Finite Group Databasebeta

← C2×#13073745 #14923898

Subgroups — C2×#13073745 #14923898

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×#66929C211yesmaximal, characteristic, complemented
2C22×#66983C211yesmaximal, characteristic
3#13073745C2116yesmaximal, direct product factor
4C2×#10622273C211yesmaximal, characteristic, complemented
5C2×#10622285C211yesmaximal, characteristic, complemented
6C2×#10622572C211yesmaximal, characteristic, complemented
7C2×#10622572C211yesmaximal, characteristic, complemented
8C2×#10622570C211yesmaximal, characteristic, complemented
9C2×#10622260C211yesmaximal, characteristic, complemented
10C2×#10622553C211yesmaximal, characteristic, complemented
11C2×#10622553C211yesmaximal, characteristic, complemented
12C2×#10622278C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622823C211yesmaximal, 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
28C2×#66983—28no—
29C2×#66983C2218yes—
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×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C2×#66929—28no—
47C2×#66929C2218yescomplemented
48C4×C11×C22⋊C4C2218yescomplemented
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51#10622823C2218yescomplemented
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58#10622572C2218yescomplemented
59#10622572C2218yescomplemented
60#10622570C2218yescomplemented
61#10622569C2218yescomplemented
62#10622553C2218yescomplemented
63#10622553C2218yescomplemented
64C4×(C2×D11)⋊C4C2218yescomplemented
65#10622285C2218yescomplemented
66#10622278C2218yescomplemented
67#10622273C2218yescomplemented
68#10622260C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C23×C4×C11—24no—
73C23×C4×C11—24no—
74C23×C4×C11—42no—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2314yes—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
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—42no—
102C22×C4×D11—42no—
103C22×C4×D11C2314yes—
104C2×C11×C22⋊C4—24no—
105C2×C11×C22⋊C4—24no—
106C2×C11×C22⋊C4C2314yes—
107C2×C11×C22⋊C4C2314yes—
108C2×C42×C11—24no—
109C2×C42×C11—42no—
110C2×C42×C11C2314yes—
111C2×C42×C11C2314yes—
112C2×C22⋊Dic11—24no—
113C2×C22⋊Dic11—42no—
114C2×C22⋊Dic11C2314yes—
115C2×C22⋊Dic11C2314yes—
116#66983—232no—
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—24no—
123C2×(C2×D11)⋊C4—42no—
124C2×(C2×D11)⋊C4—42no—
125C2×(C2×D11)⋊C4D418yes—
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×(C2×D11)⋊C4C2314yes—
135C2×C4⋊Dic11—24no—
136C2×C4⋊Dic11C2314yes—
137C2×Dic11⋊C4—24no—
138C2×Dic11⋊C4—24no—
139C2×Dic11⋊C4—24no—
140C2×Dic11⋊C4—24no—
141C2×Dic11⋊C4—42no—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×Dic11⋊C4C2314yes—
147C2×C4×Dic11—42no—
148C2×C4×Dic11C2314yes—
149#66929—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×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—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—28no—
200C22×C4×C11—28no—
201C22×C4×C11—44no—
202C22×C4×C11—416no—
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×Dic11C2×D414yes—
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—44no—
250C2×C4×D11—44no—
251C2×C4×D11—416no—
252C11×C22⋊C4—28no—
253C11×C22⋊C4—28no—
254C42×C11—28no—
255C42×C11—44no—
256C22⋊Dic11—28no—
257C22⋊Dic11—44no—
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)⋊C4C2×D4116yes—
267C4⋊Dic11—28no—
268Dic11⋊C4—28no—
269Dic11⋊C4—28no—
270Dic11⋊C4—28no—
271Dic11⋊C4—28no—
272Dic11⋊C4—44no—
273C4×Dic11—44no—
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×D412yes—
304C23×C11C2×#4114yes—
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×D11C22×D414yes—
340C2×C4×C11—28no—
341C2×C4×C11—28no—
342C2×C4×C11—28no—
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—22no—
357C2×C4×C11—22no—
358C2×C4×C11—416no—
359C2×C4×C11—44no—
360C2×C4×C11—44no—
361C2×C4×C11—44no—
362C2×C4×C11C22×D414yes—
363C2×C4×C11C2×#4114yes—
364C2×C4×C11C2×#4114yes—
365C22⋊D11—416no—
366C22⋊D11—416no—
367C2×Dic11—28no—
368C2×Dic11—28no—
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×Dic11C22×D414yes—
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—42no—
487C4×C11—42no—
488C4×C11—42no—
489Dic11—24no—
490Dic11—24no—
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—24no—
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—442no—
522C23×C4—442no—
523C23×C4C22×D1111yescharacteristic
524C23×C4C22×D1111yescharacteristic
525C23×C4C22×D1111yescharacteristic
526C23×C4C22×D1114yes—
527C23×C4C22×D1111yescharacteristic
