Finite Group Databasebeta

← #17045446

Subgroups — #17045446

Order 4352.

1028 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762887C211yesmaximal, characteristic, complemented
2C2×#11762776C211yesmaximal, characteristic, complemented
3#14529583C211yesmaximal, characteristic, complemented
4#14529579C211yesmaximal, characteristic, complemented
5#14529399C211yesmaximal, characteristic, complemented
6#14529392C211yesmaximal, characteristic, complemented
7#14529392C211yesmaximal, characteristic, complemented
8#14529392C211yesmaximal, characteristic, complemented
9#14529082C211yesmaximal, characteristic, complemented
10#14529082C211yesmaximal, characteristic, complemented
11#14529077C211yesmaximal, characteristic, complemented
12#14528964C211yesmaximal, characteristic, complemented
13#14528696C211yesmaximal, characteristic, complemented
14#14528568C211yesmaximal, characteristic, complemented
15C17×#2388C211yesmaximal, characteristic
16C22×#63223C2211yescharacteristic
17C22×#63223C2211yescharacteristic
18C23×#3622C2211yescharacteristic
19#11762887—24no—
20C2×C4⋊#3622C2211yescharacteristic
21C2×C4⋊#3622C2211yescharacteristic
22C2×C4⋊#3622C2211yescharacteristic
23#11762776—24no—
24C2×C22⋊#3622C2211yescharacteristic
25C2×C22⋊#3622C2211yescharacteristic
26C2×C22⋊#3622C2211yescharacteristic
27C2×C22⋊#3622C2211yescharacteristic
28C2×C22⋊#3622C2211yescharacteristic
29C2×C22⋊#3622C2211yescharacteristic
30C2×C22⋊#3622C2211yescharacteristic
31C2×C22⋊#3622C2211yescharacteristic
32C2×C22⋊#3622C2211yescharacteristic
33C2×C22⋊#3622C2211yescharacteristic
34C2×C22⋊#3622C2211yescharacteristic
35C2×C22⋊#3622C2211yescharacteristic
36C2×C22⋊#3622C2211yescharacteristic
37C2×#10587474C2211yescharacteristic
38C2×C4×#3622C2211yescharacteristic
39C2×C4×#3622C2211yescharacteristic
40#11762564C2211yescharacteristic
41#11762564C2211yescharacteristic
42#11762564C2211yescharacteristic
43#11762564C2211yescharacteristic
44#11762564C2211yescharacteristic
45#11762564C2211yescharacteristic
46C22×#41×C17C2211yescharacteristic
47C2×C4×D4×C17C2211yescharacteristic
48C2×C4×D4×C17C2211yescharacteristic
49C2×C4×D4×C17C2211yescharacteristic
50C17×#395C411yescharacteristic
51C17×#394C411yescharacteristic
52C17×#394C411yescharacteristic
53C17×#394C411yescharacteristic
54C17×#393C411yescharacteristic
55C17×#392C411yescharacteristic
56C17×#392C411yescharacteristic
57C17×#392C411yescharacteristic
58C4×C22⋊C4×C17C2211yescharacteristic
59C4×C22⋊C4×C17C2211yescharacteristic
60C4×C22⋊C4×C17C2211yescharacteristic
61C2×#41×C17—22no—
62C2×#41×C17—22no—
63C2×#41×C17—41no—
64C2×#41×C17—41no—
65C2×#41×C17—41no—
66C2×#41×C17—41no—
67C22×Q8×C17C2×C411yescharacteristic
68C22×D4×C17C2×C411yescharacteristic
69C22×D4×C17C2×C411yescharacteristic
70C22×D4×C17C2×C411yescharacteristic
71C22×D4×C17C2×C411yescharacteristic
72C22×D4×C17C2×C411yescharacteristic
