Finite Group Databasebeta

← C2×#13074455 #14920150

Subgroups — C2×#13074455 #14920150

Order 2816.

3218 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
2#13074455C2116yesmaximal, direct product factor
3C2×#10622597C211yesmaximal, characteristic, complemented
4C2×#10622565C211yesmaximal, characteristic, complemented
5C2×#10622561C211yesmaximal, characteristic, complemented
6C2×#10622607C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622572C211yesmaximal, characteristic, complemented
9C2×#10622835C211yesmaximal, characteristic, complemented
10C2×#10622836C211yesmaximal, characteristic
11C2×#10622557C211yesmaximal, characteristic, complemented
12C2×#10622591C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622602C211yesmaximal, characteristic, complemented
15C2×#10622825C211yesmaximal, characteristic, complemented
16C22×C11×#123C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C2×C11×#123—28no—
23C2×C11×#123C2218yescomplemented
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C2×C4×C22⋊D11—28no—
36C2×C4×C22⋊D11C2218yescomplemented
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×C4⋊Dic11C2211yescharacteristic
42C22×C4⋊Dic11C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48#10622836C2218yes—
49#10622835C2218yescomplemented
50#10622825C2218yescomplemented
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59#10622607C2218yescomplemented
60#10622602C2218yescomplemented
61#10622597C2218yescomplemented
62#10622591C2218yescomplemented
63#10622574C2218yescomplemented
64#10622572C2218yescomplemented
65#10622569C2218yescomplemented
66#10622565C2218yescomplemented
67#10622561C2218yescomplemented
68#10622557C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C22×D4×C11—24no—
73C22×D4×C11—42no—
74C22×D4×C11—42no—
75C22×D4×C11C2314yes—
76C23×C4×C11—42no—
77C23×C4×C11—42no—
78C23×C4×C11D418yescomplemented
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2314yes—
85C22×C22⋊D11—24no—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
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
100C22×C4×D11—24no—
101C22×C4×D11—42no—
102C22×C4×D11—42no—
103C22×C4×D11C2314yes—
104C11×#123—232no—
105C2×C11×C4⋊C4—24no—
106C2×C11×C4⋊C4—24no—
107C2×C11×C4⋊C4C2314yes—
108C2×C11×C4⋊C4C2314yes—
109C2×C11×C22⋊C4—24no—
110C2×C11×C22⋊C4—24no—
111C2×C11×C22⋊C4—24no—
112C2×C11×C22⋊C4C2314yes—
113C2×C11×C22⋊C4C2314yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C22⋊Dic11—24no—
116C2×C22⋊Dic11—24no—
117C2×C22⋊Dic11—42no—
118C2×C22⋊Dic11—42no—
119C2×C22⋊Dic11—42no—
120C2×C22⋊Dic11—42no—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2314yes—
127C4×C22⋊D11—232no—
128C2×(C2×D11)⋊C4—24no—
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4—42no—
131C2×(C2×D11)⋊C4—42no—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×C4⋊Dic11—42no—
137C2×C4⋊Dic11—42no—
138C2×C4⋊Dic11C2314yes—
139C2×C4⋊Dic11C2314yes—
140C2×Dic11⋊C4—24no—
141C2×Dic11⋊C4—24no—
142C2×Dic11⋊C4—42no—
143C2×Dic11⋊C4—42no—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×Dic11⋊C4C2314yes—
147C2×Dic11⋊C4C2314yes—
148C2×C4×Dic11—24no—
149C2×C4×Dic11C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2630—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×C11C2×D414yes—
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#4114yes—
183C23×D11C2412yes—
184C2×D4×C11—28no—
185C2×D4×C11—44no—
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×C11—416no—
202C22×C4×C11—44no—
203C22×C4×C11—44no—
204C22×C4×C11C2×D414yes—
205C22×C4×C11C2×D414yes—
206C22×C4×C11C2×D4116yescomplemented
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C2×C22⋊D11—232no—
