Finite Group Databasebeta

← C2×#13072348 #14921222

Subgroups — C2×#13072348 #14921222

Order 2816.

4002 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×#66991C211yesmaximal, characteristic
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
4#13072348C2116yesmaximal, direct product factor
5C2×#10622562C211yesmaximal, characteristic, complemented
6C2×#10622597C211yesmaximal, characteristic, complemented
7C2×#10622566C211yesmaximal, characteristic, complemented
8C2×#10622835C211yesmaximal, characteristic, complemented
9C2×#10622558C211yesmaximal, characteristic, complemented
10C2×#10622594C211yesmaximal, characteristic, complemented
11C2×#10622569C211yesmaximal, characteristic, complemented
12C2×#10622569C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622823C211yesmaximal, characteristic, complemented
15C2×#10622602C211yesmaximal, characteristic, complemented
16C22×C11×#123C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C2×C11×#123—28no—
25C2×C11×#123C2218yescomplemented
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C22×C22⋊Dic11C2211yescharacteristic
37C2×#66991—28no—
38C2×#66991C2218yes—
39C2×C4×C22⋊D11—28no—
40C2×C4×C22⋊D11C2218yescomplemented
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×C4⋊Dic11C2211yescharacteristic
44C22×C4⋊Dic11C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C2×C4⋊C4×D11—28no—
51C2×C4⋊C4×D11C2218yescomplemented
52#10622835C2218yescomplemented
53#10622823C2218yescomplemented
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62#10622602C2218yescomplemented
63#10622597C2218yescomplemented
64#10622594C2218yescomplemented
65#10622569C2218yescomplemented
66#10622569C2218yescomplemented
67#10622569C2218yescomplemented
68#10622566C2218yescomplemented
69#10622562C2218yescomplemented
70#10622558C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C22×D4×C11—24no—
75C22×D4×C11—24no—
76C22×D4×C11—42no—
77C22×D4×C11C2314yes—
78C23×C4×C11—24no—
79C23×C4×C11—24no—
80C23×C4×C11—42no—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2314yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11D418yes—
93C22×C22⋊D11C2314yes—
94C22×C22⋊D11C2314yes—
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C22×C4×D11—24no—
103C22×C4×D11—24no—
104C22×C4×D11—24no—
105C22×C4×D11—24no—
106C22×C4×D11—24no—
107C22×C4×D11—24no—
108C22×C4×D11—24no—
109C22×C4×D11—42no—
110C22×C4×D11—42no—
111C22×C4×D11C2314yes—
112C22×C4×D11C2314yes—
113C22×C4×D11C2314yes—
114C11×#123—232no—
115C2×C11×C4⋊C4—24no—
116C2×C11×C4⋊C4D418yescomplemented
117C2×C11×C4⋊C4C2314yes—
118C2×C11×C4⋊C4C2314yes—
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4—24no—
121C2×C11×C22⋊C4—24no—
122C2×C11×C22⋊C4C2314yes—
123C2×C11×C22⋊C4C2314yes—
124C2×C11×C22⋊C4C2314yes—
125C2×C22⋊Dic11—24no—
126C2×C22⋊Dic11—24no—
127C2×C22⋊Dic11—24no—
128C2×C22⋊Dic11—24no—
129C2×C22⋊Dic11—24no—
130C2×C22⋊Dic11—42no—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yes—
134C2×C22⋊Dic11C2314yes—
135C2×C22⋊Dic11C2314yes—
136C2×C22⋊Dic11C2314yes—
137#66991—232no—
138C4×C22⋊D11—232no—
139C2×(C2×D11)⋊C4—24no—
140C2×(C2×D11)⋊C4—24no—
141C2×(C2×D11)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2314yes—
143C2×C4⋊Dic11—24no—
144C2×C4⋊Dic11—24no—
145C2×C4⋊Dic11C2314yes—
146C2×C4⋊Dic11C2314yes—
147C2×Dic11⋊C4—24no—
