Finite Group Databasebeta

← #14764867

Subgroups — #14764867

Order 2816.

1034 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622624C211yesmaximal, characteristic, complemented
2C2×#10622723C211yesmaximal, characteristic, complemented
3#13071831C211yesmaximal, characteristic
4#13069412C211yesmaximal, characteristic, complemented
5#13069408C211yesmaximal, characteristic, complemented
6#13069230C211yesmaximal, characteristic, complemented
7#13069227C211yesmaximal, characteristic, complemented
8#13069227C211yesmaximal, characteristic, complemented
9#13069223C211yesmaximal, characteristic, complemented
10#13068906C211yesmaximal, characteristic, complemented
11#13068906C211yesmaximal, characteristic, complemented
12#13068794C211yesmaximal, characteristic, complemented
13#13068527C211yesmaximal, characteristic, complemented
14#13068402C211yesmaximal, characteristic, complemented
15C11×#1869C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26#10622836C411yescharacteristic
27#10622836C411yescharacteristic
28C4×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31#10622723—24no—
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×(C2×D11)⋊C8C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40C2×#66879C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42C2×Dic11⋊C8C2211yescharacteristic
43C2×C8×Dic11C2211yescharacteristic
44#10622624—24no—
45#10622604C411yescharacteristic
46#10622592C411yescharacteristic
47#10622573C411yescharacteristic
48#10622572C411yescharacteristic
49#10622572C411yescharacteristic
50#10622560C411yescharacteristic
51C4×(C2×D11)⋊C4C2211yescharacteristic
52C4×(C2×D11)⋊C4C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×#66867C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61C22×D4×C11C2×C411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11C2×C411yescharacteristic
65C22×C22⋊D11C2×C411yescharacteristic
66C22×C22⋊D11C2×C411yescharacteristic
67C22×C22⋊D11C2×C411yescharacteristic
68C2×#4339—22no—
69C2×#4339—22no—
70C2×#4339—41no—
71C2×#4339—41no—
72C2×#4339—41no—
73C2×#4339—41no—
74C22×D44C2×C411yescharacteristic
75C22×C4×D11C2311yescharacteristic
76C22×C4×D11C2311yescharacteristic
77C22×Dic22C2×C411yescharacteristic
78C22×C8×C11—22no—
79C22×C8×C11—41no—
80C22×C8×C11—41no—
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C2×C11×C4⋊C4C2×C411yescharacteristic
88C2×C11×C22⋊C4C2×C411yescharacteristic
89C2×C11×C22⋊C4C2×C411yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C22⋊Dic11C2×C411yescharacteristic
92C2×C22⋊Dic11C2×C411yescharacteristic
93C2×C22⋊Dic11C2×C411yescharacteristic
94C2×C22⋊Dic11C2×C411yescharacteristic
95C4×C22⋊D11—41no—
96C4×C22⋊D11—41no—
97C4×C22⋊D11—41no—
98C4×C22⋊D11—41no—
99C2×(C2×D11)⋊C4C2×C411yescharacteristic
100C2×(C2×D11)⋊C4C2×C411yescharacteristic
101C2×(C2×D11)⋊C4C2×C411yescharacteristic
102C2×(C2×D11)⋊C4C2×C411yescharacteristic
103C2×(C2×D11)⋊C4C2×C411yescharacteristic
104C2×(C2×D11)⋊C4C2×C411yescharacteristic
105C2×Dic11⋊C4C2×C411yescharacteristic
106C2×Dic11⋊C4C2×C411yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C2×#4318—41no—
110C2×#4318—41no—
111C2×#4318D414yescomplemented
112C22×C11⋊C8—22no—
