Finite Group Databasebeta

← C2×#13071318 #14912550

Subgroups — C2×#13071318 #14912550

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×#66991C211yesmaximal, characteristic
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
4#13071318C2116yesmaximal, direct product factor
5C2×#10622558C211yesmaximal, characteristic, complemented
6C2×#10622557C211yesmaximal, characteristic, complemented
7C2×#10622266C211yesmaximal, characteristic, complemented
8C2×#10622267C211yesmaximal, characteristic, complemented
9C2×#10622833C211yesmaximal, characteristic, complemented
10C2×#10622569C211yesmaximal, characteristic, complemented
11C2×#10622569C211yesmaximal, characteristic, complemented
12C2×#10622823C211yesmaximal, characteristic, complemented
13C2×#10622559C211yesmaximal, characteristic, complemented
14C2×#10622280C211yesmaximal, characteristic, complemented
15C2×D11×#95C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C2×#66991C4116yescomplemented
34C2×#66991C2218yes—
35C2×C4×C22⋊D11—28no—
36C2×C4×C22⋊D11C2218yescomplemented
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C2×(C22⋊D11)⋊C4—28no—
47C2×(C22⋊D11)⋊C4C2218yescomplemented
48C11×#386C2218yescomplemented
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51#10622833C2218yescomplemented
52#10622823C2218yescomplemented
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#10622569C2218yescomplemented
62#10622569C2218yescomplemented
63#10622559C2218yescomplemented
64#10622558C2218yescomplemented
65#10622557C2218yescomplemented
66#10622280C2218yescomplemented
67D11×#95C2218yescomplemented
68#10622267C2218yescomplemented
69#10622266C2218yescomplemented
70C25×C11C2311yescharacteristic
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C22×D4×C11—42no—
74C22×D4×C11—42no—
75C22×D4×C11C2×C418yescomplemented
76C22×D4×C11C2314yes—
77C23×C4×C11—24no—
78C23×C4×C11—42no—
79C23×C4×C11—42no—
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2314yes—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11C2×C418yescomplemented
91C22×C22⋊D11C2×C418yescomplemented
92C22×C22⋊D11C2314yes—
93C22×C22⋊D11C2314yes—
94C23×Dic11—24no—
95C23×Dic11—42no—
96C23×Dic11—42no—
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2314yes—
105C22×C4×D11—24no—
106C22×C4×D11—42no—
107C22×C4×D11—42no—
108C22×C4×D11—42no—
109C22×C4×D11—42no—
110C22×C4×D11—42no—
111C22×C4×D11—42no—
112C22×C4×D11C2×C418yescomplemented
113C22×C4×D11D418yescomplemented
114C22×C4×D11C2314yes—
115C22×C4×D11C2314yes—
116C22×C4×D11C2314yes—
117C2×C11×C22⋊C4—24no—
118C2×C11×C22⋊C4—42no—
119C2×C11×C22⋊C4—42no—
120C2×C11×C22⋊C4C2314yes—
121C2×C11×C22⋊C4C2314yes—
122C2×C11×C22⋊C4C2314yes—
123C2×C22⋊Dic11—24no—
124C2×C22⋊Dic11—42no—
125C2×C22⋊Dic11—42no—
126C2×C22⋊Dic11C2×C418yescomplemented
127C2×C22⋊Dic11C2×C418yescomplemented
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2314yes—
133#66991C2×C4164yescomplemented
134C4×C22⋊D11—232no—
135C2×(C2×D11)⋊C4—24no—
136C2×(C2×D11)⋊C4—24no—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×C4⋊Dic11C2×C418yescomplemented
