Finite Group Databasebeta

← #14769071

Subgroups — #14769071

Order 2816.

1540 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623363C211yesmaximal, characteristic
2C2×#10622342C211yesmaximal, characteristic, complemented
3C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
4C2×#10622847C211yesmaximal, characteristic, complemented
5C2×#10622340C211yesmaximal, characteristic, complemented
6#13069408C211yesmaximal, characteristic, complemented
7#13069408C211yesmaximal, characteristic, complemented
8#13068911C211yesmaximal, characteristic, complemented
9#13068910C211yesmaximal, characteristic, complemented
10#13068906C211yesmaximal, characteristic, complemented
11#13068905C211yesmaximal, characteristic, complemented
12#13068594C211yesmaximal, characteristic, complemented
13#13068527C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
15C11×#1780C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18#10623363—24no—
19#10623363—24no—
20C2×#67000C411yescharacteristic
21C2×#66997C411yescharacteristic
22C2×#66993C411yescharacteristic
23C2×#66992C411yescharacteristic
24C2×#66992C411yescharacteristic
25C2×#66992C411yescharacteristic
26C2×#66992C411yescharacteristic
27C2×#66989C411yescharacteristic
28C2×C4×C22⋊D11C2211yescharacteristic
29C2×C4×C22⋊D11C2211yescharacteristic
30C2×C4×C22⋊D11C2211yescharacteristic
31C2×C4×C22⋊D11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×#4318C2211yescharacteristic
34C23×C11⋊C8C2211yescharacteristic
35C22×#4313C2211yescharacteristic
36C22×C8×D11C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×C22⋊C8C2211yescharacteristic
41C2×C11×C22⋊C8C2211yescharacteristic
42C2×C11×C22⋊C8C2211yescharacteristic
43#10622847—24no—
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46C2×C22⋊(C11⋊C8)C2211yescharacteristic
47C2×C22⋊(C11⋊C8)C2211yescharacteristic
48C2×(C2×D11)⋊C8C2211yescharacteristic
49C2×(C2×D11)⋊C8C2211yescharacteristic
50C2×(C2×D11)⋊C8C2211yescharacteristic
51C2×(C2×D11)⋊C8C2211yescharacteristic
52C2×(C2×D11)⋊C8C2211yescharacteristic
53C2×(C2×D11)⋊C8C2211yescharacteristic
54C2×Dic11⋊C8C2211yescharacteristic
55C2×Dic11⋊C8C2211yescharacteristic
56C2×C8×Dic11C2211yescharacteristic
57C2×C8×Dic11C2211yescharacteristic
58#10622342—24no—
59#10622340—24no—
60(C22⋊D11)⋊C8—24no—
61#10622188C2211yescharacteristic
62#10622188C2211yescharacteristic
63#10622188C2211yescharacteristic
64#10622188C2211yescharacteristic
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—41no—
70C2×C11×#41—41no—
71C22×Q8×C11C2×C411yescharacteristic
72C22×D4×C11C2×C411yescharacteristic
73C22×D4×C11C2×C411yescharacteristic
74C22×D4×C11C2×C411yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C22×C22⋊D11C2×C411yescharacteristic
79C22×C22⋊D11C2×C411yescharacteristic
80C22×C22⋊D11C2×C411yescharacteristic
81C22×C22⋊D11C2×C411yescharacteristic
