Finite Group Databasebeta

← #14769073

Subgroups — #14769073

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×#10623079C211yesmaximal, characteristic
2C2×#10622741C211yesmaximal, characteristic, complemented
3C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
4C2×#10622742C211yesmaximal, characteristic, complemented
5C2×#10622340C211yesmaximal, characteristic, complemented
6#13069408C211yesmaximal, characteristic, complemented
7#13069408C211yesmaximal, characteristic, complemented
8#13068912C211yesmaximal, characteristic, complemented
9#13068909C211yesmaximal, characteristic, complemented
10#13068907C211yesmaximal, characteristic, complemented
11#13068595C211yesmaximal, characteristic, complemented
12#13068527C211yesmaximal, characteristic, complemented
13#13068527C211yesmaximal, characteristic, complemented
14#13068373C211yesmaximal, characteristic, complemented
15C11×#1870C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66993C411yescharacteristic
21C2×#66991C411yescharacteristic
22C2×C4×C22⋊D11C2211yescharacteristic
23C2×C4×C22⋊D11C2211yescharacteristic
24C23×C11⋊C8C2211yescharacteristic
25C22×#4313C2211yescharacteristic
26C22×C8×D11C2211yescharacteristic
27#10623079—24no—
28#10623079—24no—
29C2×#66948C411yescharacteristic
30C2×#66941C411yescharacteristic
31C2×#66938C411yescharacteristic
32C2×#66938C411yescharacteristic
33C2×#66937C411yescharacteristic
34C2×#66937C411yescharacteristic
35C2×C4×D44C2211yescharacteristic
36C2×C42×D11C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43#10622742—24no—
44#10622741—24no—
45C2×(C2×D11)⋊C8C2211yescharacteristic
46C2×(C2×D11)⋊C8C2211yescharacteristic
47C2×(C2×D11)⋊C8C2211yescharacteristic
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×(C2×D11)⋊C8C2211yescharacteristic
55C2×Dic11⋊C8C2211yescharacteristic
56C2×Dic11⋊C8C2211yescharacteristic
57C2×C8×Dic11C2211yescharacteristic
58C2×C8×Dic11C2211yescharacteristic
59#10622340—24no—
60(C22⋊D11)⋊C8—24no—
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63#10622162C2211yescharacteristic
64#10622162C2211yescharacteristic
65C22×D4×C11C2×C411yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11C2×C411yescharacteristic
69C22×C22⋊D11C2×C411yescharacteristic
70C22×C22⋊D11C2×C411yescharacteristic
71C22×C22⋊D11C2×C411yescharacteristic
72C22×C22⋊D11C2×C411yescharacteristic
73C22×C22⋊D11C2×C411yescharacteristic
74C2×#4339—22no—
75C2×#4339—22no—
76C2×#4339—22no—
77C2×#4339—22no—
78C2×#4339—22no—
79C2×#4339—22no—
80C2×#4339—22no—
81C2×#4339—22no—
82C2×#4339—41no—
83C2×#4339—41no—
84C2×#4339—41no—
85C2×#4339—41no—
86C22×D44C2×C411yescharacteristic
87C22×D44C2×C411yescharacteristic
88C22×D44C2×C411yescharacteristic
89C22×C4×D11C2×C411yescharacteristic
90C22×C4×D11C2×C411yescharacteristic
91C22×C4×D11C2311yescharacteristic
92C22×C4×D11C2311yescharacteristic
93C22×C4×D11C2311yescharacteristic
94C22×Dic22C2×C411yescharacteristic
95C22×Dic22C2×C411yescharacteristic
96C2×C11×M16—22no—
97C2×C11×M16—22no—
98C2×C11×M16—41no—
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C4×D4×C11—22no—
104C4×D4×C11—22no—
105C2×C11×C4⋊C4C2×C411yescharacteristic
106C2×C11×C22⋊C4C2×C411yescharacteristic
107C2×C11×C22⋊C4C2×C411yescharacteristic
108C2×C42×C11C2311yescharacteristic
109C2×C22⋊Dic11C2×C411yescharacteristic
110C2×C22⋊Dic11C2×C411yescharacteristic
