Finite Group Databasebeta

← #14764025

Subgroups — #14764025

Order 2816.

1030 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622742C211yesmaximal, characteristic
2C2×#10622340C211yesmaximal, characteristic
3#13071102C211yesmaximal, characteristic
4#13068800C211yesmaximal, characteristic, complemented
5#13068800C211yesmaximal, characteristic, complemented
6#13068799C211yesmaximal, characteristic, complemented
7#13068796C211yesmaximal, characteristic, complemented
8#13068793C211yesmaximal, characteristic, complemented
9#13068792C211yesmaximal, characteristic, complemented
10#13068792C211yesmaximal, characteristic, complemented
11#13068599C211yesmaximal, characteristic, complemented
12#13068597C211yesmaximal, characteristic, complemented
13#13068595C211yesmaximal, characteristic, complemented
14#13068593C211yesmaximal, characteristic, complemented
15C11×#1851C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21C2×#66925C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C4×C11×C22⋊C4C2211yescharacteristic
27C4×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29#10622742—24no—
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40#10622570C411yescharacteristic
41#10622570C411yescharacteristic
42#10622569C411yescharacteristic
43#10622569C411yescharacteristic
44C4×(C2×D11)⋊C4C2211yescharacteristic
45C4×(C2×D11)⋊C4C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48#10622340—24no—
49#10622278C411yescharacteristic
50#10622278C411yescharacteristic
51#10622259C411yescharacteristic
52#10622259C411yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11C2×C411yescharacteristic
63C22×C22⋊D11C2×C411yescharacteristic
64C2×#4339—41no—
65C2×#4339—41no—
66C2×#4339—41no—
67C2×#4339—41no—
68C2×#4339D414yes—
69C2×#4339Q814yes—
70C22×D44C2×C411yescharacteristic
71C22×C4×D11C2×C411yescharacteristic
72C22×C4×D11C2×C411yescharacteristic
73C22×C4×D11C2311yescharacteristic
74C22×C4×D11C2311yescharacteristic
75C22×Dic22C2×C411yescharacteristic
76C2×C11×M16—22no—
77C2×C11×M16—41no—
78C2×C11×M16—41no—
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C2×C11×C22⋊C4C2×C411yescharacteristic
84C2×C11×C22⋊C4C2×C411yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11C2×C411yescharacteristic
88C2×C22⋊Dic11C2×C411yescharacteristic
89C2×(C2×D11)⋊C4C2×C411yescharacteristic
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×Dic11⋊C4C2×C411yescharacteristic
96C2×Dic11⋊C4C2×C411yescharacteristic
97C2×C4×Dic11C2×C411yescharacteristic
98C2×C4×Dic11C2×C411yescharacteristic
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8—22no—
102C22×C11⋊C8—41no—
103C22×C11⋊C8—41no—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C2×#4313—22no—
109C2×#4313—41no—
110C2×#4313—41no—
111C2×C8×D11—22no—
112C2×C8×D11—41no—
113C2×C8×D11—41no—
114#66925—41no—
115#66925—41no—
116C42×D11—41no—
117C42×D11—41no—
118C11×C4⋊C8—41no—
119C11×C4⋊C8—41no—
120C11×C22⋊C8—22no—
121C11×#95C2×C411yescharacteristic
122C11×#95C2×C411yescharacteristic