82C22×C22⋊D11C2×C411yescharacteristic
83C22×C22⋊D11C2×C411yescharacteristic
84C23×Dic11C2×C411yescharacteristic
85C23×Dic11C2×C411yescharacteristic
86C2×#4339—22no—
87C2×#4339—22no—
88C2×#4339—22no—
89C2×#4339—22no—
90C2×#4339—41no—
91C2×#4339—41no—
92C22×D44C2×C411yescharacteristic
93C22×C4×D11C2311yescharacteristic
94C22×C4×D11C2311yescharacteristic
95C22×Dic22C2×C411yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C2×C22⋊Dic11C2×C411yescharacteristic
101C2×C22⋊Dic11C2×C411yescharacteristic
102C2×C22⋊Dic11C2×C411yescharacteristic
103C2×C22⋊Dic11C2×C411yescharacteristic
104#67000—24no—
105#66997—24no—
106#66993—24no—
107#66992—24no—
108#66992—24no—
109#66992—24no—
110#66992—24no—
111#66989—24no—
112C4×C22⋊D11—22no—
113C4×C22⋊D11—22no—
114C4×C22⋊D11—22no—
115C4×C22⋊D11—22no—
116C4×C22⋊D11—22no—
117C4×C22⋊D11—22no—
118C4×C22⋊D11D414yes—
119C4×C22⋊D11D414yes—
120C2×(C2×D11)⋊C4C2×C411yescharacteristic
121C2×(C2×D11)⋊C4C2×C411yescharacteristic
122C2×(C2×D11)⋊C4C2×C411yescharacteristic
123C2×(C2×D11)⋊C4C2×C411yescharacteristic
124C2×Dic11⋊C4C2×C411yescharacteristic
125C2×Dic11⋊C4C2×C411yescharacteristic
126C2×Dic11⋊C4C2×C411yescharacteristic
127C2×Dic11⋊C4C2×C411yescharacteristic
128C2×C4×Dic11—22no—
129C2×C4×Dic11—22no—
130C2×C4×Dic11C2×C411yescharacteristic
131C2×C4×Dic11C2×C411yescharacteristic
132C2×C4×Dic11C2311yescharacteristic
133C2×C4×Dic11C2311yescharacteristic
134C2×#4318—22no—
135C2×#4318—22no—
136C2×#4318—41no—
137C22×C11⋊C8—22no—
138C22×C11⋊C8—22no—
139C22×C11⋊C8—41no—
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142C22×C11⋊C8C2311yescharacteristic
143C22×C11⋊C8C2311yescharacteristic
144C2×#4313—22no—
145C2×#4313—22no—
146C2×#4313—41no—
147C2×C8×D11—22no—
148C2×C8×D11—22no—
149C2×C8×D11—41no—
150C11×C22⋊C8—22no—
151C11×C22⋊C8—22no—
152C11×C22⋊C8—22no—
153C11×C22⋊C8—22no—
154C11×C22⋊C8—41no—
155C11×C22⋊C8—41no—
156C22⋊(C11⋊C8)—22no—
157C22⋊(C11⋊C8)—22no—
158C22⋊(C11⋊C8)—22no—
159C22⋊(C11⋊C8)D414yescomplemented
160(C2×D11)⋊C8—22no—
161(C2×D11)⋊C8—22no—
162(C2×D11)⋊C8—22no—
163(C2×D11)⋊C8—22no—
164(C2×D11)⋊C8—41no—
165(C2×D11)⋊C8—41no—
166Dic11⋊C8—22no—
167Dic11⋊C8—22no—
168C8×Dic11—22no—
169C8×Dic11—22no—
170#22402—111nomaximal, Sylow
171C24×C11C22×C411yescharacteristic
172C24×C11C22×C411yescharacteristic
173C24×C11C22×C411yescharacteristic
174C23×D11C22×C411yescharacteristic
175C23×D11C22×C411yescharacteristic
176C11×#41—44no—
177C11×#41—44no—
178C11×#41—44no—
179C11×#41—44no—
180C2×Q8×C11—22no—
181C2×Q8×C11—22no—
182C2×Q8×C11—41no—
183C2×D4×C11—22no—
184C2×D4×C11—22no—
185C2×D4×C11—22no—
186C2×D4×C11—22no—
187C2×D4×C11—22no—
188C2×D4×C11—22no—
189C2×D4×C11—41no—
190C2×D4×C11—41no—
191C2×D4×C11—41no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11C22×C411yescharacteristic
207C22×C4×C11C22×C411yescharacteristic
208C22×C4×C11C22×C411yescharacteristic
