Finite Group Databasebeta

← #17962994

Subgroups — #17962994

Order 4352.

1406 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763758C211yesmaximal, characteristic
2C2×C4⋊C4×#595C211yesmaximal, characteristic
3#14543964C211yesmaximal, characteristic
4#14543964C211yesmaximal, characteristic
5#14543964C211yesmaximal, characteristic
6#14543963C211yesmaximal, characteristic
7#14543961C211yesmaximal, characteristic
8#14543960C211yesmaximal, characteristic
9#14543959C211yesmaximal, characteristic
10#14543959C211yesmaximal, characteristic
11#14543959C211yesmaximal, characteristic
12#14543959C211yesmaximal, characteristic
13C4×(C2×#595)⋊C4C211yesmaximal, characteristic
14#95×#595C211yesmaximal, characteristic
15D17×#387C211yesmaximal, characteristic
16C22×C4⋊#595C2211yescharacteristic
17C22×C4⋊#595C2211yescharacteristic
18C22×C4×#595C2211yescharacteristic
19C22×C4×#595C2211yescharacteristic
20C22×C4×#595C2211yescharacteristic
21C22×C4×#595C2211yescharacteristic
22C22×C4×#595C2211yescharacteristic
23C22×C4×#595C2211yescharacteristic
24#11763758C418yescomplemented
25C4⋊C4×#595C418yescomplemented
26C2×(C2×#595)⋊C4C2211yescharacteristic
27C2×(C2×#595)⋊C4C2211yescharacteristic
28C2×(C2×#595)⋊C4C2211yescharacteristic
29C2×(C2×#595)⋊C4C2211yescharacteristic
30C2×(C2×#595)⋊C4C2211yescharacteristic
31C2×(C2×#595)⋊C4C2211yescharacteristic
32C2×(C2×#595)⋊C4C2211yescharacteristic
33C2×(C2×#595)⋊C4C2211yescharacteristic
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×C4⋊C4×D17C2211yescharacteristic
47C2×C4⋊C4×D17C2211yescharacteristic
48C2×C42×D17C2211yescharacteristic
49#11762696C411yescharacteristic, complemented
50#11762695C411yescharacteristic, complemented
51#11762694C411yescharacteristic, complemented
52#11762693C411yescharacteristic, complemented
53#11762692C411yescharacteristic, complemented
54#11762691C411yescharacteristic, complemented
55#11762690C411yescharacteristic, complemented
56#95×D17C2211yescharacteristic
57#95×D17C2211yescharacteristic
58#95×D17C2211yescharacteristic
59#95×D17C2211yescharacteristic
60C17×#387C411yescharacteristic, complemented
61C23×#595C2311yescharacteristic
62C23×#595C2311yescharacteristic
63C23×#595C2311yescharacteristic
64C23×#595C2311yescharacteristic
65C23×#595C2311yescharacteristic
66C23×#595C2311yescharacteristic
67C23×#595C2311yescharacteristic
68C23×#595C2311yescharacteristic
69C22×C4×D17C2311yescharacteristic
70C22×C4×D17C2311yescharacteristic
71C22×C4×D17C2311yescharacteristic
72C22×C4×D17C2311yescharacteristic
73C22×C4×D17C2311yescharacteristic
74C22×C4×D17C2311yescharacteristic
75C22×C4×D17C2311yescharacteristic
76C2×C4⋊#595—22no—
77C2×C4⋊#595—22no—
78C2×C4⋊#595—41no—
79C2×C4⋊#595—41no—
80C2×C4⋊#595C2×C414yes—
