Finite Group Databasebeta

← #17963006

Subgroups — #17963006

Order 4352.

1434 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763760C211yesmaximal, characteristic
2C2×#11763758C211yesmaximal, characteristic
3#14543964C211yesmaximal, characteristic
4#14543964C211yesmaximal, characteristic
5#14543964C211yesmaximal, characteristic
6#14543964C211yesmaximal, characteristic
7#14543964C211yesmaximal, characteristic
8#14543963C211yesmaximal, characteristic
9#14543962C211yesmaximal, characteristic
10#14543961C211yesmaximal, characteristic
11#14543959C211yesmaximal, characteristic
12C4×(C2×#595)⋊C4C211yesmaximal, characteristic
13#95×#595C211yesmaximal, 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
24C22×C4×#595C2211yescharacteristic
25C22×C4×#595C2211yescharacteristic
26#11763760C418yescomplemented
27#11763758C418yescomplemented
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—41no—
77C2×C4⋊#595—41no—
78C2×C4⋊#595—41no—
79C2×C4⋊#595—41no—
80C2×C4⋊#595—41no—
81C2×C4⋊#595—41no—
82C2×C4⋊#595—41no—
83C2×C4⋊#595—41no—
84C2×C4⋊#595C2×C414yes—
85C2×C4⋊#595C2×C414yes—
86C2×C4⋊#595C2×C414yes—
87C2×C4⋊#595C2×C414yes—
88C2×C4×#595—22no—
89C2×C4×#595—22no—
90C2×C4×#595—22no—
91C2×C4×#595—41no—
92C2×C4×#595—41no—
93C2×C4×#595—41no—
94C2×C4×#595—41no—
95C2×C4×#595—41no—
96C2×C4×#595—41no—
97C2×C4×#595—41no—
98C2×C4×#595—41no—
99C2×C4×#595—41no—
100C2×C4×#595—41no—
101C2×C4×#595—41no—
102C2×C4×#595—41no—
103C2×C4×#595C2×C414yes—
104C2×C4×#595C2×C414yes—
105C2×C4×#595Q814yes—
106C2×C4⋊C4×C17C2×C411yescharacteristic
107C2×C4⋊C4×C17C2×C411yescharacteristic
108C2×C42×C17C2×C411yescharacteristic
109C2×C4⋊Dic17C2×C411yescharacteristic
110C2×C4⋊Dic17C2×C411yescharacteristic
111C2×#63225C2×C411yescharacteristic
112C2×#63225C2×C411yescharacteristic
113C2×#63225C2×C411yescharacteristic
114C2×#63225C2×C411yescharacteristic
115C2×C4×Dic17C2×C411yescharacteristic
116C2×C4×Dic17C2×C411yescharacteristic
117C2×C4×Dic17C2×C411yescharacteristic
118C4⋊C4×D17—41no—
119C4⋊C4×D17—41no—
120C4⋊C4×D17C2×C414yes—
121C4⋊C4×D17C2×C414yes—
122C42×D17—41no—
123C42×D17—41no—
124(C2×#595)⋊C4—22no—
125(C2×#595)⋊C4—22no—
126(C2×#595)⋊C4—22no—
127(C2×#595)⋊C4—22no—
128(C2×#595)⋊C4—22no—
129(C2×#595)⋊C4—22no—
130(C2×#595)⋊C4—41no—
131(C2×#595)⋊C4—41no—
132(C2×#595)⋊C4—41no—
133(C2×#595)⋊C4—41no—
134(C2×#595)⋊C4—41no—
135(C2×#595)⋊C4—41no—
136(C2×#595)⋊C4C2×C414yes—
137(C2×#595)⋊C4C2×C414yes—
138(C2×#595)⋊C4C2×C414yes—
139(C2×#595)⋊C4C2×C414yes—
140(C2×#595)⋊C4C2×C414yes—
141(C2×#595)⋊C4C2×C414yes—
142C17×#95C2×C411yescharacteristic
143C17×#95C2×C411yescharacteristic
144C17×#95C2×C411yescharacteristic
145C17×#95C2×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
154#10587502C2×C411yescharacteristic
155#10587502C2×C411yescharacteristic
156#10587502C2×C411yescharacteristic
157#10587502C2×C411yescharacteristic
158C23×D17C2411yescharacteristic
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×#595—21no—
200C22×#595—21no—
201C22×#595—21no—
202C22×#595—21no—
203C22×#595C22×C412yes—
204C22×#595C22×C412yes—
205C22×#595C22×C412yes—
206C22×#595C22×C412yes—
207C22×#595C22×C412yes—
