Finite Group Databasebeta

← #17045438

Subgroups — #17045438

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×#11762884C211yesmaximal, characteristic, complemented
2C2×#11762776C211yesmaximal, characteristic, complemented
3#14531997C211yesmaximal, characteristic
4#14529580C211yesmaximal, characteristic, complemented
5#14529576C211yesmaximal, characteristic, complemented
6#14529394C211yesmaximal, characteristic, complemented
7#14529393C211yesmaximal, characteristic, complemented
8#14529393C211yesmaximal, characteristic, complemented
9#14529387C211yesmaximal, characteristic, complemented
10#14529078C211yesmaximal, characteristic, complemented
11#14529078C211yesmaximal, characteristic, complemented
12#14529074C211yesmaximal, characteristic, complemented
13#14528961C211yesmaximal, characteristic, complemented
14#14528570C211yesmaximal, characteristic, complemented
15C17×#1780C211yesmaximal, characteristic, complemented
16C22×#63223C2211yescharacteristic
17C22×#63218C2211yescharacteristic
18C23×#3622C2211yescharacteristic
19C2×C4×C22⋊D17C2211yescharacteristic
20C2×C4×C22⋊D17C2211yescharacteristic
21C2×C4×C22⋊D17C2211yescharacteristic
22#11762884—24no—
23C2×#10587485C2211yescharacteristic
24C2×#10587485C2211yescharacteristic
25C2×#10587485C2211yescharacteristic
26#11762776—24no—
27C2×C22⋊#3622C2211yescharacteristic
28C2×C22⋊#3622C2211yescharacteristic
29C2×C22⋊#3622C2211yescharacteristic
30C2×C22⋊#3622C2211yescharacteristic
31C2×#10587491C2211yescharacteristic
32C2×#10587491C2211yescharacteristic
33C2×#10587491C2211yescharacteristic
34C2×#10587486C2211yescharacteristic
35C2×C8×Dic17C2211yescharacteristic
36C2×C8×Dic17C2211yescharacteristic
37#11762728C411yescharacteristic
38#11762723C411yescharacteristic
39#11762723C411yescharacteristic
40#11762723C411yescharacteristic
41#11762720C411yescharacteristic
42#11762717C411yescharacteristic
43#11762717C411yescharacteristic
44#11762717C411yescharacteristic
45C4×C22⋊Dic17C2211yescharacteristic
46C4×C22⋊Dic17C2211yescharacteristic
47C4×C22⋊Dic17C2211yescharacteristic
48#11762563C2211yescharacteristic
49#11762563C2211yescharacteristic
50#11762563C2211yescharacteristic
51#11762563C2211yescharacteristic
52#11762563C2211yescharacteristic
53#11762563C2211yescharacteristic
54C22×#41×C17C2211yescharacteristic
55C2×C17×C22⋊C8C2211yescharacteristic
56C2×C17×C22⋊C8C2211yescharacteristic
57C2×C17×C22⋊C8C2211yescharacteristic
58C2×C17×C22⋊C8C2211yescharacteristic
59C2×C17×C22⋊C8C2211yescharacteristic
60C2×C17×C22⋊C8C2211yescharacteristic
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
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C22×C22⋊D17C2×C411yescharacteristic
75C22×C22⋊D17C2×C411yescharacteristic
76C22×C22⋊D17C2×C411yescharacteristic
77C22×C4×D17C2311yescharacteristic
78C22×C8×C17C2311yescharacteristic
79C22×C8×C17C2311yescharacteristic
80C22×C8×C17C2311yescharacteristic
81C22×C8×C17C2311yescharacteristic
82C2×C22⋊Dic17C2×C411yescharacteristic
83C2×C22⋊Dic17C2×C411yescharacteristic
84C2×C22⋊Dic17C2×C411yescharacteristic
85C2×C22⋊Dic17C2×C411yescharacteristic
86C2×C22⋊Dic17C2×C411yescharacteristic
