Finite Group Databasebeta

← #14769837

Subgroups — #14769837

Order 2816.

1202 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622624C211yesmaximal, characteristic, complemented
2C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
3#13069557C211yesmaximal, characteristic, complemented
4#13069553C211yesmaximal, characteristic, complemented
5#13068914C211yesmaximal, characteristic, complemented
6#13068909C211yesmaximal, characteristic, complemented
7#13068909C211yesmaximal, characteristic, complemented
8#13068909C211yesmaximal, characteristic, complemented
9#13068687C211yesmaximal, characteristic, complemented
10#13068684C211yesmaximal, characteristic, complemented
11#13068600C211yesmaximal, characteristic, complemented
12#13068382C211yesmaximal, characteristic, complemented
13#13068313C211yesmaximal, characteristic, complemented
14C2×#10622162C211yesmaximal, characteristic, complemented
15C2×C11×#529C211yesmaximal, characteristic
16C11×#529—24no—
17C11×#529—24no—
18C2×C11×#126C411yescharacteristic
19C2×C11×#126C411yescharacteristic
20C2×C11×#125C411yescharacteristic
21C2×C11×#124C411yescharacteristic
22C2×C11×#123C411yescharacteristic
23C2×C11×#123C411yescharacteristic
24C2×C11×C22⋊Q8C411yescharacteristic
25C2×C11×#121C411yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic
31C2×C11×#117C2211yescharacteristic
32C22×C42×C11C2211yescharacteristic
33C22×#4318C2211yescharacteristic
34C23×C11⋊C8C2211yescharacteristic
35C23×C11⋊C8C2211yescharacteristic
36C23×C11⋊C8C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45#10622624—24no—
46D4×C11⋊C8—24no—
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49C2×#66867C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622162C2211yescharacteristic
52#10622162C2211yescharacteristic
53#10622162C2211yescharacteristic
54#10622162C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11C2×C411yescharacteristic
64C22×D4×C11C2×C411yescharacteristic
65C22×D4×C11C2×C411yescharacteristic
66C22×D4×C11C2×C411yescharacteristic
67C23×C4×C11C2×C411yescharacteristic
68C23×C4×C11C2×C411yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C11×#126—24no—
73C11×#126—24no—
74C11×#125—24no—
75C11×#124—24no—
76C11×#123—24no—
77C11×#123—24no—
78C11×C22⋊Q8—24no—
79C11×#121—24no—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11D414yes—
87C4×D4×C11D414yes—
88C11×#117—22no—
89C11×#117—22no—
90C11×#117—22no—
91C11×#117—22no—
92C2×C11×C4⋊C4C2×C411yescharacteristic
93C2×C11×C4⋊C4C2×C411yescharacteristic
94C2×C11×C4⋊C4C2×C411yescharacteristic
95C2×C11×C4⋊C4C2×C411yescharacteristic
96C2×C11×C4⋊C4C2×C411yescharacteristic
97C2×C11×C4⋊C4C2×C411yescharacteristic
98C2×C11×C4⋊C4C2×C411yescharacteristic
99C2×C11×C4⋊C4C2×C411yescharacteristic
100C2×C11×C4⋊C4C2×C411yescharacteristic
101C2×C11×C4⋊C4C2×C411yescharacteristic
102C2×C11×C22⋊C4C2×C411yescharacteristic
103C2×C11×C22⋊C4C2×C411yescharacteristic
104C2×C11×C22⋊C4C2×C411yescharacteristic
105C2×C11×C22⋊C4C2×C411yescharacteristic
106C2×C11×C22⋊C4C2×C411yescharacteristic
107C2×C11×C22⋊C4C2×C411yescharacteristic
