Finite Group Databasebeta

← C2×#13074228 #14925166

Subgroups — C2×#13074228 #14925166

Order 2816.

3330 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×#66982C211yesmaximal, characteristic, complemented
2#13074228C2116yesmaximal, direct product factor
3C2×#10622565C211yesmaximal, characteristic, complemented
4C2×#10622572C211yesmaximal, characteristic, complemented
5C2×#10622835C211yesmaximal, characteristic, complemented
6C2×#10622836C211yesmaximal, characteristic
7C2×#10622570C211yesmaximal, characteristic, complemented
8C2×#10622585C211yesmaximal, characteristic, complemented
9C2×#10622558C211yesmaximal, characteristic, complemented
10C2×#10622553C211yesmaximal, characteristic, complemented
11C2×#10622603C211yesmaximal, characteristic, complemented
12C2×#10622546C211yesmaximal, characteristic, complemented
13C2×#10622826C211yesmaximal, characteristic, complemented
14C2×#10622823C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
16C22×C4×D4×C11C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C2×C4×D4×C11—28no—
23C2×C4×D4×C11C2218yescomplemented
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C42×C11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C2×#66982—28no—
35C2×#66982C2218yescomplemented
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×C4×Dic11C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48#10622836C2218yes—
49#10622835C2218yescomplemented
50#10622826C2218yescomplemented
51#10622823C2218yescomplemented
52C4×C22⋊Dic11C2218yescomplemented
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622603C2218yescomplemented
62#10622585C2218yescomplemented
63#10622572C2218yescomplemented
64#10622570C2218yescomplemented
65#10622565C2218yescomplemented
66#10622558C2218yescomplemented
67#10622553C2218yescomplemented
68#10622546C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C22×D4×C11—24no—
73C22×D4×C11—24no—
74C22×D4×C11—24no—
75C22×D4×C11C2314yes—
76C23×C4×C11—24no—
77C23×C4×C11—42no—
78C23×C4×C11—42no—
79C23×C4×C11—42no—
80C23×C4×C11—42no—
81C23×C4×C11D418yescomplemented
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2314yes—
88C23×C4×C11C2314yes—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11—42no—
93C22×C22⋊D11—42no—
94C22×C22⋊D11—42no—
95C22×C22⋊D11C2314yes—
96C22×C22⋊D11C2314yes—
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C4×D4×C11—232no—
105C2×C11×C4⋊C4—24no—
106C2×C11×C4⋊C4C2314yes—
107C2×C11×C22⋊C4—24no—
108C2×C11×C22⋊C4—24no—
109C2×C11×C22⋊C4C2314yes—
110C2×C11×C22⋊C4C2314yes—
111C2×C42×C11—24no—
112C2×C42×C11C2314yes—
113C2×C22⋊Dic11—24no—
114C2×C22⋊Dic11—24no—
115C2×C22⋊Dic11—24no—
116C2×C22⋊Dic11—24no—
117C2×C22⋊Dic11—24no—
118C2×C22⋊Dic11—42no—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125#66982—232no—
126C2×(C2×D11)⋊C4—24no—
127C2×(C2×D11)⋊C4—24no—
128C2×(C2×D11)⋊C4—24no—
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4—42no—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×Dic11⋊C4—24no—
137C2×Dic11⋊C4—24no—
138C2×Dic11⋊C4—24no—
139C2×Dic11⋊C4—24no—
140C2×Dic11⋊C4—42no—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×C4×Dic11—42no—
147C2×C4×Dic11—42no—
148C2×C4×Dic11C2314yes—
149C2×C4×Dic11C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2602—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×C11C2×D414yes—
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—232no—
185C2×D4×C11—28no—
186C2×D4×C11—28no—
187C2×D4×C11—28no—
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—28no—
201C22×C4×C11—416no—
202C22×C4×C11—44no—
203C22×C4×C11—44no—
204C22×C4×C11—44no—