111#66993—24no—
112#66991—24no—
113C4×C22⋊D11—22no—
114C4×C22⋊D11—22no—
115C4×C22⋊D11D414yes—
116C4×C22⋊D11D414yes—
117C2×(C2×D11)⋊C4C2×C411yescharacteristic
118C2×(C2×D11)⋊C4C2×C411yescharacteristic
119C2×(C2×D11)⋊C4C2×C411yescharacteristic
120C2×(C2×D11)⋊C4C2×C411yescharacteristic
121C2×C4⋊Dic11C2×C411yescharacteristic
122C2×Dic11⋊C4C2×C411yescharacteristic
123C2×Dic11⋊C4C2×C411yescharacteristic
124C2×C4×Dic11C2×C411yescharacteristic
125C2×C4×Dic11C2×C411yescharacteristic
126C2×C4×Dic11C2311yescharacteristic
127C22×C11⋊C8—22no—
128C22×C11⋊C8—22no—
129C22×C11⋊C8—41no—
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C2×#4313—22no—
135C2×#4313—22no—
136C2×#4313—41no—
137C2×C8×D11—22no—
138C2×C8×D11—22no—
139C2×C8×D11—41no—
140#66948—24no—
141#66941—24no—
142#66938—24no—
143#66938—24no—
144#66937—24no—
145#66937—24no—
146C4×D44—22no—
147C4×D44—22no—
148C42×D11—22no—
149C42×D11—22no—
150C11×C22⋊C8—22no—
151C11×C22⋊C8—22no—
152C11×C22⋊C8—41no—
153C22⋊(C11⋊C8)—22no—
154C22⋊(C11⋊C8)—22no—
155C22⋊(C11⋊C8)—41no—
156(C2×D11)⋊C8—22no—
157(C2×D11)⋊C8—22no—
158(C2×D11)⋊C8—22no—
159(C2×D11)⋊C8—22no—
160(C2×D11)⋊C8—22no—
161(C2×D11)⋊C8—22no—
162(C2×D11)⋊C8—22no—
163(C2×D11)⋊C8—41no—
164(C2×D11)⋊C8—41no—
165(C2×D11)⋊C8D414yescomplemented
166Dic11⋊C8—22no—
167Dic11⋊C8—22no—
168C8×Dic11—22no—
169C8×Dic11—22no—
170#22402—111nomaximal, Sylow
171C24×C11C22×C411yescharacteristic
172C24×C11C22×C411yescharacteristic
173C23×D11C22×C411yescharacteristic
174C23×D11C22×C411yescharacteristic
175C23×D11C22×C411yescharacteristic
176C2×D4×C11—22no—
177C2×D4×C11—22no—
178C2×D4×C11—41no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11C22×C411yescharacteristic
190C22×C4×C11C22×C411yescharacteristic
191C22×C4×C11C22×C411yescharacteristic
192C22×C4×C11C22×C411yescharacteristic
193C22×C4×C11C2×D412yes—
194C22×C4×C11C2×D412yes—
195C22×C4×C11C2411yescharacteristic
196C2×C22⋊D11—22no—
197C2×C22⋊D11—22no—
198C2×C22⋊D11—22no—
199C2×C22⋊D11—22no—
200C2×C22⋊D11—22no—
201C2×C22⋊D11—22no—
202C2×C22⋊D11—22no—
203C2×C22⋊D11—22no—
204C2×C22⋊D11—22no—
205C2×C22⋊D11—22no—
206C2×C22⋊D11—22no—
207C2×C22⋊D11—22no—
208C2×C22⋊D11—22no—
209C2×C22⋊D11—41no—
210C2×C22⋊D11—41no—
211C2×C22⋊D11—41no—
212C2×C22⋊D11—41no—
213C2×C22⋊D11C22⋊C414yes—
214C22×Dic11C22×C411yescharacteristic
215C22×Dic11C22×C411yescharacteristic
216C22×Dic11C22×C411yescharacteristic
217C22×Dic11C22×C411yescharacteristic
218C22×Dic11C22×C411yescharacteristic
219#4339—44no—
220#4339—44no—
221#4339—44no—
222#4339—44no—
223#4339—44no—
224#4339—44no—
225#4339—44no—
226#4339—44no—
227C2×D44—22no—
228C2×D44—22no—
229C2×D44—22no—
230C2×D44—22no—
231C2×D44—22no—
232C2×D44—22no—
233C2×D44—41no—
234C2×D44—41no—
235C2×D44—41no—
236C2×C4×D11—22no—
237C2×C4×D11—22no—
238C2×C4×D11—22no—
239C2×C4×D11—22no—
240C2×C4×D11—22no—
241C2×C4×D11—21no—
242C2×C4×D11—21no—
243C2×C4×D11—21no—
244C2×C4×D11—21no—
245C2×C4×D11—21no—
246C2×C4×D11—21no—
247C2×C4×D11—21no—
248C2×C4×D11—21no—
249C2×C4×D11—21no—
250C2×C4×D11—21no—
251C2×C4×D11—21no—
252C2×C4×D11—21no—
253C2×C4×D11—21no—
254C2×C4×D11—21no—
255C2×C4×D11—41no—
256C2×C4×D11C2×D412yes—
257C2×C4×D11C2×D412yes—
258C2×C4×D11C2×D412yes—
259C2×C4×D11#4112yes—
260C2×Dic22—22no—
261C2×Dic22—22no—
262C2×Dic22—22no—
263C2×Dic22—22no—
264C2×Dic22—41no—
265C2×Dic22—41no—
266C11×M16—44no—
