Finite Group Databasebeta

← C2×#13071649 #14913321

Subgroups — C2×#13071649 #14913321

Order 2816.

4046 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C211yesmaximal, characteristic
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
3C22×#66925C211yesmaximal, characteristic, complemented
4#13071649C2116yesmaximal, direct product factor
5C2×#10622601C211yesmaximal, characteristic, complemented
6C2×#10622570C211yesmaximal, characteristic, complemented
7C2×#10622570C211yesmaximal, characteristic, complemented
8C2×#10622585C211yesmaximal, characteristic, complemented
9C2×#10622282C211yesmaximal, characteristic, complemented
10C2×#10622278C211yesmaximal, characteristic, complemented
11C2×#10622571C211yesmaximal, characteristic, complemented
12C2×#10622262C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C42×C11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C22×C4×Dic11C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C2×#66937C4116yescomplemented
47C2×#66937C2218yes—
48C2×(C22⋊D11)⋊C4—28no—
49C2×(C22⋊D11)⋊C4C2218yescomplemented
50C2×#66925—28no—
51C2×#66925C2218yescomplemented
52C11×#388C2218yescomplemented
53C2×C11×#95C2211yescharacteristic
54C2×C11×#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59#10622601C2218yescomplemented
60#10622585C2218yescomplemented
61#10622571C2218yescomplemented
62#10622570C2218yescomplemented
63#10622570C2218yescomplemented
64C22⋊C4×Dic11C2218yescomplemented
65C4×(C2×D11)⋊C4C2218yescomplemented
66#10622282C2218yescomplemented
67#10622279C2218yescomplemented
68#10622278C2218yescomplemented
69#10622262C2218yescomplemented
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×C418yes—
84C22×C22⋊D11C2×C418yescomplemented
85C22×C22⋊D11C2314yes—
86C22×C22⋊D11C2314yes—
87C23×Dic11—24no—
88C23×Dic11—24no—
89C23×Dic11—42no—
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2314yes—
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C22×D44—42no—
98C22×D44—42no—
99C22×D44C2×C418yescomplemented
100C22×D44C2314yes—
101C22×C4×D11—24no—
102C22×C4×D11—24no—
103C22×C4×D11—24no—
104C22×C4×D11—24no—
105C22×C4×D11—42no—
106C22×C4×D11C2×C418yescomplemented
107C22×C4×D11C2314yes—
108C22×C4×D11C2314yes—
109C2×C11×C4⋊C4—42no—
110C2×C11×C4⋊C4C2314yes—
111C2×C11×C22⋊C4—24no—
112C2×C11×C22⋊C4—42no—
113C2×C11×C22⋊C4C2×C418yescomplemented
114C2×C11×C22⋊C4C2314yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C42×C11—24no—
118C2×C42×C11C2314yes—
119C2×C22⋊Dic11—24no—
120C2×C22⋊Dic11C2314yes—
121C2×(C2×D11)⋊C4—24no—
122C2×(C2×D11)⋊C4—24no—
123C2×(C2×D11)⋊C4—24no—
124C2×(C2×D11)⋊C4—24no—
125C2×(C2×D11)⋊C4—24no—
126C2×(C2×D11)⋊C4—24no—
127C2×(C2×D11)⋊C4—42no—
128C2×(C2×D11)⋊C4C2×C418yescomplemented
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×(C2×D11)⋊C4C2314yes—
137C2×Dic11⋊C4—24no—
138C2×Dic11⋊C4—42no—
139C2×Dic11⋊C4C2×C418yescomplemented
