Finite Group Databasebeta

← C2×#13073772 #14924146

Subgroups — C2×#13073772 #14924146

Order 2816.

4166 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D11C211yesmaximal, characteristic
3#13073772C2116yesmaximal, direct product factor
4C2×#10622288C211yesmaximal, characteristic, complemented
5C2×#10622565C211yesmaximal, characteristic, complemented
6C2×#10622286C211yesmaximal, characteristic, complemented
7C2×#10622560C211yesmaximal, characteristic, complemented
8C2×#10622558C211yesmaximal, characteristic, complemented
9C2×#10622553C211yesmaximal, characteristic, complemented
10C2×#10622603C211yesmaximal, characteristic, complemented
11C2×#10622277C211yesmaximal, characteristic, complemented
12C2×#10622277C211yesmaximal, characteristic, complemented
13C2×#10622568C211yesmaximal, characteristic
14C2×#10622568C211yesmaximal, characteristic
15C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×Dic22C2211yescharacteristic, complemented
21C22×C11×C4⋊C4C2211yescharacteristic, complemented
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic, complemented
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic, complemented
40C22×Dic11⋊C4C2211yescharacteristic, complemented
41C22×C4×Dic11C2211yescharacteristic, complemented
42C2×#66949—28no—
43C2×#66949C2218yescomplemented
44C2×C22⋊C4×D11—28no—
45C2×C22⋊C4×D11C2218yes—
46C11×#388C2218yescomplemented
47C2×C11×#95C2211yescharacteristic, complemented
48C2×C11×#95C2211yescharacteristic, complemented
49C2×C11⋊#95C2211yescharacteristic, complemented
50C2×C11⋊#95C2211yescharacteristic, complemented
51C2×C11⋊#95C2211yescharacteristic, complemented
52C2×C11⋊#95C2211yescharacteristic, complemented
53C2×C11⋊#95C2211yescharacteristic, complemented
54C2×C11⋊#95C2211yescharacteristic, complemented
55C2×C11⋊#95C2211yescharacteristic, complemented
56C2×C11⋊#95C2211yescharacteristic, complemented
57#10622603C2218yescomplemented
58#10622568C2218yes—
59#10622568C2218yes—
60#10622565C2218yescomplemented
61#10622560C2218yescomplemented
62#10622558C2218yescomplemented
63#10622553C2218yescomplemented
64C4×(C2×D11)⋊C4C2218yescomplemented
65#10622288C2218yescomplemented
66#10622286C2218yescomplemented
67#10622277C2218yescomplemented
68#10622277C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11—24no—
71C24×D11—24no—
72C24×D11—24no—
73C24×D11—24no—
74C24×D11—24no—
75C24×D11—42no—
76C24×D11—42no—
77C24×D11C2311yescharacteristic
78C24×D11C2314yes—
79C24×D11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C22×C4×D11—24no—
93C22×C4×D11—24no—
94C22×C4×D11—24no—
95C22×C4×D11—42no—
96C22×C4×D11—42no—
97C22×C4×D11D418yes—
98C22×C4×D11C2314yes—
99C22×C4×D11C2314yes—
100C22×Dic22—24no—
101C22×Dic22—42no—
102C22×Dic22—42no—
103C22×Dic22C2314yescomplemented
104C2×C11×C4⋊C4—24no—
105C2×C11×C4⋊C4C2314yescomplemented
106C2×C11×C22⋊C4—24no—
107C2×C11×C22⋊C4—24no—
108C2×C11×C22⋊C4—42no—
109C2×C11×C22⋊C4C2314yes—
110C2×C11×C22⋊C4C2314yes—
111C2×C11×C22⋊C4C2314yes—
112C2×C42×C11—42no—
113C2×C42×C11C2314yescomplemented
