Finite Group Databasebeta

← C2×#13073739 #14923902

Subgroups — C2×#13073739 #14923902

Order 2816.

3266 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×#66932C211yesmaximal, characteristic, complemented
2C22×#66937C211yesmaximal, characteristic
3#13073739C2116yesmaximal, direct product factor
4C2×#10622272C211yesmaximal, characteristic, complemented
5C2×#10622285C211yesmaximal, characteristic, complemented
6C2×#10622574C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622552C211yesmaximal, characteristic, complemented
9C2×#10622541C211yesmaximal, characteristic, complemented
10C2×#10622283C211yesmaximal, characteristic, complemented
11C2×#10622553C211yesmaximal, characteristic, complemented
12C2×#10622826C211yesmaximal, characteristic, complemented
13C2×#10622826C211yesmaximal, characteristic, complemented
14C2×#10622281C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C2×#66937—28no—
45C2×#66937C2218yes—
46C2×#66932—28no—
47C2×#66932C2218yescomplemented
48C4×C11×C22⋊C4C2218yescomplemented
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51#10622826C2218yescomplemented
52#10622826C2218yescomplemented
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59#10622574C2218yescomplemented
60#10622574C2218yescomplemented
61#10622553C2218yescomplemented
62#10622552C2218yescomplemented
63C4×(C2×D11)⋊C4C2218yescomplemented
64#10622541C2218yescomplemented
65#10622285C2218yescomplemented
66#10622283C2218yescomplemented
67#10622281C2218yescomplemented
68#10622272C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C23×C4×C11—24no—
73C23×C4×C11—42no—
74C23×C4×C11—42no—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2314yes—
82C22×C22⋊D11—24no—
83C22×C22⋊D11—24no—
84C22×C22⋊D11—24no—
85C22×C22⋊D11—24no—
86C22×C22⋊D11—42no—
87C22×C22⋊D11—42no—
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—42no—
103C22×C4×D11C2314yes—
104C2×C11×C22⋊C4—24no—
105C2×C11×C22⋊C4D418yes—
106C2×C11×C22⋊C4C2314yes—
107C2×C11×C22⋊C4C2314yes—
108C2×C42×C11—42no—
109C2×C42×C11—42no—
110C2×C42×C11C2314yes—
111C2×C42×C11C2314yes—
112C2×C22⋊Dic11—24no—
113C2×C22⋊Dic11—24no—
114C2×C22⋊Dic11C2314yes—
115C2×C22⋊Dic11C2314yes—
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)⋊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×(C2×D11)⋊C4C2314yes—
134C2×C4⋊Dic11—24no—
135C2×C4⋊Dic11—24no—
136C2×C4⋊Dic11—42no—
137C2×C4⋊Dic11C2314yes—
138C2×C4⋊Dic11C2314yes—
139C2×C4⋊Dic11C2314yes—
140C2×Dic11⋊C4—24no—
141C2×Dic11⋊C4—24no—
142C2×Dic11⋊C4—24no—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×C4×Dic11—24no—
147C2×C4×Dic11C2314yes—
148#66937—232no—
149#66932—232no—
150C11×#95C2314yes—
151C11×#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2559—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×D11—22no—
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—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—28no—
199C22×C4×C11—44no—
200C22×C4×C11—44no—
201C22×C4×C11—416no—
202C22×C4×C11C2×D414yes—
203C22×C4×C11C2×D414yes—
204C22×C4×C11#4114yes—
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—28no—
213C2×C22⋊D11—28no—
214C2×C22⋊D11—28no—
215C2×C22⋊D11—28no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11—416no—
219C2×C22⋊D11—416no—
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#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—44no—
251C2×C4×D11—416no—
252C11×C22⋊C4—28no—
253C11×C22⋊C4C2×D4116yes—
254C42×C11—44no—
255C42×C11—44no—
256C22⋊Dic11—28no—
257C22⋊Dic11—28no—
258(C2×D11)⋊C4—28no—
259(C2×D11)⋊C4—28no—
