Finite Group Databasebeta

← #14769891

Subgroups — #14769891

Order 2816.

1168 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623088C211yesmaximal, characteristic
2C2×#10622624C211yesmaximal, characteristic, complemented
3#13069556C211yesmaximal, characteristic, complemented
4#13069555C211yesmaximal, characteristic, complemented
5#13068913C211yesmaximal, characteristic, complemented
6#13068911C211yesmaximal, characteristic, complemented
7#13068908C211yesmaximal, characteristic, complemented
8#13068906C211yesmaximal, characteristic, complemented
9#13068685C211yesmaximal, characteristic, complemented
10#13068685C211yesmaximal, characteristic, complemented
11#13068593C211yesmaximal, characteristic, complemented
12#13068379C211yesmaximal, characteristic, complemented
13#13068314C211yesmaximal, characteristic, complemented
14#13068312C211yesmaximal, characteristic, complemented
15C2×C11×#435C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66991C411yescharacteristic
20C2×#66989C411yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C2×C4×C22⋊D11C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C2×#66979C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27#10623088—24no—
28#10623088—24no—
29C2×#66950C411yescharacteristic
30C2×#66943C411yescharacteristic
31C2×#66936C411yescharacteristic
32C2×#66936C411yescharacteristic
33C2×#66932C411yescharacteristic
34C2×#66932C411yescharacteristic
35C2×C42×D11C2211yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C11×#435—24no—
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×C22⋊C8C2211yescharacteristic
41C2×C11×#97C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×(C2×D11)⋊C8C2211yescharacteristic
46C2×(C2×D11)⋊C8C2211yescharacteristic
47C2×(C2×D11)⋊C8C2211yescharacteristic
48#10622624—24no—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
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
72C2×C11×M16—22no—
73C2×C11×M16—22no—
74C2×C11×M16—41no—
75C22×C8×C11—22no—
76C22×C8×C11—22no—
77C22×C8×C11—41no—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C4×D4×C11D414yes—
83C4×D4×C11D414yes—
84C2×C11×C4⋊C4C2×C411yescharacteristic
85C2×C11×C22⋊C4C2×C411yescharacteristic
86C2×C11×C22⋊C4C2×C411yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C22⋊Dic11C2×C411yescharacteristic
89C2×C22⋊Dic11C2×C411yescharacteristic
90C2×C22⋊Dic11C2×C411yescharacteristic
91C2×C22⋊Dic11C2×C411yescharacteristic
92C2×C22⋊Dic11C2×C411yescharacteristic
93C2×C22⋊Dic11C2×C411yescharacteristic
94#66991—24no—
95#66989—24no—
96C4×C22⋊D11—22no—
97C4×C22⋊D11—22no—
98C4×C22⋊D11—22no—
99C4×C22⋊D11—22no—
100C2×(C2×D11)⋊C4C2×C411yescharacteristic
101C2×(C2×D11)⋊C4C2×C411yescharacteristic
102#66979—22no—
103#66979—22no—
104#66979—22no—
105#66979—22no—
106C2×C4⋊Dic11C2×C411yescharacteristic
107C2×C4⋊Dic11C2×C411yescharacteristic
108C2×C4⋊Dic11C2×C411yescharacteristic
109C2×C4⋊Dic11C2×C411yescharacteristic
