Finite Group Databasebeta

← C2×#13071320 #14912552

Subgroups — C2×#13071320 #14912552

Order 2816.

4150 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C211yesmaximal, characteristic
2C22×C4×D44C211yesmaximal, characteristic, complemented
3C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
4#13071320C2116yesmaximal, direct product factor
5C2×#10622603C211yesmaximal, characteristic, complemented
6C2×#10622268C211yesmaximal, characteristic, complemented
7C2×#10622546C211yesmaximal, characteristic, complemented
8C2×#10622278C211yesmaximal, characteristic, complemented
9C2×#10622571C211yesmaximal, characteristic, complemented
10C2×#10622569C211yesmaximal, characteristic, complemented
11C2×#10622569C211yesmaximal, characteristic, complemented
12C2×#10622563C211yesmaximal, characteristic, complemented
13C2×#10622281C211yesmaximal, characteristic, complemented
14C2×#10622600C211yesmaximal, characteristic, complemented
15C2×D11×#95C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C42×C11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C2×#66937C4116yescomplemented
43C2×#66937C2218yes—
44C2×(C22⋊D11)⋊C4—28no—
45C2×(C22⋊D11)⋊C4C2218yescomplemented
46C2×C4×D44—28no—
47C2×C4×D44C2218yescomplemented
48C11×#388C2218yescomplemented
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59#10622603C2218yescomplemented
60#10622600C2218yescomplemented
61#10622571C2218yescomplemented
62#10622569C2218yescomplemented
63#10622569C2218yescomplemented
64#10622563C2218yescomplemented
65#10622546C2218yescomplemented
66#10622281C2218yescomplemented
67#10622278C2218yescomplemented
68D11×#95C2218yescomplemented
69#10622268C2218yescomplemented
70C25×C11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C22×C22⋊D11—24no—
80C22×C22⋊D11—24no—
81C22×C22⋊D11—42no—
82C22×C22⋊D11—42no—
83C22×C22⋊D11C2×C418yescomplemented
84C22×C22⋊D11C2×C418yescomplemented
85C22×C22⋊D11C2314yes—
86C22×C22⋊D11C2314yes—
87C23×Dic11—24no—
88C23×Dic11—42no—
89C23×Dic11—42no—
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2314yes—
97C22×D44—24no—
98C22×D44—24no—
99C22×D44C2×C418yescomplemented
100C22×D44C2314yes—
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×D11—42no—
109C22×C4×D11—42no—
110C22×C4×D11—42no—
111C22×C4×D11C2×C418yescomplemented
112C22×C4×D11D418yescomplemented
113C22×C4×D11C2314yes—
114C22×C4×D11C2314yes—
115C22×C4×D11C2314yes—
116C22×C4×D11C2314yes—
117C2×C11×C4⋊C4—42no—
118C2×C11×C4⋊C4C2314yes—
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4—42no—
121C2×C11×C22⋊C4C2×C418yescomplemented
122C2×C11×C22⋊C4C2314yes—
123C2×C11×C22⋊C4C2314yes—
124C2×C11×C22⋊C4C2314yes—
125C2×C42×C11—24no—
126C2×C42×C11C2314yes—
127C2×C22⋊Dic11—42no—
128C2×C22⋊Dic11C2314yes—
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4—24no—
132C2×(C2×D11)⋊C4—42no—
133C2×(C2×D11)⋊C4—42no—
134C2×(C2×D11)⋊C4C2×C418yescomplemented