123C11⋊#95C2×C411yescharacteristic
124C11⋊#95C2×C411yescharacteristic
125C11⋊#95C2×C411yescharacteristic
126C11⋊#95C2×C411yescharacteristic
127C11⋊#95C2×C411yescharacteristic
128C11⋊#95C2×C411yescharacteristic
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—22no—
135(C2×D11)⋊C8—22no—
136Dic11⋊C8—41no—
137Dic11⋊C8—41no—
138Dic11⋊C8—41no—
139Dic11⋊C8—41no—
140C4⋊(C11⋊C8)—41no—
141C4⋊(C11⋊C8)—41no—
142#21937—111nomaximal, Sylow
143C24×C11C22×C411yescharacteristic
144C23×D11C22×C411yescharacteristic
145C23×D11C22×C411yescharacteristic
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×Q812yes—
157C22×C4×C11C2411yescharacteristic
158C2×C22⋊D11—41no—
159C2×C22⋊D11—41no—
160C2×C22⋊D11—41no—
161C2×C22⋊D11—41no—
162C2×C22⋊D11C4⋊C414yes—
163C2×C22⋊D11C4⋊C414yes—
164C22×Dic11C22×C411yescharacteristic
165C22×Dic11C22×C411yescharacteristic
166C22×Dic11C22×C411yescharacteristic
167C22×Dic11C22×C411yescharacteristic
168C22×Dic11C22×C411yescharacteristic
169C22×Dic11C22×C411yescharacteristic
170#4339—44no—
171#4339—44no—
172#4339—44no—
173#4339—44no—
174C2×D44—41no—
175C2×D44—41no—
176C2×D44C4⋊C414yes—
177C2×C4×D11—22no—
178C2×C4×D11—22no—
179C2×C4×D11—21no—
180C2×C4×D11—21no—
181C2×C4×D11—21no—
182C2×C4×D11—21no—
183C2×C4×D11—21no—
184C2×C4×D11—21no—
185C2×C4×D11—21no—
186C2×C4×D11—21no—
187C2×C4×D11—41no—
188C2×C4×D11—41no—
189C2×C4×D11—41no—
190C2×C4×D11—41no—
191C2×C4×D11C2×D412yes—
192C2×C4×D11C2×D412yes—
193C2×C4×D11C2×Q812yes—
194C2×C4×D11C2×Q812yes—
195C2×Dic22—41no—
196C2×Dic22—41no—
197C2×Dic22C4⋊C414yes—
198C11×M16—44no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
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—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—41no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—21no—
217C22⋊Dic11—22no—
218C22⋊Dic11—41no—
219(C2×D11)⋊C4—22no—
220(C2×D11)⋊C4—22no—
221(C2×D11)⋊C4—41no—
222(C2×D11)⋊C4—41no—
223(C2×D11)⋊C4—41no—
224(C2×D11)⋊C4—41no—
225Dic11⋊C4—41no—
226Dic11⋊C4—41no—
227C4×Dic11—21no—
228C4×Dic11—21no—
229C4×Dic11—21no—
230C4×Dic11—21no—
231C4×Dic11—41no—
232C4×Dic11—41no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—44no—
246#4313—44no—
247C8×D11—44no—
248C2×#408—111no—
249C2×#408—111no—
250#2297—111no—
251#1851—111no—
252#1851—111no—
253#1851—111no—
254#1851D1111yescharacteristic, complemented
255#1850—111no—
256#1850—111no—
257#1850—111no—
258#1850—111no—
259#1798—111no—
260#1798—111no—
261#1797—111no—
262#1797—111no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11C2×C4⋊C412yes—
270C23×C11C23×C411yescharacteristic
271C22×D11—21no—
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—21no—
278C22×D11—21no—
279C22×D11—21no—
280C22×D11—21no—
281C22×D11—21no—
282C22×D11—21no—
283C22×D11C2×C4⋊C412yes—
284C22×D11C2×C4⋊C412yes—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
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×C11C2×C4⋊C412yes—
303C2×C4×C11#13112yes—
304C2×C4×C11C22×D411yescharacteristic
