Finite Group Databasebeta

← #14770516

Subgroups — #14770516

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×#10623059C211yesmaximal, characteristic
2C2×#10622292C211yesmaximal, characteristic, complemented
3C2×#10622314C211yesmaximal, characteristic, complemented
4#13069414C211yesmaximal, characteristic, complemented
5#13069412C211yesmaximal, characteristic, complemented
6#13069412C211yesmaximal, characteristic, complemented
7#13069412C211yesmaximal, characteristic, complemented
8#13069410C211yesmaximal, characteristic, complemented
9#13069408C211yesmaximal, characteristic, complemented
10#13068600C211yesmaximal, characteristic, complemented
11#13068599C211yesmaximal, characteristic, complemented
12#13068595C211yesmaximal, characteristic, complemented
13#13068381C211yesmaximal, characteristic, complemented
14#13068377C211yesmaximal, characteristic, complemented
15C11×#1750C211yesmaximal, characteristic, complemented
16C2×C11×#117C2211yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C2×C4×C22⋊D11C2211yescharacteristic
19#10623059—24no—
20#10623059—24no—
21C2×#66951C411yescharacteristic
22C2×#66949C411yescharacteristic
23C2×#66947C411yescharacteristic
24C2×#66942C411yescharacteristic
25C2×#66938C411yescharacteristic
26C2×#66937C411yescharacteristic
27C2×#66936C411yescharacteristic
28C2×#66932C411yescharacteristic
29C2×C4×D44C2211yescharacteristic
30C2×#66925C2211yescharacteristic
31C2×C42×D11C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×#97C2211yescharacteristic
36C2×C4×C8×C11C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40C2×(C2×D11)⋊C8C2211yescharacteristic
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×(C2×D11)⋊C8C2211yescharacteristic
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×(C2×D11)⋊C8C2211yescharacteristic
46C2×(C2×D11)⋊C8C2211yescharacteristic
47C2×#66879C2211yescharacteristic
48C2×#66879C2211yescharacteristic
49C2×#66879C2211yescharacteristic
50C2×Dic11⋊C8C2211yescharacteristic
51C2×Dic11⋊C8C2211yescharacteristic
52C2×Dic11⋊C8C2211yescharacteristic
53C2×Dic11⋊C8C2211yescharacteristic
54C2×C8×Dic11C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4⋊(C11⋊C8)C2211yescharacteristic
57#10622314—24no—
58#10622292—24no—
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11C2×C411yescharacteristic
65C22×C22⋊D11C2×C411yescharacteristic
66C22×D44C2×C411yescharacteristic
67C22×C4×D11C2×C411yescharacteristic
68C22×C4×D11C2×C411yescharacteristic
69C22×C4×D11C2311yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C22×Dic22C2×C411yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×#117—22no—
77C11×#117—22no—
78C2×C11×C4⋊C4C2×C411yescharacteristic
79C2×C11×C4⋊C4C2×C411yescharacteristic
80C2×C11×C22⋊C4C2×C411yescharacteristic
81C2×C11×C22⋊C4C2×C411yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11C2×C411yescharacteristic
85C2×C22⋊Dic11C2×C411yescharacteristic
86C4×C22⋊D11—22no—
87C4×C22⋊D11—22no—
88C4×C22⋊D11—22no—
89C4×C22⋊D11—22no—
90C2×(C2×D11)⋊C4C2×C411yescharacteristic
91C2×(C2×D11)⋊C4C2×C411yescharacteristic
92C2×(C2×D11)⋊C4C2×C411yescharacteristic
93C2×(C2×D11)⋊C4C2×C411yescharacteristic
94C2×(C2×D11)⋊C4C2×C411yescharacteristic
95C2×(C2×D11)⋊C4C2×C411yescharacteristic
96C2×C4⋊Dic11C2×C411yescharacteristic
97C2×C4⋊Dic11C2×C411yescharacteristic
98C2×Dic11⋊C4C2×C411yescharacteristic
99C2×Dic11⋊C4C2×C411yescharacteristic
100C2×Dic11⋊C4C2×C411yescharacteristic
101C2×Dic11⋊C4C2×C411yescharacteristic