208C22×#595C22×C412yes—
209C22×#595C22×C412yes—
210C22×#595C22×C412yes—
211C22×#595C2×Q812yes—
212C22×#595C2×Q812yes—
213C22×#595#4112yes—
214C22×#595#4112yes—
215C22×C4×C17C22×C411yescharacteristic
216C22×C4×C17C22×C411yescharacteristic
217C22×C4×C17C22×C411yescharacteristic
218C22×C4×C17C22×C411yescharacteristic
219C22×C4×C17C22×C411yescharacteristic
220C22×C4×C17C22×C411yescharacteristic
221C22×C4×C17C22×C411yescharacteristic
222C22×Dic17C22×C411yescharacteristic
223C22×Dic17C22×C411yescharacteristic
224C22×Dic17C22×C411yescharacteristic
225C22×Dic17C22×C411yescharacteristic
226C22×Dic17C22×C411yescharacteristic
227C22×Dic17C22×C411yescharacteristic
228C22×Dic17C22×C411yescharacteristic
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×D17—21no—
262C2×C4×D17—21no—
263C2×C4×D17C22×C412yes—
264C2×C4×D17C22×C412yes—
265C2×C4×D17C22×C412yes—
266C2×C4×D17C22×C412yes—
267C2×C4×D17C22×C412yes—
268C2×C4×D17C22×C412yes—
269C2×C4×D17C2×Q812yes—
270C2×C4×D17#4112yes—
271C4⋊#595—44no—
272C4⋊#595—44no—
273C4⋊#595—44no—
274C4⋊#595—44no—
275C4×#595—44no—
276C4×#595—44no—
277C4×#595—44no—
278C4×#595—44no—
279C4×#595—44no—
280C4×#595—44no—
281C4⋊C4×C17—41no—
282C4⋊C4×C17C4214yescomplemented
283C42×C17—41no—
284C4⋊Dic17—41no—
285C4⋊Dic17C4214yescomplemented
286#63225—41no—
287#63225—41no—
288#63225C4214yescomplemented
289#63225C4214yescomplemented
290C4×Dic17—41no—
291C4×Dic17—41no—
292C4×Dic17—41no—
293#13792—171nomaximal, Sylow
294C23×C17C23×C411yescharacteristic
295C22×D17C23×C411yescharacteristic
296C22×D17C23×C411yescharacteristic
297C22×D17C22×Q811yescharacteristic
298C22×D17C2×#4111yescharacteristic
299C22×D17C2×#4111yescharacteristic
300C22×D17C2×#4111yescharacteristic
301C22×D17H(5,𝔽2)11yescharacteristic
302C22×D17H(5,𝔽2)11yescharacteristic
303C22×D17H(5,𝔽2)11yescharacteristic
304C22×D17H(5,𝔽2)11yescharacteristic
305C22×D17H(5,𝔽2)11yescharacteristic
306C22×D172−1+411yescharacteristic
307C22×D172−1+411yescharacteristic
308C22×D172−1+411yescharacteristic
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—22no—
334C2×#595—22no—
335C2×#595—22no—
336C2×#595—22no—
337C2×#595—22no—
338C2×#595—22no—
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—41no—
358C2×#595—41no—
359C2×#595—41no—
360C2×#595—41no—
361C2×#595—41no—
362C2×#595—41no—
363C2×#595C4×Q814yes—
364C2×#595C4×Q814yes—
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×C17—21no—
378C2×C4×C17—21no—
379C2×C4×C17—21no—
380C2×C4×C17—21no—
381C2×C4×C17—21no—
382C2×C4×C17C2×C4212yes—
383C2×C4×C17C2×C4212yes—
384C2×C4×C17C2×C4212yes—
385C2×C4×C17C4×Q812yes—
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×Dic17—21no—
399C2×Dic17—21no—
400C2×Dic17—21no—
401C2×Dic17—21no—
402C2×Dic17—21no—
403C2×Dic17C2×C4212yes—
404C2×Dic17C2×C4212yes—
405C2×Dic17C2×C4212yes—
406C2×Dic17C4×Q812yes—
407C4×D17—22no—
408C4×D17—22no—
409C4×D17—22no—
410C4×D17—22no—
411C4×D17—22no—
412C4×D17—22no—
413C4×D17—22no—
414C4×D17—22no—
415C4×D17—22no—
416C4×D17—22no—
417C4×D17—22no—
418C4×D17—22no—
419C4×D17—22no—
420C4×D17—22no—
421C4×D17—22no—
422C4×D17—22no—
423C4×D17—41no—
424C4×D17—41no—
425C4×D17—41no—
426C4×D17—41no—
