Finite Group Databasebeta

← C2×#13073672 #14923848

Subgroups — C2×#13073672 #14923848

Order 2816.

3158 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66951C211yesmaximal, characteristic, complemented
2#13073672C2116yesmaximal, direct product factor
3C2×#10622596C211yesmaximal, characteristic, complemented
4C2×#10622561C211yesmaximal, characteristic, complemented
5C2×#10622574C211yesmaximal, characteristic, complemented
6C2×#10622836C211yesmaximal, characteristic
7C2×#10622834C211yesmaximal, characteristic, complemented
8C2×#10622570C211yesmaximal, characteristic, complemented
9C2×#10622570C211yesmaximal, characteristic, complemented
10C2×#10622558C211yesmaximal, characteristic, complemented
11C2×#10622603C211yesmaximal, characteristic, complemented
12C2×#10622557C211yesmaximal, characteristic, complemented
13C2×#10622826C211yesmaximal, characteristic, complemented
14C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
16C22×C11×#123C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C2×C11×#123—28no—
22C2×C11×#123C2218yescomplemented
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×C4⋊Dic11C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C22×C4×Dic11C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C2×#66951—28no—
49C2×#66951C2218yescomplemented
50#10622836C2218yes—
51#10622834C2218yescomplemented
52#10622826C2218yescomplemented
53C4×C22⋊Dic11C2218yescomplemented
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60#10622603C2218yescomplemented
61#10622596C2218yescomplemented
62C4⋊C4×Dic11C2218yescomplemented
63#10622574C2218yescomplemented
64#10622570C2218yescomplemented
65#10622570C2218yescomplemented
66#10622561C2218yescomplemented
67#10622558C2218yescomplemented
68#10622557C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C22×D4×C11—24no—
73C22×D4×C11—24no—
74C22×D4×C11—42no—
75C22×D4×C11C2314yes—
76C23×C4×C11—24no—
77C23×C4×C11—24no—
78C23×C4×C11—42no—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2314yes—
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C22×C22⋊D11—24no—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—42no—
89C22×C22⋊D11—42no—
90C22×C22⋊D11—42no—
91C22×C22⋊D11C2314yes—
92C22×C22⋊D11C2314yes—
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C11×#123—232no—
101C2×C11×C4⋊C4—24no—
102C2×C11×C4⋊C4D418yescomplemented
103C2×C11×C4⋊C4C2314yes—
104C2×C11×C4⋊C4C2314yes—
105C2×C11×C22⋊C4—24no—
106C2×C11×C22⋊C4—24no—
107C2×C11×C22⋊C4—24no—
108C2×C11×C22⋊C4C2314yes—
109C2×C11×C22⋊C4C2314yes—
110C2×C11×C22⋊C4C2314yes—
111C2×C22⋊Dic11—24no—
112C2×C22⋊Dic11—24no—
113C2×C22⋊Dic11—24no—
114C2×C22⋊Dic11—24no—
115C2×C22⋊Dic11—42no—
116C2×C22⋊Dic11—42no—
117C2×C22⋊Dic11C2314yes—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123C2×(C2×D11)⋊C4—24no—
124C2×(C2×D11)⋊C4—24no—
125C2×(C2×D11)⋊C4—24no—
126C2×(C2×D11)⋊C4—24no—
127C2×(C2×D11)⋊C4—42no—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×C4⋊Dic11—24no—
134C2×C4⋊Dic11—24no—
135C2×C4⋊Dic11C2314yes—
136C2×C4⋊Dic11C2314yes—
137C2×Dic11⋊C4—24no—
138C2×Dic11⋊C4—42no—
139C2×Dic11⋊C4—42no—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×C4×Dic11—24no—