73C22×D4×C17C2×C411yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C4×D4×C17—22no—
79C4×D4×C17—22no—
80C4×D4×C17—41no—
81C4×D4×C17—41no—
82C4×D4×C17—41no—
83C4×D4×C17—41no—
84C2×C4⋊C4×C17C2×C411yescharacteristic
85C2×C4⋊C4×C17C2×C411yescharacteristic
86C2×C4⋊C4×C17C2×C411yescharacteristic
87C2×C22⋊C4×C17C2×C411yescharacteristic
88C2×C22⋊C4×C17C2×C411yescharacteristic
89C2×C22⋊C4×C17C2×C411yescharacteristic
90C2×C22⋊C4×C17C2×C411yescharacteristic
91C2×C22⋊C4×C17C2×C411yescharacteristic
92C2×C22⋊C4×C17C2×C411yescharacteristic
93C2×C22⋊C4×C17C2×C411yescharacteristic
94C2×C22⋊C4×C17C2×C411yescharacteristic
95C2×C22⋊C4×C17C2×C411yescharacteristic
96C2×C22⋊C4×C17C2×C411yescharacteristic
97C2×C22⋊C4×C17C2×C411yescharacteristic
98C2×C22⋊C4×C17C2×C411yescharacteristic
99C2×C42×C17C2311yescharacteristic
100C2×C42×C17C2311yescharacteristic
101C2×C42×C17C2311yescharacteristic
102C2×#63223—22no—
103C2×#63223—41no—
104C2×#63223—41no—
105C2×#63223—41no—
106C2×#63223—41no—
107C2×#63223D414yescomplemented
108C22×#3622—22no—
109C22×#3622—41no—
110C22×#3622—41no—
111C22×#3622C2311yescharacteristic
112C22×#3622C2311yescharacteristic
113C22×#3622C2311yescharacteristic
114C22×#3622C2311yescharacteristic
115C22×#3622C2311yescharacteristic
116C22×#3622C2311yescharacteristic
117C22×#3622C2311yescharacteristic
118C22×#3622C2311yescharacteristic
119C17×#95C2×C411yescharacteristic
120C17×#95C2×C411yescharacteristic
121C17×#95C2×C411yescharacteristic
122C17×#95C2×C411yescharacteristic
123C17×#95C2×C411yescharacteristic
124C17×#95C2×C411yescharacteristic
125C22⋊#3622—22no—
126C22⋊#3622—22no—
127C22⋊#3622—22no—
128C22⋊#3622—22no—
129C22⋊#3622—22no—
130C22⋊#3622—22no—
131C22⋊#3622—22no—
132C22⋊#3622—41no—
133C22⋊#3622—41no—
134C22⋊#3622—41no—
135C22⋊#3622—41no—
136C22⋊#3622—41no—
137C22⋊#3622—41no—
138C4⋊#3622—22no—
139C4⋊#3622—41no—
140C4⋊#3622—41no—
141#10587474—41no—
142C4×#3622—22no—
143C4×#3622—41no—
144C24×C17C22×C411yescharacteristic
145C24×C17C22×C411yescharacteristic
146C24×C17C22×C411yescharacteristic
147C24×C17C22×C411yescharacteristic
148#41×C17—44no—
149#41×C17—44no—
150#41×C17—44no—
151#41×C17—44no—
152C2×Q8×C17—22no—
153C2×Q8×C17—41no—
154C2×Q8×C17—41no—
155C2×D4×C17—22no—
156C2×D4×C17—22no—
157C2×D4×C17—22no—
158C2×D4×C17—22no—
159C2×D4×C17—22no—
160C2×D4×C17—22no—
161C2×D4×C17—41no—
162C2×D4×C17—41no—
163C2×D4×C17—41no—
164C2×D4×C17—41no—
165C2×D4×C17—41no—
166C2×D4×C17—41no—
167C2×D4×C17—41no—
168C2×D4×C17—41no—
169C2×D4×C17—41no—
170C2×D4×C17—41no—
171C2×D4×C17—41no—
172C2×D4×C17—41no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17C22×C411yescharacteristic
196C22×C4×C17C22×C411yescharacteristic
197C22×C4×C17C22×C411yescharacteristic
198C22×C4×C17C22×C411yescharacteristic
199C22×C4×C17C22×C411yescharacteristic
200C22×C4×C17C22×C411yescharacteristic
201C22×C4×C17C22×C411yescharacteristic
202C22×C4×C17C22×C411yescharacteristic
203C22×C4×C17C22×C411yescharacteristic
