Finite Group Databasebeta

← C2×#13071314 #14912546

Subgroups — C2×#13071314 #14912546

Order 2816.

4150 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C211yesmaximal, characteristic
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3#13071314C2116yesmaximal, direct product factor
4C2×#10622553C211yesmaximal, characteristic, complemented
5C2×#10622557C211yesmaximal, characteristic, complemented
6C2×#10622546C211yesmaximal, characteristic, complemented
7C2×#10622591C211yesmaximal, characteristic, complemented
8C2×#10622833C211yesmaximal, characteristic, complemented
9C2×#10622826C211yesmaximal, characteristic, complemented
10C2×#10622571C211yesmaximal, characteristic, complemented
11C2×#10622569C211yesmaximal, characteristic, complemented
12C2×#10622823C211yesmaximal, characteristic, complemented
13C2×#10622602C211yesmaximal, characteristic, complemented
14C2×#10622555C211yesmaximal, characteristic, complemented
15C22×C11⋊#95C211yesmaximal, characteristic, complemented
16C22×C4×D4×C11C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C24×Dic11C2211yescharacteristic
23C24×Dic11C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C2×C4×D4×C11—28no—
26C2×C4×D4×C11C2218yescomplemented
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C42×C11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C2×#66992C4116yescomplemented
36C2×#66992C2218yes—
37C2×C4×C22⋊D11—28no—
38C2×C4×C22⋊D11C2218yescomplemented
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48#10622833C2218yescomplemented
49#10622826C2218yescomplemented
50#10622823C2218yescomplemented
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2218yescomplemented
62#10622602C2218yescomplemented
63#10622591C2218yescomplemented
64#10622571C2218yescomplemented
65#10622569C2218yescomplemented
66#10622557C2218yescomplemented
67#10622555C2218yescomplemented
68#10622553C2218yescomplemented
69#10622546C2218yescomplemented
70C25×C11C2311yescharacteristic
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C22×D4×C11—24no—
74C22×D4×C11—24no—
75C22×D4×C11C2×C418yescomplemented
76C22×D4×C11C2314yes—
77C23×C4×C11—24no—
78C23×C4×C11—42no—
79C23×C4×C11—42no—
80C23×C4×C11—42no—
81C23×C4×C11—42no—
82C23×C4×C11D418yescomplemented
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2314yes—
89C23×C4×C11C2314yes—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11—42no—
93C22×C22⋊D11—42no—
94C22×C22⋊D11C2×C418yescomplemented
95C22×C22⋊D11C2×C418yescomplemented
96C22×C22⋊D11C2314yes—
97C22×C22⋊D11C2314yes—
98C23×Dic11—24no—
99C23×Dic11—42no—
100C23×Dic11—42no—
101C23×Dic11—42no—
102C23×Dic11—42no—
103C23×Dic11C2×C418yescomplemented
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2314yes—
112C23×Dic11C2314yes—
113C22×C4×D11—24no—
114C22×C4×D11—42no—
115C22×C4×D11—42no—
116C22×C4×D11C2314yes—
117C4×D4×C11—232no—
118C2×C11×C4⋊C4—24no—
119C2×C11×C4⋊C4C2314yes—
120C2×C11×C22⋊C4—24no—
121C2×C11×C22⋊C4—24no—
122C2×C11×C22⋊C4C2314yes—
123C2×C11×C22⋊C4C2314yes—
124C2×C42×C11—24no—
125C2×C42×C11C2314yes—
126C2×C22⋊Dic11—24no—
