Finite Group Databasebeta

← #14769060

Subgroups — #14769060

Order 2816.

1582 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623055C211yesmaximal, characteristic
2C2×#10622301C211yesmaximal, characteristic, complemented
3C2×#10622319C211yesmaximal, characteristic, complemented
4C2×#10622340C211yesmaximal, characteristic, complemented
5C2×#10622339C211yesmaximal, characteristic, complemented
6#13069414C211yesmaximal, characteristic, complemented
7#13069410C211yesmaximal, characteristic, complemented
8#13068912C211yesmaximal, characteristic, complemented
9#13068912C211yesmaximal, characteristic, complemented
10#13068912C211yesmaximal, characteristic, complemented
11#13068907C211yesmaximal, characteristic, complemented
12#13068600C211yesmaximal, characteristic, complemented
13#13068527C211yesmaximal, characteristic, complemented
14#13068525C211yesmaximal, characteristic, complemented
15C11×#1750C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C22×#4313C2211yescharacteristic, complemented
22C22×C8×D11C2211yescharacteristic, complemented
23#10623055—24no—
24#10623055—24no—
25C2×#66950C411yescharacteristic
26C2×#66950C411yescharacteristic
27C2×#66948C411yescharacteristic
28C2×#66948C411yescharacteristic
29C2×#66939C411yescharacteristic
30C2×#66939C411yescharacteristic
31C2×#66935C411yescharacteristic
32C2×#66935C411yescharacteristic
33C2×C4×D44C2211yescharacteristic
34C2×C4×D44C2211yescharacteristic
35C2×C4×D44C2211yescharacteristic
36C2×C4×D44C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×#97C2211yescharacteristic, complemented
40C2×C4×C8×C11C2211yescharacteristic, complemented
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×(C2×D11)⋊C8C2211yescharacteristic
46C2×(C2×D11)⋊C8C2211yescharacteristic
47C2×(C2×D11)⋊C8C2211yescharacteristic
48C2×(C2×D11)⋊C8C2211yescharacteristic
49C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
50C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
51C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
52C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
53C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
54C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
55C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
56C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
57#10622340—24no—
58#10622339—24no—
59#10622319—24no—
60#10622301—24no—
61C11×#336C2211yescharacteristic, complemented
62C11×#336C2211yescharacteristic, complemented
63#10622162C2211yescharacteristic, complemented
64#10622162C2211yescharacteristic, complemented
65C24×D11C2×C411yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11C2×C411yescharacteristic
68C22×C22⋊D11C2×C411yescharacteristic
69C23×Dic11C2×C411yescharacteristic
70C2×#4339—22no—
71C2×#4339—22no—
72C2×#4339—22no—
73C2×#4339—22no—
74C2×#4339—41no—
75C2×#4339—41no—