81C2×C4⋊#595C2×C414yes—
82C2×C4×#595—22no—
83C2×C4×#595—22no—
84C2×C4×#595—22no—
85C2×C4×#595—22no—
86C2×C4×#595—41no—
87C2×C4×#595—41no—
88C2×C4×#595—41no—
89C2×C4×#595—41no—
90C2×C4×#595—41no—
91C2×C4×#595—41no—
92C2×C4×#595—41no—
93C2×C4×#595—41no—
94C2×C4×#595—41no—
95C2×C4×#595—41no—
96C2×C4×#595C2×C414yes—
97C2×C4×#595C2×C414yes—
98C2×C4×#595C2×C414yes—
99C2×C4×#595C2×C414yes—
100C2×C4⋊C4×C17C2×C411yescharacteristic
101C2×C4⋊C4×C17C2×C411yescharacteristic
102C2×C42×C17C2×C411yescharacteristic
103C2×C4⋊Dic17C2×C411yescharacteristic
104C2×C4⋊Dic17C2×C411yescharacteristic
105C2×#63225C2×C411yescharacteristic
106C2×#63225C2×C411yescharacteristic
107C2×#63225C2×C411yescharacteristic
108C2×#63225C2×C411yescharacteristic
109C2×C4×Dic17C2×C411yescharacteristic
110C2×C4×Dic17C2×C411yescharacteristic
111C2×C4×Dic17C2×C411yescharacteristic
112C4⋊C4×D17—41no—
113C4⋊C4×D17—41no—
114C4⋊C4×D17C2×C414yes—
115C4⋊C4×D17C2×C414yes—
116C42×D17—41no—
117C42×D17—41no—
118(C2×#595)⋊C4—22no—
119(C2×#595)⋊C4—22no—
120(C2×#595)⋊C4—22no—
121(C2×#595)⋊C4—22no—
122(C2×#595)⋊C4—22no—
123(C2×#595)⋊C4—22no—
124(C2×#595)⋊C4—41no—
125(C2×#595)⋊C4—41no—
126(C2×#595)⋊C4—41no—
127(C2×#595)⋊C4—41no—
128(C2×#595)⋊C4—41no—
129(C2×#595)⋊C4—41no—
130(C2×#595)⋊C4—41no—
131(C2×#595)⋊C4—41no—
132(C2×#595)⋊C4C2×C414yes—
133(C2×#595)⋊C4C2×C414yes—
134(C2×#595)⋊C4C2×C414yes—
135(C2×#595)⋊C4C2×C414yes—
136(C2×#595)⋊C4C2×C414yes—
137(C2×#595)⋊C4C2×C414yes—
138C17×#95C2×C411yescharacteristic
139C17×#95C2×C411yescharacteristic
140C17×#95C2×C411yescharacteristic
141C17×#95C2×C411yescharacteristic
142#10587502C2×C411yescharacteristic
143#10587502C2×C411yescharacteristic
144#10587502C2×C411yescharacteristic
145#10587502C2×C411yescharacteristic
146#10587502C2×C411yescharacteristic
147#10587502C2×C411yescharacteristic
148#10587502C2×C411yescharacteristic
149#10587502C2×C411yescharacteristic
150#10587502C2×C411yescharacteristic
151#10587502C2×C411yescharacteristic
152#10587502C2×C411yescharacteristic
153#10587502C2×C411yescharacteristic
154C23×D17C2411yescharacteristic
155C22×#595—21no—
156C22×#595—21no—
157C22×#595—21no—
158C22×#595—21no—
159C22×#595—21no—
160C22×#595—21no—
161C22×#595—21no—
162C22×#595—21no—
163C22×#595—21no—
164C22×#595—21no—
165C22×#595—21no—
166C22×#595—21no—
167C22×#595—21no—
168C22×#595—21no—
169C22×#595—21no—
170C22×#595—21no—
171C22×#595—21no—
172C22×#595—21no—
173C22×#595—21no—
174C22×#595—21no—
175C22×#595—21no—
176C22×#595—21no—
177C22×#595—21no—
178C22×#595—21no—
179C22×#595—21no—
180C22×#595—21no—
181C22×#595—21no—
182C22×#595—21no—
183C22×#595—21no—
184C22×#595—21no—
185C22×#595—21no—
186C22×#595—21no—
187C22×#595—21no—
188C22×#595—21no—
189C22×#595—21no—
190C22×#595—21no—