113C22×C11⋊C8—41no—
114C22×C11⋊C8—41no—
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C11×C22⋊C8—22no—
120C11×C22⋊C8—41no—
121C11×C22⋊C8—41no—
122C11⋊#95C2×C411yescharacteristic
123C11⋊#95C2×C411yescharacteristic
124C11⋊#95C2×C411yescharacteristic
125C11⋊#95C2×C411yescharacteristic
126C11⋊#95C2×C411yescharacteristic
127C11⋊#95C2×C411yescharacteristic
128C22⋊(C11⋊C8)—22no—
129C22⋊(C11⋊C8)—22no—
130(C2×D11)⋊C8—22no—
131(C2×D11)⋊C8—22no—
132(C2×D11)⋊C8—22no—
133(C2×D11)⋊C8—22no—
134(C2×D11)⋊C8—41no—
135(C2×D11)⋊C8—41no—
136(C2×D11)⋊C8—41no—
137(C2×D11)⋊C8—41no—
138#66879—41no—
139Dic11⋊C8—41no—
140Dic11⋊C8—41no—
141C8×Dic11—41no—
142C4⋊(C11⋊C8)—22no—
143#66867—22no—
144#22037—111nomaximal, Sylow
145C24×C11C22×C411yescharacteristic
146C24×C11C22×C411yescharacteristic
147C23×D11C22×C411yescharacteristic
148C23×D11C22×C411yescharacteristic
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—41no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
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×C11C2×D412yes—
167C22×C4×C11#4112yes—
168C22×C4×C11C2411yescharacteristic
169C2×C22⋊D11—22no—
170C2×C22⋊D11—22no—
171C2×C22⋊D11—22no—
172C2×C22⋊D11—22no—
173C2×C22⋊D11—22no—
174C2×C22⋊D11—41no—
175C2×C22⋊D11—41no—
176C2×C22⋊D11—41no—
177C2×C22⋊D11—41no—
178C2×C22⋊D11—41no—
179C2×C22⋊D11—41no—
180C2×C22⋊D11—41no—
181C22×Dic11C22×C411yescharacteristic
182C22×Dic11C22×C411yescharacteristic
183C22×Dic11C22×C411yescharacteristic
184C22×Dic11C22×C411yescharacteristic
185C22×Dic11C22×C411yescharacteristic
186C22×Dic11C22×C411yescharacteristic
187#4339—44no—
188#4339—44no—
189#4339—44no—
190#4339—44no—
191C2×D44—22no—
192C2×D44—41no—
193C2×D44—41no—
194C2×C4×D11—21no—
195C2×C4×D11—21no—
196C2×C4×D11—21no—
197C2×C4×D11—21no—
198C2×C4×D11—21no—
199C2×C4×D11—21no—
200C2×C4×D11—21no—
201C2×C4×D11—21no—
202C2×C4×D11—21no—
203C2×C4×D11—21no—
204C2×C4×D11—21no—
205C2×C4×D11—21no—
206C2×Dic22—22no—
207C2×Dic22—41no—
208C2×Dic22—41no—
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—21no—
217C2×C8×C11—21no—
218C2×C8×C11—21no—
219C2×C8×C11—21no—
220C2×C8×C11—21no—
221C2×C8×C11—44no—
222C11×C4⋊C4—22no—
223C11×C22⋊C4—22no—
224C11×C22⋊C4—22no—
225C42×C11—21no—
226C42×C11—21no—
227C22⋊Dic11—22no—
228C22⋊Dic11—41no—
229C22⋊Dic11—41no—
230C22⋊Dic11—41no—
231(C2×D11)⋊C4—22no—
232(C2×D11)⋊C4—41no—
233(C2×D11)⋊C4—41no—
234(C2×D11)⋊C4—41no—
235(C2×D11)⋊C4—41no—
236(C2×D11)⋊C4—41no—
237Dic11⋊C4—41no—
238Dic11⋊C4—41no—
239C4×Dic11—21no—
240C4×Dic11—21no—
241C4×Dic11—21no—
242C4×Dic11—21no—
243#4318—44no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
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—44no—
255C2×C11⋊C8C2×D412yes—
256C2×C11⋊C8C2×D412yes—
257C2×#435—111no—
258C2×#408—111no—
259#2388—111no—
260#1955—111no—
261#1954—111no—
262#1924—111no—
263#1924—111no—
264#1924—111no—
265#1923—111no—
266#1869—111no—
267#1869—111no—
268#1869D1111yescharacteristic, complemented
269#1850—111no—
270#1780—111no—
271#1753—111no—
272C23×C11—21no—
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×C11C4×D412yes—
285C23×C11#13112yes—
286C23×C11C23×C411yescharacteristic
287C22×D11—21no—
288C22×D11—21no—