76C22×D44C2×C411yescharacteristic
77C22×D44C2×C411yescharacteristic
78C22×D44C2×C411yescharacteristic
79C22×D44C2×C411yescharacteristic
80C22×D44C2×C411yescharacteristic
81C22×C4×D11—22no—
82C22×C4×D11—22no—
83C22×C4×D11—22no—
84C22×C4×D11—22no—
85C22×C4×D11—41no—
86C22×C4×D11—41no—
87C22×C4×D11C2×C411yescharacteristic
88C22×C4×D11C2×C411yescharacteristic
89C22×C4×D11C2311yescharacteristic
90C22×C4×D11C2311yescharacteristic
91C22×C4×D11C2311yescharacteristic
92C22×C4×D11C2311yescharacteristic
93C22×Dic22C2×C411yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C11×#117—22no—
99C11×#117—22no—
100C2×C11×C4⋊C4C2×C411yescharacteristic
101C2×C11×C4⋊C4C2×C411yescharacteristic
102C2×C11×C22⋊C4C2×C411yescharacteristic
103C2×C11×C22⋊C4C2×C411yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×(C2×D11)⋊C4C2×C411yescharacteristic
107C2×(C2×D11)⋊C4C2×C411yescharacteristic
108C2×(C2×D11)⋊C4C2×C411yescharacteristic
109C2×(C2×D11)⋊C4C2×C411yescharacteristic
110C2×(C2×D11)⋊C4C2×C411yescharacteristic
111C2×(C2×D11)⋊C4C2×C411yescharacteristic
112C2×(C2×D11)⋊C4C2×C411yescharacteristic
113C2×(C2×D11)⋊C4C2×C411yescharacteristic
114C2×C4⋊Dic11C2×C411yescharacteristic
115C2×C4⋊Dic11C2×C411yescharacteristic
116C2×C4⋊Dic11C2×C411yescharacteristic
117C2×C4⋊Dic11C2×C411yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122C2×#4313—22no—
123C2×#4313—22no—
124C2×#4313—22no—
125C2×#4313—22no—
126C2×#4313—22no—
127C2×#4313—22no—
128C2×#4313—41no—
129C2×#4313—41no—
130C2×#4313—41no—
131C2×C8×D11—22no—
132C2×C8×D11—22no—
133C2×C8×D11—41no—
134#66950—24no—
135#66950—24no—
136#66948—24no—
137#66948—24no—
138#66939—24no—
139#66939—24no—
140#66935—24no—
141#66935—24no—
142C4×D44—22no—
143C4×D44—22no—
144C4×D44—22no—
145C4×D44—22no—
146C4×D44—22no—
147C4×D44—22no—
148C4×D44D414yes—
149C4×D44D414yes—
150C11×C22⋊C8—22no—
151C11×C22⋊C8D414yescomplemented
152C11×#97—22no—
153C4×C8×C11—22no—
154C22⋊(C11⋊C8)—22no—
155C22⋊(C11⋊C8)—22no—
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—22no—
164(C2×D11)⋊C8—41no—
165(C2×D11)⋊C8—41no—
166(C2×D11)⋊C8—41no—
167(C2×D11)⋊C8—41no—
168C4⋊(C11⋊C8)—22no—
169C4⋊(C11⋊C8)—22no—
170#22400—111nomaximal, Sylow
171C24×C11C22×C411yescharacteristic
172C23×D11—22no—
173C23×D11—22no—
174C23×D11—22no—
175C23×D11—41no—
176C23×D11—41no—
177C23×D11—41no—
178C23×D11—41no—
179C23×D11C22×C411yescharacteristic
180C23×D11C22×C411yescharacteristic
181C23×D11C22×C411yescharacteristic
182C23×D11C22×C411yescharacteristic
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11C22×C411yescharacteristic
188C22×C4×C11C22×C411yescharacteristic
189C22×C4×C11C22×C411yescharacteristic
190C22×C4×C11C22×C411yescharacteristic
191C22×C4×C11C22×C411yescharacteristic
192C22×C4×C11C2×D412yes—
193C22×C4×C11#4112yes—
194C22×C4×C11C2411yescharacteristic
195C2×C22⋊D11—22no—
196C2×C22⋊D11—22no—