140C2×C4⋊Dic11C2314yes—
141C2×Dic11⋊C4—24no—
142C2×Dic11⋊C4—24no—
143C2×Dic11⋊C4—42no—
144C2×Dic11⋊C4—42no—
145C2×Dic11⋊C4C2314yes—
146C2×Dic11⋊C4C2314yes—
147C2×Dic11⋊C4C2314yes—
148C2×Dic11⋊C4C2314yes—
149C2×C4×Dic11—24no—
150C2×C4×Dic11—24no—
151C2×C4×Dic11C2314yes—
152C2×C4×Dic11C2314yes—
153(C22⋊D11)⋊C4—232no—
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×C11—22no—
176C24×C11—22no—
177C24×C11C22×C414yes—
178C24×C11C22×C414yes—
179C24×C11C2412yes—
180C24×C11C2412yes—
181C24×C11C2411yescharacteristic
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11C22×C414yes—
187C23×D11C2×D414yes—
188C23×D11#4114yes—
189C23×D11C2412yes—
190C2×D4×C11—416no—
191C2×D4×C11—44no—
192C2×D4×C11—44no—
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—22no—
207C22×C4×C11—28no—
208C22×C4×C11—44no—
209C22×C4×C11—44no—
210C22×C4×C11—416no—
211C22×C4×C11C22×C414yes—
212C22×C4×C11C2×D414yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C2×C22⋊D11—232no—
219C2×C22⋊D11—232no—
220C2×C22⋊D11—28no—
221C2×C22⋊D11—28no—
222C2×C22⋊D11—28no—
223C2×C22⋊D11—28no—
224C2×C22⋊D11C22×C4116yescomplemented
225C2×C22⋊D11C22×C4116yescomplemented
226C22×Dic11—28no—
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—22no—
244C22×Dic11—44no—
245C22×Dic11—44no—
246C22×Dic11—416no—
247C22×Dic11C22×C414yes—
248C22×Dic11C22×C414yes—
249C22×Dic11C22×C414yes—
250C22×Dic11C2×D414yes—
251C22×Dic11C2412yes—
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C2×C4×D11—28no—
259C2×C4×D11—416no—
260C2×C4×D11—416no—
261C2×C4×D11—44no—
262C2×C4×D11—44no—
263C2×C4×D11—44no—
264C2×C4×D11—44no—
265C2×C4×D11—44no—
266C2×C4×D11—44no—
267C2×C4×D11—416no—
268C2×C4×D11C22×C4116yescomplemented
269C2×C4×D11C2×D4116yescomplemented
270C11×C22⋊C4—28no—
271C11×C22⋊C4—44no—
272C11×C22⋊C4—44no—
273C22⋊Dic11—28no—
274C22⋊Dic11—44no—
275C22⋊Dic11—44no—
276C22⋊Dic11C22×C4116yescomplemented
277C22⋊Dic11C22×C4116yescomplemented
278(C2×D11)⋊C4—28no—
279(C2×D11)⋊C4—28no—
280C4⋊Dic11C22×C4116yescomplemented
281Dic11⋊C4—28no—
282Dic11⋊C4—28no—
283Dic11⋊C4—44no—
284Dic11⋊C4—44no—
285C4×Dic11—28no—
286C4×Dic11—28no—
287C22×#121—111no—
288C22×C4×D4—111no—
289C22×C4×D4—111no—
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×#386D1111yescharacteristic, complemented
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—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—44no—
322C23×C11—44no—
323C23×C11—44no—
324C23×C11—44no—
325C23×C11—44no—
326C23×C11—44no—
327C23×C11—44no—
328C23×C11—44no—
329C23×C11C23×C414yes—
330C23×C11C23×C414yes—
331C23×C11C23×C412yes—
332C23×C11C22×D412yes—
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—28no—
343C22×D11—28no—
344C22×D11—28no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11C4×D4116yes—
350C22×D11C23×C414yes—
351C22×D11C22×D414yes—
352C22×D11C2×#4114yes—
353D4×C11—416no—
354C2×C4×C11—28no—
355C2×C4×C11—28no—
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—416no—
370C2×C4×C11—44no—
371C2×C4×C11—44no—
372C2×C4×C11—44no—
373C2×C4×C11C23×C414yes—
