Finite Group Databasebeta

← C2×#13072366 #14921511

Subgroups — C2×#13072366 #14921511

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×#66983C211yesmaximal, characteristic
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3#13072366C2116yesmaximal, direct product factor
4C2×#10622273C211yesmaximal, characteristic, complemented
5C2×#10622288C211yesmaximal, characteristic, complemented
6C2×#10622288C211yesmaximal, characteristic, complemented
7C2×#10622285C211yesmaximal, characteristic, complemented
8C2×#10622282C211yesmaximal, characteristic, complemented
9C2×#10622268C211yesmaximal, characteristic, complemented
10C2×#10622826C211yesmaximal, characteristic, complemented
11C2×#10622826C211yesmaximal, characteristic, complemented
12C2×#10622826C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622823C211yesmaximal, characteristic, complemented
15C2×#10622277C211yesmaximal, characteristic, complemented
16C22×C11×#95C211yesmaximal, characteristic, complemented
17C24×C4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×D44C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C2×#66983—28no—
27C2×#66983C2218yes—
28C2×C4×C22⋊D11—28no—
29C2×C4×C22⋊D11C2218yescomplemented
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×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2218yescomplemented
49#10622826C2218yescomplemented
50#10622826C2218yescomplemented
51#10622826C2218yescomplemented
52#10622823C2218yescomplemented
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622288C2218yescomplemented
62#10622288C2218yescomplemented
63#10622285C2218yescomplemented
64#10622282C2218yescomplemented
65#10622278C2218yescomplemented
66#10622277C2218yescomplemented
67#10622273C2218yescomplemented
68#10622268C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C23×C4×C11—24no—
73C23×C4×C11—24no—
74C23×C4×C11—24no—
75C23×C4×C11—24no—
76C23×C4×C11—24no—
77C23×C4×C11—42no—
78C23×C4×C11—42no—
79C23×C4×C11—42no—
80C23×C4×C11—42no—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2314yes—
86C23×C4×C11C2314yes—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2314yes—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11—24no—
93C22×C22⋊D11—24no—
94C22×C22⋊D11—24no—
95C22×C22⋊D11D418yes—
96C22×C22⋊D11C2314yes—
97C22×C22⋊D11C2314yes—
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C22×D44—24no—
105C22×D44—24no—
106C22×D44—42no—
107C22×D44C2314yes—
108C22×C4×D11—24no—
109C22×C4×D11—24no—
110C22×C4×D11—42no—
111C22×C4×D11C2314yes—
112C2×C22⋊Dic11—24no—
113C2×C22⋊Dic11—24no—
114C2×C22⋊Dic11C2314yes—
115C2×C22⋊Dic11C2314yes—
116#66983—232no—
117C4×C22⋊D11—232no—
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×C4⋊Dic11—24no—
137C2×C4⋊Dic11C2314yes—
138C2×Dic11⋊C4—24no—
139C2×Dic11⋊C4—24no—
140C2×Dic11⋊C4—42no—
141C2×Dic11⋊C4C2314yes—
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×C11C2×D414yes—
164C24×C11#4114yes—
165C24×C11#4114yes—
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×D11—22no—
181C23×D11C2×D414yes—
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—28no—
191C22×C4×C11—28no—
192C22×C4×C11—28no—
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×C11—28no—
204C22×C4×C11—28no—
205C22×C4×C11—44no—
206C22×C4×C11—44no—
207C22×C4×C11—44no—
208C22×C4×C11—44no—
209C22×C4×C11—416no—
210C22×C4×C11—416no—
211C22×C4×C11—416no—
212C22×C4×C11#4114yes—
213C22×C4×C11#4114yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C2×C22⋊D11—232no—
221C2×C22⋊D11—28no—
222C2×C22⋊D11—28no—
223C2×C22⋊D11—28no—
224C2×C22⋊D11—28no—
225C2×C22⋊D11—28no—
226C2×C22⋊D11—416no—
227C2×C22⋊D11C2×D4116yes—
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×Dic11—22no—
241C22×Dic11—22no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—22no—
245C22×Dic11C2×D414yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C22×Dic11C2412yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C2×D44—28no—
253C2×D44—28no—
254C2×D44—44no—
255C2×D44—416no—
256C2×C4×D11—28no—
257C2×C4×D11—28no—
258C2×C4×D11—44no—
259C2×C4×D11—416no—
260C22⋊Dic11—28no—
261C22⋊Dic11—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—44no—
267(C2×D11)⋊C4—44no—
268(C2×D11)⋊C4—44no—
269(C2×D11)⋊C4—44no—
270(C2×D11)⋊C4—44no—
271C4⋊Dic11—28no—
272Dic11⋊C4—28no—
273Dic11⋊C4—28no—
274Dic11⋊C4—44no—
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×#386—111no—
289C2×#385—111no—
290C2×#381—111no—
