Finite Group Databasebeta

← #14770513

Subgroups — #14770513

Order 2816.

1108 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623088C211yesmaximal, characteristic
2C2×#10622441C211yesmaximal, characteristic, complemented
3C2×#10622314C211yesmaximal, characteristic, complemented
4#13069415C211yesmaximal, characteristic, complemented
5#13069412C211yesmaximal, characteristic, complemented
6#13069412C211yesmaximal, characteristic, complemented
7#13069408C211yesmaximal, characteristic, complemented
8#13069408C211yesmaximal, characteristic, complemented
9#13068598C211yesmaximal, characteristic, complemented
10#13068598C211yesmaximal, characteristic, complemented
11#13068593C211yesmaximal, characteristic, complemented
12#13068384C211yesmaximal, characteristic, complemented
13#13068384C211yesmaximal, characteristic, complemented
14#13068379C211yesmaximal, characteristic, complemented
15C11×#1955C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66991C411yescharacteristic
18C2×#66989C411yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23#10623088—24no—
24#10623088—24no—
25C2×#66950C411yescharacteristic
26C2×#66943C411yescharacteristic
27C2×#66936C411yescharacteristic
28C2×#66936C411yescharacteristic
29C2×#66932C411yescharacteristic
30C2×#66932C411yescharacteristic
31C2×C42×D11C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C2×C11×C4⋊C8C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×#97C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×(C2×D11)⋊C8C2211yescharacteristic
46C2×(C2×D11)⋊C8C2211yescharacteristic
47C2×#66879C2211yescharacteristic
48C2×#66879C2211yescharacteristic
49C2×Dic11⋊C8C2211yescharacteristic
50C2×Dic11⋊C8C2211yescharacteristic
51C2×Dic11⋊C8C2211yescharacteristic
52C2×Dic11⋊C8C2211yescharacteristic
53C2×C8×Dic11C2211yescharacteristic
54C2×C8×Dic11C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57#10622441—24no—
58#10622314—24no—
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622188C2211yescharacteristic
62#10622188C2211yescharacteristic
63C22×D4×C11C2×C411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2×C411yescharacteristic
67C22×C22⋊D11C2×C411yescharacteristic
68C22×C4×D11C2×C411yescharacteristic
69C22×C4×D11C2×C411yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C22×Dic22C2×C411yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C4×D4×C11—22no—
77C4×D4×C11—22no—
78C2×C11×C4⋊C4C2×C411yescharacteristic
79C2×C11×C22⋊C4C2×C411yescharacteristic
80C2×C11×C22⋊C4C2×C411yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11C2×C411yescharacteristic
83C2×C22⋊Dic11C2×C411yescharacteristic
84C2×C22⋊Dic11C2×C411yescharacteristic
85C2×C22⋊Dic11C2×C411yescharacteristic
86C2×C22⋊Dic11C2×C411yescharacteristic
87C2×C22⋊Dic11C2×C411yescharacteristic
88#66991—24no—
89#66989—24no—
90C4×C22⋊D11—22no—
91C4×C22⋊D11—22no—
92C4×C22⋊D11—22no—
93C4×C22⋊D11—22no—
94C2×(C2×D11)⋊C4C2×C411yescharacteristic
95C2×(C2×D11)⋊C4C2×C411yescharacteristic
96#66979—22no—
97#66979—22no—
98#66979—22no—
99#66979—22no—
100C2×C4⋊Dic11C2×C411yescharacteristic
101C2×C4⋊Dic11C2×C411yescharacteristic
102C2×C4⋊Dic11C2×C411yescharacteristic