148C2×Dic11⋊C4—24no—
149C2×Dic11⋊C4—24no—
150C2×Dic11⋊C4—42no—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×C4×Dic11—24no—
156C2×C4×Dic11C2314yes—
157C4⋊C4×D11—232no—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C2×#2443—111nomaximal, Sylow
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—22no—
180C24×C11C2×D414yes—
181C24×C11C2412yes—
182C24×C11C2412yes—
183C24×C11C2411yescharacteristic
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11C2×D414yes—
189C23×D11#4114yes—
190C23×D11#4114yes—
191C23×D11C2412yes—
192C2×D4×C11—28no—
193C2×D4×C11—28no—
194C2×D4×C11—44no—
195C2×D4×C11—416no—
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—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—28no—
210C22×C4×C11—44no—
211C22×C4×C11—416no—
212C22×C4×C11C2×D414yes—
213C22×C4×C11C2×D414yes—
214C22×C4×C11C2×D414yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C2×C22⋊D11—232no—
221C2×C22⋊D11—28no—
222C2×C22⋊D11—28no—
223C2×C22⋊D11—28no—
224C2×C22⋊D11—28no—
225C2×C22⋊D11—28no—
226C2×C22⋊D11—416no—
227C2×C22⋊D11C2×D4116yes—
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×Dic11—22no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—22no—
245C22×Dic11—22no—
246C22×Dic11—22no—
247C22×Dic11C2×D414yes—
248C22×Dic11#4114yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C2×C4×D11—232no—
257C2×C4×D11—28no—
258C2×C4×D11—28no—
259C2×C4×D11—28no—
260C2×C4×D11—28no—
261C2×C4×D11—28no—
262C2×C4×D11—28no—
263C2×C4×D11—28no—
264C2×C4×D11—44no—
265C2×C4×D11—44no—
266C2×C4×D11—416no—
267C2×C4×D11—416no—
268C11×C4⋊C4—28no—
269C11×C4⋊C4C2×D4116yescomplemented
270C11×C22⋊C4—28no—
271C11×C22⋊C4—28no—
272C11×C22⋊C4—28no—
273C22⋊Dic11—28no—
274C22⋊Dic11—28no—
275C22⋊Dic11—28no—
276C22⋊Dic11—28no—
277C22⋊Dic11—28no—
278C22⋊Dic11—44no—
279(C2×D11)⋊C4—28no—
280(C2×D11)⋊C4—28no—
281C4⋊Dic11—28no—
282C4⋊Dic11—28no—
283Dic11⋊C4—28no—
284Dic11⋊C4—28no—
285Dic11⋊C4—28no—
286Dic11⋊C4—44no—
287C4×Dic11—28no—
288C22×#123D1111yescharacteristic, complemented
289C22×#121—111no—
290C22×C4×D4—111no—
291C23×C4⋊C4—111no—
292#2443—1116no—
293C2×#399—111no—
294C2×#398—111no—
295C2×#397—111no—
296C2×#394—111no—
297C2×#388—111no—
298C2×#387—111no—
299C2×#386—111no—
300C2×#386—111no—
301C2×#386—111no—
302C2×#385—111no—
303C2×#385—111no—
304C23×C11—28no—
305C23×C11—28no—
306C23×C11—28no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—44no—
321C23×C11—44no—
322C23×C11—44no—
323C23×C11—44no—
324C23×C11—44no—
325C23×C11—44no—
326C23×C11—44no—
327C23×C11—44no—
328C23×C11—44no—
329C23×C11—44no—
330C23×C11—44no—
331C23×C11C22×D414yes—
332C23×C11C22×D412yes—
333C23×C11C22×D412yes—
334C23×C11C2×#4112yes—
335C23×C11C2×#4112yes—
336C23×C11C2×#4112yes—
337C23×C11H(5,𝔽2)12yes—
338C23×C112−1+412yes—
339C23×C11C2511yescharacteristic
340C22×D11—28no—
341C22×D11—28no—
342C22×D11—28no—
343C22×D11—28no—
344C22×D11—28no—
345C22×D11—28no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11#123116yescomplemented
351C22×D11C22×D414yes—
352C22×D11C2×#4114yes—
353C22×D11C2×#4114yes—
354D4×C11—416no—
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—416no—
371C2×C4×C11—44no—
372C2×C4×C11—44no—
373C2×C4×C11C22×D414yes—
374C2×C4×C11C22×D414yes—
375C2×C4×C11C22×D414yes—