374C2×C4×C11C22×D414yes—
375C22⋊D11—232no—
376C22⋊D11—232no—
377C2×Dic11—28no—
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—416no—
399C2×Dic11—44no—
400C2×Dic11—44no—
401C2×Dic11—44no—
402C2×Dic11C23×C414yes—
403C2×Dic11C23×C414yes—
404C2×Dic11C23×C414yes—
405C2×Dic11C22×D414yes—
406C4×D11—416no—
407C4×D11—416no—
408C4×D11—416no—
409C23×D4—111no—
410C23×D4—111no—
411C23×D4C2×D1111yescharacteristic
412C24×C4—111no—
413C24×C4—111no—
414C24×C4—111no—
415C24×C4—111no—
416C24×C4C2×D1111yescharacteristic
417C2×#121—118no—
418C2×#121—1116no—
419C2×C4×D4—118no—
420C2×C4×D4—118no—
421C2×C4×D4—228no—
422C2×C4×D4—228no—
423C22×C4⋊C4—111no—
424C22×C4⋊C4—111no—
425C22×C4⋊C4—111no—
426C22×C4⋊C4—111no—
427C22×C4⋊C4—111no—
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⋊C4C2×D1111yescharacteristic
436C22×C22⋊C4C2×D1111yescharacteristic
437C22×C22⋊C4C2×D1111yescharacteristic
438C22×C42—111no—
439C22×C42—111no—
440#388—118no—
441#388—118no—
442#387—118no—
443#387—118no—
444#386—118no—
445#386—118no—
446#386—118no—
447#386C2×D1118yescomplemented
448#385—118no—
449#385—118no—
450#380—118no—
451C2×#95—111no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95—111no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—118no—
460C2×#95C2×D1111yescharacteristic
461C2×#95C2×D1111yescharacteristic
462C22×C11—24no—
463C22×C11—24no—
464C22×C11—24no—
465C22×C11—24no—
466C22×C11—24no—
467C22×C11—24no—
468C22×C11—416no—
469C22×C11—416no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
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—232no—
493C2×D11—24no—
494C2×D11—24no—
495C2×D11—24no—
496C2×D11—24no—
497C2×D11—24no—
498C2×D11—24no—
499C2×D11C2×C4×D418yes—
500C4×C11—24no—
501C4×C11—24no—
502C4×C11—42no—
503C4×C11—42no—
504C4×C11—42no—
505Dic11—24no—
506Dic11—24no—
507Dic11—24no—
508Dic11—24no—
509Dic11—42no—
510Dic11—42no—
511Dic11—42no—
512C25—111no—
513C25C22×D1111yescharacteristic
514C25C22×D1111yescharacteristic
515C22×D4—42no—
516C22×D4—42no—
517C22×D4—118no—
518C22×D4—118no—
519C22×D4—114no—
520C22×D4—114no—
521C22×D4—224no—
522C22×D4—224no—
523C22×D4—224no—
524C22×D4—224no—
525C22×D4C4×D1118yescomplemented
526C22×D4C22×D1114yes—
527C23×C4—24no—
528C23×C4—42no—
529C23×C4—42no—
530C23×C4—111no—
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—118no—
535C23×C4—118no—
536C23×C4—114no—
537C23×C4—114no—
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×C4—442no—
552C23×C4—442no—
553C23×C4C22×D1111yescharacteristic
554C23×C4C22×D1111yescharacteristic
555C23×C4C22×D1111yescharacteristic
556C23×C4C22×D1111yescharacteristic
557C23×C4C22×D1111yescharacteristic
558C23×C4C22×D1114yes—
559#121—1164no—
560C4×D4—2232no—
561C4×D4—2232no—
562C2×C4⋊C4—118no—
563C2×C4⋊C4—114no—
564C2×C4⋊C4—114no—
565C2×C4⋊C4—114no—
566C2×C4⋊C4—114no—
567C2×C4⋊C4—114no—
568C2×C4⋊C4—224no—
569C2×C4⋊C4—224no—
570C2×C4⋊C4—442no—
571C2×C4⋊C4—442no—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4—118no—
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—224no—
587C2×C22⋊C4—442no—
588C2×C22⋊C4—442no—