103C2×C4⋊Dic11C2×C411yescharacteristic
104C2×C4⋊Dic11C2×C411yescharacteristic
105C2×Dic11⋊C4C2×C411yescharacteristic
106C2×Dic11⋊C4C2×C411yescharacteristic
107C2×Dic11⋊C4C2×C411yescharacteristic
108C2×Dic11⋊C4C2×C411yescharacteristic
109C2×C4×Dic11C2×C411yescharacteristic
110C2×C4×Dic11C2×C411yescharacteristic
111C2×C4×Dic11C2311yescharacteristic
112C2×C4×Dic11C2311yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118#66950—24no—
119#66943—24no—
120#66936—24no—
121#66936—24no—
122#66932—24no—
123#66932—24no—
124C42×D11—22no—
125C42×D11—22no—
126C4×Dic22D414yes—
127C4×Dic22D414yes—
128C11×C4⋊C8—22no—
129C11×C22⋊C8—22no—
130C11×C22⋊C8—22no—
131C11×C22⋊C8—41no—
132C11×C22⋊C8—41no—
133C11×#97—22no—
134C22⋊(C11⋊C8)—22no—
135C22⋊(C11⋊C8)—22no—
136C22⋊(C11⋊C8)—41no—
137C22⋊(C11⋊C8)—41no—
138(C2×D11)⋊C8—22no—
139(C2×D11)⋊C8—22no—
140(C2×D11)⋊C8—41no—
141(C2×D11)⋊C8—41no—
142#66879—22no—
143#66879—22no—
144Dic11⋊C8—22no—
145Dic11⋊C8—22no—
146Dic11⋊C8—22no—
147Dic11⋊C8—22no—
148C8×Dic11—22no—
149C8×Dic11—22no—
150C4⋊(C11⋊C8)—22no—
151#66867—22no—
152#22533—111nomaximal, Sylow
153C24×C11C22×C411yescharacteristic
154C24×C11C22×C411yescharacteristic
155C23×D11C22×C411yescharacteristic
156C2×D4×C11—22no—
157C2×D4×C11—41no—
158C2×D4×C11—41no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11C22×C411yescharacteristic
172C22×C4×C11C22×C411yescharacteristic
173C22×C4×C11C22×C411yescharacteristic
174C22×C4×C11C22×C411yescharacteristic
175C22×C4×C11C2411yescharacteristic
176C2×C22⋊D11—22no—
177C2×C22⋊D11—22no—
178C2×C22⋊D11—22no—
179C2×C22⋊D11—22no—
180C2×C22⋊D11—41no—
181C2×C22⋊D11—41no—
182C22×Dic11C22×C411yescharacteristic
183C22×Dic11C22×C411yescharacteristic
184C22×Dic11C22×C411yescharacteristic
185C22×Dic11C22×C411yescharacteristic
186C22×Dic11C22×C411yescharacteristic
187C22×Dic11C22×C411yescharacteristic
188C22×Dic11C22×C411yescharacteristic
189C2×C4×D11—22no—
190C2×C4×D11—22no—
191C2×C4×D11—22no—
192C2×C4×D11—21no—
193C2×C4×D11—21no—
194C2×C4×D11—21no—
195C2×C4×D11—21no—
196C2×C4×D11—21no—
197C2×C4×D11—21no—
198C2×C4×D11—41no—
199C2×C4×D11—41no—
200C2×C4×D11—41no—
201C2×Dic22—41no—
202C2×Dic22—41no—
203C2×Dic22C22⋊C414yes—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
214C2×C8×C11—21no—
215C2×C8×C11#4112yes—
216C11×C4⋊C4—22no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—22no—
219C42×C11C2×D412yes—
220C42×C11C2×D412yes—
221C22⋊Dic11—22no—
222C22⋊Dic11—22no—
223C22⋊Dic11—22no—
224C22⋊Dic11—22no—
225C22⋊Dic11—22no—
226C22⋊Dic11—22no—
227(C2×D11)⋊C4—22no—
228(C2×D11)⋊C4—22no—
229C4⋊Dic11—22no—
230C4⋊Dic11—22no—
231C4⋊Dic11—22no—
232C4⋊Dic11—22no—
233C4⋊Dic11C22⋊C414yes—
234Dic11⋊C4—22no—
235Dic11⋊C4—22no—
236Dic11⋊C4C22⋊C414yes—
237Dic11⋊C4C22⋊C414yes—
238C4×Dic11—22no—
239C4×Dic11—22no—
240C4×Dic11—21no—
241C4×Dic11—21no—
242C4×Dic11C2×D412yes—
243C4×Dic11C2×D412yes—
244C4×Dic11C2×D412yes—
245C4×Dic11C2×D412yes—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8#4112yes—
258C2×#529—111no—
259C2×#446—111no—
260C2×#446—111no—
261#1955—111no—
262#1955—111no—
263#1955—111no—
264#1955D1111yescharacteristic, complemented
265#1954—111no—
266#1954—111no—
267#1798—111no—
268#1798—111no—
