Finite Group Databasebeta

← C2×#14537950 #17899433

Subgroups — C2×#14537950 #17899433

Order 4352.

1882 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763341C211yesmaximal, characteristic
2#14537950C2116yesmaximal, direct product factor
3C2×#11762938C211yesmaximal, characteristic, complemented
4C2×#11762937C211yesmaximal, characteristic, complemented
5C2×#11762885C211yesmaximal, characteristic, complemented
6C2×#11762884C211yesmaximal, characteristic, complemented
7C2×#11762881C211yesmaximal, characteristic, complemented
8C2×#11762880C211yesmaximal, characteristic, complemented
9C2×#11762877C211yesmaximal, characteristic, complemented
10C2×#11762867C211yesmaximal, characteristic, complemented
11C2×#11762867C211yesmaximal, characteristic, complemented
12C2×#11762864C211yesmaximal, characteristic, complemented
13C2×#11762837C211yesmaximal, characteristic, complemented
14C2×#11762835C211yesmaximal, characteristic, complemented
15C2×#11762831C211yesmaximal, characteristic, complemented
16C2×C17×#435C211yesmaximal, characteristic, complemented
17C22×#63223C2211yescharacteristic
18C22×#63218C2211yescharacteristic
19C22×#63218C2211yescharacteristic
20C23×#3622C2211yescharacteristic
21#11763341C418yes—
22#11763341C2218yes—
23C2×#10587565C411yescharacteristic
24C2×#10587565C411yescharacteristic
25C2×#10587576C411yescharacteristic
26C2×#10587622C411yescharacteristic
27C2×#10587569C411yescharacteristic
28C2×#10587569C411yescharacteristic
29C2×#10587583C411yescharacteristic
30C2×#10587624C411yescharacteristic
31C2×C4×Dic34C2211yescharacteristic
32C2×C4×C22⋊D17C2211yescharacteristic
33C2×C4×C22⋊D17C2211yescharacteristic
34C2×#10587612C2211yescharacteristic
35C2×#10587612C2211yescharacteristic
36C2×C42×D17C2211yescharacteristic
37#11762938C2218yescomplemented
38#11762937C2218yescomplemented
39#11762885C2218yescomplemented
40#11762884C2218yescomplemented
41#11762881C2218yescomplemented
42#11762880C2218yescomplemented
43#11762877C2218yescomplemented
44#11762867C2218yescomplemented
45#11762867C2218yescomplemented
46#11762864C2218yescomplemented
47#11762837C2218yescomplemented
48#11762835C2218yescomplemented
49#11762831C2218yescomplemented
50C2×C4⋊#3622C2211yescharacteristic
51C2×#10587485C2211yescharacteristic
52C2×#10587485C2211yescharacteristic
53C2×#10587485C2211yescharacteristic
54C2×#10587485C2211yescharacteristic
55C2×#10587485C2211yescharacteristic
56C2×#10587485C2211yescharacteristic
57C2×#10587485C2211yescharacteristic
58C2×#10587485C2211yescharacteristic
59C2×C22⋊#3622C2211yescharacteristic
60C2×C22⋊#3622C2211yescharacteristic
61C2×#10587491C2211yescharacteristic
62C2×#10587491C2211yescharacteristic
63C2×#10587474C2211yescharacteristic
64C2×#10587486C2211yescharacteristic
65C2×#10587486C2211yescharacteristic
66C2×C8×Dic17C2211yescharacteristic
67C2×C8×Dic17C2211yescharacteristic
68C22×M16×C17C2211yescharacteristic
69C23×C8×C17C2211yescharacteristic
70C2×C4×D4×C17C2211yescharacteristic
71C17×#435C2218yescomplemented
72C2×C17×C4⋊C8C2211yescharacteristic
73C2×C17×C22⋊C8C2211yescharacteristic
74C2×C17×C22⋊C8C2211yescharacteristic
75C2×C17×#97C2211yescharacteristic
