Finite Group Databasebeta

← C2×#13073709 #14923886

Subgroups — C2×#13073709 #14923886

Order 2816.

3330 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66938C211yesmaximal, characteristic, complemented
2C22×#66936C211yesmaximal, characteristic, complemented
3#13073709C2116yesmaximal, direct product factor
4C2×#10622287C211yesmaximal, characteristic, complemented
5C2×#10622566C211yesmaximal, characteristic, complemented
6C2×#10622286C211yesmaximal, characteristic, complemented
7C2×#10622573C211yesmaximal, characteristic
8C2×#10622542C211yesmaximal, characteristic, complemented
9C2×#10622552C211yesmaximal, characteristic, complemented
10C2×#10622553C211yesmaximal, characteristic, complemented
11C2×#10622266C211yesmaximal, characteristic, complemented
12C2×#10622826C211yesmaximal, characteristic, complemented
13C2×#10622826C211yesmaximal, characteristic, complemented
14C2×#10622278C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×Dic22C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C22×C42×C11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C2×#66938—28no—
43C2×#66938C2218yescomplemented
44C2×#66936—28no—
45C2×#66936C2218yescomplemented
46C4×C11×C22⋊C4C2218yescomplemented
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2211yescharacteristic
49#10622826C2218yescomplemented
50#10622826C2218yescomplemented
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#10622573C2218yes—
60#10622566C2218yescomplemented
61#10622553C2218yescomplemented
62#10622552C2218yescomplemented
63C4×(C2×D11)⋊C4C2218yescomplemented
64#10622542C2218yescomplemented
65#10622287C2218yescomplemented
66#10622286C2218yescomplemented
67#10622278C2218yescomplemented
68#10622266C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C23×C4×C11—24no—
73C23×C4×C11—42no—
74C23×C4×C11—42no—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2314yes—
82C22×C22⋊D11—24no—
83C22×C22⋊D11—24no—
84C22×C22⋊D11—24no—
85C22×C22⋊D11—24no—
86C22×C22⋊D11—42no—
87C22×C22⋊D11—42no—
88C22×C22⋊D11C2314yes—
89C22×C22⋊D11C2314yes—
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C22×D44—24no—
97C22×D44—24no—
98C22×D44—42no—
99C22×D44C2314yes—
100C22×C4×D11—24no—
101C22×C4×D11—24no—
102C22×C4×D11—42no—
103C22×C4×D11C2314yes—
104C22×Dic22—24no—
105C22×Dic22—24no—
106C22×Dic22—42no—
107C22×Dic22C2314yes—
108C2×C11×C22⋊C4—24no—
109C2×C11×C22⋊C4D418yescomplemented
110C2×C11×C22⋊C4C2314yes—
111C2×C11×C22⋊C4C2314yes—
112C2×C42×C11—42no—
113C2×C42×C11—42no—
114C2×C42×C11C2314yes—
115C2×C42×C11C2314yes—
116C2×C22⋊Dic11—24no—
117C2×C22⋊Dic11—24no—
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—42no—
127C2×(C2×D11)⋊C4—42no—
128C2×(C2×D11)⋊C4—42no—
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×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×C4⋊Dic11—24no—
139C2×C4⋊Dic11—24no—
140C2×C4⋊Dic11C2314yes—
141C2×C4⋊Dic11C2314yes—
142C2×Dic11⋊C4—24no—
143C2×Dic11⋊C4C2314yes—
144C2×C4×Dic11—24no—
145C2×C4×Dic11C2314yes—
146#66938—232no—
147#66936—232no—
148C11×#95C2314yes—
149C11×#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2557—111nomaximal, Sylow
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11C2×D414yes—
166C24×C11C2412yes—
167C24×C11C2411yescharacteristic
168C23×D11—22no—
169C23×D11—22no—
170C23×D11—22no—
171C23×D11—22no—
172C23×D11—22no—
173C23×D11—22no—
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11—22no—
181C23×D11#4114yes—
182C23×D11C2412yes—
183C23×D11C2412yes—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
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—28no—
199C22×C4×C11—44no—
200C22×C4×C11—44no—
201C22×C4×C11—416no—
202C22×C4×C11C2×D414yes—
203C22×C4×C11C2×D414yes—
204C22×C4×C11#4114yes—
205C22×C4×C11#4114yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C2×C22⋊D11—28no—