114C2×C22⋊Dic11—24no—
115C2×C22⋊Dic11—24no—
116C2×C22⋊Dic11—42no—
117C2×C22⋊Dic11C2314yes—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120C2×(C2×D11)⋊C4—24no—
121C2×(C2×D11)⋊C4—24no—
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—42no—
129C2×(C2×D11)⋊C4—42no—
130C2×(C2×D11)⋊C4C2314yes—
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×Dic11⋊C4—24no—
141C2×Dic11⋊C4—24no—
142C2×Dic11⋊C4C2314yescomplemented
143C2×Dic11⋊C4C2314yescomplemented
144C2×C4×Dic11—42no—
145C2×C4×Dic11C2314yescomplemented
146#66949—232no—
147C22⋊C4×D11—232no—
148C11×#95C2314yescomplemented
149C11×#95C2314yescomplemented
150C11⋊#95C2314yescomplemented
151C11⋊#95C2314yescomplemented
152C11⋊#95C2314yescomplemented
153C11⋊#95C2314yescomplemented
154C11⋊#95C2314yescomplemented
155C11⋊#95C2314yescomplemented
156C11⋊#95C2314yescomplemented
157C11⋊#95C2314yescomplemented
158C2×#2561—111nomaximal, Sylow
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11#4114yes—
166C24×C11C2412yes—
167C24×C11C2411yescharacteristic
168C23×D11—22no—
169C23×D11—22no—
170C23×D11—22no—
171C23×D11—22no—
172C23×D11—232no—
173C23×D11—22no—
174C23×D11—28no—
175C23×D11—22no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11—28no—
181C23×D11—28no—
182C23×D11—28no—
183C23×D11—28no—
184C23×D11—44no—
185C23×D11—44no—
186C23×D11—416no—
187C23×D11—416no—
188C23×D11—416no—
189C23×D11—416no—
190C23×D11—416no—
191C23×D11—416no—
192C23×D11C2×D414yes—
193C23×D11#4114yes—
194C23×D11#4114yes—
195C23×D11#4114yes—
196C23×D11C2412yes—
197C23×D11C2412yes—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
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—22no—
214C22×C4×C11—22no—
215C22×C4×C11C2×D414yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
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×Dic11C2×D414yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C2×C4×D11—28no—
247C2×C4×D11—28no—
248C2×C4×D11—28no—
249C2×C4×D11—416no—
250C2×C4×D11—44no—
251C2×C4×D11—44no—
252C2×C4×D11—416no—
253C2×C4×D11C2×D4116yes—
254C2×Dic22—28no—
255C2×Dic22—44no—
256C2×Dic22—44no—
257C2×Dic22—416no—
258C11×C4⋊C4—28no—
259C11×C22⋊C4—28no—
260C11×C22⋊C4—28no—
261C11×C22⋊C4—44no—
262C42×C11—44no—
263C22⋊Dic11—28no—
264C22⋊Dic11—28no—
265C22⋊Dic11—44no—
266(C2×D11)⋊C4—28no—
267(C2×D11)⋊C4—28no—
268(C2×D11)⋊C4—28no—
269(C2×D11)⋊C4—28no—
270(C2×D11)⋊C4—28no—
271(C2×D11)⋊C4—28no—
272(C2×D11)⋊C4—28no—
273(C2×D11)⋊C4—28no—
274(C2×D11)⋊C4—44no—
275(C2×D11)⋊C4—44no—
276Dic11⋊C4—28no—
277Dic11⋊C4—28no—
278C4×Dic11—44no—
279C22×C22⋊Q8—111no—
280C23×C22⋊C4—111no—
281#2561—1116no—
282C2×#397—111no—
283C2×#397—111no—
284C2×#393—111no—
285C2×#393—111no—
286C2×#388—111no—
287C2×#388—111no—
288C2×#388—111no—
289C2×#388D1111yescharacteristic, complemented
290C2×#381—111no—
291C2×#381—111no—
292C2×#379—111no—
293C2×#379—111no—
294C2×C4×C22⋊C4—111no—
295C23×C11—28no—
296C23×C11—28no—
297C23×C11—28no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—44no—
305C23×C11—44no—
306C23×C11—44no—
