Finite Group Databasebeta

← C2×#13071655 #14913327

Subgroups — C2×#13071655 #14913327

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×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3C22×#66925C211yesmaximal, characteristic, complemented
4#13071655C2116yesmaximal, direct product factor
5C2×#10622552C211yesmaximal, characteristic, complemented
6C2×#10622570C211yesmaximal, characteristic, complemented
7C2×#10622570C211yesmaximal, characteristic, complemented
8C2×#10622260C211yesmaximal, characteristic, complemented
9C2×#10622564C211yesmaximal, characteristic, complemented
10C2×#10622553C211yesmaximal, characteristic, complemented
11C2×#10622826C211yesmaximal, characteristic, complemented
12C2×#10622278C211yesmaximal, characteristic, complemented
13C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
14C2×#10622279C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C22×C42×C11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C2×C4×C22⋊D11—28no—
30C2×C4×C22⋊D11C2218yescomplemented
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×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C22×C4×Dic11C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C2×#66937C4116yescomplemented
49C2×#66937C2218yes—
50C2×#66925—28no—
51C2×#66925C2218yescomplemented
52C4×C11×C22⋊C4C2218yescomplemented
53C2×C11×#95C2211yescharacteristic
54C2×C11×#95C2211yescharacteristic
55#10622826C2218yescomplemented
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60#10622570C2218yescomplemented
61#10622570C2218yescomplemented
62#10622564C2218yescomplemented
63#10622553C2218yescomplemented
64#10622552C2218yescomplemented
65C4×Dic11⋊C4C2218yescomplemented
66#10622279C2218yescomplemented
67#10622279C2218yescomplemented
68#10622278C2218yescomplemented
69#10622260C2218yescomplemented
70C25×C11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C23×C4×C11—24no—
74C23×C4×C11—24no—
75C23×C4×C11—42no—
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2314yes—
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—24no—
84C22×C22⋊D11—24no—
85C22×C22⋊D11—42no—
86C22×C22⋊D11—42no—
87C22×C22⋊D11C2×C418yes—
88C22×C22⋊D11C2×C418yescomplemented
89C22×C22⋊D11C2314yes—
90C22×C22⋊D11C2314yes—
91C23×Dic11C2311yescharacteristic
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×C22⋊C4—24no—
110C2×C11×C22⋊C4C2×C418yescomplemented
111C2×C11×C22⋊C4C2314yes—
112C2×C11×C22⋊C4C2314yes—
113C2×C42×C11—24no—
114C2×C42×C11—42no—
115C2×C42×C11C2314yes—
116C2×C42×C11C2314yes—
117C2×C22⋊Dic11—24no—
118C2×C22⋊Dic11—42no—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2314yes—
121C4×C22⋊D11—232no—
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—24no—
128C2×(C2×D11)⋊C4—42no—
129C2×(C2×D11)⋊C4C2×C418yescomplemented
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×(C2×D11)⋊C4C2314yes—
138C2×C4⋊Dic11—42no—
139C2×C4⋊Dic11C2314yes—
140C2×Dic11⋊C4—24no—
141C2×Dic11⋊C4—42no—
142C2×Dic11⋊C4C2×C418yescomplemented
143C2×Dic11⋊C4D418yescomplemented
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×Dic11⋊C4C2314yes—
147C2×Dic11⋊C4C2314yes—
148C2×C4×Dic11—24no—
149C2×C4×Dic11—24no—
150C2×C4×Dic11—24no—
151C2×C4×Dic11—42no—
152C2×C4×Dic11C2314yes—
153C2×C4×Dic11C2314yes—
154C2×C4×Dic11C2314yes—
155C2×C4×Dic11C2314yes—
156#66937C2×C4164yescomplemented
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—28no—
204C22×C4×C11—28no—
205C22×C4×C11—44no—
206C22×C4×C11—416no—
207C22×C4×C11C22×C414yes—
208C22×C4×C11C22×C414yes—
209C22×C4×C11C2×D414yes—
210C22×C4×C11#4114yes—
211C22×C4×C11#4114yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C2×C22⋊D11—232no—
219C2×C22⋊D11—28no—
220C2×C22⋊D11—28no—
221C2×C22⋊D11—416no—
222C2×C22⋊D11—44no—
223C2×C22⋊D11—44no—
224C2×C22⋊D11C22×C4116yes—
225C2×C22⋊D11C22×C4116yescomplemented
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—22no—
239C22×Dic11C22×C414yes—
240C22×Dic11C22×C414yes—