108C2×C11×C22⋊C4C2×C411yescharacteristic
109C2×C11×C22⋊C4C2×C411yescharacteristic
110C2×C11×C22⋊C4C2×C411yescharacteristic
111C2×C11×C22⋊C4C2×C411yescharacteristic
112C2×C42×C11—22no—
113C2×C42×C11—22no—
114C2×C42×C11C2×C411yescharacteristic
115C2×C42×C11C2×C411yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C2×C42×C11C2311yescharacteristic
119C2×C42×C11C2311yescharacteristic
120C2×#4318—22no—
121C2×#4318—22no—
122C2×#4318—41no—
123C22×C11⋊C8—22no—
124C22×C11⋊C8—22no—
125C22×C11⋊C8—22no—
126C22×C11⋊C8—22no—
127C22×C11⋊C8—22no—
128C22×C11⋊C8—22no—
129C22×C11⋊C8—41no—
130C22×C11⋊C8—41no—
131C22×C11⋊C8—41no—
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136C22×C11⋊C8C2311yescharacteristic
137C22×C11⋊C8C2311yescharacteristic
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C22⋊(C11⋊C8)—22no—
141C22⋊(C11⋊C8)—22no—
142C22⋊(C11⋊C8)—22no—
143C22⋊(C11⋊C8)—22no—
144C22⋊(C11⋊C8)—22no—
145C22⋊(C11⋊C8)—22no—
146C22⋊(C11⋊C8)—41no—
147C22⋊(C11⋊C8)—41no—
148C4⋊(C11⋊C8)—22no—
149C4⋊(C11⋊C8)—22no—
150#66867—22no—
151C4×C11⋊C8—22no—
152#22470—111nomaximal, Sylow
153C24×C11C22×C411yescharacteristic
154C24×C11C22×C411yescharacteristic
155C24×C11C22×C411yescharacteristic
156C2×Q8×C11—22no—
157C2×Q8×C11—22no—
158C2×Q8×C11—41no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C2×D4×C11—22no—
163C2×D4×C11—22no—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11—41no—
167C2×D4×C11C22⋊C414yes—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
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—41no—
188C22×C4×C11C22×C411yescharacteristic
189C22×C4×C11C22×C411yescharacteristic
190C22×C4×C11C22×C411yescharacteristic
191C22×C4×C11C22×C411yescharacteristic
192C22×C4×C11C22×C411yescharacteristic
193C22×C4×C11C22×C411yescharacteristic
194C22×C4×C11C22×C411yescharacteristic
195C22×C4×C11C22×C411yescharacteristic
196C22×C4×C11C22×C411yescharacteristic
197C22×C4×C11C22×C411yescharacteristic
198C22×C4×C11C22×C411yescharacteristic
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2×D412yes—
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2411yescharacteristic
204C11×C4⋊C4—22no—
205C11×C4⋊C4—22no—
206C11×C4⋊C4—22no—
207C11×C4⋊C4—22no—
208C11×C4⋊C4—22no—
209C11×C4⋊C4—22no—
210C11×C4⋊C4—22no—
211C11×C4⋊C4—22no—
212C11×C4⋊C4—22no—
213C11×C4⋊C4C22⋊C414yes—
214C11×C22⋊C4—22no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4C22⋊C414yes—
223C11×C22⋊C4C22⋊C414yes—
224C42×C11—22no—
225C42×C11—22no—
226C42×C11—21no—
227C42×C11—21no—
228C42×C11—21no—
229C42×C11—21no—
230C42×C11—21no—
231C42×C11—21no—
232C42×C11C2×D412yes—
233C42×C11C2×D412yes—
234#4318—44no—
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—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—44no—
258C2×C11⋊C8—44no—
259C2×C11⋊C8—44no—
260C2×C11⋊C8#4112yes—
261C2×C11⋊C8#4112yes—
262C2×#529D1111yescharacteristic
263C2×#435—111no—
264C2×C8×D4—111no—
265#1985—111no—
266#1984—111no—
267#1870—111no—
268#1869—111no—
269#1869—111no—
270#1869—111no—
271#1818—111no—
272#1817—111no—
273#1798—111no—
274#1750—111no—
275#1729—111no—