140C2×Dic11⋊C4D418yescomplemented
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×C4×Dic11—24no—
146C2×C4×Dic11—24no—
147C2×C4×Dic11—24no—
148C2×C4×Dic11—42no—
149C2×C4×Dic11—42no—
150C2×C4×Dic11C2314yes—
151C2×C4×Dic11C2314yes—
152C2×C4×Dic11C2314yes—
153C2×C4×Dic11C2314yes—
154C2×C4×Dic11C2314yes—
155#66937C2×C4164yescomplemented
156(C22⋊D11)⋊C4—232no—
157#66925—232no—
158C11×#95C2314yes—
159C11×#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C2×#2363—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×D11—22no—
185C23×D11—22no—
186C23×D11C22×C414yes—
187C23×D11C22×C414yes—
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×C4116yes—
221C2×C22⋊D11C22×C4116yescomplemented
222C22×Dic11—28no—
223C22×Dic11—28no—
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—44no—
236C22×Dic11—416no—
237C22×Dic11C22×C414yes—
238C22×Dic11C22×C414yes—
239C22×Dic11C2×D414yes—
240C22×Dic11C2×D414yes—
241C22×Dic11#4114yes—
242C22×Dic11#4114yes—
243C22×Dic11#4114yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C22×Dic11C2412yes—
249C22×Dic11C2412yes—
250C2×D44—416no—
251C2×D44—44no—
252C2×D44—44no—
253C2×D44C22×C4116yescomplemented
254C2×C4×D11—232no—
255C2×C4×D11—28no—
256C2×C4×D11—28no—
257C2×C4×D11—28no—
258C2×C4×D11—28no—
259C2×C4×D11—44no—
260C2×C4×D11—416no—
261C2×C4×D11C22×C4116yescomplemented
262C11×C4⋊C4—44no—
263C11×C22⋊C4—28no—
264C11×C22⋊C4—44no—
265C11×C22⋊C4C22×C4116yescomplemented
266C42×C11—28no—
267C22⋊Dic11—28no—
268(C2×D11)⋊C4—28no—
269(C2×D11)⋊C4—28no—
270(C2×D11)⋊C4—28no—
271(C2×D11)⋊C4—28no—
272(C2×D11)⋊C4—28no—
273(C2×D11)⋊C4—28no—
274(C2×D11)⋊C4—44no—
275(C2×D11)⋊C4C22×C4116yescomplemented
276Dic11⋊C4—28no—
277Dic11⋊C4—44no—
278Dic11⋊C4C22×C4116yescomplemented
279Dic11⋊C4C2×D4116yescomplemented
280C4×Dic11—28no—
281C4×Dic11—28no—
282C4×Dic11—28no—
283C4×Dic11—44no—
284C4×Dic11—44no—
285C22×#121—111no—
286C22×C4×D4—111no—
287C22×#117—111no—
288#2363—1116no—
289C2×#390—111no—
290C2×#390—111no—
291C2×#390—111no—
292C2×#389—111no—
293C2×#388—111no—
294C2×#388D1111yescharacteristic, complemented
295C2×#386—111no—
296C2×#386—111no—
297C2×C4×C4⋊C4—111no—
298C2×C4×C22⋊C4—111no—
299C2×C4×C22⋊C4—111no—
300C2×C4×C22⋊C4—111no—
301C23×C11—28no—
302C23×C11—28no—
303C23×C11—28no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—44no—
311C23×C11—44no—
312C23×C11—44no—
313C23×C11—44no—
314C23×C11C23×C414yes—
315C23×C11C23×C412yes—
316C23×C11C22×D412yes—
317C23×C11C2×#4112yes—
318C23×C11C2×#4112yes—
319C23×C11C2×#4112yes—
320C23×C11H(5,𝔽2)12yes—
321C23×C11H(5,𝔽2)12yes—
322C23×C11C2511yescharacteristic
323C22×D11—28no—
324C22×D11—28no—
325C22×D11—28no—
326C22×D11—28no—
327C22×D11—28no—
328C22×D11—28no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—44no—
342C22×D11—44no—
343C22×D11—44no—
344C22×D11—44no—
345C22×D11—44no—
346C22×D11—44no—
347C22×D11—44no—
