Finite Group Databasebeta

← C2×#13072163 #14921490

Subgroups — C2×#13072163 #14921490

Order 2816.

3938 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×#66982C211yesmaximal, characteristic, complemented
2C22×#66992C211yesmaximal, characteristic
3C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
4#13072163C2116yesmaximal, direct product factor
5C2×#10622593C211yesmaximal, characteristic, complemented
6C2×#10622606C211yesmaximal, characteristic, complemented
7C2×#10622561C211yesmaximal, characteristic, complemented
8C2×#10622574C211yesmaximal, characteristic, complemented
9C2×#10622586C211yesmaximal, characteristic, complemented
10C2×#10622557C211yesmaximal, characteristic, complemented
11C2×#10622833C211yesmaximal, characteristic, complemented
12C2×#10622569C211yesmaximal, characteristic, complemented
13C2×#10622563C211yesmaximal, characteristic, complemented
14C2×#10622600C211yesmaximal, characteristic, complemented
15C22×C11⋊#95C211yesmaximal, characteristic, complemented
16C22×C11×#123C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C24×Dic11C2211yescharacteristic
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
35C2×#66992—28no—
36C2×#66992C2218yes—
37C2×#66982—28no—
38C2×#66982C2218yescomplemented
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
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×(C22⋊D11)⋊C4—28no—
51C2×(C22⋊D11)⋊C4C2218yescomplemented
52#10622833C2218yescomplemented
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2218yescomplemented
62#10622606C2218yescomplemented
63#10622600C2218yescomplemented
64#10622593C2218yescomplemented
65#10622586C2218yescomplemented
66#10622574C2218yescomplemented
67#10622569C2218yescomplemented
68#10622563C2218yescomplemented
69#10622561C2218yescomplemented
70#10622557C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C22×D4×C11—24no—
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11C2314yes—
78C23×C4×C11—24no—
79C23×C4×C11—24no—
80C23×C4×C11—24no—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2314yes—
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—42no—
92C22×C22⋊D11D418yes—
93C22×C22⋊D11C2314yes—
94C22×C22⋊D11C2314yes—
95C23×Dic11—24no—
96C23×Dic11—24no—
97C23×Dic11—24no—
98C23×Dic11—24no—
99C23×Dic11—42no—
100C23×Dic11—42no—
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2314yes—
106C23×Dic11C2314yes—
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C22×C4×D11—24no—
111C22×C4×D11—24no—
112C22×C4×D11—42no—
113C22×C4×D11C2314yes—
114C11×#123—232no—
115C2×C11×C4⋊C4—24no—
116C2×C11×C4⋊C4—24no—
117C2×C11×C4⋊C4C2314yes—
118C2×C11×C4⋊C4C2314yes—
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4—24no—
121C2×C11×C22⋊C4D418yescomplemented
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—42no—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2314yes—
133#66992—232no—
134#66982—232no—
135C2×(C2×D11)⋊C4—24no—
136C2×(C2×D11)⋊C4—24no—
137C2×(C2×D11)⋊C4—24no—
138C2×(C2×D11)⋊C4—24no—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2314yes—
143C2×C4⋊Dic11—24no—
144C2×C4⋊Dic11—42no—
145C2×C4⋊Dic11C2314yes—
146C2×C4⋊Dic11C2314yes—
147C2×Dic11⋊C4—24no—
148C2×Dic11⋊C4—24no—
149C2×Dic11⋊C4—24no—
150C2×Dic11⋊C4—24no—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×C4×Dic11—24no—
156C2×C4×Dic11C2314yes—
157(C22⋊D11)⋊C4—232no—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C2×#2425—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×C11C2×D414yes—
179C24×C11C2×D414yes—
180C24×C11#4114yes—
181C24×C11C2412yes—
182C24×C11C2412yes—
183C24×C11C2411yescharacteristic
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11—22no—