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×C4⋊Dic11—24no—
142C2×C4⋊Dic11—42no—
143C2×C4⋊Dic11C2314yes—
144C2×C4⋊Dic11C2314yes—
145C2×Dic11⋊C4—24no—
146C2×Dic11⋊C4C2×C418yescomplemented
147C2×Dic11⋊C4C2314yes—
148C2×Dic11⋊C4C2314yes—
149C2×C4×Dic11—24no—
150C2×C4×Dic11C2314yes—
151#66937C2×C4164yescomplemented
152(C22⋊D11)⋊C4—232no—
153C4×D44—232no—
154C11×#95C2314yes—
155C11×#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C2×#2325—111nomaximal, Sylow
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11C22×C414yes—
172C24×C11C2412yes—
173C24×C11C2411yescharacteristic
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11—22no—
181C23×D11—22no—
182C23×D11—22no—
183C23×D11—22no—
184C23×D11C22×C414yes—
185C23×D11C22×C414yes—
186C23×D11C2×D414yes—
187C23×D11#4114yes—
188C23×D11C2412yes—
189C23×D11C2412yes—
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×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11C22×C414yes—
206C22×C4×C11C22×C414yes—
207C22×C4×C11C2×D414yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C2×C22⋊D11—232no—
215C2×C22⋊D11—28no—
216C2×C22⋊D11—28no—
217C2×C22⋊D11—416no—
218C2×C22⋊D11—44no—
219C2×C22⋊D11—44no—
220C2×C22⋊D11C22×C4116yescomplemented
221C2×C22⋊D11C22×C4116yescomplemented
222C22×Dic11—28no—
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—22no—
238C22×Dic11—44no—
239C22×Dic11—44no—
240C22×Dic11—416no—
241C22×Dic11C22×C414yes—
242C22×Dic11C22×C414yes—
243C22×Dic11C2×D414yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C22×Dic11C2412yes—
249C22×Dic11C2412yes—
250C2×D44—232no—
251C2×D44—28no—
252C2×D44—28no—
253C2×D44C22×C4116yescomplemented
254C2×C4×D11—28no—
255C2×C4×D11—28no—
256C2×C4×D11—416no—
257C2×C4×D11—416no—
258C2×C4×D11—44no—
259C2×C4×D11—44no—
260C2×C4×D11—44no—
261C2×C4×D11—44no—
262C2×C4×D11—44no—
263C2×C4×D11—44no—
264C2×C4×D11—44no—
265C2×C4×D11—44no—
266C2×C4×D11—416no—
267C2×C4×D11—416no—
268C2×C4×D11C22×C4116yescomplemented
269C2×C4×D11C2×D4116yescomplemented
270C11×C4⋊C4—44no—
271C11×C22⋊C4—28no—
272C11×C22⋊C4—44no—
273C11×C22⋊C4C22×C4116yescomplemented
274C42×C11—28no—
275C22⋊Dic11—44no—
276(C2×D11)⋊C4—28no—
277(C2×D11)⋊C4—28no—
278(C2×D11)⋊C4—28no—
279(C2×D11)⋊C4—44no—
280(C2×D11)⋊C4—44no—
281(C2×D11)⋊C4C22×C4116yescomplemented
282C4⋊Dic11—28no—
283C4⋊Dic11—44no—
284Dic11⋊C4—28no—
285Dic11⋊C4C22×C4116yescomplemented
286C4×Dic11—28no—
287C22×#121—111no—
288C22×C4×D4—111no—
289C22×C4×D4—111no—
290#2325—1116no—
291C2×#388—111no—
292C2×#388D1111yescharacteristic, complemented
293C2×#387—111no—
294C2×#387—111no—
295C2×#386—111no—
296C2×#386—111no—
297C2×#386—111no—
298C2×#386—111no—
299C2×#385—111no—
300C2×#385—111no—
301C2×#380—111no—
302C22×#95—111no—
303C23×C11—28no—
304C23×C11—28no—
305C23×C11—28no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—44no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11—44no—
316C23×C11C23×C414yes—
317C23×C11C23×C412yes—
318C23×C11C22×D412yes—