348C22×D11—44no—
349C22×D11C23×C414yes—
350C22×D11C23×C414yes—
351C2×C4×C11—28no—
352C2×C4×C11—28no—
353C2×C4×C11—28no—
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—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—44no—
370C2×C4×C11—44no—
371C2×C4×C11—44no—
372C2×C4×C11C23×C414yes—
373C2×C4×C11C23×C414yes—
374C2×C4×C11C22×D414yes—
375C22⋊D11—232no—
376C22⋊D11—416no—
377C2×Dic11—28no—
378C2×Dic11—28no—
379C2×Dic11—28no—
380C2×Dic11—28no—
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—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—416no—
393C2×Dic11—44no—
394C2×Dic11C4×D4116yes—
395C2×Dic11C23×C414yes—
396C2×Dic11C23×C414yes—
397C2×Dic11C22×D414yes—
398C2×Dic11C22×D414yes—
399C2×Dic11C2×#4114yes—
400C2×Dic11C2×#4114yes—
401C2×Dic11C2×#4114yes—
402D44—416no—
403C4×D11—232no—
404C4×D11—416no—
405C23×D4—111no—
406C23×D4—111no—
407C23×D4—111no—
408C24×C4—111no—
409C24×C4—111no—
410C24×C4—111no—
411C2×#121—118no—
412C2×#121—1116no—
413C2×C4×D4—118no—
414C2×C4×D4—228no—
415C2×#117—118no—
416C2×#117—228no—
417C22×C4⋊C4—111no—
418C22×C4⋊C4—111no—
419C22×C4⋊C4—111no—
420C22×C4⋊C4—111no—
421C22×C4⋊C4C2×D1111yescharacteristic
422C22×C22⋊C4—111no—
423C22×C22⋊C4—111no—
424C22×C22⋊C4—111no—
425C22×C22⋊C4—111no—
426C22×C22⋊C4—111no—
427C22×C22⋊C4—111no—
428C22×C22⋊C4—111no—
429C22×C22⋊C4—111no—
430C22×C22⋊C4—111no—
431C22×C22⋊C4C2×D1111yescharacteristic
432C22×C22⋊C4C2×D1111yescharacteristic
433C22×C22⋊C4C2×D1111yescharacteristic
434C22×C42—111no—
435C22×C42—111no—
436C22×C42—111no—
437C22×C42—111no—
438C22×C42—111no—
439C22×C42C2×D1111yescharacteristic
440#390—118no—
441#390—118no—
442#390—118no—
443#389—118no—
444#388—118no—
445#388C2×D1118yescomplemented
446#386—118no—
447#386—118no—
448C4×C4⋊C4—118no—
449C4×C22⋊C4—118no—
450C4×C22⋊C4—118no—
451C4×C22⋊C4—118no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95—111no—
455C2×#95—111no—
456C2×#95C2×D1111yescharacteristic
457C2×#95C2×D1111yescharacteristic
458C22×C11—24no—
459C22×C11—24no—
460C22×C11—24no—
461C22×C11—416no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11C2×C4×D414yes—
467C22×C11C4×#4114yes—
468C22×C11#51814yes—
469C22×C11#54614yes—
470C22×C11#55014yes—
471C22×C11#55314yes—
472C22×C11#55514yes—
473C22×C11C24×C411yescharacteristic
474C22×C11C23×D411yescharacteristic
475C22×C11C22×#4111yescharacteristic
476C22×C11C22×#4111yescharacteristic
477C22×C11C22×#4111yescharacteristic
478C22×C11C2×H(5,𝔽2)11yescharacteristic
479C22×C11C2×H(5,𝔽2)11yescharacteristic
480C2×D11—24no—
481C2×D11—24no—
482C2×D11—24no—
483C2×D11—24no—
484C2×D11—24no—
485C2×D11—24no—
486C2×D11—416no—
487C2×D11—416no—
488C2×D11—42no—
489C2×D11—42no—
490C2×D11—42no—
491C2×D11—42no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—42no—
496C4×C11—24no—
497C4×C11—24no—
498C4×C11—24no—
499C4×C11—42no—
500C4×C11—42no—
501C4×C11—42no—