87C2×C22⋊Dic17C2×C411yescharacteristic
88C2×C22⋊Dic17C2×C411yescharacteristic
89C2×C22⋊Dic17C2×C411yescharacteristic
90C2×C22⋊Dic17C2×C411yescharacteristic
91C4×C22⋊D17—22no—
92C4×C22⋊D17—22no—
93C4×C22⋊D17—41no—
94C4×C22⋊D17—41no—
95C4×C22⋊D17—41no—
96C4×C22⋊D17—41no—
97C2×#63227C2×C411yescharacteristic
98C2×#63227C2×C411yescharacteristic
99C2×#63227C2×C411yescharacteristic
100C2×#63225C2×C411yescharacteristic
101C2×#63225C2×C411yescharacteristic
102C2×#63225C2×C411yescharacteristic
103C2×C4×Dic17C2311yescharacteristic
104C2×C4×Dic17C2311yescharacteristic
105C2×C4×Dic17C2311yescharacteristic
106C2×#63223—41no—
107C2×#63223—41no—
108C2×#63223D414yescomplemented
109C22×#3622—22no—
110C22×#3622—41no—
111C22×#3622—41no—
112C22×#3622C2311yescharacteristic
113C22×#3622C2311yescharacteristic
114C22×#3622C2311yescharacteristic
115C22×#3622C2311yescharacteristic
116C2×#63218—22no—
117C2×#63218—41no—
118C2×#63218—41no—
119C17×C22⋊C8—22no—
120C17×C22⋊C8—22no—
121C17×C22⋊C8—41no—
122C17×C22⋊C8—41no—
123C17×C22⋊C8—41no—
124C17×C22⋊C8—41no—
125#10587502C2×C411yescharacteristic
126#10587502C2×C411yescharacteristic
127#10587502C2×C411yescharacteristic
128#10587502C2×C411yescharacteristic
129#10587502C2×C411yescharacteristic
130#10587502C2×C411yescharacteristic
131C22⋊#3622—22no—
132C22⋊#3622—22no—
133C22⋊#3622—22no—
134C22⋊#3622—22no—
135#10587491—22no—
136#10587491—41no—
137#10587491—41no—
138#10587486—41no—
139#10587485—22no—
140#10587485—41no—
141#10587485—41no—
142C8×Dic17—22no—
143C8×Dic17—41no—
144C24×C17C22×C411yescharacteristic
145C24×C17C22×C411yescharacteristic
146C24×C17C22×C411yescharacteristic
147C23×D17C22×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—41no—
159C2×D4×C17—41no—
160C2×D4×C17—41no—
161C2×D4×C17—41no—
162C2×D4×C17—41no—
163C2×D4×C17—41no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
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×C17C22×C411yescharacteristic
181C22×C4×C17C22×C411yescharacteristic
182C22×C4×C17C22×C411yescharacteristic
183C22×C4×C17C2×D412yes—
184C22×C4×C17#4112yes—
185C22×C4×C17C2411yescharacteristic
186C2×C22⋊D17—22no—
187C2×C22⋊D17—22no—
188C2×C22⋊D17—22no—
189C2×C22⋊D17—41no—
190C2×C22⋊D17—41no—
191C2×C22⋊D17—41no—
192C2×C22⋊D17—41no—
193C2×C22⋊D17—41no—
194C2×C22⋊D17—41no—
195C22×Dic17C22×C411yescharacteristic
196C22×Dic17C22×C411yescharacteristic
197C22×Dic17C22×C411yescharacteristic
198C22×Dic17C22×C411yescharacteristic
199C22×Dic17C22×C411yescharacteristic
200C22×Dic17C22×C411yescharacteristic
201C22×Dic17C22×C411yescharacteristic
202C2×C4×D17—21no—
203C2×C4×D17—21no—
204C2×C4×D17—21no—
205C2×C4×D17—21no—
206C2×C4×D17—21no—
207C2×C4×D17—21no—
208C2×C8×C17—21no—
209C2×C8×C17—21no—
210C2×C8×C17—21no—
211C2×C8×C17—21no—
212C2×C8×C17—21no—
213C2×C8×C17—21no—
214C2×C8×C17—21no—
215C2×C8×C17—21no—
216C2×C8×C17—21no—
217C2×C8×C17—21no—
218C2×C8×C17—21no—
219C2×C8×C17—21no—
220C22⋊Dic17—22no—
221C22⋊Dic17—22no—
222C22⋊Dic17—22no—
223C22⋊Dic17—22no—
224C22⋊Dic17—22no—
225C22⋊Dic17—41no—
226C22⋊Dic17—41no—
227C22⋊Dic17—41no—
228C22⋊Dic17—41no—
229#63227—22no—
230#63227—41no—
231#63227—41no—
