Finite Group Databasebeta

← C2×#13076648 #14959902

Subgroups — C2×#13076648 #14959902

Order 2816.

2998 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66931C211yesmaximal, characteristic, complemented
2C22×#66992C211yesmaximal, characteristic
3#13076648C2116yesmaximal, direct product factor
4C2×#10622562C211yesmaximal, characteristic, complemented
5C2×#10622605C211yesmaximal, characteristic, complemented
6C2×#10622270C211yesmaximal, characteristic, complemented
7C2×#10622597C211yesmaximal, characteristic, complemented
8C2×#10622574C211yesmaximal, characteristic, complemented
9C2×#10622574C211yesmaximal, characteristic, complemented
10C2×#10622572C211yesmaximal, characteristic, complemented
11C2×#10622572C211yesmaximal, characteristic, complemented
12C2×#10622835C211yesmaximal, characteristic, complemented
13C2×#10622286C211yesmaximal, characteristic, complemented
14C2×#10622560C211yesmaximal, characteristic, complemented
15C2×#10622556C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C23×Dic22C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
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
32C2×#66992—28no—
33C2×#66992C2218yes—
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×C4⋊Dic11C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C2×#66931—28no—
47C2×#66931C2218yescomplemented
48C11×#394C2218yescomplemented
49C2×C11×#95C2211yescharacteristic
50#10622835C2218yescomplemented
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58#10622605C2218yescomplemented
59#10622597C2218yescomplemented
60#10622574C2218yescomplemented
61#10622574C2218yescomplemented
62#10622572C2218yescomplemented
63#10622572C2218yescomplemented
64#10622562C2218yescomplemented
65#10622560C2218yescomplemented
66#10622556C2218yescomplemented
67#10622286C2218yescomplemented
68#10622270C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C22×D4×C11—24no—
73C22×D4×C11—42no—
74C22×D4×C11—42no—
75C22×D4×C11C2314yes—
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—24no—
82C22×C22⋊D11—24no—
83C22×C22⋊D11—42no—
84C22×C22⋊D11—42no—
85C22×C22⋊D11—42no—
86C22×C22⋊D11—42no—
87C22×C22⋊D11C2314yes—
88C22×C22⋊D11C2314yes—
89C23×Dic11—42no—
90C23×Dic11—42no—
91C23×Dic11D418yes—
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2314yes—
100C22×Dic22—24no—
101C22×Dic22—42no—
102C22×Dic22—42no—
103C22×Dic22C2314yes—
104C2×C11×C4⋊C4—42no—
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C22⋊C4—24no—
107C2×C11×C22⋊C4—42no—
108C2×C11×C22⋊C4—42no—
109C2×C11×C22⋊C4—42no—
110C2×C11×C22⋊C4C2314yes—
111C2×C11×C22⋊C4C2314yes—
112C2×C11×C22⋊C4C2314yes—
113C2×C11×C22⋊C4C2314yes—
114C2×C22⋊Dic11—24no—
115C2×C22⋊Dic11—24no—
116C2×C22⋊Dic11—42no—
117C2×C22⋊Dic11—42no—
118C2×C22⋊Dic11—42no—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124#66992—232no—
125C2×(C2×D11)⋊C4—24no—
126C2×(C2×D11)⋊C4—42no—
127C2×(C2×D11)⋊C4—42no—
128C2×(C2×D11)⋊C4—42no—
129C2×(C2×D11)⋊C4—42no—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×C4⋊Dic11—24no—
136C2×C4⋊Dic11—42no—
137C2×C4⋊Dic11C2314yes—
138C2×C4⋊Dic11C2314yes—
139C2×Dic11⋊C4—24no—
140C2×Dic11⋊C4—24no—
141C2×Dic11⋊C4—24no—
142C2×Dic11⋊C4—42no—
143C2×Dic11⋊C4—42no—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×Dic11⋊C4C2314yes—
147C2×Dic11⋊C4C2314yes—
148C2×Dic11⋊C4C2314yes—
149#66931—232no—
150C11×#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2816—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×D11—22no—
181C23×D11—22no—
182C23×D11—22no—
183C23×D11C2412yes—
184C2×D4×C11—28no—
185C2×D4×C11—44no—