427C4×D17—41no—
428C4×D17—41no—
429C4×D17—41no—
430C4×D17—41no—
431C4×D17—41no—
432C4×D17—41no—
433C4×D17—41no—
434C4×D17—41no—
435C2×#389—171no—
436C2×#387—171no—
437C2×#387—171no—
438#1436—171no—
439#1436—171no—
440#1436—171no—
441#1436—171no—
442#1436—171no—
443#1436—171no—
444C4⋊#95—171no—
445C4⋊#95—171no—
446#1434—171no—
447C4×#95—171no—
448C4×#95—171no—
449C4×#95—171no—
450C22×C17C22×C4211yescharacteristic
451C22×C17C2×C4×Q811yescharacteristic
452C22×C17C4×#4111yescharacteristic
453C22×C17#51811yescharacteristic
454C22×C17#52011yescharacteristic
455C22×C17#52011yescharacteristic
456C22×C17#52011yescharacteristic
457C2×D17C2×C4×Q811yescharacteristic
458C2×D17C2×C4×Q811yescharacteristic
459C2×D17C4×#4111yescharacteristic
460C2×D17C4×#4111yescharacteristic
461C2×D17#51811yescharacteristic
462C2×D17#51811yescharacteristic
463C2×D17#51811yescharacteristic
464C2×D17#51911yescharacteristic
465C2×D17#52011yescharacteristic
466C2×D17#52011yescharacteristic
467C2×D17#52011yescharacteristic
468C2×D17#52011yescharacteristic
469C2×D17#53811yescharacteristic
470C2×D17#53811yescharacteristic
471C2×D17#53811yescharacteristic
472C2×D17#53911yescharacteristic
473C2×D17#53911yescharacteristic
474C2×D17#53911yescharacteristic
475C2×D17#54011yescharacteristic
476C2×D17#54011yescharacteristic
477C2×D17#54111yescharacteristic
478C2×D17#54111yescharacteristic
479C2×D17#54211yescharacteristic
480C2×D17#54211yescharacteristic
481C2×D17#54311yescharacteristic
482C2×D17#54411yescharacteristic
483C2×D17#54411yescharacteristic
484C2×D17#54411yescharacteristic
485#595—24no—
486#595—24no—
487#595—42no—
488#595—42no—
489#595—42no—
490#595—42no—
491#595—42no—
492#595—42no—
493C4×C17—22no—
494C4×C17—22no—
495C4×C17—22no—
496C4×C17—22no—
497C4×C17—41no—
498C4×C17—41no—
499C4×C17—41no—
500Dic17—22no—
501Dic17—22no—
502Dic17—22no—
503Dic17—22no—
504Dic17—41no—
505Dic17—41no—
506Dic17—41no—
507C22×C4⋊C4—171no—
508C22×C4⋊C4—171no—
509C22×C4⋊C4—171no—
510C22×C4⋊C4—171no—
511C22×C4⋊C4—171no—
512C22×C4⋊C4—171no—
513C22×C42—171no—
514C22×C42—171no—
515C22×C42—171no—
516C22×C42—171no—
517C22×C42—171no—
518C22×C42—171no—
519C22×C42—171no—
520#389—178no—
521#387—178no—
522#387—171no—
523#387—171no—
524#387—171no—
525#387—171no—
526#387—171no—
527#387—171no—
528#387—171no—
529#387#59511yescharacteristic, complemented
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×#95—171no—
547C2×#95—171no—
548C2×#95—171no—
549C2×#95—171no—
550C2×#95—171no—
551C2×#95—171no—
552C2×C17C42×Q811yescharacteristic
553C2×C17#227411yescharacteristic
554C2×C17#227511yescharacteristic
555C2×C17#232911yescharacteristic
556C2×C17#233011yescharacteristic
557C2×C17#233411yescharacteristic
558C2×C17#233511yescharacteristic
559D17#232911yescharacteristic
560D17#232911yescharacteristic
561D17#233011yescharacteristic
562D17#233111yescharacteristic
563D17#233311yescharacteristic
564D17#233411yescharacteristic
565D17#233511yescharacteristic
566D17#233611yescharacteristic
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—
576C23×C4—171no—
577C23×C4—171no—
578C23×C4—171no—
579C23×C4—171no—
580C23×C4—171no—
581C23×C4—171no—