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—
267C4⋊Dic11—28no—
268C4⋊Dic11—28no—
269C4⋊Dic11—44no—
270Dic11⋊C4—28no—
271Dic11⋊C4—28no—
272Dic11⋊C4—28no—
273C4×Dic11—28no—
274C22×#126—111no—
275C22×#121—111no—
276#2559—1116no—
277C2×#400—111no—
278C2×#394—111no—
279C2×#394—111no—
280C2×#394—111no—
281C2×#390—111no—
282C2×#389—111no—
283C2×#388—111no—
284C2×#388—111no—
285C2×#386—111no—
286C2×#386—111no—
287C2×#385—111no—
288C2×C4×C22⋊C4—111no—
289C2×C4×C22⋊C4D1111yescharacteristic, complemented
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—44no—
300C23×C11—44no—
301C23×C11—44no—
302C23×C11—44no—
303C23×C11C22×D414yes—
304C23×C11C22×D412yes—
305C23×C11C2×#4112yes—
306C23×C11C2×#4112yes—
307C23×C11C2×#4112yes—
308C23×C11C2×#4112yes—
309C23×C11H(5,𝔽2)12yes—
310C23×C11H(5,𝔽2)12yes—
311C23×C11C2511yescharacteristic
312C22×D11—28no—
313C22×D11—28no—
314C22×D11—28no—
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—22no—
327C22×D11—22no—
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—44no—
338C22×D11—44no—
339C22×D11C2×#4114yes—
340C2×C4×C11—28no—
341C2×C4×C11—28no—
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—416no—
359C2×C4×C11—44no—
360C2×C4×C11—44no—
361C2×C4×C11C22×D414yes—
362C2×C4×C11C22×D414yes—
363C2×C4×C11C2×#4114yes—
364C2×C4×C11C2×#4114yes—
365C22⋊D11—416no—
366C22⋊D11—416no—
367C2×Dic11—28no—
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—44no—
386C2×Dic11—44no—
387C2×Dic11—44no—
388C2×Dic11—44no—
389C2×Dic11—44no—
390C2×Dic11C2×#4114yes—
391D44—416no—
392C4×D11—416no—
393C23×D4—111no—
394C23×D4—111no—
395C23×D4—111no—
396C24×C4—111no—
397C24×C4C2×D1111yescharacteristic
398C2×#126—118no—
399C2×#126—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×C22⋊C4—111no—
409C22×C22⋊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⋊C4C2×D1111yescharacteristic
420C22×C22⋊C4C2×D1111yescharacteristic
421C22×C42—111no—
422C22×C42C2×D1111yescharacteristic
423C22×C42C2×D1111yescharacteristic
424#400—118no—
425#394—118no—
426#394—118no—
427#394—118no—
428#390—118no—
429#389—118no—
430#388—118no—
431#388—118no—
432#386—118no—
433#386—118no—
434#385—118no—
435C4×C22⋊C4—118no—
436C4×C22⋊C4C2×D1118yescomplemented
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95C2×D1111yescharacteristic
444C2×#95C2×D1111yescharacteristic
445C22×C11—24no—
446C22×C11—24no—
447C22×C11—24no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—416no—
453C22×C11#52914yes—
454C22×C11#53214yes—
455C22×C11#53814yes—
456C22×C11#54614yes—
457C22×C11#54614yes—
458C22×C11#55314yes—
459C22×C11#55314yes—
460C22×C11C23×D411yescharacteristic
461C22×C11C22×#4111yescharacteristic
462C22×C11C22×#4111yescharacteristic
463C22×C11C22×#4111yescharacteristic
464C22×C11C22×#4111yescharacteristic
465C22×C11C2×H(5,𝔽2)11yescharacteristic
466C22×C11C2×H(5,𝔽2)11yescharacteristic
467C2×D11—24no—
468C2×D11—24no—
469C2×D11—24no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—416no—
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—24no—
484C4×C11—24no—
485C4×C11—24no—
486C4×C11—24no—
487C4×C11—42no—
488C4×C11—42no—
489Dic11—24no—
490Dic11—42no—
491Dic11—42no—
492Dic11—42no—
493Dic11—42no—
494Dic11—42no—
495C25—111no—
496C25—111no—
497C25C22×D1111yescharacteristic
498C22×D4—114no—
499C22×D4—114no—
500C22×D4—114no—
501C22×D4—224no—
502C22×D4—224no—
503C22×D4—224no—
504C22×D4—224no—
505C22×D4—224no—
506C22×D4—224no—
507C22×D4—442no—
508C22×D4—442no—
509C22×D4—442no—
510C23×C4—24no—
511C23×C4—42no—