110C2×C4⋊Dic11C2×C411yescharacteristic
111C2×Dic11⋊C4C2×C411yescharacteristic
112C2×Dic11⋊C4C2×C411yescharacteristic
113C2×Dic11⋊C4C2×C411yescharacteristic
114C2×Dic11⋊C4C2×C411yescharacteristic
115C2×C4×Dic11C2×C411yescharacteristic
116C2×C4×Dic11C2×C411yescharacteristic
117C2×C4×Dic11C2311yescharacteristic
118C2×C4×Dic11C2311yescharacteristic
119C2×C4×Dic11C2311yescharacteristic
120C2×#4318—22no—
121C2×#4318—22no—
122C2×#4318—41no—
123C22×C11⋊C8—22no—
124C22×C11⋊C8—22no—
125C22×C11⋊C8—41no—
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130#66950—24no—
131#66943—24no—
132#66936—24no—
133#66936—24no—
134#66932—24no—
135#66932—24no—
136C42×D11—22no—
137C42×D11—22no—
138C4×Dic22—22no—
139C4×Dic22—22no—
140C11×C4⋊C8—22no—
141C11×C22⋊C8—22no—
142C11×C22⋊C8—22no—
143C11×#97—22no—
144C22⋊(C11⋊C8)—22no—
145C22⋊(C11⋊C8)—22no—
146(C2×D11)⋊C8—22no—
147(C2×D11)⋊C8—22no—
148(C2×D11)⋊C8—41no—
149(C2×D11)⋊C8—41no—
150C4⋊(C11⋊C8)—22no—
151#66867—22no—
152#22475—111nomaximal, Sylow
153C24×C11C22×C411yescharacteristic
154C24×C11C22×C411yescharacteristic
155C23×D11C22×C411yescharacteristic
156C2×D4×C11—41no—
157C2×D4×C11—41no—
158C2×D4×C11C22⋊C414yes—
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×C11C22×C411yescharacteristic
168C22×C4×C11C22×C411yescharacteristic
169C22×C4×C11C22×C411yescharacteristic
170C22×C4×C11C22×C411yescharacteristic
171C22×C4×C11C2×D412yes—
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×D412yes—
174C22×C4×C11C2×D412yes—
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—22no—
202C2×Dic22—41no—
203C2×Dic22—41no—
204C11×M16—44no—
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—21no—
216C2×C8×C11—44no—
217C2×C8×C11#4112yes—
218C11×C4⋊C4C22⋊C414yes—
219C11×C22⋊C4C22⋊C414yes—
220C11×C22⋊C4C22⋊C414yes—
221C42×C11C2×D412yes—
222C42×C11C2×D412yes—
223C22⋊Dic11—22no—
224C22⋊Dic11—22no—
225C22⋊Dic11—22no—
226C22⋊Dic11—22no—
227C22⋊Dic11—22no—
228C22⋊Dic11—22no—
229(C2×D11)⋊C4—22no—
230(C2×D11)⋊C4—22no—
231C4⋊Dic11—22no—
232C4⋊Dic11—22no—
233C4⋊Dic11—22no—
234C4⋊Dic11—22no—
235C4⋊Dic11—22no—
236Dic11⋊C4—22no—
237Dic11⋊C4—22no—
238Dic11⋊C4—22no—
239Dic11⋊C4—22no—
240C4×Dic11—22no—
241C4×Dic11—22no—
242C4×Dic11—21no—
243C4×Dic11—21no—
244C4×Dic11—21no—
245C4×Dic11—21no—
246C4×Dic11—21no—
247C4×Dic11—21no—
248#4318—44no—
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×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—44no—
261C2×C11⋊C8#4112yes—
262C2×#529—111no—
263C2×#435—111no—
264C2×#435D1111yescharacteristic, complemented
265#1985—111no—
266#1985—111no—
267#1870—111no—
268#1870—111no—
269#1869—111no—
270#1869—111no—
271#1818—111no—
272#1818—111no—
273#1797—111no—
274#1749—111no—
275#1729—111no—
276#1729—111no—
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×C11—21no—
288C23×C11—21no—
289C23×C11C2×C22⋊C412yes—
290C23×C11C2×C22⋊C412yes—
291C23×C11C23×C411yescharacteristic
292C22×D11—21no—