305C2×C4×C11C22×Q811yescharacteristic
306C2×C4×C11H(5,𝔽2)11yescharacteristic
307C2×C4×C11H(5,𝔽2)11yescharacteristic
308C2×C4×C11H(5,𝔽2)11yescharacteristic
309C2×C4×C11H(5,𝔽2)11yescharacteristic
310C22⋊D11—44no—
311C22⋊D11—44no—
312C2×Dic11—21no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11C2×C4⋊C412yes—
328C2×Dic11C2×C4⋊C412yes—
329C2×Dic11#13112yes—
330D44—44no—
331C4×D11—22no—
332C4×D11—22no—
333C4×D11—22no—
334C4×D11—22no—
335C4×D11—22no—
336C4×D11—22no—
337C4×D11—22no—
338C4×D11—22no—
339C4×D11—44no—
340C4×D11—44no—
341Dic22—44no—
342C8×C11—41no—
343C8×C11—41no—
344C8×C11—41no—
345C8×C11—41no—
346C11⋊C8—41no—
347C11⋊C8—41no—
348C11⋊C8—41no—
349C11⋊C8—41no—
350C22×#41—111no—
351C22×M16—111no—
352C22×M16C2×D1111yescharacteristic
353C23×C8—111no—
354C23×C8—111no—
355C2×#117—111no—
356C22×C42—111no—
357C2×C4⋊C8—111no—
358C2×C4⋊C8—111no—
359C2×C4⋊C8—111no—
360C2×C4⋊C8—111no—
361C2×C4⋊C8—111no—
362C2×C4⋊C8—111no—
363C2×C4⋊C8C2×D1111yescharacteristic
364C2×C4⋊C8C2×D1111yescharacteristic
365#408—224no—
366#408—224no—
367C2×C22⋊C8—111no—
368C2×C22⋊C8—111no—
369C2×C22⋊C8—111no—
370C2×C22⋊C8—111no—
371C2×C22⋊C8—111no—
372C2×C22⋊C8—111no—
373C2×C22⋊C8—111no—
374C2×C22⋊C8C2×D1111yescharacteristic
375#391—111no—
376#391—111no—
377#390—111no—
378#390—111no—
379#386—111no—
380#386—111no—
381#386—111no—
382#386—111no—
383C4×C22⋊C4—111no—
384C4×C22⋊C4—111no—
385C4×C22⋊C4—111no—
386C4×C22⋊C4C2×D1111yescharacteristic
387#336—111no—
388#336—111no—
389#336—111no—
390#336—111no—
391#336—111no—
392#336—111no—
393#336C2×D1111yescharacteristic
394#336C2×D1111yescharacteristic
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11C22×C4⋊C411yescharacteristic
403C22×C11#51811yescharacteristic
404C22×C11#51811yescharacteristic
405C22×C11C2×#13111yescharacteristic
406C22×C11C2×#13111yescharacteristic
407C22×C11#56811yescharacteristic
408C22×C11#56811yescharacteristic
409C2×D11—22no—
410C2×D11—22no—
411C2×D11—22no—
412C2×D11—22no—
413C2×D11—22no—
414C2×D11—22no—
415C2×D11—41no—
416C2×D11—41no—
417C2×D11—41no—
418C2×D11—41no—
419C2×D11—41no—
420C2×D11—41no—
421C2×D11—41no—
422C2×D11—41no—
423C4×C11—22no—
424C4×C11—22no—
425C4×C11—41no—
426C4×C11—41no—
427C4×C11—41no—
428C4×C11#53411yescharacteristic
429C4×C11#53411yescharacteristic
430C4×C11#54311yescharacteristic
431C4×C11#54311yescharacteristic
432Dic11—22no—
433Dic11—22no—
434Dic11—22no—
435Dic11—41no—
436Dic11—41no—
437Dic11—41no—
438C2×#41—114no—
439C2×#41—114no—
440C2×#41—441no—
441C2×#41—441no—
442C2×#41—441no—
443C2×#41—441no—
444C22×Q8—111no—
445C22×D4—111no—
446C22×D4—111no—
447C22×D4—111no—
448C23×C4—111no—
449C23×C4—111no—
450C23×C4—111no—
451C23×C4—111no—
452C23×C4C22×D1111yescharacteristic
453C2×M16—22no—
454C2×M16—41no—
455C2×M16—41no—
456C2×M16—222no—
457C2×M16—441no—
458C2×M16—441no—
459C22×C8—111no—
460C22×C8—111no—
461C22×C8—111no—
462C22×C8—111no—
463C22×C8—222no—
464C22×C8—222no—
465C22×C8—441no—
466C22×C8—441no—
467C22×C8—441no—