269#1797—111no—
270#1750—111no—
271#1750—111no—
272#1749—111no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11C23×C411yescharacteristic
288C22×D11—21no—
289C22×D11—21no—
290C22×D11—21no—
291C22×D11—21no—
292C22×D11—21no—
293C22×D11—21no—
294C22×D11#13112yes—
295D4×C11—44no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11C2×C22⋊C412yes—
315C2×C4×C11C2×C22⋊C412yes—
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C22×D411yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C2×C4×C11C2×#4111yescharacteristic
320C2×C4×C11H(5,𝔽2)11yescharacteristic
321C2×C4×C112−1+411yescharacteristic
322C22⋊D11—44no—
323C22⋊D11—44no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11—21no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—21no—
331C2×Dic11—21no—
332C2×Dic11—21no—
333C2×Dic11—21no—
334C2×Dic11—21no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—21no—
339C2×Dic11—21no—
340C2×Dic11—21no—
341C2×Dic11C2×C22⋊C412yes—
342C2×Dic11C2×C22⋊C412yes—
343C2×Dic11C2×C22⋊C412yes—
344C2×Dic11C2×C22⋊C412yes—
345C4×D11—44no—
346C4×D11—44no—
347C4×D11—41no—
348C4×D11—41no—
349C4×D11—41no—
350C4×D11—41no—
351Dic22—44no—
352C8×C11—22no—
353C8×C11—41no—
354C8×C11—41no—
355C8×C11—41no—
356C11⋊C8—22no—
357C11⋊C8—41no—
358C11⋊C8—41no—
359C11⋊C8—41no—
360#529—224no—
361#529—224no—
362C2×#126—111no—
363C2×#126—111no—
364C2×#125—111no—
365C2×#124—111no—
366C2×#123—111no—
367C2×#123—111no—
368C2×C22⋊Q8—111no—
369C2×#121—111no—
370C2×C4×Q8—111no—
371C2×C4×D4—111no—
372C2×C4×D4—111no—
373C2×C4×D4C2×D1111yescharacteristic
374C2×#117—111no—
375C2×#117—111no—
376C22×C42—111no—
377#446—224no—
378#446—224no—
379C2×C4⋊C8—111no—
380C2×C4⋊C8—111no—
381C2×C4⋊C8—111no—
382C2×C4⋊C8—111no—
383C2×C4⋊C8—111no—
384C2×C4⋊C8C2×D1111yescharacteristic
385C2×C22⋊C8—111no—
386C2×C22⋊C8—111no—
387C2×C22⋊C8—111no—
388C2×C22⋊C8—111no—
389C2×C22⋊C8—111no—
390C2×C22⋊C8—111no—
391C2×C22⋊C8—111no—
392C2×C22⋊C8—111no—
393C2×C22⋊C8C2×D1111yescharacteristic
394C2×C22⋊C8C2×D1111yescharacteristic
395C2×C22⋊C8C2×D1111yescharacteristic
396C2×C22⋊C8C2×D1111yescharacteristic
397C2×#97—111no—
398C2×#97—111no—
399C2×#97—111no—
400C2×#97C2×D1111yescharacteristic
401C2×C4×C8—111no—
402C2×C4×C8—111no—
403#336—111no—
404#336—111no—
405#336—111no—
406#336—111no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11C22×C22⋊C411yescharacteristic
422C22×C11C4×#4111yescharacteristic
423C22×C11#52011yescharacteristic
424C22×C11C2×#13111yescharacteristic
425C22×C11#56811yescharacteristic
426C22×C11#56811yescharacteristic
427C22×C11#56811yescharacteristic
428C2×D11—22no—
429C2×D11—22no—
430C2×D11—22no—
431C2×D11—41no—
432C2×D11—41no—
433C2×D11—41no—
434C2×D11—41no—
435C4×C11—22no—
436C4×C11—22no—
437C4×C11—41no—
438C4×C11—41no—
439C4×C11#54811yescharacteristic
440C4×C11#54811yescharacteristic
441C4×C11#55011yescharacteristic
442C4×C11#55011yescharacteristic
443Dic11—22no—
444Dic11—22no—
445Dic11—22no—
446Dic11—22no—
447Dic11—41no—
448Dic11—41no—
449Dic11—41no—
450C22×Q8—111no—
451C22×D4—111no—
452C22×D4—111no—
453C22×D4C4×D1111yescharacteristic
454C23×C4—111no—
455C23×C4—111no—
456C23×C4—111no—
457C23×C4C22×D1111yescharacteristic
