Finite Group Databasebeta

← C2×#13072888 #14923536

Subgroups — C2×#13072888 #14923536

Order 2816.

4166 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66925C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D11C211yesmaximal, characteristic
3#13072888C2116yesmaximal, direct product factor
4C2×#10622562C211yesmaximal, characteristic, complemented
5C2×#10622605C211yesmaximal, characteristic, complemented
6C2×#10622288C211yesmaximal, characteristic, complemented
7C2×#10622565C211yesmaximal, characteristic, complemented
8C2×#10622283C211yesmaximal, characteristic, complemented
9C2×#10622553C211yesmaximal, characteristic, complemented
10C2×#10622557C211yesmaximal, characteristic, complemented
11C2×#10622281C211yesmaximal, characteristic, complemented
12C2×#10622602C211yesmaximal, characteristic, complemented
13C2×#10622277C211yesmaximal, characteristic, complemented
14C2×#10622568C211yesmaximal, characteristic
15C2×#10622568C211yesmaximal, characteristic
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic, complemented
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic, complemented
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic, complemented
39C22×Dic11⋊C4C2211yescharacteristic, complemented
40C22×Dic11⋊C4C2211yescharacteristic, complemented
41C22×Dic11⋊C4C2211yescharacteristic, complemented
42C22×Dic11⋊C4C2211yescharacteristic, complemented
43C22×C4×Dic11C2211yescharacteristic, complemented
44C2×C22⋊C4×D11—28no—
45C2×C22⋊C4×D11C2218yes—
46C2×#66925—28no—
47C2×#66925C2218yescomplemented
48C11×#388C2218yescomplemented
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#10622605C2218yescomplemented
58#10622602C2218yescomplemented
59#10622568C2218yes—
60#10622568C2218yes—
61#10622565C2218yescomplemented
62#10622562C2218yescomplemented
63#10622557C2218yescomplemented
64#10622553C2218yescomplemented
65#10622288C2218yescomplemented
66#10622283C2218yescomplemented
67#10622281C2218yescomplemented
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—
100C2×C11×C4⋊C4—42no—
101C2×C11×C4⋊C4C2314yescomplemented
102C2×C11×C22⋊C4—24no—
103C2×C11×C22⋊C4—24no—
104C2×C11×C22⋊C4—42no—
105C2×C11×C22⋊C4C2314yes—
106C2×C11×C22⋊C4C2314yes—
107C2×C11×C22⋊C4C2314yes—
108C2×C42×C11—24no—
109C2×C42×C11C2314yescomplemented
110C2×C22⋊Dic11—24no—
111C2×C22⋊Dic11—24no—
112C2×C22⋊Dic11—42no—
113C2×C22⋊Dic11C2314yes—
114C2×C22⋊Dic11C2314yes—
115C2×C22⋊Dic11C2314yes—
116C2×(C2×D11)⋊C4—24no—
117C2×(C2×D11)⋊C4—24no—
118C2×(C2×D11)⋊C4—24no—
119C2×(C2×D11)⋊C4—24no—
120C2×(C2×D11)⋊C4—24no—
121C2×(C2×D11)⋊C4—24no—
122C2×(C2×D11)⋊C4—24no—
123C2×(C2×D11)⋊C4—24no—
124C2×(C2×D11)⋊C4—42no—
125C2×(C2×D11)⋊C4—42no—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
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×C4⋊Dic11—42no—
137C2×C4⋊Dic11C2314yescomplemented
138C2×Dic11⋊C4—24no—
139C2×Dic11⋊C4—24no—
140C2×Dic11⋊C4—42no—
141C2×Dic11⋊C4—42no—
142C2×Dic11⋊C4C2314yescomplemented
143C2×Dic11⋊C4C2314yescomplemented
144C2×Dic11⋊C4C2314yescomplemented
145C2×Dic11⋊C4C2314yescomplemented