319C23×C11C2×#4112yes—
320C23×C11H(5,𝔽2)12yes—
321C23×C11H(5,𝔽2)12yes—
322C23×C11H(5,𝔽2)12yes—
323C23×C112−1+412yes—
324C23×C11C2511yescharacteristic
325C22×D11—28no—
326C22×D11—28no—
327C22×D11—28no—
328C22×D11—28no—
329C22×D11—28no—
330C22×D11—28no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—28no—
336C22×D11—28no—
337C22×D11—28no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—44no—
345C22×D11—44no—
346C22×D11—44no—
347C22×D11—44no—
348C22×D11C4×D4116yes—
349C22×D11C23×C414yes—
350C22×D11C23×C414yes—
351C22×D11C22×D414yes—
352C22×D11C2×#4114yes—
353C2×C4×C11—28no—
354C2×C4×C11—28no—
355C2×C4×C11—28no—
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—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—44no—
372C2×C4×C11—44no—
373C2×C4×C11—44no—
374C2×C4×C11C23×C414yes—
375C2×C4×C11C23×C414yes—
376C2×C4×C11C22×D414yes—
377C22⋊D11—232no—
378C22⋊D11—416no—
379C2×Dic11—28no—
380C2×Dic11—28no—
381C2×Dic11—28no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—416no—
398C2×Dic11—44no—
399C2×Dic11—44no—
400C2×Dic11—44no—
401C2×Dic11C23×C414yes—
402C2×Dic11C23×C414yes—
403C2×Dic11C22×D414yes—
404D44—232no—
405C4×D11—416no—
406C4×D11—416no—
407C4×D11—416no—
408C4×D11—416no—
409C23×D4—111no—
410C23×D4—111no—
411C23×D4—111no—
412C24×C4—111no—
413C24×C4—111no—
414C24×C4—111no—
415C24×C4—111no—
416C24×C4—111no—
417C2×#121—118no—
418C2×#121—1116no—
419C2×C4×D4—118no—
420C2×C4×D4—118no—
421C2×C4×D4—228no—
422C2×C4×D4—228no—
423C22×C4⋊C4—111no—
424C22×C4⋊C4—111no—
425C22×C4⋊C4—111no—
426C22×C4⋊C4—111no—
427C22×C4⋊C4C2×D1111yescharacteristic
428C22×C22⋊C4—111no—
429C22×C22⋊C4—111no—
430C22×C22⋊C4—111no—
431C22×C22⋊C4—111no—
432C22×C22⋊C4—111no—
433C22×C22⋊C4—111no—
434C22×C22⋊C4—111no—
435C22×C22⋊C4C2×D1111yescharacteristic
436C22×C22⋊C4C2×D1111yescharacteristic
437C22×C22⋊C4C2×D1111yescharacteristic
438C22×C42—111no—
439C22×C42C2×D1111yescharacteristic
440#388—118no—
441#388C2×D1118yescomplemented
442#387—118no—
443#387—118no—
444#386—118no—
445#386—118no—
446#386—118no—
447#386—118no—
448#385—118no—
449#385—118no—
450#380—118no—
451C2×#95—111no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95—111no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—118no—
460C2×#95C2×D1111yescharacteristic
461C2×#95C2×D1111yescharacteristic
462C22×C11—24no—
463C22×C11—24no—
464C22×C11—24no—
465C22×C11—416no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11C2×C4×D414yes—
471C22×C11#51814yes—
472C22×C11#52014yes—
473C22×C11#53414yes—
474C22×C11#53714yes—
475C22×C11#53814yes—
476C22×C11#53914yes—
477C22×C11C24×C411yescharacteristic
478C22×C11C23×D411yescharacteristic
479C22×C11C22×#4111yescharacteristic
480C22×C11C2×H(5,𝔽2)11yescharacteristic
481C22×C11C2×H(5,𝔽2)11yescharacteristic
482C22×C11C2×H(5,𝔽2)11yescharacteristic
483C22×C11C2×2−1+411yescharacteristic
484C2×D11—232no—
485C2×D11—24no—
486C2×D11—24no—
487C2×D11—24no—
