Finite Group Databasebeta

← C2×#13071667 #14913357

Subgroups — C2×#13071667 #14913357

Order 2816.

4262 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×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4#13071667C2116yesmaximal, direct product factor
5C2×#10622564C211yesmaximal, characteristic, complemented
6C2×#10622553C211yesmaximal, characteristic, complemented
7C2×#10622268C211yesmaximal, characteristic, complemented
8C2×#10622546C211yesmaximal, characteristic, complemented
9C2×#10622826C211yesmaximal, characteristic, complemented
10C2×#10622278C211yesmaximal, characteristic, complemented
11C2×#10622569C211yesmaximal, characteristic, complemented
12C2×#10622569C211yesmaximal, characteristic, complemented
13C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
14C2×#10622279C211yesmaximal, characteristic, complemented
15C2×D11×#95C211yesmaximal, 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
23C23×C4×D11C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C42×C11C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C2×C4×C22⋊D11—28no—
32C2×C4×C22⋊D11C2218yescomplemented
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×C4×Dic11C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C2×#66937C4116yescomplemented
45C2×#66937C2218yes—
46C2×C4×D44—28no—
47C2×C4×D44C2218yescomplemented
48C4×C11×C22⋊C4C2218yescomplemented
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51#10622826C2218yescomplemented
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60#10622569C2218yescomplemented
61#10622569C2218yescomplemented
62#10622564C2218yescomplemented
63#10622553C2218yescomplemented
64C4×(C2×D11)⋊C4C2218yescomplemented
65#10622546C2218yescomplemented
66#10622279C2218yescomplemented
67#10622278C2218yescomplemented
68D11×#95C2218yescomplemented
69#10622268C2218yescomplemented
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×C418yescomplemented
88C22×C22⋊D11C2×C418yescomplemented
89C22×C22⋊D11C2314yes—
90C22×C22⋊D11C2314yes—
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C22×D44—24no—
98C22×D44—24no—
99C22×D44C2×C418yescomplemented
100C22×D44C2314yes—
101C22×C4×D11—24no—
102C22×C4×D11—24no—
103C22×C4×D11—24no—
104C22×C4×D11—24no—
105C22×C4×D11—24no—
106C22×C4×D11—24no—
107C22×C4×D11—42no—
108C22×C4×D11—42no—
109C22×C4×D11—42no—
110C22×C4×D11—42no—
111C22×C4×D11—42no—
112C22×C4×D11C2×C418yescomplemented
113C22×C4×D11C2314yes—
114C22×C4×D11C2314yes—
115C22×C4×D11C2314yes—
116C22×C4×D11C2314yes—
117C2×C11×C22⋊C4—24no—
118C2×C11×C22⋊C4C2×C418yescomplemented
119C2×C11×C22⋊C4C2314yes—
120C2×C11×C22⋊C4C2314yes—
121C2×C42×C11—24no—
122C2×C42×C11—42no—
123C2×C42×C11C2314yes—
124C2×C42×C11C2314yes—
125C2×C22⋊Dic11—24no—
126C2×C22⋊Dic11—42no—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2314yes—
129C4×C22⋊D11—232no—
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4—24no—
132C2×(C2×D11)⋊C4—24no—
133C2×(C2×D11)⋊C4—42no—
134C2×(C2×D11)⋊C4C2×C418yescomplemented
135C2×(C2×D11)⋊C4D418yescomplemented
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×C4⋊Dic11—24no—
143C2×C4⋊Dic11C2314yes—
144C2×Dic11⋊C4—24no—
145C2×Dic11⋊C4C2×C418yescomplemented
146C2×Dic11⋊C4C2314yes—
147C2×Dic11⋊C4C2314yes—
148C2×C4×Dic11—24no—
149C2×C4×Dic11—42no—
150C2×C4×Dic11C2314yes—
151C2×C4×Dic11C2314yes—
152#66937C2×C4164yescomplemented