213C2×C22⋊D11—28no—
214C2×C22⋊D11—28no—
215C2×C22⋊D11—28no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11—416no—
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#4114yes—
238C22×Dic11C2412yes—
239C22×Dic11C2412yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C2×D44—28no—
245C2×D44—28no—
246C2×D44—44no—
247C2×D44—416no—
248C2×C4×D11—28no—
249C2×C4×D11—28no—
250C2×C4×D11—44no—
251C2×C4×D11—416no—
252C2×Dic22—28no—
253C2×Dic22—28no—
254C2×Dic22—44no—
255C2×Dic22—416no—
256C11×C22⋊C4—28no—
257C11×C22⋊C4C2×D4116yescomplemented
258C42×C11—44no—
259C42×C11—44no—
260C22⋊Dic11—28no—
261C22⋊Dic11—28no—
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—44no—
269(C2×D11)⋊C4—44no—
270(C2×D11)⋊C4—44no—
271C4⋊Dic11—28no—
272C4⋊Dic11—28no—
273Dic11⋊C4—28no—
274C4×Dic11—28no—
275C22×#124—111no—
276C22×#123—111no—
277#2557—1116no—
278C2×#397—111no—
279C2×#397—111no—
280C2×#393—111no—
281C2×#392—111no—
282C2×#391—111no—
283C2×#390—111no—
284C2×#388—111no—
285C2×#387—111no—
286C2×#386—111no—
287C2×#386—111no—
288C2×#386—111no—
289C2×C4×C22⋊C4—111no—
290C2×C4×C22⋊C4D1111yescharacteristic, complemented
291C23×C11—28no—
292C23×C11—28no—
293C23×C11—28no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—44no—
301C23×C11—44no—
302C23×C11—44no—
303C23×C11—44no—
304C23×C11C22×D414yes—
305C23×C11C22×D412yes—
306C23×C11C2×#4112yes—
307C23×C11C2×#4112yes—
308C23×C11C2×#4112yes—
309C23×C11C2×#4112yes—
310C23×C11H(5,𝔽2)12yes—
311C23×C11H(5,𝔽2)12yes—
312C23×C11C2511yescharacteristic
313C22×D11—28no—
314C22×D11—28no—
315C22×D11—28no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—44no—
330C22×D11—44no—
331C22×D11—44no—
332C22×D11—44no—
333C22×D11—44no—
334C22×D11—44no—
335C22×D11—44no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11—44no—
339C22×D11—44no—
340C22×D11C2×#4114yes—
341C2×C4×C11—28no—
342C2×C4×C11—28no—
343C2×C4×C11—28no—
344C2×C4×C11—28no—
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—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—416no—
360C2×C4×C11—44no—
361C2×C4×C11—44no—
362C2×C4×C11C22×D414yes—
363C2×C4×C11C22×D414yes—
364C2×C4×C11C2×#4114yes—
365C2×C4×C11C2×#4114yes—
366C22⋊D11—416no—
367C22⋊D11—416no—
368C2×Dic11—28no—
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—
392D44—416no—
393C4×D11—416no—
394Dic22—416no—
395C23×Q8—111no—
396C23×D4—111no—
397C23×D4—111no—
398C23×D4—111no—
399C24×C4—111no—
400C24×C4C2×D1111yescharacteristic
401C2×#124—118no—
402C2×#124—228no—
403C2×#123—118no—
404C2×#123—228no—
405C22×C4⋊C4—111no—
406C22×C4⋊C4—111no—
407C22×C4⋊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⋊C4—111no—
417C22×C22⋊C4—111no—
418C22×C22⋊C4—111no—
419C22×C22⋊C4C2×D1111yescharacteristic
420C22×C22⋊C4C2×D1111yescharacteristic
421C22×C42—111no—
422C22×C42C2×D1111yescharacteristic
423C22×C42C2×D1111yescharacteristic
424#397—118no—
425#397—118no—
426#393—118no—
427#392—118no—
428#391—118no—
429#390—118no—
430#388—118no—
431#387—118no—
432#386—118no—
433#386—118no—
434#386—118no—
435C4×C22⋊C4—118no—
436C4×C22⋊C4C2×D1118yescomplemented
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95—111no—
444C2×#95—111no—
445C2×#95C2×D1111yescharacteristic
446C2×#95C2×D1111yescharacteristic
447C22×C11—24no—
448C22×C11—24no—
449C22×C11—24no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—416no—
455C22×C11#52914yes—
456C22×C11#53214yes—
457C22×C11#53814yes—
458C22×C11#54614yes—
459C22×C11#54614yes—
460C22×C11#55114yes—
461C22×C11#55914yes—
462C22×C11C23×D411yescharacteristic
463C22×C11C22×#4111yescharacteristic
464C22×C11C22×#4111yescharacteristic
465C22×C11C22×#4111yescharacteristic
466C22×C11C22×#4111yescharacteristic
467C22×C11C2×H(5,𝔽2)11yescharacteristic
468C22×C11C2×H(5,𝔽2)11yescharacteristic