205C22×C4×C11—44no—
206C22×C4×C11—416no—
207C22×C4×C11C2×D414yes—
208C22×C4×C11C2×D414yes—
209C22×C4×C11C2×D4116yescomplemented
210C22×C4×C11#4114yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C2×C22⋊D11—28no—
217C2×C22⋊D11—28no—
218C2×C22⋊D11—28no—
219C2×C22⋊D11—44no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—416no—
223C2×C22⋊D11—416no—
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—22no—
241C22×Dic11—22no—
242C22×Dic11—22no—
243C22×Dic11#4114yes—
244C22×Dic11#4114yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C22×Dic11C2412yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C11×C4⋊C4—28no—
253C11×C22⋊C4—28no—
254C11×C22⋊C4—28no—
255C42×C11—28no—
256C22⋊Dic11—28no—
257C22⋊Dic11—28no—
258C22⋊Dic11—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—44no—
267Dic11⋊C4—28no—
268Dic11⋊C4—28no—
269Dic11⋊C4—28no—
270Dic11⋊C4—28no—
271Dic11⋊C4—44no—
272C4×Dic11—44no—
273C4×Dic11—44no—
274C22×#123—111no—
275C22×C4×D4D1111yescharacteristic, complemented
276#2602—1116no—
277C2×#397—111no—
278C2×#394—111no—
279C2×#394—111no—
280C2×#392—111no—
281C2×#390—111no—
282C2×#389—111no—
283C2×#388—111no—
284C2×#388—111no—
285C2×#388—111no—
286C2×#387—111no—
287C2×#386—111no—
288C2×#385—111no—
289C2×C4×C22⋊C4—111no—
290C23×C11—28no—
291C23×C11—28no—
292C23×C11—28no—
293C23×C11—28no—
294C23×C11—28no—
295C23×C11—28no—
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—22no—
307C23×C11—22no—
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×D414yes—
317C23×C11C22×D412yes—
318C23×C11C2×#4114yes—
319C23×C11C2×#4112yes—
320C23×C11C2×#4112yes—
321C23×C11C2×#4112yes—
322C23×C11C2×#4112yes—
323C23×C11H(5,𝔽2)12yes—
324C23×C11H(5,𝔽2)12yes—
325C23×C11C2511yescharacteristic
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—44no—
334C22×D11—44no—
335C22×D11—44no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11—44no—
339C22×D11—44no—
340D4×C11—232no—
341C2×C4×C11—28no—
342C2×C4×C11—28no—
343C2×C4×C11—28no—
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—416no—
358C2×C4×C11—44no—
359C2×C4×C11—44no—
360C2×C4×C11C22×D414yes—
361C2×C4×C11C22×D414yes—
362C2×C4×C11C2×#4114yes—
363C22⋊D11—416no—
364C22⋊D11—416no—
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—22no—
385C2×Dic11—22no—
386C2×Dic11—44no—
387C2×Dic11—44no—
388C2×Dic11—44no—
389C2×Dic11—44no—
390C2×Dic11—44no—
391C2×Dic11C2×#4114yes—
392C2×Dic11C2×#4114yes—
393C23×D4—111no—
394C23×D4—111no—
395C23×D4C2×D1111yescharacteristic
396C24×C4C2×D1111yescharacteristic
397C24×C4C2×D1111yescharacteristic
398C2×#123—118no—
399C2×#123—228no—
400C2×C4×D4—28no—
401C2×C4×D4C2×D1118yescomplemented
402C22×C4⋊C4—111no—
403C22×C4⋊C4—111no—
404C22×C4⋊C4—111no—
405C22×C4⋊C4—111no—
406C22×C4⋊C4—111no—
407C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
418C22×C22⋊C4—111no—
419C22×C22⋊C4C2×D1111yescharacteristic
420C22×C22⋊C4C2×D1111yescharacteristic
421C22×C42—111no—
422C22×C42—111no—
423C22×C42C2×D1111yescharacteristic
424#397—118no—
425#394—118no—
426#394—118no—
427#392—118no—
428#390—118no—
429#389—118no—
430#388—118no—
431#388—118no—
432#388—118no—
433#387—118no—
434#386—118no—
435#385—118no—
436C4×C22⋊C4—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—24no—
449C22×C11—24no—
450C22×C11—24no—
451C22×C11—416no—
452C22×C11—416no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11#52514yes—
462C22×C11#53214yes—
463C22×C11#53414yes—
464C22×C11#55114yes—
465C22×C11#55314yes—
466C22×C11#55314yes—
467C22×C11#55914yes—
468C22×C11C23×D411yescharacteristic
469C22×C11C22×#4111yescharacteristic
