Finite Group Databasebeta

← C2×#13072965 #14923217

Subgroups — C2×#13072965 #14923217

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×#66942C211yesmaximal, characteristic, complemented
2C22×#66992C211yesmaximal, characteristic
3#13072965C2116yesmaximal, direct product factor
4C2×#10622565C211yesmaximal, characteristic, complemented
5C2×#10622606C211yesmaximal, characteristic, complemented
6C2×#10622574C211yesmaximal, characteristic, complemented
7C2×#10622835C211yesmaximal, characteristic, complemented
8C2×#10622570C211yesmaximal, characteristic, complemented
9C2×#10622570C211yesmaximal, characteristic, complemented
10C2×#10622570C211yesmaximal, characteristic, complemented
11C2×#10622564C211yesmaximal, characteristic, complemented
12C2×#10622553C211yesmaximal, characteristic, complemented
13C2×#10622555C211yesmaximal, characteristic, complemented
14C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#390C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C42×C11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C2×#66992—28no—
33C2×#66992C2218yes—
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C22×C4×Dic11C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C2×#66942—28no—
49C2×#66942C2218yescomplemented
50C11×#390C2218yescomplemented
51#10622835C2218yescomplemented
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58#10622606C2218yescomplemented
59#10622574C2218yescomplemented
60#10622570C2218yescomplemented
61#10622570C2218yescomplemented
62#10622570C2218yescomplemented
63#10622565C2218yescomplemented
64#10622564C2218yescomplemented
65#10622555C2218yescomplemented
66C22⋊C4×Dic11C2218yescomplemented
67#10622553C2218yescomplemented
68C4×Dic11⋊C4C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C22×D4×C11—24no—
73C22×D4×C11—24no—
74C22×D4×C11—42no—
75C22×D4×C11C2314yes—
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—24no—
82C22×C22⋊D11—24no—
83C22×C22⋊D11—24no—
84C22×C22⋊D11—24no—
85C22×C22⋊D11—24no—
86C22×C22⋊D11—42no—
87C22×C22⋊D11C2314yes—
88C22×C22⋊D11C2314yes—
89C23×Dic11—24no—
90C23×Dic11—24no—
91C23×Dic11—24no—
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2314yes—
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C2×C11×C4⋊C4—24no—
101C2×C11×C4⋊C4C2314yes—
102C2×C11×C22⋊C4—24no—
103C2×C11×C22⋊C4—24no—
104C2×C11×C22⋊C4—42no—
105C2×C11×C22⋊C4—42no—
106C2×C11×C22⋊C4C2314yes—
107C2×C11×C22⋊C4C2314yes—
108C2×C11×C22⋊C4C2314yes—
109C2×C11×C22⋊C4C2314yes—
110C2×C42×C11—42no—
111C2×C42×C11C2314yes—
112C2×C22⋊Dic11—24no—
113C2×C22⋊Dic11—24no—
114C2×C22⋊Dic11—42no—
115C2×C22⋊Dic11—42no—
116C2×C22⋊Dic11—42no—
117C2×C22⋊Dic11C2314yes—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122#66992—232no—
123C2×(C2×D11)⋊C4—24no—
124C2×(C2×D11)⋊C4—24no—
125C2×(C2×D11)⋊C4—42no—
126C2×(C2×D11)⋊C4—42no—
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⋊Dic11C2314yes—
135C2×Dic11⋊C4—24no—
136C2×Dic11⋊C4—24no—
137C2×Dic11⋊C4—24no—
138C2×Dic11⋊C4—24no—
139C2×Dic11⋊C4D418yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×C4×Dic11—24no—
146C2×C4×Dic11—24no—
147C2×C4×Dic11—42no—
148C2×C4×Dic11C2314yes—
149C2×C4×Dic11C2314yes—
150C2×C4×Dic11C2314yes—
151#66942—232no—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2490—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—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11C2×D414yes—
202C22×C4×C11#4114yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C2×C22⋊D11—28no—
209C2×C22⋊D11—28no—
210C2×C22⋊D11—28no—
211C2×C22⋊D11—28no—
212C2×C22⋊D11—28no—
213C2×C22⋊D11—44no—
214C2×C22⋊D11—416no—
215C2×C22⋊D11—416no—
216C22×Dic11—28no—
217C22×Dic11—28no—
218C22×Dic11—28no—
219C22×Dic11—22no—
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—416no—
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×C4⋊C4—28no—
