Finite Group Databasebeta

← #17963049

Subgroups — #17963049

Order 4352.

2298 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763756C211yesmaximal, characteristic
2C2×C4⋊C4×#595C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×#595C211yesmaximal, characteristic
4C2×C22⋊C4×#595C211yesmaximal, characteristic
5C2×C4×C22⋊#595C211yesmaximal, characteristic
6C22×(C2×#595)⋊C4C211yesmaximal, characteristic
7#14543964C211yesmaximal, characteristic, complemented
8#14543964C211yesmaximal, characteristic, complemented
9#14543963C211yesmaximal, characteristic, complemented
10#14543963C211yesmaximal, characteristic, complemented
11#14543961C211yesmaximal, characteristic, complemented
12#14543959C211yesmaximal, characteristic, complemented
13#14543957C211yesmaximal, characteristic
14#95×#595C211yesmaximal, characteristic, complemented
15D17×#385C211yesmaximal, characteristic
16C24×#595C2211yescharacteristic
17C24×#595C2211yescharacteristic
18C22×C4⋊#595C2211yescharacteristic
19C22×C4⋊#595C2211yescharacteristic
20C22×C22⋊#595C2211yescharacteristic
21C22×C22⋊#595C2211yescharacteristic
22C22×C4×#595C2211yescharacteristic
23C22×C4×#595C2211yescharacteristic
24C22×C4×#595C2211yescharacteristic
25C22×C4×#595C2211yescharacteristic
26C22×C4×#595C2211yescharacteristic
27C22×C4×#595C2211yescharacteristic
28#11763756C418yescomplemented
29C4⋊C4×#595—24no—
30C22⋊C4×#595—24no—
31C22⋊C4×#595C418yescomplemented
32C4×C22⋊#595—24no—
33C2×(C2×#595)⋊C4—24no—
34C2×(C2×#595)⋊C4C2211yescharacteristic
35C2×(C2×#595)⋊C4C2211yescharacteristic
36C2×(C2×#595)⋊C4C2211yescharacteristic
37C2×(C2×#595)⋊C4C2211yescharacteristic
38C2×(C2×#595)⋊C4C2211yescharacteristic
39C2×(C2×#595)⋊C4C2211yescharacteristic
40C2×(C2×#595)⋊C4C2211yescharacteristic
41C2×(C2×#595)⋊C4C2211yescharacteristic
42C2×(C2×#595)⋊C4C2211yescharacteristic
43C2×(C2×#595)⋊C4C2211yescharacteristic
44C2×(C2×#595)⋊C4C2211yescharacteristic
45C2×(C2×#595)⋊C4C2211yescharacteristic
46C2×(C2×#595)⋊C4C2211yescharacteristic
47C2×(C2×#595)⋊C4C2211yescharacteristic
48C2×(C2×#595)⋊C4C2211yescharacteristic
49C2×(C2×#595)⋊C4C2211yescharacteristic
50C23×C4×D17C2211yescharacteristic
51C2×C4⋊C4×D17C2211yescharacteristic
52C2×C4⋊C4×D17C2211yescharacteristic
53C2×C22⋊C4×D17C2211yescharacteristic
54C2×C22⋊C4×D17C2211yescharacteristic
55#11762684C411yescharacteristic, complemented
56#11762683C411yescharacteristic, complemented
57#11762683C411yescharacteristic, complemented
58#11762682C411yescharacteristic, complemented
59#11762681C411yescharacteristic, complemented
60#11762680C411yescharacteristic, complemented
61#11762680C411yescharacteristic, complemented
62#95×D17C2211yescharacteristic
63#95×D17C2211yescharacteristic
64C17×#385C411yescharacteristic, complemented
65C24×D17C2311yescharacteristic
66C23×#595—22no—
67C23×#595—22no—
68C23×#595—22no—
69C23×#595—22no—
70C23×#595—22no—
71C23×#595—22no—
72C23×#595—22no—
73C23×#595—22no—
74C23×#595—41no—
75C23×#595—41no—
76C23×#595—41no—
77C23×#595—41no—
78C23×#595C2×C414yes—
79C23×#595C2×C414yes—
80C23×#595C2311yescharacteristic
81C23×#595C2311yescharacteristic
82C23×#595C2311yescharacteristic
83C23×#595C2311yescharacteristic
84C23×#595C2311yescharacteristic
85C23×#595C2311yescharacteristic
86C23×#595C2311yescharacteristic
87C23×#595C2311yescharacteristic
88C23×C4×C17C2×C411yescharacteristic
89C23×Dic17C2×C411yescharacteristic
90C22×C4×D17—22no—
91C22×C4×D17—22no—
92C22×C4×D17—22no—
93C22×C4×D17—22no—
94C22×C4×D17—41no—
95C22×C4×D17—41no—
96C22×C4×D17C2×C411yescharacteristic
97C22×C4×D17C2×C411yescharacteristic
98C22×C4×D17C2311yescharacteristic
99C22×C4×D17C2311yescharacteristic