102C2×Dic11⋊C4C2×C411yescharacteristic
103C2×Dic11⋊C4C2×C411yescharacteristic
104C2×C4×Dic11C2×C411yescharacteristic
105C2×C4×Dic11C2×C411yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112#66951—24no—
113#66949—24no—
114#66947—24no—
115#66942—24no—
116#66938—24no—
117#66937—24no—
118#66936—24no—
119#66932—24no—
120C4×D44—22no—
121C4×D44—22no—
122#66925—22no—
123#66925—22no—
124C42×D11—22no—
125C42×D11—22no—
126C4×Dic22D414yes—
127C4×Dic22D414yes—
128C11×C22⋊C8—22no—
129C11×C22⋊C8—22no—
130C11×#97—22no—
131C4×C8×C11—22no—
132C22⋊(C11⋊C8)—41no—
133C22⋊(C11⋊C8)—41no—
134(C2×D11)⋊C8—22no—
135(C2×D11)⋊C8—22no—
136(C2×D11)⋊C8—22no—
137(C2×D11)⋊C8—22no—
138(C2×D11)⋊C8—41no—
139(C2×D11)⋊C8—41no—
140(C2×D11)⋊C8—41no—
141(C2×D11)⋊C8—41no—
142#66879—22no—
143#66879—22no—
144#66879—22no—
145Dic11⋊C8—22no—
146Dic11⋊C8—22no—
147Dic11⋊C8—22no—
148Dic11⋊C8—22no—
149C8×Dic11—22no—
150C4⋊(C11⋊C8)—22no—
151C4⋊(C11⋊C8)—22no—
152#22533—111nomaximal, Sylow
153C24×C11C22×C411yescharacteristic
154C23×D11C22×C411yescharacteristic
155C23×D11C22×C411yescharacteristic
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C22×C411yescharacteristic
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C22×C411yescharacteristic
166C22×C4×C11C22×C411yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C2×C22⋊D11—22no—
169C2×C22⋊D11—22no—
170C2×C22⋊D11—22no—
171C2×C22⋊D11—41no—
172C2×C22⋊D11—41no—
173C2×C22⋊D11—41no—
174C22×Dic11C22×C411yescharacteristic
175C22×Dic11C22×C411yescharacteristic
176C22×Dic11C22×C411yescharacteristic
177C22×Dic11C22×C411yescharacteristic
178C22×Dic11C22×C411yescharacteristic
179C22×Dic11C22×C411yescharacteristic
180C2×D44—22no—
181C2×D44—22no—
182C2×D44—41no—
183C2×C4×D11—22no—
184C2×C4×D11—22no—
185C2×C4×D11—22no—
186C2×C4×D11—21no—
187C2×C4×D11—21no—
188C2×C4×D11—21no—
189C2×C4×D11—21no—
190C2×C4×D11—21no—
191C2×C4×D11—21no—
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#4112yes—
215C2×C8×C11#4112yes—
216C11×C4⋊C4—22no—
217C11×C4⋊C4—22no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—22no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11C2×D412yes—
223C42×C11C2×D412yes—
224C22⋊Dic11—22no—
225C22⋊Dic11—22no—
226(C2×D11)⋊C4—22no—
227(C2×D11)⋊C4—22no—
228(C2×D11)⋊C4—22no—
229(C2×D11)⋊C4—22no—
230(C2×D11)⋊C4—22no—
231(C2×D11)⋊C4—22no—
232C4⋊Dic11—22no—
233C4⋊Dic11C22⋊C414yes—
234Dic11⋊C4—22no—
235Dic11⋊C4—22no—
236Dic11⋊C4—22no—
237Dic11⋊C4—22no—
238Dic11⋊C4C22⋊C414yes—
239Dic11⋊C4C22⋊C414yes—
240C4×Dic11—22no—
241C4×Dic11—22no—
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—21no—
258C2×#529—111no—
259C2×#446—111no—
260C2×#446—111no—
261#1955—111no—
262#1955—111no—
263#1955—111no—
264#1955—111no—
265#1954—111no—
266#1954—111no—
267#1798—111no—
268#1798—111no—
269#1797—111no—
270#1750—111no—
271#1750D1111yescharacteristic, complemented
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×C11C23×C411yescharacteristic
281C22×D11—21no—
282C22×D11—21no—
283C22×D11—21no—
284C22×D11—21no—
285C22×D11—21no—
286C22×D11—21no—
287C22×D11—21no—
288C22×D11—21no—
289C22×D11—21no—
290C22×D11—21no—
291C22×D11—21no—
292C22×D11—21no—
293C22×D11—21no—
294C22×D11#13112yes—
295C2×C4×C11—21no—
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—21no—
307C2×C4×C11—21no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11C2×C22⋊C412yes—
313C2×C4×C11C2×C22⋊C412yes—
314C2×C4×C11C22×D411yescharacteristic
315C2×C4×C11C22×D411yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11H(5,𝔽2)11yescharacteristic