307C23×C11—44no—
308C23×C11C22×D412yes—
309C23×C11C2×#4114yes—
310C23×C11C2×#4112yes—
311C23×C11C2×#4112yes—
312C23×C11C2×#4112yes—
313C23×C11C2×#4112yes—
314C23×C11H(5,𝔽2)12yes—
315C23×C11H(5,𝔽2)12yes—
316C23×C11C2511yescharacteristic
317C22×D11—28no—
318C22×D11—28no—
319C22×D11—28no—
320C22×D11—28no—
321C22×D11—28no—
322C22×D11—28no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—232no—
328C22×D11—28no—
329C22×D11—28no—
330C22×D11—28no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—416no—
338C22×D11—416no—
339C22×D11—416no—
340C22×D11—416no—
341C22×D11—4128no—
342C22×D11—416no—
343C22×D11—44no—
344C22×D11—44no—
345C22×D11—44no—
346C22×D11—44no—
347C22×D11—416no—
348C22×D11#124116yes—
349C22×D11C22×D414yes—
350C22×D11C2×#4114yes—
351C22×D11C2×#4114yes—
352C22×D11C2×#4114yes—
353C2×C4×C11—28no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
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—44no—
372C2×C4×C11—44no—
373C2×C4×C11—44no—
374C2×C4×C11—44no—
375C2×C4×C11—44no—
376C2×C4×C11C22×D414yes—
377C2×Dic11—28no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
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—44no—
396C2×Dic11—44no—
397C2×Dic11—44no—
398C2×Dic11—44no—
399C2×Dic11—44no—
400C2×Dic11C22×D414yes—
401C4×D11—416no—
402C4×D11—416no—
403Dic22—416no—
404C26—111no—
405C23×Q8—111no—
406C24×C4—111no—
407C24×C4—111no—
408C2×C22⋊Q8—118no—
409C2×C22⋊Q8—228no—
410C22×C4⋊C4—111no—
411C22×C4⋊C4—111no—
412C22×C4⋊C4C2×D1111yescharacteristic, complemented
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⋊C4—111no—
421C22×C22⋊C4—111no—
422C22×C22⋊C4—111no—
423C22×C22⋊C4—111no—
424C22×C22⋊C4—111no—
425C22×C22⋊C4—111no—
426C22×C22⋊C4—118no—
427C22×C22⋊C4—228no—
428C22×C22⋊C4C2×D1111yescharacteristic
429C22×C22⋊C4C2×D1111yescharacteristic
430C22×C22⋊C4C2×D1111yescharacteristic
431C22×C42—111no—
432C22×C42C2×D1111yescharacteristic, complemented
433#397—118no—
434#397—118no—
435#393—118no—
436#393—118no—
437#388—118no—
438#388—118no—
439#388—118no—
440#388C2×D1118yescomplemented
441#381—118no—
442#381—118no—
443#379—118no—
444#379—118no—
445C4×C22⋊C4—118no—
446C2×#95—111no—
447C2×#95—111no—
448C2×#95—111no—
449C2×#95—111no—
450C2×#95—111no—
451C2×#95—111no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95C2×D1111yescharacteristic, complemented
455C2×#95C2×D1111yescharacteristic, complemented
456C22×C11—24no—
457C22×C11—24no—
458C22×C11—24no—
459C22×C11—416no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11#52514yes—
465C22×C11C2×#12414yes—
466C22×C11#53414yes—
467C22×C11#55114yes—
468C22×C11#55114yes—
469C22×C11#55114yes—
470C22×C11#55114yes—
471C22×C11C23×D411yescharacteristic
472C22×C11C22×#4111yescharacteristic
473C22×C11C22×#4111yescharacteristic
474C22×C11C22×#4111yescharacteristic
475C22×C11C22×#4111yescharacteristic
476C22×C11C2×H(5,𝔽2)11yescharacteristic
477C22×C11C2×H(5,𝔽2)11yescharacteristic
478C2×D11—232no—
479C2×D11—24no—
480C2×D11—24no—
481C2×D11—24no—
482C2×D11—24no—
483C2×D11—24no—
484C2×D11—24no—