100C22×C4×D17C2311yescharacteristic
101C22×C4×D17C2311yescharacteristic
102C22×C4×D17C2311yescharacteristic
103C22×C4×D17C2311yescharacteristic
104C2×C22⋊#595—22no—
105C2×C22⋊#595—22no—
106C2×C22⋊#595C2×C414yes—
107C2×C22⋊#595C2×C414yes—
108C2×C22⋊#595D414yes—
109C2×C22⋊#595Q814yes—
110C2×C4⋊#595—22no—
111C2×C4⋊#595—22no—
112C2×C4⋊#595—41no—
113C2×C4⋊#595—41no—
114C2×C4⋊#595C2×C414yescomplemented
115C2×C4⋊#595C2×C414yescomplemented
116C2×C4×#595—22no—
117C2×C4×#595—22no—
118C2×C4×#595—22no—
119C2×C4×#595—22no—
120C2×C4×#595—22no—
121C2×C4×#595—22no—
122C2×C4×#595—22no—
123C2×C4×#595—22no—
124C2×C4×#595—22no—
125C2×C4×#595—22no—
126C2×C4×#595—41no—
127C2×C4×#595—41no—
128C2×C4×#595—41no—
129C2×C4×#595—41no—
130C2×C4×#595—41no—
131C2×C4×#595—41no—
132C2×C4×#595C2×C414yescomplemented
133C2×C4×#595C2×C414yescomplemented
134C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
135C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
136C2×C22⋊C4×C17C2×C411yescharacteristic
137C2×C22⋊C4×C17C2×C411yescharacteristic
138C2×C22⋊Dic17C2×C411yescharacteristic
139C2×C22⋊Dic17C2×C411yescharacteristic
140C2×#63227C2×C411yescharacteristic
141C2×#63227C2×C411yescharacteristic
142C2×#63227C2×C411yescharacteristic
143C2×#63227C2×C411yescharacteristic
144C2×C4⋊Dic17C2×C411yescharacteristic, complemented
145C2×C4⋊Dic17C2×C411yescharacteristic, complemented
146C2×#63225C2×C411yescharacteristic, complemented
147C2×#63225C2×C411yescharacteristic, complemented
148C2×#63225C2×C411yescharacteristic, complemented
149C2×#63225C2×C411yescharacteristic, complemented
150C4⋊C4×D17—22no—
151C4⋊C4×D17—22no—
152C4⋊C4×D17—41no—
153C4⋊C4×D17—41no—
154C22⋊C4×D17—22no—
155C22⋊C4×D17—22no—
156C22⋊C4×D17C2×C414yes—
157C22⋊C4×D17C2×C414yes—
158(C2×#595)⋊C4—22no—
159(C2×#595)⋊C4—22no—
160(C2×#595)⋊C4—22no—
161(C2×#595)⋊C4—22no—
162(C2×#595)⋊C4—22no—
163(C2×#595)⋊C4—22no—
164(C2×#595)⋊C4—22no—
165(C2×#595)⋊C4—22no—
166(C2×#595)⋊C4—22no—
167(C2×#595)⋊C4—41no—
168(C2×#595)⋊C4—41no—
169(C2×#595)⋊C4C2×C414yescomplemented
170(C2×#595)⋊C4C2×C414yescomplemented
171(C2×#595)⋊C4C2×C414yescomplemented
172(C2×#595)⋊C4C2×C414yescomplemented
173(C2×#595)⋊C4D414yes—
174C17×#95C2×C411yescharacteristic, complemented
175C17×#95C2×C411yescharacteristic, complemented
176#10587502C2×C411yescharacteristic, complemented
177#10587502C2×C411yescharacteristic, complemented
178#10587502C2×C411yescharacteristic, complemented
179#10587502C2×C411yescharacteristic, complemented
180#10587502C2×C411yescharacteristic, complemented
181#10587502C2×C411yescharacteristic, complemented
182C24×C17C22×C411yescharacteristic
183C23×D17—21no—
184C23×D17—21no—
185C23×D17—21no—
186C23×D17—21no—
187C23×D17—21no—
188C23×D17—21no—
189C23×D17—21no—
190C23×D17—21no—
191C23×D17C22×C411yescharacteristic
192C23×D17C22×C412yes—
193C23×D17C22×C412yes—
194C23×D17C2×D412yes—
195C23×D17C2×Q812yes—
196C23×D17#4112yes—
197C23×D17#4112yes—
198C23×D17C2411yescharacteristic
199C22×#595—21no—
200C22×#595—21no—
201C22×#595—21no—
202C22×#595—21no—
203C22×#595—21no—
204C22×#595—21no—
205C22×#595—21no—
206C22×#595—21no—
207C22×#595—21no—
208C22×#595—21no—
209C22×#595—21no—
210C22×#595—21no—
211C22×#595—21no—
212C22×#595—21no—
213C22×#595—21no—
214C22×#595—21no—
215C22×#595—28no—
216C22×#595—28no—
217C22×#595—21no—
218C22×#595—21no—
219C22×#595—21no—
220C22×#595—21no—
221C22×#595—21no—
222C22×#595—21no—
223C22×#595—21no—
224C22×#595—21no—
225C22×#595—21no—
226C22×#595—21no—
227C22×#595—21no—
228C22×#595—21no—
229C22×#595—21no—
230C22×#595—21no—
231C22×#595—21no—
232C22×#595—21no—
233C22×#595—21no—
234C22×#595—21no—
235C22×#595—21no—
236C22×#595—21no—