189C23×D11—22no—
190C23×D11C2×D414yes—
191C23×D11C2412yes—
192C2×D4×C11—28no—
193C2×D4×C11—28no—
194C2×D4×C11—28no—
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—28no—
208C22×C4×C11—28no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—416no—
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—28no—
221C2×C22⋊D11—232no—
222C2×C22⋊D11—28no—
223C2×C22⋊D11—28no—
224C2×C22⋊D11—28no—
225C2×C22⋊D11—44no—
226C2×C22⋊D11—416no—
227C2×C22⋊D11C2×D4116yes—
228C22×Dic11—28no—
229C22×Dic11—28no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—28no—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—22no—
238C22×Dic11—28no—
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×Dic11—22no—
248C22×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11—44no—
251C22×Dic11—44no—
252C22×Dic11—416no—
253C22×Dic11—416no—
254C22×Dic11C2×D414yes—
255C22×Dic11#4114yes—
256C22×Dic11#4114yes—
257C22×Dic11C2412yes—
258C22×Dic11C2412yes—
259C22×Dic11C2412yes—
260C22×Dic11C2412yes—
261C22×Dic11C2412yes—
262C22×Dic11C2412yes—
263C22×Dic11C2412yes—
264C2×C4×D11—28no—
265C2×C4×D11—28no—
266C2×C4×D11—44no—
267C2×C4×D11—416no—
268C11×C4⋊C4—28no—
269C11×C4⋊C4—28no—
270C11×C22⋊C4—28no—
271C11×C22⋊C4—28no—
272C11×C22⋊C4C2×D4116yescomplemented
273C22⋊Dic11—28no—
274C22⋊Dic11—28no—
275C22⋊Dic11—28no—
276C22⋊Dic11—44no—
277(C2×D11)⋊C4—28no—
278(C2×D11)⋊C4—28no—
279(C2×D11)⋊C4—28no—
280(C2×D11)⋊C4—28no—
281C4⋊Dic11—28no—
282C4⋊Dic11—44no—
283Dic11⋊C4—28no—
284Dic11⋊C4—28no—
285Dic11⋊C4—28no—
286Dic11⋊C4—28no—
287C4×Dic11—28no—
288C22×#123—111no—
289C22×#123D1111yescharacteristic, complemented
290C22×#121—111no—
291C22×C4×D4—111no—
292#2425—1116no—
293C2×#398—111no—
294C2×#397—111no—
295C2×#396—111no—
296C2×#394—111no—
297C2×#389—111no—
298C2×#388—111no—
299C2×#386—111no—
300C2×#386—111no—
301C2×#385—111no—
302C2×#380—111no—
303C22×#95—111no—
304C23×C11—28no—
305C23×C11—28no—
306C23×C11—28no—
307C23×C11—28no—
308C23×C11—28no—
309C23×C11—28no—
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—22no—
321C23×C11—44no—
322C23×C11—44no—
323C23×C11—44no—
324C23×C11—44no—
325C23×C11—44no—
326C23×C11—44no—
327C23×C11—44no—
328C23×C11#121116yes—
329C23×C11C22×D414yes—
330C23×C11C22×D412yes—
331C23×C11C22×D414yes—
332C23×C11C22×D412yes—
333C23×C11C2×#4114yes—
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—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—44no—
350C22×D11—44no—
351C22×D11—44no—
352C22×D11—44no—
353C22×D11C22×D414yes—
354D4×C11—416no—
355C2×C4×C11—28no—
356C2×C4×C11—28no—
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—416no—
371C2×C4×C11—44no—
372C2×C4×C11—44no—
373C2×C4×C11—44no—
374C2×C4×C11C22×D414yes—
375C2×C4×C11C22×D414yes—
376C22⋊D11—232no—
377C22⋊D11—416no—
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—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—416no—
400C2×Dic11—416no—
401C2×Dic11—44no—
402C2×Dic11—44no—
403C2×Dic11—44no—
404C2×Dic11—44no—
405C2×Dic11C22×D414yes—
406C2×Dic11C2×#4114yes—
407C2×Dic11C2×#4114yes—
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×#123—118no—
418C2×#123—228no—
419C2×#123C2×D1118yescomplemented
420C2×#121—118no—
421C2×#121—228no—
422C2×C4×D4—118no—
423C2×C4×D4—228no—
424C22×C4⋊C4—111no—
425C22×C4⋊C4—111no—
426C22×C4⋊C4—111no—
427C22×C4⋊C4—111no—
428C22×C4⋊C4—111no—
429C22×C4⋊C4—111no—
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#398—118no—
445#397—118no—
446#396—118no—
447#394—118no—
448#389—118no—
449#388—118no—
450#386—118no—
451#386—118no—
452#385—118no—
453#380—118no—
454C2×#95—111no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95—111no—
461C2×#95—111no—