293C22×D11—21no—
294C22×D11—21no—
295C22×D11—21no—
296C22×D11—21no—
297C22×D11—21no—
298C22×D11#13112yes—
299D4×C11—44no—
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—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11C2×C22⋊C412yes—
317C2×C4×C11C2×C22⋊C412yes—
318C2×C4×C11C2×C22⋊C412yes—
319C2×C4×C11C2×C22⋊C412yes—
320C2×C4×C11C22×D411yescharacteristic
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C2×#4111yescharacteristic
323C2×C4×C11C2×#4111yescharacteristic
324C2×C4×C11H(5,𝔽2)11yescharacteristic
325C2×C4×C112−1+411yescharacteristic
326C22⋊D11—44no—
327C22⋊D11—44no—
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×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11—21no—
344C2×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11—21no—
347C2×Dic11—21no—
348C2×Dic11—21no—
349C4×D11—44no—
350C4×D11—44no—
351C4×D11—41no—
352C4×D11—41no—
353C4×D11—41no—
354C4×D11—41no—
355Dic22—44no—
356C8×C11—22no—
357C8×C11—41no—
358C8×C11—41no—
359C8×C11—41no—
360C11⋊C8—22no—
361C11⋊C8—41no—
362C11⋊C8—41no—
363C11⋊C8—41no—
364C22×M16—111no—
365C22×M16C2×D1111yescharacteristic
366C23×C8—111no—
367C23×C8C2×D1111yescharacteristic
368#529—224no—
369#529—224no—
370C2×#126—111no—
371C2×#126—111no—
372C2×#125—111no—
373C2×#124—111no—
374C2×#123—111no—
375C2×#123—111no—
376C2×C22⋊Q8—111no—
377C2×#121—111no—
378C2×C4×Q8—111no—
379C2×C4×D4—111no—
380C2×C4×D4—111no—
381C2×C4×D4C2×D1111yescharacteristic
382C2×#117—111no—
383C2×#117—111no—
384C22×C42—111no—
385#435—24no—
386#435—224no—
387C2×C4⋊C8—111no—
388C2×C4⋊C8C2×D1111yescharacteristic
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×#97C2×D1111yescharacteristic
399#336—111no—
400#336—111no—
401#336—111no—
402#336—111no—
403#336—111no—
404#336—111no—
405#336—111no—
406#336—111no—
407#336—111no—
408#336—111no—
409#336—111no—
410#336—111no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11C22×C22⋊C411yescharacteristic
426C22×C11C4×#4111yescharacteristic
427C22×C11#52011yescharacteristic
428C22×C11C2×#13111yescharacteristic
429C22×C11#56811yescharacteristic
430C22×C11#56811yescharacteristic
431C22×C11#56811yescharacteristic
432C2×D11—22no—
433C2×D11—22no—
434C2×D11—22no—
435C2×D11—41no—
436C2×D11—41no—
437C2×D11—41no—
438C2×D11—41no—
439C4×C11—22no—
440C4×C11—22no—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11#54611yescharacteristic
444C4×C11#54611yescharacteristic
445C4×C11#54711yescharacteristic
446C4×C11#54711yescharacteristic
447Dic11—41no—
448Dic11—41no—
449Dic11—41no—
450Dic11—41no—
451Dic11—41no—
452Dic11—41no—
453Dic11—41no—
454C22×Q8—111no—
455C22×D4—111no—
456C22×D4—111no—
457C22×D4C4×D1111yescharacteristic
458C23×C4—111no—
459C23×C4—111no—
460C23×C4—111no—
461C23×C4C22×D1111yescharacteristic
462C23×C4C22×D1111yescharacteristic
463C2×M16—22no—
464C2×M16—22no—
465C2×M16—41no—
466C2×M16—222no—
467C2×M16—222no—
468C2×M16—441no—
469C22×C8—22no—
470C22×C8—22no—
