Finite Group Databasebeta

← C2×#13072523 #14921888

Subgroups — C2×#13072523 #14921888

Order 2816.

3438 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×#66982C211yesmaximal, characteristic, complemented
2C22×C4×D44C211yesmaximal, characteristic, complemented
3#13072523C2116yesmaximal, direct product factor
4C2×#10622273C211yesmaximal, characteristic, complemented
5C2×#10622561C211yesmaximal, characteristic, complemented
6C2×#10622285C211yesmaximal, characteristic, complemented
7C2×#10622573C211yesmaximal, characteristic
8C2×#10622553C211yesmaximal, characteristic, complemented
9C2×#10622553C211yesmaximal, characteristic, complemented
10C2×#10622546C211yesmaximal, characteristic, complemented
11C2×#10622826C211yesmaximal, characteristic, complemented
12C2×#10622569C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622277C211yesmaximal, characteristic, complemented
15C2×#10622280C211yesmaximal, characteristic, complemented
16C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C22×C42×C11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C2×#66982—28no—
30C2×#66982C2218yescomplemented
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×C4⋊Dic11C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C2×C4×D44—28no—
45C2×C4×D44C2218yescomplemented
46C4×C11×C22⋊C4C2218yescomplemented
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2211yescharacteristic
49#10622826C2218yescomplemented
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58#10622573C2218yes—
59#10622569C2218yescomplemented
60#10622569C2218yescomplemented
61#10622561C2218yescomplemented
62#10622553C2218yescomplemented
63#10622553C2218yescomplemented
64#10622546C2218yescomplemented
65#10622285C2218yescomplemented
66#10622280C2218yescomplemented
67#10622277C2218yescomplemented
68#10622273C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C23×C4×C11—24no—
73C23×C4×C11—24no—
74C23×C4×C11—42no—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2314yes—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
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—24no—
99C22×D44C2314yes—
100C22×C4×D11—24no—
101C22×C4×D11—24no—
102C22×C4×D11—24no—
103C22×C4×D11—24no—
104C22×C4×D11—42no—
105C22×C4×D11—42no—
106C22×C4×D11C2314yes—
107C22×C4×D11C2314yes—
108C2×C11×C22⋊C4—24no—
109C2×C11×C22⋊C4—24no—
110C2×C11×C22⋊C4C2314yes—
111C2×C11×C22⋊C4C2314yes—
112C2×C42×C11—24no—
113C2×C42×C11—42no—
114C2×C42×C11C2314yes—
115C2×C42×C11C2314yes—
116C2×C22⋊Dic11—24no—
117C2×C22⋊Dic11—42no—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120#66982—232no—
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)⋊C4—42no—
127C2×(C2×D11)⋊C4—42no—
128C2×(C2×D11)⋊C4D418yescomplemented
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×C4⋊Dic11—24no—
138C2×C4⋊Dic11C2314yes—
139C2×Dic11⋊C4—24no—
140C2×Dic11⋊C4—24no—
141C2×Dic11⋊C4—24no—
142C2×Dic11⋊C4—42no—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×Dic11⋊C4C2314yes—
147C4×D44—232no—
148C11×#95C2314yes—
149C11×#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2457—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—22no—
173C23×D11—22no—
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11C2×D414yes—
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—28no—
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—44no—
202C22×C4×C11—416no—
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×Dic11C2×D414yes—
238C22×Dic11C2412yes—
239C22×Dic11C2412yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C2×D44—232no—
245C2×D44—28no—
246C2×D44—28no—
247C2×D44—28no—
248C2×C4×D11—28no—
249C2×C4×D11—28no—
250C2×C4×D11—28no—
251C2×C4×D11—28no—
252C2×C4×D11—44no—
253C2×C4×D11—44no—
254C2×C4×D11—416no—
255C2×C4×D11—416no—
256C11×C22⋊C4—28no—
257C11×C22⋊C4—28no—
258C42×C11—28no—
259C42×C11—44no—
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—44no—
266(C2×D11)⋊C4—44no—
267(C2×D11)⋊C4—44no—
268(C2×D11)⋊C4—44no—
269(C2×D11)⋊C4C2×D4116yescomplemented
270C4⋊Dic11—28no—
271Dic11⋊C4—28no—
272Dic11⋊C4—28no—
273Dic11⋊C4—28no—
274Dic11⋊C4—44no—
275C22×#123—111no—
276C22×C4×D4—111no—
277#2457—1116no—
278C2×#400—111no—
279C2×#396—111no—
280C2×#394—111no—