589C2×C22⋊C4C22×D1114yes—
590C2×C22⋊C4C22×D1114yes—
591C2×C22⋊C4C22×D1114yes—
592C2×C42—114no—
593C2×C42—114no—
594C2×C42—224no—
595C2×C42—224no—
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#95C22×D1114yes—
605#95C22×D1114yes—
606C2×C11—44no—
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—28no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—114no—
630C24—114no—
631C24—114no—
632C24—112no—
633C24—222no—
634C24—222no—
635C24—222no—
636C24—222no—
637C24C2×C4×D1114yes—
638C24C2×C4×D1114yes—
639C24C23×D1112yes—
640C24C23×D1112yes—
641C24C23×D1111yescharacteristic
642C2×D4—44no—
643C2×D4—44no—
644C2×D4—416no—
645C2×D4—1116no—
646C2×D4—1116no—
647C2×D4—228no—
648C2×D4—228no—
649C2×D4—2232no—
650C2×D4—2232no—
651C2×D4—228no—
652C2×D4—228no—
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—22no—
667C22×C4—28no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—416no—
671C22×C4—114no—
672C22×C4—114no—
673C22×C4—114no—
674C22×C4—114no—
675C22×C4—112no—
676C22×C4—112no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—1116no—
680C22×C4—1116no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—112no—
684C22×C4—228no—
685C22×C4—228no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—222no—
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—4416no—
704C22×C4—4416no—
705C22×C4—444no—
706C22×C4—444no—
707C22×C4—444no—
708C22×C4—444no—
709C22×C4—444no—
710C22×C4—444no—
711C22×C4—4416no—
712C22×C4—444no—
713C22×C4—444no—
714C22×C4—4416no—
715C22×C4C2×C4×D1114yes—
716C22×C4D4×D1114yes—
717C22×C4C23×D1112yes—
718C22×C4C23×D1112yes—
719C22×C4C23×D1112yes—
720C22×C4C23×D1112yes—
721C22×C4C23×D1112yes—
722C4⋊C4—1116no—
723C4⋊C4—228no—
724C4⋊C4—228no—
725C4⋊C4—444no—
726C4⋊C4—444no—
727C22⋊C4—28no—
728C22⋊C4—44no—
729C22⋊C4—44no—
730C22⋊C4—1116no—
731C22⋊C4—1116no—
732C22⋊C4—228no—
733C22⋊C4—228no—
734C22⋊C4—228no—
735C22⋊C4—444no—
736C22⋊C4—444no—
737C42—228no—
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—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—1116no—
767C23—114no—
768C23—114no—
769C23—114no—
770C23—228no—
771C23—228no—
772C23—228no—
773C23—228no—
774C23—228no—
775C23—222no—
776C23—222no—
777C23—222no—
778C23—228no—
779C23—222no—
780C23C22×C4×D1114yes—
781C23C22×C4×D1114yes—
782C23C22×C4×D1112yes—
783C23C2×D4×D1112yes—
784C23#6703712yes—
785C23#6703712yes—
786C23#6703712yes—
787C23#41×D1112yes—
788C23#6704312yes—
789C23C24×D1111yescharacteristic
790D4—416no—
791D4—2232no—
792D4—2232no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—22no—
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—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—114no—
813C2×C4—114no—
814C2×C4—114no—
815C2×C4—114no—
816C2×C4—228no—
817C2×C4—228no—
818C2×C4—228no—
819C2×C4—228no—
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—222no—
837C2×C4—4416no—
838C2×C4—4416no—
839C2×C4—4416no—
840C2×C4—4416no—
841C2×C4—444no—
842C2×C4—444no—
843C2×C4—444no—
844C2×C4C22×C4×D1114yes—
845C2×C4C2×D4×D1114yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—416no—