146C2×C4×Dic11—24no—
147C2×C4×Dic11C2314yescomplemented
148C22⋊C4×D11—232no—
149#66925—232no—
150C11×#95C2314yescomplemented
151C11×#95C2314yescomplemented
152C11⋊#95C2314yescomplemented
153C11⋊#95C2314yescomplemented
154C11⋊#95C2314yescomplemented
155C11⋊#95C2314yescomplemented
156C11⋊#95C2314yescomplemented
157C11⋊#95C2314yescomplemented
158C2×#2482—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—232no—
247C2×C4×D11—28no—
248C2×C4×D11—28no—
249C2×C4×D11—28no—
250C2×C4×D11—44no—
251C2×C4×D11—44no—
252C2×C4×D11—416no—
253C2×C4×D11C2×D4116yes—
254C11×C4⋊C4—44no—
255C11×C22⋊C4—28no—
256C11×C22⋊C4—28no—
257C11×C22⋊C4—44no—
258C42×C11—28no—
259C22⋊Dic11—28no—
260C22⋊Dic11—28no—
261C22⋊Dic11—44no—
262(C2×D11)⋊C4—28no—
263(C2×D11)⋊C4—28no—
264(C2×D11)⋊C4—28no—
265(C2×D11)⋊C4—28no—
266(C2×D11)⋊C4—28no—
267(C2×D11)⋊C4—28no—
268(C2×D11)⋊C4—28no—
269(C2×D11)⋊C4—28no—
270(C2×D11)⋊C4—44no—
271(C2×D11)⋊C4—44no—
272C4⋊Dic11—44no—
273Dic11⋊C4—28no—
274Dic11⋊C4—28no—
275Dic11⋊C4—44no—
276Dic11⋊C4—44no—
277C4×Dic11—28no—
278C22×#117—111no—
279C23×C22⋊C4—111no—
280#2482—1116no—
281C2×#399—111no—
282C2×#399—111no—
283C2×#397—111no—
284C2×#397—111no—
285C2×#388—111no—
286C2×#388—111no—
287C2×#388—111no—
288C2×#388D1111yescharacteristic, complemented
289C2×#385—111no—
290C2×#385—111no—
291C2×#381—111no—
292C2×#379—111no—
293C2×#379—111no—
294C23×C11—28no—
295C23×C11—28no—
296C23×C11—28no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—44no—
304C23×C11—44no—
305C23×C11—44no—
306C23×C11—44no—
307C23×C11C22×D412yes—
308C23×C11C2×#4114yes—
309C23×C11C2×#4112yes—
310C23×C11C2×#4112yes—
311C23×C11C2×#4112yes—
312C23×C11C2×#4112yes—
313C23×C11H(5,𝔽2)12yes—
314C23×C11H(5,𝔽2)12yes—
315C23×C11C2511yescharacteristic
316C22×D11—28no—
317C22×D11—28no—
318C22×D11—28no—
319C22×D11—28no—
320C22×D11—28no—
321C22×D11—28no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—232no—
327C22×D11—28no—
328C22×D11—28no—
329C22×D11—28no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—416no—
337C22×D11—416no—
338C22×D11—416no—
339C22×D11—416no—
340C22×D11—416no—
341C22×D11—4128no—
342C22×D11—44no—
343C22×D11—44no—
344C22×D11—44no—
345C22×D11—44no—
346C22×D11—416no—
347C22×D11#123116yes—
348C22×D11C22×D414yes—
349C22×D11C2×#4114yes—
350C22×D11C2×#4114yes—
351C22×D11C2×#4114yes—
352C2×C4×C11—28no—
353C2×C4×C11—22no—
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—44no—
371C2×C4×C11—44no—
372C2×C4×C11—44no—
373C2×C4×C11—44no—
374C2×C4×C11—44no—
375C2×C4×C11C22×D414yes—
376C2×Dic11—28no—
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—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—44no—
395C2×Dic11—44no—
396C2×Dic11—44no—
397C2×Dic11—44no—
398C2×Dic11—44no—
399C2×Dic11C22×D414yes—
400C4×D11—232no—
401C4×D11—416no—
402C26—111no—
403C24×C4—111no—
404C24×C4—111no—
405C2×#117—118no—
406C2×#117—228no—
407C22×C4⋊C4—111no—
408C22×C4⋊C4—111no—
409C22×C4⋊C4—111no—
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#399—118no—
434#399—118no—
435#397—118no—
436#397—118no—