471C22×C8—41no—
472C22×C8—111no—
473C22×C8—111no—
474C22×C8—111no—
475C22×C8—111no—
476C22×C8—222no—
477C22×C8—222no—
478C22×C8—441no—
479C22×C8C22×D1111yescharacteristic
480C22×C8C22×D1111yescharacteristic
481C22×C8C22×D1111yescharacteristic
482C22×C8C22×D1111yescharacteristic
483#126—224no—
484#126—224no—
485#125—224no—
486#124—224no—
487#123—224no—
488#123—224no—
489C22⋊Q8—224no—
490#121—224no—
491C4×Q8—222no—
492C4×Q8—222no—
493C4×D4—222no—
494C4×D4—222no—
495C4×D4—222no—
496C4×D4—222no—
497C4×D4D4414yes—
498C4×D4C22⋊D1114yes—
499#117—222no—
500#117—222no—
501#117—222no—
502#117—222no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—111no—
506C2×C4⋊C4—111no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4C4×D1111yescharacteristic
513C2×C22⋊C4—111no—
514C2×C22⋊C4—111no—
515C2×C22⋊C4—111no—
516C2×C22⋊C4—111no—
517C2×C22⋊C4—111no—
518C2×C22⋊C4—111no—
519C2×C22⋊C4—111no—
520C2×C22⋊C4—111no—
521C2×C22⋊C4C4×D1111yescharacteristic
522C2×C22⋊C4C4×D1111yescharacteristic
523C2×C42—111no—
524C2×C42—111no—
525C2×C42—111no—
526C2×C42—111no—
527C2×C42—111no—
528C2×C42—222no—
529C2×C42—222no—
530C2×C42C22×D1111yescharacteristic
531C4⋊C8—22no—
532C4⋊C8—222no—
533C22⋊C8—22no—
534C22⋊C8—22no—
535C22⋊C8—222no—
536C22⋊C8—222no—
537C22⋊C8—222no—
538C22⋊C8—222no—
539C22⋊C8—441no—
540C22⋊C8—441no—
541#97—22no—
542#97—222no—
543C2×C11—42no—
544C2×C11—42no—
545C2×C11#233911yescharacteristic
546C2×C11#287911yescharacteristic
547C2×C11#288011yescharacteristic
548C2×C11#296711yescharacteristic
549C2×C11#296811yescharacteristic
550C2×C11#299211yescharacteristic
551C2×C11#299511yescharacteristic
552D11—42no—
553C24—111no—
554C24C2×C4×D1111yescharacteristic
555C24C2×C4×D1111yescharacteristic
556C2×Q8—222no—
557C2×Q8—441no—
558C2×Q8—441no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—222no—
562C2×D4—222no—
563C2×D4—222no—
564C2×D4—222no—
565C2×D4—441no—
566C2×D4—441no—
567C2×D4(C2×D11)⋊C414yes—
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×C4C2×D4412yes—
600C22×C4C2×D4412yes—
601C22×C4C2×C22⋊D1112yes—
602C22×C4C2×C22⋊D1112yes—
603C22×C4C23×D1111yescharacteristic
604M16—44no—
605M16—444no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—44no—
618C2×C8—112no—
619C2×C8—221no—
620C2×C8—221no—
621C2×C8—221no—
622C2×C8—221no—
623C2×C8—221no—
624C2×C8—221no—
625C2×C8—221no—
626C2×C8—221no—
627C2×C8—221no—
628C2×C8—221no—
629C2×C8—221no—
630C2×C8—444no—
631C2×C8#434112yes—
632C4⋊C4—222no—
633C4⋊C4—222no—
634C4⋊C4—222no—
635C4⋊C4—222no—
636C4⋊C4—222no—
637C4⋊C4—222no—
638C4⋊C4—222no—
639C4⋊C4—222no—
640C4⋊C4—222no—
641C4⋊C4(C2×D11)⋊C414yes—
642C22⋊C4—222no—
643C22⋊C4—222no—
644C22⋊C4—222no—
645C22⋊C4—222no—
646C22⋊C4—222no—
647C22⋊C4—222no—
648C22⋊C4—222no—
649C22⋊C4—222no—
650C22⋊C4(C2×D11)⋊C414yes—
651C22⋊C4(C2×D11)⋊C414yes—
652C42—222no—
653C42—222no—
654C42—221no—
655C42—221no—
656C42—221no—
657C42—221no—
658C42—221no—
659C42—221no—
660C42C2×D4412yes—