76C22×D4×C17C2×C411yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C23×C4×C17C2311yescharacteristic
79C22×C22⋊D17C2×C411yescharacteristic
80C22×C22⋊D17C2×C411yescharacteristic
81C22×C4×D17C2×C411yescharacteristic
82C22×C4×D17C2×C411yescharacteristic
83C22×C4×D17C2311yescharacteristic
84C22×Dic34C2×C411yescharacteristic
85C2×M16×C17—42no—
86C2×M16×C17C2314yes—
87C22×C8×C17—42no—
88C22×C8×C17C2311yescharacteristic
89C22×C8×C17C2311yescharacteristic
90C22×C8×C17C2311yescharacteristic
91C22×C8×C17C2311yescharacteristic
92C22×C8×C17C2314yes—
93C4×D4×C17C2×C414yes—
94C4×D4×C17C2314yes—
95C2×C4⋊C4×C17C2×C411yescharacteristic
96C2×C22⋊C4×C17C2×C411yescharacteristic
97C2×C22⋊C4×C17C2×C411yescharacteristic
98C2×C42×C17C2311yescharacteristic
99C2×C22⋊Dic17C2×C411yescharacteristic
100C2×C22⋊Dic17C2×C411yescharacteristic
101C2×C22⋊Dic17C2×C411yescharacteristic
102C2×C22⋊Dic17C2×C411yescharacteristic
103C2×C22⋊Dic17C2×C411yescharacteristic
104C2×C22⋊Dic17C2×C411yescharacteristic
105#10587624C2×C418yes—
106#10587622C2×C418yes—
107C4×C22⋊D17C2×C414yes—
108C4×C22⋊D17C2×C414yes—
109C4×C22⋊D17C2314yes—
110C4×C22⋊D17C2314yes—
111C2×#63227C2×C411yescharacteristic
112C2×#63227C2×C411yescharacteristic
113#10587612C2×C414yes—
114#10587612C2×C414yes—
115#10587612C2314yes—
116#10587612C2314yes—
117C2×C4⋊Dic17C2×C411yescharacteristic
118C2×C4⋊Dic17C2×C411yescharacteristic
119C2×C4⋊Dic17C2×C411yescharacteristic
120C2×C4⋊Dic17C2×C411yescharacteristic
121C2×C4⋊Dic17C2×C411yescharacteristic
122C2×#63225C2×C411yescharacteristic
123C2×#63225C2×C411yescharacteristic
124C2×#63225C2×C411yescharacteristic
125C2×#63225C2×C411yescharacteristic
126C2×C4×Dic17C2×C411yescharacteristic
127C2×C4×Dic17C2×C411yescharacteristic
128C2×C4×Dic17C2311yescharacteristic
129C2×C4×Dic17C2311yescharacteristic
130C2×C4×Dic17C2311yescharacteristic
131C2×#63223—42no—
132C2×#63223C2314yes—
133C22×#3622—42no—
134C22×#3622C2311yescharacteristic
135C22×#3622C2311yescharacteristic
136C22×#3622C2311yescharacteristic
137C22×#3622C2311yescharacteristic
138C22×#3622C2314yes—
139C2×#63218—42no—
140C2×#63218—42no—
141C2×#63218C2314yes—
142C2×#63218C2314yes—
143#10587583C2×C418yes—
144#10587576C2×C418yes—
145#10587569C2×C418yes—
146#10587569C2×C418yes—
147#10587565C2×C418yes—
148#10587565C2×C418yes—
149C42×D17C2×C414yes—
150C42×D17C2314yes—
151C4×Dic34C2×C414yes—
152C4×Dic34C2314yes—
153C17×C4⋊C8C2314yes—
154C17×C22⋊C8C2314yes—
155C17×C22⋊C8C2314yes—
156C17×#97C2314yes—
157C22⋊#3622C2314yes—
158C22⋊#3622C2314yes—
159#10587491C2314yes—
160#10587491C2314yes—
161#10587486C2314yes—
162#10587486C2314yes—
163#10587485C2314yes—
164#10587485C2314yes—
165#10587485C2314yes—
166#10587485C2314yes—
167#10587485C2314yes—
168#10587485C2314yes—
169#10587485C2314yes—
170#10587485C2314yes—
171C8×Dic17C2314yes—
172C8×Dic17C2314yes—
173C4⋊#3622C2314yes—
174#10587474C2314yes—
175C24×C17C22×C411yescharacteristic
176C24×C17C22×C411yescharacteristic
177C23×D17C22×C411yescharacteristic
178C2×D4×C17—42no—
179C2×D4×C17C22×C414yes—
180C22×C4×C17—22no—
181C22×C4×C17—22no—
182C22×C4×C17—22no—
183C22×C4×C17—22no—
184C22×C4×C17C22×C411yescharacteristic
185C22×C4×C17C22×C411yescharacteristic
186C22×C4×C17C22×C411yescharacteristic