276C2×#336—111no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11C2×C22⋊C412yes—
295C23×C11C2×C22⋊C412yes—
296C23×C11#13112yes—
297C23×C11#13112yes—
298C23×C11C23×C411yescharacteristic
299Q8×C11—44no—
300D4×C11—28no—
301D4×C11—44no—
302D4×C11—44no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—44no—
340C2×C4×C11—44no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11C2×C22⋊C412yes—
346C2×C4×C11C2×C22⋊C412yes—
347C2×C4×C11C2×C22⋊C412yes—
348C2×C4×C11C2×C22⋊C412yes—
349C2×C4×C11#13112yes—
350C2×C4×C11C22×D411yescharacteristic
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11C2×#4111yescharacteristic
353C2×C4×C11C2×#4111yescharacteristic
354C2×C4×C11H(5,𝔽2)11yescharacteristic
355C2×C4×C112−1+411yescharacteristic
356C11⋊C8—22no—
357C11⋊C8—22no—
358C11⋊C8—41no—
359C11⋊C8—41no—
360C11⋊C8—41no—
361C11⋊C8—41no—
362C11⋊C8—41no—
363C11⋊C8—41no—
364C22×M16—111no—
365C23×C8—111no—
366C23×C8—111no—
367C23×C8—111no—
368#529—24no—
369#529—24no—
370C2×#126Dic1111yescharacteristic
371C2×#126Dic1111yescharacteristic
372C2×#125Dic1111yescharacteristic
373C2×#124Dic1111yescharacteristic
374C2×#123Dic1111yescharacteristic
375C2×#123Dic1111yescharacteristic
376C2×C22⋊Q8Dic1111yescharacteristic
377C2×#121Dic1111yescharacteristic
378C2×C4×Q8C2×D1111yescharacteristic
379C2×C4×D4C2×D1111yescharacteristic
380C2×C4×D4C2×D1111yescharacteristic
381C2×C4×D4C2×D1111yescharacteristic
382C2×#117C2×D1111yescharacteristic
383C2×#117C2×D1111yescharacteristic
384C22×C42C2×D1111yescharacteristic
385#435—224no—
386C8×D4—224no—
387C2×C4⋊C8—111no—
388C2×C4⋊C8—111no—
389C2×C22⋊C8—111no—
390C2×C22⋊C8—111no—
391C2×C22⋊C8—111no—
392C2×C22⋊C8—111no—
393C2×C22⋊C8—111no—
394C2×C22⋊C8—111no—
395C2×C22⋊C8—111no—
396C2×C22⋊C8—111no—
397C2×#97—111no—
398C2×C4×C8—111no—
399#336—111no—
400#336—111no—
401#336—111no—
402#336—111no—
403#336—111no—
404#336—111no—
405#336—111no—
406#336—111no—
407#336—111no—
408#336—111no—
409#336—111no—
410#336—111no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11—41no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—41no—
431C22×C11#40814yes—
432C22×C11C22×C22⋊C411yescharacteristic
433C22×C11C4×#4111yescharacteristic
434C22×C11#52011yescharacteristic
435C22×C11C2×#13111yescharacteristic
436C22×C11C2×#13111yescharacteristic
437C22×C11C2×#13111yescharacteristic
438C22×C11#56811yescharacteristic
439C4×C11—22no—
440C4×C11—22no—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—22no—
444C4×C11—41no—
445C4×C11—41no—
446C4×C11—41no—
447C4×C11—41no—
448C4×C11—41no—
449C4×C11—41no—
450C4×C11#54611yescharacteristic
451C4×C11#54611yescharacteristic
452C4×C11#54711yescharacteristic
453C4×C11#54711yescharacteristic
454C22×Q8C2×Dic1111yescharacteristic
455C22×D4C2×Dic1111yescharacteristic
456C22×D4C2×Dic1111yescharacteristic
457C22×D4C2×Dic1111yescharacteristic
458C23×C4C2×Dic1111yescharacteristic
459C23×C4C2×Dic1111yescharacteristic
460C23×C4C22×D1111yescharacteristic
461C23×C4C22×D1111yescharacteristic
462C23×C4C22×D1111yescharacteristic
463C2×M16—222no—
464C2×M16—222no—
465C2×M16—441no—
466C22×C8—111no—