291C22×#95D1111yescharacteristic, complemented
292C23×C11—28no—
293C23×C11—28no—
294C23×C11—28no—
295C23×C11—28no—
296C23×C11—28no—
297C23×C11—28no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11#123116yes—
303C23×C11C22×D414yes—
304C23×C11C22×D412yes—
305C23×C11C2×#4114yes—
306C23×C11C2×#4112yes—
307C23×C11C2×#4112yes—
308C23×C11C2×#4112yes—
309C23×C11C2×#4114yes—
310C23×C11C2×#4112yes—
311C23×C11H(5,𝔽2)12yes—
312C23×C11H(5,𝔽2)12yes—
313C23×C11C2511yescharacteristic
314C22×D11—28no—
315C22×D11—28no—
316C22×D11—28no—
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—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—44no—
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×D11—44no—
340C22×D11—44no—
341C22×D11C22×D414yes—
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—416no—
361C2×C4×C11—416no—
362C2×C4×C11—416no—
363C2×C4×C11—44no—
364C2×C4×C11—44no—
365C2×C4×C11—44no—
366C2×C4×C11—44no—
367C2×C4×C11C2×#4114yes—
368C2×C4×C11C2×#4114yes—
369C22⋊D11—232no—
370C22⋊D11—416no—
371C2×Dic11—28no—
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—22no—
388C2×Dic11—22no—
389C2×Dic11—44no—
390C2×Dic11—44no—
391C2×Dic11—44no—
392C2×Dic11—44no—
393C2×Dic11—44no—
394C2×Dic11C22×D414yes—
395D44—416no—
396C4×D11—416no—
397C23×D4—111no—
398C23×D4—111no—
399C23×D4—111no—
400C24×C4—111no—
401C24×C4C2×D1111yescharacteristic
402C24×C4C2×D1111yescharacteristic
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⋊C4—111no—
421C22×C22⋊C4—111no—
422C22×C22⋊C4—111no—
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#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—111no—
444C2×#95C2×D1111yescharacteristic
445C2×#95C2×D1111yescharacteristic
446C2×#95C2×D1111yescharacteristic
447C2×#95C2×D1111yescharacteristic
448C2×#95C2×D1118yescomplemented
449C22×C11—24no—
450C22×C11—24no—
451C22×C11—24no—
452C22×C11—24no—
453C22×C11—232no—
454C22×C11—24no—
455C22×C11—24no—
456C22×C11C2×#12318yes—
457C22×C11C2×#12314yes—
458C22×C11#52914yes—
459C22×C11#53814yes—
460C22×C11#54614yes—
461C22×C11#54614yes—
462C22×C11#55314yes—
463C22×C11#55314yes—
464C22×C11C23×D411yescharacteristic
465C22×C11C22×#4111yescharacteristic
466C22×C11C22×#4111yescharacteristic
467C22×C11C22×#4111yescharacteristic
468C22×C11C22×#4111yescharacteristic
469C22×C11C2×H(5,𝔽2)11yescharacteristic
470C22×C11C2×H(5,𝔽2)11yescharacteristic
471C2×D11—24no—
472C2×D11—24no—
473C2×D11—24no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—416no—
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—42no—
486C2×D11—88no—
487C4×C11—24no—
488C4×C11—24no—
489C4×C11—42no—
490C4×C11—42no—
491C4×C11—42no—
492C4×C11—42no—
493Dic11—24no—
494Dic11—42no—
495Dic11—42no—
496Dic11—42no—
497Dic11—42no—
498Dic11—42no—
499C25—111no—
500C25—111no—
501C25C22×D1111yescharacteristic
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—24no—
515C23×C4—24no—
516C23×C4—24no—
517C23×C4—24no—
518C23×C4—24no—
519C23×C4—42no—
520C23×C4—42no—
521C23×C4—42no—
522C23×C4—42no—
523C23×C4—111no—
524C23×C4—111no—
525C23×C4—111no—
526C23×C4—111no—
527C23×C4—111no—
528C23×C4—111no—
529C23×C4—114no—
530C23×C4—224no—
531C23×C4—224no—
532C23×C4—442no—
533C23×C4C22×D1111yescharacteristic
534C23×C4C22×D1111yescharacteristic
535C23×C4C22×D1111yescharacteristic
536C23×C4C22×D1111yescharacteristic
537C23×C4C22×D1114yes—
538C23×C4C22×D1114yes—
539C23×C4C22×D1111yescharacteristic
540C23×C4C22×D1111yescharacteristic
541C23×C4C22×D1114yes—
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—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#95—114no—
584#95C22×D1114yes—
585#95C22×D1114yes—
586#95C22×D1114yes—
587#95C22×D1114yes—
588C2×C11—28no—
589C2×C11#244418yescomplemented
590C2×C11C22×#12311yescharacteristic
591C2×C11C2×#52911yescharacteristic
592C2×C11C2×#53811yescharacteristic
593C2×C11C2×#54611yescharacteristic
594C2×C11C2×#54611yescharacteristic
595C2×C11C2×#55311yescharacteristic
596C2×C11C2×#55311yescharacteristic
597D11—44no—
598D11—82no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
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#433914yes—
620C24D4×D1114yes—
621C24#434314yes—
622C24C23×D1112yes—
623C24C23×D1111yescharacteristic
624C2×D4—1116no—
625C2×D4—228no—
626C2×D4—2232no—
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—28no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—28no—