237C22×#595—21no—
238C22×#595—21no—
239C22×#595—21no—
240C22×#595—21no—
241C22×#595—28no—
242C22×#595—28no—
243C22×#595—44no—
244C22×#595—44no—
245C22×#595—44no—
246C22×#595—44no—
247C22×#595—44no—
248C22×#595—44no—
249C22×#595—44no—
250C22×#595—44no—
251C22×#595—44no—
252C22×#595—44no—
253C22×#595C22×C412yes—
254C22×#595C22×C412yes—
255C22×#595C22×C412yes—
256C22×#595C22×C412yes—
257C22×#595C22×C412yes—
258C22×#595C22×C412yes—
259C22×#595C22×C412yes—
260C22×#595C22×C412yes—
261C22×#595C2×D412yes—
262C22×#595C2×D412yes—
263C22×#595C2×D412yes—
264C22×#595C2×D412yes—
265C22×#595C2×Q812yes—
266C22×#595C2×Q812yes—
267C22×#595#4112yes—
268C22×#595#4112yes—
269C22×C4×C17—22no—
270C22×C4×C17—22no—
271C22×C4×C17—41no—
272C22×C4×C17C22×C411yescharacteristic
273C22×C4×C17C22×C411yescharacteristic
274C22×C4×C17C22×C411yescharacteristic
275C22×C4×C17C22×C411yescharacteristic
276C22×C4×C17C22×C411yescharacteristic
277C22×C4×C17C22×C411yescharacteristic
278C22×Dic17—22no—
279C22×Dic17—22no—
280C22×Dic17—41no—
281C22×Dic17C22×C411yescharacteristic
282C22×Dic17C22×C411yescharacteristic
283C22×Dic17C22×C411yescharacteristic
284C22×Dic17C22×C411yescharacteristic
285C22×Dic17C22×C411yescharacteristic
286C22×Dic17C22×C411yescharacteristic
287C2×C4×D17—21no—
288C2×C4×D17—21no—
289C2×C4×D17—21no—
290C2×C4×D17—21no—
291C2×C4×D17—21no—
292C2×C4×D17—21no—
293C2×C4×D17—21no—
294C2×C4×D17—21no—
295C2×C4×D17—21no—
296C2×C4×D17—21no—
297C2×C4×D17—21no—
298C2×C4×D17—21no—
299C2×C4×D17—22no—
300C2×C4×D17—22no—
301C2×C4×D17—21no—
302C2×C4×D17—21no—
303C2×C4×D17—21no—
304C2×C4×D17—21no—
305C2×C4×D17—21no—
306C2×C4×D17—21no—
307C2×C4×D17—21no—
308C2×C4×D17—21no—
309C2×C4×D17—21no—
310C2×C4×D17—21no—
311C2×C4×D17—21no—
312C2×C4×D17—21no—
313C2×C4×D17—21no—
314C2×C4×D17—21no—
315C2×C4×D17—21no—
316C2×C4×D17—21no—
317C2×C4×D17—21no—
318C2×C4×D17—21no—
319C2×C4×D17—22no—
320C2×C4×D17—22no—
321C2×C4×D17—44no—
322C2×C4×D17—44no—
323C2×C4×D17—44no—
324C2×C4×D17—44no—
325C2×C4×D17—41no—
326C2×C4×D17—41no—
327C2×C4×D17C22×C412yes—
328C2×C4×D17C22×C412yes—
329C2×C4×D17C22×C412yes—
330C2×C4×D17C22×C412yes—
331C2×C4×D17C2×D412yes—
332C2×C4×D17#4112yes—
333C22⋊#595—28no—
334C22⋊#595C4⋊C4116yescomplemented
335C4⋊#595—28no—
336C4⋊#595—44no—
337C4×#595—28no—
338C4×#595—44no—
339C4×#595—44no—
340C4×#595—44no—
341C4×#595—44no—
342C4×#595—44no—
343C4⋊C4×C17—22no—
344C4⋊C4×C17—41no—
345C22⋊C4×C17—22no—
346C22⋊C4×C17C4214yescomplemented
347C22⋊Dic17—22no—
348C22⋊Dic17C4214yescomplemented
349#63227—22no—
350#63227—22no—
351#63227C4214yescomplemented
352#63227C4214yescomplemented
353C4⋊Dic17—22no—
354C4⋊Dic17—41no—
355#63225—22no—
356#63225—22no—
357#63225—41no—
358#63225—41no—
359#13814—171nomaximal, Sylow
360C23×C17—21no—
361C23×C17—21no—
362C23×C17—21no—
363C23×C17—21no—
364C23×C17C2×C4212yes—
365C23×C17C4×D412yes—
366C23×C17C4×Q812yes—
367C23×C17C23×C411yescharacteristic
368C22×D17—21no—
369C22×D17—21no—
370C22×D17—21no—
371C22×D17—21no—
372C22×D17—22no—
373C22×D17—22no—
374C22×D17—22no—
375C22×D17—22no—
376C22×D17—22no—
377C22×D17—22no—
378C22×D17—22no—
379C22×D17—22no—
380C22×D17—22no—
381C22×D17—22no—
382C22×D17—22no—
383C22×D17—22no—
384C22×D17—22no—
385C22×D17—22no—
386C22×D17—22no—
387C22×D17—22no—
388C22×D17—22no—
389C22×D17—22no—
390C22×D17—22no—
391C22×D17—22no—
392C22×D17—22no—
393C22×D17—22no—
394C22×D17—22no—
395C22×D17—22no—
396C22×D17C2×C4212yes—
397C22×D17C2×C4⋊C414yes—
398C22×D17#11714yes—
399C22×D17C4×D414yes—
400C22×D17C4×D412yes—
401C22×D17C4×Q814yes—
402C22×D17C4×Q812yes—
403C22×D17C23×C411yescharacteristic
404C22×D17C23×C411yescharacteristic
405C22×D17C22×D411yescharacteristic