289C22×D11—21no—
290C22×D11—21no—
291C22×D11—21no—
292C22×D11—21no—
293C22×D11—21no—
294C22×D11—21no—
295C22×D11—21no—
296C22×D11—21no—
297C22×D11—21no—
298C22×D11—21no—
299C22×D11—21no—
300C22×D11—21no—
301D4×C11—44no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11C4×D412yes—
322C2×C4×C11C22×D411yescharacteristic
323C2×C4×C11C2×#4111yescharacteristic
324C2×C4×C11H(5,𝔽2)11yescharacteristic
325C2×C4×C11H(5,𝔽2)11yescharacteristic
326C2×C4×C11H(5,𝔽2)11yescharacteristic
327C2×C4×C11H(5,𝔽2)11yescharacteristic
328C22⋊D11—44no—
329C22⋊D11—44no—
330C22⋊D11—44no—
331C22⋊D11—44no—
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—
349C2×Dic11#13112yes—
350D44—44no—
351C4×D11—41no—
352C4×D11—41no—
353C4×D11—41no—
354C4×D11—41no—
355C4×D11—41no—
356C4×D11—41no—
357C4×D11—41no—
358C4×D11—41no—
359Dic22—44no—
360C8×C11—41no—
361C8×C11—41no—
362C8×C11—41no—
363C8×C11—41no—
364C11⋊C8—22no—
365C11⋊C8—22no—
366C11⋊C8—41no—
367C11⋊C8—41no—
368C22×#41—111no—
369C22×M16—111no—
370C23×C8—111no—
371C23×C8C2×D1111yescharacteristic
372C2×C4×D4—111no—
373C2×C4×D4—111no—
374C2×C4×D4C2×D1111yescharacteristic
375#435—224no—
376C2×C4⋊C8—111no—
377C2×C4⋊C8—111no—
378C2×C4⋊C8—111no—
379#408—224no—
380C2×C22⋊C8—111no—
381C2×C22⋊C8—111no—
382C2×C22⋊C8—111no—
383C2×C22⋊C8—111no—
384C2×C22⋊C8—111no—
385C2×C22⋊C8—111no—
386C2×C22⋊C8—111no—
387C2×C22⋊C8—111no—
388C2×C22⋊C8—111no—
389C2×C22⋊C8—111no—
390C2×C22⋊C8C2×D1111yescharacteristic
391C2×C22⋊C8C2×D1111yescharacteristic
392C2×C22⋊C8C2×D1111yescharacteristic
393C2×#97—111no—
394C2×#97—111no—
395C2×C4×C8—111no—
396#395—111no—
397#394—111no—
398#394—111no—
399#394—111no—
400#393—111no—
401#392—111no—
402#392—111no—
403#392—111no—
404C4×C22⋊C4—111no—
405C4×C22⋊C4—111no—
406C4×C22⋊C4—111no—
407#336—111no—
408#336—111no—
409#336—111no—
410#336—111no—
411#336C2×D1111yescharacteristic
412#336C2×D1111yescharacteristic
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—22no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11C2×C4×D411yescharacteristic
428C22×C11#51811yescharacteristic
429C22×C11#51811yescharacteristic
430C22×C11C2×#13111yescharacteristic
431C22×C11C2×#13111yescharacteristic
432C22×C11#56811yescharacteristic
433C22×C11#56811yescharacteristic
434C2×D11—41no—
435C2×D11—41no—
436C2×D11—41no—
437C2×D11—41no—
438C2×D11—41no—
439C2×D11—41no—
440C2×D11—41no—
441C2×D11—41no—
442C2×D11—41no—
443C2×D11—41no—
444C2×D11—41no—
445C2×D11—41no—
446C2×D11—41no—
447C2×D11—41no—
448C4×C11—22no—
449C4×C11—41no—
450C4×C11—41no—
451C4×C11—41no—
452C4×C11#53411yescharacteristic
453C4×C11#53511yescharacteristic
454C4×C11#53811yescharacteristic
455C4×C11#53811yescharacteristic
456Dic11—22no—
457Dic11—41no—
458Dic11—41no—
459Dic11—41no—
460Dic11—41no—
461Dic11—41no—
462C2×#41—222no—
463C2×#41—222no—
464C2×#41—441no—
465C2×#41—441no—
466C2×#41—441no—
467C2×#41—441no—
468C22×Q8—111no—
469C22×D4—111no—
470C22×D4—111no—
471C22×D4—111no—
472C22×D4—111no—
473C22×D4—111no—
474C22×D4C4×D1111yescharacteristic
475C23×C4—111no—
476C23×C4—111no—
477C23×C4C22×D1111yescharacteristic
478C23×C4C22×D1111yescharacteristic
479C2×M16—114no—
480C2×M16—441no—
481C2×M16—441no—
