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—416no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—88no—
465C22×C11C2×#12314yes—
466C22×C11#52914yes—
467C22×C11#53814yes—
468C22×C11#54614yes—
469C22×C11#54614yes—
470C22×C11#55314yes—
471C22×C11#55314yes—
472C22×C11C23×D411yescharacteristic
473C22×C11C22×#4111yescharacteristic
474C22×C11C22×#4111yescharacteristic
475C22×C11C22×#4111yescharacteristic
476C22×C11C22×#4111yescharacteristic
477C22×C11C2×H(5,𝔽2)11yescharacteristic
478C22×C11C2×H(5,𝔽2)11yescharacteristic
479C2×D11—24no—
480C2×D11—24no—
481C2×D11—24no—
482C2×D11—24no—
483C2×D11—232no—
484C2×D11—24no—
485C2×D11—24no—
486C2×D11C2×#12318yes—
487C4×C11—24no—
488C4×C11—24no—
489C4×C11—42no—
490C4×C11—42no—
491C4×C11—42no—
492Dic11—24no—
493Dic11—42no—
494Dic11—42no—
495Dic11—42no—
496Dic11—42no—
497Dic11—42no—
498Dic11—42no—
499C25—111no—
500C25C22×D1111yescharacteristic
501C25C22×D1111yescharacteristic
502C22×D4—24no—
503C22×D4—24no—
504C22×D4—42no—
505C22×D4—118no—
506C22×D4—114no—
507C22×D4—114no—
508C22×D4—224no—
509C22×D4—224no—
510C22×D4—224no—
511C22×D4—224no—
512C22×D4—224no—
513C22×D4C22×D1114yes—
514C23×C4—24no—
515C23×C4—24no—
516C23×C4—42no—
517C23×C4—111no—
518C23×C4—111no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—111no—
522C23×C4—111no—
523C23×C4—111no—
524C23×C4—114no—
525C23×C4—114no—
526C23×C4—114no—
527C23×C4—224no—
528C23×C4—224no—
529C23×C4—224no—
530C23×C4—224no—
531C23×C4—224no—
532C23×C4—442no—
533C23×C4—442no—
534C23×C4—442no—
535C23×C4—442no—
536C23×C4C22×D1111yescharacteristic
537C23×C4C22×D1111yescharacteristic
538C23×C4C22×D1111yescharacteristic
539C23×C4C22×D1114yes—
540C23×C4C22×D1111yescharacteristic
541C23×C4C22×D1111yescharacteristic
542#121—2232no—
543C4×D4—2232no—
544C2×C4⋊C4—114no—
545C2×C4⋊C4—114no—
546C2×C4⋊C4—114no—
547C2×C4⋊C4—114no—
548C2×C4⋊C4—224no—
549C2×C4⋊C4—224no—
550C2×C4⋊C4—224no—
551C2×C4⋊C4—442no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—114no—
557C2×C22⋊C4—114no—
558C2×C22⋊C4—114no—
559C2×C22⋊C4—114no—
560C2×C22⋊C4—114no—
561C2×C22⋊C4—114no—
562C2×C22⋊C4—114no—
563C2×C22⋊C4—224no—
564C2×C22⋊C4—224no—
565C2×C22⋊C4—224no—
566C2×C22⋊C4—224no—
567C2×C22⋊C4—224no—
568C2×C22⋊C4—442no—
569C2×C22⋊C4—442no—
570C2×C22⋊C4—442no—
571C2×C22⋊C4C22×D1114yes—
572C2×C22⋊C4C22×D1114yes—
573C2×C22⋊C4C22×D1114yes—
574C2×C42—114no—
575C2×C42—224no—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—114no—
580#95—114no—
581#95—114no—
582#95—114no—
583#95—114no—
584#95—114no—
585#95—114no—
586#95C22×D1114yes—
587#95C22×D1114yes—
588C2×C11—44no—
589C2×C11—82no—
590C2×C11#244418yescomplemented
591C2×C11C22×#12311yescharacteristic
592C2×C11C2×#52911yescharacteristic
593C2×C11C2×#53811yescharacteristic
594C2×C11C2×#54611yescharacteristic
595C2×C11C2×#54611yescharacteristic
596C2×C11C2×#55311yescharacteristic
597C2×C11C2×#55311yescharacteristic
598D11—28no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—114no—
613C24—114no—
614C24—114no—
615C24—112no—
616C24—222no—
617C24—222no—
618C24—222no—
619C24—222no—
620C24D4×D1114yes—
621C24C23×D1112yes—
622C24C23×D1112yes—
623C24C23×D1111yescharacteristic
624C2×D4—28no—
625C2×D4—28no—
626C2×D4—44no—
627C2×D4—416no—
628C2×D4—1116no—
629C2×D4—2232no—
630C2×D4—228no—
631C2×D4—228no—
632C2×D4—228no—
633C2×D4—228no—
634C2×D4—228no—
635C2×D4—4416no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—28no—
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—28no—
651C22×C4—44no—
652C22×C4—416no—
653C22×C4—114no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—112no—
660C22×C4—112no—
661C22×C4—228no—
662C22×C4—228no—
663C22×C4—228no—
664C22×C4—222no—
665C22×C4—222no—
666C22×C4—222no—
667C22×C4—222no—
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—222no—
684C22×C4—228no—
685C22×C4—228no—
686C22×C4—444no—
687C22×C4—444no—
688C22×C4—444no—
689C22×C4—444no—
690C22×C4—4416no—
691C22×C4—4416no—
692C22×C4—4416no—