406C22×D17C22×D411yescharacteristic
407C22×D17C22×Q811yescharacteristic
408C22×D17C2×#4111yescharacteristic
409C22×D17C2×#4111yescharacteristic
410C22×D17C2×#4111yescharacteristic
411C22×D17C2×#4111yescharacteristic
412C22×D17C2×#4111yescharacteristic
413C22×D17H(5,𝔽2)11yescharacteristic
414C22×D17H(5,𝔽2)11yescharacteristic
415C22×D17H(5,𝔽2)11yescharacteristic
416C22×D172−1+411yescharacteristic
417C2×#595—22no—
418C2×#595—22no—
419C2×#595—22no—
420C2×#595—22no—
421C2×#595—22no—
422C2×#595—22no—
423C2×#595—22no—
424C2×#595—22no—
425C2×#595—22no—
426C2×#595—22no—
427C2×#595—22no—
428C2×#595—22no—
429C2×#595—22no—
430C2×#595—22no—
431C2×#595—22no—
432C2×#595—22no—
433C2×#595—22no—
434C2×#595—22no—
435C2×#595—22no—
436C2×#595—22no—
437C2×#595—22no—
438C2×#595—22no—
439C2×#595—22no—
440C2×#595—22no—
441C2×#595—22no—
442C2×#595—22no—
443C2×#595—22no—
444C2×#595—22no—
445C2×#595—22no—
446C2×#595—22no—
447C2×#595—22no—
448C2×#595—22no—
449C2×#595—22no—
450C2×#595—22no—
451C2×#595—22no—
452C2×#595—22no—
453C2×#595—416no—
454C2×#595—416no—
455C2×#595—41no—
456C2×#595—41no—
457C2×#595—41no—
458C2×#595—41no—
459C2×#595—41no—
460C2×#595—41no—
461C2×#595—41no—
462C2×#595—41no—
463C2×#595—41no—
464C2×#595—41no—
465C2×#595—41no—
466C2×#595—41no—
467C2×#595—41no—
468C2×#595—41no—
469C2×#595—41no—
470C2×#595—41no—
471C2×#595C2×C4⋊C414yes—
472C2×#595C2×C4⋊C414yes—
473C2×#595C4×D414yes—
474C2×#595C4×D414yes—
475C2×C4×C17—21no—
476C2×C4×C17—21no—
477C2×C4×C17—21no—
478C2×C4×C17—21no—
479C2×C4×C17—21no—
480C2×C4×C17—21no—
481C2×C4×C17—21no—
482C2×C4×C17—21no—
483C2×C4×C17—21no—
484C2×C4×C17—21no—
485C2×C4×C17—21no—
486C2×C4×C17—21no—
487C2×C4×C17—21no—
488C2×C4×C17—21no—
489C2×C4×C17—21no—
490C2×C4×C17—44no—
491C2×C4×C17C2×C4212yes—
492C2×C4×C17C2×C4212yes—
493C2×C4×C17C4×D412yes—
494C2×Dic17—21no—
495C2×Dic17—21no—
496C2×Dic17—21no—
497C2×Dic17—21no—
498C2×Dic17—21no—
499C2×Dic17—21no—
500C2×Dic17—21no—
501C2×Dic17—21no—
502C2×Dic17—21no—
503C2×Dic17—21no—
504C2×Dic17—21no—
505C2×Dic17—21no—
506C2×Dic17—21no—
507C2×Dic17—21no—
508C2×Dic17—21no—
509C2×Dic17—44no—
510C2×Dic17C2×C4212yes—
511C2×Dic17C2×C4212yes—
512C2×Dic17C4×D412yes—
513C4×D17—22no—
514C4×D17—22no—
515C4×D17—22no—
516C4×D17—22no—
517C4×D17—22no—
518C4×D17—22no—
519C4×D17—22no—
520C4×D17—22no—
521C4×D17—22no—
522C4×D17—22no—
523C4×D17—22no—
524C4×D17—22no—
525C4×D17—44no—
526C4×D17—44no—
527C4×D17—41no—
528C4×D17—41no—
529C4×D17—41no—
530C4×D17—41no—
531C4×D17—41no—
532C4×D17—41no—
533C4×D17—41no—
534C4×D17—41no—
535C4×D17—41no—
536C4×D17—41no—
537C4×D17—41no—
538C4×D17—41no—
539C2×#385—171no—
540C2×#385—171no—
541C2×C4×C4⋊C4—171no—
542C2×C4×C22⋊C4—171no—
543C2×C4×C22⋊C4—171no—
544C2×C4×C22⋊C4—171no—
545C22×#95—171no—
546#1436—171no—
547#1436—171no—
548#1436—171no—
549#1436—171no—
550C4⋊#95—171no—
551#1434—171no—
552C22⋊#95—171no—
553C4×#95—171no—
554C22×C17—22no—
555C22×C17—22no—
556C22×C17—22no—
557C22×C17—22no—
558C22×C17—22no—
559C22×C17—22no—
560C22×C17C4×C4⋊C414yescomplemented
561C22×C17C22×C4211yescharacteristic
562C22×C17C2×C4×D411yescharacteristic
563C22×C17C2×C4×D411yescharacteristic
564C22×C17C2×C4×Q811yescharacteristic
565C22×C17C4×#4111yescharacteristic
566C22×C17#51811yescharacteristic
567C22×C17#52011yescharacteristic
568C2×D17—22no—
569C2×D17—22no—
570C2×D17—22no—
571C2×D17—22no—
572C2×D17—22no—
573C2×D17—22no—
574C2×D17—24no—
575C2×D17—24no—
576C2×D17—24no—
577C2×D17—24no—
578C2×D17—24no—
579C2×D17—24no—
580C2×D17—24no—
581C2×D17—24no—
582C2×D17C4×C4⋊C414yescomplemented
583C2×D17C22×C4⋊C411yescharacteristic
584C2×D17C2×#11711yescharacteristic
585C2×D17C2×C4×D411yescharacteristic