213C2×C22⋊D11—28no—
214C2×C22⋊D11—28no—
215C2×C22⋊D11—28no—
216C2×C22⋊D11—28no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11—44no—
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—22no—
239C22×Dic11—22no—
240C22×Dic11#4114yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C2×C4×D11—28no—
249C2×C4×D11—44no—
250C2×C4×D11—44no—
251C2×C4×D11—416no—
252C11×C4⋊C4—28no—
253C11×C4⋊C4—28no—
254C11×C22⋊C4—28no—
255C11×C22⋊C4—28no—
256C11×C22⋊C4—28no—
257C22⋊Dic11—28no—
258C22⋊Dic11—28no—
259C22⋊Dic11—44no—
260C22⋊Dic11—44no—
261C22⋊Dic11—44no—
262C22⋊Dic11—44no—
263(C2×D11)⋊C4—28no—
264(C2×D11)⋊C4—28no—
265(C2×D11)⋊C4—44no—
266(C2×D11)⋊C4—44no—
267C4⋊Dic11—44no—
268C4⋊Dic11—44no—
269Dic11⋊C4—28no—
270Dic11⋊C4—28no—
271Dic11⋊C4—44no—
272Dic11⋊C4—44no—
273C4×Dic11—28no—
274C22×#123D1111yescharacteristic, complemented
275C22×C4×D4—111no—
276#2630—1116no—
277C2×#398—111no—
278C2×#397—111no—
279C2×#396—111no—
280C2×#396—111no—
281C2×#394—111no—
282C2×#394—111no—
283C2×#394—111no—
284C2×#392—111no—
285C2×#388—111no—
286C2×#387—111no—
287C2×#386—111no—
288C2×#385—111no—
289C2×#380—111no—
290C23×C11—28no—
291C23×C11—28no—
292C23×C11—28no—
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—22no—
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×C11—44no—
317C23×C11C22×D414yes—
318C23×C11C22×D412yes—
319C23×C11C2×#4112yes—
320C23×C11C2×#4112yes—
321C23×C11H(5,𝔽2)12yes—
322C23×C11H(5,𝔽2)12yes—
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—44no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11—44no—
339C22×D11C2×#4114yes—
340D4×C11—416no—
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—22no—
356C2×C4×C11—416no—
357C2×C4×C11—44no—
358C2×C4×C11—44no—
359C2×C4×C11—44no—
360C2×C4×C11C22×D414yes—
361C2×C4×C11C22×D414yes—
362C22⋊D11—232no—
363C22⋊D11—416no—
364C2×Dic11—28no—
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—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—44no—
386C2×Dic11—44no—
387C2×Dic11—44no—
388C2×Dic11—44no—
389C2×Dic11—44no—
390C2×Dic11—44no—
391C2×Dic11C2×#4114yes—
392C4×D11—416no—
393C23×D4—111no—
394C23×D4—111no—
395C23×D4C2×D1111yescharacteristic
396C24×C4—111no—
397C24×C4C2×D1111yescharacteristic
398C2×#123—28no—
399C2×#123C2×D1118yescomplemented
400C2×C4×D4—118no—
401C2×C4×D4—228no—
402C22×C4⋊C4—111no—
403C22×C4⋊C4—111no—
404C22×C4⋊C4—111no—
405C22×C4⋊C4—111no—
406C22×C4⋊C4—111no—
407C22×C4⋊C4—111no—
408C22×C4⋊C4C2×D1111yescharacteristic
409C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
418C22×C22⋊C4—111no—
419C22×C22⋊C4—111no—
420C22×C22⋊C4C2×D1111yescharacteristic
421C22×C22⋊C4C2×D1111yescharacteristic
422C22×C22⋊C4C2×D1111yescharacteristic
423C22×C42—111no—
424#398—118no—
425#397—118no—
426#396—118no—
427#396—118no—
428#394—118no—
429#394—118no—
430#394—118no—
431#392—118no—
432#388—118no—
433#387—118no—
434#386—118no—
435#385—118no—
436#380—118no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95—111no—
444C2×#95—111no—
445C22×C11—24no—
446C22×C11—24no—
447C22×C11—24no—
448C22×C11—416no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—88no—
461C22×C11#52514yes—
462C22×C11#53414yes—
463C22×C11#53714yes—
464C22×C11#53814yes—
465C22×C11#53914yes—
466C22×C11#54014yes—
467C22×C11#54214yes—
468C22×C11C23×D411yescharacteristic
469C22×C11C22×#4111yescharacteristic
470C22×C11C22×#4111yescharacteristic
471C22×C11C2×H(5,𝔽2)11yescharacteristic
472C22×C11C2×H(5,𝔽2)11yescharacteristic
473C22×C11C2×H(5,𝔽2)11yescharacteristic
474C22×C11C2×2−1+411yescharacteristic
475C2×D11—24no—
476C2×D11—24no—
477C2×D11—24no—
478C2×D11—416no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C4×C11—24no—