467C22×C8—111no—
468C22×C8—111no—
469C22×C8—111no—
470C22×C8—111no—
471C22×C8—111no—
472C22×C8—111no—
473C22×C8—111no—
474C22×C8—222no—
475C22×C8—222no—
476C22×C8—222no—
477C22×C8—222no—
478C22×C8—222no—
479C22×C8—222no—
480C22×C8—441no—
481C22×C8—441no—
482C22×C8—441no—
483#126—24no—
484#126—24no—
485#125—24no—
486#124—24no—
487#123—24no—
488#123—24no—
489C22⋊Q8—24no—
490#121—24no—
491C4×Q8—22no—
492C4×Q8—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4C22⋊D1114yes—
498C4×D4C22⋊D1114yes—
499#117—22no—
500#117—22no—
501#117—22no—
502#117—22no—
503C2×C4⋊C4C2×Dic1111yescharacteristic
504C2×C4⋊C4C2×Dic1111yescharacteristic
505C2×C4⋊C4C2×Dic1111yescharacteristic
506C2×C4⋊C4C2×Dic1111yescharacteristic
507C2×C4⋊C4C2×Dic1111yescharacteristic
508C2×C4⋊C4C2×Dic1111yescharacteristic
509C2×C4⋊C4C2×Dic1111yescharacteristic
510C2×C4⋊C4C2×Dic1111yescharacteristic
511C2×C4⋊C4C2×Dic1111yescharacteristic
512C2×C4⋊C4C2×Dic1111yescharacteristic
513C2×C22⋊C4C2×Dic1111yescharacteristic
514C2×C22⋊C4C2×Dic1111yescharacteristic
515C2×C22⋊C4C2×Dic1111yescharacteristic
516C2×C22⋊C4C2×Dic1111yescharacteristic
517C2×C22⋊C4C2×Dic1111yescharacteristic
518C2×C22⋊C4C2×Dic1111yescharacteristic
519C2×C22⋊C4C2×Dic1111yescharacteristic
520C2×C22⋊C4C2×Dic1111yescharacteristic
521C2×C22⋊C4C2×Dic1111yescharacteristic
522C2×C22⋊C4C2×Dic1111yescharacteristic
523C2×C42—22no—
524C2×C42—22no—
525C2×C42C2×Dic1111yescharacteristic
526C2×C42C2×Dic1111yescharacteristic
527C2×C42C22×D1111yescharacteristic
528C2×C42C22×D1111yescharacteristic
529C2×C42C22×D1111yescharacteristic
530C2×C42C22×D1111yescharacteristic
531C4⋊C8—222no—
532C4⋊C8—222no—
533C22⋊C8—222no—
534C22⋊C8—222no—
535C22⋊C8—222no—
536C22⋊C8—222no—
537C22⋊C8—222no—
538C22⋊C8—222no—
539C22⋊C8—441no—
540C22⋊C8—441no—
541#97—222no—
542C4×C8—222no—
543C2×C11—24no—
544C2×C11—42no—
545C2×C11—81no—
546C2×C11#233911yescharacteristic
547C2×C11C2×#40811yescharacteristic
548C2×C11#288011yescharacteristic
549C2×C11#296611yescharacteristic
550C2×C11#296811yescharacteristic
551C2×C11#299211yescharacteristic
552C2×C11#299411yescharacteristic
553C24C22×Dic1111yescharacteristic
554C24C22×Dic1111yescharacteristic
555C24C22×Dic1111yescharacteristic
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—41no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—41no—
567C2×D4C22⋊Dic1114yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—41no—
588C22×C4C22×Dic1111yescharacteristic
589C22×C4C22×Dic1111yescharacteristic
590C22×C4C22×Dic1111yescharacteristic
591C22×C4C22×Dic1111yescharacteristic
592C22×C4C22×Dic1111yescharacteristic
593C22×C4C22×Dic1111yescharacteristic
594C22×C4C22×Dic1111yescharacteristic
595C22×C4C22×Dic1111yescharacteristic
596C22×C4C22×Dic1111yescharacteristic
597C22×C4C22×Dic1111yescharacteristic
598C22×C4C22×Dic1111yescharacteristic
599C22×C4C2×C22⋊D1112yes—
600C22×C4C2×C22⋊D1112yes—
601C22×C4C2×C22⋊D1112yes—
602C22×C4C2×C22⋊D1112yes—
603C22×C4C23×D1111yescharacteristic
604M16—444no—
605C2×C8—112no—
606C2×C8—112no—
607C2×C8—221no—
608C2×C8—221no—
609C2×C8—221no—
610C2×C8—221no—