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—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×C11C2412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C2×C22⋊D11—28no—
209C2×C22⋊D11—28no—
210C2×C22⋊D11—44no—
211C2×C22⋊D11—44no—
212C2×C22⋊D11—44no—
213C2×C22⋊D11—44no—
214C2×C22⋊D11—416no—
215C2×C22⋊D11—416no—
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—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—416no—
236C22×Dic11—44no—
237C22×Dic11—44no—
238C22×Dic11C2×D414yes—
239C22×Dic11C2×D414yes—
240C22×Dic11C2×D4116yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C2×Dic22—28no—
249C2×Dic22—44no—
250C2×Dic22—44no—
251C2×Dic22—416no—
252C11×C4⋊C4—44no—
253C11×C22⋊C4—28no—
254C11×C22⋊C4—44no—
255C11×C22⋊C4—44no—
256C11×C22⋊C4—44no—
257C22⋊Dic11—28no—
258C22⋊Dic11—28no—
259C22⋊Dic11—44no—
260C22⋊Dic11—44no—
261C22⋊Dic11—44no—
262(C2×D11)⋊C4—28no—
263(C2×D11)⋊C4—44no—
264(C2×D11)⋊C4—44no—
265(C2×D11)⋊C4—44no—
266(C2×D11)⋊C4—44no—
267C4⋊Dic11—28no—
268C4⋊Dic11—44no—
269Dic11⋊C4—28no—
270Dic11⋊C4—28no—
271Dic11⋊C4—28no—
272Dic11⋊C4—44no—
273Dic11⋊C4—44no—
274C22×C22⋊Q8—111no—
275C22×#121—111no—
276#2816—1116no—
277C2×#399—111no—
278C2×#399—111no—
279C2×#398—111no—
280C2×#398—111no—
281C2×#394—111no—
282C2×#394—111no—
283C2×#394—111no—
284C2×#394—111no—
285C2×#394—111no—
286C2×#394D1111yescharacteristic, complemented
287C2×#393—111no—
288C2×#393—111no—
289C2×#381—111no—
290C23×C11—28no—
291C23×C11—28no—
292C23×C11—28no—
293C23×C11—22no—
294C23×C11—22no—
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—44no—
307C23×C11—44no—
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×C11C22×D414yes—
318C23×C11C22×D412yes—
319C23×C11H(5,𝔽2)12yes—
320C23×C11H(5,𝔽2)12yes—
321C23×C11H(5,𝔽2)12yes—
322C23×C11H(5,𝔽2)12yes—
323C23×C112−1+412yes—
324C23×C112−1+412yes—
325C23×C11C2511yescharacteristic
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—44no—
334C22×D11—44no—
335C22×D11—44no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11—44no—
339C22×D11—44no—
340D4×C11—416no—
341C2×C4×C11—22no—
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—44no—
357C2×C4×C11—44no—
358C2×C4×C11—44no—
359C2×C4×C11—44no—
360C2×C4×C11—44no—
361C22⋊D11—416no—
362C22⋊D11—416no—
363C2×Dic11—28no—
364C2×Dic11—28no—
365C2×Dic11—22no—
366C2×Dic11—22no—
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—416no—
385C2×Dic11—44no—
386C2×Dic11—44no—
387C2×Dic11—44no—
388C2×Dic11—44no—
389C2×Dic11—44no—
390C2×Dic11C22×D414yes—
391C2×Dic11C22×D414yes—
392Dic22—416no—
393C23×Q8—111no—
394C23×D4—111no—
395C23×D4—111no—
396C23×D4C2×D1111yescharacteristic
397C24×C4—111no—
398C2×C22⋊Q8—118no—
399C2×C22⋊Q8—228no—
400C2×#121—118no—
401C2×#121—228no—
402C22×C4⋊C4—111no—
403C22×C4⋊C4—111no—
404C22×C4⋊C4—111no—
405C22×C4⋊C4—111no—
406C22×C4⋊C4—111no—
407C22×C4⋊C4—111no—
408C22×C4⋊C4—111no—
409C22×C4⋊C4C2×D1111yescharacteristic
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×C22⋊C4C2×D1111yescharacteristic
423C22×C22⋊C4C2×D1111yescharacteristic
424#399—118no—
425#399—118no—
426#398—118no—
427#398—118no—
428#394—118no—
429#394—118no—
430#394—118no—
431#394—118no—
432#394—118no—
433#394C2×D1118yescomplemented
434#393—118no—
435#393—118no—
436#381—118no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95—111no—
444C2×#95C2×D1111yescharacteristic
445C22×C11—24no—
446C22×C11—24no—
447C22×C11—24no—
448C22×C11—416no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—88no—
461C22×C11#53414yes—
462C22×C11#53514yes—
463C22×C11#53614yes—
464C22×C11#56214yes—
465C22×C11#56214yes—
466C22×C11#56214yes—