488C2×D11—24no—
489C2×D11—24no—
490C2×D11—24no—
491C2×D11—24no—
492C2×D11—24no—
493C2×D11—24no—
494C2×D11—416no—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11C2×C4×D418yes—
500C4×C11—24no—
501C4×C11—24no—
502C4×C11—24no—
503C4×C11—42no—
504C4×C11—42no—
505C4×C11—42no—
506Dic11—24no—
507Dic11—24no—
508Dic11—24no—
509Dic11—42no—
510Dic11—42no—
511Dic11—42no—
512C25—111no—
513C25—111no—
514C25C22×D1111yescharacteristic
515C22×D4—118no—
516C22×D4—114no—
517C22×D4—118no—
518C22×D4—114no—
519C22×D4—118no—
520C22×D4—114no—
521C22×D4—224no—
522C22×D4—224no—
523C22×D4—224no—
524C22×D4—224no—
525C22×D4—442no—
526C22×D4—442no—
527C23×C4—111no—
528C23×C4—111no—
529C23×C4—111no—
530C23×C4—118no—
531C23×C4—118no—
532C23×C4—114no—
533C23×C4—114no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—114no—
538C23×C4—114no—
539C23×C4—114no—
540C23×C4—224no—
541C23×C4—224no—
542C23×C4—224no—
543C23×C4—442no—
544C23×C4—442no—
545C23×C4—442no—
546C23×C4—442no—
547C23×C4—442no—
548C23×C4—442no—
549C23×C4—442no—
550C23×C4—442no—
551C23×C4—442no—
552C23×C4—442no—
553C23×C4C22×D1111yescharacteristic
554C23×C4C22×D1111yescharacteristic
555C23×C4C22×D1111yescharacteristic
556C23×C4C22×D1111yescharacteristic
557C23×C4C22×D1111yescharacteristic
558C23×C4C22×D1111yescharacteristic
559#121—1164no—
560C4×D4—2232no—
561C4×D4—2232no—
562C2×C4⋊C4—42no—
563C2×C4⋊C4—118no—
564C2×C4⋊C4—114no—
565C2×C4⋊C4—114no—
566C2×C4⋊C4—114no—
567C2×C4⋊C4—114no—
568C2×C4⋊C4—224no—
569C2×C4⋊C4—224no—
570C2×C4⋊C4—442no—
571C2×C4⋊C4C22×D1114yes—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—118no—
575C2×C22⋊C4—114no—
576C2×C22⋊C4—114no—
577C2×C22⋊C4—114no—
578C2×C22⋊C4—114no—
579C2×C22⋊C4—114no—
580C2×C22⋊C4—114no—
581C2×C22⋊C4—114no—
582C2×C22⋊C4—224no—
583C2×C22⋊C4—224no—
584C2×C22⋊C4—224no—
585C2×C22⋊C4—442no—
586C2×C22⋊C4—442no—
587C2×C22⋊C4—442no—
588C2×C22⋊C4C4×D1118yescomplemented
589C2×C22⋊C4C22×D1114yes—
590C2×C22⋊C4C22×D1114yes—
591C2×C22⋊C4C22×D1114yes—
592C2×C42—24no—
593C2×C42—114no—
594C2×C42—224no—
595C2×C42C22×D1114yes—
596#95—114no—
597#95—114no—
598#95—114no—
599#95—114no—
600#95—114no—
601#95—114no—
602#95—114no—
603#95—114no—
604#95C22×D1114yes—
605#95C22×D1114yes—
606C2×C11—44no—
607C2×C11#232518yescomplemented
608C2×C11C22×C4×D411yescharacteristic
609C2×C11C2×#51811yescharacteristic
610C2×C11C2×#52011yescharacteristic
611C2×C11C2×#53411yescharacteristic
612C2×C11C2×#53711yescharacteristic
613C2×C11C2×#53811yescharacteristic
614C2×C11C2×#53911yescharacteristic
615D11—28no—
616D11—44no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—114no—
624C24—114no—
625C24—114no—
626C24—112no—
627C24—114no—
628C24—112no—
629C24—222no—
630C24—222no—
631C24—222no—
632C24—222no—
633C24—222no—
634C24—222no—
635C24—222no—
636C24—222no—
637C24—222no—
638C24—222no—
639C24C2×C4×D1114yes—
640C24C23×D1112yes—
641C24C23×D1111yescharacteristic
642C2×D4—1116no—