482C22×C8—22no—
483C22×C8—41no—
484C22×C8—41no—
485C22×C8—111no—
486C22×C8—111no—
487C22×C8—111no—
488C22×C8—111no—
489C22×C8—222no—
490C22×C8—441no—
491C22×C8—441no—
492C22×C8C22×D1111yescharacteristic
493C22×C8C22×D1111yescharacteristic
494C22×C8C22×D1111yescharacteristic
495C22×C8C22×D1111yescharacteristic
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—441no—
499C4×D4—441no—
500C4×D4—441no—
501C4×D4—441no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4C4×D1111yescharacteristic
505C2×C22⋊C4—111no—
506C2×C22⋊C4—111no—
507C2×C22⋊C4—111no—
508C2×C22⋊C4—111no—
509C2×C22⋊C4—111no—
510C2×C22⋊C4—111no—
511C2×C22⋊C4—111no—
512C2×C22⋊C4—111no—
513C2×C22⋊C4—111no—
514C2×C22⋊C4—111no—
515C2×C22⋊C4C4×D1111yescharacteristic
516C2×C22⋊C4C4×D1111yescharacteristic
517C2×C42—111no—
518C2×C42—111no—
519C2×C42C22×D1111yescharacteristic
520C4⋊C8—222no—
521C4⋊C8—441no—
522C4⋊C8—441no—
523C22⋊C8—22no—
524C22⋊C8—41no—
525C22⋊C8—41no—
526C22⋊C8—222no—
527C22⋊C8—222no—
528C22⋊C8—222no—
529C22⋊C8—222no—
530C22⋊C8—222no—
531C22⋊C8—222no—
532C22⋊C8—441no—
533C22⋊C8—441no—
534C22⋊C8—441no—
535C22⋊C8—441no—
536#97—222no—
537#97—441no—
538C4×C8—441no—
539#95—111no—
540#95—111no—
541#95—111no—
542#95—111no—
543#95—111no—
544#95—111no—
545C2×C11—42no—
546C2×C11—42no—
547C2×C11#232111yescharacteristic
548C2×C11#293311yescharacteristic
549C2×C11#293511yescharacteristic
550C2×C11#297611yescharacteristic
551C2×C11#297711yescharacteristic
552C2×C11#298011yescharacteristic
553C2×C11#298111yescharacteristic
554D11—81no—
555D11—81no—
556C24—111no—
557C24—111no—
558C24C2×C4×D1111yescharacteristic
559C24C2×C4×D1111yescharacteristic
560#41—444no—
561#41—444no—
562#41—444no—
563#41—444no—
564C2×Q8—222no—
565C2×Q8—441no—
566C2×Q8—441no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—41no—
570C2×D4—222no—
571C2×D4—222no—
572C2×D4—222no—
573C2×D4—222no—
574C2×D4—222no—
575C2×D4—222no—
576C2×D4—441no—
577C2×D4—441no—
578C2×D4—441no—
579C2×D4—441no—
580C2×D4—441no—
581C2×D4—441no—
582C2×D4—441no—
583C2×D4—441no—
584C2×D4—441no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—111no—
596C22×C4—111no—
597C22×C4—111no—
598C22×C4—111no—
599C22×C4—111no—
600C22×C4—111no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4C2×C4×D1111yescharacteristic
614C22×C4C2×C4×D1111yescharacteristic
615C22×C4C2×C4×D1111yescharacteristic
616C22×C4C2×C4×D1111yescharacteristic
617C22×C4D4×D1112yes—
618C22×C4#434112yes—
619C22×C4C23×D1111yescharacteristic
620M16—444no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—44no—
634C2×C8—112no—
635C2×C8—112no—
636C2×C8—221no—
637C2×C8—221no—
638C2×C8—221no—
639C2×C8—221no—
640C2×C8—221no—
641C2×C8—221no—
642C2×C8—221no—
643C2×C8—221no—
644C2×C8—221no—
645C2×C8—221no—
646C2×C8—444no—
647C4⋊C4—22no—
648C4⋊C4—441no—
649C4⋊C4—441no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—222no—
653C22⋊C4—222no—
654C22⋊C4—441no—
655C22⋊C4—441no—
656C22⋊C4—441no—
657C22⋊C4—441no—
658C22⋊C4—441no—
659C22⋊C4—441no—
660C22⋊C4—441no—
661C22⋊C4—441no—
662C42—21no—
663C42—21no—
664C42—221no—
665C42—221no—
666C42—221no—
667C42—221no—
668C11#2203711yescharacteristic, complemented, Sylow