582C2×C4⋊C4—171no—
583C2×C4⋊C4—171no—
584C2×C4⋊C4—171no—
585C2×C4⋊C4—174no—
586C2×C4⋊C4—174no—
587C2×C4⋊C4—174no—
588C2×C4⋊C4—174no—
589C2×C4⋊C4—174no—
590C2×C4⋊C4—174no—
591C2×C4⋊C4—171no—
592C2×C4⋊C4—171no—
593C2×C4⋊C4—171no—
594C2×C4⋊C4—681no—
595C2×C4⋊C4—681no—
596C2×C4⋊C4—681no—
597C2×C4⋊C4—681no—
598C2×C4⋊C4—681no—
599C2×C4⋊C4—681no—
600C2×C4⋊C4—681no—
601C2×C4⋊C4—681no—
602C2×C4⋊C4—681no—
603C2×C4⋊C4—681no—
604C2×C4⋊C4C2×#59511yescharacteristic
605C2×C4⋊C4C2×#59511yescharacteristic
606C2×C42—174no—
607C2×C42—174no—
608C2×C42—174no—
609C2×C42—171no—
610C2×C42—171no—
611C2×C42—171no—
612C2×C42—342no—
613C2×C42—342no—
614C2×C42—342no—
615C2×C42—681no—
616C2×C42—681no—
617C2×C42—681no—
618C2×C42—681no—
619C2×C42—681no—
620C2×C42—681no—
621C2×C42—681no—
622C2×C42—681no—
623C2×C42—681no—
624C2×C42—681no—
625C2×C42—681no—
626C2×C42—681no—
627C2×C42—681no—
628C2×C42—681no—
629C2×C42C2×#59511yescharacteristic
630#95—174no—
631#95—174no—
632#95—174no—
633#95—174no—
634#95—174no—
635#95—174no—
636#95—171no—
637#95—171no—
638#95—171no—
639#95—171no—
640#95—171no—
641#95—171no—
642#95—171no—
643#95—171no—
644#95—171no—
645#95—171no—
646#95—171no—
647#95—171no—
648#95—342no—
649#95—342no—
650#95—342no—
651#95—342no—
652#95—342no—
653#95—342no—
654#95—681no—
655#95—681no—
656#95—681no—
657#95—681no—
658#95—681no—
659#95—681no—
660#95C2×#59511yescharacteristic
661#95C2×#59511yescharacteristic
662#95C2×#59511yescharacteristic
663#95C2×#59511yescharacteristic
664C17#1379211yescharacteristic, complemented, Sylow
665C24—171no—
666C22×C4—172no—
667C22×C4—172no—
668C22×C4—172no—
669C22×C4—172no—
670C22×C4—172no—
671C22×C4—172no—
672C22×C4—171no—
673C22×C4—171no—
674C22×C4—171no—
675C22×C4—171no—
676C22×C4—172no—
677C22×C4—172no—
678C22×C4—172no—
679C22×C4—172no—
680C22×C4—172no—
681C22×C4—172no—
682C22×C4—172no—
683C22×C4—172no—
684C22×C4—172no—
685C22×C4—172no—
686C22×C4—172no—
687C22×C4—172no—
688C22×C4—172no—
689C22×C4—172no—
690C22×C4—171no—
691C22×C4—171no—
692C22×C4—171no—
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×C4—341no—
762C22×C4—341no—
763C22×C4—341no—
764C22×C4—341no—
765C22×C4—341no—
766C22×C4—341no—
767C22×C4—341no—
768C22×C4—341no—
769C22×C4—341no—
770C22×C4—341no—
771C22×C4C22×#59511yescharacteristic
772C22×C4C22×#59511yescharacteristic
773C22×C4C22×#59511yescharacteristic
774C22×C4C22×#59511yescharacteristic
775C22×C4C22×#59511yescharacteristic
776C22×C4C22×#59511yescharacteristic
777C22×C4C22×#59511yescharacteristic
778C4⋊C4—41no—
779C4⋊C4—174no—
780C4⋊C4—174no—
781C4⋊C4—174no—
782C4⋊C4—681no—
783C4⋊C4—681no—
784C4⋊C4—681no—
785C4⋊C4—684no—
786C4⋊C4—684no—
787C4⋊C4—684no—
788C4⋊C4—684no—
789C4⋊C4C4×#59514yescomplemented
790C42—41no—
791C42—681no—
792C42—681no—
793C42—681no—
794C42—684no—
795C42—684no—
796C42—684no—
797C42—684no—
798C42—684no—
799C42—684no—
800C23—171no—
801C23—171no—
802C23—171no—
803C23—171no—
804C23—171no—
805C23—171no—
806C23—171no—
807C23—171no—
808C23—171no—
809C23—171no—
810C23—171no—
811C23—171no—
812C23—171no—
813C23—171no—
814C23C23×#59511yescharacteristic
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—174no—