197C2×C22⋊D11—22no—
198C2×C22⋊D11—22no—
199C2×C22⋊D11—41no—
200C2×C22⋊D11—41no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—41no—
204C22×Dic11C22×C411yescharacteristic
205C22×Dic11C22×C411yescharacteristic
206C22×Dic11C22×C411yescharacteristic
207C22×Dic11C22×C411yescharacteristic
208#4339—44no—
209#4339—44no—
210#4339—44no—
211#4339—44no—
212C2×D44—22no—
213C2×D44—22no—
214C2×D44—22no—
215C2×D44—22no—
216C2×D44—22no—
217C2×D44—22no—
218C2×D44—22no—
219C2×D44—41no—
220C2×D44—41no—
221C2×D44—41no—
222C2×D44—41no—
223C2×D44—41no—
224C2×D44—41no—
225C2×D44—41no—
226C2×D44C22⋊C414yes—
227C2×C4×D11—22no—
228C2×C4×D11—22no—
229C2×C4×D11—22no—
230C2×C4×D11—22no—
231C2×C4×D11—21no—
232C2×C4×D11—21no—
233C2×C4×D11—21no—
234C2×C4×D11—21no—
235C2×C4×D11—21no—
236C2×C4×D11—21no—
237C2×C4×D11—21no—
238C2×C4×D11—21no—
239C2×C4×D11—21no—
240C2×C4×D11—21no—
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—41no—
252C2×C4×D11—41no—
253C2×C4×D11—44no—
254C2×C4×D11—44no—
255C2×C4×D11—44no—
256C2×C4×D11—44no—
257C2×C4×D11C2×D412yes—
258C2×C4×D11C2×D412yes—
259C2×C4×D11C2×D412yes—
260C2×C4×D11C2×D412yes—
261C2×Dic22—22no—
262C2×Dic22—22no—
263C2×Dic22—41no—
264C2×C8×C11—21no—
265C2×C8×C11—21no—
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×C11C2×D412yes—
275C2×C8×C11C2×D412yes—
276C11×C4⋊C4—22no—
277C11×C4⋊C4—22no—
278C11×C22⋊C4—22no—
279C11×C22⋊C4—22no—
280C42×C11—21no—
281C42×C11—21no—
282C42×C11C2×D412yes—
283C42×C11C2×D412yes—
284(C2×D11)⋊C4—22no—
285(C2×D11)⋊C4—22no—
286(C2×D11)⋊C4—22no—
287(C2×D11)⋊C4—22no—
288(C2×D11)⋊C4—22no—
289(C2×D11)⋊C4—22no—
290(C2×D11)⋊C4C22⋊C414yes—
291(C2×D11)⋊C4C22⋊C414yes—
292C4⋊Dic11—22no—
293C4⋊Dic11—22no—
294C4⋊Dic11—22no—
295C4⋊Dic11C22⋊C414yes—
296C2×C11⋊C8—21no—
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—
308#4313—44no—
309#4313—44no—
310#4313—44no—
311C8×D11—44no—
312C2×#525—111no—
313C2×#436—111no—
314C2×#435—111no—
315C2×#408—111no—
316C2×#407—111no—
317#1955—111no—
318#1954—111no—
319#1870—111no—
320#1870—111no—
321#1870—111no—
322#1869—111no—
323#1798—111no—
324#1780—111no—
325#1779—111no—
326#1750D1111yescharacteristic, complemented
327C23×C11—21no—
328C23×C11—21no—
329C23×C11—21no—
330C23×C11—21no—
331C23×C11—21no—
332C23×C11—21no—
333C23×C11C4×D412yes—
334C23×C11C23×C411yescharacteristic
335C22×D11—21no—
336C22×D11—21no—
337C22×D11—21no—
338C22×D11—21no—
339C22×D11—21no—
340C22×D11—21no—
341C22×D11—21no—
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—44no—
361C22×D11—44no—
362C22×D11—44no—
363C22×D11—44no—
364C22×D11—44no—
365C22×D11—44no—
366C22×D11—44no—
367C22×D11C2×C22⋊C412yes—
368C22×D11C2×C22⋊C412yes—
369C22×D11#13112yes—
370C2×C4×C11—21no—
371C2×C4×C11—21no—
372C2×C4×C11—21no—
373C2×C4×C11—21no—
374C2×C4×C11—21no—