661C42C2×C22⋊D1112yes—
662C11#2247511yescharacteristic, complemented, Sylow
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—112no—
676C23—221no—
677C23—221no—
678C23—221no—
679C23—221no—
680C23—221no—
681C23—221no—
682C23C2×(C2×D11)⋊C412yes—
683C23C2×(C2×D11)⋊C412yes—
684C23C22×C4×D1111yescharacteristic
685Q8—444no—
686D4—44no—
687D4—444no—
688D4—444no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
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—221no—
721C2×C4—221no—
722C2×C4—221no—
723C2×C4—221no—
724C2×C4—221no—
725C2×C4—221no—
726C2×C4—444no—
727C2×C4—444no—
728C2×C4—441no—
729C2×C4—441no—
730C2×C4—441no—
731C2×C4—441no—
732C2×C4C2×(C2×D11)⋊C412yes—
733C2×C4C2×(C2×D11)⋊C412yes—
734C2×C4C2×(C2×D11)⋊C412yes—
735C2×C4C2×(C2×D11)⋊C412yes—
736C2×C4C22×D4411yescharacteristic
737C2×C4C2×#434111yescharacteristic
738C2×C4#6703711yescharacteristic
739C2×C4#41×D1111yescharacteristic
740C2×C4#6704311yescharacteristic
741C2×C4C22×C22⋊D1111yescharacteristic
742C8—22no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—222no—
747C8—441no—
748C8—441no—
749C8—441no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—222no—
765C22—222no—
766C22—222no—
767C22—441no—
768C22—441no—
769C22—441no—
770C22—441no—
771C22C4×#434111yescharacteristic
772C22#1062307711yescharacteristic
773C22#1062327611yescharacteristic
774C22#1062327611yescharacteristic
775C22D11×#13111yescharacteristic
776C22#1062328111yescharacteristic
777C22C22×(C2×D11)⋊C411yescharacteristic
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—441no—
783C4—441no—
784C4—441no—
785C4—441no—
786C4—441no—
787C4—441no—
788C4—441no—
789C4#1062308511yescharacteristic
790C4#1062308611yescharacteristic
791C4#1062333711yescharacteristic
792C4#1062335511yescharacteristic
793C2—42no—
794C2—42no—
795C2—442no—
796C2#1307144111yescharacteristic
797C2#1307706011yescharacteristic
798C2#1307706311yescharacteristic
799C2#1307759811yescharacteristic
800C2#1307760711yescharacteristic
801C2#1307775111yescharacteristic
802C2#1307778211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#435C2
prime radicalC2×#66991C4
cosocleC22×C4×C11C24
hypercenterC2×#435D11
hypocenterC11#22475
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#10622624C2semidirect
3. #13069556C2semidirect
4. #13069555C2semidirect
5. #13068913C2semidirect
6. #13068911C2semidirect
7. #13068908C2semidirect
8. #13068906C2semidirect
9. #13068685C2semidirect
10. #13068685C2semidirect
11. #13068593C2semidirect
12. #13068379C2semidirect
13. #13068314C2semidirect
14. #13068312C2semidirect
15. C2×C11×#435C2semidirect
264. C2×#435D11semidirect
662. C11#22475semidirect

Maximal subgroups

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

subgroupindex
C2×#106230882
C2×#106226242
#130695562
#130695552
#130689132
#130689112
#130689082
#130689062
#130686852
#130685932
#130683792
#130683142
#130683122
C2×C11×#4352
#2247511