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—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—44no—
400C2×Dic11—44no—
401C2×Dic11—44no—
402C2×Dic11—44no—
403C2×Dic11—44no—
404C2×Dic11C22×D414yes—
405C2×Dic11C2×#4114yes—
406C4×D11—232no—
407C4×D11—416no—
408C4×D11—416no—
409C23×D4—111no—
410C23×D4—111no—
411C23×D4C2×D1111yescharacteristic
412C24×C4—111no—
413C24×C4—111no—
414C24×C4—111no—
415C24×C4C2×D1111yescharacteristic
416C2×#123—28no—
417C2×#123C2×D1118yescomplemented
418C2×#121—118no—
419C2×#121—228no—
420C2×C4×D4—118no—
421C2×C4×D4—228no—
422C22×C4⋊C4—111no—
423C22×C4⋊C4—111no—
424C22×C4⋊C4—111no—
425C22×C4⋊C4—111no—
426C22×C4⋊C4—111no—
427C22×C4⋊C4—111no—
428C22×C4⋊C4—118no—
429C22×C4⋊C4—228no—
430C22×C4⋊C4C2×D1111yescharacteristic
431C22×C4⋊C4C2×D1111yescharacteristic
432C22×C22⋊C4—111no—
433C22×C22⋊C4—111no—
434C22×C22⋊C4—111no—
435C22×C22⋊C4—111no—
436C22×C22⋊C4—111no—
437C22×C22⋊C4—111no—
438C22×C22⋊C4—111no—
439C22×C22⋊C4—111no—
440C22×C22⋊C4C2×D1111yescharacteristic
441C22×C22⋊C4C2×D1111yescharacteristic
442C22×C22⋊C4C2×D1111yescharacteristic
443C22×C42—111no—
444#399—118no—
445#398—118no—
446#397—118no—
447#394—118no—
448#388—118no—
449#387—118no—
450#386—118no—
451#386—118no—
452#386—118no—
453#385—118no—
454#385—118no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95—111no—
461C2×#95—111no—
462C2×#95—111no—
463C22×C11—24no—
464C22×C11—24no—
465C22×C11—24no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—416no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—88no—
479C22×C11C2×#12314yes—
480C22×C11#52514yes—
481C22×C11#53914yes—
482C22×C11D4214yes—
483C22×C11#54714yes—
484C22×C11#54814yes—
485C22×C11#55314yes—
486C22×C11C23×D411yescharacteristic
487C22×C11C23×D411yescharacteristic
488C22×C11C22×#4111yescharacteristic
489C22×C11C22×#4111yescharacteristic
490C22×C11C22×#4111yescharacteristic
491C22×C11C2×H(5,𝔽2)11yescharacteristic
492C22×C11C2×2−1+411yescharacteristic
493C2×D11—24no—
494C2×D11—24no—
495C2×D11—24no—
496C2×D11—24no—
497C2×D11—24no—
498C2×D11—232no—
499C2×D11—24no—
500C2×D11C2×#12318yescomplemented
501C4×C11—24no—
502C4×C11—24no—
503C4×C11—24no—
504C4×C11—42no—
505C4×C11—42no—
506Dic11—24no—
507Dic11—24no—
508Dic11—42no—
509Dic11—42no—
510Dic11—42no—
511Dic11—42no—
512Dic11—42no—
513C25—111no—
514C25C22×D1111yescharacteristic
515C25C22×D1111yescharacteristic
516C22×D4—24no—
517C22×D4—24no—
518C22×D4—42no—
519C22×D4—118no—
520C22×D4—114no—
521C22×D4—114no—
522C22×D4—224no—
523C22×D4—224no—
524C22×D4—224no—
525C22×D4—224no—
526C22×D4—224no—
527C22×D4C22×D1114yes—
528C23×C4—24no—
529C23×C4—24no—
530C23×C4—42no—
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
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—224no—
548C23×C4—442no—
549C23×C4—442no—
550C23×C4C22×D1111yescharacteristic
551C23×C4C22×D1111yescharacteristic
552C23×C4C22×D1114yes—
553C23×C4C22×D1111yescharacteristic
554C23×C4C22×D1111yescharacteristic
555C23×C4C22×D1111yescharacteristic
556#123—232no—
557#121—2232no—
558C4×D4—2232no—
559C2×C4⋊C4—24no—
560C2×C4⋊C4—114no—
561C2×C4⋊C4—114no—
562C2×C4⋊C4—114no—
563C2×C4⋊C4—114no—
564C2×C4⋊C4—114no—
565C2×C4⋊C4—114no—
566C2×C4⋊C4—224no—
567C2×C4⋊C4—224no—
568C2×C4⋊C4—224no—
569C2×C4⋊C4—224no—
570C2×C4⋊C4—224no—
571C2×C4⋊C4—2232no—
572C2×C4⋊C4—442no—
573C2×C4⋊C4C22⋊D1118yescomplemented