281C2×#392—111no—
282C2×#388—111no—
283C2×#388—111no—
284C2×#387—111no—
285C2×#386—111no—
286C2×#386—111no—
287C2×#386—111no—
288C2×#381—111no—
289C2×#380—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×D412yes—
305C23×C11C2×#4114yes—
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—28no—
317C22×D11—28no—
318C22×D11—28no—
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—22no—
330C22×D11—22no—
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×D11C22×D414yes—
340C22×D11C2×#4114yes—
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—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—416no—
360C2×C4×C11—44no—
361C2×C4×C11—44no—
362C2×C4×C11—44no—
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×Dic11C22×D414yes—
392D44—232no—
393C4×D11—416no—
394C4×D11—416no—
395C23×D4—111no—
396C23×D4—111no—
397C23×D4—111no—
398C24×C4—111no—
399C24×C4—111no—
400C24×C4C2×D1111yescharacteristic
401C2×#123—118no—
402C2×#123—228no—
403C2×C4×D4—118no—
404C2×C4×D4—228no—
405C22×C4⋊C4—111no—
406C22×C4⋊C4—111no—
407C22×C4⋊C4—111no—
408C22×C4⋊C4—111no—
409C22×C4⋊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⋊C4—111no—
420C22×C22⋊C4C2×D1111yescharacteristic
421C22×C22⋊C4C2×D1111yescharacteristic
422C22×C42C2×D1111yescharacteristic
423C22×C42C2×D1111yescharacteristic
424#400—118no—
425#396—118no—
426#394—118no—
427#392—118no—
428#388—118no—
429#388—118no—
430#387—118no—
431#386—118no—
432#386—118no—
433#386—118no—
434#381—118no—
435#380—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#52514yes—
456C22×C11#52914yes—
457C22×C11#54014yes—
458C22×C11#54614yes—
459C22×C11#54614yes—
460C22×C11#55114yes—
461C22×C11#55314yes—
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—24no—
473C2×D11—24no—
474C2×D11—24no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—416no—
484C2×D11—416no—
485C4×C11—24no—
486C4×C11—24no—
487C4×C11—24no—
488C4×C11—42no—
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×D4—114no—
501C22×D4—114no—
502C22×D4—114no—
503C22×D4—224no—
504C22×D4—224no—
505C22×D4—224no—
506C22×D4—224no—
507C22×D4—224no—
508C22×D4—224no—
509C22×D4—224no—
510C22×D4—442no—
511C22×D4—442no—
512C23×C4—24no—
513C23×C4—24no—
514C23×C4—42no—
515C23×C4—111no—
516C23×C4—111no—
517C23×C4—111no—
518C23×C4—111no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—114no—
522C23×C4—114no—
523C23×C4—224no—
524C23×C4—224no—
525C23×C4—224no—
526C23×C4—224no—
527C23×C4—442no—
528C23×C4—442no—
529C23×C4C22×D1111yescharacteristic
530C23×C4C22×D1111yescharacteristic
531C23×C4C22×D1111yescharacteristic
532C23×C4C22×D1114yes—
533C23×C4C22×D1111yescharacteristic
534C23×C4C22×D1111yescharacteristic
535C23×C4C22×D1111yescharacteristic
536#123—2232no—
537C4×D4—2232no—
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—224no—
546C2×C4⋊C4—224no—
547C2×C4⋊C4—442no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—118no—
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⋊C4C22×D1114yes—
571C2×C22⋊C4C22×D1114yes—
572C2×C42—24no—
573C2×C42—42no—
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#245718yescomplemented
588C2×C11C2×#52511yescharacteristic
589C2×C11C2×#52911yescharacteristic
590C2×C11C2×#54011yescharacteristic
591C2×C11C2×#54611yescharacteristic
592C2×C11C2×#54611yescharacteristic
593C2×C11C2×#55111yescharacteristic
594C2×C11C2×#55311yescharacteristic
595D11—44no—
596D11—44no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—114no—
604C24—114no—
605C24—112no—
606C24—112no—
607C24—222no—
608C24—222no—
609C24—222no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24—222no—
616C24—222no—
617C24—222no—
618C24—222no—
619C24#433914yes—
620C24C23×D1112yes—
621C24C23×D1111yescharacteristic
622C2×D4—228no—
623C2×D4—228no—
624C2×D4—2232no—
625C2×D4—228no—
626C2×D4—228no—
627C2×D4—228no—
628C2×D4—228no—
629C2×D4—228no—
630C2×D4—444no—
631C2×D4—444no—
632C2×D4—4416no—
633C2×D4—4416no—
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—28no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—28no—
651C22×C4—44no—
652C22×C4—416no—
653C22×C4—114no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—112no—
660C22×C4—228no—
661C22×C4—228no—