241C22×Dic11C2×D414yes—
242C22×Dic11C2×D414yes—
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×C22⋊C4—28no—
263C11×C22⋊C4C22×C4116yescomplemented
264C42×C11—28no—
265C42×C11—44no—
266C22⋊Dic11—28no—
267C22⋊Dic11—44no—
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
276C4⋊Dic11—44no—
277Dic11⋊C4—28no—
278Dic11⋊C4—44no—
279Dic11⋊C4C22×C4116yescomplemented
280Dic11⋊C4C2×D4116yescomplemented
281C4×Dic11—28no—
282C4×Dic11—28no—
283C4×Dic11—28no—
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×#388—111no—
295C2×#386—111no—
296C2×#386—111no—
297C2×C4×C4⋊C4—111no—
298C2×C4×C22⋊C4—111no—
299C2×C4×C22⋊C4—111no—
300C2×C4×C22⋊C4D1111yescharacteristic, complemented
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—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—416no—
370C2×C4×C11—44no—
371C2×C4×C11C23×C414yes—
372C2×C4×C11C23×C414yes—
373C2×C4×C11C22×D414yes—
374C2×C4×C11C2×#4114yes—
375C2×C4×C11C2×#4114yes—
376C22⋊D11—232no—
377C22⋊D11—416no—
378C2×Dic11—28no—
379C2×Dic11—28no—
380C2×Dic11—22no—
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—22no—
393C2×Dic11—44no—
394C2×Dic11—44no—
395C2×Dic11—44no—
396C2×Dic11C4×D4116yes—
397C2×Dic11C23×C414yes—
398C2×Dic11C23×C414yes—
399C2×Dic11C22×D414yes—
400C2×Dic11C22×D414yes—
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×C4C2×D1111yescharacteristic
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⋊C4—111no—
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⋊C4—111no—
432C22×C22⋊C4C2×D1111yescharacteristic
433C22×C22⋊C4C2×D1111yescharacteristic
434C22×C42—111no—
435C22×C42—111no—
436C22×C42—111no—
437C22×C42—111no—
438C22×C42C2×D1111yescharacteristic
439C22×C42C2×D1111yescharacteristic
440#390—118no—
441#390—118no—
442#390—118no—
443#389—118no—
444#388—118no—
445#388—118no—
446#386—118no—
447#386—118no—
448C4×C4⋊C4—118no—
449C4×C22⋊C4—118no—
450C4×C22⋊C4—118no—
451C4×C22⋊C4C2×D1118yescomplemented
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—24no—
500C4×C11—24no—
501C4×C11—42no—
502Dic11—24no—
503Dic11—24no—
504Dic11—42no—
505Dic11—42no—
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—24no—
524C23×C4—24no—
525C23×C4—42no—
526C23×C4—111no—
527C23×C4—111no—
528C23×C4—111no—
529C23×C4—118no—
530C23×C4—114no—
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—114no—
535C23×C4—224no—
536C23×C4—224no—
537C23×C4—224no—
538C23×C4—224no—
539C23×C4—442no—
540C23×C4C22×D1111yescharacteristic
541C23×C4C22×D1114yes—
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—118no—
551C2×C4⋊C4—118no—
552C2×C4⋊C4—114no—
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⋊C4—442no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—118no—
562C2×C22⋊C4—114no—
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⋊C4—442no—
581C2×C22⋊C4C4×D1118yescomplemented
582C2×C22⋊C4C22×D1114yes—
583C2×C22⋊C4C22×D1114yes—
584C2×C42—24no—
585C2×C42—42no—
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×C42C22×D1114yes—
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—28no—
664C22×C4—28no—
665C22×C4—44no—
666C22×C4—416no—
667C22×C4—114no—
668C22×C4—114no—
669C22×C4—114no—
670C22×C4—112no—
671C22×C4—114no—
672C22×C4—114no—
673C22×C4—112no—
674C22×C4—112no—
675C22×C4—1116no—
676C22×C4—112no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—228no—
680C22×C4—2232no—
681C22×C4—228no—
682C22×C4—228no—
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—228no—
697C22×C4—444no—
698C22×C4—4416no—
699C22×C4C2×C4×D1114yes—
700C22×C4C2×C4×D1114yes—
701C22×C4#433914yes—
702C22×C4#433914yes—
703C22×C4D4×D1114yes—
704C22×C4C23×D1112yes—
705C22×C4C23×D1112yes—
706C22×C4C23×D1112yes—
707C22×C4C23×D1112yes—
708C22×C4C23×D1112yes—
709C22×C4C23×D1112yes—
710C4⋊C4—1116no—
711C4⋊C4—1116no—
712C4⋊C4—228no—
713C4⋊C4—444no—
714C4⋊C4—444no—
715C22⋊C4—28no—
716C22⋊C4—1116no—
717C22⋊C4—228no—
718C22⋊C4—228no—
719C22⋊C4—228no—
720C22⋊C4—228no—