643C2×D4—1116no—
644C2×D4—1116no—
645C2×D4—228no—
646C2×D4—2232no—
647C2×D4—228no—
648C2×D4—228no—
649C2×D4—2232no—
650C2×D4—228no—
651C2×D4—4416no—
652C2×D4—444no—
653C2×D4—444no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—114no—
670C22×C4—114no—
671C22×C4—114no—
672C22×C4—112no—
673C22×C4—112no—
674C22×C4—112no—
675C22×C4—1116no—
676C22×C4—1116no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—228no—
681C22×C4—228no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—222no—
685C22×C4—222no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—222no—
691C22×C4—222no—
692C22×C4—222no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—222no—
696C22×C4—222no—
697C22×C4—228no—
698C22×C4—4416no—
699C22×C4—4416no—
700C22×C4—444no—
701C22×C4—444no—
702C22×C4—444no—
703C22×C4—444no—
704C22×C4—444no—
705C22×C4—444no—
706C22×C4—444no—
707C22×C4—444no—
708C22×C4—4416no—
709C22×C4—4416no—
710C22×C4—444no—
711C22×C4—444no—
712C22×C4—4416no—
713C22×C4C2×C4×D1114yes—
714C22×C4C2×C4×D1114yes—
715C22×C4D4×D1114yes—
716C22×C4C23×D1112yes—
717C22×C4C23×D1112yes—
718C22×C4C23×D1112yes—
719C22×C4C23×D1112yes—
720C22×C4C23×D1112yes—
721C22×C4C23×D1112yes—
722C4⋊C4—44no—
723C4⋊C4—1116no—
724C4⋊C4—228no—
725C4⋊C4—228no—
726C4⋊C4—444no—
727C22⋊C4—28no—
728C22⋊C4—44no—
729C22⋊C4—1116no—
730C22⋊C4—228no—
731C22⋊C4—228no—
732C22⋊C4—228no—
733C22⋊C4—444no—
734C22⋊C4—444no—
735C22⋊C4—444no—
736C22⋊C4C2×C4×D11116yescomplemented
737C42—28no—
738C42—228no—
739C11C2×#232511yescharacteristic, complemented, Sylow
740C23—28no—
741C23—28no—
742C23—28no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—1116no—
754C23—114no—
755C23—114no—
756C23—114no—
757C23—114no—
758C23—228no—
759C23—228no—
760C23—228no—
761C23—228no—
762C23—228no—
763C23—222no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23—228no—
768C23—228no—
769C23—228no—
770C23—228no—
771C23—222no—
772C23—222no—
773C23—222no—
774C23—222no—
775C23—222no—
776C23—222no—
777C23—444no—
778C23—444no—
779C23—444no—
780C23—444no—
781C23C22×C4×D1114yes—
782C23C22×C4×D1112yes—
783C23C2×D4×D1112yes—
784C23#6703712yes—
785C23#41×D1112yes—
786C23#6704212yes—
787C23#6704212yes—
788C23#6704312yes—
789C23C24×D1111yescharacteristic
790D4—2232no—
791D4—2232no—
792D4—4416no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—114no—
815C2×C4—114no—
816C2×C4—114no—
817C2×C4—228no—
818C2×C4—228no—
819C2×C4—228no—
820C2×C4—222no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—222no—
835C2×C4—4416no—
836C2×C4—4416no—
837C2×C4—4416no—
838C2×C4—4416no—
839C2×C4—4416no—
840C2×C4—444no—
841C2×C4—444no—
842C2×C4—444no—
843C2×C4C22×C4×D1114yes—
844C2×C4C22×C4×D1114yes—
845C2×C4C2×D4×D1114yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—416no—
854C22—118no—
855C22—224no—
856C22—224no—
857C22—224no—
858C22—224no—
859C22—224no—
860C22—224no—
861C22—2232no—
862C22—224no—
863C22—224no—
864C22—224no—