586C2×D17C2×C4×D411yescharacteristic
587C2×D17C2×C4×D411yescharacteristic
588C2×D17C2×C4×Q811yescharacteristic
589C2×D17C4×#4111yescharacteristic
590C2×D17C4×#4111yescharacteristic
591C2×D17#51811yescharacteristic
592C2×D17#51811yescharacteristic
593C2×D17#52011yescharacteristic
594C2×D17#52011yescharacteristic
595C2×D17D4211yescharacteristic
596C2×D17#54611yescharacteristic
597C2×D17#54611yescharacteristic
598C2×D17#54611yescharacteristic
599C2×D17#54611yescharacteristic
600C2×D17#54711yescharacteristic
601C2×D17D4×Q811yescharacteristic
602C2×D17#55111yescharacteristic
603C2×D17#55111yescharacteristic
604C2×D17#55111yescharacteristic
605C2×D17#55111yescharacteristic
606C2×D17#55211yescharacteristic
607C2×D17#55211yescharacteristic
608C2×D17#55411yescharacteristic
609C2×D17#55411yescharacteristic
610C2×D17#55411yescharacteristic
611#595—24no—
612#595—24no—
613#595—24no—
614#595—24no—
615#595—42no—
616#595—42no—
617#595—42no—
618#595—42no—
619C4×C17—22no—
620C4×C17—22no—
621C4×C17—22no—
622C4×C17—41no—
623C4×C17—41no—
624C4×C17—41no—
625Dic17—22no—
626Dic17—22no—
627Dic17—22no—
628Dic17—41no—
629Dic17—41no—
630Dic17—41no—
631C24×C4—171no—
632C24×C4—171no—
633C24×C4—171no—
634C22×C4⋊C4—171no—
635C22×C4⋊C4—171no—
636C22×C4⋊C4—171no—
637C22×C4⋊C4—171no—
638C22×C22⋊C4—171no—
639C22×C22⋊C4—171no—
640C22×C22⋊C4—171no—
641C22×C22⋊C4—171no—
642C22×C42—171no—
643C22×C42—171no—
644C22×C42—171no—
645C22×C42—171no—
646C22×C42—171no—
647C22×C42—171no—
648#385—178no—
649#385—171no—
650#385—171no—
651#385—171no—
652#385—171no—
653#385—171no—
654#385—171no—
655#385—171no—
656#385#59511yescharacteristic, complemented
657C4×C4⋊C4—344no—
658C4×C22⋊C4—178no—
659C4×C22⋊C4—344no—
660C4×C22⋊C4—344no—
661C2×#95—171no—
662C2×#95—171no—
663C2×#95—171no—
664C2×#95—171no—
665C2×#95—171no—
666C2×#95—171no—
667C2×#95—171no—
668C2×#95—171no—
669C2×#95—171no—
670C2×#95—171no—
671C2×#95—171no—
672C2×#95—171no—
673C2×#95—171no—
674C2×#95—171no—
675C2×#95—171no—
676C2×#95—171no—
677C2×#95—171no—
678C2×#95—171no—
679C2×#95—344no—
680C2×C17—24no—
681C2×C17C2×C4×C4⋊C411yescharacteristic
682C2×C17C42×D411yescharacteristic
683C2×C17#227511yescharacteristic
684C2×C17#235811yescharacteristic
685C2×C17#235911yescharacteristic
686C2×C17#236011yescharacteristic
687C2×C17#236811yescharacteristic
688D17—24no—
689D17#234211yescharacteristic
690D17#234311yescharacteristic
691D17D4×C4⋊C411yescharacteristic
692D17#234911yescharacteristic
693D17#235811yescharacteristic
694D17#235911yescharacteristic
695D17#236011yescharacteristic
696D17#236811yescharacteristic
697C25—171no—
698C23×C4—171no—
699C23×C4—171no—
700C23×C4—171no—
701C23×C4—171no—
702C23×C4—171no—
703C23×C4—171no—
704C23×C4—171no—
705C23×C4—171no—
706C23×C4—171no—
707C23×C4—171no—
708C23×C4—171no—
709C23×C4—174no—
710C23×C4—174no—
711C23×C4—171no—
712C23×C4—171no—
713C23×C4—171no—
714C23×C4—171no—
715C23×C4—171no—
716C23×C4—171no—
717C23×C4—342no—
718C23×C4—342no—
719C23×C4—342no—
720C23×C4—342no—
721C23×C4—342no—
722C23×C4—342no—
723C23×C4—342no—
724C23×C4—342no—
725C23×C4—342no—
726C23×C4—342no—
727C23×C4—342no—
728C23×C4—342no—
729C23×C4—681no—
730C23×C4—681no—
731C23×C4—681no—
732C23×C4—681no—
733C23×C4—681no—
734C23×C4—681no—
735C23×C4C2×#59511yescharacteristic
736C2×C4⋊C4—174no—
737C2×C4⋊C4—171no—
738C2×C4⋊C4—171no—
739C2×C4⋊C4—171no—
740C2×C4⋊C4—174no—
741C2×C4⋊C4—171no—
742C2×C4⋊C4—171no—
743C2×C4⋊C4—171no—
744C2×C4⋊C4—342no—
745C2×C4⋊C4—342no—
746C2×C4⋊C4—342no—
747C2×C4⋊C4—342no—
748C2×C4⋊C4—681no—
749C2×C4⋊C4—681no—
750C2×C4⋊C4—681no—
751C2×C4⋊C4—681no—
752C2×C4⋊C4C2×#59511yescharacteristic, complemented