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—
278C2×C8×C11C2×D412yes—
279C11×C4⋊C4—22no—
280C11×C22⋊C4—22no—
281C11×C22⋊C4—22no—
282C42×C11—21no—
283C42×C11—21no—
284C22⋊Dic11—22no—
285C22⋊Dic11C22⋊C414yes—
286(C2×D11)⋊C4—22no—
287(C2×D11)⋊C4—22no—
288(C2×D11)⋊C4—22no—
289(C2×D11)⋊C4C22⋊C414yes—
290C4⋊Dic11—22no—
291Dic11⋊C4—22no—
292Dic11⋊C4C22⋊C414yes—
293C4×Dic11—22no—
294C4×Dic11—22no—
295C4×Dic11C2×D412yes—
296C4×Dic11C2×D412yes—
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—21no—
308C2×C11⋊C8—44no—
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#1870D1111yescharacteristic, complemented
321#1869—111no—
322#1869—111no—
323#1797—111no—
324#1780—111no—
325#1780—111no—
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×C11C2×C22⋊C412yes—
341C23×C11C23×C411yescharacteristic
342C22×D11—21no—
343C22×D11—21no—
344C22×D11—21no—
345C22×D11—21no—
346C22×D11—21no—
347C22×D11—21no—
348C22×D11—21no—
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×D11C2×C22⋊C412yes—
362C22×D11C4×D412yes—
363D4×C11—44no—
364C2×C4×C11—21no—
365C2×C4×C11—21no—
366C2×C4×C11—21no—
367C2×C4×C11—21no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—21no—
373C2×C4×C11—21no—
374C2×C4×C11—21no—
375C2×C4×C11—21no—
376C2×C4×C11—21no—
377C2×C4×C11—21no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11C2×C22⋊C412yes—
383C2×C4×C11#13112yes—
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C11C22×D411yescharacteristic
386C2×C4×C11C22×D411yescharacteristic
387C2×C4×C11C2×#4111yescharacteristic
388C2×C4×C11H(5,𝔽2)11yescharacteristic
389C2×C4×C11H(5,𝔽2)11yescharacteristic
390C22⋊D11—28no—
391C22⋊D11—44no—
392C22⋊D11—44no—
393C22⋊D11—44no—
394C22⋊D11—44no—
395C22⋊D11—44no—
396C2×Dic11—21no—
397C2×Dic11—21no—
398C2×Dic11—21no—
399C2×Dic11—21no—
400C2×Dic11—21no—
401C2×Dic11—21no—
402C2×Dic11—21no—
403C2×Dic11—21no—
404C2×Dic11—21no—
405C2×Dic11C2×C22⋊C412yes—
406C2×Dic11C2×C22⋊C412yes—
407C2×Dic11C2×C22⋊C412yes—
408C2×Dic11C4×D412yes—
409C2×Dic11#13112yes—
410C2×Dic11#13112yes—
411D44—44no—
412D44—44no—
413D44—44no—
414C4×D11—22no—
415C4×D11—22no—
416C4×D11—22no—
417C4×D11—22no—
418C4×D11—22no—
419C4×D11—22no—
420C4×D11—22no—
421C4×D11—22no—
422C4×D11—44no—
423C4×D11—41no—
424C4×D11—41no—
425C4×D11—41no—
426C4×D11—41no—
427C4×D11—44no—
428Dic22—44no—
429Dic22—44no—
430C8×C11—22no—
431C8×C11—41no—
432C8×C11—41no—
433C8×C11—41no—
434C11⋊C8—22no—
435C11⋊C8—41no—
436C11⋊C8—41no—
437C11⋊C8—41no—
438C22×#41—111no—
439C22×#41—111no—
440C22×M16—111no—
441C22×M16C2×D1111yescharacteristic
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×D4C2×D1111yescharacteristic
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⋊C8—111no—
476C2×C22⋊C8—111no—
477C2×C22⋊C8—111no—
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#336C2×D1111yescharacteristic
486#336C2×D1111yescharacteristic
487C22×C11—22no—
488C22×C11—22no—
489C22×C11—22no—
490C22×C11—41no—
491C22×C11—41no—
492C22×C11—41no—
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×C11C22×C22⋊C411yescharacteristic
502C22×C11C2×C4×D411yescharacteristic
503C22×C11#51811yescharacteristic
504C22×C11C2×#13111yescharacteristic
505C22×C11C2×#13111yescharacteristic
506C22×C11C2×#13111yescharacteristic
507C22×C11#56811yescharacteristic
508C2×D11—22no—
509C2×D11—22no—
510C2×D11—22no—
511C2×D11—22no—
512C2×D11—22no—
513C2×D11—22no—
514C2×D11—41no—