191C22×#595—21no—
192C22×#595—21no—
193C22×#595—21no—
194C22×#595—21no—
195C22×#595—21no—
196C22×#595—21no—
197C22×#595—21no—
198C22×#595—21no—
199C22×#595C22×C412yes—
200C22×#595C22×C412yes—
201C22×#595C22×C412yes—
202C22×#595C22×C412yes—
203C22×#595C22×C412yes—
204C22×#595C22×C412yes—
205C22×#595C22×C412yes—
206C22×#595C22×C412yes—
207C22×#595#4112yes—
208C22×#595#4112yes—
209C22×#595#4112yes—
210C22×#595#4112yes—
211C22×C4×C17C22×C411yescharacteristic
212C22×C4×C17C22×C411yescharacteristic
213C22×C4×C17C22×C411yescharacteristic
214C22×C4×C17C22×C411yescharacteristic
215C22×C4×C17C22×C411yescharacteristic
216C22×C4×C17C22×C411yescharacteristic
217C22×C4×C17C22×C411yescharacteristic
218C22×Dic17C22×C411yescharacteristic
219C22×Dic17C22×C411yescharacteristic
220C22×Dic17C22×C411yescharacteristic
221C22×Dic17C22×C411yescharacteristic
222C22×Dic17C22×C411yescharacteristic
223C22×Dic17C22×C411yescharacteristic
224C22×Dic17C22×C411yescharacteristic
225C2×C4×D17—21no—
226C2×C4×D17—21no—
227C2×C4×D17—21no—
228C2×C4×D17—21no—
229C2×C4×D17—21no—
230C2×C4×D17—21no—
231C2×C4×D17—21no—
232C2×C4×D17—21no—
233C2×C4×D17—21no—
234C2×C4×D17—21no—
235C2×C4×D17—21no—
236C2×C4×D17—21no—
237C2×C4×D17—21no—
238C2×C4×D17—21no—
239C2×C4×D17—21no—
240C2×C4×D17—21no—
241C2×C4×D17—21no—
242C2×C4×D17—21no—
243C2×C4×D17—21no—
244C2×C4×D17—21no—
245C2×C4×D17—21no—
246C2×C4×D17—21no—
247C2×C4×D17—21no—
248C2×C4×D17—21no—
249C2×C4×D17—21no—
250C2×C4×D17—21no—
251C2×C4×D17—21no—
252C2×C4×D17—21no—
253C2×C4×D17—21no—
254C2×C4×D17—21no—
255C2×C4×D17—21no—
256C2×C4×D17—21no—
257C2×C4×D17—21no—
258C2×C4×D17—21no—
259C2×C4×D17—21no—
260C2×C4×D17—21no—
261C2×C4×D17C22×C412yes—
262C2×C4×D17C22×C412yes—
263C2×C4×D17C22×C412yes—
264C2×C4×D17C22×C412yes—
265C2×C4×D17C22×C412yes—
266C2×C4×D17C22×C412yes—
267C4⋊#595—28no—
268C4⋊#595—44no—
269C4×#595—28no—
270C4×#595—44no—
271C4×#595—44no—
272C4×#595—44no—
273C4×#595—44no—
274C4×#595—44no—
275C4⋊C4×C17—41no—
276C4⋊C4×C17C4214yescomplemented
277C42×C17—41no—
278C4⋊Dic17—41no—
279C4⋊Dic17C4214yescomplemented
280#63225—41no—
281#63225—41no—
282#63225C4214yescomplemented
283#63225C4214yescomplemented
284C4×Dic17—41no—
285C4×Dic17—41no—
286C4×Dic17—41no—
287#13787—171nomaximal, Sylow
288C23×C17C23×C411yescharacteristic
289C22×D17C23×C411yescharacteristic
290C22×D17C23×C411yescharacteristic
291C22×D17C2×#4111yescharacteristic
292C22×D17C2×#4111yescharacteristic
293C22×D17C2×#4111yescharacteristic
294C22×D17C2×#4111yescharacteristic
295C22×D17H(5,𝔽2)11yescharacteristic
296C22×D17H(5,𝔽2)11yescharacteristic
297C22×D17H(5,𝔽2)11yescharacteristic
298C22×D17H(5,𝔽2)11yescharacteristic
299C22×D172−1+411yescharacteristic
300C22×D172−1+411yescharacteristic
