Finite Group Databasebeta

← C2×#13072167 #14921495

Subgroups — C2×#13072167 #14921495

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×#66982C211yesmaximal, characteristic, complemented
3C22×#66983C211yesmaximal, characteristic
4C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
5#13072167C2116yesmaximal, direct product factor
6C2×#10622270C211yesmaximal, characteristic, complemented
7C2×#10622288C211yesmaximal, characteristic, complemented
8C2×#10622289C211yesmaximal, characteristic, complemented
9C2×#10622285C211yesmaximal, characteristic, complemented
10C2×#10622260C211yesmaximal, characteristic, complemented
11C2×#10622282C211yesmaximal, characteristic, complemented
12C2×#10622826C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622823C211yesmaximal, characteristic, complemented
15C2×#10622280C211yesmaximal, characteristic, complemented
16C22×C11×#95C211yesmaximal, characteristic, complemented
17C24×C4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×D44C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C2×#66983—28no—
27C2×#66983C2218yes—
28C2×#66982—28no—
29C2×#66982—28no—
30C2×#66982C2218yescomplemented
31C2×#66982C2218yescomplemented
32C2×C4×C22⋊D11—28no—
33C2×C4×C22⋊D11C2218yescomplemented
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×C4⋊Dic11C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×Dic11⋊C4C2211yescharacteristic
50C22×Dic11⋊C4C2211yescharacteristic
51C22×C4×Dic11C2211yescharacteristic
52C2×C11×#95C2211yescharacteristic
53C2×C11×#95C2211yescharacteristic
54C2×C11×#95C2211yescharacteristic
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2218yescomplemented
57#10622826C2218yescomplemented
58#10622823C2218yescomplemented
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63#10622289C2218yescomplemented
64#10622288C2218yescomplemented
65#10622285C2218yescomplemented
66#10622282C2218yescomplemented
67#10622280C2218yescomplemented
68#10622278C2218yescomplemented
69#10622270C2218yescomplemented
70#10622260C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C23×C4×C11—24no—
75C23×C4×C11—24no—
76C23×C4×C11—24no—
77C23×C4×C11—24no—
78C23×C4×C11—24no—
79C23×C4×C11—24no—
80C23×C4×C11—24no—
81C23×C4×C11—42no—
82C23×C4×C11—42no—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2314yes—
88C23×C4×C11C2314yes—
89C23×C4×C11C2314yes—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C22×C22⋊D11—24no—
93C22×C22⋊D11—24no—
94C22×C22⋊D11—24no—
95C22×C22⋊D11—24no—
96C22×C22⋊D11—24no—
97C22×C22⋊D11D418yes—
98C22×C22⋊D11C2314yes—
99C22×C22⋊D11C2314yes—
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C22×D44—24no—
107C22×D44—24no—
108C22×D44—42no—
109C22×D44C2314yes—
110C22×C4×D11—24no—
111C22×C4×D11—24no—
112C22×C4×D11—42no—
113C22×C4×D11C2314yes—
114C2×C22⋊Dic11—24no—
115C2×C22⋊Dic11D418yescomplemented
116C2×C22⋊Dic11C2314yes—
117C2×C22⋊Dic11C2314yes—
118#66983—232no—
119#66982—232no—
120#66982—232no—
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—24no—
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4—42no—
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×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×C4⋊Dic11—24no—
141C2×C4⋊Dic11C2314yes—
142C2×Dic11⋊C4—24no—
143C2×Dic11⋊C4—24no—
144C2×Dic11⋊C4—24no—
145C2×Dic11⋊C4—24no—
146C2×Dic11⋊C4—24no—
147C2×Dic11⋊C4—24no—
148C2×Dic11⋊C4—42no—
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×Dic11⋊C4C2314yes—
156C2×C4×Dic11—24no—
157C2×C4×Dic11C2314yes—
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×C11C2×D414yes—
172C24×C11C2×D414yes—
173C24×C11#4114yes—
174C24×C11C2412yes—
175C24×C11C2411yescharacteristic
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×D11—22no—
187C23×D11—22no—
188C23×D11—22no—
189C23×D11C2×D414yes—
190C23×D11C2412yes—
191C23×D11C2412yes—
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—28no—
203C22×C4×C11—28no—