144C2×C4×Dic11—24no—
145C2×C4×Dic11—42no—
146C2×C4×Dic11—42no—
147C2×C4×Dic11C2314yes—
148C2×C4×Dic11C2314yes—
149C2×C4×Dic11C2314yes—
150C2×C4×Dic11C2314yes—
151#66951—232no—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2554—111nomaximal, Sylow
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11#4114yes—
173C24×C11C2412yes—
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×D11C2412yes—
184C2×D4×C11—28no—
185C2×D4×C11—28no—
186C2×D4×C11—44no—
187C2×D4×C11—416no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
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—28no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—28no—
202C22×C4×C11—44no—
203C22×C4×C11—416no—
204C22×C4×C11C2×D414yes—
205C22×C4×C11C2×D414yes—
206C22×C4×C11C2×D414yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C2×C22⋊D11—28no—
213C2×C22⋊D11—28no—
214C2×C22⋊D11—28no—
215C2×C22⋊D11—44no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11—416no—
219C2×C22⋊D11—416no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
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#4114yes—
239C22×Dic11#4114yes—
240C22×Dic11#4114yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C11×C4⋊C4—28no—
249C11×C4⋊C4C2×D4116yescomplemented
250C11×C22⋊C4—28no—
251C11×C22⋊C4—28no—
252C11×C22⋊C4—28no—
253C22⋊Dic11—28no—
254C22⋊Dic11—28no—
255C22⋊Dic11—28no—
256C22⋊Dic11—28no—
257C22⋊Dic11—44no—
258C22⋊Dic11—44no—
259(C2×D11)⋊C4—28no—
260(C2×D11)⋊C4—28no—
261(C2×D11)⋊C4—28no—
262(C2×D11)⋊C4—28no—
263(C2×D11)⋊C4—44no—
264C4⋊Dic11—28no—
265C4⋊Dic11—28no—
266Dic11⋊C4—28no—
267Dic11⋊C4—44no—
268Dic11⋊C4—44no—
269C4×Dic11—28no—
270C4×Dic11—28no—
271C4×Dic11—44no—
272C4×Dic11—44no—
273C22×#126—111no—
274C22×#123D1111yescharacteristic, complemented
275#2554—1116no—
276C2×#398—111no—
277C2×#396—111no—
278C2×#394—111no—
279C2×#392—111no—
280C2×#390—111no—
281C2×#390—111no—
282C2×#390—111no—
283C2×#388—111no—
284C2×#388—111no—
285C2×#388—111no—
286C2×#386—111no—
287C2×C4×C4⋊C4—111no—
288C2×C4×C22⋊C4—111no—
289C23×C11—28no—
290C23×C11—28no—
291C23×C11—28no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—44no—
306C23×C11—44no—
307C23×C11—44no—
308C23×C11—44no—
309C23×C11—44no—
310C23×C11—44no—
311C23×C11—44no—
312C23×C11—44no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11—44no—
316C23×C11C22×D412yes—
317C23×C11C2×#4114yes—
318C23×C11C2×#4112yes—
319C23×C11C2×#4112yes—
320C23×C11C2×#4112yes—
321C23×C11C2×#4112yes—
322C23×C11H(5,𝔽2)12yes—
323C23×C11H(5,𝔽2)12yes—
324C23×C11C2511yescharacteristic
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—44no—
333C22×D11—44no—
334C22×D11—44no—
335C22×D11—44no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11—44no—
339D4×C11—416no—
340C2×C4×C11—28no—
341C2×C4×C11—28no—
342C2×C4×C11—28no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—416no—
356C2×C4×C11—44no—
357C2×C4×C11—44no—
358C2×C4×C11C22×D414yes—
359C2×C4×C11C22×D414yes—
360C2×C4×C11C22×D414yes—
361C22⋊D11—416no—
362C22⋊D11—416no—
363C2×Dic11—28no—
364C2×Dic11—28no—
365C2×Dic11—28no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—44no—
385C2×Dic11—44no—
386C2×Dic11—44no—
