Finite Group Databasebeta

← #14775916

Subgroups — #14775916

Order 2816.

1050 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622741C211yesmaximal, characteristic, complemented
2C2×#10622449C211yesmaximal, characteristic, complemented
3C2×#10622740C211yesmaximal, characteristic, complemented
4C4×#66983C211yesmaximal, characteristic
5#13069413C211yesmaximal, characteristic, complemented
6#13069337C211yesmaximal, characteristic, complemented
7#13069228C211yesmaximal, characteristic, complemented
8#13069221C211yesmaximal, characteristic, complemented
9#13068913C211yesmaximal, characteristic, complemented
10#13068913C211yesmaximal, characteristic, complemented
11#13068797C211yesmaximal, characteristic, complemented
12#13068792C211yesmaximal, characteristic, complemented
13#13068493C211yesmaximal, characteristic, complemented
14#13068378C211yesmaximal, characteristic, complemented
15C2×C11×#423C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C2×#66983C411yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C22×#4313C2211yescharacteristic
23C22×C8×D11C2211yescharacteristic
24C2×C4×D44C2211yescharacteristic
25C11×#423—24no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30#10622826C411yescharacteristic
31#10622826C411yescharacteristic
32#10622825C411yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622741—24no—
36#10622740—24no—
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×(C2×D11)⋊C8C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40C2×(C2×D11)⋊C8C2211yescharacteristic
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×(C2×D11)⋊C8C2211yescharacteristic
43C2×#66879C2211yescharacteristic
44C2×Dic11⋊C8C2211yescharacteristic
45C2×Dic11⋊C8C2211yescharacteristic
46C2×C8×Dic11C2211yescharacteristic
47#10622553C411yescharacteristic
48#10622553C411yescharacteristic
49#10622552C411yescharacteristic
50C4×(C2×D11)⋊C4C2211yescharacteristic
51C4×(C2×D11)⋊C4C2211yescharacteristic
52C4×C4⋊Dic11C2211yescharacteristic
53#10622541C411yescharacteristic
54C2×#66867C2211yescharacteristic
55C2×#66867C2211yescharacteristic
56#10622449—24no—
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C23×C4×C11C2×C411yescharacteristic
64C23×C4×C11C2×C411yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2×C411yescharacteristic
67C22×C22⋊D11C2×C411yescharacteristic
68C22×D44C2×C411yescharacteristic
69C22×C4×D11C2311yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C2×C11×M16—22no—
72C2×C11×M16—22no—
73C2×C11×M16—22no—
74C2×C11×M16—22no—
75C2×C11×M16—41no—
76C2×C11×M16—41no—
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C2×C42×C11—22no—
82C2×C42×C11—22no—
83C2×C42×C11C2×C411yescharacteristic
84C2×C42×C11C2×C411yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11C2×C411yescharacteristic
88C2×C22⋊Dic11C2×C411yescharacteristic
89#66983—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
96C2×(C2×D11)⋊C4C2×C411yescharacteristic
97C2×(C2×D11)⋊C4C2×C411yescharacteristic
98C2×(C2×D11)⋊C4C2×C411yescharacteristic
99C2×(C2×D11)⋊C4C2×C411yescharacteristic
