Finite Group Databasebeta

← C2×#13072367 #14921516

Subgroups — C2×#13072367 #14921516

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×#66948C211yesmaximal, characteristic
2C22×#66946C211yesmaximal, characteristic, complemented
3#13072367C2116yesmaximal, direct product factor
4C2×#10622287C211yesmaximal, characteristic, complemented
5C2×#10622606C211yesmaximal, characteristic, complemented
6C2×#10622285C211yesmaximal, characteristic, complemented
7C2×#10622283C211yesmaximal, characteristic, complemented
8C2×#10622591C211yesmaximal, characteristic, complemented
9C2×#10622278C211yesmaximal, characteristic, complemented
10C2×#10622278C211yesmaximal, characteristic, complemented
11C2×#10622278C211yesmaximal, characteristic, complemented
12C2×#10622278C211yesmaximal, characteristic, complemented
13C2×#10622281C211yesmaximal, characteristic, complemented
14C2×#10622277C211yesmaximal, characteristic, complemented
15C2×D11×#95C211yesmaximal, characteristic, complemented
16C2×C11×#400C211yesmaximal, characteristic, complemented
17C23×D44C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
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×C4×Dic11C2211yescharacteristic
40C2×#66948—28no—
41C2×#66948C2218yes—
42C2×#66946—28no—
43C2×#66946C2218yescomplemented
44C11×#400C2218yescomplemented
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2211yescharacteristic
49C2×C11×#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622606C2218yescomplemented
58#10622591C2218yescomplemented
59#10622287C2218yescomplemented
60#10622285C2218yescomplemented
61#10622283C2218yescomplemented
62#10622281C2218yescomplemented
63#10622278C2218yescomplemented
64#10622278C2218yescomplemented
65#10622278C2218yescomplemented
66#10622278C2218yescomplemented
67#10622277C2218yescomplemented
68D11×#95C2218yescomplemented
69C24×D11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C22×D44—24no—
85C22×D44—24no—
86C22×D44—24no—
87C22×D44—24no—
88C22×D44—24no—
89C22×D44—24no—
90C22×D44—24no—
91C22×D44—42no—
92C22×D44D418yes—
93C22×D44C2314yes—
94C22×D44C2314yes—
95C22×D44C2314yes—
96C22×C4×D11—24no—
97C22×C4×D11—24no—
98C22×C4×D11—24no—
99C22×C4×D11—24no—
100C22×C4×D11—24no—
101C22×C4×D11—24no—
102C22×C4×D11—24no—
103C22×C4×D11—42no—
104C22×C4×D11—42no—
105C22×C4×D11—42no—
106C22×C4×D11—42no—
107C22×C4×D11—42no—
108C22×C4×D11C2314yes—
109C22×C4×D11C2314yes—
110C22×C4×D11C2314yes—
111C22×C4×D11C2314yes—
112C2×C11×C4⋊C4—24no—
113C2×C11×C4⋊C4—24no—
114C2×C11×C4⋊C4C2314yes—
115C2×C11×C4⋊C4C2314yes—
116C2×(C2×D11)⋊C4—24no—
117C2×(C2×D11)⋊C4—24no—
118C2×(C2×D11)⋊C4—24no—
119C2×(C2×D11)⋊C4—24no—
120C2×(C2×D11)⋊C4—24no—
121C2×(C2×D11)⋊C4—24no—
122C2×(C2×D11)⋊C4—42no—
123C2×(C2×D11)⋊C4—42no—
124C2×(C2×D11)⋊C4—42no—
125C2×(C2×D11)⋊C4—42no—
126C2×(C2×D11)⋊C4—42no—
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×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×C4⋊Dic11—42no—
139C2×C4⋊Dic11C2314yes—
140C2×Dic11⋊C4—24no—
141C2×Dic11⋊C4C2314yes—