127C2×C22⋊Dic11—42no—
128C2×C22⋊Dic11—42no—
129C2×C22⋊Dic11C2×C418yescomplemented
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yes—
134#66992C2×C4164yescomplemented
135C4×C22⋊D11—232no—
136C2×(C2×D11)⋊C4—24no—
137C2×(C2×D11)⋊C4—42no—
138C2×(C2×D11)⋊C4—42no—
139C2×(C2×D11)⋊C4C2×C418yescomplemented
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×Dic11⋊C4—24no—
145C2×Dic11⋊C4—42no—
146C2×Dic11⋊C4—42no—
147C2×Dic11⋊C4C2×C418yescomplemented
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×C4×Dic11—24no—
153C2×C4×Dic11C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C2×#2325—111nomaximal, Sylow
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11—22no—
175C24×C11C22×C414yes—
176C24×C11C22×C414yes—
177C24×C11C2×D414yes—
178C24×C11#4114yes—
179C24×C11C2412yes—
180C24×C11C2412yes—
181C24×C11C2411yescharacteristic
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11C22×C414yes—
189C23×D11C2412yes—
190C2×D4×C11—232no—
191C2×D4×C11—28no—
192C2×D4×C11—28no—
193C2×D4×C11C22×C4116yescomplemented
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—22no—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—28no—
207C22×C4×C11—416no—
208C22×C4×C11—44no—
209C22×C4×C11—44no—
210C22×C4×C11—44no—
211C22×C4×C11—44no—
212C22×C4×C11—416no—
213C22×C4×C11C22×C414yes—
214C22×C4×C11C2×D414yes—
215C22×C4×C11C2×D414yes—
216C22×C4×C11C2×D4116yescomplemented
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C2×C22⋊D11—232no—
223C2×C22⋊D11—28no—
224C2×C22⋊D11—28no—
225C2×C22⋊D11—416no—
226C2×C22⋊D11—44no—
227C2×C22⋊D11—44no—
228C2×C22⋊D11C22×C4116yescomplemented
229C2×C22⋊D11C22×C4116yescomplemented
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—28no—
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—22no—
244C22×Dic11—22no—
245C22×Dic11—22no—
246C22×Dic11—22no—
247C22×Dic11—22no—
248C22×Dic11—22no—
249C22×Dic11—416no—
250C22×Dic11—44no—
251C22×Dic11—44no—
252C22×Dic11—44no—
253C22×Dic11—44no—
254C22×Dic11—416no—
255C22×Dic11C22×C414yes—
256C22×Dic11C22×C414yes—
257C22×Dic11C22×C414yes—
258C22×Dic11C22×C4116yescomplemented
259C22×Dic11C2412yes—
260C22×Dic11C2412yes—
261C22×Dic11C2412yes—
262C22×Dic11C2412yes—
263C22×Dic11C2412yes—
264C22×Dic11C2412yes—
265C22×Dic11C2412yes—
266C2×C4×D11—28no—
267C2×C4×D11—44no—
268C2×C4×D11—44no—
269C2×C4×D11—416no—
270C11×C4⋊C4—28no—
271C11×C22⋊C4—28no—
272C11×C22⋊C4—28no—
273C42×C11—28no—
274C22⋊Dic11—28no—
275C22⋊Dic11—44no—
276C22⋊Dic11—44no—
277C22⋊Dic11C22×C4116yescomplemented
278(C2×D11)⋊C4—28no—
279(C2×D11)⋊C4—44no—
280(C2×D11)⋊C4—44no—
281(C2×D11)⋊C4C22×C4116yescomplemented
282Dic11⋊C4—28no—
283Dic11⋊C4—44no—
284Dic11⋊C4—44no—
285Dic11⋊C4C22×C4116yescomplemented
286C4×Dic11—28no—
287C22×#121—111no—
288C22×C4×D4—111no—
289C22×C4×D4D1111yescharacteristic, complemented
290#2325—1116no—
291C2×#388—111no—
292C2×#388—111no—
293C2×#387—111no—
294C2×#387—111no—
295C2×#386—111no—
296C2×#386—111no—
297C2×#386—111no—
298C2×#386—111no—
299C2×#385—111no—
300C2×#385—111no—
301C2×#380—111no—
302C22×#95—111no—
303C23×C11—28no—