301C22×D172−1+411yescharacteristic
302C22×D172−1+411yescharacteristic
303C2×#595—22no—
304C2×#595—22no—
305C2×#595—22no—
306C2×#595—22no—
307C2×#595—22no—
308C2×#595—22no—
309C2×#595—22no—
310C2×#595—22no—
311C2×#595—22no—
312C2×#595—22no—
313C2×#595—22no—
314C2×#595—22no—
315C2×#595—22no—
316C2×#595—22no—
317C2×#595—22no—
318C2×#595—22no—
319C2×#595—22no—
320C2×#595—22no—
321C2×#595—22no—
322C2×#595—22no—
323C2×#595—22no—
324C2×#595—22no—
325C2×#595—22no—
326C2×#595—22no—
327C2×#595—22no—
328C2×#595—22no—
329C2×#595—22no—
330C2×#595—22no—
331C2×#595—22no—
332C2×#595—22no—
333C2×#595—41no—
334C2×#595—41no—
335C2×#595—41no—
336C2×#595—41no—
337C2×#595—41no—
338C2×#595—41no—
339C2×#595—41no—
340C2×#595—41no—
341C2×#595—41no—
342C2×#595—41no—
343C2×#595—41no—
344C2×#595—41no—
345C2×#595—41no—
346C2×#595—41no—
347C2×#595—41no—
348C2×#595—41no—
349C2×#595—41no—
350C2×#595—41no—
351C2×#595—41no—
352C2×#595—41no—
353C2×#595—41no—
354C2×#595—41no—
355C2×#595—41no—
356C2×#595—41no—
357C2×#595#11714yes—
358C2×#595#11714yes—
359C2×C4×C17—21no—
360C2×C4×C17—21no—
361C2×C4×C17—21no—
362C2×C4×C17—21no—
363C2×C4×C17—21no—
364C2×C4×C17—21no—
365C2×C4×C17—21no—
366C2×C4×C17—21no—
367C2×C4×C17—21no—
368C2×C4×C17—21no—
369C2×C4×C17—21no—
370C2×C4×C17—21no—
371C2×C4×C17—21no—
372C2×C4×C17—21no—
373C2×C4×C17—21no—
374C2×C4×C17—21no—
375C2×C4×C17—21no—
376C2×C4×C17—21no—
377C2×C4×C17C2×C4212yes—
378C2×C4×C17C2×C4212yes—
379C2×C4×C17C2×C4212yes—
380C2×Dic17—21no—
381C2×Dic17—21no—
382C2×Dic17—21no—
383C2×Dic17—21no—
384C2×Dic17—21no—
385C2×Dic17—21no—
386C2×Dic17—21no—
387C2×Dic17—21no—
388C2×Dic17—21no—
389C2×Dic17—21no—
390C2×Dic17—21no—
391C2×Dic17—21no—
392C2×Dic17—21no—
393C2×Dic17—21no—
394C2×Dic17—21no—
395C2×Dic17—21no—
396C2×Dic17—21no—
397C2×Dic17—21no—
398C2×Dic17C2×C4212yes—
399C2×Dic17C2×C4212yes—
400C2×Dic17C2×C4212yes—
401C4×D17—22no—
402C4×D17—22no—
403C4×D17—22no—
404C4×D17—22no—
405C4×D17—22no—
406C4×D17—22no—
407C4×D17—22no—
408C4×D17—22no—
409C4×D17—22no—
410C4×D17—22no—
411C4×D17—22no—
412C4×D17—22no—
413C4×D17—41no—
414C4×D17—41no—
415C4×D17—41no—
416C4×D17—41no—
417C4×D17—41no—
418C4×D17—41no—
419C4×D17—41no—
420C4×D17—41no—
421C4×D17—41no—
422C4×D17—41no—
423C4×D17—41no—
424C4×D17—41no—
425C4×D17—41no—
426C4×D17—41no—
427C4×D17—41no—
428C4×D17—41no—
429C2×#387—171no—
430C2×#387—171no—
431C2×C4×C4⋊C4—171no—
432#1436—171no—
433#1436—171no—
434#1436—171no—
435#1436—171no—
436C4⋊#95—171no—
437#1434—171no—
438#1434—171no—
439#1434—171no—
440#1434—171no—
441#1434—171no—
442C4×#95—171no—
443C4×#95—171no—
444C22×C17C22×C4211yescharacteristic
445C22×C17C4×#4111yescharacteristic
446C22×C17C4×#4111yescharacteristic
447C22×C17#51811yescharacteristic
448C22×C17#51911yescharacteristic