515C2×D11—41no—
516C2×D11—41no—
517C2×D11—41no—
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×C11—41no—
533C4×C11D4211yescharacteristic
534C4×C11D4211yescharacteristic
535C4×C11#54611yescharacteristic
536C4×C11#54611yescharacteristic
537Dic11—22no—
538Dic11—22no—
539Dic11—22no—
540Dic11—41no—
541Dic11#40814yescomplemented
542C2×#41—222no—
543C2×#41—222no—
544C2×#41—222no—
545C2×#41—222no—
546C2×#41—222no—
547C2×#41—222no—
548C2×#41—222no—
549C2×#41—222no—
550C2×#41—441no—
551C2×#41—441no—
552C2×#41—441no—
553C2×#41—441no—
554C22×Q8—111no—
555C22×Q8—111no—
556C22×D4—111no—
557C22×D4—111no—
558C22×D4—111no—
559C22×D4—111no—
560C22×D4—111no—
561C22×D4—111no—
562C22×D4—111no—
563C22×D4—111no—
564C22×D4—111no—
565C22×D4C4×D1111yescharacteristic
566C23×C4—111no—
567C23×C4—111no—
568C23×C4—111no—
569C23×C4—111no—
570C23×C4—111no—
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1111yescharacteristic
573C2×M16—22no—
574C2×M16—22no—
575C2×M16—41no—
576C2×M16—222no—
577C2×M16—222no—
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—22no—
602C4×D4—22no—
603C4×D4—114no—
604C4×D4—114no—
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⋊C4C4×D1111yescharacteristic
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⋊C4C4×D1111yescharacteristic
620C2×C22⋊C4C4×D1111yescharacteristic
621C2×C42—111no—
622C2×C42—111no—
623C2×C42—111no—
624C2×C42—222no—
625C2×C42—222no—
626C2×C42C22×D1111yescharacteristic
627C4⋊C8—222no—
628C4⋊C8—222no—
629C22⋊C8—22no—
630C22⋊C8—22no—
631C22⋊C8—41no—
632C22⋊C8—114no—
633C22⋊C8—222no—
634C22⋊C8—222no—
635C22⋊C8—222no—
636C22⋊C8—222no—
637C22⋊C8—222no—
638C22⋊C8—222no—
639C22⋊C8—222no—
640C22⋊C8—222no—
641C22⋊C8—222no—
642C22⋊C8—441no—
643C22⋊C8—441no—
644C22⋊C8—441no—
645C4×C8—222no—
646C4×C8—222no—
647C2×C11—42no—
648C2×C11—81no—
649C2×C11D4×C22⋊C411yescharacteristic
650C2×C11C2×#40811yescharacteristic
651C2×C11#288011yescharacteristic
652C2×C11#293111yescharacteristic
653C2×C11#293511yescharacteristic
654C2×C11#297911yescharacteristic
655C2×C11#298111yescharacteristic
656D11—42no—
657D11—42no—
658D11—81no—
659C24—111no—
660C24—111no—
661C24—111no—
662C24C2×C4×D1111yescharacteristic
663C24C2×C4×D1111yescharacteristic
664#41—444no—
665#41—444no—
666#41—444no—
667#41—444no—
668#41—444no—
669#41—444no—
670#41—444no—
671#41—444no—
672C2×Q8—222no—
673C2×Q8—222no—
674C2×Q8—222no—
675C2×Q8—222no—
676C2×Q8—441no—
677C2×Q8—441no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—41no—
681C2×D4—114no—
682C2×D4—222no—
683C2×D4—222no—
684C2×D4—222no—
685C2×D4—222no—
686C2×D4—222no—
687C2×D4—222no—
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—441no—
702C2×D4—441no—
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—111no—
719C22×C4—111no—
720C22×C4—111no—
721C22×C4—111no—
722C22×C4—112no—
723C22×C4—112no—
724C22×C4—112no—
725C22×C4—112no—
726C22×C4—111no—
727C22×C4—222no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—222no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—441no—
747C22×C4C2×C4×D1111yescharacteristic
748C22×C4C2×C4×D1111yescharacteristic
749C22×C4C2×C4×D1111yescharacteristic
750C22×C4C2×C4×D1111yescharacteristic
751C22×C4D4×D1112yes—
752C22×C4D4×D1112yes—
753C22×C4C23×D1111yescharacteristic
754M16—44no—
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—112no—
768C2×C8—221no—