458C23×C4C22×D1111yescharacteristic
459C22×C8—111no—
460C22×C8—111no—
461C22×C8—111no—
462C22×C8—111no—
463C22×C8C22×D1111yescharacteristic
464C22×C8C22×D1111yescharacteristic
465C22×C8C22×D1111yescharacteristic
466C22×C8C22×D1111yescharacteristic
467#126—224no—
468#126—224no—
469#125—224no—
470#124—224no—
471#123—224no—
472#123—224no—
473C22⋊Q8—224no—
474#121—224no—
475C4×Q8—114no—
476C4×Q8—114no—
477C4×D4—22no—
478C4×D4—22no—
479C4×D4—222no—
480C4×D4—222no—
481C4×D4—222no—
482C4×D4—222no—
483#117—222no—
484#117—222no—
485#117—222no—
486#117—222no—
487C2×C4⋊C4—111no—
488C2×C4⋊C4—111no—
489C2×C4⋊C4—111no—
490C2×C4⋊C4—111no—
491C2×C4⋊C4—111no—
492C2×C4⋊C4—111no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4C4×D1111yescharacteristic
497C2×C22⋊C4—111no—
498C2×C22⋊C4—111no—
499C2×C22⋊C4—111no—
500C2×C22⋊C4—111no—
501C2×C22⋊C4—111no—
502C2×C22⋊C4—111no—
503C2×C22⋊C4—111no—
504C2×C22⋊C4—111no—
505C2×C22⋊C4C4×D1111yescharacteristic
506C2×C22⋊C4C4×D1111yescharacteristic
507C2×C42—111no—
508C2×C42—111no—
509C2×C42—111no—
510C2×C42—111no—
511C2×C42—111no—
512C2×C42—222no—
513C2×C42—222no—
514C2×C42C22×D1111yescharacteristic
515C4⋊C8—22no—
516C4⋊C8—222no—
517C4⋊C8—222no—
518C4⋊C8—222no—
519C4⋊C8—222no—
520C4⋊C8—222no—
521C22⋊C8—22no—
522C22⋊C8—22no—
523C22⋊C8—41no—
524C22⋊C8—41no—
525C22⋊C8—222no—
526C22⋊C8—222no—
527C22⋊C8—222no—
528C22⋊C8—222no—
529C22⋊C8—441no—
530C22⋊C8—441no—
531C22⋊C8—441no—
532C22⋊C8—441no—
533#97—22no—
534#97—222no—
535#97—222no—
536#97—222no—
537C4×C8—222no—
538C4×C8—222no—
539C2×C11—81no—
540C2×C11—81no—
541C2×C11#234111yescharacteristic
542C2×C11#287911yescharacteristic
543C2×C11#288011yescharacteristic
544C2×C11#296711yescharacteristic
545C2×C11#296811yescharacteristic
546C2×C11#299211yescharacteristic
547C2×C11#299511yescharacteristic
548D11—42no—
549C24—111no—
550C24C2×C4×D1111yescharacteristic
551C24C2×C4×D1111yescharacteristic
552C2×Q8—114no—
553C2×Q8—441no—
554C2×Q8—441no—
555C2×D4—22no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—222no—
559C2×D4—222no—
560C2×D4—222no—
561C2×D4—222no—
562C2×D4—441no—
563C2×D4—441no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—111no—
577C22×C4—111no—
578C22×C4—111no—
579C22×C4—111no—
580C22×C4—111no—
581C22×C4—111no—
582C22×C4—111no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—441no—
593C22×C4—441no—
594C22×C4—441no—
595C22×C4C2×C4×D1111yescharacteristic
596C22×C4C2×C4×D1111yescharacteristic
597C22×C4C2×C4×D1111yescharacteristic
598C22×C4C2×C4×D1111yescharacteristic
599C22×C4C23×D1111yescharacteristic
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—112no—
612C2×C8—221no—
613C2×C8—221no—
614C2×C8—221no—
615C2×C8—221no—
616C2×C8—221no—
617C2×C8—221no—
618C2×C8—221no—
619C2×C8—221no—
620C2×C8—221no—
621C2×C8—221no—
622C2×C8—221no—
623C2×C8#434112yes—
624C4⋊C4—22no—
625C4⋊C4—114no—
626C4⋊C4—114no—
627C4⋊C4—114no—
628C4⋊C4—222no—
629C4⋊C4—222no—
630C4⋊C4—222no—
631C4⋊C4—222no—
632C4⋊C4—222no—
633C4⋊C4—222no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—222no—
637C22⋊C4—222no—
638C22⋊C4—222no—
639C22⋊C4—222no—
640C22⋊C4—222no—
641C22⋊C4—222no—
642C22⋊C4—222no—
643C22⋊C4—222no—