502Dic11—24no—
503Dic11—24no—
504Dic11—24no—
505Dic11—24no—
506Dic11—42no—
507Dic11C2×C4×D418yes—
508C25—111no—
509C25—111no—
510C25C22×D1111yescharacteristic
511C22×D4—118no—
512C22×D4—114no—
513C22×D4—118no—
514C22×D4—114no—
515C22×D4—118no—
516C22×D4—114no—
517C22×D4—224no—
518C22×D4—224no—
519C22×D4—442no—
520C22×D4—442no—
521C22×D4—442no—
522C22×D4—442no—
523C23×C4—111no—
524C23×C4—111no—
525C23×C4—111no—
526C23×C4—111no—
527C23×C4—111no—
528C23×C4—118no—
529C23×C4—114no—
530C23×C4—111no—
531C23×C4—114no—
532C23×C4—114no—
533C23×C4—224no—
534C23×C4—224no—
535C23×C4—224no—
536C23×C4—224no—
537C23×C4—224no—
538C23×C4—224no—
539C23×C4—442no—
540C23×C4—442no—
541C23×C4C22×D1111yescharacteristic
542C23×C4C22×D1111yescharacteristic
543C23×C4C22×D1111yescharacteristic
544C23×C4C22×D1111yescharacteristic
545C23×C4C22×D1111yescharacteristic
546C23×C4C22×D1111yescharacteristic
547#121—1164no—
548C4×D4—2232no—
549#117—2232no—
550C2×C4⋊C4—42no—
551C2×C4⋊C4—118no—
552C2×C4⋊C4—118no—
553C2×C4⋊C4—114no—
554C2×C4⋊C4—114no—
555C2×C4⋊C4—114no—
556C2×C4⋊C4—114no—
557C2×C4⋊C4—224no—
558C2×C4⋊C4—442no—
559C2×C4⋊C4C22×D1114yes—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—118no—
563C2×C22⋊C4—114no—
564C2×C22⋊C4—114no—
565C2×C22⋊C4—114no—
566C2×C22⋊C4—114no—
567C2×C22⋊C4—114no—
568C2×C22⋊C4—114no—
569C2×C22⋊C4—114no—
570C2×C22⋊C4—114no—
571C2×C22⋊C4—114no—
572C2×C22⋊C4—224no—
573C2×C22⋊C4—224no—
574C2×C22⋊C4—224no—
575C2×C22⋊C4—224no—
576C2×C22⋊C4—224no—
577C2×C22⋊C4—224no—
578C2×C22⋊C4—224no—
579C2×C22⋊C4—442no—
580C2×C22⋊C4C4×D1118yescomplemented
581C2×C22⋊C4C22×D1114yes—
582C2×C22⋊C4C22×D1114yes—
583C2×C22⋊C4C22×D1114yes—
584C2×C42—24no—
585C2×C42—114no—
586C2×C42—114no—
587C2×C42—114no—
588C2×C42—114no—
589C2×C42—114no—
590C2×C42—224no—
591C2×C42—224no—
592C2×C42—224no—
593C2×C42—442no—
594C2×C42—442no—
595C2×C42C22×D1114yes—
596#95—114no—
597#95—114no—
598#95—114no—
599#95—114no—
600#95C22×D1114yes—
601#95C22×D1114yes—
602C2×C11—44no—
603C2×C11#236318yescomplemented
604C2×C11C22×C4×D411yescharacteristic
605C2×C11C2×C4×#4111yescharacteristic
606C2×C11C2×#51811yescharacteristic
607C2×C11C2×#54611yescharacteristic
608C2×C11C2×#55011yescharacteristic
609C2×C11C2×#55311yescharacteristic
610C2×C11C2×#55511yescharacteristic
611D11—44no—
612D11—44no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—114no—
620C24—114no—
621C24—112no—
622C24—112no—
623C24—222no—
624C24—222no—
625C24—222no—
626C24—222no—
627C24—222no—
628C24—222no—
629C24—222no—
630C24—222no—
631C24—222no—
632C24—222no—
633C24—222no—
634C24—222no—
635C24C2×C4×D1114yes—
636C24C23×D1112yes—
637C24C23×D1111yescharacteristic
638C2×D4—1116no—
639C2×D4—1116no—
640C2×D4—1116no—
641C2×D4—228no—
642C2×D4—2232no—
643C2×D4—228no—
644C2×D4—4416no—
645C2×D4—444no—
646C2×D4—444no—
647C2×D4—4416no—
648C2×D4—444no—