574C2×C4⋊C4C22×D1114yes—
575C2×C4⋊C4C22×D1114yes—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—24no—
579C2×C22⋊C4—114no—
580C2×C22⋊C4—114no—
581C2×C22⋊C4—114no—
582C2×C22⋊C4—114no—
583C2×C22⋊C4—114no—
584C2×C22⋊C4—114no—
585C2×C22⋊C4—114no—
586C2×C22⋊C4—114no—
587C2×C22⋊C4—224no—
588C2×C22⋊C4—224no—
589C2×C22⋊C4—224no—
590C2×C22⋊C4—224no—
591C2×C22⋊C4—224no—
592C2×C22⋊C4—224no—
593C2×C22⋊C4—224no—
594C2×C22⋊C4—442no—
595C2×C22⋊C4C22×D1114yes—
596C2×C22⋊C4C22×D1114yes—
597C2×C22⋊C4C22×D1114yes—
598C2×C42—114no—
599C2×C42—224no—
600#95—114no—
601#95—114no—
602#95—114no—
603#95—114no—
604#95—114no—
605#95—114no—
606#95—114no—
607#95—114no—
608C2×C11—44no—
609C2×C11—82no—
610C2×C11#244318yescomplemented
611C2×C11C22×#12311yescharacteristic
612C2×C11C2×#52511yescharacteristic
613C2×C11C2×#53911yescharacteristic
614C2×C11C2×D4211yescharacteristic
615C2×C11C2×#54711yescharacteristic
616C2×C11C2×#54811yescharacteristic
617C2×C11C2×#55311yescharacteristic
618D11—28no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—114no—
633C24—114no—
634C24—114no—
635C24—112no—
636C24—222no—
637C24—222no—
638C24—222no—
639C24—222no—
640C24D4×D1114yes—
641C24C23×D1112yes—
642C24C23×D1112yes—
643C24C23×D1111yescharacteristic
644C2×D4—28no—
645C2×D4—28no—
646C2×D4—44no—
647C2×D4—416no—
648C2×D4—1116no—
649C2×D4—2232no—
650C2×D4—228no—
651C2×D4—228no—
652C2×D4—228no—
653C2×D4—228no—
654C2×D4—228no—
655C2×D4—4416no—
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—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—28no—
670C22×C4—44no—
671C22×C4—416no—
672C22×C4—114no—
673C22×C4—114no—
674C22×C4—112no—
675C22×C4—112no—
676C22×C4—112no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—228no—
682C22×C4—228no—
683C22×C4—2232no—
684C22×C4—228no—
685C22×C4—228no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—228no—
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—222no—
700C22×C4—222no—
701C22×C4—222no—
702C22×C4—222no—
703C22×C4—222no—
704C22×C4—222no—
705C22×C4—222no—
706C22×C4—228no—
707C22×C4—228no—
708C22×C4—444no—
709C22×C4—444no—
710C22×C4—4416no—
711C22×C4—4416no—
712C22×C4C2×C22⋊D1114yes—
713C22×C4C2×C22⋊D1114yes—
714C22×C4C2×C22⋊D1114yes—
715C22×C4C23×D1112yes—
716C22×C4C23×D1112yes—
717C22×C4C23×D1112yes—
718C22×C4C23×D1112yes—
719C22×C4C23×D1112yes—
720C4⋊C4—28no—
721C4⋊C4—228no—
722C4⋊C4—228no—
723C4⋊C4—228no—
724C4⋊C4—228no—
725C4⋊C4—228no—
726C4⋊C4—444no—
727C4⋊C4C2×C22⋊D11116yescomplemented
728C22⋊C4—28no—
729C22⋊C4—28no—
730C22⋊C4—28no—
731C22⋊C4—228no—
732C22⋊C4—228no—
733C22⋊C4—228no—
734C22⋊C4—228no—
735C22⋊C4—228no—
736C22⋊C4—228no—
737C22⋊C4—228no—
738C22⋊C4—444no—
739C42—228no—
740C11C2×#244311yescharacteristic, complemented, Sylow
741C23—28no—
742C23—28no—
743C23—28no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—1116no—
769C23—114no—
770C23—114no—
771C23—114no—
772C23—228no—
773C23—228no—
774C23—228no—
775C23—228no—
776C23—222no—
777C23—228no—
778C23—228no—
779C23—222no—
780C23—222no—
781C23—222no—
782C23C2×D4×D1114yes—
783C23C2×D4×D1112yes—
784C23#6703712yes—
785C23#41×D1112yes—
786C23#41×D1112yes—
787C23#41×D1112yes—
788C23#6704312yes—
789C23C22×C22⋊D1112yes—
790C23C24×D1111yescharacteristic
791D4—416no—
792D4—2232no—