100C2×(C2×D11)⋊C4C2×C411yescharacteristic
101C2×(C2×D11)⋊C4C2×C411yescharacteristic
102C2×C4⋊Dic11C2×C411yescharacteristic
103C2×C4⋊Dic11C2×C411yescharacteristic
104C2×C4⋊Dic11C2×C411yescharacteristic
105C2×Dic11⋊C4C2×C411yescharacteristic
106C2×Dic11⋊C4C2×C411yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C2×#4313—22no—
114C2×#4313—22no—
115C2×#4313—41no—
116C2×C8×D11—22no—
117C2×C8×D11—22no—
118C2×C8×D11—41no—
119C4×D44—22no—
120C4×D44—22no—
121C11×C4⋊C8—22no—
122C11×C4⋊C8—22no—
123C11×C4⋊C8—22no—
124C11×C4⋊C8D414yescomplemented
125C11⋊#95C2×C411yescharacteristic
126C11⋊#95C2×C411yescharacteristic
127C11⋊#95C2×C411yescharacteristic
128C11⋊#95C2×C411yescharacteristic
129C11⋊#95C2×C411yescharacteristic
130C11⋊#95C2×C411yescharacteristic
131C22⋊(C11⋊C8)—22no—
132C22⋊(C11⋊C8)D414yescomplemented
133(C2×D11)⋊C8—22no—
134(C2×D11)⋊C8—22no—
135(C2×D11)⋊C8—22no—
136(C2×D11)⋊C8—22no—
137(C2×D11)⋊C8—41no—
138(C2×D11)⋊C8—41no—
139#66879—22no—
140Dic11⋊C8—22no—
141Dic11⋊C8—22no—
142C8×Dic11—22no—
143#66867—22no—
144#66867—22no—
145#22988—111nomaximal, Sylow
146C24×C11C22×C411yescharacteristic
147C23×D11C22×C411yescharacteristic
148C23×D11C22×C411yescharacteristic
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—41no—
157C22×C4×C11—41no—
158C22×C4×C11—41no—
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11C22×C411yescharacteristic
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C22×C411yescharacteristic
164C22×C4×C11C2×D412yes—
165C22×C4×C11#4112yes—
166C22×C4×C11C2411yescharacteristic
167C2×C22⋊D11—22no—
168C2×C22⋊D11—22no—
169C2×C22⋊D11—22no—
170C2×C22⋊D11—22no—
171C2×C22⋊D11—41no—
172C2×C22⋊D11—41no—
173C22×Dic11C22×C411yescharacteristic
174C22×Dic11C22×C411yescharacteristic
175C22×Dic11C22×C411yescharacteristic
176C22×Dic11C22×C411yescharacteristic
177C22×Dic11C22×C411yescharacteristic
178C22×Dic11C22×C411yescharacteristic
179C2×D44—22no—
180C2×D44—22no—
181C2×D44—41no—
182C2×C4×D11—21no—
183C2×C4×D11—21no—
184C2×C4×D11—21no—
185C2×C4×D11—21no—
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—
194C11×M16—44no—
195C11×M16—44no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
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×C11C2×D412yes—
207C2×C8×C11C2×D412yes—
208C42×C11—22no—
209C42×C11—22no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11C2×D412yes—
213C42×C11#4112yes—
214C22⋊Dic11—22no—
215C22⋊Dic11—22no—
216(C2×D11)⋊C4—22no—
217(C2×D11)⋊C4—22no—
218(C2×D11)⋊C4—22no—
219(C2×D11)⋊C4—22no—
220(C2×D11)⋊C4—22no—
221(C2×D11)⋊C4—41no—
222(C2×D11)⋊C4—41no—
223(C2×D11)⋊C4M1614yescomplemented
224C4⋊Dic11—22no—
225C4⋊Dic11—22no—
226C4⋊Dic11—41no—
227Dic11⋊C4—22no—
228Dic11⋊C4—22no—
229C4×Dic11—21no—
230C4×Dic11—21no—
231C4×Dic11—21no—
232C4×Dic11—21no—
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⋊C8C2×D412yes—
244C2×C11⋊C8C2×D412yes—
245#4313—44no—
246C8×D11—44no—
247C2×#436—111no—
248C2×#435—111no—
249C2×#435—111no—
250C2×#423D1111yescharacteristic, complemented
251C4×#121—111no—
252#1955—111no—
253#1940—111no—
254#1924—111no—
255#1923—111no—
256#1870—111no—