469C2×D11—24no—
470C2×D11—24no—
471C2×D11—24no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—416no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—88no—
485C4×C11—24no—
486C4×C11—24no—
487C4×C11—24no—
488C4×C11—24no—
489C4×C11—42no—
490C4×C11—42no—
491Dic11—24no—
492Dic11—42no—
493Dic11—42no—
494Dic11—42no—
495Dic11—42no—
496Dic11—42no—
497C25—111no—
498C25—111no—
499C25C22×D1111yescharacteristic
500C22×Q8—114no—
501C22×Q8—224no—
502C22×Q8—224no—
503C22×Q8—442no—
504C22×D4—114no—
505C22×D4—114no—
506C22×D4—114no—
507C22×D4—224no—
508C22×D4—224no—
509C22×D4—224no—
510C22×D4—224no—
511C22×D4—224no—
512C22×D4—224no—
513C22×D4—442no—
514C22×D4—442no—
515C22×D4—442no—
516C23×C4—24no—
517C23×C4—42no—
518C23×C4—42no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—111no—
522C23×C4—111no—
523C23×C4—111no—
524C23×C4—111no—
525C23×C4—114no—
526C23×C4—224no—
527C23×C4—224no—
528C23×C4—442no—
529C23×C4C22×D1111yescharacteristic
530C23×C4C22×D1111yescharacteristic
531C23×C4C22×D1111yescharacteristic
532C23×C4C22×D1111yescharacteristic
533C23×C4C22×D1111yescharacteristic
534C23×C4C22×D1111yescharacteristic
535C23×C4C22×D1114yes—
536#124—2232no—
537#123—2232no—
538C2×C4⋊C4—114no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—114no—
541C2×C4⋊C4—224no—
542C2×C4⋊C4—224no—
543C2×C4⋊C4—224no—
544C2×C22⋊C4—24no—
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—114no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—224no—
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—442no—
565C2×C22⋊C4—442no—
566C2×C22⋊C4—442no—
567C2×C22⋊C4D4418yescomplemented
568C2×C22⋊C4C22×D1114yes—
569C2×C22⋊C4C22×D1114yes—
570C2×C42—42no—
571C2×C42—42no—
572C2×C42—114no—
573C2×C42—224no—
574C2×C42C22×D1114yes—
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—
584#95C22×D1114yes—
585#95C22×D1114yes—
586C2×C11—44no—
587C2×C11#255718yescomplemented
588C2×C11C2×#52911yescharacteristic
589C2×C11C2×#53211yescharacteristic
590C2×C11C2×#53811yescharacteristic
591C2×C11C2×#54611yescharacteristic
592C2×C11C2×#54611yescharacteristic
593C2×C11C2×#55111yescharacteristic
594C2×C11C2×#55911yescharacteristic
595D11—44no—
596D11—82no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—114no—
604C24—112no—
605C24—112no—
606C24—222no—
607C24—222no—
608C24—222no—
609C24—222no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24—222no—
616C24—222no—
617C24—222no—
618C24—222no—
619C24C2×D4414yes—
620C24C23×D1112yes—
621C24C23×D1111yescharacteristic
622C2×Q8—228no—
623C2×Q8—228no—
624C2×Q8—444no—
625C2×Q8—4416no—
626C2×D4—228no—
627C2×D4—228no—
628C2×D4—228no—
629C2×D4—228no—
630C2×D4—228no—
631C2×D4—228no—
632C2×D4—444no—
633C2×D4—4416no—
634C2×D4—444no—
635C2×D4—444no—
636C2×D4—4416no—
637C2×D4—4416no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
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—28no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—416no—
656C22×C4—114no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—112no—
660C22×C4—112no—
661C22×C4—112no—
662C22×C4—112no—
663C22×C4—228no—
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—222no—
680C22×C4—222no—
681C22×C4—228no—
682C22×C4—444no—
683C22×C4—4416no—
684C22×C4C2×D4414yes—
685C22×C4C2×D4414yes—
686C22×C4#433914yes—
687C22×C4#433914yes—
688C22×C4C23×D1112yes—
689C22×C4C23×D1112yes—
690C22×C4C23×D1112yes—
691C22×C4C23×D1112yes—
692C22×C4C23×D1112yes—
693C22×C4C23×D1112yes—
694C4⋊C4—228no—
695C4⋊C4—228no—
696C4⋊C4—228no—
697C22⋊C4—28no—
698C22⋊C4—228no—
699C22⋊C4—228no—
700C22⋊C4—228no—
701C22⋊C4—228no—
702C22⋊C4—228no—
703C22⋊C4—228no—
704C22⋊C4—228no—
705C22⋊C4—228no—
706C22⋊C4—444no—
707C22⋊C4—444no—
708C22⋊C4—444no—
709C22⋊C4C2×D44116yescomplemented
710C42—44no—
711C42—44no—
712C42—228no—