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2×D412yes—
212C22×C4×C11#4112yes—
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11—22no—
215C2×C22⋊D11—22no—
216C2×C22⋊D11—22no—
217C2×C22⋊D11—22no—
218C2×C22⋊D11—22no—
219C2×C22⋊D11—22no—
220C2×C22⋊D11—22no—
221C2×C22⋊D11—22no—
222C2×C22⋊D11—22no—
223C2×C22⋊D11—22no—
224C2×C22⋊D11—22no—
225C2×C22⋊D11—22no—
226C2×C22⋊D11—22no—
227C2×C22⋊D11—41no—
228C2×C22⋊D11—41no—
229C2×C22⋊D11—41no—
230C2×C22⋊D11—41no—
231C2×C22⋊D11C22⋊C414yes—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—41no—
238C22×Dic11C22×C411yescharacteristic
239C22×Dic11C22×C411yescharacteristic
240C22×Dic11C22×C411yescharacteristic
241C22×Dic11C22×C411yescharacteristic
242C22×Dic11C22×C411yescharacteristic
243C22×Dic11C22×C411yescharacteristic
244#4339—44no—
245#4339—44no—
246#4339—44no—
247#4339—44no—
248C2×D44—22no—
249C2×D44—22no—
250C2×D44—41no—
251C2×C4×D11—21no—
252C2×C4×D11—21no—
253C2×C4×D11—21no—
254C2×C4×D11—21no—
255C2×C4×D11—21no—
256C2×C4×D11—21no—
257C2×C4×D11—21no—
258C2×C4×D11—21no—
259C2×C4×D11—21no—
260C2×C4×D11—21no—
261C2×C4×D11C2×D412yes—
262C2×C4×D11C2×D412yes—
263C2×Dic22—22no—
264C2×Dic22—22no—
265C2×Dic22—41no—
266C2×C8×C11—21no—
267C2×C8×C11—21no—
268C2×C8×C11—21no—
269C2×C8×C11—21no—
270C2×C8×C11—21no—
271C2×C8×C11—21no—
272C2×C8×C11—21no—
273C2×C8×C11—21no—
274C2×C8×C11—21no—
275C2×C8×C11—21no—
276C2×C8×C11—21no—
277C2×C8×C11—21no—
278C22⋊Dic11—22no—
279C22⋊Dic11—22no—
280C22⋊Dic11—22no—
281C22⋊Dic11C22⋊C414yes—
282(C2×D11)⋊C4—22no—
283(C2×D11)⋊C4—22no—
284(C2×D11)⋊C4—22no—
285(C2×D11)⋊C4C22⋊C414yes—
286Dic11⋊C4—22no—
287Dic11⋊C4—22no—
288Dic11⋊C4—22no—
289Dic11⋊C4C22⋊C414yes—
290C4×Dic11—22no—
291C4×Dic11—22no—
292C4×Dic11—21no—
293C4×Dic11—21no—
294C4×Dic11C2×D412yes—
295C4×Dic11C2×D412yes—
296#4318—44no—
297C2×C11⋊C8—21no—
298C2×C11⋊C8—21no—
299C2×C11⋊C8—21no—
300C2×C11⋊C8—21no—
301C2×C11⋊C8—21no—
302C2×C11⋊C8—21no—
303C2×C11⋊C8—21no—
304C2×C11⋊C8—21no—
305C2×C11⋊C8—21no—
306C2×C11⋊C8—21no—
307C2×C11⋊C8—44no—
308C2×C11⋊C8C2×D412yes—
309C2×C11⋊C8C2×D412yes—
310#4313—44no—
311C8×D11—44no—
312C2×#532—111no—
313C2×#436—111no—
314C2×C8×D4—111no—
315C2×#408—111no—
316C2×#408—111no—
317#1954—111no—
318#1954—111no—
319#1870—111no—
320#1870—111no—
321#1869—111no—
322#1869—111no—
323#1797—111no—
324#1780—111no—
325#1780D1111yescharacteristic, complemented
326C4×C22⋊C8—111no—
327C23×C11—21no—
328C23×C11—21no—
329C23×C11—21no—
330C23×C11—21no—
331C23×C11—21no—
332C23×C11—21no—
333C23×C11—21no—
334C23×C11—21no—
335C23×C11—21no—
336C23×C11—21no—
337C23×C11—21no—
338C23×C11—21no—
339C23×C11—21no—
340C23×C11—21no—
341C23×C11—21no—
342C23×C11—21no—
343C23×C11—21no—
344C23×C11—21no—
345C23×C11—21no—
346C23×C11C2×C22⋊C412yes—
347C23×C11C4×D412yes—
348C23×C11C23×C411yescharacteristic
349C22×D11—21no—
350C22×D11—21no—
351C22×D11—21no—