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—221no—
682C23—221no—
683C23—221no—
684C23—221no—
685C23—221no—
686C23—221no—
687C23—221no—
688C23—221no—
689C23—221no—
690C23—221no—
691C23—221no—
692C23—221no—
693C23—221no—
694C23—221no—
695C23(C22⋊D11)⋊C412yes—
696C23#6695412yes—
697C23C22×C4×D1111yescharacteristic
698Q8—444no—
699D4—44no—
700D4—444no—
701D4—444no—
702D4—444no—
703D4—444no—
704D4—444no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—112no—
725C2×C4—221no—
726C2×C4—221no—
727C2×C4—221no—
728C2×C4—221no—
729C2×C4—221no—
730C2×C4—221no—
731C2×C4—221no—
732C2×C4—221no—
733C2×C4—221no—
734C2×C4—221no—
735C2×C4—221no—
736C2×C4—221no—
737C2×C4—221no—
738C2×C4—221no—
739C2×C4—221no—
740C2×C4—221no—
741C2×C4—221no—
742C2×C4—441no—
743C2×C4—441no—
744C2×C4—441no—
745C2×C4—441no—
746C2×C4—441no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4—441no—
750C2×C4(C22⋊D11)⋊C412yes—
751C2×C4C2×D4×D1111yescharacteristic
752C2×C4C2×#434111yescharacteristic
753C2×C4#6703711yescharacteristic
754C2×C4#6703711yescharacteristic
755C2×C4#6704211yescharacteristic
756C2×C4#6704211yescharacteristic
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C8—222no—
762C8—222no—
763C8—441no—
764C8—441no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—441no—
780C22—441no—
781C22—441no—
782C22—441no—
783C22—441no—
784C22—441no—
785C22—441no—
786C22—441no—
787C22—441no—
788C22—441no—
789C22—441no—
790C22—441no—
791C22—441no—
792C22—441no—
793C22C2×(C22⋊D11)⋊C411yescharacteristic
794C22#1062307611yescharacteristic
795C22#1062307611yescharacteristic
796C22C2×#6695411yescharacteristic
797C22#1062327611yescharacteristic
798C22D11×#13111yescharacteristic
799C22#1062328111yescharacteristic
800C4—22no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—222no—
805C4—441no—
806C4—441no—
807C4—441no—
808C4—441no—
809C4—441no—
810C4#1062312311yescharacteristic
811C4#1062314811yescharacteristic
812C4#1062314811yescharacteristic
813C4#1062318411yescharacteristic
814C2—42no—
815C2—42no—
816C2—881no—
817C2—881no—
818C2#1307127911yescharacteristic
819C2#1307733711yescharacteristic
820C2#1307735611yescharacteristic
821C2#1307765811yescharacteristic
822C2#1307766911yescharacteristic
823C2#1307768411yescharacteristic
824C2#1307768811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1869C2
prime radical#13071831C2
cosocleC22×C4×C11C24
hypercenter#1869D11
hypocenterC11#22037
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
1. C2×#10622624C2semidirect
2. C2×#10622723C2semidirect
4. #13069412C2semidirect
5. #13069408C2semidirect
6. #13069230C2semidirect
7. #13069227C2semidirect
8. #13069227C2semidirect
9. #13069223C2semidirect
10. #13068906C2semidirect
11. #13068906C2semidirect
12. #13068794C2semidirect
13. #13068527C2semidirect
14. #13068402C2semidirect
15. C11×#1869C2semidirect
111. C2×#4318D4semidirect
268. #1869D11semidirect
668. C11#22037semidirect

Maximal subgroups

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

subgroupindex
C2×#106226242
C2×#106227232
#130718312
#130694122
#130694082
#130692302
#130692272
#130692232
#130689062
#130687942
#130685272
#130684022
C11×#18692
#2203711