153C4×D44—232no—
154C11×#95C2314yes—
155C11×#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C2×#2364—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—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×C4116yescomplemented
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×Dic11—22no—
240C22×Dic11—22no—
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—28no—
257C2×C4×D11—28no—
258C2×C4×D11—28no—
259C2×C4×D11—28no—
260C2×C4×D11—416no—
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×D11—416no—
269C2×C4×D11C22×C4116yescomplemented
270C11×C22⋊C4—28no—
271C11×C22⋊C4C22×C4116yescomplemented
272C42×C11—28no—
273C42×C11—44no—
274C22⋊Dic11—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)⋊C4C22×C4116yescomplemented
281(C2×D11)⋊C4C2×D4116yescomplemented
282C4⋊Dic11—28no—
283Dic11⋊C4—28no—
284Dic11⋊C4C22×C4116yescomplemented
285C4×Dic11—28no—
286C4×Dic11—44no—
287C22×#121—111no—
288C22×C4×D4—111no—
289C22×C4×D4—111no—
290#2364—1116no—
291C2×#388—111no—
292C2×#388—111no—
293C2×#387—111no—
294C2×#387—111no—
295C2×#386—111no—
296C2×#386—111no—
297C2×#386—111no—
298C2×#386—111no—
299C2×C4×C22⋊C4—111no—
300C2×C4×C22⋊C4—111no—
301C2×C4×C22⋊C4D1111yescharacteristic, complemented
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×C11C2×#4112yes—
321C23×C11C2×#4112yes—
322C23×C11H(5,𝔽2)12yes—
323C23×C11H(5,𝔽2)12yes—
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—28no—
357C2×C4×C11—28no—
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—416no—
372C2×C4×C11—44no—
373C2×C4×C11C23×C414yes—
374C2×C4×C11C23×C414yes—
375C2×C4×C11C22×D414yes—
376C2×C4×C11C2×#4114yes—
377C2×C4×C11C2×#4114yes—
378C22⋊D11—232no—
379C22⋊D11—416no—
380C2×Dic11—28no—
381C2×Dic11—28no—
382C2×Dic11—28no—
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—22no—
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×C4C2×D1111yescharacteristic
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×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⋊C4—111no—
433C22×C22⋊C4—111no—
434C22×C22⋊C4C2×D1111yescharacteristic
435C22×C22⋊C4C2×D1111yescharacteristic
436C22×C42—111no—
437C22×C42—111no—
438C22×C42C2×D1111yescharacteristic
439C22×C42C2×D1111yescharacteristic
440#388—118no—
441#388—118no—
442#387—118no—
443#387—118no—
444#386—118no—
445#386—118no—
446#386—118no—
447#386—118no—
448C4×C22⋊C4—118no—
449C4×C22⋊C4—118no—
450C4×C22⋊C4C2×D1118yescomplemented
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×C11C4×#4114yes—
472C22×C11#51814yes—
473C22×C11#54614yes—
474C22×C11#54614yes—
475C22×C11#55314yes—
476C22×C11#55314yes—
477C22×C11C24×C411yescharacteristic
478C22×C11C23×D411yescharacteristic
479C22×C11C22×#4111yescharacteristic
480C22×C11C22×#4111yescharacteristic
481C22×C11C22×#4111yescharacteristic
482C22×C11C2×H(5,𝔽2)11yescharacteristic
483C22×C11C2×H(5,𝔽2)11yescharacteristic
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—24no—
504C4×C11—24no—
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—24no—
528C23×C4—24no—
529C23×C4—42no—
530C23×C4—111no—
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—118no—
534C23×C4—114no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—111no—
538C23×C4—114no—
539C23×C4—114no—
540C23×C4—114no—
541C23×C4—224no—
542C23×C4—224no—
543C23×C4—224no—
544C23×C4—224no—
