Finite Group Databasebeta

← C2×#13073680 #14923852

Subgroups — C2×#13073680 #14923852

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×#66932C211yesmaximal, characteristic, complemented
2C22×#66982C211yesmaximal, characteristic, complemented
3#13073680C2116yesmaximal, direct product factor
4C2×#10622270C211yesmaximal, characteristic, complemented
5C2×#10622561C211yesmaximal, characteristic, complemented
6C2×#10622572C211yesmaximal, characteristic, complemented
7C2×#10622836C211yesmaximal, characteristic
8C2×#10622834C211yesmaximal, characteristic, complemented
9C2×#10622570C211yesmaximal, characteristic, complemented
10C2×#10622570C211yesmaximal, characteristic, complemented
11C2×#10622283C211yesmaximal, characteristic, complemented
12C2×#10622283C211yesmaximal, characteristic, complemented
13C2×#10622557C211yesmaximal, characteristic, complemented
14C2×#10622262C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C2×#66982—28no—
31C2×#66982C2218yescomplemented
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C22×C4×Dic11C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C2×#66932—28no—
49C2×#66932C2218yescomplemented
50C11×#386C2218yescomplemented
51C2×C11×#95C2211yescharacteristic
52C2×C11×#95C2211yescharacteristic
53#10622836C2218yes—
54#10622834C2218yescomplemented
55C4×C22⋊Dic11C2218yescomplemented
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60#10622572C2218yescomplemented
61#10622570C2218yescomplemented
62#10622570C2218yescomplemented
63#10622561C2218yescomplemented
64#10622557C2218yescomplemented
65#10622283C2218yescomplemented
66#10622283C2218yescomplemented
67#10622270C2218yescomplemented
68#10622262C2218yescomplemented
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×C11C2311yescharacteristic
82C23×C4×C11C2314yes—
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
100C2×C11×C22⋊C4—24no—
101C2×C11×C22⋊C4—42no—
102C2×C11×C22⋊C4—42no—
103C2×C11×C22⋊C4C2314yes—
104C2×C11×C22⋊C4C2314yes—
105C2×C11×C22⋊C4C2314yes—
106C2×C22⋊Dic11—24no—
107C2×C22⋊Dic11—24no—
108C2×C22⋊Dic11—24no—
109C2×C22⋊Dic11—24no—
110C2×C22⋊Dic11—24no—
111C2×C22⋊Dic11—24no—
112C2×C22⋊Dic11C2314yes—
113C2×C22⋊Dic11C2314yes—
114C2×C22⋊Dic11C2314yes—
115C2×C22⋊Dic11C2314yes—
116C2×C22⋊Dic11C2314yes—
117C2×C22⋊Dic11C2314yes—
118#66982—232no—
119C2×(C2×D11)⋊C4—24no—
120C2×(C2×D11)⋊C4—24no—
121C2×(C2×D11)⋊C4—24no—
122C2×(C2×D11)⋊C4—24no—
123C2×(C2×D11)⋊C4—42no—
124C2×(C2×D11)⋊C4C2314yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×C4⋊Dic11—24no—
130C2×C4⋊Dic11—42no—
131C2×C4⋊Dic11C2314yes—
132C2×C4⋊Dic11C2314yes—
133C2×Dic11⋊C4—24no—
134C2×Dic11⋊C4—24no—
135C2×Dic11⋊C4—24no—
136C2×Dic11⋊C4—42no—
137C2×Dic11⋊C4D418yescomplemented
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2314yes—
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#66932—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—28no—
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—44no—
204C22×C4×C11—416no—
205C22×C4×C11C2×D414yes—
206C22×C4×C11#4114yes—
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×Dic11C2×D414yes—
238C22×Dic11C2×D414yes—
239C22×Dic11#4114yes—
240C22×Dic11#4114yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C11×C22⋊C4—28no—
249C11×C22⋊C4—44no—
250C11×C22⋊C4—44no—
251C22⋊Dic11—28no—
252C22⋊Dic11—28no—
253C22⋊Dic11—28no—
254C22⋊Dic11—28no—
255C22⋊Dic11—28no—
256C22⋊Dic11—28no—
257(C2×D11)⋊C4—28no—
258(C2×D11)⋊C4—28no—
259(C2×D11)⋊C4—28no—
260(C2×D11)⋊C4—28no—
261(C2×D11)⋊C4—44no—
262C4⋊Dic11—28no—
263C4⋊Dic11—44no—
264Dic11⋊C4—28no—
265Dic11⋊C4—28no—
266Dic11⋊C4—28no—
267Dic11⋊C4—44no—
268Dic11⋊C4C2×D4116yescomplemented
269C4×Dic11—28no—
270C4×Dic11—28no—
271C4×Dic11—44no—
272C4×Dic11—44no—
273C22×#126—111no—
274C22×#123—111no—
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×#386D1111yescharacteristic, complemented
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×#4112yes—
318C23×C11C2×#4114yes—
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—22no—
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×C11—44no—
359C2×C4×C11C22×D414yes—
360C2×C4×C11C2×#4114yes—
361C22⋊D11—416no—
362C22⋊D11—416no—
363C2×Dic11—28no—
364C2×Dic11—28no—
365C2×Dic11—28no—
366C2×Dic11—28no—
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×Dic11C22×D414yes—
388C2×Dic11C22×D414yes—
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—118no—
398C2×#123—228no—
399C22×C4⋊C4—111no—
400C22×C4⋊C4—111no—
401C22×C4⋊C4—111no—
402C22×C4⋊C4—111no—
403C22×C4⋊C4—111no—
404C22×C4⋊C4—111no—
405C22×C4⋊C4—111no—
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#386C2×D1118yescomplemented
435C4×C4⋊C4—118no—