468C22×C8—441no—
469C22×C8C22×D1111yescharacteristic
470C22×C8C22×D1111yescharacteristic
471C22×C8C22×D1111yescharacteristic
472C22×C8C22×D1111yescharacteristic
473#117—441no—
474#117—441no—
475C2×C4⋊C4—111no—
476C2×C4⋊C4—111no—
477C2×C22⋊C4—111no—
478C2×C22⋊C4—111no—
479C2×C22⋊C4—111no—
480C2×C22⋊C4—111no—
481C2×C22⋊C4—111no—
482C2×C22⋊C4—111no—
483C2×C22⋊C4—111no—
484C2×C22⋊C4—111no—
485C2×C22⋊C4C4×D1111yescharacteristic
486C2×C22⋊C4C4×D1111yescharacteristic
487C2×C42—111no—
488C2×C42—111no—
489C2×C42—111no—
490C2×C42—111no—
491C2×C42—441no—
492C2×C42—441no—
493C2×C42C22×D1111yescharacteristic
494C2×C42C22×D1111yescharacteristic
495C4⋊C8—41no—
496C4⋊C8—41no—
497C4⋊C8—441no—
498C4⋊C8—441no—
499C4⋊C8—441no—
500C4⋊C8—441no—
501C4⋊C8—441no—
502C4⋊C8—441no—
503C22⋊C8—22no—
504C22⋊C8—222no—
505C22⋊C8—222no—
506C22⋊C8—222no—
507C22⋊C8—222no—
508C22⋊C8—222no—
509C22⋊C8—222no—
510C22⋊C8—222no—
511#95—111no—
512#95—111no—
513#95—111no—
514#95—111no—
515#95—111no—
516#95—111no—
517#95C4×D1111yescharacteristic
518#95C4×D1111yescharacteristic
519C2×C11—42no—
520C2×C11#231511yescharacteristic
521C2×C11#290611yescharacteristic
522C2×C11#290611yescharacteristic
523C2×C11#297711yescharacteristic
524C2×C11#297811yescharacteristic
525C2×C11#298111yescharacteristic
526C2×C11#298111yescharacteristic
527D11—42no—
528D11—42no—
529C24—111no—
530C24—111no—
531C24C2×C4×D1111yescharacteristic
532#41—444no—
533#41—444no—
534#41—444no—
535#41—444no—
536C2×Q8—114no—
537C2×Q8—441no—
538C2×Q8—441no—
539C2×D4—114no—
540C2×D4—114no—
541C2×D4—114no—
542C2×D4—441no—
543C2×D4—441no—
544C2×D4—441no—
545C2×D4—441no—
546C2×D4—441no—
547C2×D4—441no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—111no—
553C22×C4—111no—
554C22×C4—111no—
555C22×C4—112no—
556C22×C4—112no—
557C22×C4—112no—
558C22×C4—112no—
559C22×C4—111no—
560C22×C4—111no—
561C22×C4—111no—
562C22×C4—222no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—222no—
572C22×C4—441no—
573C22×C4—441no—
574C22×C4—441no—
575C22×C4—441no—
576C22×C4C2×C4×D1111yescharacteristic
577C22×C4C2×C4×D1111yescharacteristic
578C22×C4C2×C4×D1111yescharacteristic
579C22×C4C2×C4×D1111yescharacteristic
580C22×C4C2×C4×D1111yescharacteristic
581C22×C4D4×D1112yes—
582C22×C4Q8×D1112yes—
583C22×C4C23×D1111yescharacteristic
584M16—44no—
585M16—444no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—221no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—221no—
602C2×C8—221no—
603C2×C8—221no—
604C2×C8—221no—
605C2×C8—221no—
606C2×C8—221no—
607C2×C8—221no—
608C2×C8—221no—
609C2×C8—221no—
610C2×C8—444no—
611C2×C8—444no—
612C4⋊C4—441no—
613C4⋊C4—441no—
614C22⋊C4—22no—
615C22⋊C4—41no—
616C22⋊C4—222no—
617C22⋊C4—222no—
618C22⋊C4—222no—
619C22⋊C4—441no—
620C22⋊C4—441no—
621C22⋊C4—441no—
622C22⋊C4—441no—
623C22⋊C4—441no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—221no—
629C42—221no—
630C42—221no—
631C42—221no—
632C42—441no—
633C42—441no—
634C11#2193711yescharacteristic, complemented, Sylow