437#388—118no—
438#388—118no—
439#388—118no—
440#388C2×D1118yescomplemented
441#385—118no—
442#385—118no—
443#381—118no—
444#379—118no—
445#379—118no—
446C2×#95—111no—
447C2×#95—111no—
448C2×#95—111no—
449C2×#95—111no—
450C2×#95—111no—
451C2×#95—111no—
452C2×#95C2×D1111yescharacteristic, complemented
453C2×#95C2×D1111yescharacteristic, complemented
454C22×C11—24no—
455C22×C11—24no—
456C22×C11—24no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—416no—
462C22×C11C2×#12314yes—
463C22×C11#52514yes—
464C22×C11#53514yes—
465C22×C11#55114yes—
466C22×C11#55114yes—
467C22×C11#55114yes—
468C22×C11#55114yes—
469C22×C11C23×D411yescharacteristic
470C22×C11C22×#4111yescharacteristic
471C22×C11C22×#4111yescharacteristic
472C22×C11C22×#4111yescharacteristic
473C22×C11C22×#4111yescharacteristic
474C22×C11C2×H(5,𝔽2)11yescharacteristic
475C22×C11C2×H(5,𝔽2)11yescharacteristic
476C2×D11—24no—
477C2×D11—24no—
478C2×D11—24no—
479C2×D11—24no—
480C2×D11—24no—
481C2×D11—24no—
482C2×D11—232no—
483C2×D11—24no—
484C2×D11—24no—
485C2×D11—24no—
486C2×D11—464no—
487C2×D11—42no—
488C2×D11—42no—
489C2×D11—42no—
490C2×D11—42no—
491C2×D11—416no—
492C2×D11C2×#12318yes—
493C4×C11—24no—
494C4×C11—42no—
495C4×C11—42no—
496C4×C11—42no—
497C4×C11—42no—
498C4×C11—42no—
499Dic11—24no—
500Dic11—42no—
501Dic11—42no—
502Dic11—42no—
503Dic11—42no—
504Dic11—42no—
505C25—111no—
506C25—111no—
507C25—114no—
508C25—224no—
509C25—224no—
510C25—224no—
511C25—224no—
512C25—224no—
513C25—442no—
514C25—442no—
515C25C22×D1111yescharacteristic
516C23×C4—111no—
517C23×C4—118no—
518C23×C4—114no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—111no—
522C23×C4—111no—
523C23×C4—111no—
524C23×C4—114no—
525C23×C4—224no—
526C23×C4—224no—
527C23×C4—224no—
528C23×C4—442no—
529C23×C4—442no—
530C23×C4C22×D1111yescharacteristic
531C23×C4C22×D1111yescharacteristic
532C23×C4C22×D1111yescharacteristic
533C23×C4C22×D1111yescharacteristic
534C23×C4C22×D1111yescharacteristic
535C23×C4C22×D1111yescharacteristic
536#117—2232no—
537C2×C4⋊C4—42no—
538C2×C4⋊C4—114no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—114no—
541C2×C4⋊C4—114no—
542C2×C4⋊C4—114no—
543C2×C4⋊C4—224no—
544C2×C4⋊C4—224no—
545C2×C4⋊C4—442no—
546C2×C4⋊C4—442no—
547C2×C4⋊C4—442no—
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—24no—
583C2×C42—114no—
584C2×C42—224no—
585C2×C42C22×D1114yescomplemented
586#95—114no—
587#95—114no—
588#95—114no—
589#95—114no—
590#95—114no—
591#95—114no—
592#95C22×D1114yescomplemented
593#95C22×D1114yescomplemented
594C2×C11—44no—
595C2×C11#248218yescomplemented
596C2×C11C22×#12311yescharacteristic
597C2×C11C2×#52511yescharacteristic
598C2×C11C2×#53511yescharacteristic
599C2×C11C2×#55111yescharacteristic
600C2×C11C2×#55111yescharacteristic
601C2×C11C2×#55111yescharacteristic
602C2×C11C2×#55111yescharacteristic
603D11—28no—
604D11—44no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—114no—
612C24—114no—
613C24—114no—
614C24—112no—
615C24—114no—
616C24—112no—
617C24—228no—
618C24—228no—
619C24—228no—
620C24—228no—
621C24—2232no—