352C22×D11—21no—
353C22×D11—21no—
354C22×D11—21no—
355C22×D11—21no—
356C22×D11—21no—
357C22×D11—21no—
358C22×D11—21no—
359C22×D11—21no—
360C22×D11—21no—
361C22×D11—21no—
362C22×D11C2×C22⋊C412yes—
363Q8×C11—44no—
364D4×C11—44no—
365D4×C11—44no—
366D4×C11—44no—
367C2×C4×C11—21no—
368C2×C4×C11—21no—
369C2×C4×C11—21no—
370C2×C4×C11—21no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11C2×C22⋊C412yes—
387C2×C4×C11C4×D412yes—
388C2×C4×C11C22×D411yescharacteristic
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C22×D411yescharacteristic
391C2×C4×C11C2×#4111yescharacteristic
392C2×C4×C11H(5,𝔽2)11yescharacteristic
393C2×C4×C11H(5,𝔽2)11yescharacteristic
394C22⋊D11—28no—
395C22⋊D11—44no—
396C22⋊D11—44no—
397C22⋊D11—44no—
398C22⋊D11—44no—
399C22⋊D11—44no—
400C2×Dic11—21no—
401C2×Dic11—21no—
402C2×Dic11—21no—
403C2×Dic11—21no—
404C2×Dic11—21no—
405C2×Dic11—21no—
406C2×Dic11—21no—
407C2×Dic11—21no—
408C2×Dic11—21no—
409C2×Dic11—21no—
410C2×Dic11—21no—
411C2×Dic11—21no—
412C2×Dic11—44no—
413C2×Dic11—44no—
414C2×Dic11C2×C22⋊C412yes—
415C2×Dic11C2×C22⋊C412yes—
416C2×Dic11C2×C22⋊C412yes—
417C2×Dic11#13112yes—
418C2×Dic11#13112yes—
419C2×Dic11#13112yes—
420D44—44no—
421C4×D11—22no—
422C4×D11—22no—
423C4×D11—22no—
424C4×D11—22no—
425C4×D11—41no—
426C4×D11—41no—
427C4×D11—41no—
428C4×D11—41no—
429Dic22—44no—
430C8×C11—41no—
431C8×C11—41no—
432C8×C11—41no—
433C8×C11—41no—
434C11⋊C8—22no—
435C11⋊C8—22no—
436C11⋊C8—41no—
437C11⋊C8—41no—
438C22×#41—111no—
439C22×#41C2×D1111yescharacteristic
440C22×M16—111no—
441C22×M16—111no—
442C23×C8—111no—
443C23×C8—111no—
444#532—224no—
445#532—224no—
446C2×C4⋊Q8—111no—
447C2×#127—111no—
448C2×#124—111no—
449C2×#124—111no—
450C2×#121—111no—
451C2×#121—111no—
452C2×#121—111no—
453C2×#121—111no—
454C2×C4×D4—111no—
455C2×C4×D4—111no—
456C2×C4×D4—111no—
457C2×C4×D4—111no—
458C22×C42—111no—
459#436—224no—
460C8×D4—224no—
461C2×C4⋊C8—111no—
462C2×C4⋊C8—111no—
463#408—224no—
464#408—224no—
465C2×C22⋊C8—111no—
466C2×C22⋊C8—111no—
467C2×C22⋊C8—111no—
468C2×C22⋊C8—111no—
469C2×C22⋊C8—111no—
470C2×C22⋊C8—111no—
471C2×C22⋊C8—111no—
472C2×C22⋊C8—111no—
473C2×C22⋊C8—111no—
474C2×C22⋊C8—111no—
475C2×C22⋊C8C2×D1111yescharacteristic
476C2×C22⋊C8C2×D1111yescharacteristic
477C2×C22⋊C8C2×D1111yescharacteristic
478C2×C22⋊C8C2×D1111yescharacteristic
479C2×C22⋊C8C2×D1111yescharacteristic
480C2×C22⋊C8C2×D1111yescharacteristic
481C2×C4×C8—111no—
482C2×C4×C8—111no—
483#336—111no—
484#336—111no—
485#336—111no—
486#336—111no—
487C22×C11—22no—
488C22×C11—22no—
489C22×C11—22no—
490C22×C11—22no—
491C22×C11—22no—
492C22×C11—22no—
493C22×C11—41no—
494C22×C11—41no—
495C22×C11—41no—
496C22×C11—41no—
497C22×C11—41no—
498C22×C11—41no—
499C22×C11—41no—
500C22×C11—41no—
501C22×C11—41no—
502C22×C11—41no—
503C22×C11—41no—
504C22×C11—41no—
505C22×C11—41no—
506C22×C11—41no—
507C22×C11—41no—