512C23×C4—42no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—111no—
517C23×C4—111no—
518C23×C4—111no—
519C23×C4—114no—
520C23×C4—224no—
521C23×C4—224no—
522C23×C4—442no—
523C23×C4C22×D1111yescharacteristic
524C23×C4C22×D1111yescharacteristic
525C23×C4C22×D1111yescharacteristic
526C23×C4C22×D1111yescharacteristic
527C23×C4C22×D1111yescharacteristic
528C23×C4C22×D1111yescharacteristic
529C23×C4C22×D1114yes—
530#126—2232no—
531#121—2232no—
532C2×C4⋊C4—114no—
533C2×C4⋊C4—114no—
534C2×C4⋊C4—114no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4—114no—
537C2×C4⋊C4—114no—
538C2×C4⋊C4—224no—
539C2×C4⋊C4—224no—
540C2×C4⋊C4—224no—
541C2×C4⋊C4—224no—
542C2×C4⋊C4—224no—
543C2×C4⋊C4—442no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—114no—
546C2×C22⋊C4—114no—
547C2×C22⋊C4—114no—
548C2×C22⋊C4—114no—
549C2×C22⋊C4—114no—
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—224no—
557C2×C22⋊C4—224no—
558C2×C22⋊C4—224no—
559C2×C22⋊C4—224no—
560C2×C22⋊C4—224no—
561C2×C22⋊C4—224no—
562C2×C22⋊C4—224no—
563C2×C22⋊C4—224no—
564C2×C22⋊C4—442no—
565C2×C22⋊C4—442no—
566C2×C22⋊C4—442no—
567C2×C22⋊C4D4418yes—
568C2×C22⋊C4C22×D1114yes—
569C2×C22⋊C4C22×D1114yes—
570C2×C42—42no—
571C2×C42—42no—
572C2×C42—114no—
573C2×C42—224no—
574C2×C42C22×D1114yes—
575C2×C42C22×D1114yes—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—114no—
580#95—114no—
581#95—114no—
582#95C22×D1114yes—
583#95C22×D1114yes—
584C2×C11—44no—
585C2×C11#255918yescomplemented
586C2×C11C2×#52911yescharacteristic
587C2×C11C2×#53211yescharacteristic
588C2×C11C2×#53811yescharacteristic
589C2×C11C2×#54611yescharacteristic
590C2×C11C2×#54611yescharacteristic
591C2×C11C2×#55311yescharacteristic
592C2×C11C2×#55311yescharacteristic
593D11—44no—
594D11—82no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—114no—
602C24—112no—
603C24—112no—
604C24—222no—
605C24—222no—
606C24—222no—
607C24—222no—
608C24—222no—
609C24—222no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24—222no—
616C24—222no—
617C24C2×D4414yes—
618C24C23×D1112yes—
619C24C23×D1111yescharacteristic
620C2×D4—228no—
621C2×D4—228no—
622C2×D4—228no—
623C2×D4—228no—
624C2×D4—228no—
625C2×D4—228no—
626C2×D4—444no—
627C2×D4—4416no—
628C2×D4—444no—
629C2×D4—444no—
630C2×D4—4416no—
631C2×D4—4416no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
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—28no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—416no—
650C22×C4—114no—
651C22×C4—112no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—228no—
658C22×C4—222no—
659C22×C4—222no—
660C22×C4—222no—
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—228no—
676C22×C4—444no—
677C22×C4—4416no—
678C22×C4C2×D4414yes—
679C22×C4C2×D4414yes—
680C22×C4#433914yes—
681C22×C4#433914yes—
682C22×C4C23×D1112yes—
683C22×C4C23×D1112yes—
684C22×C4C23×D1112yes—
685C22×C4C23×D1112yes—
686C22×C4C23×D1112yes—
687C22×C4C23×D1112yes—
688C4⋊C4—228no—
689C4⋊C4—228no—
690C4⋊C4—228no—
691C4⋊C4—228no—
692C4⋊C4—228no—
693C4⋊C4—444no—
694C22⋊C4—28no—
695C22⋊C4—228no—
696C22⋊C4—228no—
697C22⋊C4—228no—
698C22⋊C4—228no—
699C22⋊C4—228no—
700C22⋊C4—228no—
701C22⋊C4—228no—
702C22⋊C4—228no—
703C22⋊C4—444no—
704C22⋊C4—444no—
705C22⋊C4—444no—
706C22⋊C4C2×D44116yes—
707C42—44no—
708C42—44no—
709C42—228no—
710C11C2×#255911yescharacteristic, complemented, Sylow
711C23—28no—
712C23—28no—
713C23—28no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—114no—
725C23—228no—
726C23—228no—
727C23—228no—
728C23—222no—
729C23—222no—
730C23—222no—
731C23—222no—
732C23—222no—