449C22×C17#52011yescharacteristic
450C22×C17#52011yescharacteristic
451C2×D17C2×#11711yescharacteristic
452C2×D17C2×#11711yescharacteristic
453C2×D17C4×#4111yescharacteristic
454C2×D17C4×#4111yescharacteristic
455C2×D17#51811yescharacteristic
456C2×D17#51811yescharacteristic
457C2×D17#51911yescharacteristic
458C2×D17#51911yescharacteristic
459C2×D17#52011yescharacteristic
460C2×D17#52011yescharacteristic
461C2×D17#52011yescharacteristic
462C2×D17#52011yescharacteristic
463C2×D17#53811yescharacteristic
464C2×D17#53811yescharacteristic
465C2×D17#53911yescharacteristic
466C2×D17#53911yescharacteristic
467C2×D17#53911yescharacteristic
468C2×D17#53911yescharacteristic
469C2×D17#53911yescharacteristic
470C2×D17#53911yescharacteristic
471C2×D17#54011yescharacteristic
472C2×D17#54111yescharacteristic
473C2×D17#54111yescharacteristic
474C2×D17#54111yescharacteristic
475C2×D17#54211yescharacteristic
476C2×D17#54211yescharacteristic
477C2×D17#54211yescharacteristic
478C2×D17#54211yescharacteristic
479#595—24no—
480#595—24no—
481#595—42no—
482#595—42no—
483#595—42no—
484#595—42no—
485#595—42no—
486#595—42no—
487C4×C17—22no—
488C4×C17—22no—
489C4×C17—22no—
490C4×C17—41no—
491C4×C17—41no—
492C4×C17—41no—
493C4×C17—41no—
494Dic17—22no—
495Dic17—22no—
496Dic17—22no—
497Dic17—41no—
498Dic17—41no—
499Dic17—41no—
500Dic17—41no—
501C22×C4⋊C4—171no—
502C22×C4⋊C4—171no—
503C22×C4⋊C4—171no—
504C22×C4⋊C4—171no—
505C22×C42—171no—
506C22×C42—171no—
507C22×C42—171no—
508C22×C42—171no—
509C22×C42—171no—
510C22×C42—171no—
511C22×C42—171no—
512#387—178no—
513#387—171no—
514#387—171no—
515#387—171no—
516#387—171no—
517#387—171no—
518#387—171no—
519#387—171no—
520#387#59511yescharacteristic, complemented
521C4×C4⋊C4—178no—
522C2×#95—171no—
523C2×#95—171no—
524C2×#95—171no—
525C2×#95—171no—
526C2×#95—171no—
527C2×#95—171no—
528C2×#95—171no—
529C2×#95—171no—
530C2×#95—171no—
531C2×#95—171no—
532C2×#95—171no—
533C2×#95—171no—
534C2×#95—171no—
535C2×#95—171no—
536C2×#95—171no—
537C2×#95—171no—
538C2×#95—171no—
539C2×#95—171no—
540C2×#95—171no—
541C2×#95—171no—
542C2×#95—171no—
543C2×#95—171no—
544C2×#95—171no—
545C2×#95—171no—
546C2×C17C4×#11711yescharacteristic
547C2×C17#227511yescharacteristic
548C2×C17#227611yescharacteristic
549C2×C17#233211yescharacteristic
550C2×C17#233411yescharacteristic
551C2×C17#233511yescharacteristic
552C2×C17#233611yescharacteristic
553D17#231311yescharacteristic
554D17#231411yescharacteristic
555D17#231811yescharacteristic
556D17#232011yescharacteristic
557D17#233211yescharacteristic
558D17#233411yescharacteristic
559D17#233511yescharacteristic
560D17#233611yescharacteristic
561C23×C4—171no—
562C23×C4—171no—
563C23×C4—171no—
564C23×C4—171no—
565C23×C4—171no—