257#1870—111no—
258#1851—111no—
259#1850—111no—
260#1771—111no—
261#1749—111no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11C4×D412yes—
269C23×C11C23×C411yescharacteristic
270C22×D11—21no—
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×M1612yes—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—44no—
300C2×C4×C11—44no—
301C2×C4×C11C4×D412yes—
302C2×C4×C11C4×D412yes—
303C2×C4×C11C4×D412yes—
304C2×C4×C11C2×M1612yes—
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11H(5,𝔽2)11yescharacteristic
310C2×C4×C112−1+411yescharacteristic
311C22⋊D11—44no—
312C22⋊D11—44no—
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×Dic11—21no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11C2×M1612yes—
331D44—44no—
332C4×D11—41no—
333C4×D11—41no—
334C4×D11—41no—
335C4×D11—41no—
336C4×D11—41no—
337C4×D11—41no—
338C4×D11—41no—
339C4×D11—41no—
340C8×C11—22no—
341C8×C11—22no—
342C8×C11—41no—
343C8×C11—41no—
344C11⋊C8—22no—
345C11⋊C8—22no—
346C11⋊C8—41no—
347C11⋊C8—41no—
348C22×M16—111no—
349C22×M16C2×D1111yescharacteristic
350C22×M16C2×D1111yescharacteristic
351C23×C8—111no—
352C2×#121—111no—
353C2×C4×D4—111no—
354C2×C4×D4—111no—
355C2×C4×D4—111no—
356C22×C42C2×D1111yescharacteristic
357#436—224no—
358#435—224no—
359#435—224no—
360#423—24no—
361C2×C4⋊C8—111no—
362C2×C4⋊C8—111no—
363C2×C4⋊C8C2×D1111yescharacteristic
364C2×C4⋊C8C2×D1111yescharacteristic
365C2×C4⋊C8C2×D1111yescharacteristic
366C2×C4⋊C8C2×D1111yescharacteristic
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⋊C8—111no—
375C2×#97—111no—
376C2×#97—111no—
377C2×#97—111no—
378C2×C4×C8—111no—
379#390—111no—
380#389—111no—
381#388—111no—
382#388—111no—
383#386—111no—
384#386—111no—
385#380—111no—
386C4×C4⋊C4—111no—
387C4×C22⋊C4—111no—
388C4×C22⋊C4—111no—
389#336—111no—
390#336—111no—
391#336—111no—
392#336—111no—
393#336—111no—
394#336—111no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11C2×C4×D411yescharacteristic
403C22×C11C2×C4×D411yescharacteristic
404C22×C11#52011yescharacteristic
405C22×C11C22×M1611yescharacteristic
406C22×C11#56811yescharacteristic
407C22×C11#56811yescharacteristic
408C22×C11#56811yescharacteristic
409C2×D11—22no—
410C2×D11—22no—
411C2×D11—22no—
412C2×D11—41no—
413C2×D11—41no—
414C2×D11—41no—
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—22no—
426C4×C11—22no—
427C4×C11—41no—
428C4×C11D4211yescharacteristic
429C4×C11#54711yescharacteristic
430C4×C11#54811yescharacteristic
431C4×C11#55311yescharacteristic
432Dic11—22no—
433Dic11—41no—
434Dic11—41no—
435Dic11—41no—
436Dic11—41no—
437Dic11—41no—
438C22×D4—111no—
439C22×D4—111no—
440C22×D4—111no—
441C23×C4—111no—
442C23×C4—111no—
443C23×C4C4×D1111yescharacteristic
444C23×C4C4×D1111yescharacteristic
445C23×C4C22×D1111yescharacteristic
446C2×M16—22no—
447C2×M16—22no—
448C2×M16—22no—
449C2×M16—22no—
450C2×M16—41no—
451C2×M16—41no—
452C2×M16—222no—
453C2×M16—222no—
454C2×M16—441no—
455C22×C8—111no—
456C22×C8—111no—
457C22×C8—111no—
458C22×C8—111no—
459C22×C8—222no—
460C22×C8—222no—
461C22×C8—441no—
462C22×C8C22×D1111yescharacteristic