485C2×D11—24no—
486C2×D11—24no—
487C2×D11—24no—
488C2×D11—464no—
489C2×D11—416no—
490C2×D11—42no—
491C2×D11—42no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11C2×#12418yes—
495C4×C11—24no—
496C4×C11—42no—
497C4×C11—42no—
498C4×C11—42no—
499C4×C11—42no—
500C4×C11—42no—
501Dic11—24no—
502Dic11—42no—
503Dic11—42no—
504Dic11—42no—
505Dic11—42no—
506Dic11—42no—
507C25—111no—
508C25—111no—
509C25—114no—
510C25—224no—
511C25—224no—
512C25—224no—
513C25—224no—
514C25—224no—
515C25—442no—
516C25—442no—
517C25C22×D1111yescharacteristic
518C22×Q8—114no—
519C22×Q8—224no—
520C22×Q8—442no—
521C22×Q8—442no—
522C23×C4—111no—
523C23×C4—118no—
524C23×C4—114no—
525C23×C4—111no—
526C23×C4—111no—
527C23×C4—111no—
528C23×C4—111no—
529C23×C4—111no—
530C23×C4—114no—
531C23×C4—224no—
532C23×C4—224no—
533C23×C4—224no—
534C23×C4—442no—
535C23×C4—442no—
536C23×C4C22×D1111yescharacteristic
537C23×C4C22×D1111yescharacteristic
538C23×C4C22×D1111yescharacteristic
539C23×C4C22×D1111yescharacteristic
540C23×C4C22×D1111yescharacteristic
541C23×C4C22×D1111yescharacteristic
542C22⋊Q8—2232no—
543C2×C4⋊C4—24no—
544C2×C4⋊C4—114no—
545C2×C4⋊C4—114no—
546C2×C4⋊C4—224no—
547C2×C4⋊C4—224no—
548C2×C4⋊C4C22×D1114yescomplemented
549C2×C22⋊C4—24no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—42no—
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—114no—
562C2×C22⋊C4—114no—
563C2×C22⋊C4—114no—
564C2×C22⋊C4—114no—
565C2×C22⋊C4—2232no—
566C2×C22⋊C4—224no—
567C2×C22⋊C4—224no—
568C2×C22⋊C4—224no—
569C2×C22⋊C4—224no—
570C2×C22⋊C4—224no—
571C2×C22⋊C4—224no—
572C2×C22⋊C4—224no—
573C2×C22⋊C4—224no—
574C2×C22⋊C4—224no—
575C2×C22⋊C4—224no—
576C2×C22⋊C4—442no—
577C2×C22⋊C4—442no—
578C2×C22⋊C4—442no—
579C2×C22⋊C4C22×D1114yes—
580C2×C22⋊C4C22×D1114yes—
581C2×C22⋊C4C22×D1114yes—
582C2×C42—42no—
583C2×C42—114no—
584C2×C42—442no—
585C2×C42C22×D1114yescomplemented
586#95—114no—
587#95—114no—
588#95—114no—
589#95—114no—
590#95—114no—
591#95—114no—
592#95—114no—
593#95—114no—
594#95C22×D1114yescomplemented
595#95C22×D1114yescomplemented
596C2×C11—44no—
597C2×C11#256118yescomplemented
598C2×C11C2×#52511yescharacteristic
599C2×C11C22×#12411yescharacteristic
600C2×C11C2×#53411yescharacteristic
601C2×C11C2×#55111yescharacteristic
602C2×C11C2×#55111yescharacteristic
603C2×C11C2×#55111yescharacteristic
604C2×C11C2×#55111yescharacteristic
605D11—28no—
606D11—44no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—114no—
614C24—114no—
615C24—114no—
616C24—112no—
617C24—114no—
618C24—112no—
619C24—228no—
620C24—228no—
621C24—228no—
622C24—228no—
623C24—2232no—
624C24—222no—
625C24—222no—
626C24—222no—
627C24—222no—
628C24—228no—
629C24—222no—
630C24—222no—
631C24—222no—
632C24—222no—
633C24—222no—
634C24—222no—
635C24—444no—
636C24—444no—
637C24—4416no—
638C24—4416no—
639C24—4416no—
640C24—4416no—
641C24—4416no—
642C24—4416no—
643C24#433914yes—
644C24C23×D1112yes—
645C24C23×D1111yescharacteristic
646C2×Q8—228no—
647C2×Q8—444no—
648C2×Q8—444no—
649C2×Q8—4416no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—114no—