470C22×C11C22×#4111yescharacteristic
471C22×C11C22×#4111yescharacteristic
472C22×C11C22×#4111yescharacteristic
473C22×C11C2×H(5,𝔽2)11yescharacteristic
474C22×C11C2×H(5,𝔽2)11yescharacteristic
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—88no—
483C4×C11—24no—
484C4×C11—24no—
485C4×C11—24no—
486C4×C11—42no—
487C4×C11—42no—
488Dic11—24no—
489Dic11—24no—
490Dic11—42no—
491Dic11—42no—
492Dic11—42no—
493Dic11—42no—
494Dic11—42no—
495C25—111no—
496C25C22×D1111yescharacteristic
497C25C22×D1111yescharacteristic
498C22×D4—24no—
499C22×D4—24no—
500C22×D4—24no—
501C22×D4—114no—
502C22×D4—114no—
503C22×D4—224no—
504C22×D4—224no—
505C22×D4—224no—
506C22×D4—442no—
507C22×D4—442no—
508C22×D4—442no—
509C22×D4C22×D1114yes—
510C23×C4—24no—
511C23×C4—42no—
512C23×C4—42no—
513C23×C4—42no—
514C23×C4—42no—
515C23×C4—111no—
516C23×C4—111no—
517C23×C4—111no—
518C23×C4—111no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—111no—
522C23×C4C22⋊D1118yescomplemented
523C23×C4C22×D1111yescharacteristic
524C23×C4C22×D1111yescharacteristic
525C23×C4C22×D1111yescharacteristic
526C23×C4C22×D1111yescharacteristic
527C23×C4C22×D1111yescharacteristic
528C23×C4C22×D1114yes—
529C23×C4C22×D1114yes—
530#123—2232no—
531C4×D4—232no—
532C2×C4⋊C4—24no—
533C2×C4⋊C4—114no—
534C2×C4⋊C4—114no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4—114no—
537C2×C4⋊C4—114no—
538C2×C4⋊C4—224no—
539C2×C4⋊C4—224no—
540C2×C4⋊C4—224no—
541C2×C4⋊C4—224no—
542C2×C4⋊C4—442no—
543C2×C4⋊C4C22×D1114yes—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
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—114no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—114no—
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—224no—
565C2×C22⋊C4—224no—
566C2×C22⋊C4—442no—
567C2×C22⋊C4—442no—
568C2×C22⋊C4C22×D1114yes—
569C2×C22⋊C4C22×D1114yes—
570C2×C42—24no—
571C2×C42—114no—
572C2×C42—114no—
573C2×C42—442no—
574C2×C42—442no—
575C2×C42C22×D1114yes—
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—44no—
586C2×C11#260218yescomplemented
587C2×C11C2×#52511yescharacteristic
588C2×C11C2×#53211yescharacteristic
589C2×C11C2×#53411yescharacteristic
590C2×C11C2×#55111yescharacteristic
591C2×C11C2×#55311yescharacteristic
592C2×C11C2×#55311yescharacteristic
593C2×C11C2×#55911yescharacteristic
594D11—82no—
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—112no—
608C24—222no—
609C24—222no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24#433914yes—
616C24C2×C22⋊D1114yes—
617C24C23×D1112yes—
618C24C23×D1112yes—
619C24C23×D1111yescharacteristic
620C2×D4—232no—
621C2×D4—28no—
622C2×D4—28no—
623C2×D4—28no—
624C2×D4—228no—
625C2×D4—228no—
626C2×D4—228no—
627C2×D4—444no—
628C2×D4—444no—
629C2×D4—444no—
630C2×D4—4416no—
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—28no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—416no—
650C22×C4—416no—
651C22×C4—114no—
652C22×C4—114no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—112no—
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—222no—
677C22×C4—222no—
678C22×C4—222no—
679C22×C4#433914yes—
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—228no—
690C4⋊C4—228no—
691C4⋊C4—228no—
692C4⋊C4—228no—
693C4⋊C4—444no—
694C22⋊C4—28no—
695C22⋊C4—28no—
696C22⋊C4—228no—
697C22⋊C4—228no—
698C22⋊C4—228no—
699C22⋊C4—228no—
700C22⋊C4—228no—
701C22⋊C4—228no—
702C22⋊C4—228no—
703C22⋊C4—228no—
704C22⋊C4—228no—
705C22⋊C4—444no—
706C22⋊C4—444no—
707C42—28no—
708C42—444no—
709C42—444no—
710C11C2×#260211yescharacteristic, complemented, Sylow
711C23—28no—