463C22×C8C22×D1111yescharacteristic
464C22×C8C22×D1111yescharacteristic
465C22×C8C22×D1111yescharacteristic
466#121—224no—
467C4×D4—222no—
468C4×D4—222no—
469C4×D4—222no—
470C4×D4—222no—
471C4×D4—222no—
472C4×D4—222no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4—111no—
475C2×C4⋊C4—111no—
476C2×C4⋊C4—111no—
477C2×C4⋊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⋊C4—111no—
486C2×C22⋊C4—111no—
487C2×C22⋊C4—111no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—111no—
491C2×C42—111no—
492C2×C42C4×D1111yescharacteristic
493C2×C42C4×D1111yescharacteristic
494C2×C42C22×D1111yescharacteristic
495C2×C42C22×D1111yescharacteristic
496C4⋊C8—22no—
497C4⋊C8—22no—
498C4⋊C8—22no—
499C4⋊C8—222no—
500C4⋊C8—222no—
501C4⋊C8C22⋊D1114yescomplemented
502C22⋊C8—114no—
503C22⋊C8—222no—
504C22⋊C8—222no—
505C22⋊C8—222no—
506C22⋊C8—222no—
507C22⋊C8—222no—
508C22⋊C8—441no—
509C22⋊C8—441no—
510#97—222no—
511#97—222no—
512#97—222no—
513C4×C8—222no—
514#95—111no—
515#95—111no—
516#95—111no—
517#95—111no—
518#95—111no—
519#95—111no—
520C2×C11—42no—
521C2×C11#236111yescharacteristic
522C2×C11#293011yescharacteristic
523C2×C11#293211yescharacteristic
524C2×C11D4×M1611yescharacteristic
525C2×C11D4×M1611yescharacteristic
526C2×C11#298911yescharacteristic
527C2×C11#299511yescharacteristic
528D11—42no—
529D11—81no—
530C24—111no—
531C24—111no—
532C24C2×C4×D1111yescharacteristic
533C2×D4—222no—
534C2×D4—222no—
535C2×D4—222no—
536C2×D4—222no—
537C2×D4—222no—
538C2×D4—222no—
539C2×D4—441no—
540C2×D4—441no—
541C2×D4—441no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—111no—
553C22×C4—111no—
554C22×C4—111no—
555C22×C4—111no—
556C22×C4—111no—
557C22×C4—111no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4C2×C4×D1111yescharacteristic
571C22×C4C2×C4×D1111yescharacteristic
572C22×C4C2×C4×D1111yescharacteristic
573C22×C4C2×C4×D1111yescharacteristic
574C22×C4C2×C4×D1111yescharacteristic
575C22×C4D4×D1112yes—
576C22×C4#434312yes—
577C22×C4C23×D1111yescharacteristic
578M16—44no—
579M16—44no—
580M16—444no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—112no—
592C2×C8—112no—
593C2×C8—221no—
594C2×C8—221no—
595C2×C8—221no—
596C2×C8—221no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—221no—
602C2×C8—221no—
603C2×C8—444no—
604C2×C8C2×C22⋊D1112yes—
605C2×C8C2×C22⋊D1112yes—
606C4⋊C4—222no—
607C4⋊C4—222no—
608C4⋊C4—222no—
609C4⋊C4—222no—
610C4⋊C4—441no—
611C22⋊C4—114no—
612C22⋊C4—222no—
613C22⋊C4—222no—
614C22⋊C4—222no—
615C22⋊C4—222no—
616C22⋊C4—222no—
617C22⋊C4—222no—
618C22⋊C4—222no—
619C22⋊C4—441no—
620C22⋊C4—441no—
621C42—22no—
622C42—22no—
623C42—21no—
624C42—21no—
625C42—221no—
626C42—221no—
627C42—221no—
628C42—221no—
629C42#433912yes—
630C42C2×C22⋊D1112yes—
631C11#2298811yescharacteristic, complemented, Sylow
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—112no—
639C23—221no—
640C23—221no—
641C23—221no—
642C23—221no—
643C23—221no—
644C23—221no—
645C23—221no—
646C23—221no—
647C23—221no—
648C23—221no—
649C23—221no—
650C23—221no—
651C23—221no—
652C23#6694612yes—