649C2×D4—444no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
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—114no—
666C22×C4—114no—
667C22×C4—114no—
668C22×C4—112no—
669C22×C4—114no—
670C22×C4—114no—
671C22×C4—114no—
672C22×C4—114no—
673C22×C4—112no—
674C22×C4—112no—
675C22×C4—112no—
676C22×C4—112no—
677C22×C4—1116no—
678C22×C4—112no—
679C22×C4—228no—
680C22×C4—2232no—
681C22×C4—228no—
682C22×C4—228no—
683C22×C4—228no—
684C22×C4—228no—
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—228no—
697C22×C4—444no—
698C22×C4—4416no—
699C22×C4—444no—
700C22×C4—4416no—
701C22×C4C2×C4×D1114yes—
702C22×C4C2×C4×D1114yes—
703C22×C4D4×D1114yes—
704C22×C4C23×D1112yes—
705C22×C4C23×D1112yes—
706C22×C4C23×D1112yes—
707C22×C4C23×D1112yes—
708C22×C4C23×D1112yes—
709C22×C4C23×D1112yes—
710C4⋊C4—44no—
711C4⋊C4—1116no—
712C4⋊C4—1116no—
713C4⋊C4—228no—
714C4⋊C4—444no—
715C22⋊C4—28no—
716C22⋊C4—44no—
717C22⋊C4—1116no—
718C22⋊C4—228no—
719C22⋊C4—228no—
720C22⋊C4—228no—
721C22⋊C4—228no—
722C22⋊C4—228no—
723C22⋊C4—228no—
724C22⋊C4—228no—
725C22⋊C4—444no—
726C22⋊C4C2×C4×D11116yescomplemented
727C42—28no—
728C42—228no—
729C42—228no—
730C42—228no—
731C42—444no—
732C42—444no—
733C11C2×#236311yescharacteristic, complemented, Sylow
734C23—28no—
735C23—28no—
736C23—28no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—114no—
748C23—114no—
749C23—228no—
750C23—228no—
751C23—228no—
752C23—228no—
753C23—228no—
754C23—228no—
755C23—222no—
756C23—222no—
757C23—222no—
758C23—222no—
759C23—222no—
760C23—222no—
761C23—222no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23—444no—
768C23—444no—
769C23—444no—
770C23—444no—
771C23—444no—
772C23—444no—
773C23—444no—
774C23—444no—
775C23C22×C4×D1114yes—
776C23C22×C4×D1112yes—
777C23C2×D4×D1112yes—
778C23#6703712yes—
779C23#41×D1112yes—
780C23#41×D1112yes—
781C23#41×D1112yes—
782C23#6704212yes—
783C23C24×D1111yescharacteristic
784D4—2232no—
785D4—4416no—
786D4—4416no—
787C2×C4—28no—
788C2×C4—28no—
789C2×C4—28no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
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—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—1116no—
809C2×C4—114no—
810C2×C4—114no—
811C2×C4—114no—
812C2×C4—114no—
813C2×C4—114no—
814C2×C4—114no—
815C2×C4—114no—
816C2×C4—2232no—
817C2×C4—228no—
818C2×C4—228no—
819C2×C4—228no—
820C2×C4—228no—
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—4416no—
833C2×C4—4416no—
834C2×C4—444no—
835C2×C4C22×C4×D1114yes—
836C2×C4C22×C4×D1114yes—
837C2×C4C2×D4×D1114yes—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—42no—
842C22—416no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—224no—
847C22—224no—
848C22—224no—
849C22—224no—
850C22—224no—
851C22—224no—
852C22—442no—
853C22—442no—
854C22—4416no—
855C22—4416no—
856C22—442no—
857C22—442no—
858C22—442no—
859C22—442no—
860C22—442no—
861C22—442no—