644C42—112no—
645C42—112no—
646C42—112no—
647C42—112no—
648C42—222no—
649C42—222no—
650C42—221no—
651C42—221no—
652C42D4×D1112yes—
653C42D4×D1112yes—
654C11#2253311yescharacteristic, complemented, Sylow
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—112no—
670C23—221no—
671C23—221no—
672C23—221no—
673C23—221no—
674C23—221no—
675C23—221no—
676C23C22×C4×D1111yescharacteristic
677Q8—444no—
678D4—44no—
679D4—444no—
680D4—444no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—112no—
700C2×C4—112no—
701C2×C4—112no—
702C2×C4—112no—
703C2×C4—221no—
704C2×C4—221no—
705C2×C4—221no—
706C2×C4—221no—
707C2×C4—221no—
708C2×C4—221no—
709C2×C4—221no—
710C2×C4—221no—
711C2×C4—221no—
712C2×C4—221no—
713C2×C4—221no—
714C2×C4—221no—
715C2×C4—221no—
716C2×C4—221no—
717C2×C4—221no—
718C2×C4—221no—
719C2×C4—221no—
720C2×C4—444no—
721C2×C4—444no—
722C2×C4—441no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4—441no—
726C2×C4C22⋊C4×D1112yes—
727C2×C4C22⋊C4×D1112yes—
728C2×C4C2×D4×D1111yescharacteristic
729C2×C4C2×D4×D1111yescharacteristic
730C2×C4C2×#434111yescharacteristic
731C2×C4#6703711yescharacteristic
732C2×C4#41×D1111yescharacteristic
733C2×C4#6704311yescharacteristic
734C8—22no—
735C8—41no—
736C8—41no—
737C8—41no—
738C8—222no—
739C8—441no—
740C8—441no—
741C8—441no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—222no—
757C22—222no—
758C22—222no—
759C22—441no—
760C22—441no—
761C22—441no—
762C22—441no—
763C22C2×C22⋊C4×D1111yescharacteristic
764C22C4×#434111yescharacteristic
765C22#1062307711yescharacteristic
766C22#1062327611yescharacteristic
767C22#1062327611yescharacteristic
768C22D11×#13111yescharacteristic
769C22#1062328111yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—41no—
774C4—222no—
775C4—222no—
776C4—222no—
777C4—222no—
778C4—441no—
779C4—441no—
780C4—441no—
781C4#1062312911yescharacteristic
782C4#1062313011yescharacteristic
783C4#1062320811yescharacteristic
784C4#1062324911yescharacteristic
785C2—81no—
786C2—81no—
787C2—442no—
788C2#1307145511yescharacteristic
789C2#1307705911yescharacteristic
790C2#1307706411yescharacteristic
791C2#1307759811yescharacteristic
792C2#1307760711yescharacteristic
793C2#1307775111yescharacteristic
794C2#1307778211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1955C2
prime radicalC2×#66991C4
cosocleC22×C4×C11C24
hypercenter#1955D11
hypocenterC11#22533
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1955

Complements

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

NH ≅ G/Ntype
2. C2×#10622441C2semidirect
3. C2×#10622314C2semidirect
4. #13069415C2semidirect
5. #13069412C2semidirect
6. #13069412C2semidirect
7. #13069408C2semidirect
8. #13069408C2semidirect
9. #13068598C2semidirect
10. #13068598C2semidirect
11. #13068593C2semidirect
12. #13068384C2semidirect
13. #13068384C2semidirect
14. #13068379C2semidirect
15. C11×#1955C2semidirect
264. #1955D11semidirect
654. C11#22533semidirect

Maximal subgroups

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

subgroupindex
C2×#106230882
C2×#106224412
C2×#106223142
#130694152
#130694122
#130694082
#130685982
#130685932
#130683842
#130683792
C11×#19552
#2253311