611C2×C8—221no—
612C2×C8—221no—
613C2×C8—221no—
614C2×C8—221no—
615C2×C8—221no—
616C2×C8—221no—
617C2×C8—221no—
618C2×C8—221no—
619C2×C8—221no—
620C2×C8—221no—
621C2×C8—221no—
622C2×C8—221no—
623C2×C8—221no—
624C2×C8—221no—
625C2×C8—221no—
626C2×C8—221no—
627C2×C8—221no—
628C2×C8—221no—
629C2×C8—444no—
630C2×C8—444no—
631C2×C8—444no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4C22⋊Dic1114yes—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4C22⋊Dic1114yes—
651C22⋊C4C22⋊Dic1114yes—
652C42—22no—
653C42—22no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42C2×C22⋊D1112yes—
661C42C2×C22⋊D1112yes—
662C11#2247011yescharacteristic, complemented, Sylow
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23#6700112yes—
681C23#6700112yes—
682C23C2×C22⋊Dic1112yes—
683C23C2×C22⋊Dic1112yes—
684C23C23×Dic1111yescharacteristic
685Q8—44no—
686D4—28no—
687D4—44no—
688D4—44no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4#6700112yes—
732C2×C4C2×C22⋊Dic1112yes—
733C2×C4C2×C22⋊Dic1112yes—
734C2×C4C2×C22⋊Dic1112yes—
735C2×C4C2×C22⋊Dic1112yes—
736C2×C4#41×D1111yescharacteristic
737C2×C4#41×D1111yescharacteristic
738C2×C4#6704211yescharacteristic
739C2×C4#6704311yescharacteristic
740C2×C4C22×C22⋊D1111yescharacteristic
741C2×C4C22×C22⋊D1111yescharacteristic
742C8—222no—
743C8—222no—
744C8—441no—
745C8—441no—
746C8—441no—
747C8—441no—
748C8—441no—
749C8—441no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22#1062284714yes—
771C22C2×#6700111yescharacteristic
772C22C2×#6700111yescharacteristic
773C22C2×#6700111yescharacteristic
774C22#1062335011yescharacteristic
775C22#41×Dic1111yescharacteristic
776C22#1062335811yescharacteristic
777C22C22×C22⋊Dic1111yescharacteristic
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—22no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4#1062335511yescharacteristic
790C4#1062335511yescharacteristic
791C4#1062336011yescharacteristic
792C4#1062336011yescharacteristic
793C2—24no—
794C2—42no—
795C2—81no—
796C2#1307144611yescharacteristic
797C2C2×#1062284711yescharacteristic
798C2#1307706511yescharacteristic
799C2#1307759211yescharacteristic
800C2#1307761211yescharacteristic
801C2#1307775511yescharacteristic
802C2#1307777611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#529C2
prime radicalC2×C11×#121C4
cosocleC22×C4×C11C24
hypercenterC2×#529D11
hypocenterC11#22470
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#10622624C2semidirect
2. C2×D4×C11⋊C8C2semidirect
3. #13069557C2semidirect
4. #13069553C2semidirect
5. #13068914C2semidirect
6. #13068909C2semidirect
7. #13068909C2semidirect
8. #13068909C2semidirect
9. #13068687C2semidirect
10. #13068684C2semidirect
11. #13068600C2semidirect
12. #13068382C2semidirect
13. #13068313C2semidirect
14. C2×#10622162C2semidirect
662. C11#22470semidirect

Maximal subgroups

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

subgroupindex
C2×#106226242
C2×D4×C11⋊C82
#130695572
#130695532
#130689142
#130689092
#130686872
#130686842
#130686002
#130683822
#130683132
C2×#106221622
C2×C11×#5292
#2247011