387C2×Dic11—44no—
388C2×Dic11C2×#4114yes—
389C2×Dic11C2×#4114yes—
390C2×Dic11C2×#4114yes—
391C23×D4—111no—
392C23×D4—111no—
393C23×D4C2×D1111yescharacteristic
394C24×C4C2×D1111yescharacteristic
395C2×#126—118no—
396C2×#126—228no—
397C2×#123—28no—
398C2×#123C2×D1118yescomplemented
399C22×C4⋊C4—111no—
400C22×C4⋊C4—111no—
401C22×C4⋊C4—111no—
402C22×C4⋊C4—111no—
403C22×C4⋊C4—111no—
404C22×C4⋊C4C2×D1111yescharacteristic
405C22×C4⋊C4C2×D1111yescharacteristic
406C22×C22⋊C4—111no—
407C22×C22⋊C4—111no—
408C22×C22⋊C4—111no—
409C22×C22⋊C4—111no—
410C22×C22⋊C4—111no—
411C22×C22⋊C4—111no—
412C22×C22⋊C4—111no—
413C22×C22⋊C4—111no—
414C22×C22⋊C4—111no—
415C22×C22⋊C4—111no—
416C22×C22⋊C4—111no—
417C22×C22⋊C4C2×D1111yescharacteristic
418C22×C22⋊C4C2×D1111yescharacteristic
419C22×C22⋊C4C2×D1111yescharacteristic
420C22×C42—111no—
421C22×C42—111no—
422C22×C42—111no—
423C22×C42—111no—
424#398—118no—
425#396—118no—
426#394—118no—
427#392—118no—
428#390—118no—
429#390—118no—
430#390—118no—
431#388—118no—
432#388—118no—
433#388—118no—
434#386—118no—
435C4×C4⋊C4—118no—
436C4×C22⋊C4—118no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C22×C11—24no—
444C22×C11—24no—
445C22×C11—24no—
446C22×C11—42no—
447C22×C11—42no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—416no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—88no—
459C22×C11#52914yes—
460C22×C11#53214yes—
461C22×C11#53814yes—
462C22×C11#54614yes—
463C22×C11#55014yes—
464C22×C11#55114yes—
465C22×C11#55314yes—
466C22×C11C23×D411yescharacteristic
467C22×C11C22×#4111yescharacteristic
468C22×C11C22×#4111yescharacteristic
469C22×C11C22×#4111yescharacteristic
470C22×C11C22×#4111yescharacteristic
471C22×C11C2×H(5,𝔽2)11yescharacteristic
472C22×C11C2×H(5,𝔽2)11yescharacteristic
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—88no—
481C4×C11—24no—
482C4×C11—24no—
483C4×C11—24no—
484C4×C11—42no—
485C4×C11—42no—
486Dic11—24no—
487Dic11—24no—
488Dic11—24no—
489Dic11—42no—
490Dic11—42no—
491Dic11—42no—
492Dic11—42no—
493C25—111no—
494C25C22×D1111yescharacteristic
495C25C22×D1111yescharacteristic
496C22×D4—24no—
497C22×D4—24no—
498C22×D4—42no—
499C22×D4—114no—
500C22×D4—114no—
501C22×D4—224no—
502C22×D4—224no—
503C22×D4—224no—
504C22×D4—442no—
505C22×D4—442no—
506C22×D4—442no—
507C22×D4C22×D1114yes—
508C23×C4—24no—
509C23×C4—24no—
510C23×C4—42no—
511C23×C4—111no—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—111no—
517C23×C4—111no—
518C23×C4C22×D1111yescharacteristic
519C23×C4C22×D1111yescharacteristic
520C23×C4C22×D1114yes—
521C23×C4C22×D1111yescharacteristic
522C23×C4C22×D1111yescharacteristic
523C23×C4C22×D1111yescharacteristic
524#126—2232no—
525#123—232no—
526C2×C4⋊C4—24no—
527C2×C4⋊C4—114no—
528C2×C4⋊C4—114no—
529C2×C4⋊C4—114no—
530C2×C4⋊C4—114no—
531C2×C4⋊C4—114no—
532C2×C4⋊C4—224no—
533C2×C4⋊C4—224no—
534C2×C4⋊C4—224no—
535C2×C4⋊C4—442no—
536C2×C4⋊C4—442no—
537C2×C4⋊C4C22⋊D1118yescomplemented
538C2×C4⋊C4C22×D1114yes—
539C2×C4⋊C4C22×D1114yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—114no—
544C2×C22⋊C4—114no—
545C2×C22⋊C4—114no—
546C2×C22⋊C4—114no—
547C2×C22⋊C4—114no—
548C2×C22⋊C4—114no—