467C22×C11#56214yes—
468C22×C11C23×D411yescharacteristic
469C22×C11C2×H(5,𝔽2)11yescharacteristic
470C22×C11C2×H(5,𝔽2)11yescharacteristic
471C22×C11C2×H(5,𝔽2)11yescharacteristic
472C22×C11C2×H(5,𝔽2)11yescharacteristic
473C22×C11C2×2−1+411yescharacteristic
474C22×C11C2×2−1+411yescharacteristic
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—88no—
483C4×C11—42no—
484C4×C11—42no—
485C4×C11—42no—
486C4×C11—42no—
487C4×C11—42no—
488Dic11—24no—
489Dic11—24no—
490Dic11—42no—
491Dic11—42no—
492Dic11—42no—
493Dic11—42no—
494Dic11—42no—
495C25—111no—
496C25C22×D1111yescharacteristic
497C25C22×D1111yescharacteristic
498C22×Q8—114no—
499C22×Q8—224no—
500C22×Q8—442no—
501C22×Q8—442no—
502C22×D4—24no—
503C22×D4—42no—
504C22×D4—42no—
505C22×D4—114no—
506C22×D4—114no—
507C22×D4—224no—
508C22×D4—224no—
509C22×D4—442no—
510C22×D4—442no—
511C22×D4—442no—
512C22×D4—442no—
513C22×D4C22×D1114yes—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—118no—
517C23×C4—114no—
518C23×C4—111no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—111no—
522C23×C4—111no—
523C23×C4—442no—
524C23×C4—442no—
525C23×C4C22×D1111yescharacteristic
526C23×C4C22×D1111yescharacteristic
527C23×C4C22×D1111yescharacteristic
528C23×C4C22×D1111yescharacteristic
529C23×C4C22×D1111yescharacteristic
530C22⋊Q8—2232no—
531#121—2232no—
532C2×C4⋊C4—42no—
533C2×C4⋊C4—114no—
534C2×C4⋊C4—114no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4—114no—
537C2×C4⋊C4—114no—
538C2×C4⋊C4—114no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—224no—
541C2×C4⋊C4—224no—
542C2×C4⋊C4—224no—
543C2×C4⋊C4—224no—
544C2×C4⋊C4—442no—
545C2×C4⋊C4—442no—
546C2×C4⋊C4—442no—
547C2×C4⋊C4C22×D1114yes—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
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—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⋊C4—442no—
571C2×C22⋊C4—442no—
572C2×C22⋊C4C22×D1114yes—
573C2×C22⋊C4C22×D1114yes—
574C2×C22⋊C4C22×D1114yes—
575C2×C22⋊C4C22×D1114yes—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—114no—
580#95—114no—
581#95—114no—
582#95—114no—
583#95C22×D1114yes—
584C2×C11—44no—
585C2×C11—82no—
586C2×C11#281618yescomplemented
587C2×C11C2×#53411yescharacteristic
588C2×C11C2×#53511yescharacteristic
589C2×C11C2×#53611yescharacteristic
590C2×C11C2×#56211yescharacteristic
591C2×C11C2×#56211yescharacteristic
592C2×C11C2×#56211yescharacteristic
593C2×C11C2×#56211yescharacteristic
594D11—82no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—112no—
609C24—222no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24—222no—
616C24D4×D1114yes—
617C24C23×D1112yes—
618C24C23×D1112yes—
619C24C23×D1111yescharacteristic
620C2×Q8—228no—
621C2×Q8—444no—
622C2×Q8—444no—
623C2×Q8—4416no—
624C2×D4—28no—
625C2×D4—44no—
626C2×D4—44no—
627C2×D4—416no—
628C2×D4—228no—
629C2×D4—228no—
630C2×D4—444no—
631C2×D4—444no—
632C2×D4—444no—
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—114no—
652C22×C4—114no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—1116no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—112no—
660C22×C4—112no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—222no—
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—4416no—
681C22×C4—444no—
682C22×C4—444no—
683C22×C4C23×D1112yes—
684C22×C4C23×D1112yes—
685C22×C4C23×D1112yes—
686C22×C4C23×D1112yes—
687C22×C4C23×D1112yes—
688C4⋊C4—44no—
689C4⋊C4—228no—
690C4⋊C4—228no—
691C4⋊C4—228no—
692C4⋊C4—228no—
693C4⋊C4—444no—
694C4⋊C4—444no—
695C4⋊C4—444no—
696C22⋊C4—28no—
697C22⋊C4—44no—
698C22⋊C4—44no—
699C22⋊C4—44no—
700C22⋊C4—228no—