861C22—416no—
862C22—118no—
863C22—224no—
864C22—224no—
865C22—224no—
866C22—224no—
867C22—224no—
868C22—224no—
869C22—2232no—
870C22#1062301714yes—
871C22C4×D4×D1114yes—
872C22#1062307714yes—
873C22#1062312014yes—
874C22#1062313914yes—
875C22#1062314414yes—
876C22#1062319114yes—
877C22C23×C4×D1111yescharacteristic
878C22C22×D4×D1111yescharacteristic
879C22C2×#6703711yescharacteristic
880C22C2×#6703711yescharacteristic
881C22C2×#6703711yescharacteristic
882C22C2×#41×D1111yescharacteristic
883C22C2×#6704311yescharacteristic
884C4—24no—
885C4—24no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—224no—
890C4—224no—
891C4—224no—
892C4—224no—
893C4—442no—
894C4—442no—
895C4—442no—
896C2—44no—
897C2—44no—
898C2—228no—
899C2#1307131818yesdirect product factor
900C2C2×C4×D4×D1111yescharacteristic
901C2C2×#1062301711yescharacteristic
902C2C2×#1062307711yescharacteristic
903C2C2×#1062312011yescharacteristic
904C2C2×#1062313911yescharacteristic
905C2C2×#1062314411yescharacteristic
906C2C2×#1062319111yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC22×#66991C2
cosocleC23×C11C25
hypercenterC2×#386D11
hypocenterC11C2×#2325
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D11C2semidirect
3. C22×(C22⋊D11)⋊C4C2semidirect
4. #13071318C2direct (N × H)
5. C2×#10622558C2semidirect
6. C2×#10622557C2semidirect
7. C2×#10622266C2semidirect
8. C2×#10622267C2semidirect
9. C2×#10622833C2semidirect
10. C2×#10622569C2semidirect
11. C2×#10622569C2semidirect
12. C2×#10622823C2semidirect
13. C2×#10622559C2semidirect
14. C2×#10622280C2semidirect
15. C2×D11×#95C2semidirect
16. C2×C11×#386C2semidirect
33. C2×#66991C4semidirect
36. C2×C4×C22⋊D11C22semidirect
47. C2×(C22⋊D11)⋊C4C22semidirect
48. C11×#386C22semidirect
51. #10622833C22semidirect
52. #10622823C22semidirect
61. #10622569C22semidirect
62. #10622569C22semidirect
63. #10622559C22semidirect
64. #10622558C22semidirect
65. #10622557C22semidirect
66. #10622280C22semidirect
67. D11×#95C22semidirect
68. #10622267C22semidirect
69. #10622266C22semidirect
75. C22×D4×C11C2×C4semidirect
90. C22×C22⋊D11C2×C4semidirect
91. C22×C22⋊D11C2×C4semidirect
112. C22×C4×D11C2×C4semidirect
113. C22×C4×D11D4semidirect
126. C2×C22⋊Dic11C2×C4semidirect
127. C2×C22⋊Dic11C2×C4semidirect
133. #66991C2×C4semidirect
139. C2×C4⋊Dic11C2×C4semidirect
193. C2×D4×C11C22×C4semidirect
224. C2×C22⋊D11C22×C4semidirect
225. C2×C22⋊D11C22×C4semidirect
268. C2×C4×D11C22×C4semidirect
269. C2×C4×D11C2×D4semidirect
276. C22⋊Dic11C22×C4semidirect
277. C22⋊Dic11C22×C4semidirect
280. C4⋊Dic11C22×C4semidirect
298. C2×#386D11semidirect
447. #386C2×D11semidirect
525. C22×D4C4×D11semidirect
608. C2×C11#2325semidirect
653. C2×D4C2×C4×D11semidirect
739. C11C2×#2325semidirect
899. C2#13071318direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669912
C22×C4×C22⋊D112
C22×(C22⋊D11)⋊C42
#130713182
C2×#106225582
C2×#106225572
C2×#106222662
C2×#106222672
C2×#106228332
C2×#106225692
C2×#106228232
C2×#106225592
C2×#106222802
C2×D11×#952
C2×C11×#3862
C2×#232511