304C23×C11—28no—
305C23×C11—28no—
306C23×C11—28no—
307C23×C11—28no—
308C23×C11—28no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—28no—
314C23×C11—28no—
315C23×C11—28no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—44no—
323C23×C11—44no—
324C23×C11—44no—
325C23×C11—44no—
326C23×C11C4×D4116yes—
327C23×C11C23×C414yes—
328C23×C11C23×C414yes—
329C23×C11C23×C412yes—
330C23×C11C22×D414yes—
331C23×C11C22×D412yes—
332C23×C11C2×#4114yes—
333C23×C11C2×#4112yes—
334C23×C11H(5,𝔽2)12yes—
335C23×C11H(5,𝔽2)12yes—
336C23×C11H(5,𝔽2)12yes—
337C23×C112−1+412yes—
338C23×C11C2511yescharacteristic
339C22×D11—28no—
340C22×D11—28no—
341C22×D11—28no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—44no—
349C22×D11—44no—
350C22×D11—44no—
351C22×D11—44no—
352C22×D11C23×C414yes—
353D4×C11—232no—
354C2×C4×C11—28no—
355C2×C4×C11—28no—
356C2×C4×C11—28no—
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—416no—
370C2×C4×C11—416no—
371C2×C4×C11—44no—
372C2×C4×C11—44no—
373C2×C4×C11C23×C414yes—
374C2×C4×C11C22×D414yes—
375C2×C4×C11C22×D414yes—
376C22⋊D11—232no—
377C22⋊D11—416no—
378C2×Dic11—28no—
379C2×Dic11—28no—
380C2×Dic11—28no—
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—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—416no—
400C2×Dic11—416no—
401C2×Dic11—44no—
402C2×Dic11—44no—
403C2×Dic11—44no—
404C2×Dic11—44no—
405C2×Dic11C23×C414yes—
406C2×Dic11C23×C414yes—
407C2×Dic11C23×C414yes—
408C4×D11—416no—
409C23×D4—111no—
410C23×D4—111no—
411C23×D4C2×D1111yescharacteristic
412C24×C4—111no—
413C24×C4—111no—
414C24×C4—111no—
415C24×C4C2×D1111yescharacteristic
416C24×C4C2×D1111yescharacteristic
417C2×#121—118no—
418C2×#121—1116no—
419C2×C4×D4—28no—
420C2×C4×D4—118no—
421C2×C4×D4—228no—
422C2×C4×D4C2×D1118yescomplemented
423C22×C4⋊C4—111no—
424C22×C4⋊C4—111no—
425C22×C4⋊C4—111no—
426C22×C4⋊C4—111no—
427C22×C4⋊C4C2×D1111yescharacteristic
428C22×C22⋊C4—111no—
429C22×C22⋊C4—111no—
430C22×C22⋊C4—111no—
431C22×C22⋊C4—111no—
432C22×C22⋊C4—111no—
433C22×C22⋊C4—111no—
434C22×C22⋊C4—111no—
435C22×C22⋊C4—111no—
436C22×C22⋊C4C2×D1111yescharacteristic
437C22×C22⋊C4C2×D1111yescharacteristic
438C22×C42—111no—
439C22×C42C2×D1111yescharacteristic
440#388—118no—
441#388—118no—
442#387—118no—
443#387—118no—
444#386—118no—
445#386—118no—
446#386—118no—
447#386—118no—
448#385—118no—
449#385—118no—
450#380—118no—
451C2×#95—118no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95—111no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95—111no—
461C2×#95—111no—
462C22×C11—232no—
463C22×C11—24no—
464C22×C11—24no—
465C22×C11—24no—
466C22×C11—24no—
467C22×C11—24no—
468C22×C11—24no—
469C22×C11—24no—
470C22×C11—24no—
471C22×C11—24no—
472C22×C11—416no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11C2×C4×D418yes—
478C22×C11C2×C4×D414yes—
479C22×C11#51814yes—
480C22×C11#52014yes—
481C22×C11#53414yes—
482C22×C11#53714yes—
483C22×C11#53814yes—
484C22×C11#53914yes—
485C22×C11C24×C411yescharacteristic
486C22×C11C23×D411yescharacteristic
487C22×C11C22×#4111yescharacteristic