545C23×C4—224no—
546C23×C4—224no—
547C23×C4—442no—
548C23×C4—442no—
549C23×C4—442no—
550C23×C4—442no—
551C23×C4—442no—
552C23×C4C22×D1111yescharacteristic
553C23×C4C22×D1114yes—
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—118no—
563C2×C4⋊C4—114no—
564C2×C4⋊C4—114no—
565C2×C4⋊C4—114no—
566C2×C4⋊C4—224no—
567C2×C4⋊C4—224no—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—118no—
570C2×C22⋊C4—118no—
571C2×C22⋊C4—114no—
572C2×C22⋊C4—114no—
573C2×C22⋊C4—114no—
574C2×C22⋊C4—114no—
575C2×C22⋊C4—114no—
576C2×C22⋊C4—114no—
577C2×C22⋊C4—114no—
578C2×C22⋊C4—114no—
579C2×C22⋊C4—224no—
580C2×C22⋊C4—224no—
581C2×C22⋊C4—224no—
582C2×C22⋊C4—224no—
583C2×C22⋊C4—442no—
584C2×C22⋊C4—442no—
585C2×C22⋊C4C4×D1118yescomplemented
586C2×C22⋊C4C22×D1114yes—
587C2×C22⋊C4C22×D1114yes—
588C2×C42—24no—
589C2×C42—42no—
590C2×C42—114no—
591C2×C42—114no—
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#95—114no—
601#95—114no—
602#95—114no—
603#95—114no—
604#95C22×D1114yes—
605#95C22×D1114yes—
606C2×C11—44no—
607C2×C11#236418yescomplemented
608C2×C11C22×C4×D411yescharacteristic
609C2×C11C2×C4×#4111yescharacteristic
610C2×C11C2×#51811yescharacteristic
611C2×C11C2×#54611yescharacteristic
612C2×C11C2×#54611yescharacteristic
613C2×C11C2×#55311yescharacteristic
614C2×C11C2×#55311yescharacteristic
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—28no—
668C22×C4—28no—
669C22×C4—44no—
670C22×C4—416no—
671C22×C4—114no—
672C22×C4—114no—
673C22×C4—114no—
674C22×C4—112no—
675C22×C4—112no—
676C22×C4—112no—
677C22×C4—1116no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—228no—
682C22×C4—228no—
683C22×C4—228no—
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—222no—
698C22×C4—222no—
699C22×C4—228no—
700C22×C4—228no—
701C22×C4—228no—
702C22×C4—4416no—
703C22×C4—444no—
704C22×C4—444no—
705C22×C4—444no—
706C22×C4—444no—
707C22×C4—444no—
708C22×C4—4416no—
709C22×C4—4416no—
710C22×C4—4416no—
711C22×C4C2×C4×D1114yes—
712C22×C4C2×C4×D1114yes—
713C22×C4#433914yes—
714C22×C4#433914yes—
715C22×C4D4×D1114yes—
716C22×C4C23×D1112yes—
717C22×C4C23×D1112yes—
718C22×C4C23×D1112yes—
719C22×C4C23×D1112yes—
720C22×C4C23×D1112yes—
721C22×C4C23×D1112yes—
722C4⋊C4—1116no—
723C4⋊C4—228no—
724C4⋊C4—228no—
725C22⋊C4—28no—
726C22⋊C4—1116no—
727C22⋊C4—1116no—
728C22⋊C4—228no—
729C22⋊C4—228no—
730C22⋊C4—228no—
731C22⋊C4—228no—
732C22⋊C4—444no—
733C22⋊C4—444no—
734C22⋊C4C2×C4×D11116yescomplemented
735C42—28no—
736C42—44no—
737C42—228no—
738C42—444no—
739C11C2×#236411yescharacteristic, 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—228no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23—222no—
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×#433912yes—
784C23C2×#433912yes—
785C23C2×D4×D1112yes—
786C23#6703712yes—
787C23#41×D1112yes—
788C23#6704212yes—
789C23C24×D1111yescharacteristic
790D4—2232no—
791D4—2232no—
792D4—4416no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
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—416no—
812C2×C4—44no—
813C2×C4—114no—
814C2×C4—114no—
815C2×C4—114no—
816C2×C4—228no—
817C2×C4—228no—
818C2×C4—228no—
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—222no—
830C2×C4—222no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—4416no—
835C2×C4—4416no—
836C2×C4—4416no—
837C2×C4—4416no—
838C2×C4—444no—
839C2×C4—444no—