865C22—442no—
866C22—442no—
867C22—442no—
868C22—442no—
869C22—4416no—
870C22#1062305414yes—
871C22C4×D4×D1114yes—
872C22#1062307614yes—
873C22#1062313914yes—
874C22#1062318414yes—
875C22#1062320914yes—
876C22#1062323814yes—
877C22C23×C4×D1111yescharacteristic
878C22C22×D4×D1111yescharacteristic
879C22C2×#6703711yescharacteristic
880C22C2×#41×D1111yescharacteristic
881C22C2×#6704211yescharacteristic
882C22C2×#6704211yescharacteristic
883C22C2×#6704311yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—224no—
891C4—224no—
892C4—224no—
893C4—442no—
894C4—442no—
895C4—442no—
896C2—44no—
897C2—228no—
898C2—444no—
899C2#1307132018yesdirect product factor
900C2C2×C4×D4×D1111yescharacteristic
901C2C2×#1062307611yescharacteristic
902C2C2×#1062305411yescharacteristic
903C2C2×#1062318411yescharacteristic
904C2C2×#1062313911yescharacteristic
905C2C2×#1062320911yescharacteristic
906C2C2×#1062323811yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC22×#66937C2
cosocleC23×C11C25
hypercenterC2×#388D11
hypocenterC11C2×#2325
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×D44C2semidirect
3. C22×(C22⋊D11)⋊C4C2semidirect
4. #13071320C2direct (N × H)
5. C2×#10622603C2semidirect
6. C2×#10622268C2semidirect
7. C2×#10622546C2semidirect
8. C2×#10622278C2semidirect
9. C2×#10622571C2semidirect
10. C2×#10622569C2semidirect
11. C2×#10622569C2semidirect
12. C2×#10622563C2semidirect
13. C2×#10622281C2semidirect
14. C2×#10622600C2semidirect
15. C2×D11×#95C2semidirect
16. C2×C11×#388C2semidirect
42. C2×#66937C4semidirect
45. C2×(C22⋊D11)⋊C4C22semidirect
47. C2×C4×D44C22semidirect
48. C11×#388C22semidirect
59. #10622603C22semidirect
60. #10622600C22semidirect
61. #10622571C22semidirect
62. #10622569C22semidirect
63. #10622569C22semidirect
64. #10622563C22semidirect
65. #10622546C22semidirect
66. #10622281C22semidirect
67. #10622278C22semidirect
68. D11×#95C22semidirect
69. #10622268C22semidirect
83. C22×C22⋊D11C2×C4semidirect
84. C22×C22⋊D11C2×C4semidirect
99. C22×D44C2×C4semidirect
111. C22×C4×D11C2×C4semidirect
112. C22×C4×D11D4semidirect
121. C2×C11×C22⋊C4C2×C4semidirect
134. C2×(C2×D11)⋊C4C2×C4semidirect
146. C2×Dic11⋊C4C2×C4semidirect
151. #66937C2×C4semidirect
220. C2×C22⋊D11C22×C4semidirect
221. C2×C22⋊D11C22×C4semidirect
253. C2×D44C22×C4semidirect
268. C2×C4×D11C22×C4semidirect
269. C2×C4×D11C2×D4semidirect
273. C11×C22⋊C4C22×C4semidirect
281. (C2×D11)⋊C4C22×C4semidirect
285. Dic11⋊C4C22×C4semidirect
292. C2×#388D11semidirect
441. #388C2×D11semidirect
588. C2×C22⋊C4C4×D11semidirect
607. C2×C11#2325semidirect
736. C22⋊C4C2×C4×D11semidirect
739. C11C2×#2325semidirect
899. C2#13071320direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669372
C22×C4×D442
C22×(C22⋊D11)⋊C42
#130713202
C2×#106226032
C2×#106222682
C2×#106225462
C2×#106222782
C2×#106225712
C2×#106225692
C2×#106225632
C2×#106222812
C2×#106226002
C2×D11×#952
C2×C11×#3882
C2×#232511