488C22×C11C2×H(5,𝔽2)11yescharacteristic
489C22×C11C2×H(5,𝔽2)11yescharacteristic
490C22×C11C2×H(5,𝔽2)11yescharacteristic
491C22×C11C2×2−1+411yescharacteristic
492C2×D11—24no—
493C2×D11—24no—
494C2×D11—24no—
495C2×D11—416no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C4×C11—24no—
501C4×C11—24no—
502C4×C11—24no—
503C4×C11—42no—
504C4×C11—42no—
505Dic11—24no—
506Dic11—24no—
507Dic11—24no—
508Dic11—42no—
509Dic11—42no—
510Dic11—42no—
511Dic11—42no—
512C25—111no—
513C25C22×D1111yescharacteristic
514C25C22×D1111yescharacteristic
515C22×D4—24no—
516C22×D4—24no—
517C22×D4—118no—
518C22×D4—114no—
519C22×D4—118no—
520C22×D4—114no—
521C22×D4—224no—
522C22×D4—224no—
523C22×D4—442no—
524C22×D4—442no—
525C22×D4C4×D1118yescomplemented
526C22×D4C22×D1114yes—
527C23×C4—24no—
528C23×C4—42no—
529C23×C4—42no—
530C23×C4—42no—
531C23×C4—42no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—118no—
536C23×C4—114no—
537C23×C4—111no—
538C23×C4—111no—
539C23×C4—111no—
540C23×C4—111no—
541C23×C4—114no—
542C23×C4—114no—
543C23×C4—224no—
544C23×C4—224no—
545C23×C4—442no—
546C23×C4—442no—
547C23×C4—442no—
548C23×C4—442no—
549C23×C4—442no—
550C23×C4—442no—
551C23×C4C22⋊D1118yescomplemented
552C23×C4C22×D1111yescharacteristic
553C23×C4C22×D1111yescharacteristic
554C23×C4C22×D1111yescharacteristic
555C23×C4C22×D1111yescharacteristic
556C23×C4C22×D1111yescharacteristic
557C23×C4C22×D1114yes—
558C23×C4C22×D1114yes—
559#121—1164no—
560C4×D4—232no—
561C4×D4—2232no—
562C2×C4⋊C4—24no—
563C2×C4⋊C4—118no—
564C2×C4⋊C4—114no—
565C2×C4⋊C4—114no—
566C2×C4⋊C4—114no—
567C2×C4⋊C4—114no—
568C2×C4⋊C4—224no—
569C2×C4⋊C4—442no—
570C2×C4⋊C4—442no—
571C2×C4⋊C4C22×D1114yes—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—118no—
575C2×C22⋊C4—114no—
576C2×C22⋊C4—118no—
577C2×C22⋊C4—114no—
578C2×C22⋊C4—114no—
579C2×C22⋊C4—114no—
580C2×C22⋊C4—114no—
581C2×C22⋊C4—114no—
582C2×C22⋊C4—114no—
583C2×C22⋊C4—114no—
584C2×C22⋊C4—224no—
585C2×C22⋊C4—224no—
586C2×C22⋊C4—442no—
587C2×C22⋊C4—442no—
588C2×C22⋊C4—442no—
589C2×C22⋊C4—442no—
590C2×C22⋊C4C22×D1114yes—
591C2×C22⋊C4C22×D1114yes—
592C2×C42—24no—
593C2×C42—114no—
594C2×C42—224no—
595C2×C42C22×D1114yes—
596#95—114no—
597#95—114no—
598#95—114no—
599#95—114no—
600#95—114no—
601#95—114no—
602#95—114no—
603#95—114no—
604#95—114no—
605#95—114no—
606C2×C11—28no—
607C2×C11—44no—
608C2×C11#232518yescomplemented
609C2×C11C22×C4×D411yescharacteristic
610C2×C11C2×#51811yescharacteristic
611C2×C11C2×#52011yescharacteristic
612C2×C11C2×#53411yescharacteristic
613C2×C11C2×#53711yescharacteristic
614C2×C11C2×#53811yescharacteristic
615C2×C11C2×#53911yescharacteristic
616D11—44no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—114no—
628C24—112no—
629C24—222no—
630C24—222no—
631C24—222no—
632C24—222no—
633C24—222no—
634C24—222no—
635C24C2×C4×D1114yes—
636C24C2×C4×D1114yes—
637C24#433914yes—
638C24C2×C22⋊D1114yes—
639C24C23×D1112yes—
640C24C23×D1112yes—
641C24C23×D1111yescharacteristic
642C2×D4—232no—
643C2×D4—28no—
644C2×D4—28no—
645C2×D4—1116no—
646C2×D4—1116no—
647C2×D4—2232no—
648C2×D4—228no—