462C2×#95—118no—
463C22×C11—24no—
464C22×C11—232no—
465C22×C11—24no—
466C22×C11—24no—
467C22×C11—24no—
468C22×C11—24no—
469C22×C11—24no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—88no—
478C22×C11C2×#12118yes—
479C22×C11C2×#12114yes—
480C22×C11#52914yes—
481C22×C11#53914yes—
482C22×C11#54614yes—
483C22×C11#54614yes—
484C22×C11#54714yes—
485C22×C11#54714yes—
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—42no—
497C2×D11—416no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—42no—
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—
512Dic11—42no—
513C25—111no—
514C25C22×D1111yescharacteristic
515C25C22×D1111yescharacteristic
516C22×D4—24no—
517C22×D4—24no—
518C22×D4—24no—
519C22×D4—118no—
520C22×D4—114no—
521C22×D4—114no—
522C22×D4—224no—
523C22×D4—224no—
524C22×D4—224no—
525C22×D4—224no—
526C22×D4—442no—
527C22×D4C22×D1114yes—
528C23×C4—24no—
529C23×C4—24no—
530C23×C4—24no—
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—442no—
548C23×C4—442no—
549C23×C4—442no—
550C23×C4C22×D1114yes—
551C23×C4C22×D1111yescharacteristic
552C23×C4C22×D1111yescharacteristic
553C23×C4C22×D1111yescharacteristic
554C23×C4C22×D1111yescharacteristic
555C23×C4C22×D1111yescharacteristic
556#123—232no—
557#123—2232no—
558#121—2232no—
559C4×D4—2232no—
560C2×C4⋊C4—24no—
561C2×C4⋊C4—24no—
562C2×C4⋊C4—114no—
563C2×C4⋊C4—114no—
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—224no—
571C2×C4⋊C4—224no—
572C2×C4⋊C4—224no—
573C2×C4⋊C4—442no—
574C2×C4⋊C4C22×D1114yes—
575C2×C4⋊C4C22×D1114yes—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—114no—
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—224no—
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—442no—
594C2×C22⋊C4C22⋊D1118yescomplemented
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—28no—
609C2×C11—82no—
610C2×C11#242518yescomplemented
611C2×C11C22×#12111yescharacteristic
612C2×C11C2×#52911yescharacteristic
613C2×C11C2×#53911yescharacteristic
614C2×C11C2×#54611yescharacteristic
615C2×C11C2×#54611yescharacteristic
616C2×C11C2×#54711yescharacteristic
617C2×C11C2×#54711yescharacteristic
618D11—44no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—114no—
631C24—112no—
632C24—222no—
633C24—222no—
634C24—222no—
635C24—222no—
636C24—222no—
637C24—222no—
638C24D4×D1114yes—
639C24#434114yes—
640C24C2×C22⋊D1114yes—
641C24C23×D1112yes—
642C24C23×D1112yes—
643C24C23×D1111yescharacteristic
644C2×D4—28no—
645C2×D4—28no—
646C2×D4—28no—
647C2×D4—416no—
648C2×D4—1116no—
649C2×D4—228no—
650C2×D4—2232no—
651C2×D4—228no—
652C2×D4—228no—
653C2×D4—228no—
654C2×D4—444no—
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—28no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—28no—
672C22×C4—416no—
673C22×C4—114no—
674C22×C4—114no—
675C22×C4—114no—
676C22×C4—112no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—228no—
684C22×C4—228no—
685C22×C4—228no—
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—228no—
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—228no—
706C22×C4—228no—
707C22×C4—444no—
708C22×C4—4416no—
709C22×C4—444no—
710C22×C4—444no—
711C22×C4—4416no—
712C22×C4—4416no—
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—28no—
722C4⋊C4—228no—
723C4⋊C4—228no—
724C4⋊C4—228no—
725C4⋊C4—228no—
726C4⋊C4—228no—
727C4⋊C4—444no—
728C22⋊C4—28no—
729C22⋊C4—28no—
730C22⋊C4—228no—
731C22⋊C4—228no—
732C22⋊C4—228no—
733C22⋊C4—228no—
734C22⋊C4—228no—
735C22⋊C4—228no—
736C22⋊C4—228no—
737C22⋊C4—444no—
738C22⋊C4C2×C22⋊D11116yescomplemented
739C42—228no—
740C11C2×#242511yescharacteristic, complemented, Sylow