833C2×C4—174no—
834C2×C4—172no—
835C2×C4—172no—
836C2×C4—172no—
837C2×C4—172no—
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—342no—
851C2×C4—342no—
852C2×C4—342no—
853C2×C4—342no—
854C2×C4—342no—
855C2×C4—342no—
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—341no—
867C2×C4—341no—
868C2×C4—341no—
869C2×C4—341no—
870C2×C4—341no—
871C2×C4—341no—
872C2×C4—341no—
873C2×C4—341no—
874C2×C4—342no—
875C2×C4—342no—
876C2×C4—342no—
877C2×C4—342no—
878C2×C4—342no—
879C2×C4—342no—
880C2×C4—342no—
881C2×C4—342no—
882C2×C4—342no—
883C2×C4—342no—
884C2×C4—342no—
885C2×C4—342no—
886C2×C4—342no—
887C2×C4—342no—
888C2×C4—342no—
889C2×C4—342no—
890C2×C4—342no—
891C2×C4—342no—
892C2×C4—341no—
893C2×C4—341no—
894C2×C4—341no—
895C2×C4—341no—
896C2×C4—341no—
897C2×C4—341no—
898C2×C4—341no—
899C2×C4—341no—
900C2×C4—341no—
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×C4—681no—
927C2×C4—681no—
928C2×C4—681no—
929C2×C4—681no—
930C2×C4—681no—
931C2×C4—681no—
932C2×C4—681no—
933C2×C4—681no—
934C2×C4—681no—
935C2×C4—681no—
936C2×C4—681no—
937C2×C4C2×C4×#59512yes—
938C2×C4C2×C4×#59512yes—
939C2×C4C2×C4×#59512yes—
940C2×C4Q8×#59512yes—
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—
957C22—171no—
958C22—171no—
959C22—171no—
960C22—171no—
961C22—171no—
962C22—171no—
963C22—171no—
964C22—171no—
965C22—171no—
966C22—171no—
967C22—171no—
968C22—171no—
969C22C22×C4×#59511yescharacteristic
970C22C2×Q8×#59511yescharacteristic
971C22#41×#59511yescharacteristic
972C22#1176387611yescharacteristic
973C22#1176387811yescharacteristic
974C22#1176387811yescharacteristic
975C22#1176387811yescharacteristic
976C4—22no—
977C4—22no—
978C4—22no—
979C4—22no—
980C4—41no—
981C4—41no—
982C4—41no—
983C4—344no—
984C4—344no—
985C4—342no—
986C4—342no—
987C4—342no—
988C4—342no—
989C4—682no—
990C4—682no—
991C4—682no—
992C4—682no—
993C4—682no—
994C4—682no—
995C4—681no—
996C4—681no—
997C4—681no—
998C2—171no—
999C2—171no—
1000C2—171no—
1001C2—171no—
1002C2—171no—
1003C2—171no—
1004C2—171no—
1005C2—171no—
1006C2C4×Q8×#59511yescharacteristic
1007C2#1454522111yescharacteristic
1008C2#1454522311yescharacteristic
1009C2#1454527711yescharacteristic
1010C2#1454527811yescharacteristic
1011C2#1454528211yescharacteristic
1012C2#1454528311yescharacteristic
subgroupG/H
center, FrattiniC23C23×#595
commutatorC22×C17C22×C42
FittingC17×#387C4
socleC23×C17C23×C4
prime radical, cosocleC23×D17C24
hypercenter#387#595
hypocenterC17#13792
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
26. #11763760C4semidirect
27. #11763758C4semidirect
49. #11762696C4semidirect
50. #11762695C4semidirect
51. #11762694C4semidirect
52. #11762693C4semidirect
53. #11762692C4semidirect
54. #11762691C4semidirect
55. #11762690C4semidirect
60. C17×#387C4semidirect
282. C4⋊C4×C17C42semidirect
285. C4⋊Dic17C42semidirect
288. #63225C42semidirect
289. #63225C42semidirect
529. #387#595semidirect
664. C17#13792semidirect
789. C4⋊C4C4×#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117637602
C2×#117637582
#145439642
#145439632
#145439622
#145439612
#145439592
C4×(C2×#595)⋊C42
#95×#5952
D17×#3872
#1379217