649C2×D4—228no—
650C2×D4—4416no—
651C2×D4—444no—
652C2×D4—444no—
653C2×D4C2×C4×D11116yescomplemented
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—28no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—416no—
672C22×C4—416no—
673C22×C4—114no—
674C22×C4—114no—
675C22×C4—114no—
676C22×C4—112no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—1116no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—112no—
684C22×C4—222no—
685C22×C4—222no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—228no—
691C22×C4—222no—
692C22×C4—222no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—222no—
696C22×C4—222no—
697C22×C4—222no—
698C22×C4—222no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—222no—
702C22×C4—222no—
703C22×C4—228no—
704C22×C4—444no—
705C22×C4—444no—
706C22×C4—4416no—
707C22×C4—4416no—
708C22×C4—444no—
709C22×C4—444no—
710C22×C4—444no—
711C22×C4—444no—
712C22×C4—4416no—
713C22×C4C2×C4×D1114yes—
714C22×C4C2×C22⋊D1114yes—
715C22×C4C2×C22⋊D1114yes—
716C22×C4C2×C22⋊D11116yescomplemented
717C22×C4C23×D1112yes—
718C22×C4C23×D1112yes—
719C22×C4C23×D1112yes—
720C22×C4C23×D1112yes—
721C22×C4C23×D1112yes—
722C4⋊C4—28no—
723C4⋊C4—1116no—
724C4⋊C4—228no—
725C4⋊C4—444no—
726C4⋊C4—444no—
727C22⋊C4—28no—
728C22⋊C4—28no—
729C22⋊C4—1116no—
730C22⋊C4—1116no—
731C22⋊C4—228no—
732C22⋊C4—228no—
733C22⋊C4—444no—
734C22⋊C4—444no—
735C22⋊C4—444no—
736C22⋊C4—444no—
737C42—28no—
738C42—228no—
739C11C2×#232511yescharacteristic, complemented, Sylow
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—28no—
751C23—28no—
752C23—28no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—114no—
764C23—228no—
765C23—228no—
766C23—228no—
767C23—222no—
768C23—222no—
769C23—222no—
770C23—222no—
771C23—222no—
772C23—222no—
773C23—444no—
774C23—444no—
775C23—444no—
776C23—444no—
777C23C4×C22⋊D11116yes—
778C23C22×C4×D1114yes—
779C23C22×C4×D1114yes—
780C23C22×C4×D1112yes—
781C23C2×#433914yes—
782C23C2×#433912yes—
783C23#6703712yes—
784C23#6703712yes—
785C23#6704212yes—
786C23#6704312yes—
787C23C22×C22⋊D1114yes—
788C23C22×C22⋊D1112yes—
789C23C24×D1111yescharacteristic
790D4—232no—
791D4—2232no—
792D4—4416no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
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—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—416no—
809C2×C4—416no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—114no—
813C2×C4—114no—
814C2×C4—114no—
815C2×C4—228no—
816C2×C4—228no—
817C2×C4—228no—
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—222no—
830C2×C4—222no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—222no—
835C2×C4—222no—
836C2×C4—4416no—
837C2×C4—4416no—
838C2×C4—4416no—
839C2×C4—444no—
840C2×C4—444no—
841C2×C4—444no—
842C2×C4—444no—
843C2×C4C22×C4×D1114yes—
844C2×C4C22×C22⋊D1114yes—
845C2×C4C22×C22⋊D1114yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—232no—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—416no—
861C22—224no—
862C22—224no—
863C22—224no—
864C22—442no—
865C22—442no—
866C22—442no—
867C22—442no—