319C2×C4×C112−1+411yescharacteristic
320C22⋊D11—44no—
321C22⋊D11—44no—
322C2×Dic11—21no—
323C2×Dic11—21no—
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×Dic11C2×C22⋊C412yes—
337C2×Dic11C2×C22⋊C412yes—
338C2×Dic11C2×C22⋊C412yes—
339C2×Dic11C2×C22⋊C412yes—
340D44—44no—
341C4×D11—44no—
342C4×D11—44no—
343C4×D11—41no—
344C4×D11—41no—
345C4×D11—41no—
346C4×D11—41no—
347C4×D11—41no—
348C4×D11—41no—
349C4×D11—41no—
350C4×D11—41no—
351Dic22—44no—
352C8×C11—22no—
353C8×C11—22no—
354C8×C11—41no—
355C8×C11—41no—
356C11⋊C8—41no—
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×D4—111no—
374C2×#117—111no—
375C2×#117C2×D1111yescharacteristic
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⋊C8—111no—
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⋊C8—111no—
394C2×C22⋊C8—111no—
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×C8C2×D1111yescharacteristic
403#336—111no—
404#336—111no—
405#336C2×D1111yescharacteristic
406#336C2×D1111yescharacteristic
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11C22×C22⋊C411yescharacteristic
415C22×C11C4×#4111yescharacteristic
416C22×C11#52011yescharacteristic
417C22×C11C2×#13111yescharacteristic
418C22×C11#56811yescharacteristic
419C22×C11#56811yescharacteristic
420C22×C11#56811yescharacteristic
421C2×D11—22no—
422C2×D11—22no—
423C2×D11—22no—
424C2×D11—41no—
425C2×D11—41no—
426C2×D11—41no—
427C2×D11—41no—
428C2×D11—41no—
429C2×D11—41no—
430C2×D11—41no—
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—41no—
440C4×C11#54811yescharacteristic
441C4×C11#54811yescharacteristic
442C4×C11#55011yescharacteristic
443C4×C11#55011yescharacteristic
444Dic11—22no—
445Dic11—22no—
446Dic11—22no—
447Dic11—22no—
448Dic11—41no—
449Dic11—41no—
450C22×Q8—111no—
451C22×D4—111no—
452C22×D4—111no—
453C22×D4—111no—
454C23×C4—111no—
455C23×C4—111no—
456C23×C4—111no—
457C23×C4—111no—
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—222no—
478C4×D4—222no—
479C4×D4—222no—
480C4×D4—222no—
481C4×D4—222no—
482C4×D4—222no—
483#117—22no—
484#117—22no—
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⋊C4C4×D1111yescharacteristic
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—222no—
512C2×C42—222no—
513C2×C42C22×D1111yescharacteristic
514C2×C42C22×D1111yescharacteristic
515C4⋊C8—222no—
516C4⋊C8—222no—
517C4⋊C8—222no—
518C4⋊C8—222no—
519C4⋊C8—222no—
520C4⋊C8—222no—
521C22⋊C8—22no—
522C22⋊C8—22no—
523C22⋊C8—222no—
524C22⋊C8—222no—
525C22⋊C8—222no—
526C22⋊C8—222no—
527C22⋊C8—441no—
528C22⋊C8—441no—
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—22no—
538C4×C8—222no—
539C2×C11—81no—
540C2×C11#234111yescharacteristic
541C2×C11#287911yescharacteristic
542C2×C11#288011yescharacteristic
543C2×C11#296711yescharacteristic
544C2×C11#296811yescharacteristic
545C2×C11#299211yescharacteristic
546C2×C11#299511yescharacteristic
547D11—42no—
548D11—81no—
549C24—111no—
550C24—111no—
551C24C2×C4×D1111yescharacteristic
552C2×Q8—114no—
553C2×Q8—441no—
554C2×Q8—441no—
555C2×D4—222no—
556C2×D4—222no—
557C2×D4—222no—
558C2×D4—222no—
559C2×D4—222no—
560C2×D4—441no—
561C2×D4—441no—
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—111no—
571C22×C4—111no—
572C22×C4—111no—
573C22×C4—111no—
574C22×C4—111no—
575C22×C4—111no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—221no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—441no—
592C22×C4—441no—
593C22×C4—441no—
594C22×C4C2×C4×D1111yescharacteristic