508C22×C11C22×C22⋊C411yescharacteristic
509C22×C11C2×C4×D411yescharacteristic
510C22×C11#51811yescharacteristic
511C22×C11C2×#13111yescharacteristic
512C22×C11C2×#13111yescharacteristic
513C22×C11C2×#13111yescharacteristic
514C22×C11#56811yescharacteristic
515C2×D11—22no—
516C2×D11—22no—
517C2×D11—22no—
518C2×D11—41no—
519C2×D11—41no—
520C2×D11—41no—
521C2×D11—41no—
522C2×D11—41no—
523C2×D11—41no—
524C2×D11—41no—
525C2×D11—41no—
526C2×D11—41no—
527C2×D11—41no—
528C2×D11—41no—
529C4×C11—22no—
530C4×C11—22no—
531C4×C11—41no—
532C4×C11D4211yescharacteristic
533C4×C11D4211yescharacteristic
534C4×C11#54611yescharacteristic
535C4×C11#54611yescharacteristic
536Dic11—22no—
537Dic11—22no—
538Dic11—22no—
539Dic11—41no—
540Dic11—41no—
541Dic11#40814yescomplemented
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—41no—
547C2×#41—41no—
548C2×#41—222no—
549C2×#41—222no—
550C2×#41—222no—
551C2×#41—222no—
552C2×#41—441no—
553C2×#41—441no—
554C22×Q8—111no—
555C22×Q8C4×D1111yescharacteristic
556C22×D4—111no—
557C22×D4—111no—
558C22×D4—111no—
559C22×D4—111no—
560C22×D4—111no—
561C22×D4—111no—
562C22×D4—111no—
563C22×D4C4×D1111yescharacteristic
564C22×D4C4×D1111yescharacteristic
565C22×D4C4×D1111yescharacteristic
566C23×C4—111no—
567C23×C4—111no—
568C23×C4—111no—
569C23×C4—111no—
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1111yescharacteristic
573C2×M16—222no—
574C2×M16—222no—
575C2×M16—222no—
576C2×M16—222no—
577C2×M16—441no—
578C2×M16—441no—
579C22×C8—111no—
580C22×C8—111no—
581C22×C8—111no—
582C22×C8—111no—
583C22×C8—222no—
584C22×C8—222no—
585C22×C8—222no—
586C22×C8—222no—
587C22×C8—441no—
588C22×C8—441no—
589C22×C8C22×D1111yescharacteristic
590C22×C8C22×D1111yescharacteristic
591C22×C8C22×D1111yescharacteristic
592C22×C8C22×D1111yescharacteristic
593C4⋊Q8—224no—
594#127—224no—
595#124—224no—
596#124—224no—
597#121—224no—
598#121—224no—
599#121—224no—
600#121—224no—
601C4×D4—114no—
602C4×D4—114no—
603C4×D4—222no—
604C4×D4—222no—
605C4×D4—222no—
606C4×D4—222no—
607C4×D4—222no—
608C4×D4—222no—
609C2×C4⋊C4—111no—
610C2×C4⋊C4—111no—
611C2×C4⋊C4—111no—
612C2×C4⋊C4—111no—
613C2×C22⋊C4—111no—
614C2×C22⋊C4—111no—
615C2×C22⋊C4—111no—
616C2×C22⋊C4—111no—
617C2×C22⋊C4—111no—
618C2×C22⋊C4—111no—
619C2×C22⋊C4—111no—
620C2×C22⋊C4—111no—
621C2×C42—111no—
622C2×C42—111no—
623C2×C42—111no—
624C2×C42—111no—
625C2×C42—222no—
626C2×C42—222no—
627C4⋊C8—222no—
628C4⋊C8—222no—
629C22⋊C8—22no—
630C22⋊C8—22no—
631C22⋊C8—22no—
632C22⋊C8—22no—
633C22⋊C8—41no—
634C22⋊C8—41no—
635C22⋊C8—114no—
636C22⋊C8—222no—
637C22⋊C8—222no—
638C22⋊C8—222no—
639C22⋊C8—222no—
640C22⋊C8—222no—
641C22⋊C8—222no—
642C22⋊C8—222no—
643C22⋊C8—441no—
644C22⋊C8—441no—
645C4×C8—222no—
646C4×C8—222no—
647C2×C11—42no—
648C2×C11—42no—
649C2×C11—81no—
650C2×C11D4×C22⋊C411yescharacteristic
651C2×C11C2×#40811yescharacteristic