375C2×C4×C11—21no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—21no—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11C2×C22⋊C412yes—
387C2×C4×C11C2×C22⋊C412yes—
388C2×C4×C11C4×D412yes—
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C22×D411yescharacteristic
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C2×#4111yescharacteristic
393C2×C4×C11H(5,𝔽2)11yescharacteristic
394C2×C4×C11H(5,𝔽2)11yescharacteristic
395C22⋊D11—44no—
396C22⋊D11—44no—
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×Dic11—21no—
406C2×Dic11—21no—
407C2×Dic11—44no—
408C2×Dic11C2×C22⋊C412yes—
409C2×Dic11C2×C22⋊C412yes—
410D44—44no—
411D44—44no—
412D44—44no—
413D44—44no—
414D44—44no—
415C4×D11—22no—
416C4×D11—22no—
417C4×D11—22no—
418C4×D11—22no—
419C4×D11—22no—
420C4×D11—22no—
421C4×D11—22no—
422C4×D11—22no—
423C4×D11—44no—
424C4×D11—44no—
425C4×D11—41no—
426C4×D11—41no—
427C4×D11—41no—
428C4×D11—41no—
429C4×D11—41no—
430C4×D11—41no—
431C4×D11—41no—
432C4×D11—41no—
433Dic22—44no—
434C8×C11—22no—
435C8×C11—22no—
436C8×C11—41no—
437C8×C11—41no—
438C11⋊C8—41no—
439C11⋊C8—41no—
440C11⋊C8—41no—
441C11⋊C8—41no—
442C22×#41—111no—
443C24×C4—111no—
444C22×M16—111no—
445C22×M16—111no—
446C22×M16—111no—
447C23×C8—111no—
448#525—224no—
449#525—224no—
450C2×#123—111no—
451C2×#123—111no—
452C2×C22⋊Q8—111no—
453C2×C22⋊Q8—111no—
454C2×#121—111no—
455C2×#121—111no—
456C2×#120—111no—
457C2×#120—111no—
458C2×C4×D4—111no—
459C2×C4×D4—111no—
460C2×C4×D4—111no—
461C2×C4×D4—111no—
462C2×#117C2×D1111yescharacteristic
463#436—224no—
464#435—224no—
465C2×C4⋊C8—111no—
466C2×C4⋊C8—111no—
467#408—224no—
468#407—224no—
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⋊C8—111no—
479C2×C22⋊C8—111no—
480C2×C22⋊C8—111no—
481C2×C22⋊C8—111no—
482C2×C22⋊C8—111no—
483C2×C22⋊C8C2×D1111yescharacteristic
484C2×C22⋊C8C2×D1111yescharacteristic
485C2×#97C2×D1111yescharacteristic, complemented
486C2×C4×C8C2×D1111yescharacteristic, complemented
487#336—111no—
488#336—111no—
489#336C2×D1111yescharacteristic, complemented
490#336C2×D1111yescharacteristic, complemented
491C22×C11—22no—
492C22×C11—22no—
493C22×C11—22no—
494C22×C11—41no—
495C22×C11—41no—
496C22×C11—41no—
497C22×C11—41no—
498C22×C11C22×C22⋊C411yescharacteristic
499C22×C11C2×C4×D411yescharacteristic
500C22×C11#51811yescharacteristic
501C22×C11C2×#13111yescharacteristic
502C22×C11#56811yescharacteristic
503C22×C11#56811yescharacteristic
504C22×C11#56811yescharacteristic
505C2×D11—22no—
506C2×D11—22no—
507C2×D11—22no—
508C2×D11—22no—
509C2×D11—22no—
510C2×D11—22no—
511C2×D11—22no—
512C2×D11—22no—
513C2×D11—22no—
514C2×D11—416no—
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—
529C2×D11—41no—
530C2×D11—41no—
531C2×D11—41no—
532C2×D11—41no—
533C2×D11—41no—
534C4×C11—22no—
535C4×C11—22no—
536C4×C11—22no—
537C4×C11—41no—
538C4×C11—41no—
539C4×C11D4211yescharacteristic
540C4×C11D4211yescharacteristic