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—221no—
611C2×C8—221no—
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#433912yes—
623C2×C8#433912yes—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—114no—
627C4⋊C4—114no—
628C4⋊C4—114no—
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—21no—
645C42—21no—
646C42—112no—
647C42—112no—
648C42—112no—
649C42—112no—
650C42—222no—
651C42—222no—
652C42D4×D1112yes—
653C42D4×D1112yes—
654C11#2253311yescharacteristic, complemented, Sylow
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—112no—
663C23—221no—
664C23—221no—
665C23—221no—
666C23—221no—
667C23—221no—
668C23—221no—
669C23—221no—
670C23—221no—
671C23—221no—
672C23—221no—
673C23—221no—
674C23—221no—
675C23—221no—
676C23C22×C4×D1111yescharacteristic
677Q8—444no—
678D4—444no—
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—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—112no—
699C2×C4—112no—
700C2×C4—112no—
701C2×C4—112no—
702C2×C4—221no—
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—444no—
717C2×C4—444no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—441no—
721C2×C4—441no—
722C2×C4—441no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4—441no—
726C2×C4C22⋊C4×D1112yes—
727C2×C4C22⋊C4×D1112yes—
728C2×C4C2×#433911yescharacteristic
729C2×C4C2×#433911yescharacteristic
730C2×C4C2×D4×D1111yescharacteristic
731C2×C4C2×D4×D1111yescharacteristic
732C2×C4#6704211yescharacteristic
733C2×C4#6704311yescharacteristic
734C8—22no—
735C8—22no—
736C8—41no—
737C8—41no—
738C8—441no—
739C8—441no—
740C8—441no—
741C8—441no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—222no—
750C22—222no—
751C22—222no—
752C22—441no—
753C22—441no—
754C22—441no—
755C22—441no—
756C22—441no—
757C22—441no—
758C22—441no—
759C22—441no—
760C22—441no—
761C22—441no—
762C22—441no—
763C22C4×#433911yescharacteristic
764C22C2×C22⋊C4×D1111yescharacteristic
765C22#1062305411yescharacteristic
766C22D11×#13111yescharacteristic
767C22#1062328111yescharacteristic
768C22#1062328111yescharacteristic
769C22#1062328111yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—222no—
776C4—222no—
777C4—222no—
778C4—222no—
779C4—441no—
780C4—441no—
781C4#1062308311yescharacteristic
782C4#1062308311yescharacteristic
783C4#1062308411yescharacteristic
784C4#1062308411yescharacteristic
785C2—81no—
786C2—442no—
787C2—881no—
788C2#1307145611yescharacteristic
789C2#1307705811yescharacteristic
790C2#1307706411yescharacteristic
791C2#1307759711yescharacteristic
792C2#1307760611yescharacteristic
793C2#1307775011yescharacteristic
794C2#1307778111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1750C2
prime radicalC2×#66937C4
cosocleC22×C4×C11C24
hypercenter#1750D11
hypocenterC11#22533
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. C2×#10622292C2semidirect
3. C2×#10622314C2semidirect
4. #13069414C2semidirect
5. #13069412C2semidirect
6. #13069412C2semidirect
7. #13069412C2semidirect
8. #13069410C2semidirect
9. #13069408C2semidirect
10. #13068600C2semidirect
11. #13068599C2semidirect
12. #13068595C2semidirect
13. #13068381C2semidirect
14. #13068377C2semidirect
15. C11×#1750C2semidirect
271. #1750D11semidirect
654. C11#22533semidirect

Maximal subgroups

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

subgroupindex
C2×#106230592
C2×#106222922
C2×#106223142
#130694142
#130694122
#130694102
#130694082
#130686002
#130685992
#130685952
#130683812
#130683772
C11×#17502
#2253311