204C22×C4×C11—28no—
205C22×C4×C11—28no—
206C22×C4×C11—28no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—28no—
214C22×C4×C11—28no—
215C22×C4×C11—44no—
216C22×C4×C11—44no—
217C22×C4×C11—416no—
218C22×C4×C11—416no—
219C22×C4×C11—416no—
220C22×C4×C11#4114yes—
221C22×C4×C11#4114yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2412yes—
226C22×C4×C11C2412yes—
227C22×C4×C11C2412yes—
228C2×C22⋊D11—232no—
229C2×C22⋊D11—28no—
230C2×C22⋊D11—28no—
231C2×C22⋊D11—28no—
232C2×C22⋊D11—28no—
233C2×C22⋊D11—28no—
234C2×C22⋊D11—416no—
235C2×C22⋊D11C2×D4116yes—
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×Dic11—22no—
248C22×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11C2×D414yes—
252C22×Dic11C2×D414yes—
253C22×Dic11C2×D414yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C22×Dic11C2412yes—
259C22×Dic11C2412yes—
260C2×D44—28no—
261C2×D44—28no—
262C2×D44—44no—
263C2×D44—416no—
264C2×C4×D11—28no—
265C2×C4×D11—28no—
266C2×C4×D11—44no—
267C2×C4×D11—416no—
268C22⋊Dic11—28no—
269C22⋊Dic11C2×D4116yescomplemented
270(C2×D11)⋊C4—28no—
271(C2×D11)⋊C4—28no—
272(C2×D11)⋊C4—28no—
273(C2×D11)⋊C4—28no—
274(C2×D11)⋊C4—28no—
275(C2×D11)⋊C4—28no—
276(C2×D11)⋊C4—28no—
277(C2×D11)⋊C4—28no—
278(C2×D11)⋊C4—44no—
279C4⋊Dic11—28no—
280Dic11⋊C4—28no—
281Dic11⋊C4—28no—
282Dic11⋊C4—28no—
283Dic11⋊C4—28no—
284Dic11⋊C4—28no—
285Dic11⋊C4—28no—
286Dic11⋊C4—44no—
287C4×Dic11—28no—
288C22×#123—111no—
289C22×#123—111no—
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×#95D1111yescharacteristic, complemented
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#121116yes—
315C23×C11C22×D414yes—
316C23×C11C22×D414yes—
317C23×C11C22×D412yes—
318C23×C11C22×D412yes—
319C23×C11C2×#4114yes—
320C23×C11C2×#4112yes—
321C23×C11C2×#4112yes—
322C23×C11C2×#4112yes—
323C23×C11H(5,𝔽2)12yes—
324C23×C112−1+412yes—
325C23×C11C2511yescharacteristic
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—22no—
342C22×D11—44no—
343C22×D11—44no—
344C22×D11—44no—
345C22×D11—44no—
346C22×D11—44no—
347C22×D11—44no—
348C22×D11—44no—
349C22×D11—44no—
350C22×D11—44no—
351C22×D11—44no—
352C22×D11—44no—
353C22×D11C22×D414yes—
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—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—416no—
373C2×C4×C11—416no—
374C2×C4×C11—416no—
375C2×C4×C11—44no—
376C2×C4×C11—44no—
377C2×C4×C11—44no—
378C2×C4×C11—44no—
379C2×C4×C11C2×#4114yes—
380C2×C4×C11C2×#4114yes—
381C22⋊D11—232no—
382C22⋊D11—416no—
383C2×Dic11—28no—
384C2×Dic11—28no—
385C2×Dic11—28no—
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—22no—
400C2×Dic11—22no—
401C2×Dic11—44no—
402C2×Dic11—44no—
403C2×Dic11—44no—
404C2×Dic11C22×D414yes—
405C2×Dic11C22×D414yes—
406C2×Dic11C22×D414yes—
407D44—416no—
408C4×D11—416no—
409C23×D4—111no—
410C23×D4—111no—
411C23×D4—111no—
412C24×C4—111no—
413C24×C4C2×D1111yescharacteristic
414C24×C4C2×D1111yescharacteristic
415C24×C4C2×D1111yescharacteristic
416C2×#123—118no—
417C2×#123—118no—
418C2×#123—228no—
419C2×#123—228no—
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⋊C4—111no—
431C22×C4⋊C4—111no—
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⋊C4—111no—
441C22×C22⋊C4—111no—
442C22×C22⋊C4—111no—
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×#95C2×D1111yescharacteristic
459C2×#95C2×D1111yescharacteristic
460C2×#95C2×D1111yescharacteristic
461C2×#95C2×D1111yescharacteristic
462C2×#95C2×D1118yescomplemented
463C22×C11—24no—
464C22×C11—232no—
465C22×C11—24no—
466C22×C11—24no—
467C22×C11—24no—
468C22×C11—24no—
469C22×C11—24no—
470C22×C11C2×#12118yes—
471C22×C11C2×#12114yes—
472C22×C11#52914yes—
473C22×C11#53914yes—
474C22×C11#54614yes—
475C22×C11#54614yes—
476C22×C11#54714yes—
477C22×C11#54714yes—
478C22×C11C23×D411yescharacteristic
479C22×C11C23×D411yescharacteristic
480C22×C11C22×#4111yescharacteristic
481C22×C11C22×#4111yescharacteristic
482C22×C11C22×#4111yescharacteristic