541C4×C11#54611yescharacteristic
542C4×C11#54611yescharacteristic
543Dic11—22no—
544Dic11—22no—
545Dic11—41no—
546Dic11—41no—
547C25—111no—
548C2×#41—222no—
549C2×#41—222no—
550C2×#41—222no—
551C2×#41—222no—
552C2×#41—441no—
553C2×#41—441no—
554C22×Q8—111no—
555C22×D4—111no—
556C22×D4—111no—
557C22×D4—111no—
558C22×D4—111no—
559C22×D4—111no—
560C22×D4—111no—
561C22×D4—111no—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—111no—
565C23×C4—111no—
566C23×C4—111no—
567C23×C4—111no—
568C23×C4—111no—
569C23×C4—222no—
570C23×C4—222no—
571C23×C4—222no—
572C23×C4—222no—
573C23×C4—441no—
574C23×C4—441no—
575C23×C4C22×D1111yescharacteristic
576C2×M16—222no—
577C2×M16—222no—
578C2×M16—222no—
579C2×M16—222no—
580C2×M16—222no—
581C2×M16—222no—
582C2×M16—441no—
583C2×M16—441no—
584C2×M16—441no—
585C22×C8—111no—
586C22×C8—111no—
587C22×C8—111no—
588C22×C8—111no—
589C22×C8—222no—
590C22×C8—222no—
591C22×C8—441no—
592C22×C8C22×D1111yescharacteristic
593C22×C8C22×D1111yescharacteristic
594C22×C8C22×D1111yescharacteristic
595C22×C8C22×D1111yescharacteristic
596#123—224no—
597#123—224no—
598C22⋊Q8—224no—
599C22⋊Q8—224no—
600#121—224no—
601#121—224no—
602#120—224no—
603#120—224no—
604C4×D4—114no—
605C4×D4—114no—
606C4×D4—222no—
607C4×D4—222no—
608C4×D4—222no—
609C4×D4—222no—
610C4×D4—222no—
611C4×D4—222no—
612#117—22no—
613#117—22no—
614C2×C4⋊C4—111no—
615C2×C4⋊C4—111no—
616C2×C4⋊C4—111no—
617C2×C4⋊C4—111no—
618C2×C4⋊C4C4×D1111yescharacteristic
619C2×C4⋊C4C4×D1111yescharacteristic
620C2×C22⋊C4—111no—
621C2×C22⋊C4—111no—
622C2×C22⋊C4—111no—
623C2×C22⋊C4—111no—
624C2×C22⋊C4—111no—
625C2×C22⋊C4—111no—
626C2×C22⋊C4—111no—
627C2×C22⋊C4—111no—
628C2×C22⋊C4C4×D1111yescharacteristic
629C2×C22⋊C4C4×D1111yescharacteristic
630C2×C42C22×D1111yescharacteristic
631C2×C42C22×D1111yescharacteristic
632C4⋊C8—222no—
633C4⋊C8—222no—
634C22⋊C8—22no—
635C22⋊C8—222no—
636C22⋊C8—222no—
637C22⋊C8—222no—
638C22⋊C8—222no—
639C22⋊C8—222no—
640C22⋊C8—222no—
641C22⋊C8—222no—
642C22⋊C8—222no—
643C22⋊C8—222no—
644C22⋊C8—222no—
645C22⋊C8—441no—
646C22⋊C8—441no—
647C22⋊C8—441no—
648C22⋊C8—441no—
649C22⋊C8D4414yescomplemented
650#97—22no—
651C4×C8—22no—
652C2×C11—42no—
653C2×C11D4×C22⋊C411yescharacteristic
654C2×C11#287911yescharacteristic
655C2×C11#288011yescharacteristic
656C2×C11#293011yescharacteristic
657C2×C11#293311yescharacteristic
658C2×C11#297611yescharacteristic
659C2×C11#297811yescharacteristic
660D11—42no—
661D11—42no—
662D11—42no—
663D11—81no—
664C24—111no—
665C24—111no—
666C24—111no—
667C24—111no—
668C24—222no—
669C24—222no—
670C24—222no—
671C24—441no—
672C24—441no—
673C24—441no—
674C24—441no—
675C24C2×C4×D1111yescharacteristic
676#41—444no—
677#41—444no—
678#41—444no—
679#41—444no—
680C2×Q8—222no—
681C2×Q8—222no—
682C2×Q8—441no—
683C2×D4—114no—
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—441no—