868C22—4416no—
869C22#1062307614yes—
870C22#1062307714yes—
871C22#1062309114yes—
872C22#1062309514yes—
873C22C2×C4×C22⋊D1118yes—
874C22C2×C4×C22⋊D1114yes—
875C22#1062333514yes—
876C22#1062336414yes—
877C22C23×C4×D1111yescharacteristic
878C22C22×#433911yescharacteristic
879C22C2×#6703711yescharacteristic
880C22C2×#6703711yescharacteristic
881C22C2×#6704211yescharacteristic
882C22C2×#6704311yescharacteristic
883C22C23×C22⋊D1111yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—42no—
888C4—42no—
889C4—224no—
890C4—224no—
891C4—224no—
892C4—442no—
893C4—442no—
894C4—442no—
895C4—442no—
896C2—28no—
897C2—44no—
898C2—444no—
899C2#1307131418yesdirect product factor
900C2C22×C4×C22⋊D1111yescharacteristic
901C2C2×#1062307611yescharacteristic
902C2C2×#1062307711yescharacteristic
903C2C2×#1062333511yescharacteristic
904C2C2×#1062336411yescharacteristic
905C2C2×#1062309111yescharacteristic
906C2C2×#1062309511yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC22×C4×D4×C11C2
socleC24×C11C24
prime radicalC22×#66992C2
cosocleC23×C11C25
hypercenterC22×C4×D4D11
hypocenterC11C2×#2325
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D11C2semidirect
3. #13071314C2direct (N × H)
4. C2×#10622553C2semidirect
5. C2×#10622557C2semidirect
6. C2×#10622546C2semidirect
7. C2×#10622591C2semidirect
8. C2×#10622833C2semidirect
9. C2×#10622826C2semidirect
10. C2×#10622571C2semidirect
11. C2×#10622569C2semidirect
12. C2×#10622823C2semidirect
13. C2×#10622602C2semidirect
14. C2×#10622555C2semidirect
15. C22×C11⋊#95C2semidirect
16. C22×C4×D4×C11C2semidirect
26. C2×C4×D4×C11C22semidirect
35. C2×#66992C4semidirect
38. C2×C4×C22⋊D11C22semidirect
48. #10622833C22semidirect
49. #10622826C22semidirect
50. #10622823C22semidirect
61. C2×C11⋊#95C22semidirect
62. #10622602C22semidirect
63. #10622591C22semidirect
64. #10622571C22semidirect
65. #10622569C22semidirect
66. #10622557C22semidirect
67. #10622555C22semidirect
68. #10622553C22semidirect
69. #10622546C22semidirect
75. C22×D4×C11C2×C4semidirect
82. C23×C4×C11D4semidirect
94. C22×C22⋊D11C2×C4semidirect
95. C22×C22⋊D11C2×C4semidirect
103. C23×Dic11C2×C4semidirect
129. C2×C22⋊Dic11C2×C4semidirect
134. #66992C2×C4semidirect
139. C2×(C2×D11)⋊C4C2×C4semidirect
147. C2×Dic11⋊C4C2×C4semidirect
193. C2×D4×C11C22×C4semidirect
216. C22×C4×C11C2×D4semidirect
228. C2×C22⋊D11C22×C4semidirect
229. C2×C22⋊D11C22×C4semidirect
258. C22×Dic11C22×C4semidirect
277. C22⋊Dic11C22×C4semidirect
281. (C2×D11)⋊C4C22×C4semidirect
285. Dic11⋊C4C22×C4semidirect
289. C22×C4×D4D11semidirect
422. C2×C4×D4C2×D11semidirect
525. C22×D4C4×D11semidirect
551. C23×C4C22⋊D11semidirect
608. C2×C11#2325semidirect
653. C2×D4C2×C4×D11semidirect
716. C22×C4C2×C22⋊D11semidirect
739. C11C2×#2325semidirect
899. C2#13071314direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669922
C22×C4×C22⋊D112
#130713142
C2×#106225532
C2×#106225572
C2×#106225462
C2×#106225912
C2×#106228332
C2×#106228262
C2×#106225712
C2×#106225692
C2×#106228232
C2×#106226022
C2×#106225552
C22×C11⋊#952
C22×C4×D4×C112
C2×#232511