721C22⋊C4—228no—
722C22⋊C4—228no—
723C22⋊C4—228no—
724C22⋊C4—444no—
725C22⋊C4—444no—
726C22⋊C4C2×C4×D11116yescomplemented
727C42—28no—
728C42—44no—
729C42—228no—
730C42—228no—
731C42—228no—
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×#433912yes—
778C23C2×#433912yes—
779C23C2×D4×D1112yes—
780C23#6703712yes—
781C23#41×D1112yes—
782C23#6704212yes—
783C23C24×D1111yescharacteristic
784D4—2232no—
785D4—4416no—
786D4—4416no—
787C2×C4—28no—
788C2×C4—28no—
789C2×C4—28no—
790C2×C4—28no—
791C2×C4—28no—
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—416no—
806C2×C4—44no—
807C2×C4—1116no—
808C2×C4—114no—
809C2×C4—114no—
810C2×C4—114no—
811C2×C4—114no—
812C2×C4—114no—
813C2×C4—2232no—
814C2×C4—228no—
815C2×C4—228no—
816C2×C4—222no—
817C2×C4—222no—
818C2×C4—222no—
819C2×C4—222no—
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—4416no—
830C2×C4—444no—
831C2×C4—444no—
832C2×C4—444no—
833C2×C4C22×C4×D1114yes—
834C2×C4C22×C4×D1114yes—
835C2×C4C2×#433914yes—
836C2×C4C2×#433914yes—
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—
862C22C4×#433914yes—
863C22#1062302114yes—
864C22#1062306314yes—
865C22#1062307114yes—
866C22C4×D4×D1114yes—
867C22#1062307614yes—
868C22#1062308414yes—
869C22C23×C4×D1111yescharacteristic
870C22C22×#433911yescharacteristic
871C22C22×#433911yescharacteristic
872C22C22×D4×D1111yescharacteristic
873C22C2×#6703711yescharacteristic
874C22C2×#41×D1111yescharacteristic
875C22C2×#6704211yescharacteristic
876C4—24no—
877C4—24no—
878C4—24no—
879C4—24no—
880C4—24no—
881C4—42no—
882C4—118no—
883C4—224no—
884C4—224no—
885C4—442no—
886C4—442no—
887C4—442no—
888C2—44no—
889C2—444no—
890C2—444no—
891C2#1307165518yesdirect product factor
892C2C2×C4×D4×D1111yescharacteristic
893C2C2×C4×#433911yescharacteristic
894C2C2×#1062307611yescharacteristic
895C2C2×#1062302111yescharacteristic
896C2C2×#1062308411yescharacteristic
897C2C2×#1062307111yescharacteristic
898C2C2×#1062306311yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC22×#66937C2
cosocleC23×C11C25
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#2363
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D11C2semidirect
3. C22×#66925C2semidirect
4. #13071655C2direct (N × H)
5. C2×#10622552C2semidirect
6. C2×#10622570C2semidirect
7. C2×#10622570C2semidirect
8. C2×#10622260C2semidirect
9. C2×#10622564C2semidirect
10. C2×#10622553C2semidirect
11. C2×#10622826C2semidirect
12. C2×#10622278C2semidirect
13. C2×C4×Dic11⋊C4C2semidirect
14. C2×#10622279C2semidirect
15. C2×#10622279C2semidirect
16. C2×C4×C11×C22⋊C4C2semidirect
30. C2×C4×C22⋊D11C22semidirect
48. C2×#66937C4semidirect
51. C2×#66925C22semidirect
52. C4×C11×C22⋊C4C22semidirect
55. #10622826C22semidirect
60. #10622570C22semidirect
61. #10622570C22semidirect
62. #10622564C22semidirect
63. #10622553C22semidirect
64. #10622552C22semidirect
65. C4×Dic11⋊C4C22semidirect
66. #10622279C22semidirect
67. #10622279C22semidirect
68. #10622278C22semidirect
69. #10622260C22semidirect
88. C22×C22⋊D11C2×C4semidirect
99. C22×D44C2×C4semidirect
106. C22×C4×D11C2×C4semidirect
110. C2×C11×C22⋊C4C2×C4semidirect
129. C2×(C2×D11)⋊C4C2×C4semidirect
142. C2×Dic11⋊C4C2×C4semidirect
143. C2×Dic11⋊C4D4semidirect
156. #66937C2×C4semidirect
225. C2×C22⋊D11C22×C4semidirect
253. C2×D44C22×C4semidirect
261. C2×C4×D11C22×C4semidirect
263. C11×C22⋊C4C22×C4semidirect
275. (C2×D11)⋊C4C22×C4semidirect
279. Dic11⋊C4C22×C4semidirect
280. Dic11⋊C4C2×D4semidirect
300. C2×C4×C22⋊C4D11semidirect
451. C4×C22⋊C4C2×D11semidirect
581. C2×C22⋊C4C4×D11semidirect
603. C2×C11#2363semidirect
726. C22⋊C4C2×C4×D11semidirect
733. C11C2×#2363semidirect
891. C2#13071655direct (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×C22⋊D112
C22×#669252
#130716552
C2×#106225522
C2×#106225702
C2×#106222602
C2×#106225642
C2×#106225532
C2×#106228262
C2×#106222782
C2×C4×Dic11⋊C42
C2×#106222792
C2×C4×C11×C22⋊C42
C2×#236311