696C2×D4—441no—
697C2×D4—441no—
698C2×D4—441no—
699C2×D4—441no—
700C2×D4—441no—
701C2×D4—441no—
702C2×D4—441no—
703C2×D4—441no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—111no—
709C22×C4—111no—
710C22×C4—112no—
711C22×C4—112no—
712C22×C4—112no—
713C22×C4—112no—
714C22×C4—111no—
715C22×C4—111no—
716C22×C4—222no—
717C22×C4—222no—
718C22×C4—222no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—221no—
727C22×C4—222no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—221no—
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—221no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—441no—
743C22×C4—441no—
744C22×C4—444no—
745C22×C4—444no—
746C22×C4—444no—
747C22×C4—444no—
748C22×C4—441no—
749C22×C4C2×C4×D1111yescharacteristic
750C22×C4C2×C4×D1111yescharacteristic
751C22×C4C2×C4×D1111yescharacteristic
752C22×C4C2×C4×D1111yescharacteristic
753C22×C4C2×C4×D1111yescharacteristic
754C22×C4C2×D4412yes—
755C22×C4#433912yes—
756C22×C4C23×D1111yescharacteristic
757M16—444no—
758M16—444no—
759M16—444no—
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—21no—
769C2×C8—21no—
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—221no—
781C2×C8—221no—
782C2×C8—444no—
783C2×C8C2×D4412yes—
784C2×C8C2×D4412yes—
785C4⋊C4—22no—
786C4⋊C4—22no—
787C4⋊C4—114no—
788C4⋊C4—222no—
789C4⋊C4—222no—
790C4⋊C4—222no—
791C22⋊C4—22no—
792C22⋊C4—22no—
793C22⋊C4—114no—
794C22⋊C4—114no—
795C22⋊C4—222no—
796C22⋊C4—222no—
797C22⋊C4—222no—
798C22⋊C4—222no—
799C22⋊C4—222no—
800C22⋊C4—222no—
801C42—21no—
802C42—21no—
803C42D4×D1112yes—
804C42D4×D1112yes—
805C11#2240011yescharacteristic, complemented, Sylow
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—112no—
813C23—112no—
814C23—112no—
815C23—221no—
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—
835C23—221no—
836C23—221no—
837C23—221no—
838C23—221no—
839C23—221no—
840C23—444no—
841C23—444no—
842C23—444no—
843C23—444no—
844C23—444no—
845C23—444no—
846C23—444no—
847C23C4×D4412yes—
848C23C22×C4×D1111yescharacteristic
849Q8—444no—
850D4—444no—
851D4—444no—
852D4—444no—
853D4—444no—
854D4—444no—
855D4—444no—
856D4—444no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—112no—
874C2×C4—112no—
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—221no—
891C2×C4—221no—
892C2×C4—221no—
893C2×C4—444no—
894C2×C4—444no—
895C2×C4—444no—
896C2×C4—441no—
897C2×C4—441no—
898C2×C4—441no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4—441no—
902C2×C4—441no—
903C2×C4—441no—
904C2×C4C4×D4412yes—
905C2×C4C22⋊C4×D1112yes—
906C2×C4C22⋊C4×D1112yes—
907C2×C4C22×D4411yescharacteristic
908C2×C4C2×#433911yescharacteristic
909C2×C4C2×D4×D1111yescharacteristic
910C2×C4C2×D4×D1111yescharacteristic
911C2×C4#6704211yescharacteristic
912C2×C4#6704211yescharacteristic
913C8—22no—
914C8—22no—
915C8—41no—
916C8—41no—
917C8—441no—