862C22#1062305314yes—
863C22C4×D4×D1114yes—
864C22#1062307614yes—
865C22#1062313014yes—
866C22#1062318514yes—
867C22#1062320114yes—
868C22#1062324014yes—
869C22C23×C4×D1111yescharacteristic
870C22C22×D4×D1111yescharacteristic
871C22C2×#6703711yescharacteristic
872C22C2×#41×D1111yescharacteristic
873C22C2×#41×D1111yescharacteristic
874C22C2×#41×D1111yescharacteristic
875C22C2×#6704211yescharacteristic
876C4—24no—
877C4—24no—
878C4—24no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—118no—
883C4—224no—
884C4—224no—
885C4—224no—
886C4—224no—
887C4—442no—
888C2—44no—
889C2—444no—
890C2—444no—
891C2#1307164918yesdirect product factor
892C2C2×C4×D4×D1111yescharacteristic
893C2C2×#1062305311yescharacteristic
894C2C2×#1062307611yescharacteristic
895C2C2×#1062318511yescharacteristic
896C2C2×#1062313011yescharacteristic
897C2C2×#1062324011yescharacteristic
898C2C2×#1062320111yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC22×#66937C2
cosocleC23×C11C25
hypercenterC2×#388D11
hypocenterC11C2×#2363
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×(C22⋊D11)⋊C4C2semidirect
3. C22×#66925C2semidirect
4. #13071649C2direct (N × H)
5. C2×#10622601C2semidirect
6. C2×#10622570C2semidirect
7. C2×#10622570C2semidirect
8. C2×#10622585C2semidirect
9. C2×#10622282C2semidirect
10. C2×#10622278C2semidirect
11. C2×#10622571C2semidirect
12. C2×#10622262C2semidirect
13. C2×C22⋊C4×Dic11C2semidirect
14. C2×C4×(C2×D11)⋊C4C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#388C2semidirect
46. C2×#66937C4semidirect
49. C2×(C22⋊D11)⋊C4C22semidirect
51. C2×#66925C22semidirect
52. C11×#388C22semidirect
59. #10622601C22semidirect
60. #10622585C22semidirect
61. #10622571C22semidirect
62. #10622570C22semidirect
63. #10622570C22semidirect
64. C22⋊C4×Dic11C22semidirect
65. C4×(C2×D11)⋊C4C22semidirect
66. #10622282C22semidirect
67. #10622279C22semidirect
68. #10622278C22semidirect
69. #10622262C22semidirect
84. C22×C22⋊D11C2×C4semidirect
99. C22×D44C2×C4semidirect
106. C22×C4×D11C2×C4semidirect
113. C2×C11×C22⋊C4C2×C4semidirect
128. C2×(C2×D11)⋊C4C2×C4semidirect
139. C2×Dic11⋊C4C2×C4semidirect
140. C2×Dic11⋊C4D4semidirect
155. #66937C2×C4semidirect
221. C2×C22⋊D11C22×C4semidirect
253. C2×D44C22×C4semidirect
261. C2×C4×D11C22×C4semidirect
265. C11×C22⋊C4C22×C4semidirect
275. (C2×D11)⋊C4C22×C4semidirect
278. Dic11⋊C4C22×C4semidirect
279. Dic11⋊C4C2×D4semidirect
294. C2×#388D11semidirect
445. #388C2×D11semidirect
580. C2×C22⋊C4C4×D11semidirect
603. C2×C11#2363semidirect
726. C22⋊C4C2×C4×D11semidirect
733. C11C2×#2363semidirect
891. C2#13071649direct (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×(C22⋊D11)⋊C42
C22×#669252
#130716492
C2×#106226012
C2×#106225702
C2×#106225852
C2×#106222822
C2×#106222782
C2×#106225712
C2×#106222622
C2×C22⋊C4×Dic112
C2×C4×(C2×D11)⋊C42
C2×#106222792
C2×C11×#3882
C2×#236311