232#63225—22no—
233#63225—41no—
234#63225—41no—
235C4×Dic17—21no—
236C4×Dic17—21no—
237C4×Dic17—21no—
238C4×Dic17—21no—
239C4×Dic17—21no—
240C4×Dic17—21no—
241#63223—44no—
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—44no—
253C2×#3622C2×D412yes—
254C2×#3622C2×D412yes—
255#63218—44no—
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×C17C4×D412yes—
278C23×C17C23×C411yescharacteristic
279C22×D17—21no—
280C22×D17—21no—
281C22×D17—21no—
282C22×D17—21no—
283C22×D17—21no—
284C22×D17—21no—
285C22×D17—21no—
286Q8×C17—44no—
287D4×C17—44no—
288D4×C17—44no—
289D4×C17—44no—
290C2×C4×C17—21no—
291C2×C4×C17—21no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—21no—
297C2×C4×C17—21no—
298C2×C4×C17—21no—
299C2×C4×C17—21no—
300C2×C4×C17—21no—
301C2×C4×C17—21no—
302C2×C4×C17—41no—
303C2×C4×C17—41no—
304C2×C4×C17—41no—
305C2×C4×C17—41no—
306C2×C4×C17—41no—
307C2×C4×C17—41no—
308C2×C4×C17—41no—
309C2×C4×C17—41no—
310C2×C4×C17C4×D412yes—
311C2×C4×C17C22×D411yescharacteristic
312C2×C4×C17C2×#4111yescharacteristic
313C2×C4×C17H(5,𝔽2)11yescharacteristic
314C2×C4×C17H(5,𝔽2)11yescharacteristic
315C2×C4×C17H(5,𝔽2)11yescharacteristic
316C2×C4×C17H(5,𝔽2)11yescharacteristic
317C22⋊D17—44no—
318C22⋊D17—44no—
319C22⋊D17—44no—
320C2×Dic17—21no—
321C2×Dic17—21no—
322C2×Dic17—21no—
323C2×Dic17—21no—
324C2×Dic17—21no—
325C2×Dic17—21no—
326C2×Dic17—21no—
327C2×Dic17—21no—
328C2×Dic17—21no—
329C2×Dic17—21no—
330C2×Dic17—21no—
331C2×Dic17—21no—
332C2×Dic17—21no—
333C2×Dic17—21no—
334C2×Dic17—21no—
335C2×Dic17—21no—
336C2×Dic17—21no—
337C2×Dic17—21no—
338C2×Dic17—21no—
339C2×Dic17#13112yes—
340C2×Dic17#13112yes—
341C4×D17—41no—
342C4×D17—41no—
343C4×D17—41no—
344C4×D17—41no—
345C8×C17—41no—
346C8×C17—41no—
347C8×C17—41no—
348C8×C17—41no—
349#3622—22no—
350#3622—22no—
351#3622—41no—
352#3622—41no—
353C2×#436—171no—
354C2×#408—171no—
355#2388—171no—
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#1780D1711yescharacteristic, complemented
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×C17C2×C4×D411yescharacteristic
390C22×C17#51811yescharacteristic
391C22×C17#51811yescharacteristic
392C22×C17C2×#13111yescharacteristic
393C22×C17C2×#13111yescharacteristic
394C22×C17#56811yescharacteristic
395C22×C17#56811yescharacteristic
396C2×D17—41no—
397C2×D17—41no—
398C2×D17—41no—
399C2×D17—41no—
400C2×D17—41no—
401C2×D17—41no—
402C2×D17—41no—
403C4×C17—22no—
404C4×C17—41no—
405C4×C17—41no—
406C4×C17#53411yescharacteristic
407C4×C17#53511yescharacteristic
408C4×C17#53811yescharacteristic
409C4×C17#53811yescharacteristic
410Dic17—22no—
411Dic17—22no—
412Dic17—41no—
413Dic17—41no—
414Dic17—41no—
415Dic17—41no—
416Dic17—41no—
417C22×#41C2×D1711yescharacteristic
418C22×M16—171no—
419C22×M16—171no—
420C23×C8—171no—
421C2×C4×D4—171no—
422C2×C4×D4—171no—
423C2×C4×D4—171no—
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⋊C8C2×D1711yescharacteristic
437C2×C22⋊C8C2×D1711yescharacteristic
438C2×C22⋊C8C2×D1711yescharacteristic
439C2×C22⋊C8C2×D1711yescharacteristic
440C2×C22⋊C8C2×D1711yescharacteristic
441C2×C22⋊C8C2×D1711yescharacteristic
442C2×#97—171no—
443C2×C4×C8—171no—