918C8—441no—
919C8—441no—
920C8—441no—
921C22—22no—
922C22—22no—
923C22—22no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—222no—
929C22—222no—
930C22—222no—
931C22—222no—
932C22—222no—
933C22—222no—
934C22—222no—
935C22—222no—
936C22—222no—
937C22—4416no—
938C22—441no—
939C22—441no—
940C22—441no—
941C22—441no—
942C22—441no—
943C22—441no—
944C22—441no—
945C22—441no—
946C22—441no—
947C22—441no—
948C22—441no—
949C22—441no—
950C22—441no—
951C22—441no—
952C22—441no—
953C22—441no—
954C22—441no—
955C22—441no—
956C22—441no—
957C22C2×C4×D4411yescharacteristic
958C22C2×C22⋊C4×D1111yescharacteristic
959C22#1062305211yescharacteristic
960C22D11×#13111yescharacteristic
961C22#1062328111yescharacteristic
962C22#1062328111yescharacteristic
963C22#1062328111yescharacteristic
964C4—22no—
965C4—22no—
966C4—22no—
967C4—41no—
968C4—41no—
969C4—222no—
970C4—222no—
971C4—441no—
972C4—441no—
973C4D4×D4411yescharacteristic
974C4D4×D4411yescharacteristic
975C4#1062308111yescharacteristic
976C4#1062308111yescharacteristic
977C2—42no—
978C2—442no—
979C2—442no—
980C2—442no—
981C2—881no—
982C2C22⋊C4×D4411yescharacteristic
983C2#1307705811yescharacteristic
984C2#1307706411yescharacteristic
985C2#1307732111yescharacteristic
986C2#1307734411yescharacteristic
987C2#1307766211yescharacteristic
988C2#1307767711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1750C2
prime radicalC2×#10623055C2
cosocleC22×C4×C11C24
hypercenter#1750D11
hypocenterC11#22400
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. C2×#10622301C2semidirect
3. C2×#10622319C2semidirect
4. C2×#10622340C2semidirect
5. C2×#10622339C2semidirect
6. #13069414C2semidirect
7. #13069410C2semidirect
8. #13068912C2semidirect
9. #13068912C2semidirect
10. #13068912C2semidirect
11. #13068907C2semidirect
12. #13068600C2semidirect
13. #13068527C2semidirect
14. #13068525C2semidirect
15. C11×#1750C2semidirect
21. C22×#4313C22semidirect
22. C22×C8×D11C22semidirect
39. C2×C11×#97C22semidirect
40. C2×C4×C8×C11C22semidirect
49. C2×(C2×D11)⋊C8C22semidirect
50. C2×(C2×D11)⋊C8C22semidirect
51. C2×(C2×D11)⋊C8C22semidirect
52. C2×(C2×D11)⋊C8C22semidirect
53. C2×(C2×D11)⋊C8C22semidirect
54. C2×(C2×D11)⋊C8C22semidirect
55. C2×C4⋊(C11⋊C8)C22semidirect
56. C2×C4⋊(C11⋊C8)C22semidirect
61. C11×#336C22semidirect
62. C11×#336C22semidirect
63. #10622162C22semidirect
64. #10622162C22semidirect
151. C11×C22⋊C8D4semidirect
326. #1750D11semidirect
485. C2×#97C2×D11semidirect
486. C2×C4×C8C2×D11semidirect
489. #336C2×D11semidirect
490. #336C2×D11semidirect
649. C22⋊C8D44semidirect
805. C11#22400semidirect

Maximal subgroups

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

subgroupindex
C2×#106230552
C2×#106223012
C2×#106223192
C2×#106223402
C2×#106223392
#130694142
#130694102
#130689122
#130689072
#130686002
#130685272
#130685252
C11×#17502
#2240011