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—112no—
642C23—112no—
643C23—221no—
644C23—221no—
645C23—221no—
646C23—221no—
647C23—221no—
648C23—221no—
649C23—221no—
650C23—221no—
651C23—221no—
652C23—221no—
653C23—221no—
654C23—221no—
655C23C4⋊C4×D1112yes—
656C23C22×C4×D1111yescharacteristic
657Q8—444no—
658D4—444no—
659D4—444no—
660D4—444no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—112no—
679C2×C4—112no—
680C2×C4—112no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—221no—
685C2×C4—221no—
686C2×C4—221no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—221no—
696C2×C4—221no—
697C2×C4—221no—
698C2×C4—221no—
699C2×C4—221no—
700C2×C4—221no—
701C2×C4—221no—
702C2×C4—221no—
703C2×C4—221no—
704C2×C4—444no—
705C2×C4—444no—
706C2×C4C4⋊C4×D1112yes—
707C2×C4#6696012yes—
708C2×C4C2×D4×D1111yescharacteristic
709C2×C4#6703711yescharacteristic
710C2×C4#6703711yescharacteristic
711C2×C4C2×Q8×D1111yescharacteristic
712C2×C4#6704211yescharacteristic
713C2×C4#6704211yescharacteristic
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C8—441no—
719C8—441no—
720C8—441no—
721C8—441no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—222no—
730C22—222no—
731C22—222no—
732C22—222no—
733C22—222no—
734C22—222no—
735C22—441no—
736C22—441no—
737C22—441no—
738C22—441no—
739C22—441no—
740C22—441no—
741C22—441no—
742C22—441no—
743C22C2×C4⋊C4×D1111yescharacteristic
744C22#1062307611yescharacteristic
745C22#1062307611yescharacteristic
746C22C2×#6696011yescharacteristic
747C22#1062327611yescharacteristic
748C22D11×#13111yescharacteristic
749C22#1062328111yescharacteristic
750C4—22no—
751C4—22no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—222no—
756C4—222no—
757C4—222no—
758C4—441no—
759C4—441no—
760C4—441no—
761C4#1062312011yescharacteristic
762C4#1062316511yescharacteristic
763C4#1062316511yescharacteristic
764C4#1062318411yescharacteristic
765C2—42no—
766C2—442no—
767C2—442no—
768C2#1307122711yescharacteristic
769C2#1307718311yescharacteristic
770C2#1307718511yescharacteristic
771C2#1307766711yescharacteristic
772C2#1307767311yescharacteristic
773C2#1307768811yescharacteristic
774C2#1307769311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1851C2
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1851D11
hypocenterC11#21937
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
4. #13068800C2semidirect
5. #13068800C2semidirect
6. #13068799C2semidirect
7. #13068796C2semidirect
8. #13068793C2semidirect
9. #13068792C2semidirect
10. #13068792C2semidirect
11. #13068599C2semidirect
12. #13068597C2semidirect
13. #13068595C2semidirect
14. #13068593C2semidirect
15. C11×#1851C2semidirect
254. #1851D11semidirect
634. C11#21937semidirect

Maximal subgroups

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

subgroupindex
C2×#106227422
C2×#106223402
#130711022
#130688002
#130687992
#130687962
#130687932
#130687922
#130685992
#130685972
#130685952
#130685932
C11×#18512
#2193711