622C24—222no—
623C24—222no—
624C24—222no—
625C24—222no—
626C24—228no—
627C24—222no—
628C24—222no—
629C24—222no—
630C24—222no—
631C24—222no—
632C24—222no—
633C24—444no—
634C24—444no—
635C24—4416no—
636C24—4416no—
637C24—4416no—
638C24—4416no—
639C24—4416no—
640C24—4416no—
641C24#433914yes—
642C24C23×D1112yes—
643C24C23×D1111yescharacteristic
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
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—114no—
662C22×C4—112no—
663C22×C4—1116no—
664C22×C4—112no—
665C22×C4—112no—
666C22×C4—112no—
667C22×C4—112no—
668C22×C4—112no—
669C22×C4—2232no—
670C22×C4—228no—
671C22×C4—228no—
672C22×C4—228no—
673C22×C4—222no—
674C22×C4—222no—
675C22×C4—222no—
676C22×C4—222no—
677C22×C4—222no—
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—444no—
691C22×C4—444no—
692C22×C4—4416no—
693C22×C4D4×D1114yes—
694C22×C4C23×D1112yes—
695C22×C4C23×D1112yes—
696C22×C4C23×D1112yes—
697C22×C4C23×D1112yes—
698C22×C4C23×D1112yes—
699C22×C4C23×D1112yes—
700C4⋊C4—44no—
701C4⋊C4—228no—
702C4⋊C4—228no—
703C4⋊C4—444no—
704C4⋊C4—444no—
705C4⋊C4—444no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—44no—
709C22⋊C4—228no—
710C22⋊C4—228no—
711C22⋊C4—228no—
712C22⋊C4—228no—
713C22⋊C4—228no—
714C22⋊C4—228no—
715C22⋊C4—228no—
716C22⋊C4—228no—
717C22⋊C4—228no—
718C22⋊C4—228no—
719C22⋊C4—444no—
720C22⋊C4—444no—
721C22⋊C4—444no—
722C42—28no—
723C42—228no—
724C11C2×#248211yescharacteristic, complemented, Sylow
725C23—28no—
726C23—28no—
727C23—28no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—1116no—
739C23—114no—
740C23—114no—
741C23—114no—
742C23—114no—
743C23—2232no—
744C23—228no—
745C23—228no—
746C23—228no—
747C23—228no—
748C23—228no—
749C23—222no—
750C23—222no—
751C23—222no—
752C23—222no—
753C23—228no—
754C23—228no—
755C23—228no—
756C23—222no—
757C23—222no—
758C23—222no—
759C23—222no—
760C23—222no—
761C23—222no—
762C23—228no—
763C23—4416no—
764C23—4416no—
765C23—4416no—
766C23—4416no—
767C23—4416no—
768C23—4416no—
769C23—44128no—
770C23—444no—
771C23—444no—
772C23—444no—
773C23—444no—
774C23C2×#433914yes—
775C23C2×#433912yes—
776C23C2×D4×D1112yes—
777C23#6703712yes—
778C23#41×D1112yes—
779C23#41×D1112yes—
780C23#41×D1112yes—
781C23#6704212yes—
782C23C24×D1111yescharacteristic
783C2×C4—28no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
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—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—114no—
807C2×C4—2232no—
808C2×C4—228no—
809C2×C4—222no—
810C2×C4—222no—
811C2×C4—222no—
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—4416no—
827C2×C4—444no—
828C2×C4—444no—
829C2×C4—444no—
830C2×C4—444no—
831C2×C4—444no—
832C2×C4C2×D4×D1114yes—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—416no—
841C22—118no—
842C22—224no—
843C22—224no—
844C22—224no—
845C22—224no—
846C22—224no—
847C22—2232no—
848C22—224no—
849C22—224no—
850C22—224no—
851C22—224no—
852C22—4464no—
853C22—442no—
854C22—442no—
855C22—442no—
856C22—4416no—
857C22—442no—
858C22#1062305814yes—
859C22#1062307814yes—