712C23—28no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—28no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—222no—
744C23—444no—
745C23—444no—
746C23—444no—
747C23—444no—
748C23—444no—
749C23—444no—
750C23—444no—
751C23C2×#433914yes—
752C23C2×#433912yes—
753C23C2×#433912yes—
754C23#6703712yes—
755C23#6703712yes—
756C23#41×D1112yes—
757C23#41×D1112yes—
758C23C22×C22⋊D1114yes—
759C23C22×C22⋊D1112yes—
760C23C24×D1111yescharacteristic
761D4—232no—
762D4—4416no—
763D4—4416no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
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—416no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—114no—
784C2×C4—114no—
785C2×C4—228no—
786C2×C4—228no—
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—222no—
806C2×C4—444no—
807C2×C4—444no—
808C2×C4—444no—
809C2×C4—444no—
810C2×C4—444no—
811C2×C4C2×#433914yes—
812C2×C4C22×C22⋊D1114yes—
813C2×C4C22×C22⋊D1114yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—416no—
826C22—416no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—442no—
831C22—442no—
832C22—442no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—888no—
838C22#1062307114yes—
839C22#1062308714yes—
840C22#1062308914yes—
841C22#1062309014yes—
842C22#1062332214yes—
843C22#1062333514yes—
844C22#1062336314yes—
845C22C22×#433911yescharacteristic
846C22C22×#433911yescharacteristic
847C22C2×#6703711yescharacteristic
848C22C2×#6703711yescharacteristic
849C22C2×#41×D1111yescharacteristic
850C22C2×#41×D1111yescharacteristic
851C22C23×C22⋊D1111yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—42no—
856C4—42no—
857C4—224no—
858C4—224no—
859C4—442no—
860C4—442no—
861C4—442no—
862C4—442no—
863C4—442no—
864C2—44no—
865C2—44no—
866C2—882no—
867C2#1307422818yesdirect product factor
868C2C2×#1062332211yescharacteristic
869C2C2×#1062336311yescharacteristic
870C2C2×#1062333511yescharacteristic
871C2C2×#1062308711yescharacteristic
872C2C2×#1062307111yescharacteristic
873C2C2×#1062308911yescharacteristic
874C2C2×#1062309011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C4×D4×C11C2
socleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC22×C4×D4D11
hypocenterC11C2×#2602
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#66982C2semidirect
2. #13074228C2direct (N × H)
3. C2×#10622565C2semidirect
4. C2×#10622572C2semidirect
5. C2×#10622835C2semidirect
7. C2×#10622570C2semidirect
8. C2×#10622585C2semidirect
9. C2×#10622558C2semidirect
10. C2×#10622553C2semidirect
11. C2×#10622603C2semidirect
12. C2×#10622546C2semidirect
13. C2×#10622826C2semidirect
14. C2×#10622823C2semidirect
15. C2×C4×C22⋊Dic11C2semidirect
16. C22×C4×D4×C11C2semidirect
23. C2×C4×D4×C11C22semidirect
35. C2×#66982C22semidirect
49. #10622835C22semidirect
50. #10622826C22semidirect
51. #10622823C22semidirect
52. C4×C22⋊Dic11C22semidirect
61. #10622603C22semidirect
62. #10622585C22semidirect
63. #10622572C22semidirect
64. #10622570C22semidirect
65. #10622565C22semidirect
66. #10622558C22semidirect
67. #10622553C22semidirect
68. #10622546C22semidirect
81. C23×C4×C11D4semidirect
209. C22×C4×C11C2×D4semidirect
275. C22×C4×D4D11semidirect
401. C2×C4×D4C2×D11semidirect
522. C23×C4C22⋊D11semidirect
586. C2×C11#2602semidirect
682. C22×C4C2×C22⋊D11semidirect
710. C11C2×#2602semidirect
867. C2#13074228direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669822
#130742282
C2×#106225652
C2×#106225722
C2×#106228352
C2×#106228362
C2×#106225702
C2×#106225852
C2×#106225582
C2×#106225532
C2×#106226032
C2×#106225462
C2×#106228262
C2×#106228232
C2×C4×C22⋊Dic112
C22×C4×D4×C112
C2×#260211