249C11×C22⋊C4—28no—
250C11×C22⋊C4—28no—
251C11×C22⋊C4—44no—
252C11×C22⋊C4—44no—
253C42×C11—44no—
254C22⋊Dic11—28no—
255C22⋊Dic11—28no—
256C22⋊Dic11—44no—
257C22⋊Dic11—44no—
258C22⋊Dic11—44no—
259(C2×D11)⋊C4—28no—
260(C2×D11)⋊C4—28no—
261(C2×D11)⋊C4—44no—
262(C2×D11)⋊C4—44no—
263(C2×D11)⋊C4—44no—
264C4⋊Dic11—28no—
265Dic11⋊C4—28no—
266Dic11⋊C4—28no—
267Dic11⋊C4—28no—
268Dic11⋊C4—28no—
269Dic11⋊C4C2×D4116yes—
270C4×Dic11—28no—
271C4×Dic11—28no—
272C4×Dic11—44no—
273C22×#125—111no—
274C22×#121—111no—
275#2490—1116no—
276C2×#397—111no—
277C2×#397—111no—
278C2×#394—111no—
279C2×#394—111no—
280C2×#390—111no—
281C2×#390—111no—
282C2×#390—111no—
283C2×#390D1111yescharacteristic, complemented
284C2×#388—111no—
285C2×#388—111no—
286C2×#380—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—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—44no—
356C2×C4×C11—44no—
357C2×C4×C11—44no—
358C2×C4×C11C22×D414yes—
359C2×C4×C11C2×#4114yes—
360C22⋊D11—416no—
361C22⋊D11—416no—
362C2×Dic11—28no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
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—44no—
381C2×Dic11—44no—
382C2×Dic11—44no—
383C2×Dic11—44no—
384C2×Dic11—44no—
385C2×Dic11—416no—
386C2×Dic11#124116yes—
387C2×Dic11C22×D414yes—
388C2×Dic11C22×D414yes—
389C2×Dic11C2×#4114yes—
390C2×Dic11C2×#4114yes—
391C23×D4—111no—
392C23×D4—111no—
393C23×D4C2×D1111yescharacteristic
394C24×C4—111no—
395C2×#125—118no—
396C2×#125—228no—
397C2×#121—118no—
398C2×#121—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⋊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⋊C4C2×D1111yescharacteristic
417C22×C22⋊C4C2×D1111yescharacteristic
418C22×C22⋊C4C2×D1111yescharacteristic
419C22×C22⋊C4C2×D1111yescharacteristic
420C22×C42—111no—
421C22×C42—111no—
422C22×C42—111no—
423C22×C42C2×D1111yescharacteristic
424#397—118no—
425#397—118no—
426#394—118no—
427#394—118no—
428#390—118no—
429#390—118no—
430#390—118no—
431#390C2×D1118yescomplemented
432#388—118no—
433#388—118no—
434#380—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×C11C2×#12414yes—
460C22×C11#52914yes—
461C22×C11#54014yes—
462C22×C11#54614yes—
463C22×C11#55014yes—
464C22×C11#55314yes—
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—42no—
488Dic11—42no—
489Dic11—42no—
490Dic11—42no—
491Dic11—42no—
492Dic11C2×#12418yes—
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—224no—
505C22×D4—224no—
506C22×D4—442no—
507C22×D4C22×D1114yes—
508C23×C4—111no—
509C23×C4—111no—
510C23×C4—114no—
511C23×C4—111no—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—224no—
517C23×C4—224no—
518C23×C4—224no—
519C23×C4C22×D1111yescharacteristic
520C23×C4C22×D1111yescharacteristic
521C23×C4C22×D1111yescharacteristic
522C23×C4C22×D1111yescharacteristic
523C23×C4C22×D1111yescharacteristic
524#125—2232no—
525#121—2232no—
526C2×C4⋊C4—24no—
527C2×C4⋊C4—118no—
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—224no—
539C2×C4⋊C4C22×D1114yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
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—442no—
559C2×C22⋊C4—442no—
560C2×C22⋊C4—442no—
561C2×C22⋊C4—442no—
562C2×C22⋊C4—442no—
563C2×C22⋊C4—442no—
564C2×C22⋊C4C22×D1114yes—
565C2×C22⋊C4C22×D1114yes—
566C2×C22⋊C4C22×D1114yes—
567C2×C22⋊C4C22×D1114yes—
568C2×C42—42no—
569C2×C42—114no—
570C2×C42—114no—
571C2×C42—114no—
572C2×C42—224no—
573C2×C42—224no—
574C2×C42—442no—
575C2×C42C22×D1114yes—
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#249018yescomplemented
585C2×C11C22×#12411yescharacteristic
586C2×C11C2×#52911yescharacteristic
587C2×C11C2×#54011yescharacteristic
588C2×C11C2×#54611yescharacteristic
589C2×C11C2×#55011yescharacteristic
590C2×C11C2×#55311yescharacteristic
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#433914yes—