693C22×C4#433914yes—
694C22×C4#434114yes—
695C22×C4C23×D1112yes—
696C22×C4C23×D1112yes—
697C22×C4C23×D1112yes—
698C22×C4C23×D1112yes—
699C22×C4C23×D1112yes—
700C4⋊C4—228no—
701C4⋊C4—228no—
702C4⋊C4—228no—
703C4⋊C4—444no—
704C22⋊C4—28no—
705C22⋊C4—44no—
706C22⋊C4—44no—
707C22⋊C4—228no—
708C22⋊C4—228no—
709C22⋊C4—228no—
710C22⋊C4—228no—
711C22⋊C4—228no—
712C22⋊C4—444no—
713C22⋊C4—444no—
714C22⋊C4—444no—
715C42—228no—
716C11C2×#244411yescharacteristic, complemented, Sylow
717C23—28no—
718C23—28no—
719C23—28no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—1116no—
745C23—114no—
746C23—114no—
747C23—114no—
748C23—228no—
749C23—228no—
750C23—228no—
751C23—228no—
752C23—228no—
753C23—228no—
754C23—222no—
755C23—222no—
756C23—222no—
757C23—222no—
758C23C2×#433912yes—
759C23C2×D4×D1114yes—
760C23C2×D4×D1112yes—
761C23C2×#434112yes—
762C23#6703712yes—
763C23#6703712yes—
764C23#41×D1112yes—
765C23#41×D1112yes—
766C23C24×D1111yescharacteristic
767D4—416no—
768D4—2232no—
769D4—4416no—
770C2×C4—28no—
771C2×C4—28no—
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—114no—
790C2×C4—228no—
791C2×C4—222no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—222no—
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—222no—
811C2×C4—4416no—
812C2×C4—4416no—
813C2×C4—4416no—
814C2×C4—444no—
815C2×C4—444no—
816C2×C4—444no—
817C2×C4—444no—
818C2×C4—444no—
819C2×C4—444no—
820C2×C4C2×#433914yes—
821C2×C4C2×#434114yes—
822C22—24no—
823C22—24no—
824C22—24no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—416no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—88no—
838C22—118no—
839C22—224no—
840C22—224no—
841C22—224no—
842C22—224no—
843C22—224no—
844C22—224no—
845C22—2232no—
846C22#1062302114yes—
847C22#1062308814yes—
848C22#1062308914yes—
849C22#1062312214yes—
850C22#1062314414yes—
851C22#1062314514yes—
852C22D11×#12314yes—
853C22C22×#433911yescharacteristic
854C22C22×D4×D1111yescharacteristic
855C22C22×#434111yescharacteristic
856C22C2×#6703711yescharacteristic
857C22C2×#6703711yescharacteristic
858C22C2×#41×D1111yescharacteristic
859C22C2×#41×D1111yescharacteristic
860C4—24no—
861C4—24no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—224no—
866C4—442no—
867C4—442no—
868C4—442no—
869C4—442no—
870C4—442no—
871C4—442no—
872C2—44no—
873C2—82no—
874C2—228no—
875C2#1307236318yesdirect product factor
876C2C2×D11×#12311yescharacteristic
877C2C2×#1062308811yescharacteristic
878C2C2×#1062314411yescharacteristic
879C2C2×#1062312211yescharacteristic
880C2C2×#1062302111yescharacteristic
881C2C2×#1062314511yescharacteristic
882C2C2×#1062308911yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC22×#66991C2
hypercenterC2×#386D11
hypocenterC11C2×#2444
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D11C2semidirect
3. #13072363C2direct (N × H)
4. C2×#10622273C2semidirect
5. C2×#10622565C2semidirect
6. C2×#10622566C2semidirect
7. C2×#10622835C2semidirect
8. C2×#10622564C2semidirect
9. C2×#10622268C2semidirect
10. C2×#10622569C2semidirect
11. C2×#10622569C2semidirect
12. C2×#10622569C2semidirect
13. C2×#10622281C2semidirect
14. C2×#10622824C2semidirect
15. C2×D11×#95C2semidirect
16. C2×C11×#386C2semidirect
36. C2×C4×C22⋊D11C22semidirect
44. C11×#386C22semidirect
47. #10622835C22semidirect
48. #10622824C22semidirect
59. #10622569C22semidirect
60. #10622569C22semidirect
61. #10622569C22semidirect
62. #10622566C22semidirect
63. #10622565C22semidirect
64. #10622564C22semidirect
65. #10622281C22semidirect
66. D11×#95C22semidirect
67. #10622273C22semidirect
68. #10622268C22semidirect
288. C2×#386D11semidirect
433. #386C2×D11semidirect
590. C2×C11#2444semidirect
716. C11C2×#2444semidirect
875. C2#13072363direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669912
C22×C4×C22⋊D112
#130723632
C2×#106222732
C2×#106225652
C2×#106225662
C2×#106228352
C2×#106225642
C2×#106222682
C2×#106225692
C2×#106222812
C2×#106228242
C2×D11×#952
C2×C11×#3862
C2×#244411