444C2×C4×C8—171no—
445#395—171no—
446#394—171no—
447#394—171no—
448#394—171no—
449#393—171no—
450#392—171no—
451#392—171no—
452#392—171no—
453C4×C22⋊C4—171no—
454C4×C22⋊C4—171no—
455C4×C22⋊C4—171no—
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#232111yescharacteristic
466C2×C17#293311yescharacteristic
467C2×C17#293511yescharacteristic
468C2×C17#297611yescharacteristic
469C2×C17#297811yescharacteristic
470C2×C17#297911yescharacteristic
471C2×C17#298111yescharacteristic
472D17—81no—
473C2×#41—22no—
474C2×#41—22no—
475C2×#41—41no—
476C2×#41—41no—
477C2×#41—41no—
478C2×#41—41no—
479C22×Q8C4×D1711yescharacteristic
480C22×D4—171no—
481C22×D4—171no—
482C22×D4—171no—
483C22×D4C4×D1711yescharacteristic
484C22×D4C4×D1711yescharacteristic
485C22×D4C4×D1711yescharacteristic
486C23×C4—171no—
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—342no—
501C22×C8—681no—
502C22×C8—681no—
503C22×C8C22×D1711yescharacteristic
504C22×C8C22×D1711yescharacteristic
505C22×C8C22×D1711yescharacteristic
506C22×C8C22×D1711yescharacteristic
507C4×D4—342no—
508C4×D4—342no—
509C4×D4—681no—
510C4×D4—681no—
511C4×D4—681no—
512C4×D4—681no—
513C2×C4⋊C4—171no—
514C2×C4⋊C4—171no—
515C2×C4⋊C4—171no—
516C2×C22⋊C4—171no—
517C2×C22⋊C4—171no—
518C2×C22⋊C4—171no—
519C2×C22⋊C4—171no—
520C2×C22⋊C4—171no—
521C2×C22⋊C4—171no—
522C2×C22⋊C4—171no—
523C2×C22⋊C4—171no—
524C2×C22⋊C4—171no—
525C2×C22⋊C4—171no—
526C2×C22⋊C4—171no—
527C2×C22⋊C4—171no—
528C2×C42—171no—
529C2×C42—171no—
530C2×C42—171no—
531C4⋊C8—342no—
532C4⋊C8—681no—
533C4⋊C8—681no—
534C22⋊C8—22no—
535C22⋊C8—22no—
536C22⋊C8—41no—
537C22⋊C8—41no—
538C22⋊C8—41no—
539C22⋊C8—41no—
540C22⋊C8—342no—
541C22⋊C8—342no—
542C22⋊C8—342no—
543C22⋊C8—342no—
544C22⋊C8—342no—
545C22⋊C8—681no—
546C22⋊C8—681no—
547#97—681no—
548C4×C8—342no—
549C4×C8—681no—
550#95—171no—
551#95—171no—
552#95—171no—
553#95—171no—
554#95—171no—
555#95—171no—
556C17#2203911yescharacteristic, complemented, Sylow
557C24—171no—
558C24C2×C4×D1711yescharacteristic
559C24C2×C4×D1711yescharacteristic
560C24C2×C4×D1711yescharacteristic
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—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—342no—
578C2×D4—342no—
579C2×D4—342no—
580C2×D4—681no—
581C2×D4—681no—
582C2×D4—681no—
583C2×D4—681no—
584C2×D4—681no—
585C2×D4—681no—
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—171no—
603C22×C4—171no—
604C22×C4—171no—
605C22×C4—171no—
606C22×C4—171no—
607C22×C4—171no—
608C22×C4—171no—
609C22×C4—341no—
610C22×C4—341no—
611C22×C4—341no—
612C22×C4—341no—
613C22×C4—341no—
614C22×C4—341no—
615C22×C4C2×C4×D1711yescharacteristic
616C22×C4C2×C4×D1711yescharacteristic
617C22×C4C2×C4×D1711yescharacteristic
618C22×C4D4×D1712yes—
619C22×C4#6325412yes—
620C22×C4C23×D1711yescharacteristic
621M16—684no—
622M16—684no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—172no—
636C2×C8—172no—
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—342no—
649C4⋊C4—681no—
650C4⋊C4—681no—
651C22⋊C4—342no—
652C22⋊C4—342no—
653C22⋊C4—342no—
654C22⋊C4—342no—
655C22⋊C4—342no—
656C22⋊C4—342no—
657C22⋊C4—681no—
658C22⋊C4—681no—
659C22⋊C4—681no—