204C22×C4×C17C22×C411yescharacteristic
205C22×C4×C17C2×D412yes—
206C22×C4×C17#4112yes—
207C22×C4×C17C2411yescharacteristic
208C4⋊C4×C17—22no—
209C4⋊C4×C17—41no—
210C4⋊C4×C17—41no—
211C22⋊C4×C17—22no—
212C22⋊C4×C17—22no—
213C22⋊C4×C17—22no—
214C22⋊C4×C17—22no—
215C22⋊C4×C17—22no—
216C22⋊C4×C17—22no—
217C22⋊C4×C17—41no—
218C22⋊C4×C17—41no—
219C22⋊C4×C17—41no—
220C22⋊C4×C17—41no—
221C22⋊C4×C17—41no—
222C22⋊C4×C17—41no—
223C42×C17—21no—
224C42×C17—21no—
225C42×C17—21no—
226C42×C17—21no—
227C42×C17—21no—
228C42×C17—21no—
229#63223—44no—
230#63223—44no—
231C2×#3622—21no—
232C2×#3622—21no—
233C2×#3622—21no—
234C2×#3622—21no—
235C2×#3622—21no—
236C2×#3622—21no—
237C2×#3622—21no—
238C2×#3622—21no—
239C2×#3622—21no—
240C2×#3622—21no—
241C2×#3622—21no—
242C2×#3622—21no—
243C2×#3622—21no—
244C2×#3622—21no—
245C2×#3622—21no—
246C2×#3622—21no—
247C2×#3622—21no—
248C2×#3622—21no—
249C2×#3622—21no—
250C2×#3622—21no—
251C2×#3622—21no—
252C2×#3622—21no—
253C2×#3622—44no—
254C2×#3622C2×D412yes—
255C2×#3622C2×D412yes—
256#22039—171nomaximal, Sylow
257C23×C17—21no—
258C23×C17—21no—
259C23×C17—21no—
260C23×C17—21no—
261C23×C17—21no—
262C23×C17—21no—
263C23×C17—21no—
264C23×C17—21no—
265C23×C17—21no—
266C23×C17—21no—
267C23×C17—21no—
268C23×C17—21no—
269C23×C17—21no—
270C23×C17—21no—
271C23×C17—21no—
272C23×C17—21no—
273C23×C17—21no—
274C23×C17—21no—
275C23×C17—21no—
276C23×C17—21no—
277C23×C17—21no—
278C23×C17—21no—
279C23×C17—21no—
280C23×C17—21no—
281C23×C17—21no—
282C23×C17—21no—
283C23×C17—21no—
284C23×C17C4×D412yes—
285C23×C17C23×C411yescharacteristic
286Q8×C17—44no—
287D4×C17—44no—
288D4×C17—44no—
289D4×C17—44no—
290D4×C17—44no—
291D4×C17—44no—
292D4×C17—44no—
293C2×C4×C17—21no—
294C2×C4×C17—21no—
295C2×C4×C17—21no—
296C2×C4×C17—21no—
297C2×C4×C17—21no—
298C2×C4×C17—21no—
299C2×C4×C17—22no—
300C2×C4×C17—22no—
301C2×C4×C17—22no—
302C2×C4×C17—22no—
303C2×C4×C17—21no—
304C2×C4×C17—21no—
305C2×C4×C17—21no—
306C2×C4×C17—21no—
307C2×C4×C17—21no—
308C2×C4×C17—21no—
309C2×C4×C17—21no—
310C2×C4×C17—21no—
311C2×C4×C17—21no—
312C2×C4×C17—21no—
313C2×C4×C17—21no—
314C2×C4×C17—21no—
315C2×C4×C17—21no—
316C2×C4×C17—21no—
317C2×C4×C17—21no—
318C2×C4×C17—21no—
319C2×C4×C17—21no—
320C2×C4×C17—21no—
321C2×C4×C17—21no—
322C2×C4×C17—21no—
323C2×C4×C17—21no—
324C2×C4×C17—41no—
325C2×C4×C17—41no—
326C2×C4×C17—41no—
327C2×C4×C17—41no—
328C2×C4×C17—41no—
329C2×C4×C17—41no—
330C2×C4×C17—41no—
331C2×C4×C17—41no—
332C2×C4×C17—41no—
333C2×C4×C17—41no—
334C2×C4×C17—41no—
335C2×C4×C17—41no—
336C2×C4×C17C4×D412yes—
337C2×C4×C17#13112yes—
338C2×C4×C17#13112yes—
339C2×C4×C17C22×D411yescharacteristic
340C2×C4×C17C2×#4111yescharacteristic
341C2×C4×C17H(5,𝔽2)11yescharacteristic
342C2×C4×C17H(5,𝔽2)11yescharacteristic
343C2×C4×C17H(5,𝔽2)11yescharacteristic
344C2×C4×C17H(5,𝔽2)11yescharacteristic
345#3622—22no—
346#3622—22no—
347#3622—41no—
348#3622—41no—
349#3622—41no—