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—28no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—114no—
766C23—228no—
767C23—228no—
768C23—228no—
769C23—222no—
770C23—222no—
771C23—222no—
772C23—222no—
773C23—222no—
774C23—222no—
775C23—444no—
776C23—444no—
777C23—444no—
778C23—444no—
779C23#66991116yes—
780C23C2×D4×D1114yes—
781C23C2×D4×D1112yes—
782C23C2×#434114yes—
783C23C2×#434112yes—
784C23#41×D1112yes—
785C23#41×D1112yes—
786C23#6704212yes—
787C23#6704312yes—
788C23C22×C22⋊D1114yes—
789C23C22×C22⋊D1112yes—
790C23C24×D1111yescharacteristic
791D4—416no—
792D4—2232no—
793D4—4416no—
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—416no—
810C2×C4—44no—
811C2×C4—44no—
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—222no—
835C2×C4—222no—
836C2×C4—222no—
837C2×C4—4416no—
838C2×C4—4416no—
839C2×C4—4416no—
840C2×C4—444no—
841C2×C4—444no—
842C2×C4—444no—
843C2×C4—444no—
844C2×C4C22×C22⋊D1114yes—
845C2×C4C22×C22⋊D1114yes—
846C22—24no—
847C22—232no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—24no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—88no—
861C22—224no—
862C22—224no—
863C22—224no—
864C22—442no—
865C22—4416no—
866C22—442no—
867C22—442no—
868C22—442no—
869C22#1062318014yes—
870C22#1062318514yes—
871C22#1062318614yes—
872C22#1062319614yes—
873C22C2×#6699118yes—
874C22C2×#6699114yes—
875C22#1062335514yes—
876C22#1062336014yes—
877C22C22×D4×D1111yescharacteristic
878C22C22×#434111yescharacteristic
879C22C2×#41×D1111yescharacteristic
880C22C2×#41×D1111yescharacteristic
881C22C2×#6704211yescharacteristic
882C22C2×#6704311yescharacteristic
883C22C23×C22⋊D1111yescharacteristic
884C4—24no—
885C4—24no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—224no—
890C4—224no—
891C4—224no—
892C4—442no—
893C4—442no—
894C4—442no—
895C4—442no—
896C2—28no—
897C2—82no—
898C2—444no—
899C2#1307216318yesdirect product factor
900C2C22×#6699111yescharacteristic
901C2C2×#1062318011yescharacteristic
902C2C2×#1062319611yescharacteristic
903C2C2×#1062336011yescharacteristic
904C2C2×#1062318511yescharacteristic
905C2C2×#1062318611yescharacteristic
906C2C2×#1062335511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#123C2
socleC24×C11C24
prime radicalC22×#66992C2
hypercenterC22×#123D11
hypocenterC11C2×#2425
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×#66982C2semidirect
3. C22×(C22⋊D11)⋊C4C2semidirect
4. #13072163C2direct (N × H)
5. C2×#10622593C2semidirect
6. C2×#10622606C2semidirect
7. C2×#10622561C2semidirect
8. C2×#10622574C2semidirect
9. C2×#10622586C2semidirect
10. C2×#10622557C2semidirect
11. C2×#10622833C2semidirect
12. C2×#10622569C2semidirect
13. C2×#10622563C2semidirect
14. C2×#10622600C2semidirect
15. C22×C11⋊#95C2semidirect
16. C22×C11×#123C2semidirect
25. C2×C11×#123C22semidirect
38. C2×#66982C22semidirect
51. C2×(C22⋊D11)⋊C4C22semidirect
52. #10622833C22semidirect
61. C2×C11⋊#95C22semidirect
62. #10622606C22semidirect
63. #10622600C22semidirect
64. #10622593C22semidirect
65. #10622586C22semidirect
66. #10622574C22semidirect
67. #10622569C22semidirect
68. #10622563C22semidirect
69. #10622561C22semidirect
70. #10622557C22semidirect
121. C2×C11×C22⋊C4D4semidirect
272. C11×C22⋊C4C2×D4semidirect
289. C22×#123D11semidirect
419. C2×#123C2×D11semidirect
594. C2×C22⋊C4C22⋊D11semidirect
610. C2×C11#2425semidirect
738. C22⋊C4C2×C22⋊D11semidirect
740. C11C2×#2425semidirect
899. C2#13072163direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669822
C22×#669922
C22×(C22⋊D11)⋊C42
#130721632
C2×#106225932
C2×#106226062
C2×#106225612
C2×#106225742
C2×#106225862
C2×#106225572
C2×#106228332
C2×#106225692
C2×#106225632
C2×#106226002
C22×C11⋊#952
C22×C11×#1232
C2×#242511