566C23×C4—171no—
567C23×C4—171no—
568C23×C4—171no—
569C23×C4—171no—
570C23×C4—171no—
571C23×C4—171no—
572C23×C4—171no—
573C23×C4—171no—
574C23×C4—171no—
575C23×C4—171no—
576C2×C4⋊C4—171no—
577C2×C4⋊C4—171no—
578C2×C4⋊C4—171no—
579C2×C4⋊C4—174no—
580C2×C4⋊C4—174no—
581C2×C4⋊C4—174no—
582C2×C4⋊C4—174no—
583C2×C4⋊C4—171no—
584C2×C4⋊C4—171no—
585C2×C4⋊C4—171no—
586C2×C4⋊C4—342no—
587C2×C4⋊C4—342no—
588C2×C4⋊C4—681no—
589C2×C4⋊C4—681no—
590C2×C4⋊C4—681no—
591C2×C4⋊C4—681no—
592C2×C4⋊C4C2×#59511yescharacteristic
593C2×C4⋊C4C2×#59511yescharacteristic
594C2×C42—174no—
595C2×C42—174no—
596C2×C42—174no—
597C2×C42—174no—
598C2×C42—171no—
599C2×C42—171no—
600C2×C42—171no—
601C2×C42—342no—
602C2×C42—342no—
603C2×C42—342no—
604C2×C42—342no—
605C2×C42—681no—
606C2×C42—681no—
607C2×C42—681no—
608C2×C42—681no—
609C2×C42—681no—
610C2×C42—681no—
611C2×C42—681no—
612C2×C42—681no—
613C2×C42—681no—
614C2×C42—681no—
615C2×C42—681no—
616C2×C42—681no—
617C2×C42C2×#59511yescharacteristic
618#95—174no—
619#95—174no—
620#95—174no—
621#95—174no—
622#95—174no—
623#95—174no—
624#95—171no—
625#95—171no—
626#95—171no—
627#95—171no—
628#95—171no—
629#95—171no—
630#95—171no—
631#95—171no—
632#95—171no—
633#95—171no—
634#95—171no—
635#95—171no—
636#95—342no—
637#95—342no—
638#95—342no—
639#95—342no—
640#95—342no—
641#95—342no—
642#95—681no—
643#95—681no—
644#95—681no—
645#95—681no—
646#95—681no—
647#95—681no—
648#95—681no—
649#95—681no—
650#95C2×#59511yescharacteristic
651#95C2×#59511yescharacteristic
652#95C2×#59511yescharacteristic
653#95C2×#59511yescharacteristic
654C17#1378711yescharacteristic, complemented, Sylow
655C24—171no—
656C22×C4—172no—
657C22×C4—172no—
658C22×C4—172no—
659C22×C4—172no—
660C22×C4—172no—
661C22×C4—172no—
662C22×C4—171no—
663C22×C4—171no—
664C22×C4—171no—
665C22×C4—172no—
666C22×C4—172no—
667C22×C4—172no—
668C22×C4—172no—
669C22×C4—172no—
670C22×C4—172no—
671C22×C4—172no—
672C22×C4—172no—
673C22×C4—172no—
674C22×C4—172no—
675C22×C4—172no—
676C22×C4—172no—
677C22×C4—171no—
678C22×C4—171no—
679C22×C4—171no—
680C22×C4—171no—
681C22×C4—341no—
682C22×C4—341no—
683C22×C4—341no—
684C22×C4—341no—
685C22×C4—341no—
686C22×C4—341no—
687C22×C4—341no—
688C22×C4—341no—
689C22×C4—341no—
690C22×C4—341no—
691C22×C4—341no—
692C22×C4—341no—
693C22×C4—341no—
694C22×C4—341no—
695C22×C4—341no—
696C22×C4—341no—
697C22×C4—341no—
698C22×C4—341no—
699C22×C4—341no—
700C22×C4—341no—
701C22×C4—341no—
702C22×C4—341no—
703C22×C4—341no—
704C22×C4—341no—
705C22×C4—341no—
706C22×C4—341no—
707C22×C4—341no—
708C22×C4—341no—
709C22×C4—341no—
710C22×C4—341no—
711C22×C4—341no—
712C22×C4—341no—
713C22×C4—341no—
714C22×C4—341no—
715C22×C4—341no—
716C22×C4—341no—
717C22×C4—341no—
718C22×C4—341no—