753C2×C4⋊C4C2×#59511yescharacteristic, complemented
754C2×C22⋊C4—174no—
755C2×C22⋊C4—174no—
756C2×C22⋊C4—174no—
757C2×C22⋊C4—171no—
758C2×C22⋊C4—171no—
759C2×C22⋊C4—171no—
760C2×C22⋊C4—174no—
761C2×C22⋊C4—174no—
762C2×C22⋊C4—174no—
763C2×C22⋊C4—171no—
764C2×C22⋊C4—171no—
765C2×C22⋊C4—171no—
766C2×C22⋊C4—342no—
767C2×C22⋊C4—342no—
768C2×C22⋊C4—342no—
769C2×C22⋊C4—342no—
770C2×C22⋊C4C2×#59511yescharacteristic
771C2×C22⋊C4C2×#59511yescharacteristic
772C2×C42—174no—
773C2×C42—174no—
774C2×C42—342no—
775C2×C42—342no—
776C2×C42—342no—
777C2×C42—342no—
778C2×C42—342no—
779C2×C42—342no—
780C2×C42—342no—
781C2×C42—342no—
782C2×C42—342no—
783C2×C42—342no—
784C2×C42—681no—
785C2×C42—681no—
786C2×C42—681no—
787C2×C42—681no—
788C2×C42—681no—
789C2×C42—681no—
790#95—174no—
791#95—174no—
792#95—174no—
793#95—174no—
794#95—174no—
795#95—171no—
796#95—171no—
797#95—171no—
798#95—171no—
799#95—171no—
800#95—171no—
801#95—342no—
802#95—342no—
803#95—342no—
804#95—342no—
805#95—342no—
806#95—342no—
807#95—342no—
808#95—342no—
809#95—342no—
810#95—681no—
811#95—681no—
812#95C2×#59511yescharacteristic, complemented
813#95C2×#59511yescharacteristic, complemented
814C17#1381411yescharacteristic, complemented, Sylow
815C24—171no—
816C24—172no—
817C24—172no—
818C24—172no—
819C24—172no—
820C24—172no—
821C24—172no—
822C24—171no—
823C24—341no—
824C24—341no—
825C24—341no—
826C24—341no—
827C24—341no—
828C24—341no—
829C24—341no—
830C24—341no—
831C24C22×#59511yescharacteristic
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—41no—
835C22×C4—172no—
836C22×C4—172no—
837C22×C4—172no—
838C22×C4—172no—
839C22×C4—172no—
840C22×C4—172no—
841C22×C4—172no—
842C22×C4—172no—
843C22×C4—172no—
844C22×C4—172no—
845C22×C4—172no—
846C22×C4—172no—
847C22×C4—171no—
848C22×C4—171no—
849C22×C4—171no—
850C22×C4—172no—
851C22×C4—172no—
852C22×C4—172no—
853C22×C4—172no—
854C22×C4—172no—
855C22×C4—172no—
856C22×C4—172no—
857C22×C4—172no—
858C22×C4—172no—
859C22×C4—172no—
860C22×C4—171no—
861C22×C4—171no—
862C22×C4—171no—
863C22×C4—342no—
864C22×C4—341no—
865C22×C4—341no—
866C22×C4—341no—
867C22×C4—341no—
868C22×C4—341no—
869C22×C4—341no—
870C22×C4—341no—
871C22×C4—341no—
872C22×C4—341no—
873C22×C4—341no—
874C22×C4—341no—
875C22×C4—341no—
876C22×C4—341no—
877C22×C4—341no—
878C22×C4—341no—
879C22×C4—341no—
880C22×C4—341no—
881C22×C4—341no—
882C22×C4—341no—
883C22×C4—341no—
884C22×C4—341no—
885C22×C4—341no—
886C22×C4—341no—
887C22×C4—341no—
888C22×C4—341no—
889C22×C4—341no—
890C22×C4—341no—
891C22×C4—341no—
892C22×C4—342no—
893C22×C4—342no—
894C22×C4—341no—
895C22×C4—341no—
896C22×C4—342no—
897C22×C4—348no—
898C22×C4—348no—
899C22×C4—341no—
900C22×C4—341no—
901C22×C4—341no—
902C22×C4—341no—
903C22×C4—341no—
904C22×C4—341no—
905C22×C4—341no—
906C22×C4—341no—
907C22×C4—341no—
908C22×C4—341no—
909C22×C4—341no—
910C22×C4—341no—
911C22×C4—341no—
912C22×C4—341no—
913C22×C4—341no—
914C22×C4—341no—
915C22×C4—341no—
916C22×C4—341no—
917C22×C4—341no—
918C22×C4—341no—
919C22×C4—341no—
920C22×C4—341no—
921C22×C4—341no—
922C22×C4—341no—
923C22×C4—341no—
924C22×C4—341no—
925C22×C4—341no—
926C22×C4—341no—
927C22×C4—341no—
928C22×C4—341no—
929C22×C4—341no—
930C22×C4—341no—
931C22×C4—341no—
932C22×C4—341no—
933C22×C4—341no—
934C22×C4—348no—
935C22×C4—348no—
936C22×C4—341no—
937C22×C4—341no—
938C22×C4—341no—
939C22×C4—341no—
940C22×C4—341no—
941C22×C4—342no—
942C22×C4—342no—
943C22×C4—681no—
944C22×C4—681no—
945C22×C4—684no—
946C22×C4—684no—
947C22×C4—684no—
948C22×C4—684no—
949C22×C4—681no—
950C22×C4—684no—
951C22×C4—684no—
952C22×C4—684no—
953C22×C4—684no—
954C22×C4—684no—
955C22×C4—684no—
956C22×C4—684no—