142C2×C4×Dic11—24no—
143C2×C4×Dic11C2314yes—
144#66948—232no—
145#66946—232no—
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×C11C2411yescharacteristic
160C23×D11—22no—
161C23×D11—22no—
162C23×D11—22no—
163C23×D11—22no—
164C23×D11—22no—
165C23×D11—22no—
166C23×D11—22no—
167C23×D11—22no—
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×D11C2×D414yes—
178C23×D11C2×D414yes—
179C23×D11#4114yes—
180C23×D11#4114yes—
181C23×D11C2412yes—
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—22no—
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—22no—
203C22×C4×C11C2×D414yes—
204C22×C4×C11#4114yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11#4114yes—
227C22×Dic11C2412yes—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C22×Dic11C2412yes—
231C22×Dic11C2412yes—
232C2×D44—232no—
233C2×D44—28no—
234C2×D44—28no—
235C2×D44—28no—
236C2×D44—28no—
237C2×D44—28no—
238C2×D44—28no—
239C2×D44—28no—
240C2×D44—44no—
241C2×D44—416no—
242C2×D44—416no—
243C2×D44C2×D4116yes—
244C2×C4×D11—28no—
245C2×C4×D11—28no—
246C2×C4×D11—28no—
247C2×C4×D11—28no—
248C2×C4×D11—28no—
249C2×C4×D11—28no—
250C2×C4×D11—28no—
251C2×C4×D11—44no—
252C2×C4×D11—44no—
253C2×C4×D11—44no—
254C2×C4×D11—44no—
255C2×C4×D11—44no—
256C2×C4×D11—416no—
257C2×C4×D11—416no—
258C2×C4×D11—416no—
259C2×C4×D11—416no—
260C11×C4⋊C4—28no—
261C11×C4⋊C4—28no—
262(C2×D11)⋊C4—28no—
263(C2×D11)⋊C4—28no—
264(C2×D11)⋊C4—28no—
265(C2×D11)⋊C4—28no—
266(C2×D11)⋊C4—28no—
267(C2×D11)⋊C4—28no—
268(C2×D11)⋊C4—44no—
269(C2×D11)⋊C4—44no—
270(C2×D11)⋊C4—44no—
271(C2×D11)⋊C4—44no—
272(C2×D11)⋊C4—44no—
273C4⋊Dic11—44no—
274Dic11⋊C4—28no—
275C4×Dic11—28no—
276C22×#121—111no—
277C22×C4×D4—111no—
278#2444—1116no—
279C2×#400D1111yescharacteristic, complemented
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×#386—111no—
289C2×#385—111no—
290C2×#381—111no—
291C22×#95—111no—
292C23×C11C22×D412yes—
293C23×C11C2×#4112yes—
294C23×C11C2×#4112yes—
295C23×C11C2×#4112yes—
296C23×C11C2×#4112yes—
297C23×C11H(5,𝔽2)12yes—
298C23×C11H(5,𝔽2)12yes—
299C23×C11C2511yescharacteristic
300C22×D11—28no—
301C22×D11—28no—
302C22×D11—28no—
303C22×D11—28no—
304C22×D11—28no—
305C22×D11—28no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—28no—
311C22×D11—28no—
312C22×D11—28no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—44no—
327C22×D11—44no—
328C22×D11—44no—
329C22×D11—44no—
330C22×D11—44no—
331C22×D11—44no—
332C22×D11—44no—
333C22×D11—44no—
334C22×D11—44no—
335C22×D11—44no—
336C22×D11—44no—
337C22×D11#123116yes—
338C22×D11C22×D414yes—
339C22×D11C22×D414yes—
340C22×D11C2×#4114yes—
341C22×D11C2×#4114yes—
342C2×C4×C11—28no—
343C2×C4×C11—28no—
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—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—44no—
364C2×C4×C11—44no—
365C2×C4×C11—44no—
366C2×C4×C11—44no—
367C2×C4×C11—44no—
368C2×C4×C11C22×D414yes—
369C2×C4×C11C2×#4114yes—
370C2×Dic11—28no—
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—44no—
386C2×Dic11—44no—