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—228no—
626C2×D4—228no—
627C2×D4—4416no—
628C2×D4—444no—
629C2×D4—4416no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—114no—
644C22×C4—114no—
645C22×C4—114no—
646C22×C4—112no—
647C22×C4—114no—
648C22×C4—112no—
649C22×C4—112no—
650C22×C4—112no—
651C22×C4—112no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—228no—
655C22×C4—228no—
656C22×C4—228no—
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×C4—4416no—
675C22×C4D4×D1114yes—
676C22×C4#434114yes—
677C22×C4C23×D1112yes—
678C22×C4C23×D1112yes—
679C22×C4C23×D1112yes—
680C22×C4C23×D1112yes—
681C22×C4C23×D1112yes—
682C4⋊C4—28no—
683C4⋊C4—1116no—
684C4⋊C4—228no—
685C4⋊C4—228no—
686C4⋊C4—228no—
687C4⋊C4—228no—
688C4⋊C4—228no—
689C22⋊C4—28no—
690C22⋊C4—28no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—228no—
694C22⋊C4—228no—
695C22⋊C4—228no—
696C22⋊C4—228no—
697C22⋊C4—444no—
698C22⋊C4—444no—
699C22⋊C4—444no—
700C22⋊C4—444no—
701C22⋊C4—444no—
702C22⋊C4—444no—
703C42—44no—
704C42—228no—
705C42—228no—
706C42—444no—
707C11C2×#249011yescharacteristic, 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×#433914yes—
750C23C2×#433912yes—
751C23C2×D4×D1112yes—
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—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—114no—
780C2×C4—114no—
781C2×C4—114no—
782C2×C4—1116no—
783C2×C4—114no—
784C2×C4—228no—
785C2×C4—222no—
786C2×C4—222no—
787C2×C4—222no—
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—4416no—
803C2×C4—444no—
804C2×C4—444no—
805C2×C4—444no—
806C2×C4—444no—
807C2×C4—444no—
808C2×C4C2×D4×D1114yes—
809C2×C4C2×#434114yes—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—42no—
814C22—42no—
815C22—416no—
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#1062302114yes—
835C22#1062306914yes—
836C22#1062307114yes—
837C22#1062313214yes—
838C22#1062314614yes—
839C22D11×#12414yes—
840C22#1062324914yes—
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—118no—
854C4—224no—
855C4—442no—
856C4—442no—
857C4—442no—
858C4—442no—
859C4—442no—
860C2—44no—
861C2—82no—
862C2—882no—
863C2#1307296518yesdirect product factor
864C2C2×D11×#12411yescharacteristic
865C2C2×#1062306911yescharacteristic
866C2C2×#1062314611yescharacteristic
867C2C2×#1062302111yescharacteristic
868C2C2×#1062324911yescharacteristic
869C2C2×#1062313211yescharacteristic
870C2C2×#1062307111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#390C2
socleC24×C11C24
prime radicalC22×#66992C2
hypercenterC2×#390D11
hypocenterC11C2×#2490
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#66942C2semidirect
3. #13072965C2direct (N × H)
4. C2×#10622565C2semidirect
5. C2×#10622606C2semidirect
6. C2×#10622574C2semidirect
7. C2×#10622835C2semidirect
8. C2×#10622570C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622570C2semidirect
11. C2×#10622564C2semidirect
12. C2×#10622553C2semidirect
13. C2×#10622555C2semidirect
14. C2×C4×Dic11⋊C4C2semidirect
15. C2×C22⋊C4×Dic11C2semidirect
16. C2×C11×#390C2semidirect
49. C2×#66942C22semidirect
50. C11×#390C22semidirect
51. #10622835C22semidirect
58. #10622606C22semidirect
59. #10622574C22semidirect
60. #10622570C22semidirect
61. #10622570C22semidirect
62. #10622570C22semidirect
63. #10622565C22semidirect
64. #10622564C22semidirect
65. #10622555C22semidirect
66. C22⋊C4×Dic11C22semidirect
67. #10622553C22semidirect
68. C4×Dic11⋊C4C22semidirect
283. C2×#390D11semidirect
431. #390C2×D11semidirect
584. C2×C11#2490semidirect
707. C11C2×#2490semidirect
863. C2#13072965direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669422
C22×#669922
#130729652
C2×#106225652
C2×#106226062
C2×#106225742
C2×#106228352
C2×#106225702
C2×#106225642
C2×#106225532
C2×#106225552
C2×C4×Dic11⋊C42
C2×C22⋊C4×Dic112
C2×C11×#3902
C2×#249011