957C22×C4—684no—
958C22×C4—684no—
959C22×C4—684no—
960C22×C4C22×#59511yescharacteristic
961C22×C4C22×#59511yescharacteristic
962C22×C4C22×#59511yescharacteristic
963C22×C4C22×#59511yescharacteristic
964C22×C4C22×#59511yescharacteristic
965C22×C4C22×#59511yescharacteristic
966C4⋊C4—22no—
967C4⋊C4—41no—
968C4⋊C4—342no—
969C4⋊C4—342no—
970C4⋊C4—348no—
971C4⋊C4—342no—
972C4⋊C4—681no—
973C4⋊C4—681no—
974C4⋊C4—681no—
975C4⋊C4—684no—
976C22⋊C4—22no—
977C22⋊C4—1716no—
978C22⋊C4—174no—
979C22⋊C4—174no—
980C22⋊C4—174no—
981C22⋊C4—342no—
982C22⋊C4—342no—
983C22⋊C4—348no—
984C22⋊C4—342no—
985C22⋊C4C4×#59514yescomplemented
986C42—348no—
987C42—684no—
988C42—684no—
989C42—684no—
990C42—684no—
991C42—684no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—171no—
997C23—171no—
998C23—171no—
999C23—171no—
1000C23—171no—
1001C23—171no—
1002C23—171no—
1003C23—171no—
1004C23—171no—
1005C23—171no—
1006C23—171no—
1007C23—171no—
1008C23—171no—
1009C23—171no—
1010C23—174no—
1011C23—174no—
1012C23—174no—
1013C23—174no—
1014C23—172no—
1015C23—172no—
1016C23—172no—
1017C23—342no—
1018C23—342no—
1019C23—342no—
1020C23—342no—
1021C23—342no—
1022C23—342no—
1023C23—342no—
1024C23—342no—
1025C23—342no—
1026C23—342no—
1027C23—342no—
1028C23—342no—
1029C23—342no—
1030C23—342no—
1031C23—342no—
1032C23—342no—
1033C23—342no—
1034C23—342no—
1035C23—342no—
1036C23—342no—
1037C23—342no—
1038C23—342no—
1039C23—342no—
1040C23—342no—
1041C23—341no—
1042C23—341no—
1043C23—341no—
1044C23—341no—
1045C23C2×C4×#59512yes—
1046C23D4×#59512yes—
1047C23Q8×#59512yes—
1048C23C23×#59511yescharacteristic
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—44no—
1065C2×C4—174no—
1066C2×C4—174no—
1067C2×C4—174no—
1068C2×C4—174no—
1069C2×C4—172no—
1070C2×C4—172no—
1071C2×C4—172no—
1072C2×C4—342no—
1073C2×C4—342no—
1074C2×C4—342no—
1075C2×C4—342no—
1076C2×C4—342no—
1077C2×C4—342no—
1078C2×C4—342no—
1079C2×C4—342no—
1080C2×C4—342no—
1081C2×C4—342no—
1082C2×C4—342no—
1083C2×C4—342no—
1084C2×C4—342no—
1085C2×C4—342no—
1086C2×C4—342no—
1087C2×C4—342no—
1088C2×C4—342no—
1089C2×C4—342no—
1090C2×C4—342no—
1091C2×C4—342no—
1092C2×C4—342no—
1093C2×C4—342no—
1094C2×C4—342no—
1095C2×C4—342no—
1096C2×C4—342no—
1097C2×C4—342no—
1098C2×C4—342no—
1099C2×C4—342no—
1100C2×C4—342no—
1101C2×C4—342no—
1102C2×C4—342no—
1103C2×C4—342no—
1104C2×C4—342no—
1105C2×C4—342no—
1106C2×C4—342no—
1107C2×C4—342no—
1108C2×C4—341no—
1109C2×C4—341no—
1110C2×C4—341no—
1111C2×C4—341no—
1112C2×C4—341no—
1113C2×C4—341no—
1114C2×C4—342no—
1115C2×C4—342no—
1116C2×C4—342no—
1117C2×C4—342no—
1118C2×C4—342no—
1119C2×C4—342no—
1120C2×C4—342no—
1121C2×C4—342no—
1122C2×C4—342no—
1123C2×C4—342no—
1124C2×C4—342no—
1125C2×C4—342no—
1126C2×C4—341no—
1127C2×C4—341no—
1128C2×C4—341no—
1129C2×C4—341no—
1130C2×C4—341no—
1131C2×C4—341no—
1132C2×C4—341no—
1133C2×C4—341no—
1134C2×C4—341no—
1135C2×C4—684no—
1136C2×C4—684no—
1137C2×C4—681no—
1138C2×C4—681no—
1139C2×C4—681no—
1140C2×C4—681no—
1141C2×C4—681no—
1142C2×C4—681no—
1143C2×C4—681no—
1144C2×C4—681no—
1145C2×C4—681no—
1146C2×C4—681no—
1147C2×C4—681no—
1148C2×C4—681no—
1149C2×C4—684no—
1150C2×C4—6816no—
1151C2×C4—6816no—
1152C2×C4—681no—
1153C2×C4—681no—
1154C2×C4—681no—
1155C2×C4—681no—
1156C2×C4—681no—
1157C2×C4—681no—
1158C2×C4—681no—
1159C2×C4—681no—
1160C2×C4—681no—
1161C2×C4—681no—
1162C2×C4—681no—
1163C2×C4—681no—
1164C2×C4—681no—
1165C2×C4—681no—
1166C2×C4—681no—
1167C2×C4—681no—
1168C2×C4C2×C4×#59512yes—
1169C2×C4C2×C4×#59512yes—
1170C2×C4D4×#59512yes—
1171C22—22no—
1172C22—22no—
1173C22—22no—
1174C22—22no—
1175C22—22no—
1176C22—22no—
1177C22—171no—
1178C22—171no—
1179C22—171no—
1180C22—171no—