549C2×C22⋊C4—114no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—224no—
555C2×C22⋊C4—224no—
556C2×C22⋊C4—224no—
557C2×C22⋊C4—224no—
558C2×C22⋊C4—224no—
559C2×C22⋊C4—224no—
560C2×C22⋊C4—224no—
561C2×C22⋊C4—224no—
562C2×C22⋊C4—442no—
563C2×C22⋊C4—442no—
564C2×C22⋊C4—442no—
565C2×C22⋊C4C22×D1114yes—
566C2×C22⋊C4C22×D1114yes—
567C2×C22⋊C4C22×D1114yes—
568C2×C42—114no—
569C2×C42—114no—
570C2×C42—114no—
571C2×C42—114no—
572C2×C42—224no—
573C2×C42—224no—
574C2×C42—442no—
575C2×C42—442no—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—114no—
580#95—114no—
581#95—114no—
582C2×C11—44no—
583C2×C11—82no—
584C2×C11#255418yescomplemented
585C2×C11C2×#52911yescharacteristic
586C2×C11C2×#53211yescharacteristic
587C2×C11C2×#53811yescharacteristic
588C2×C11C2×#54611yescharacteristic
589C2×C11C2×#55011yescharacteristic
590C2×C11C2×#55111yescharacteristic
591C2×C11C2×#55311yescharacteristic
592D11—82no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—112no—
607C24—222no—
608C24—222no—
609C24—222no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24#434114yes—
615C24C23×D1112yes—
616C24C23×D1112yes—
617C24C23×D1111yescharacteristic
618C2×D4—28no—
619C2×D4—28no—
620C2×D4—44no—
621C2×D4—416no—
622C2×D4—228no—
623C2×D4—228no—
624C2×D4—228no—
625C2×D4—444no—
626C2×D4—444no—
627C2×D4—444no—
628C2×D4—4416no—
629C2×D4—4416no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—28no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—28no—
644C22×C4—44no—
645C22×C4—416no—
646C22×C4—114no—
647C22×C4—114no—
648C22×C4—114no—
649C22×C4—112no—
650C22×C4—112no—
651C22×C4—112no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—222no—
657C22×C4—222no—
658C22×C4—222no—
659C22×C4—222no—
660C22×C4—222no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—222no—
665C22×C4—222no—
666C22×C4—222no—
667C22×C4—222no—
668C22×C4—222no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—222no—
674C22×C4C2×C22⋊D1114yes—
675C22×C4C2×C22⋊D1114yes—
676C22×C4C2×C22⋊D1114yes—
677C22×C4C23×D1112yes—
678C22×C4C23×D1112yes—
679C22×C4C23×D1112yes—
680C22×C4C23×D1112yes—
681C22×C4C23×D1112yes—
682C4⋊C4—28no—
683C4⋊C4—228no—
684C4⋊C4—228no—
685C4⋊C4—228no—
686C4⋊C4—444no—
687C4⋊C4—444no—
688C4⋊C4C2×C22⋊D11116yescomplemented
689C22⋊C4—28no—
690C22⋊C4—28no—
691C22⋊C4—28no—
692C22⋊C4—228no—
693C22⋊C4—228no—
694C22⋊C4—228no—
695C22⋊C4—228no—
696C22⋊C4—228no—
697C22⋊C4—228no—
698C22⋊C4—228no—
699C22⋊C4—228no—
700C22⋊C4—444no—
701C22⋊C4—444no—
702C22⋊C4—444no—
703C42—228no—
704C42—228no—
705C42—444no—
706C42—444no—
707C11C2×#255411yescharacteristic, complemented, Sylow
708C23—28no—
709C23—28no—
710C23—28no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—222no—
736C23—222no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—444no—
743C23—444no—
744C23—444no—
745C23—444no—
746C23—444no—
747C23—444no—
748C23—444no—
749C23C2×#434114yes—
750C23C2×#434112yes—
751C23#6703712yes—
752C23#41×D1112yes—
753C23#41×D1112yes—
754C23#41×D1112yes—
755C23#6704212yes—
756C23C22×C22⋊D1112yes—
757C23C24×D1111yescharacteristic
758D4—416no—
759D4—4416no—