860C22#1062308714yes—
861C22#1062313814yes—
862C22D11×#12314yes—
863C22#1062321014yes—
864C22#1062323614yes—
865C22C22×#433911yescharacteristic
866C22C22×D4×D1111yescharacteristic
867C22C2×#6703711yescharacteristic
868C22C2×#41×D1111yescharacteristic
869C22C2×#41×D1111yescharacteristic
870C22C2×#41×D1111yescharacteristic
871C22C2×#6704211yescharacteristic
872C4—24no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—224no—
879C4—442no—
880C4—442no—
881C4—442no—
882C4—442no—
883C4—442no—
884C2—44no—
885C2—228no—
886C2—444no—
887C2#1307288818yesdirect product factor
888C2C2×D11×#12311yescharacteristic
889C2C2×#1062307811yescharacteristic
890C2C2×#1062313811yescharacteristic
891C2C2×#1062305811yescharacteristic
892C2C2×#1062323611yescharacteristic
893C2C2×#1062308711yescharacteristic
894C2C2×#1062321011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC25×D11C22
hypercenterC2×#388D11
hypocenterC11C2×#2482
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#66925C2semidirect
3. #13072888C2direct (N × H)
4. C2×#10622562C2semidirect
5. C2×#10622605C2semidirect
6. C2×#10622288C2semidirect
7. C2×#10622565C2semidirect
8. C2×#10622283C2semidirect
9. C2×#10622553C2semidirect
10. C2×#10622557C2semidirect
11. C2×#10622281C2semidirect
12. C2×#10622602C2semidirect
13. C2×#10622277C2semidirect
16. C2×C11×#388C2semidirect
20. C22×C11×C4⋊C4C22semidirect
24. C22×C42×C11C22semidirect
38. C22×C4⋊Dic11C22semidirect
39. C22×Dic11⋊C4C22semidirect
40. C22×Dic11⋊C4C22semidirect
41. C22×Dic11⋊C4C22semidirect
42. C22×Dic11⋊C4C22semidirect
43. C22×C4×Dic11C22semidirect
47. C2×#66925C22semidirect
48. C11×#388C22semidirect
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. #10622605C22semidirect
58. #10622602C22semidirect
61. #10622565C22semidirect
62. #10622562C22semidirect
63. #10622557C22semidirect
64. #10622553C22semidirect
65. #10622288C22semidirect
66. #10622283C22semidirect
67. #10622281C22semidirect
68. #10622277C22semidirect
101. C2×C11×C4⋊C4C23semidirect
109. C2×C42×C11C23semidirect
137. C2×C4⋊Dic11C23semidirect
142. C2×Dic11⋊C4C23semidirect
143. C2×Dic11⋊C4C23semidirect
144. C2×Dic11⋊C4C23semidirect
145. C2×Dic11⋊C4C23semidirect
147. C2×C4×Dic11C23semidirect
150. C11×#95C23semidirect
151. C11×#95C23semidirect
152. C11⋊#95C23semidirect
153. C11⋊#95C23semidirect
154. C11⋊#95C23semidirect
155. C11⋊#95C23semidirect
156. C11⋊#95C23semidirect
157. C11⋊#95C23semidirect
288. C2×#388D11semidirect
412. C22×C4⋊C4C2×D11semidirect
432. C22×C42C2×D11semidirect
440. #388C2×D11semidirect
452. C2×#95C2×D11semidirect
453. C2×#95C2×D11semidirect
548. C2×C4⋊C4C22×D11semidirect
585. C2×C42C22×D11semidirect
592. #95C22×D11semidirect
593. #95C22×D11semidirect
595. C2×C11#2482semidirect
724. C11C2×#2482semidirect
887. C2#13072888direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669252
C22×C22⋊C4×D112
#130728882
C2×#106225622
C2×#106226052
C2×#106222882
C2×#106225652
C2×#106222832
C2×#106225532
C2×#106225572
C2×#106222812
C2×#106226022
C2×#106222772
C2×#106225682
C2×C11×#3882
C2×#248211