1181C22—171no—
1182C22—171no—
1183C22—171no—
1184C22—171no—
1185C22—171no—
1186C22—171no—
1187C22—171no—
1188C22—171no—
1189C22—171no—
1190C22—171no—
1191C22—171no—
1192C22—171no—
1193C22—171no—
1194C22—171no—
1195C22—171no—
1196C22—171no—
1197C22—171no—
1198C22—171no—
1199C22—171no—
1200C22—171no—
1201C22—171no—
1202C22—171no—
1203C22—171no—
1204C22—171no—
1205C22—174no—
1206C22—344no—
1207C22—344no—
1208C22—344no—
1209C22—344no—
1210C22—344no—
1211C22—344no—
1212C22—344no—
1213C22—344no—
1214C22—342no—
1215C22—342no—
1216C22—342no—
1217C22—342no—
1218C22—342no—
1219C22—342no—
1220C22C4⋊C4×#59514yescomplemented
1221C22C22×C4×#59511yescharacteristic
1222C22C2×D4×#59511yescharacteristic
1223C22C2×D4×#59511yescharacteristic
1224C22C2×Q8×#59511yescharacteristic
1225C22#41×#59511yescharacteristic
1226C22#1176387611yescharacteristic
1227C22#1176387811yescharacteristic
1228C4—22no—
1229C4—22no—
1230C4—22no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—344no—
1235C4—344no—
1236C4—344no—
1237C4—344no—
1238C4—342no—
1239C4—342no—
1240C4—342no—
1241C4—682no—
1242C4—682no—
1243C4—682no—
1244C4—682no—
1245C4—681no—
1246C4—681no—
1247C4—681no—
1248C2—24no—
1249C2—171no—
1250C2—171no—
1251C2—171no—
1252C2—171no—
1253C2—171no—
1254C2—171no—
1255C2—171no—
1256C2—171no—
1257C2—344no—
1258C2C2×C4⋊C4×#59511yescharacteristic
1259C2C4×D4×#59511yescharacteristic
1260C2#1454522311yescharacteristic
1261C2#1454530611yescharacteristic
1262C2#1454530711yescharacteristic
1263C2#1454530811yescharacteristic
1264C2#1454531611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#595
commutatorC22×C17C22×C42
FittingC17×#385C4
socleC23×C17C23×C4
prime radicalC24×D17C23
cosocleC23×D17C24
hypercenter#385#595
hypocenterC17#13814
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×#595C2semidirect
7. #14543964C2semidirect
8. #14543964C2semidirect
9. #14543963C2semidirect
10. #14543963C2semidirect
11. #14543961C2semidirect
12. #14543959C2semidirect
14. #95×#595C2semidirect
28. #11763756C4semidirect
31. C22⋊C4×#595C4semidirect
55. #11762684C4semidirect
56. #11762683C4semidirect
57. #11762683C4semidirect
58. #11762682C4semidirect
59. #11762681C4semidirect
60. #11762680C4semidirect
61. #11762680C4semidirect
64. C17×#385C4semidirect
114. C2×C4⋊#595C2×C4semidirect
115. C2×C4⋊#595C2×C4semidirect
132. C2×C4×#595C2×C4semidirect
133. C2×C4×#595C2×C4semidirect
134. C2×C4⋊C4×C17C2×C4semidirect
135. C2×C4⋊C4×C17C2×C4semidirect
144. C2×C4⋊Dic17C2×C4semidirect
145. C2×C4⋊Dic17C2×C4semidirect
146. C2×#63225C2×C4semidirect
147. C2×#63225C2×C4semidirect
148. C2×#63225C2×C4semidirect
149. C2×#63225C2×C4semidirect
169. (C2×#595)⋊C4C2×C4semidirect
170. (C2×#595)⋊C4C2×C4semidirect
171. (C2×#595)⋊C4C2×C4semidirect
172. (C2×#595)⋊C4C2×C4semidirect
174. C17×#95C2×C4semidirect
175. C17×#95C2×C4semidirect
176. #10587502C2×C4semidirect
177. #10587502C2×C4semidirect
178. #10587502C2×C4semidirect
179. #10587502C2×C4semidirect
180. #10587502C2×C4semidirect
181. #10587502C2×C4semidirect
334. C22⋊#595C4⋊C4semidirect
346. C22⋊C4×C17C42semidirect
348. C22⋊Dic17C42semidirect
351. #63227C42semidirect
352. #63227C42semidirect
560. C22×C17C4×C4⋊C4semidirect
582. C2×D17C4×C4⋊C4semidirect
656. #385#595semidirect
752. C2×C4⋊C4C2×#595semidirect
753. C2×C4⋊C4C2×#595semidirect
812. #95C2×#595semidirect
813. #95C2×#595semidirect
814. C17#13814semidirect
985. C22⋊C4C4×#595semidirect
1220. C22C4⋊C4×#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117637562
C2×C4⋊C4×#5952
C2×C22⋊C4×#5952
C2×C4×C22⋊#5952
C22×(C2×#595)⋊C42
#145439642
#145439632
#145439612
#145439592
#145439572
#95×#5952
D17×#3852
#1381417