484C4×C11—24no—
485C4×C11—42no—
486C4×C11—42no—
487C4×C11—42no—
488Dic11—24no—
489Dic11—42no—
490Dic11—42no—
491Dic11—42no—
492Dic11—42no—
493Dic11—42no—
494Dic11—42no—
495C25—111no—
496C25C22×D1111yescharacteristic
497C25C22×D1111yescharacteristic
498C22×D4—24no—
499C22×D4—42no—
500C22×D4—42no—
501C22×D4—114no—
502C22×D4—114no—
503C22×D4—224no—
504C22×D4—224no—
505C22×D4—224no—
506C22×D4—224no—
507C22×D4—442no—
508C22×D4—442no—
509C22×D4C22×D1114yes—
510C23×C4—42no—
511C23×C4—42no—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—111no—
517C23×C4—111no—
518C23×C4—111no—
519C23×C4—114no—
520C23×C4—224no—
521C23×C4—442no—
522C23×C4—442no—
523C23×C4C22⋊D1118yescomplemented
524C23×C4C22×D1111yescharacteristic
525C23×C4C22×D1111yescharacteristic
526C23×C4C22×D1111yescharacteristic
527C23×C4C22×D1111yescharacteristic
528C23×C4C22×D1111yescharacteristic
529C23×C4C22×D1114yes—
530#123—232no—
531C4×D4—2232no—
532C2×C4⋊C4—24no—
533C2×C4⋊C4—24no—
534C2×C4⋊C4—114no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4—114no—
537C2×C4⋊C4—114no—
538C2×C4⋊C4—114no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—224no—
541C2×C4⋊C4—224no—
542C2×C4⋊C4—442no—
543C2×C4⋊C4—442no—
544C2×C4⋊C4—442no—
545C2×C4⋊C4—442no—
546C2×C4⋊C4C22×D1114yes—
547C2×C4⋊C4C22×D1114yes—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—114no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—114no—
557C2×C22⋊C4—114no—
558C2×C22⋊C4—114no—
559C2×C22⋊C4—114no—
560C2×C22⋊C4—114no—
561C2×C22⋊C4—224no—
562C2×C22⋊C4—224no—
563C2×C22⋊C4—224no—
564C2×C22⋊C4—224no—
565C2×C22⋊C4—442no—
566C2×C22⋊C4—442no—
567C2×C22⋊C4—442no—
568C2×C22⋊C4—442no—
569C2×C22⋊C4—442no—
570C2×C22⋊C4—442no—
571C2×C22⋊C4C22×D1114yes—
572C2×C22⋊C4C22×D1114yes—
573C2×C22⋊C4C22×D1114yes—
574C2×C42—114no—
575C2×C42—224no—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—114no—
580#95—114no—
581#95—114no—
582#95—114no—
583#95—114no—
584C2×C11—44no—
585C2×C11—82no—
586C2×C11#263018yescomplemented
587C2×C11C2×#52511yescharacteristic
588C2×C11C2×#53411yescharacteristic
589C2×C11C2×#53711yescharacteristic
590C2×C11C2×#53811yescharacteristic
591C2×C11C2×#53911yescharacteristic
592C2×C11C2×#54011yescharacteristic
593C2×C11C2×#54211yescharacteristic
594D11—44no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—114no—
609C24—112no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24—222no—
616C24C2×C22⋊D1114yes—
617C24C23×D1112yes—
618C24C23×D1112yes—
619C24C23×D1111yescharacteristic
620C2×D4—28no—
621C2×D4—44no—
622C2×D4—44no—
623C2×D4—416no—
624C2×D4—228no—
625C2×D4—228no—
626C2×D4—2232no—
627C2×D4—228no—
628C2×D4—228no—
629C2×D4—444no—
630C2×D4—444no—
631C2×D4—4416no—
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—22no—
644C22×C4—22no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—416no—
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×C4—222no—
675C22×C4—222no—
676C22×C4—228no—
677C22×C4—444no—
678C22×C4—444no—
679C22×C4—4416no—
680C22×C4C2×C22⋊D1114yes—
681C22×C4C2×C22⋊D1114yes—
682C22×C4C2×C22⋊D11116yescomplemented
683C22×C4C23×D1112yes—
684C22×C4C23×D1112yes—
685C22×C4C23×D1112yes—
686C22×C4C23×D1112yes—
687C22×C4C23×D1112yes—
688C4⋊C4—28no—
689C4⋊C4—28no—
690C4⋊C4—228no—
691C4⋊C4—228no—
692C4⋊C4—444no—
693C4⋊C4—444no—
694C4⋊C4—444no—
695C4⋊C4—444no—
696C22⋊C4—28no—
697C22⋊C4—28no—
698C22⋊C4—28no—
699C22⋊C4—228no—
700C22⋊C4—228no—
701C22⋊C4—228no—
702C22⋊C4—228no—
703C22⋊C4—444no—
704C22⋊C4—444no—
705C22⋊C4—444no—
706C22⋊C4—444no—
707C22⋊C4—444no—
708C22⋊C4—444no—
709C42—228no—
710C11C2×#263011yescharacteristic, complemented, Sylow