436C4×C22⋊C4—118no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95C2×D1111yescharacteristic
442C2×#95C2×D1111yescharacteristic
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—42no—
484C4×C11—42no—
485C4×C11—42no—
486Dic11—24no—
487Dic11—24no—
488Dic11—24no—
489Dic11—24no—
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×D1111yescharacteristic
521C23×C4C22×D1114yes—
522C23×C4C22×D1111yescharacteristic
523C23×C4C22×D1111yescharacteristic
524#126—2232no—
525#123—2232no—
526C2×C4⋊C4—118no—
527C2×C4⋊C4—114no—
528C2×C4⋊C4—114no—
529C2×C4⋊C4—114no—
530C2×C4⋊C4—114no—
531C2×C4⋊C4—114no—
532C2×C4⋊C4—114no—
533C2×C4⋊C4—114no—
534C2×C4⋊C4—224no—
535C2×C4⋊C4—224no—
536C2×C4⋊C4—224no—
537C2×C4⋊C4—224no—
538C2×C4⋊C4—442no—
539C2×C4⋊C4—442no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
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—224no—
563C2×C22⋊C4—224no—
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#95C22×D1114yes—
581#95C22×D1114yes—
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—22no—
644C22×C4—28no—
645C22×C4—44no—
646C22×C4—416no—
647C22×C4—114no—
648C22×C4—114no—
649C22×C4—114no—
650C22×C4—114no—
651C22×C4—112no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—112no—
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×C4—222no—
675C22×C4#433914yes—
676C22×C4D4×D1114yes—
677C22×C4C23×D1112yes—
678C22×C4C23×D1112yes—
679C22×C4C23×D1112yes—
680C22×C4C23×D1112yes—
681C22×C4C23×D1112yes—
682C4⋊C4—1116no—
683C4⋊C4—228no—
684C4⋊C4—228no—
685C4⋊C4—228no—
686C4⋊C4—228no—
687C4⋊C4—444no—
688C4⋊C4—444no—
689C22⋊C4—28no—
690C22⋊C4—44no—
691C22⋊C4—44no—
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—228no—
701C22⋊C4—228no—
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×#433912yes—
750C23C2×D4×D1112yes—
751C23C2×#434114yes—
752C23C2×#434112yes—
753C23#6703712yes—
754C23#6703712yes—
755C23#41×D1112yes—
756C23#41×D1112yes—
757C23C24×D1111yescharacteristic
758D4—416no—
759D4—4416no—
760D4—4416no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—22no—
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—44no—
780C2×C4—114no—
781C2×C4—114no—
782C2×C4—114no—
783C2×C4—114no—
784C2×C4—228no—
785C2×C4—228no—
786C2×C4—228no—
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—222no—
804C2×C4—222no—
805C2×C4—444no—
806C2×C4—444no—
807C2×C4—444no—
808C2×C4C2×#433914yes—
809C2×C4C2×D4×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#1062302614yes—
835C22#1062307914yes—
836C22#1062308914yes—
837C22#1062312214yes—
838C22#1062313014yes—
839C22#1062314414yes—
840C22#1062318014yes—
841C22C22×#433911yescharacteristic
842C22C22×D4×D1111yescharacteristic
843C22C22×#434111yescharacteristic
844C22C2×#6703711yescharacteristic
845C22C2×#6703711yescharacteristic
846C22C2×#41×D1111yescharacteristic
847C22C2×#41×D1111yescharacteristic
848C4—24no—
849C4—24no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—224no—
854C4—224no—
855C4—224no—
856C4—224no—
857C4—442no—
858C4—442no—
859C4—442no—
860C2—44no—
861C2—82no—
862C2—882no—
863C2#1307368018yesdirect product factor
864C2C2×#1062318011yescharacteristic
865C2C2×#1062307911yescharacteristic
866C2C2×#1062314411yescharacteristic
867C2C2×#1062312211yescharacteristic
868C2C2×#1062313011yescharacteristic
869C2C2×#1062302611yescharacteristic
870C2C2×#1062308911yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC2×#386D11
hypocenterC11C2×#2554
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#66932C2semidirect
2. C22×#66982C2semidirect
3. #13073680C2direct (N × H)
4. C2×#10622270C2semidirect
5. C2×#10622561C2semidirect
6. C2×#10622572C2semidirect
8. C2×#10622834C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622570C2semidirect
11. C2×#10622283C2semidirect
12. C2×#10622283C2semidirect
13. C2×#10622557C2semidirect
14. C2×#10622262C2semidirect
15. C2×C4×C22⋊Dic11C2semidirect
16. C2×C11×#386C2semidirect
31. C2×#66982C22semidirect
49. C2×#66932C22semidirect
50. C11×#386C22semidirect
54. #10622834C22semidirect
55. C4×C22⋊Dic11C22semidirect
60. #10622572C22semidirect
61. #10622570C22semidirect
62. #10622570C22semidirect
63. #10622561C22semidirect
64. #10622557C22semidirect
65. #10622283C22semidirect
66. #10622283C22semidirect
67. #10622270C22semidirect
68. #10622262C22semidirect
137. C2×Dic11⋊C4D4semidirect
268. Dic11⋊C4C2×D4semidirect
286. C2×#386D11semidirect
434. #386C2×D11semidirect
584. C2×C11#2554semidirect
707. C11C2×#2554semidirect
863. C2#13073680direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669322
C22×#669822
#130736802
C2×#106222702
C2×#106225612
C2×#106225722
C2×#106228362
C2×#106228342
C2×#106225702
C2×#106222832
C2×#106225572
C2×#106222622
C2×C4×C22⋊Dic112
C2×C11×#3862
C2×#255411