660C22⋊C4—681no—
661C22⋊C4—681no—
662C22⋊C4—681no—
663C42—341no—
664C42—341no—
665C42—341no—
666C42—341no—
667C42—341no—
668C42—341no—
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—341no—
690C23—341no—
691C23—341no—
692C23—341no—
693C23—341no—
694C23—341no—
695C23—341no—
696C23#1058756712yes—
697C23C22×C4×D1711yescharacteristic
698Q8—44no—
699D4—44no—
700D4—44no—
701D4—44no—
702D4—684no—
703D4—684no—
704D4—684no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—172no—
726C2×C4—172no—
727C2×C4—341no—
728C2×C4—341no—
729C2×C4—341no—
730C2×C4—341no—
731C2×C4—341no—
732C2×C4—341no—
733C2×C4—341no—
734C2×C4—341no—
735C2×C4—341no—
736C2×C4—341no—
737C2×C4—341no—
738C2×C4—341no—
739C2×C4—341no—
740C2×C4—341no—
741C2×C4—341no—
742C2×C4—341no—
743C2×C4—341no—
744C2×C4—341no—
745C2×C4—341no—
746C2×C4—681no—
747C2×C4—681no—
748C2×C4—681no—
749C2×C4—681no—
750C2×C4#1058756712yes—
751C2×C4C2×D4×D1711yescharacteristic
752C2×C4C2×#6325411yescharacteristic
753C2×C4#1058769111yescharacteristic
754C2×C4#1058769111yescharacteristic
755C2×C4#1058769111yescharacteristic
756C2×C4#1058769111yescharacteristic
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C8—342no—
762C8—342no—
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—681no—
787C22—681no—
788C22—681no—
789C22—681no—
790C22—681no—
791C22—681no—
792C22—681no—
793C22C2×#1058756711yescharacteristic
794C22#1176328211yescharacteristic
795C22#1176328211yescharacteristic
796C22#131×D1711yescharacteristic
797C22#131×D1711yescharacteristic
798C22#1176357411yescharacteristic
799C22#1176357411yescharacteristic
800C4—22no—
801C4—41no—
802C4—41no—
803C4—342no—
804C4—342no—
805C4—681no—
806C4—681no—
807C4—681no—
808C4—681no—
809C4—681no—
810C4#1176336911yescharacteristic
811C4#1176337411yescharacteristic
812C4#1176339411yescharacteristic
813C4#1176339411yescharacteristic
814C2—42no—
815C2—81no—
816C2—81no—
817C2—1361no—
818C2#1453143911yescharacteristic
819C2#1453751411yescharacteristic
820C2#1453752411yescharacteristic
821C2#1453782711yescharacteristic
822C2#1453784211yescharacteristic
823C2#1453784811yescharacteristic
824C2#1453785711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC17×#1780C2
prime radical#14531997C2
cosocleC22×C4×C17C24
hypercenter#1780D17
hypocenterC17#22039
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #1780

Complements

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

NH ≅ G/Ntype
1. C2×#11762884C2semidirect
2. C2×#11762776C2semidirect
4. #14529580C2semidirect
5. #14529576C2semidirect
6. #14529394C2semidirect
7. #14529393C2semidirect
8. #14529393C2semidirect
9. #14529387C2semidirect
10. #14529078C2semidirect
11. #14529078C2semidirect
12. #14529074C2semidirect
13. #14528961C2semidirect
14. #14528570C2semidirect
15. C17×#1780C2semidirect
108. C2×#63223D4semidirect
366. #1780D17semidirect
556. C17#22039semidirect

Maximal subgroups

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

subgroupindex
C2×#117628842
C2×#117627762
#145319972
#145295802
#145295762
#145293942
#145293932
#145293872
#145290782
#145290742
#145289612
#145285702
C17×#17802
#2203917