760D4—4416no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—28no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—416no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—114no—
780C2×C4—114no—
781C2×C4—114no—
782C2×C4—228no—
783C2×C4—228no—
784C2×C4—222no—
785C2×C4—222no—
786C2×C4—222no—
787C2×C4—228no—
788C2×C4—222no—
789C2×C4—222no—
790C2×C4—222no—
791C2×C4—222no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—444no—
804C2×C4—444no—
805C2×C4—444no—
806C2×C4—444no—
807C2×C4C22×C22⋊D1114yes—
808C2×C4C22×C22⋊D1114yes—
809C2×C4C22×C22⋊D1114yes—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—416no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—88no—
826C22—442no—
827C22—442no—
828C22—442no—
829C22—442no—
830C22—442no—
831C22—442no—
832C22—442no—
833C22—888no—
834C22#1062318014yes—
835C22#1062318814yes—
836C22#1062318914yes—
837C22#1062319214yes—
838C22#1062333714yes—
839C22#1062336314yes—
840C22#1062336514yes—
841C22C22×#434111yescharacteristic
842C22C2×#6703711yescharacteristic
843C22C2×#41×D1111yescharacteristic
844C22C2×#41×D1111yescharacteristic
845C22C2×#41×D1111yescharacteristic
846C22C2×#6704211yescharacteristic
847C22C23×C22⋊D1111yescharacteristic
848C4—24no—
849C4—24no—
850C4—24no—
851C4—42no—
852C4—42no—
853C4—224no—
854C4—224no—
855C4—224no—
856C4—442no—
857C4—442no—
858C4—442no—
859C4—442no—
860C2—44no—
861C2—82no—
862C2—882no—
863C2#1307367218yesdirect product factor
864C2C2×#1062318011yescharacteristic
865C2C2×#1062336311yescharacteristic
866C2C2×#1062318811yescharacteristic
867C2C2×#1062333711yescharacteristic
868C2C2×#1062336511yescharacteristic
869C2C2×#1062318911yescharacteristic
870C2C2×#1062319211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#123C2
socleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC22×#123D11
hypocenterC11C2×#2554
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×#66951C2semidirect
2. #13073672C2direct (N × H)
3. C2×#10622596C2semidirect
4. C2×#10622561C2semidirect
5. C2×#10622574C2semidirect
7. C2×#10622834C2semidirect
8. C2×#10622570C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622558C2semidirect
11. C2×#10622603C2semidirect
12. C2×#10622557C2semidirect
13. C2×#10622826C2semidirect
14. C2×C4⋊C4×Dic11C2semidirect
15. C2×C4×C22⋊Dic11C2semidirect
16. C22×C11×#123C2semidirect
22. C2×C11×#123C22semidirect
49. C2×#66951C22semidirect
51. #10622834C22semidirect
52. #10622826C22semidirect
53. C4×C22⋊Dic11C22semidirect
60. #10622603C22semidirect
61. #10622596C22semidirect
62. C4⋊C4×Dic11C22semidirect
63. #10622574C22semidirect
64. #10622570C22semidirect
65. #10622570C22semidirect
66. #10622561C22semidirect
67. #10622558C22semidirect
68. #10622557C22semidirect
102. C2×C11×C4⋊C4D4semidirect
249. C11×C4⋊C4C2×D4semidirect
274. C22×#123D11semidirect
398. C2×#123C2×D11semidirect
537. C2×C4⋊C4C22⋊D11semidirect
584. C2×C11#2554semidirect
688. C4⋊C4C2×C22⋊D11semidirect
707. C11C2×#2554semidirect
863. C2#13073672direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669512
#130736722
C2×#106225962
C2×#106225612
C2×#106225742
C2×#106228362
C2×#106228342
C2×#106225702
C2×#106225582
C2×#106226032
C2×#106225572
C2×#106228262
C2×C4⋊C4×Dic112
C2×C4×C22⋊Dic112
C22×C11×#1232
C2×#255411