719C22×C4—341no—
720C22×C4—341no—
721C22×C4—341no—
722C22×C4—341no—
723C22×C4—341no—
724C22×C4—341no—
725C22×C4—341no—
726C22×C4—341no—
727C22×C4—341no—
728C22×C4—341no—
729C22×C4—341no—
730C22×C4—341no—
731C22×C4—341no—
732C22×C4—341no—
733C22×C4—341no—
734C22×C4—341no—
735C22×C4—341no—
736C22×C4—341no—
737C22×C4—341no—
738C22×C4—341no—
739C22×C4—341no—
740C22×C4—341no—
741C22×C4—341no—
742C22×C4—341no—
743C22×C4—341no—
744C22×C4—341no—
745C22×C4—341no—
746C22×C4—341no—
747C22×C4—341no—
748C22×C4—341no—
749C22×C4—341no—
750C22×C4—341no—
751C22×C4—341no—
752C22×C4—341no—
753C22×C4—341no—
754C22×C4—341no—
755C22×C4—341no—
756C22×C4—341no—
757C22×C4—341no—
758C22×C4—341no—
759C22×C4—341no—
760C22×C4—341no—
761C22×C4C22×#59511yescharacteristic
762C22×C4C22×#59511yescharacteristic
763C22×C4C22×#59511yescharacteristic
764C22×C4C22×#59511yescharacteristic
765C22×C4C22×#59511yescharacteristic
766C22×C4C22×#59511yescharacteristic
767C22×C4C22×#59511yescharacteristic
768C4⋊C4—41no—
769C4⋊C4—174no—
770C4⋊C4—174no—
771C4⋊C4—174no—
772C4⋊C4—348no—
773C4⋊C4—681no—
774C4⋊C4—681no—
775C4⋊C4—681no—
776C4⋊C4—684no—
777C4⋊C4C4×#59514yescomplemented
778C42—41no—
779C42—348no—
780C42—681no—
781C42—681no—
782C42—681no—
783C42—684no—
784C42—684no—
785C42—684no—
786C42—684no—
787C42—684no—
788C23—171no—
789C23—171no—
790C23—171no—
791C23—171no—
792C23—171no—
793C23—171no—
794C23—171no—
795C23—171no—
796C23—171no—
797C23—171no—
798C23—171no—
799C23—171no—
800C23—171no—
801C23—171no—
802C23C23×#59511yescharacteristic
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—174no—
822C2×C4—174no—
823C2×C4—172no—
824C2×C4—172no—
825C2×C4—172no—
826C2×C4—342no—
827C2×C4—342no—
828C2×C4—342no—
829C2×C4—342no—
830C2×C4—342no—
831C2×C4—342no—
832C2×C4—342no—
833C2×C4—342no—
834C2×C4—342no—
835C2×C4—342no—
836C2×C4—342no—
837C2×C4—342no—
838C2×C4—342no—
839C2×C4—342no—
840C2×C4—342no—
841C2×C4—342no—
842C2×C4—342no—
843C2×C4—342no—
844C2×C4—342no—
845C2×C4—342no—
846C2×C4—342no—
847C2×C4—342no—
848C2×C4—342no—
849C2×C4—342no—
850C2×C4—341no—
851C2×C4—341no—
852C2×C4—341no—
853C2×C4—341no—
854C2×C4—341no—
855C2×C4—341no—
856C2×C4—342no—
857C2×C4—342no—
858C2×C4—342no—
859C2×C4—342no—
860C2×C4—342no—
861C2×C4—342no—
862C2×C4—342no—
863C2×C4—342no—
864C2×C4—342no—
865C2×C4—342no—
866C2×C4—342no—
867C2×C4—342no—
868C2×C4—342no—
869C2×C4—342no—
870C2×C4—342no—
871C2×C4—342no—
872C2×C4—342no—
873C2×C4—342no—
874C2×C4—341no—
875C2×C4—341no—
876C2×C4—341no—
877C2×C4—341no—
878C2×C4—341no—
879C2×C4—341no—
880C2×C4—341no—
881C2×C4—341no—
882C2×C4—341no—
883C2×C4—341no—
884C2×C4—341no—
885C2×C4—341no—
886C2×C4—681no—
887C2×C4—681no—
888C2×C4—681no—
889C2×C4—681no—
890C2×C4—681no—
891C2×C4—681no—
892C2×C4—681no—