793D4—4416no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
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—416no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—114no—
813C2×C4—114no—
814C2×C4—2232no—
815C2×C4—228no—
816C2×C4—228no—
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—222no—
830C2×C4—222no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—222no—
835C2×C4—222no—
836C2×C4—4416no—
837C2×C4—4416no—
838C2×C4—444no—
839C2×C4—444no—
840C2×C4—444no—
841C2×C4—444no—
842C2×C4—444no—
843C2×C4C22×C22⋊D1114yes—
844C2×C4C22×C22⋊D1114yes—
845C2×C4C22×C22⋊D1114yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—42no—
850C22—42no—
851C22—416no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—88no—
862C22—118no—
863C22—224no—
864C22—224no—
865C22—224no—
866C22—224no—
867C22—2232no—
868C22—224no—
869C22—224no—
870C22D11×#12314yes—
871C22#1062318614yes—
872C22#1062319114yes—
873C22#1062319214yes—
874C22D4×C22⋊D1114yes—
875C22#1062335914yes—
876C22#1062336214yes—
877C22C22×D4×D1111yescharacteristic
878C22C2×#6703711yescharacteristic
879C22C2×#41×D1111yescharacteristic
880C22C2×#41×D1111yescharacteristic
881C22C2×#41×D1111yescharacteristic
882C22C2×#6704311yescharacteristic
883C22C23×C22⋊D1111yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—42no—
888C4—42no—
889C4—224no—
890C4—224no—
891C4—442no—
892C4—442no—
893C4—442no—
894C4—442no—
895C4—442no—
896C2—44no—
897C2—82no—
898C2—228no—
899C2#1307234818yesdirect product factor
900C2C2×D11×#12311yescharacteristic
901C2C2×#1062335911yescharacteristic
902C2C2×#1062319111yescharacteristic
903C2C2×D4×C22⋊D1111yescharacteristic
904C2C2×#1062318611yescharacteristic
905C2C2×#1062336211yescharacteristic
906C2C2×#1062319211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#123C2
socleC24×C11C24
prime radicalC22×#66991C2
hypercenterC22×#123D11
hypocenterC11C2×#2443
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D11C2semidirect
3. C22×C4⋊C4×D11C2semidirect
4. #13072348C2direct (N × H)
5. C2×#10622562C2semidirect
6. C2×#10622597C2semidirect
7. C2×#10622566C2semidirect
8. C2×#10622835C2semidirect
9. C2×#10622558C2semidirect
10. C2×#10622594C2semidirect
11. C2×#10622569C2semidirect
12. C2×#10622569C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622823C2semidirect
15. C2×#10622602C2semidirect
16. C22×C11×#123C2semidirect
25. C2×C11×#123C22semidirect
40. C2×C4×C22⋊D11C22semidirect
51. C2×C4⋊C4×D11C22semidirect
52. #10622835C22semidirect
53. #10622823C22semidirect
62. #10622602C22semidirect
63. #10622597C22semidirect
64. #10622594C22semidirect
65. #10622569C22semidirect
66. #10622569C22semidirect
67. #10622569C22semidirect
68. #10622566C22semidirect
69. #10622562C22semidirect
70. #10622558C22semidirect
116. C2×C11×C4⋊C4D4semidirect
269. C11×C4⋊C4C2×D4semidirect
288. C22×#123D11semidirect
350. C22×D11#123semidirect
417. C2×#123C2×D11semidirect
500. C2×D11C2×#123semidirect
573. C2×C4⋊C4C22⋊D11semidirect
610. C2×C11#2443semidirect
727. C4⋊C4C2×C22⋊D11semidirect
740. C11C2×#2443semidirect
899. C2#13072348direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669912
C22×C4×C22⋊D112
C22×C4⋊C4×D112
#130723482
C2×#106225622
C2×#106225972
C2×#106225662
C2×#106228352
C2×#106225582
C2×#106225942
C2×#106225692
C2×#106228232
C2×#106226022
C22×C11×#1232
C2×#244311