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—228no—
680C22×C4—228no—
681C22×C4—444no—
682C22×C4—444no—
683C22×C4—4416no—
684C22×C4—4416no—
685C22×C4#433914yes—
686C22×C4#433914yes—
687C22×C4D4×D1114yes—
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—
697C4⋊C4—228no—
698C4⋊C4—444no—
699C22⋊C4—28no—
700C22⋊C4—28no—
701C22⋊C4—1116no—
702C22⋊C4—228no—
703C22⋊C4—228no—
704C22⋊C4—228no—
705C22⋊C4—228no—
706C22⋊C4—444no—
707C22⋊C4—444no—
708C22⋊C4—444no—
709C22⋊C4—444no—
710C22⋊C4—444no—
711C42—28no—
712C42—44no—
713C11C2×#245711yescharacteristic, 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—114no—
729C23—228no—
730C23—228no—
731C23—228no—
732C23—228no—
733C23—228no—
734C23—228no—
735C23—222no—
736C23—222no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—222no—
744C23—222no—
745C23—222no—
746C23—222no—
747C23—444no—
748C23—444no—
749C23—444no—
750C23—444no—
751C23—444no—
752C23—444no—
753C23—444no—
754C23—444no—
755C23C2×#433914yes—
756C23C2×#433912yes—
757C23C2×#433912yes—
758C23C2×#433912yes—
759C23C2×D4×D1112yes—
760C23#6703712yes—
761C23#41×D1112yes—
762C23#6704212yes—
763C23C24×D1111yescharacteristic
764D4—2232no—
765D4—4416no—
766D4—4416no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—28no—
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—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—416no—
786C2×C4—44no—
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—4416no—
810C2×C4—444no—
811C2×C4—444no—
812C2×C4—444no—
813C2×C4—444no—
814C2×C4—444no—
815C2×C4C2×#433914yes—
816C2×C4C2×#433914yes—
817C2×C4C2×D4×D1114yes—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—416no—
825C22—42no—
826C22—224no—
827C22—224no—
828C22—224no—
829C22—224no—
830C22—224no—
831C22—224no—
832C22—442no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—4416no—
838C22—4416no—
839C22—442no—
840C22—442no—
841C22—442no—
842C22#1062301014yes—
843C22#1062302114yes—
844C22#1062305814yes—
845C22#1062307814yes—
846C22#1062308114yes—
847C22#1062308914yes—
848C22#1062309314yes—
849C22C22×#433911yescharacteristic
850C22C22×#433911yescharacteristic
851C22C22×#433911yescharacteristic
852C22C22×D4×D1111yescharacteristic
853C22C2×#6703711yescharacteristic
854C22C2×#41×D1111yescharacteristic
855C22C2×#6704211yescharacteristic
856C4—24no—
857C4—24no—
858C4—24no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—224no—
863C4—442no—
864C4—442no—
865C4—442no—
866C4—442no—
867C4—442no—
868C2—44no—
869C2—444no—
870C2—444no—
871C2#1307252318yesdirect product factor
872C2C2×#1062307811yescharacteristic
873C2C2×#1062301011yescharacteristic
874C2C2×#1062309311yescharacteristic
875C2C2×#1062302111yescharacteristic
876C2C2×#1062308111yescharacteristic
877C2C2×#1062305811yescharacteristic
878C2C2×#1062308911yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#2457
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×#66982C2semidirect
2. C22×C4×D44C2semidirect
3. #13072523C2direct (N × H)
4. C2×#10622273C2semidirect
5. C2×#10622561C2semidirect
6. C2×#10622285C2semidirect
8. C2×#10622553C2semidirect
9. C2×#10622553C2semidirect
10. C2×#10622546C2semidirect
11. C2×#10622826C2semidirect
12. C2×#10622569C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622277C2semidirect
15. C2×#10622280C2semidirect
16. C2×C4×C11×C22⋊C4C2semidirect
30. C2×#66982C22semidirect
45. C2×C4×D44C22semidirect
46. C4×C11×C22⋊C4C22semidirect
49. #10622826C22semidirect
59. #10622569C22semidirect
60. #10622569C22semidirect
61. #10622561C22semidirect
62. #10622553C22semidirect
63. #10622553C22semidirect
64. #10622546C22semidirect
65. #10622285C22semidirect
66. #10622280C22semidirect
67. #10622277C22semidirect
68. #10622273C22semidirect
128. C2×(C2×D11)⋊C4D4semidirect
269. (C2×D11)⋊C4C2×D4semidirect
290. C2×C4×C22⋊C4D11semidirect
436. C4×C22⋊C4C2×D11semidirect
587. C2×C11#2457semidirect
713. C11C2×#2457semidirect
871. C2#13072523direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669822
C22×C4×D442
#130725232
C2×#106222732
C2×#106225612
C2×#106222852
C2×#106225732
C2×#106225532
C2×#106225462
C2×#106228262
C2×#106225692
C2×#106222772
C2×#106222802
C2×C4×C11×C22⋊C42
C2×#245711