893C2×C4—681no—
894C2×C4—681no—
895C2×C4—681no—
896C2×C4—681no—
897C2×C4—681no—
898C2×C4—681no—
899C2×C4—681no—
900C2×C4—681no—
901C2×C4—681no—
902C2×C4—681no—
903C2×C4—681no—
904C2×C4—681no—
905C2×C4—681no—
906C2×C4—681no—
907C2×C4—681no—
908C2×C4—681no—
909C2×C4—681no—
910C2×C4—681no—
911C2×C4—681no—
912C2×C4—681no—
913C2×C4—681no—
914C2×C4—681no—
915C2×C4—681no—
916C2×C4—681no—
917C2×C4—681no—
918C2×C4—681no—
919C2×C4—681no—
920C2×C4—681no—
921C2×C4—681no—
922C2×C4—681no—
923C2×C4—681no—
924C2×C4—681no—
925C2×C4—681no—
926C2×C4C2×C4×#59512yes—
927C2×C4C2×C4×#59512yes—
928C2×C4C2×C4×#59512yes—
929C22—171no—
930C22—171no—
931C22—171no—
932C22—171no—
933C22—171no—
934C22—171no—
935C22—171no—
936C22—171no—
937C22—171no—
938C22—171no—
939C22—171no—
940C22—171no—
941C22—171no—
942C22—171no—
943C22—171no—
944C22—171no—
945C22—171no—
946C22—171no—
947C22—171no—
948C22—171no—
949C22—171no—
950C22—171no—
951C22—171no—
952C22—171no—
953C22—171no—
954C22—171no—
955C22—171no—
956C22—171no—
957C22C22×C4×#59511yescharacteristic
958C22#41×#59511yescharacteristic
959C22#41×#59511yescharacteristic
960C22#1176387611yescharacteristic
961C22#1176387711yescharacteristic
962C22#1176387811yescharacteristic
963C22#1176387811yescharacteristic
964C4—22no—
965C4—22no—
966C4—22no—
967C4—41no—
968C4—41no—
969C4—41no—
970C4—41no—
971C4—344no—
972C4—344no—
973C4—342no—
974C4—342no—
975C4—342no—
976C4—682no—
977C4—682no—
978C4—682no—
979C4—682no—
980C4—682no—
981C4—682no—
982C4—681no—
983C4—681no—
984C4—681no—
985C4—681no—
986C2—171no—
987C2—171no—
988C2—171no—
989C2—171no—
990C2—171no—
991C2—171no—
992C2—171no—
993C2—171no—
994C2#117×#59511yescharacteristic
995C2#1454522311yescharacteristic
996C2#1454522411yescharacteristic
997C2#1454528011yescharacteristic
998C2#1454528211yescharacteristic
999C2#1454528311yescharacteristic
1000C2#1454528411yescharacteristic
subgroupG/H
center, FrattiniC23C23×#595
commutatorC22×C17C22×C42
FittingC17×#387C4
socleC23×C17C23×C4
prime radical, cosocleC23×D17C24
hypercenter#387#595
hypocenterC17#13787
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
24. #11763758C4semidirect
25. C4⋊C4×#595C4semidirect
49. #11762696C4semidirect
50. #11762695C4semidirect
51. #11762694C4semidirect
52. #11762693C4semidirect
53. #11762692C4semidirect
54. #11762691C4semidirect
55. #11762690C4semidirect
60. C17×#387C4semidirect
276. C4⋊C4×C17C42semidirect
279. C4⋊Dic17C42semidirect
282. #63225C42semidirect
283. #63225C42semidirect
520. #387#595semidirect
654. C17#13787semidirect
777. C4⋊C4C4×#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117637582
C2×C4⋊C4×#5952
#145439642
#145439632
#145439612
#145439602
#145439592
C4×(C2×#595)⋊C42
#95×#5952
D17×#3872
#1378717