350#3622—41no—
351#3622—41no—
352#3622—41no—
353C2×#436—171no—
354C2×#408—171no—
355#2388D1711yescharacteristic
356#1955—171no—
357#1954—171no—
358#1924—171no—
359#1923—171no—
360#1923—171no—
361#1923—171no—
362#1870—171no—
363#1870—171no—
364#1869—171no—
365#1850—171no—
366#1780—171no—
367#1753—171no—
368C22×C17—22no—
369C22×C17—22no—
370C22×C17—22no—
371C22×C17—41no—
372C22×C17—41no—
373C22×C17—41no—
374C22×C17—41no—
375C22×C17—41no—
376C22×C17—41no—
377C22×C17—41no—
378C22×C17—41no—
379C22×C17—41no—
380C22×C17—41no—
381C22×C17—41no—
382C22×C17—41no—
383C22×C17—41no—
384C22×C17—41no—
385C22×C17—41no—
386C22×C17—41no—
387C22×C17—41no—
388C22×C17—41no—
389C22×C17—41no—
390C22×C17—41no—
391C22×C17—41no—
392C22×C17—41no—
393C22×C17—41no—
394C22×C17—41no—
395C22×C17—41no—
396C22×C17C2×C4×D411yescharacteristic
397C22×C17#51811yescharacteristic
398C22×C17#51811yescharacteristic
399C22×C17C2×#13111yescharacteristic
400C22×C17C2×#13111yescharacteristic
401C22×C17#56811yescharacteristic
402C22×C17#56811yescharacteristic
403C4×C17—22no—
404C4×C17—22no—
405C4×C17—22no—
406C4×C17—41no—
407C4×C17—41no—
408C4×C17—41no—
409C4×C17—41no—
410C4×C17—41no—
411C4×C17—41no—
412C4×C17—41no—
413C4×C17#53411yescharacteristic
414C4×C17#53511yescharacteristic
415C4×C17#53811yescharacteristic
416C4×C17#53811yescharacteristic
417C22×#41C2×D1711yescharacteristic
418C22×M16—171no—
419C22×M16—171no—
420C23×C8—171no—
421C2×C4×D4C2×D1711yescharacteristic
422C2×C4×D4C2×D1711yescharacteristic
423C2×C4×D4C2×D1711yescharacteristic
424#436—344no—
425C2×C4⋊C8—171no—
426C2×C4⋊C8—171no—
427C2×C4⋊C8—171no—
428#408—344no—
429C2×C22⋊C8—171no—
430C2×C22⋊C8—171no—
431C2×C22⋊C8—171no—
432C2×C22⋊C8—171no—
433C2×C22⋊C8—171no—
434C2×C22⋊C8—171no—
435C2×C22⋊C8—171no—
436C2×C22⋊C8—171no—
437C2×C22⋊C8—171no—
438C2×C22⋊C8—171no—
439C2×C22⋊C8—171no—
440C2×C22⋊C8—171no—
441C2×C22⋊C8—171no—
442C2×#97—171no—
443C2×C4×C8—171no—
444C2×C4×C8—171no—
445#395Dic1711yescharacteristic
446#394Dic1711yescharacteristic
447#394Dic1711yescharacteristic
448#394Dic1711yescharacteristic
449#393Dic1711yescharacteristic
450#392Dic1711yescharacteristic
451#392Dic1711yescharacteristic
452#392Dic1711yescharacteristic
453C4×C22⋊C4C2×D1711yescharacteristic
454C4×C22⋊C4C2×D1711yescharacteristic
455C4×C22⋊C4C2×D1711yescharacteristic
456#336—171no—
457#336—171no—
458#336—171no—
459#336—171no—
460#336—171no—
461#336—171no—
462C2×C17—42no—
463C2×C17—81no—
464C2×C17—81no—
465C2×C17—81no—
466C2×C17#232111yescharacteristic
467C2×C17#293311yescharacteristic
468C2×C17#293511yescharacteristic
469C2×C17#297611yescharacteristic
470C2×C17#297811yescharacteristic
471C2×C17#297911yescharacteristic
472C2×C17#298111yescharacteristic
473C2×#41—22no—
474C2×#41—22no—
475C2×#41—41no—
476C2×#41—41no—
477C2×#41—41no—
478C2×#41—41no—
479C22×Q8C2×Dic1711yescharacteristic
480C22×D4C2×Dic1711yescharacteristic
481C22×D4C2×Dic1711yescharacteristic