668C22×C4—112no—
669C22×C4—1116no—
670C22×C4—112no—
671C22×C4—112no—
672C22×C4—112no—
673C22×C4—112no—
674C22×C4—112no—
675C22×C4—228no—
676C22×C4—228no—
677C22×C4—228no—
678C22×C4—222no—
679C22×C4—222no—
680C22×C4—222no—
681C22×C4—222no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—222no—
685C22×C4—222no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—222no—
691C22×C4—222no—
692C22×C4—222no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—4416no—
696C22×C4—444no—
697C22×C4—444no—
698C22×C4—4416no—
699C22×C4D4×D1114yes—
700C22×C4C23×D1112yes—
701C22×C4C23×D1112yes—
702C22×C4C23×D1112yes—
703C22×C4C23×D1112yes—
704C22×C4C23×D1112yes—
705C22×C4C23×D1112yes—
706C4⋊C4—28no—
707C4⋊C4—228no—
708C4⋊C4—228no—
709C22⋊C4—28no—
710C22⋊C4—28no—
711C22⋊C4—44no—
712C22⋊C4—228no—
713C22⋊C4—228no—
714C22⋊C4—228no—
715C22⋊C4—228no—
716C22⋊C4—228no—
717C22⋊C4—228no—
718C22⋊C4—228no—
719C22⋊C4—228no—
720C22⋊C4—228no—
721C22⋊C4—228no—
722C22⋊C4—444no—
723C22⋊C4—444no—
724C22⋊C4—444no—
725C42—44no—
726C42—444no—
727C11C2×#256111yescharacteristic, complemented, Sylow
728C23—28no—
729C23—28no—
730C23—28no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—114no—
742C23—114no—
743C23—114no—
744C23—1116no—
745C23—114no—
746C23—2232no—
747C23—228no—
748C23—228no—
749C23—228no—
750C23—228no—
751C23—228no—
752C23—222no—
753C23—228no—
754C23—222no—
755C23—222no—
756C23—222no—
757C23—228no—
758C23—228no—
759C23—222no—
760C23—222no—
761C23—228no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—222no—
766C23—4416no—
767C23—4416no—
768C23—4416no—
769C23—4416no—
770C23—4416no—
771C23—4416no—
772C23—44128no—
773C23—444no—
774C23—444no—
775C23—444no—
776C23—444no—
777C23C2×#433914yes—
778C23C2×#433912yes—
779C23C2×D4×D1112yes—
780C23#6703712yes—
781C23#41×D1112yes—
782C23#41×D1112yes—
783C23#41×D1112yes—
784C23#6704212yes—
785C23C24×D1111yescharacteristic
786Q8—4416no—
787C2×C4—28no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
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—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—114no—
811C2×C4—228no—
812C2×C4—222no—
813C2×C4—222no—
814C2×C4—222no—
815C2×C4—222no—
816C2×C4—222no—
817C2×C4—222no—
818C2×C4—222no—
819C2×C4—222no—
820C2×C4—222no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—4416no—
830C2×C4—4416no—
831C2×C4—444no—
832C2×C4—444no—
833C2×C4—444no—
834C2×C4—444no—
835C2×C4—444no—
836C2×C4C2×D4×D1114yes—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—416no—
845C22—118no—
846C22—224no—
847C22—224no—
848C22—224no—
849C22—224no—
850C22—224no—
851C22—2232no—
852C22—224no—
853C22—224no—
854C22—224no—
855C22—224no—
856C22—4464no—
857C22—442no—
858C22—442no—
859C22—442no—
860C22—4416no—
861C22—442no—
862C22#1062305814yes—
863C22#1062307814yes—
864C22#1062308714yes—
865C22#1062313614yes—
866C22#1062319014yes—
867C22D11×#12414yes—
868C22#1062323614yes—
869C22C22×#433911yescharacteristic
870C22C22×D4×D1111yescharacteristic