840C2×C4—444no—
841C2×C4C22×C4×D1114yes—
842C2×C4C22×C4×D1114yes—
843C2×C4C2×#433914yes—
844C2×C4C2×#433914yes—
845C2×C4C2×D4×D1114yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—42no—
850C22—42no—
851C22—416no—
852C22—42no—
853C22—42no—
854C22—118no—
855C22—224no—
856C22—224no—
857C22—2232no—
858C22—224no—
859C22—224no—
860C22—224no—
861C22—224no—
862C22—224no—
863C22—224no—
864C22—224no—
865C22—442no—
866C22—442no—
867C22—4416no—
868C22—442no—
869C22—442no—
870C22C4×#433914yes—
871C22#1062302114yes—
872C22#1062306114yes—
873C22C4×D4×D1114yes—
874C22#1062307614yes—
875C22#1062308114yes—
876C22#1062308914yes—
877C22C23×C4×D1111yescharacteristic
878C22C22×#433911yescharacteristic
879C22C22×#433911yescharacteristic
880C22C22×D4×D1111yescharacteristic
881C22C2×#6703711yescharacteristic
882C22C2×#41×D1111yescharacteristic
883C22C2×#6704211yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—24no—
888C4—24no—
889C4—42no—
890C4—224no—
891C4—224no—
892C4—224no—
893C4—442no—
894C4—442no—
895C4—442no—
896C2—44no—
897C2—228no—
898C2—444no—
899C2#1307166718yesdirect product factor
900C2C2×C4×D4×D1111yescharacteristic
901C2C2×C4×#433911yescharacteristic
902C2C2×#1062307611yescharacteristic
903C2C2×#1062302111yescharacteristic
904C2C2×#1062308111yescharacteristic
905C2C2×#1062306111yescharacteristic
906C2C2×#1062308911yescharacteristic
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×#2364
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×D44C2semidirect
3. C22×C4×C22⋊D11C2semidirect
4. #13071667C2direct (N × H)
5. C2×#10622564C2semidirect
6. C2×#10622553C2semidirect
7. C2×#10622268C2semidirect
8. C2×#10622546C2semidirect
9. C2×#10622826C2semidirect
10. C2×#10622278C2semidirect
11. C2×#10622569C2semidirect
12. C2×#10622569C2semidirect
13. C2×C4×(C2×D11)⋊C4C2semidirect
14. C2×#10622279C2semidirect
15. C2×D11×#95C2semidirect
16. C2×C4×C11×C22⋊C4C2semidirect
32. C2×C4×C22⋊D11C22semidirect
44. C2×#66937C4semidirect
47. C2×C4×D44C22semidirect
48. C4×C11×C22⋊C4C22semidirect
51. #10622826C22semidirect
60. #10622569C22semidirect
61. #10622569C22semidirect
62. #10622564C22semidirect
63. #10622553C22semidirect
64. C4×(C2×D11)⋊C4C22semidirect
65. #10622546C22semidirect
66. #10622279C22semidirect
67. #10622278C22semidirect
68. D11×#95C22semidirect
69. #10622268C22semidirect
87. C22×C22⋊D11C2×C4semidirect
88. C22×C22⋊D11C2×C4semidirect
99. C22×D44C2×C4semidirect
112. C22×C4×D11C2×C4semidirect
118. C2×C11×C22⋊C4C2×C4semidirect
134. C2×(C2×D11)⋊C4C2×C4semidirect
135. C2×(C2×D11)⋊C4D4semidirect
145. C2×Dic11⋊C4C2×C4semidirect
152. #66937C2×C4semidirect
224. C2×C22⋊D11C22×C4semidirect
225. C2×C22⋊D11C22×C4semidirect
253. C2×D44C22×C4semidirect
269. C2×C4×D11C22×C4semidirect
271. C11×C22⋊C4C22×C4semidirect
280. (C2×D11)⋊C4C22×C4semidirect
281. (C2×D11)⋊C4C2×D4semidirect
284. Dic11⋊C4C22×C4semidirect
301. C2×C4×C22⋊C4D11semidirect
450. C4×C22⋊C4C2×D11semidirect
585. C2×C22⋊C4C4×D11semidirect
607. C2×C11#2364semidirect
734. C22⋊C4C2×C4×D11semidirect
739. C11C2×#2364semidirect
899. C2#13071667direct (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×C4×C22⋊D112
#130716672
C2×#106225642
C2×#106225532
C2×#106222682
C2×#106225462
C2×#106228262
C2×#106222782
C2×#106225692
C2×C4×(C2×D11)⋊C42
C2×#106222792
C2×D11×#952
C2×C4×C11×C22⋊C42
C2×#236411