652C2×C11#288011yescharacteristic
653C2×C11#293111yescharacteristic
654C2×C11#293511yescharacteristic
655C2×C11#297911yescharacteristic
656C2×C11#298111yescharacteristic
657D11—42no—
658D11—81no—
659C24—111no—
660C24—111no—
661C24C2×C4×D1111yescharacteristic
662C24C2×C4×D1111yescharacteristic
663C24C2×C4×D1111yescharacteristic
664#41—44no—
665#41—44no—
666#41—44no—
667#41—44no—
668#41—444no—
669#41—444no—
670#41—444no—
671#41—444no—
672C2×Q8—22no—
673C2×Q8—22no—
674C2×Q8—41no—
675C2×Q8—222no—
676C2×Q8—222no—
677C2×Q8—441no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—41no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—114no—
688C2×D4—222no—
689C2×D4—222no—
690C2×D4—222no—
691C2×D4—222no—
692C2×D4—222no—
693C2×D4—222no—
694C2×D4—222no—
695C2×D4—222no—
696C2×D4—222no—
697C2×D4—222no—
698C2×D4—222no—
699C2×D4—222no—
700C2×D4—222no—
701C2×D4—222no—
702C2×D4—222no—
703C2×D4—441no—
704C2×D4—441no—
705C2×D4—441no—
706C2×D4—441no—
707C2×D4—441no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—111no—
723C22×C4—111no—
724C22×C4—111no—
725C22×C4—111no—
726C22×C4—112no—
727C22×C4—112no—
728C22×C4—111no—
729C22×C4—111no—
730C22×C4—222no—
731C22×C4—222no—
732C22×C4—222no—
733C22×C4—222no—
734C22×C4—222no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—441no—
746C22×C4C2×C4×D1111yescharacteristic
747C22×C4C2×C4×D1111yescharacteristic
748C22×C4C2×C4×D1111yescharacteristic
749C22×C4D4×D1112yes—
750C22×C4D4×D1112yes—
751C22×C4D4×D1112yes—
752C22×C4#434112yes—
753C22×C4C23×D1111yescharacteristic
754M16—444no—
755M16—444no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—112no—
769C2×C8—112no—
770C2×C8—221no—
771C2×C8—221no—
772C2×C8—221no—
773C2×C8—221no—
774C2×C8—221no—
775C2×C8—221no—
776C2×C8—221no—
777C2×C8—221no—
778C2×C8—221no—
779C2×C8—221no—
780C2×C8—444no—
781C2×C8—444no—
782C4⋊C4—114no—
783C4⋊C4—222no—
784C4⋊C4—222no—
785C4⋊C4—222no—
786C22⋊C4—114no—
787C22⋊C4—114no—
788C22⋊C4—222no—
789C22⋊C4—222no—
790C22⋊C4—222no—
791C22⋊C4—222no—
792C22⋊C4—222no—
793C22⋊C4—222no—
794C42—112no—
795C42—112no—
796C42—222no—
797C42—222no—
798C42—221no—
799C42—221no—
800C11#2240211yescharacteristic, complemented, Sylow
801C23—21no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—112no—
821C23—221no—
822C23—221no—
823C23—221no—
824C23—221no—
825C23—221no—
826C23—221no—
827C23—221no—
828C23—221no—
829C23—221no—
830C23—221no—
831C23—221no—
832C23—221no—
833C23—221no—
834C23C22⋊C4×D1112yes—
835C23(C22⋊D11)⋊C412yes—
836C23C22×C4×D1111yescharacteristic
837Q8—44no—
838Q8—444no—
839D4—44no—
840D4—44no—
841D4—44no—
842D4—228no—
843D4—444no—
844D4—444no—
845D4—444no—
846D4—444no—
847D4—444no—
848D4—444no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—112no—
869C2×C4—112no—
870C2×C4—112no—
871C2×C4—112no—
872C2×C4—112no—
873C2×C4—112no—
874C2×C4—221no—
875C2×C4—221no—