713C11C2×#255711yescharacteristic, complemented, Sylow
714C23—28no—
715C23—28no—
716C23—28no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—114no—
728C23—228no—
729C23—228no—
730C23—228no—
731C23—222no—
732C23—222no—
733C23—222no—
734C23—222no—
735C23—222no—
736C23—222no—
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—
751C23—444no—
752C23—444no—
753C23—444no—
754C23—444no—
755C23C22×D4414yes—
756C23C22×D4412yes—
757C23C2×#433912yes—
758C23C2×#433912yes—
759C23#6703712yes—
760C23#6703712yes—
761C23#41×D1112yes—
762C23#41×D1112yes—
763C23C24×D1111yescharacteristic
764Q8—4416no—
765D4—4416no—
766D4—4416no—
767D4—4416no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—28no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—416no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—114no—
790C2×C4—228no—
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—222no—
807C2×C4—222no—
808C2×C4—4416no—
809C2×C4—444no—
810C2×C4—444no—
811C2×C4—444no—
812C2×C4—444no—
813C2×C4—444no—
814C2×C4C22×D4414yes—
815C2×C4C22×D4414yes—
816C2×C4C2×#433914yes—
817C2×C4C2×#433914yes—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—42no—
822C22—42no—
823C22—416no—
824C22—42no—
825C22—42no—
826C22—224no—
827C22—224no—
828C22—224no—
829C22—442no—
830C22—4416no—
831C22—442no—
832C22—442no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—442no—
838C22—442no—
839C22—442no—
840C22—442no—
841C22—888no—
842C22#1062300814yes—
843C22#1062302514yes—
844C22#1062305914yes—
845C22#1062308514yes—
846C22#1062308514yes—
847C22#1062308714yes—
848C22#1062309014yes—
849C22C23×D4411yescharacteristic
850C22C22×#433911yescharacteristic
851C22C22×#433911yescharacteristic
852C22C2×#6703711yescharacteristic
853C22C2×#6703711yescharacteristic
854C22C2×#41×D1111yescharacteristic
855C22C2×#41×D1111yescharacteristic
856C4—24no—
857C4—24no—
858C4—24no—
859C4—24no—
860C4—42no—
861C4—42no—
862C4—224no—
863C4—442no—
864C4—442no—
865C4—442no—
866C4—442no—
867C4—442no—
868C2—44no—
869C2—444no—
870C2—882no—
871C2#1307370918yesdirect product factor
872C2C2×#1062305911yescharacteristic
873C2C2×#1062300811yescharacteristic
874C2C2×#1062302511yescharacteristic
875C2C2×#1062308511yescharacteristic
876C2C2×#1062308511yescharacteristic
877C2C2×#1062308711yescharacteristic
878C2C2×#1062309011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#2557
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#66938C2semidirect
2. C22×#66936C2semidirect
3. #13073709C2direct (N × H)
4. C2×#10622287C2semidirect
5. C2×#10622566C2semidirect
6. C2×#10622286C2semidirect
8. C2×#10622542C2semidirect
9. C2×#10622552C2semidirect
10. C2×#10622553C2semidirect
11. C2×#10622266C2semidirect
12. C2×#10622826C2semidirect
13. C2×#10622826C2semidirect
14. C2×#10622278C2semidirect
15. C2×C4×(C2×D11)⋊C4C2semidirect
16. C2×C4×C11×C22⋊C4C2semidirect
43. C2×#66938C22semidirect
45. C2×#66936C22semidirect
46. C4×C11×C22⋊C4C22semidirect
49. #10622826C22semidirect
50. #10622826C22semidirect
60. #10622566C22semidirect
61. #10622553C22semidirect
62. #10622552C22semidirect
63. C4×(C2×D11)⋊C4C22semidirect
64. #10622542C22semidirect
65. #10622287C22semidirect
66. #10622286C22semidirect
67. #10622278C22semidirect
68. #10622266C22semidirect
109. C2×C11×C22⋊C4D4semidirect
257. C11×C22⋊C4C2×D4semidirect
290. C2×C4×C22⋊C4D11semidirect
436. C4×C22⋊C4C2×D11semidirect
567. C2×C22⋊C4D44semidirect
587. C2×C11#2557semidirect
709. C22⋊C4C2×D44semidirect
713. C11C2×#2557semidirect
871. C2#13073709direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669382
C22×#669362
#130737092
C2×#106222872
C2×#106225662
C2×#106222862
C2×#106225732
C2×#106225422
C2×#106225522
C2×#106225532
C2×#106222662
C2×#106228262
C2×#106222782
C2×C4×(C2×D11)⋊C42
C2×C4×C11×C22⋊C42
C2×#255711