387C2×Dic11—44no—
388C2×Dic11—44no—
389C2×Dic11C2×#4114yes—
390D44—232no—
391D44—416no—
392D44—416no—
393C4×D11—416no—
394C4×D11—416no—
395C4×D11—416no—
396C4×D11—416no—
397C23×D4—111no—
398C23×D4—111no—
399C23×D4—111no—
400C24×C4—111no—
401C24×C4—111no—
402C24×C4—111no—
403C24×C4—111no—
404C2×#121—118no—
405C2×#121—228no—
406C2×C4×D4—118no—
407C2×C4×D4—228no—
408C22×C4⋊C4—111no—
409C22×C4⋊C4—111no—
410C22×C4⋊C4C2×D1111yescharacteristic
411C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
421C22×C22⋊C4—111no—
422C22×C22⋊C4—111no—
423C22×C42—111no—
424#400C2×D1118yescomplemented
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#386—118no—
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—118no—
444C2×#95C2×D1111yescharacteristic
445C2×#95C2×D1111yescharacteristic
446C2×#95C2×D1111yescharacteristic
447C2×#95C2×D1111yescharacteristic
448C2×#95C2×D1111yescharacteristic
449C22×C11C2×#12314yes—
450C22×C11#52914yes—
451C22×C11#53814yes—
452C22×C11#54614yes—
453C22×C11#54614yes—
454C22×C11#55314yes—
455C22×C11#55314yes—
456C22×C11C23×D411yescharacteristic
457C22×C11C22×#4111yescharacteristic
458C22×C11C22×#4111yescharacteristic
459C22×C11C22×#4111yescharacteristic
460C22×C11C22×#4111yescharacteristic
461C22×C11C2×H(5,𝔽2)11yescharacteristic
462C22×C11C2×H(5,𝔽2)11yescharacteristic
463C2×D11—24no—
464C2×D11—24no—
465C2×D11—24no—
466C2×D11—24no—
467C2×D11—232no—
468C2×D11—24no—
469C2×D11—24no—
470C2×D11—24no—
471C2×D11—24no—
472C2×D11—24no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—416no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—88no—
486C2×D11C2×#12318yes—
487C4×C11—24no—
488C4×C11—24no—
489C4×C11—42no—
490C4×C11—42no—
491C4×C11—42no—
492C4×C11—42no—
493C4×C11—42no—
494Dic11—24no—
495Dic11—42no—
496Dic11—42no—
497Dic11—42no—
498Dic11—42no—
499C25—111no—
500C25—111no—
501C25—111no—
502C22×D4—118no—
503C22×D4—114no—
504C22×D4—114no—
505C22×D4—114no—
506C22×D4—224no—
507C22×D4—224no—
508C22×D4—224no—
509C22×D4—224no—
510C22×D4—224no—
511C22×D4—224no—
512C22×D4—224no—
513C22×D4—442no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—111no—
517C23×C4—111no—
518C23×C4—111no—
519C23×C4—114no—
520C23×C4—114no—
521C23×C4—114no—
522C23×C4—114no—
523C23×C4—224no—
524C23×C4—224no—
525C23×C4—224no—
526C23×C4—224no—
527C23×C4—224no—
528C23×C4—224no—
529C23×C4—224no—
530C23×C4—442no—
531C23×C4—442no—
532C23×C4—442no—
533C23×C4—442no—
534C23×C4—442no—
535C23×C4C22×D1111yescharacteristic
536C23×C4C22×D1111yescharacteristic
537C23×C4C22×D1111yescharacteristic
538C23×C4C22×D1111yescharacteristic
539C23×C4C22×D1111yescharacteristic
540C23×C4C22×D1111yescharacteristic
541C23×C4C22×D1111yescharacteristic
542#121—2232no—
543C4×D4—2232no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—24no—
546C2×C4⋊C4—114no—
547C2×C4⋊C4—114no—
548C2×C4⋊C4—224no—
549C2×C4⋊C4—442no—
550C2×C4⋊C4C22×D1114yes—
551C2×C4⋊C4C22×D1114yes—
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—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—224no—