871C22C2×#6703711yescharacteristic
872C22C2×#41×D1111yescharacteristic
873C22C2×#41×D1111yescharacteristic
874C22C2×#41×D1111yescharacteristic
875C22C2×#6704211yescharacteristic
876C4—24no—
877C4—42no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—224no—
883C4—442no—
884C4—442no—
885C4—442no—
886C4—442no—
887C4—442no—
888C2—44no—
889C2—228no—
890C2—444no—
891C2#1307377218yesdirect product factor
892C2C2×#1062307811yescharacteristic
893C2C2×D11×#12411yescharacteristic
894C2C2×#1062313611yescharacteristic
895C2C2×#1062305811yescharacteristic
896C2C2×#1062323611yescharacteristic
897C2C2×#1062319011yescharacteristic
898C2C2×#1062308711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC25×D11C22
hypercenterC2×#388D11
hypocenterC11C2×#2561
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#66949C2semidirect
3. #13073772C2direct (N × H)
4. C2×#10622288C2semidirect
5. C2×#10622565C2semidirect
6. C2×#10622286C2semidirect
7. C2×#10622560C2semidirect
8. C2×#10622558C2semidirect
9. C2×#10622553C2semidirect
10. C2×#10622603C2semidirect
11. C2×#10622277C2semidirect
12. C2×#10622277C2semidirect
15. C2×C4×(C2×D11)⋊C4C2semidirect
16. C2×C11×#388C2semidirect
20. C23×Dic22C22semidirect
21. C22×C11×C4⋊C4C22semidirect
25. C22×C42×C11C22semidirect
39. C22×Dic11⋊C4C22semidirect
40. C22×Dic11⋊C4C22semidirect
41. C22×C4×Dic11C22semidirect
43. C2×#66949C22semidirect
46. C11×#388C22semidirect
47. C2×C11×#95C22semidirect
48. C2×C11×#95C22semidirect
49. C2×C11⋊#95C22semidirect
50. C2×C11⋊#95C22semidirect
51. C2×C11⋊#95C22semidirect
52. C2×C11⋊#95C22semidirect
53. C2×C11⋊#95C22semidirect
54. C2×C11⋊#95C22semidirect
55. C2×C11⋊#95C22semidirect
56. C2×C11⋊#95C22semidirect
57. #10622603C22semidirect
60. #10622565C22semidirect
61. #10622560C22semidirect
62. #10622558C22semidirect
63. #10622553C22semidirect
64. C4×(C2×D11)⋊C4C22semidirect
65. #10622288C22semidirect
66. #10622286C22semidirect
67. #10622277C22semidirect
68. #10622277C22semidirect
103. C22×Dic22C23semidirect
105. C2×C11×C4⋊C4C23semidirect
113. C2×C42×C11C23semidirect
142. C2×Dic11⋊C4C23semidirect
143. C2×Dic11⋊C4C23semidirect
145. C2×C4×Dic11C23semidirect
148. C11×#95C23semidirect
149. C11×#95C23semidirect
150. C11⋊#95C23semidirect
151. C11⋊#95C23semidirect
152. C11⋊#95C23semidirect
153. C11⋊#95C23semidirect
154. C11⋊#95C23semidirect
155. C11⋊#95C23semidirect
156. C11⋊#95C23semidirect
157. C11⋊#95C23semidirect
289. C2×#388D11semidirect
412. C22×C4⋊C4C2×D11semidirect
432. C22×C42C2×D11semidirect
440. #388C2×D11semidirect
454. C2×#95C2×D11semidirect
455. C2×#95C2×D11semidirect
548. C2×C4⋊C4C22×D11semidirect
585. C2×C42C22×D11semidirect
594. #95C22×D11semidirect
595. #95C22×D11semidirect
597. C2×C11#2561semidirect
727. C11C2×#2561semidirect
891. C2#13073772direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669492
C22×C22⋊C4×D112
#130737722
C2×#106222882
C2×#106225652
C2×#106222862
C2×#106225602
C2×#106225582
C2×#106225532
C2×#106226032
C2×#106222772
C2×#106225682
C2×C4×(C2×D11)⋊C42
C2×C11×#3882
C2×#256111