711C23—28no—
712C23—28no—
713C23—28no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—114no—
739C23—228no—
740C23—228no—
741C23—222no—
742C23—222no—
743C23—228no—
744C23—222no—
745C23—222no—
746C23—222no—
747C23—222no—
748C23—444no—
749C23—444no—
750C23—444no—
751C23—444no—
752C23#6703712yes—
753C23#6703712yes—
754C23#41×D1112yes—
755C23#41×D1112yes—
756C23#6704212yes—
757C23#6704312yes—
758C23C22×C22⋊D1114yes—
759C23C22×C22⋊D1112yes—
760C23C24×D1111yescharacteristic
761D4—416no—
762D4—2232no—
763D4—4416no—
764C2×C4—28no—
765C2×C4—28no—
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—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—416no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
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—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—4416no—
806C2×C4—444no—
807C2×C4—444no—
808C2×C4—444no—
809C2×C4—444no—
810C2×C4—444no—
811C2×C4—444no—
812C2×C4C22×C22⋊D1114yes—
813C2×C4C22×C22⋊D1114yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—416no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—88no—
830C22—224no—
831C22—224no—
832C22—224no—
833C22—4416no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—442no—
838C22#1062318814yes—
839C22#1062319114yes—
840C22#1062319314yes—
841C22#1062319414yes—
842C22#1062333514yes—
843C22#1062335914yes—
844C22#1062336414yes—
845C22C2×#6703711yescharacteristic
846C22C2×#6703711yescharacteristic
847C22C2×#41×D1111yescharacteristic
848C22C2×#41×D1111yescharacteristic
849C22C2×#6704211yescharacteristic
850C22C2×#6704311yescharacteristic
851C22C23×C22⋊D1111yescharacteristic
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—224no—
858C4—442no—
859C4—442no—
860C4—442no—
861C4—442no—
862C4—442no—
863C4—442no—
864C2—44no—
865C2—82no—
866C2—444no—
867C2#1307445518yesdirect product factor
868C2C2×#1062335911yescharacteristic
869C2C2×#1062333511yescharacteristic
870C2C2×#1062336411yescharacteristic
871C2C2×#1062318811yescharacteristic
872C2C2×#1062319111yescharacteristic
873C2C2×#1062319411yescharacteristic
874C2C2×#1062319311yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#123C2
socleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC22×#123D11
hypocenterC11C2×#2630
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×C4×C22⋊D11C2semidirect
2. #13074455C2direct (N × H)
3. C2×#10622597C2semidirect
4. C2×#10622565C2semidirect
5. C2×#10622561C2semidirect
6. C2×#10622607C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622835C2semidirect
11. C2×#10622557C2semidirect
12. C2×#10622591C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622602C2semidirect
15. C2×#10622825C2semidirect
16. C22×C11×#123C2semidirect
23. C2×C11×#123C22semidirect
36. C2×C4×C22⋊D11C22semidirect
49. #10622835C22semidirect
50. #10622825C22semidirect
59. #10622607C22semidirect
60. #10622602C22semidirect
61. #10622597C22semidirect
62. #10622591C22semidirect
63. #10622574C22semidirect
64. #10622572C22semidirect
65. #10622569C22semidirect
66. #10622565C22semidirect
67. #10622561C22semidirect
68. #10622557C22semidirect
78. C23×C4×C11D4semidirect
206. C22×C4×C11C2×D4semidirect
274. C22×#123D11semidirect
399. C2×#123C2×D11semidirect
523. C23×C4C22⋊D11semidirect
586. C2×C11#2630semidirect
682. C22×C4C2×C22⋊D11semidirect
710. C11C2×#2630semidirect
867. C2#13074455direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
#130744552
C2×#106225972
C2×#106225652
C2×#106225612
C2×#106226072
C2×#106225742
C2×#106225722
C2×#106228352
C2×#106228362
C2×#106225572
C2×#106225912
C2×#106225692
C2×#106226022
C2×#106228252
C22×C11×#1232
C2×#263011