482C22×D4C2×Dic1711yescharacteristic
483C22×D4C2×Dic1711yescharacteristic
484C22×D4C2×Dic1711yescharacteristic
485C22×D4C2×Dic1711yescharacteristic
486C23×C4C22×D1711yescharacteristic
487C23×C4C22×D1711yescharacteristic
488C23×C4C22×D1711yescharacteristic
489C23×C4C22×D1711yescharacteristic
490C2×M16—174no—
491C2×M16—342no—
492C2×M16—681no—
493C2×M16—681no—
494C2×M16—681no—
495C2×M16—681no—
496C22×C8—171no—
497C22×C8—171no—
498C22×C8—171no—
499C22×C8—171no—
500C22×C8—171no—
501C22×C8—171no—
502C22×C8—171no—
503C22×C8—171no—
504C22×C8—342no—
505C22×C8—681no—
506C22×C8—681no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—41no—
510C4×D4—41no—
511C4×D4—41no—
512C4×D4—41no—
513C2×C4⋊C4C2×Dic1711yescharacteristic
514C2×C4⋊C4C2×Dic1711yescharacteristic
515C2×C4⋊C4C2×Dic1711yescharacteristic
516C2×C22⋊C4C2×Dic1711yescharacteristic
517C2×C22⋊C4C2×Dic1711yescharacteristic
518C2×C22⋊C4C2×Dic1711yescharacteristic
519C2×C22⋊C4C2×Dic1711yescharacteristic
520C2×C22⋊C4C2×Dic1711yescharacteristic
521C2×C22⋊C4C2×Dic1711yescharacteristic
522C2×C22⋊C4C2×Dic1711yescharacteristic
523C2×C22⋊C4C2×Dic1711yescharacteristic
524C2×C22⋊C4C2×Dic1711yescharacteristic
525C2×C22⋊C4C2×Dic1711yescharacteristic
526C2×C22⋊C4C2×Dic1711yescharacteristic
527C2×C22⋊C4C2×Dic1711yescharacteristic
528C2×C42C22×D1711yescharacteristic
529C2×C42C22×D1711yescharacteristic
530C2×C42C22×D1711yescharacteristic
531C4⋊C8—342no—
532C4⋊C8—681no—
533C4⋊C8—681no—
534C22⋊C8—342no—
535C22⋊C8—342no—
536C22⋊C8—342no—
537C22⋊C8—342no—
538C22⋊C8—342no—
539C22⋊C8—342no—
540C22⋊C8—342no—
541C22⋊C8—681no—
542C22⋊C8—681no—
543C22⋊C8—681no—
544C22⋊C8—681no—
545C22⋊C8—681no—
546C22⋊C8—681no—
547#97—681no—
548C4×C8—342no—
549C4×C8—681no—
550#95C2×Dic1711yescharacteristic
551#95C2×Dic1711yescharacteristic
552#95C2×Dic1711yescharacteristic
553#95C2×Dic1711yescharacteristic
554#95C2×Dic1711yescharacteristic
555#95C2×Dic1711yescharacteristic
556C17#2203911yescharacteristic, complemented, Sylow
557C24C22×Dic1711yescharacteristic
558C24C22×Dic1711yescharacteristic
559C24C22×Dic1711yescharacteristic
560C24C22×Dic1711yescharacteristic
561#41—44no—
562#41—44no—
563#41—44no—
564#41—44no—
565C2×Q8—22no—
566C2×Q8—41no—
567C2×Q8—41no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4D4×D1712yes—
609C22×C4#6325412yes—
610C22×C4C22×Dic1711yescharacteristic
611C22×C4C22×Dic1711yescharacteristic
612C22×C4C22×Dic1711yescharacteristic
613C22×C4C22×Dic1711yescharacteristic
614C22×C4C22×Dic1711yescharacteristic
615C22×C4C22×Dic1711yescharacteristic
616C22×C4C22×Dic1711yescharacteristic
617C22×C4C22×Dic1711yescharacteristic
618C22×C4C22×Dic1711yescharacteristic
619C22×C4C22×Dic1711yescharacteristic
620C22×C4C23×D1711yescharacteristic
621M16—684no—
622M16—684no—
623C2×C8—172no—
624C2×C8—172no—
625C2×C8—341no—
626C2×C8—341no—
627C2×C8—341no—
628C2×C8—341no—
629C2×C8—341no—
630C2×C8—341no—
631C2×C8—341no—