483C22×C11C2×H(5,𝔽2)11yescharacteristic
484C22×C11C2×2−1+411yescharacteristic
485C2×D11—24no—
486C2×D11—24no—
487C2×D11—24no—
488C2×D11—42no—
489C2×D11—416no—
490C2×D11—42no—
491C2×D11—42no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—88no—
501C4×C11—24no—
502C4×C11—24no—
503C4×C11—42no—
504C4×C11—42no—
505C4×C11—42no—
506C4×C11—42no—
507Dic11—24no—
508Dic11—24no—
509Dic11—24no—
510Dic11—42no—
511Dic11—42no—
512Dic11—42no—
513C25—111no—
514C25—111no—
515C25C22×D1111yescharacteristic
516C22×D4—118no—
517C22×D4—114no—
518C22×D4—114no—
519C22×D4—114no—
520C22×D4—224no—
521C22×D4—224no—
522C22×D4—224no—
523C22×D4—224no—
524C22×D4—224no—
525C22×D4—224no—
526C22×D4—224no—
527C22×D4—442no—
528C23×C4—24no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—24no—
532C23×C4—24no—
533C23×C4—24no—
534C23×C4—24no—
535C23×C4—42no—
536C23×C4—42no—
537C23×C4—111no—
538C23×C4—111no—
539C23×C4—111no—
540C23×C4—111no—
541C23×C4—111no—
542C23×C4—111no—
543C23×C4—114no—
544C23×C4—224no—
545C23×C4—224no—
546C23×C4—442no—
547C23×C4C22×D1114yes—
548C23×C4C22×D1111yescharacteristic
549C23×C4C22×D1111yescharacteristic
550C23×C4C22×D1111yescharacteristic
551C23×C4C22×D1111yescharacteristic
552C23×C4C22×D1114yes—
553C23×C4C22×D1114yes—
554C23×C4C22×D1111yescharacteristic
555C23×C4C22×D1111yescharacteristic
556#123—2232no—
557#123—2232no—
558#121—2232no—
559C4×D4—2232no—
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—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—224no—
574C2×C4⋊C4—224no—
575C2×C4⋊C4—442no—
576C2×C22⋊C4—118no—
577C2×C22⋊C4—114no—
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—114no—
587C2×C22⋊C4—114no—
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—224no—
595C2×C22⋊C4—224no—
596C2×C22⋊C4—224no—
597C2×C22⋊C4—442no—
598C2×C42—114no—
599C2×C42—224no—
600#95—114no—
601#95—114no—
602#95—114no—
603#95—114no—
604#95C22×D1114yes—
605#95C22×D1114yes—
606#95C22×D1114yes—
607#95C22×D1114yes—
608C2×C11—28no—
609C2×C11#242518yescomplemented
610C2×C11C22×#12111yescharacteristic
611C2×C11C2×#52911yescharacteristic
612C2×C11C2×#53911yescharacteristic
613C2×C11C2×#54611yescharacteristic
614C2×C11C2×#54611yescharacteristic
615C2×C11C2×#54711yescharacteristic
616C2×C11C2×#54711yescharacteristic
617D11—44no—
618D11—82no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—114no—
624C24—112no—
625C24—112no—
626C24—222no—
627C24—222no—
628C24—222no—
629C24—222no—
630C24—222no—
631C24—222no—
632C24—222no—
633C24—222no—
634C24—222no—
635C24—222no—
636C24—222no—
637C24—222no—
638C24—222no—
639C24#433914yes—
640C24D4×D1114yes—
641C24D4×D1114yes—
642C24C23×D1112yes—
643C24C23×D1111yescharacteristic
644C2×D4—1116no—
645C2×D4—228no—
646C2×D4—2232no—
647C2×D4—228no—
648C2×D4—228no—
649C2×D4—228no—
650C2×D4—228no—
651C2×D4—228no—
652C2×D4—228no—
653C2×D4—444no—
654C2×D4—4416no—
655C2×D4—4416no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—28no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—28no—
672C22×C4—28no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—28no—
678C22×C4—28no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—416no—
682C22×C4—416no—
683C22×C4—416no—
684C22×C4—114no—
685C22×C4—114no—
686C22×C4—114no—
687C22×C4—112no—
688C22×C4—112no—
689C22×C4—112no—
690C22×C4—112no—
691C22×C4—112no—
692C22×C4—112no—
693C22×C4—228no—
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—222no—
707C22×C4—222no—
708C22×C4—222no—
709C22×C4—228no—
710C22×C4—444no—
711C22×C4—4416no—
712C22×C4#433914yes—
713C22×C4#433914yes—
714C22×C4C23×D1112yes—
715C22×C4C23×D1112yes—
716C22×C4C23×D1112yes—
717C22×C4C23×D1112yes—
718C22×C4C23×D1112yes—
719C22×C4C23×D1112yes—
720C4⋊C4—228no—
721C4⋊C4—228no—
722C4⋊C4—228no—
723C4⋊C4—228no—
724C4⋊C4—228no—
725C4⋊C4—228no—
726C4⋊C4—228no—
727C4⋊C4—444no—
728C22⋊C4—1116no—
729C22⋊C4—228no—
730C22⋊C4—228no—