648C22×C4—28no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—28no—
656C22×C4—28no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—44no—
661C22×C4—416no—
662C22×C4—416no—
663C22×C4—416no—
664C22×C4—114no—
665C22×C4—112no—
666C22×C4—112no—
667C22×C4—112no—
668C22×C4—112no—
669C22×C4—112no—
670C22×C4—112no—
671C22×C4—228no—
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—222no—
685C22×C4—222no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—222no—
689C22×C4—228no—
690C22×C4—444no—
691C22×C4—4416no—
692C22×C4#433914yes—
693C22×C4#433914yes—
694C22×C4C23×D1112yes—
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—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—28no—
718C23—28no—
719C23—28no—
720C23—28no—
721C23—28no—
722C23—28no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—114no—
728C23—228no—
729C23—228no—
730C23—228no—
731C23—222no—
732C23—222no—
733C23—222no—
734C23—222no—
735C23—222no—
736C23—222no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—222no—
744C23—444no—
745C23—444no—
746C23—444no—
747C23—444no—
748C23—444no—
749C23—444no—
750C23—444no—
751C23—444no—
752C23—444no—
753C23—444no—
754C23—444no—
755C23#66947116yes—
756C23C2×#433914yes—
757C23C2×#433912yes—
758C23C2×#433912yes—
759C23C2×#433912yes—
760C23C2×D4×D1114yes—
761C23C2×D4×D1112yes—
762C23#6703712yes—
763C23#6703712yes—
764C23C2×#434314yes—
765C23C2×#434312yes—
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—416no—
789C2×C4—416no—
790C2×C4—416no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—114no—
796C2×C4—228no—
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—222no—
812C2×C4—222no—
813C2×C4—222no—
814C2×C4—4416no—
815C2×C4—444no—
816C2×C4—444no—
817C2×C4—444no—
818C2×C4—444no—
819C2×C4—444no—
820C2×C4C2×#433914yes—
821C2×C4C2×#433914yes—
822C22—24no—
823C22—24no—
824C22—24no—
825C22—24no—
826C22—24no—
827C22—24no—
828C22—232no—
829C22—224no—
830C22—224no—
831C22—224no—
832C22—442no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—4416no—
837C22—442no—
838C22—442no—
839C22—442no—
840C22—442no—
841C22—442no—
842C22—442no—
843C22—442no—
844C22—888no—
845C22#1062301014yes—
846C22#1062302114yes—
847C22#1062302114yes—
848C22#1062302514yes—
849C22C2×#6694718yes—
850C22C2×#6694714yes—
851C22#1062304514yes—
852C22#1062304514yes—
853C22C22×#433911yescharacteristic
854C22C22×#433911yescharacteristic
855C22C22×#433911yescharacteristic
856C22C22×D4×D1111yescharacteristic
857C22C2×#6703711yescharacteristic
858C22C2×#6703711yescharacteristic
859C22C22×#434311yescharacteristic
860C4—24no—
861C4—24no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—224no—
867C4—442no—
868C4—442no—
869C4—442no—
870C4—442no—
871C4—442no—
872C2—28no—
873C2—444no—
874C2—882no—
875C2#1307236618yesdirect product factor
876C2C22×#6694711yescharacteristic
877C2C2×#1062301011yescharacteristic
878C2C2×#1062302511yescharacteristic
879C2C2×#1062302111yescharacteristic
880C2C2×#1062302111yescharacteristic
881C2C2×#1062304511yescharacteristic
882C2C2×#1062304511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#95C2
socleC24×C11C24
prime radicalC22×#66983C2
hypercenterC22×#95D11
hypocenterC11C2×#2444
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D11C2semidirect
3. #13072366C2direct (N × H)
4. C2×#10622273C2semidirect
5. C2×#10622288C2semidirect
6. C2×#10622288C2semidirect
7. C2×#10622285C2semidirect
8. C2×#10622282C2semidirect
9. C2×#10622268C2semidirect
10. C2×#10622826C2semidirect
11. C2×#10622826C2semidirect
12. C2×#10622826C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622823C2semidirect
15. C2×#10622277C2semidirect
16. C22×C11×#95C2semidirect
29. C2×C4×C22⋊D11C22semidirect
48. C2×C11×#95C22semidirect
49. #10622826C22semidirect
50. #10622826C22semidirect
51. #10622826C22semidirect
52. #10622823C22semidirect
61. #10622288C22semidirect
62. #10622288C22semidirect
63. #10622285C22semidirect
64. #10622282C22semidirect
65. #10622278C22semidirect
66. #10622277C22semidirect
67. #10622273C22semidirect
68. #10622268C22semidirect
291. C22×#95D11semidirect
448. C2×#95C2×D11semidirect
589. C2×C11#2444semidirect
716. C11C2×#2444semidirect
875. C2#13072366direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669832
C22×C4×C22⋊D112
#130723662
C2×#106222732
C2×#106222882
C2×#106222852
C2×#106222822
C2×#106222682
C2×#106228262
C2×#106222782
C2×#106228232
C2×#106222772
C22×C11×#952
C2×#244411