569C2×C22⋊C4—442no—
570C2×C22⋊C4—442no—
571C2×C22⋊C4—442no—
572C2×C22⋊C4—442no—
573C2×C22⋊C4—442no—
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#95C22×D1114yes—
584#95C22×D1114yes—
585#95C22×D1114yes—
586#95C22×D1114yes—
587#95C22×D1114yes—
588C2×C11#244418yescomplemented
589C2×C11C22×#12311yescharacteristic
590C2×C11C2×#52911yescharacteristic
591C2×C11C2×#53811yescharacteristic
592C2×C11C2×#54611yescharacteristic
593C2×C11C2×#54611yescharacteristic
594C2×C11C2×#55311yescharacteristic
595C2×C11C2×#55311yescharacteristic
596D11—28no—
597D11—44no—
598D11—82no—
599C24—114no—
600C24—114no—
601C24—114no—
602C24—112no—
603C24—114no—
604C24—112no—
605C24—112no—
606C24—222no—
607C24—222no—
608C24—222no—
609C24—222no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24—222no—
616C24—222no—
617C24—222no—
618C24—222no—
619C24—222no—
620C24—222no—
621C24—222no—
622C24—222no—
623C24C23×D1111yescharacteristic
624C2×D4—1116no—
625C2×D4—2232no—
626C2×D4—228no—
627C2×D4—228no—
628C2×D4—228no—
629C2×D4—228no—
630C2×D4—228no—
631C2×D4—228no—
632C2×D4—228no—
633C2×D4—444no—
634C2×D4—4416no—
635C2×D4—4416no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
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—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—114no—
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—228no—
665C22×C4—228no—
666C22×C4—228no—
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—228no—
682C22×C4—444no—
683C22×C4—444no—
684C22×C4—444no—
685C22×C4—444no—
686C22×C4—444no—
687C22×C4—4416no—
688C22×C4—4416no—
689C22×C4—4416no—
690C22×C4—4416no—
691C22×C4D4×D1114yes—
692C22×C4#434314yes—
693C22×C4C23×D1112yes—
694C22×C4C23×D1112yes—
695C22×C4C23×D1112yes—
696C22×C4C23×D1112yes—
697C22×C4C23×D1112yes—
698C22×C4C23×D1112yes—
699C22×C4C23×D1112yes—
700C4⋊C4—28no—
701C4⋊C4—28no—
702C4⋊C4—228no—
703C4⋊C4—444no—
704C22⋊C4—228no—
705C22⋊C4—228no—
706C22⋊C4—228no—
707C22⋊C4—228no—
708C22⋊C4—228no—
709C22⋊C4—228no—
710C22⋊C4—444no—
711C22⋊C4—444no—
712C22⋊C4—444no—
713C22⋊C4—444no—
714C22⋊C4—444no—
715C42—228no—
716C11C2×#244411yescharacteristic, complemented, Sylow
717C23—1116no—
718C23—114no—
719C23—114no—
720C23—114no—
721C23—114no—
722C23—228no—
723C23—228no—
724C23—228no—
725C23—222no—
726C23—222no—
727C23—222no—
728C23—222no—
729C23—228no—
730C23—228no—
731C23—228no—
732C23—228no—
733C23—228no—
734C23—222no—
735C23—222no—
736C23—222no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—228no—
741C23—222no—
742C23—222no—
743C23—222no—
744C23—222no—
745C23—222no—
746C23—222no—
747C23—222no—
748C23—444no—
749C23—444no—
750C23—444no—
751C23—444no—
752C23—444no—
753C23—444no—
754C23—444no—
755C23—444no—
756C23—444no—
757C23—444no—
758C23—444no—
759C23C2×D4×D1112yes—
760C23C2×#434312yes—
761C23#41×D1112yes—
762C23#41×D1112yes—
763C23#41×D1112yes—
764C23#6704212yes—
765C23#6704212yes—
766C23C24×D1111yescharacteristic
767D4—2232no—
768D4—4416no—