632C2×C8—341no—
633C2×C8—341no—
634C2×C8—341no—
635C2×C8—341no—
636C2×C8—341no—
637C2×C8—341no—
638C2×C8—341no—
639C2×C8—341no—
640C2×C8—341no—
641C2×C8—341no—
642C2×C8—341no—
643C2×C8—341no—
644C2×C8—341no—
645C2×C8—341no—
646C2×C8—341no—
647C2×C8—684no—
648C4⋊C4—22no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—41no—
658C22⋊C4—41no—
659C22⋊C4—41no—
660C22⋊C4—41no—
661C22⋊C4—41no—
662C22⋊C4—41no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23D4×Dic1712yes—
697C23C23×Dic1711yescharacteristic
698Q8—44no—
699D4—44no—
700D4—44no—
701D4—44no—
702D4—44no—
703D4—44no—
704D4—44no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
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—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4D4×Dic1712yes—
749C2×C4#1058763412yes—
750C2×C4#1058763412yes—
751C2×C4C2×D4×D1711yescharacteristic
752C2×C4C2×#6325411yescharacteristic
753C2×C4#1058769111yescharacteristic
754C2×C4#1058769111yescharacteristic
755C2×C4#1058769111yescharacteristic
756C2×C4#1058769111yescharacteristic
757C8—342no—
758C8—342no—
759C8—681no—
760C8—681no—
761C8—681no—
762C8—681no—
763C8—681no—
764C8—681no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22C2×D4×Dic1711yescharacteristic
794C22#1176328411yescharacteristic
795C22#1176328411yescharacteristic
796C22C2×#1058763411yescharacteristic
797C22C2×#1058763411yescharacteristic
798C22#1176357611yescharacteristic
799C22#1176357611yescharacteristic
800C4—22no—
801C4—22no—
802C4—22no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4#1176336911yescharacteristic
811C4#1176337411yescharacteristic
812C4#1176339411yescharacteristic
813C4#1176339411yescharacteristic
814C2—42no—
815C2—81no—
816C2—81no—
817C2—81no—
818C2#1453144511yescharacteristic
819C2#1453751111yescharacteristic
820C2#1453752811yescharacteristic
821C2#1453783211yescharacteristic
822C2#1453784611yescharacteristic
823C2#1453785111yescharacteristic
824C2#1453786011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
Fitting, prime radicalC17×#2388C2
cosocleC22×C4×C17C24
hypercenter#2388D17
hypocenterC17#22039
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #2388

Complements

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

NH ≅ G/Ntype
1. C2×#11762887C2semidirect
2. C2×#11762776C2semidirect
3. #14529583C2semidirect
4. #14529579C2semidirect
5. #14529399C2semidirect
6. #14529392C2semidirect
7. #14529392C2semidirect
8. #14529392C2semidirect
9. #14529082C2semidirect
10. #14529082C2semidirect
11. #14529077C2semidirect
12. #14528964C2semidirect
13. #14528696C2semidirect
14. #14528568C2semidirect
107. C2×#63223D4semidirect
556. C17#22039semidirect

Maximal subgroups

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

subgroupindex
C2×#117628872
C2×#117627762
#145295832
#145295792
#145293992
#145293922
#145290822
#145290772
#145289642
#145286962
#145285682
C17×#23882
#2203917