876C2×C4—221no—
877C2×C4—221no—
878C2×C4—221no—
879C2×C4—221no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—221no—
885C2×C4—221no—
886C2×C4—221no—
887C2×C4—221no—
888C2×C4—221no—
889C2×C4—221no—
890C2×C4—444no—
891C2×C4—444no—
892C2×C4—441no—
893C2×C4—441no—
894C2×C4—441no—
895C2×C4—441no—
896C2×C4C22⋊C4×D1112yes—
897C2×C4(C22⋊D11)⋊C412yes—
898C2×C4C2×D4×D1111yescharacteristic
899C2×C4C2×D4×D1111yescharacteristic
900C2×C4C2×D4×D1111yescharacteristic
901C2×C4C2×#434111yescharacteristic
902C2×C4#6703711yescharacteristic
903C2×C4#6703711yescharacteristic
904C8—41no—
905C8—41no—
906C8—41no—
907C8—41no—
908C8—222no—
909C8—222no—
910C8—441no—
911C8—441no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—22no—
916C22—22no—
917C22—22no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—222no—
934C22—222no—
935C22—222no—
936C22—441no—
937C22—441no—
938C22—441no—
939C22—441no—
940C22—441no—
941C22—441no—
942C22—441no—
943C22—441no—
944C22—441no—
945C22—441no—
946C22—441no—
947C22C2×C22⋊C4×D1111yescharacteristic
948C22C2×(C22⋊D11)⋊C411yescharacteristic
949C22#1062301711yescharacteristic
950C22D11×#13111yescharacteristic
951C22D11×#13111yescharacteristic
952C22D11×#13111yescharacteristic
953C22#1062328111yescharacteristic
954C4—22no—
955C4—22no—
956C4—41no—
957C4—114no—
958C4—222no—
959C4—222no—
960C4—222no—
961C4—441no—
962C4—441no—
963C4#1062312111yescharacteristic
964C4#1062312111yescharacteristic
965C4#1062312211yescharacteristic
966C4#1062312211yescharacteristic
967C2—42no—
968C2—42no—
969C2—81no—
970C2—442no—
971C2—881no—
972C2#1307143211yescharacteristic
973C2D11×#40811yescharacteristic
974C2#1307706411yescharacteristic
975C2#1307732411yescharacteristic
976C2#1307735611yescharacteristic
977C2#1307768011yescharacteristic
978C2#1307768911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1780C2
prime radicalC2×#10623363C2
cosocleC22×C4×C11C24
hypercenter#1780D11
hypocenterC11#22402
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1780

Complements

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

NH ≅ G/Ntype
2. C2×#10622342C2semidirect
3. C2×(C22⋊D11)⋊C8C2semidirect
4. C2×#10622847C2semidirect
5. C2×#10622340C2semidirect
6. #13069408C2semidirect
7. #13069408C2semidirect
8. #13068911C2semidirect
9. #13068910C2semidirect
10. #13068906C2semidirect
11. #13068905C2semidirect
12. #13068594C2semidirect
13. #13068527C2semidirect
14. C22⋊C8×Dic11C2semidirect
15. C11×#1780C2semidirect
159. C22⋊(C11⋊C8)D4semidirect
325. #1780D11semidirect
541. Dic11#408semidirect
800. C11#22402semidirect

Maximal subgroups

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

subgroupindex
C2×#106233632
C2×#106223422
C2×(C22⋊D11)⋊C82
C2×#106228472
C2×#106223402
#130694082
#130689112
#130689102
#130689062
#130689052
#130685942
#130685272
C22⋊C8×Dic112
C11×#17802
#2240211