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—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—114no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—228no—
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—222no—
812C2×C4—4416no—
813C2×C4—4416no—
814C2×C4—4416no—
815C2×C4—4416no—
816C2×C4—444no—
817C2×C4—444no—
818C2×C4—444no—
819C2×C4—444no—
820C2×C4C2×D4×D1114yes—
821C2×C4C2×#434314yes—
822C22—118no—
823C22—224no—
824C22—224no—
825C22—224no—
826C22—224no—
827C22—224no—
828C22—224no—
829C22—2232no—
830C22—224no—
831C22—224no—
832C22—224no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—4416no—
838C22—442no—
839C22—442no—
840C22—442no—
841C22—442no—
842C22—442no—
843C22—442no—
844C22—442no—
845C22—888no—
846C22#1062316114yes—
847C22D11×#12314yes—
848C22#1062320714yes—
849C22#1062322214yes—
850C22#1062322614yes—
851C22#1062323514yes—
852C22#1062324014yes—
853C22C22×D4×D1111yescharacteristic
854C22C22×#434311yescharacteristic
855C22C2×#41×D1111yescharacteristic
856C22C2×#41×D1111yescharacteristic
857C22C2×#41×D1111yescharacteristic
858C22C2×#6704211yescharacteristic
859C22C2×#6704211yescharacteristic
860C4—24no—
861C4—24no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—42no—
867C4—224no—
868C4—442no—
869C4—442no—
870C4—442no—
871C4—442no—
872C2—228no—
873C2—444no—
874C2—882no—
875C2#1307236718yesdirect product factor
876C2C2×D11×#12311yescharacteristic
877C2C2×#1062322211yescharacteristic
878C2C2×#1062323511yescharacteristic
879C2C2×#1062316111yescharacteristic
880C2C2×#1062320711yescharacteristic
881C2C2×#1062324011yescharacteristic
882C2C2×#1062322611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#400C2
socleC24×C11C24
prime radicalC22×#66948C2
hypercenterC2×#400D11
hypocenterC11C2×#2444
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
2. C22×#66946C2semidirect
3. #13072367C2direct (N × H)
4. C2×#10622287C2semidirect
5. C2×#10622606C2semidirect
6. C2×#10622285C2semidirect
7. C2×#10622283C2semidirect
8. C2×#10622591C2semidirect
9. C2×#10622278C2semidirect
10. C2×#10622278C2semidirect
11. C2×#10622278C2semidirect
12. C2×#10622278C2semidirect
13. C2×#10622281C2semidirect
14. C2×#10622277C2semidirect
15. C2×D11×#95C2semidirect
16. C2×C11×#400C2semidirect
43. C2×#66946C22semidirect
44. C11×#400C22semidirect
57. #10622606C22semidirect
58. #10622591C22semidirect
59. #10622287C22semidirect
60. #10622285C22semidirect
61. #10622283C22semidirect
62. #10622281C22semidirect
63. #10622278C22semidirect
64. #10622278C22semidirect
65. #10622278C22semidirect
66. #10622278C22semidirect
67. #10622277C22semidirect
68. D11×#95C22semidirect
279. C2×#400D11semidirect
424. #400C2×D11semidirect
588. C2×C11#2444semidirect
716. C11C2×#2444semidirect
875. C2#13072367direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669482
C22×#669462
#130723672
C2×#106222872
C2×#106226062
C2×#106222852
C2×#106222832
C2×#106225912
C2×#106222782
C2×#106222812
C2×#106222772
C2×D11×#952
C2×C11×#4002
C2×#244411