528C23×C4C22×D1111yescharacteristic
529C23×C4C22×D1111yescharacteristic
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—24no—
546C2×C22⋊C4—118no—
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—114no—
557C2×C22⋊C4—114no—
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—224no—
565C2×C22⋊C4—442no—
566C2×C22⋊C4—442no—
567C2×C22⋊C4—442no—
568C2×C22⋊C4C22×D1114yes—
569C2×C22⋊C4C22×D1114yes—
570C2×C42—24no—
571C2×C42—42no—
572C2×C42—114no—
573C2×C42—442no—
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—
617C24#433914yes—
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—22no—
647C22×C4—28no—
648C22×C4—28no—
649C22×C4—44no—
650C22×C4—416no—
651C22×C4—114no—
652C22×C4—114no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—112no—
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—444no—
678C22×C4—4416no—
679C22×C4#433914yes—
680C22×C4#433914yes—
681C22×C4D4×D1114yes—
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—28no—
696C22⋊C4—1116no—
697C22⋊C4—228no—
698C22⋊C4—228no—
699C22⋊C4—228no—
700C22⋊C4—228no—
701C22⋊C4—228no—
702C22⋊C4—228no—
703C22⋊C4—228no—
704C22⋊C4—444no—
705C22⋊C4—444no—
706C22⋊C4—444no—
707C42—28no—
708C42—44no—
709C42—444no—
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—
752C23C2×#433914yes—
753C23C2×#433912yes—
754C23C2×#433912yes—
755C23C2×#433912yes—
756C23C2×D4×D1112yes—
757C23#6703712yes—
758C23#41×D1112yes—
759C23#6704212yes—
760C23C24×D1111yescharacteristic
761D4—4416no—
762D4—4416no—
763D4—4416no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
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—22no—
781C2×C4—22no—
782C2×C4—416no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—114no—
787C2×C4—114no—
788C2×C4—228no—
789C2×C4—228no—
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—4416no—
807C2×C4—444no—
808C2×C4—444no—
809C2×C4—444no—
810C2×C4—444no—
811C2×C4C2×#433914yes—
812C2×C4C2×#433914yes—
813C2×C4C2×D4×D1114yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—42no—
819C22—416no—
820C22—42no—
821C22—42no—
822C22—224no—
823C22—224no—
824C22—224no—
825C22—442no—
826C22—442no—
827C22—442no—
828C22—4416no—
829C22—442no—
830C22—442no—
831C22—442no—
832C22—442no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—888no—
838C22#1062301014yes—
839C22#1062302114yes—
840C22#1062306114yes—
841C22#1062307114yes—
842C22#1062307914yes—
843C22#1062308114yes—
844C22#1062309114yes—
845C22C22×#433911yescharacteristic
846C22C22×#433911yescharacteristic
847C22C22×#433911yescharacteristic
848C22C22×D4×D1111yescharacteristic
849C22C2×#6703711yescharacteristic
850C22C2×#41×D1111yescharacteristic
851C22C2×#6704211yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—224no—
859C4—224no—
860C4—442no—
861C4—442no—
862C4—442no—
863C4—442no—
864C2—44no—
865C2—444no—
866C2—882no—
867C2#1307374518yesdirect product factor
868C2C2×#1062301011yescharacteristic
869C2C2×#1062307911yescharacteristic
870C2C2×#1062309111yescharacteristic
871C2C2×#1062302111yescharacteristic
872C2C2×#1062308111yescharacteristic
873C2C2×#1062306111yescharacteristic
874C2C2×#1062307111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC22×#66983C2
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×#66929C2semidirect
3. #13073745C2direct (N × H)
4. C2×#10622273C2semidirect
5. C2×#10622285C2semidirect
6. C2×#10622572C2semidirect
7. C2×#10622572C2semidirect
8. C2×#10622570C2semidirect
9. C2×#10622260C2semidirect
10. C2×#10622553C2semidirect
11. C2×#10622553C2semidirect
12. C2×#10622278C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622823C2semidirect
15. C2×C4×(C2×D11)⋊C4C2semidirect
16. C2×C4×C11×C22⋊C4C2semidirect
47. C2×#66929C22semidirect
48. C4×C11×C22⋊C4C22semidirect
51. #10622823C22semidirect
58. #10622572C22semidirect
59. #10622572C22semidirect
60. #10622570C22semidirect
61. #10622569C22semidirect
62. #10622553C22semidirect
63. #10622553C22semidirect
64. C4×(C2×D11)⋊C4C22semidirect
65. #10622285C22semidirect
66. #10622278C22semidirect
67. #10622273C22semidirect
68. #10622260C22semidirect
289. C2×C4×C22⋊C4D11semidirect
436. C4×C22⋊C4C2×D11semidirect
585. C2×C11#2559semidirect
710. C11C2×#2559semidirect
867. C2#13073745direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669292
C22×#669832
#130737452
C2×#106222732
C2×#106222852
C2×#106225722
C2×#106225702
C2×#106222602
C2×#106225532
C2×#106222782
C2×#106225692
C2×#106228232
C2×C4×(C2×D11)⋊C42
C2×C4×C11×C22⋊C42
C2×#255911