653C23C22×C4×D1111yescharacteristic
654D4—444no—
655D4—444no—
656D4—444no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
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—44no—
673C2×C4—44no—
674C2×C4—112no—
675C2×C4—221no—
676C2×C4—221no—
677C2×C4—221no—
678C2×C4—221no—
679C2×C4—221no—
680C2×C4—221no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—221no—
685C2×C4—221no—
686C2×C4—221no—
687C2×C4—221no—
688C2×C4—221no—
689C2×C4—221no—
690C2×C4—221no—
691C2×C4—221no—
692C2×C4—441no—
693C2×C4—441no—
694C2×C4—441no—
695C2×C4—441no—
696C2×C4—441no—
697C2×C4—441no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4#6694612yes—
701C2×C4M16×D1112yes—
702C2×C4C4×C22⋊D1112yes—
703C2×C4C4×C22⋊D1112yes—
704C2×C4C2×#433911yescharacteristic
705C2×C4C2×D4×D1111yescharacteristic
706C2×C4#6703711yescharacteristic
707C2×C4C2×#434311yescharacteristic
708C2×C4#6704011yescharacteristic
709C2×C4C22×C22⋊D1111yescharacteristic
710C8—22no—
711C8—22no—
712C8—41no—
713C8—41no—
714C8—222no—
715C8—222no—
716C8—441no—
717C8—441no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—222no—
726C22—222no—
727C22—222no—
728C22—441no—
729C22—441no—
730C22—441no—
731C22—441no—
732C22—441no—
733C22—441no—
734C22—441no—
735C22—441no—
736C22—441no—
737C22—441no—
738C22—441no—
739C22C2×#6694611yescharacteristic
740C22#1062303511yescharacteristic
741C22C2×M16×D1111yescharacteristic
742C22#1062327611yescharacteristic
743C22#1062327611yescharacteristic
744C22#1062327611yescharacteristic
745C22C2×C4×C22⋊D1111yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—41no—
751C4—222no—
752C4—441no—
753C4—441no—
754C4—441no—
755C4—441no—
756C4—441no—
757C4#1062303811yescharacteristic
758C4#1062304511yescharacteristic
759C4D4×C22⋊D1111yescharacteristic
760C4#1062334811yescharacteristic
761C2—42no—
762C2—442no—
763C2—881no—
764C2#1307163211yescharacteristic
765C2#1307731911yescharacteristic
766C2#1307733311yescharacteristic
767C2M16×C22⋊D1111yescharacteristic
768C2#1307735111yescharacteristic
769C2#1307773011yescharacteristic
770C2#1307778311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#423C2
prime radicalC2×#66983C4
cosocleC22×C4×C11C24
hypercenterC2×#423D11
hypocenterC11#22988
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
1. C2×#10622741C2semidirect
2. C2×#10622449C2semidirect
3. C2×#10622740C2semidirect
5. #13069413C2semidirect
6. #13069337C2semidirect
7. #13069228C2semidirect
8. #13069221C2semidirect
9. #13068913C2semidirect
10. #13068913C2semidirect
11. #13068797C2semidirect
12. #13068792C2semidirect
13. #13068493C2semidirect
14. #13068378C2semidirect
15. C2×C11×#423C2semidirect
124. C11×C4⋊C8D4semidirect
132. C22⋊(C11⋊C8)D4semidirect
223. (C2×D11)⋊C4M16semidirect
250. C2×#423D11semidirect
501. C4⋊C8C22⋊D11semidirect
631. C11#22988semidirect

Maximal subgroups

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

subgroupindex
C2×#106227412
C2×#106224492
C2×#106227402
C4×#669832
#130694132
#130693372
#130692282
#130692212
#130689132
#130687972
#130687922
#130684932
#130683782
C2×C11×#4232
#2298811