769C2×C8—221no—
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—444no—
780C2×C8—444no—
781C2×C8D4×D1112yes—
782C4⋊C4—22no—
783C4⋊C4—114no—
784C4⋊C4—222no—
785C4⋊C4—222no—
786C22⋊C4—22no—
787C22⋊C4—22no—
788C22⋊C4—114no—
789C22⋊C4—114no—
790C22⋊C4—222no—
791C22⋊C4—222no—
792C22⋊C4—222no—
793C22⋊C4—222no—
794C42—21no—
795C42—21no—
796C42—112no—
797C42—112no—
798C42—222no—
799C42—222no—
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—112no—
815C23—112no—
816C23—221no—
817C23—221no—
818C23—221no—
819C23—221no—
820C23—221no—
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—
834C23—221no—
835C23C22⋊C4×D1112yes—
836C23C22×C4×D1111yescharacteristic
837Q8—444no—
838Q8—444no—
839D4—44no—
840D4—228no—
841D4—444no—
842D4—444no—
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—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—112no—
868C2×C4—112no—
869C2×C4—112no—
870C2×C4—112no—
871C2×C4—112no—
872C2×C4—112no—
873C2×C4—221no—
874C2×C4—221no—
875C2×C4—221no—
876C2×C4—221no—
877C2×C4—221no—
878C2×C4—221no—
879C2×C4—222no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—222no—
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#6696012yes—
898C2×C4C2×D4×D1111yescharacteristic
899C2×C4C2×D4×D1111yescharacteristic
900C2×C4C2×D4×D1111yescharacteristic
901C2×C4#6703711yescharacteristic
902C2×C4#41×D1111yescharacteristic
903C2×C4#6704211yescharacteristic
904C8—22no—
905C8—41no—
906C8—41no—
907C8—41no—
908C8—222no—
909C8—441no—
910C8—441no—
911C8—441no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—222no—
927C22—222no—
928C22—222no—
929C22—222no—
930C22—222no—
931C22—222no—
932C22—441no—
933C22—441no—
934C22—441no—
935C22—441no—
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
948C22C4×D4×D1111yescharacteristic
949C22#1062307611yescharacteristic
950C22C2×#6696011yescharacteristic
951C22#1062327611yescharacteristic
952C22D11×#13111yescharacteristic
953C22D11×#13111yescharacteristic
954C4—22no—
955C4—22no—
956C4—41no—
957C4—41no—
958C4—114no—
959C4—222no—
960C4—222no—
961C4—222no—
962C4—441no—
963C4#1062312111yescharacteristic
964C4#1062314011yescharacteristic
965C4#1062314111yescharacteristic
966C4#1062318511yescharacteristic
967C2—42no—
968C2—81no—
969C2—442no—
970C2—442no—
971C2—881no—
972C2#1307143411yescharacteristic
973C2D11×#40811yescharacteristic
974C2#1307706611yescharacteristic
975C2#1307732511yescharacteristic
976C2#1307735711yescharacteristic
977C2#1307768111yescharacteristic
978C2#1307768811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1870C2
prime radicalC2×#10623079C2
cosocleC22×C4×C11C24
hypercenter#1870D11
hypocenterC11#22402
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×#10622741C2semidirect
3. C2×(C22⋊D11)⋊C8C2semidirect
4. C2×#10622742C2semidirect
5. C2×#10622340C2semidirect
6. #13069408C2semidirect
7. #13069408C2semidirect
8. #13068912C2semidirect
9. #13068909C2semidirect
10. #13068907C2semidirect
11. #13068595C2semidirect
12. #13068527C2semidirect
13. #13068527C2semidirect
14. #13068373C2semidirect
15. C11×#1870C2semidirect
165. (C2×D11)⋊C8D4semidirect
320. #1870D11semidirect
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×#106230792
C2×#106227412
C2×(C22⋊D11)⋊C82
C2×#106227422
C2×#106223402
#130694082
#130689122
#130689092
#130689072
#130685952
#130685272
#130683732
C11×#18702
#2240211