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×#242511yescharacteristic, complemented, Sylow
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—28no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—114no—
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—222no—
768C23—444no—
769C23—444no—
770C23—444no—
771C23—444no—
772C23—444no—
773C23—444no—
774C23—444no—
775C23—444no—
776C23—444no—
777C23—444no—
778C23—444no—
779C23#66937116yes—
780C23C2×#433914yes—
781C23C2×#433912yes—
782C23C2×#433912yes—
783C23C2×#433912yes—
784C23C2×D4×D1114yes—
785C23C2×D4×D1114yes—
786C23C2×D4×D1112yes—
787C23C2×D4×D1112yes—
788C23#6703712yes—
789C23#6704012yes—
790C23C24×D1111yescharacteristic
791D4—2232no—
792D4—4416no—
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—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—416no—
813C2×C4—416no—
814C2×C4—416no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—114no—
820C2×C4—114no—
821C2×C4—114no—
822C2×C4—228no—
823C2×C4—228no—
824C2×C4—228no—
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—222no—
838C2×C4—222no—
839C2×C4—222no—
840C2×C4—4416no—
841C2×C4—444no—
842C2×C4—444no—
843C2×C4—444no—
844C2×C4C2×#433914yes—
845C2×C4C2×#433914yes—
846C22—24no—
847C22—232no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—24no—
853C22—224no—
854C22—224no—
855C22—224no—
856C22—442no—
857C22—4416no—
858C22—442no—
859C22—442no—
860C22—442no—
861C22—442no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—442no—
866C22—442no—
867C22—442no—
868C22—888no—
869C22#1062301014yes—
870C22C2×#6693718yes—
871C22C2×#6693714yes—
872C22#1062302114yes—
873C22#1062302114yes—
874C22#1062303814yes—
875C22#1062303814yes—
876C22#1062304614yes—
877C22C22×#433911yescharacteristic
878C22C22×#433911yescharacteristic
879C22C22×#433911yescharacteristic
880C22C22×D4×D1111yescharacteristic
881C22C22×D4×D1111yescharacteristic
882C22C2×#6703711yescharacteristic
883C22C2×#6704011yescharacteristic
884C4—24no—
885C4—24no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—224no—
891C4—224no—
892C4—224no—
893C4—442no—
894C4—442no—
895C4—442no—
896C2—28no—
897C2—444no—
898C2—882no—
899C2#1307216718yesdirect product factor
900C2C22×#6693711yescharacteristic
901C2C2×#1062301011yescharacteristic
902C2C2×#1062304611yescharacteristic
903C2C2×#1062302111yescharacteristic
904C2C2×#1062302111yescharacteristic
905C2C2×#1062303811yescharacteristic
906C2C2×#1062303811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#95C2
socleC24×C11C24
prime radicalC22×#66983C2
hypercenterC22×#95D11
hypocenterC11C2×#2425
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
1. C22×#66982C2semidirect
2. C22×#66982C2semidirect
4. C22×C4×C22⋊D11C2semidirect
5. #13072167C2direct (N × H)
6. C2×#10622270C2semidirect
7. C2×#10622288C2semidirect
8. C2×#10622289C2semidirect
9. C2×#10622285C2semidirect
10. C2×#10622260C2semidirect
11. C2×#10622282C2semidirect
12. C2×#10622826C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622823C2semidirect
15. C2×#10622280C2semidirect
16. C22×C11×#95C2semidirect
30. C2×#66982C22semidirect
31. C2×#66982C22semidirect
33. C2×C4×C22⋊D11C22semidirect
56. C2×C11×#95C22semidirect
57. #10622826C22semidirect
58. #10622823C22semidirect
63. #10622289C22semidirect
64. #10622288C22semidirect
65. #10622285C22semidirect
66. #10622282C22semidirect
67. #10622280C22semidirect
68. #10622278C22semidirect
69. #10622270C22semidirect
70. #10622260C22semidirect
115. C2×C22⋊Dic11D4semidirect
269. C22⋊Dic11C2×D4semidirect
303. C22×#95D11semidirect
462. C2×#95C2×D11semidirect
609. C2×C11#2425semidirect
740. C11C2×#2425semidirect
899. C2#13072167direct (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×#669832
C22×C4×C22⋊D112
#130721672
C2×#106222702
C2×#106222882
C2×#106222892
C2×#106222852
C2×#106222602
C2×#106222822
C2×#106228262
C2×#106222782
C2×#106228232
C2×#106222802
C22×C11×#952
C2×#242511