733C23—222no—
734C23—222no—
735C23—222no—
736C23—222no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—222no—
741C23—444no—
742C23—444no—
743C23—444no—
744C23—444no—
745C23—444no—
746C23—444no—
747C23—444no—
748C23—444no—
749C23—444no—
750C23—444no—
751C23—444no—
752C23C22×D4414yes—
753C23C22×D4412yes—
754C23C2×#433912yes—
755C23C2×#433912yes—
756C23#6703712yes—
757C23#6703712yes—
758C23#41×D1112yes—
759C23#41×D1112yes—
760C23C24×D1111yescharacteristic
761D4—4416no—
762D4—4416no—
763D4—4416no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
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—416no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—114no—
786C2×C4—228no—
787C2×C4—222no—
788C2×C4—222no—
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—4416no—
805C2×C4—444no—
806C2×C4—444no—
807C2×C4—444no—
808C2×C4—444no—
809C2×C4—444no—
810C2×C4C22×D4414yes—
811C2×C4C22×D4414yes—
812C2×C4C2×#433914yes—
813C2×C4C2×#433914yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—416no—
821C22—42no—
822C22—224no—
823C22—224no—
824C22—224no—
825C22—442no—
826C22—442no—
827C22—4416no—
828C22—442no—
829C22—442no—
830C22—442no—
831C22—442no—
832C22—442no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—888no—
838C22#1062300814yes—
839C22#1062302514yes—
840C22#1062305914yes—
841C22#1062307114yes—
842C22#1062308514yes—
843C22#1062308514yes—
844C22#1062308914yes—
845C22C23×D4411yescharacteristic
846C22C22×#433911yescharacteristic
847C22C22×#433911yescharacteristic
848C22C2×#6703711yescharacteristic
849C22C2×#6703711yescharacteristic
850C22C2×#41×D1111yescharacteristic
851C22C2×#41×D1111yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—24no—
856C4—42no—
857C4—42no—
858C4—224no—
859C4—442no—
860C4—442no—
861C4—442no—
862C4—442no—
863C4—442no—
864C2—44no—
865C2—444no—
866C2—882no—
867C2#1307373918yesdirect product factor
868C2C2×#1062305911yescharacteristic
869C2C2×#1062300811yescharacteristic
870C2C2×#1062302511yescharacteristic
871C2C2×#1062308511yescharacteristic
872C2C2×#1062308511yescharacteristic
873C2C2×#1062307111yescharacteristic
874C2C2×#1062308911yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC22×#66937C2
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#2559
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#66932C2semidirect
3. #13073739C2direct (N × H)
4. C2×#10622272C2semidirect
5. C2×#10622285C2semidirect
6. C2×#10622574C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622552C2semidirect
9. C2×#10622541C2semidirect
10. C2×#10622283C2semidirect
11. C2×#10622553C2semidirect
12. C2×#10622826C2semidirect
13. C2×#10622826C2semidirect
14. C2×#10622281C2semidirect
15. C2×C4×(C2×D11)⋊C4C2semidirect
16. C2×C4×C11×C22⋊C4C2semidirect
47. C2×#66932C22semidirect
48. C4×C11×C22⋊C4C22semidirect
51. #10622826C22semidirect
52. #10622826C22semidirect
59. #10622574C22semidirect
60. #10622574C22semidirect
61. #10622553C22semidirect
62. #10622552C22semidirect
63. C4×(C2×D11)⋊C4C22semidirect
64. #10622541C22semidirect
65. #10622285C22semidirect
66. #10622283C22semidirect
67. #10622281C22semidirect
68. #10622272C22semidirect
289. C2×C4×C22⋊C4D11semidirect
436. C4×C22⋊C4C2×D11semidirect
585. C2×C11#2559semidirect
710. C11C2×#2559semidirect
867. C2#13073739direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669322
C22×#669372
#130737392
C2×#106222722
C2×#106222852
C2×#106225742
C2×#106225522
C2×#106225412
C2×#106222832
C2×#106225532
C2×#106228262
C2×#106222812
C2×C4×(C2×D11)⋊C42
C2×C4×C11×C22⋊C42
C2×#255911