701C22⋊C4—228no—
702C22⋊C4—228no—
703C22⋊C4—444no—
704C22⋊C4—444no—
705C22⋊C4—444no—
706C22⋊C4—444no—
707C22⋊C4—444no—
708C22⋊C4—444no—
709C22⋊C4—444no—
710C11C2×#281611yescharacteristic, complemented, Sylow
711C23—28no—
712C23—28no—
713C23—28no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—222no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—222no—
744C23—222no—
745C23—444no—
746C23—444no—
747C23—444no—
748C23—444no—
749C23—444no—
750C23—444no—
751C23—444no—
752C23C2×D4×D1114yes—
753C23C2×D4×D1112yes—
754C23#6703712yes—
755C23#6703712yes—
756C23#6703712yes—
757C23#6704212yes—
758C23#6704312yes—
759C23#6704312yes—
760C23C24×D1111yescharacteristic
761Q8—4416no—
762D4—416no—
763D4—4416no—
764D4—4416no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
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—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—114no—
786C2×C4—114no—
787C2×C4—228no—
788C2×C4—228no—
789C2×C4—222no—
790C2×C4—222no—
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—4416no—
809C2×C4—444no—
810C2×C4—444no—
811C2×C4—444no—
812C2×C4—444no—
813C2×C4—444no—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—416no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—88no—
830C22—442no—
831C22—442no—
832C22—442no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—888no—
838C22#1062312314yes—
839C22#1062313614yes—
840C22#1062315214yes—
841C22#1062315214yes—
842C22#1062317914yes—
843C22#1062319814yes—
844C22#1062321514yes—
845C22C22×D4×D1111yescharacteristic
846C22C2×#6703711yescharacteristic
847C22C2×#6703711yescharacteristic
848C22C2×#6703711yescharacteristic
849C22C2×#6704211yescharacteristic
850C22C2×#6704311yescharacteristic
851C22C2×#6704311yescharacteristic
852C4—42no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—224no—
858C4—224no—
859C4—442no—
860C4—442no—
861C4—442no—
862C4—442no—
863C4—442no—
864C2—44no—
865C2—82no—
866C2—882no—
867C2#1307664818yesdirect product factor
868C2C2×#1062313611yescharacteristic
869C2C2×#1062312311yescharacteristic
870C2C2×#1062317911yescharacteristic
871C2C2×#1062321511yescharacteristic
872C2C2×#1062315211yescharacteristic
873C2C2×#1062315211yescharacteristic
874C2C2×#1062319811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
prime radicalC22×#66992C2
hypercenterC2×#394D11
hypocenterC11C2×#2816
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66931C2semidirect
3. #13076648C2direct (N × H)
4. C2×#10622562C2semidirect
5. C2×#10622605C2semidirect
6. C2×#10622270C2semidirect
7. C2×#10622597C2semidirect
8. C2×#10622574C2semidirect
9. C2×#10622574C2semidirect
10. C2×#10622572C2semidirect
11. C2×#10622572C2semidirect
12. C2×#10622835C2semidirect
13. C2×#10622286C2semidirect
14. C2×#10622560C2semidirect
15. C2×#10622556C2semidirect
16. C2×C11×#394C2semidirect
47. C2×#66931C22semidirect
48. C11×#394C22semidirect
50. #10622835C22semidirect
58. #10622605C22semidirect
59. #10622597C22semidirect
60. #10622574C22semidirect
61. #10622574C22semidirect
62. #10622572C22semidirect
63. #10622572C22semidirect
64. #10622562C22semidirect
65. #10622560C22semidirect
66. #10622556C22semidirect
67. #10622286C22semidirect
68. #10622270C22semidirect
286. C2×#394D11semidirect
433. #394C2×D11semidirect
586. C2×C11#2816semidirect
710. C11C2×#2816semidirect
867. C2#13076648direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669312
C22×#669922
#130766482
C2×#106225622
C2×#106226052
C2×#106222702
C2×#106225972
C2×#106225742
C2×#106225722
C2×#106228352
C2×#106222862
C2×#106225602
C2×#106225562
C2×C11×#3942
C2×#281611