187C22×C4×C17C22×C411yescharacteristic
188C22×C4×C17C22×C412yes—
189C22×C4×C17C22×C412yes—
190C22×C4×C17C2412yes—
191C22×C4×C17C2412yes—
192C22×C4×C17C2411yescharacteristic
193C2×C22⋊D17—42no—
194C2×C22⋊D17—42no—
195C2×C22⋊D17C22×C414yes—
196C2×C22⋊D17C22×C414yes—
197C22×Dic17C22×C411yescharacteristic
198C22×Dic17C22×C411yescharacteristic
199C22×Dic17C22×C411yescharacteristic
200C22×Dic17C22×C411yescharacteristic
201C22×Dic17C22×C411yescharacteristic
202C22×Dic17C22×C411yescharacteristic
203C22×Dic17C22×C411yescharacteristic
204C2×C4×D17—22no—
205C2×C4×D17—22no—
206C2×C4×D17—42no—
207C2×C4×D17—42no—
208C2×C4×D17C22×C412yes—
209C2×C4×D17C22×C414yes—
210C2×C4×D17C22×C414yes—
211C2×C4×D17C2412yes—
212C2×Dic34—42no—
213C2×Dic34C22×C414yes—
214M16×C17—44no—
215C2×C8×C17—22no—
216C2×C8×C17—22no—
217C2×C8×C17—22no—
218C2×C8×C17—22no—
219C2×C8×C17—44no—
220C2×C8×C17C2412yes—
221C2×C8×C17C2412yes—
222C2×C8×C17C2412yes—
223C2×C8×C17C2412yes—
224C4⋊C4×C17C22×C414yes—
225C22⋊C4×C17C22×C414yes—
226C22⋊C4×C17C22×C414yes—
227C42×C17C22×C412yes—
228C42×C17C2412yes—
229C22⋊Dic17C22×C414yes—
230C22⋊Dic17C22×C414yes—
231C22⋊Dic17C22×C414yes—
232C22⋊Dic17C22×C414yes—
233C22⋊Dic17C22×C414yes—
234C22⋊Dic17C22×C414yes—
235#63227C22×C414yes—
236#63227C22×C414yes—
237C4⋊Dic17C22×C414yes—
238C4⋊Dic17C22×C414yes—
239C4⋊Dic17C22×C414yes—
240C4⋊Dic17C22×C414yes—
241C4⋊Dic17C22×C414yes—
242#63225C22×C414yes—
243#63225C22×C414yes—
244#63225C22×C414yes—
245#63225C22×C414yes—
246C4×Dic17C22×C412yes—
247C4×Dic17C22×C412yes—
248C4×Dic17C22×C412yes—
249C4×Dic17C22×C414yes—
250C4×Dic17C22×C414yes—
251C4×Dic17C2412yes—
252C4×Dic17C2412yes—
253C4×Dic17C2412yes—
254#63223—44no—
255C2×#3622—22no—
256C2×#3622—22no—
257C2×#3622—22no—
258C2×#3622—22no—
259C2×#3622—44no—
260C2×#3622C2412yes—
261C2×#3622C2412yes—
262C2×#3622C2412yes—
263C2×#3622C2412yes—
264#63218—44no—
265#63218—44no—
266C2×#2995—171nomaximal, Sylow
267C23×C17—22no—
268C23×C17—22no—
269C23×C17—22no—
270C23×C17—22no—
271C23×C17—22no—
272C23×C17—22no—
273C23×C17C23×C412yes—
274C23×C17C23×C412yes—
275C23×C17C23×C411yescharacteristic
276C22×D17—22no—
277C22×D17—22no—
278C22×D17—22no—
279C22×D17C23×C412yes—
280D4×C17—44no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—24no—
286C2×C4×C17—24no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17C23×C412yes—
292C2×C4×C17C23×C412yes—
293C2×C4×C17C23×C412yes—
294C2×C4×C17C23×C412yes—
295C2×C4×C17C23×C411yescharacteristic
296C2×C4×C17H(5,𝔽2)12yes—
297C2×C4×C172−1+412yes—
298C2×C4×C17C2511yescharacteristic
299C22⋊D17—44no—
300C22⋊D17—44no—
301C2×Dic17—22no—
302C2×Dic17—22no—
303C2×Dic17—22no—
304C2×Dic17—22no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17C23×C412yes—
309C2×Dic17C23×C412yes—
310C2×Dic17C23×C412yes—
311C2×Dic17C23×C412yes—
312C2×Dic17C23×C412yes—
313C2×Dic17C23×C412yes—
314C2×Dic17C23×C412yes—
315C4×D17—24no—
316C4×D17—22no—
317C4×D17—22no—
318C4×D17—44no—
319C4×D17—44no—
320Dic34—44no—
321C8×C17—22no—
322C8×C17—22no—
323C8×C17—22no—
324C8×C17—22no—
325#3622—22no—
326#3622—22no—
327#3622—22no—
328#3622—22no—
329C2×#529—171no—
330#2995—1716no—
331C2×#446—171no—
332C2×#446—171no—
333C2×#436—171no—
334C2×#436—171no—
335C2×#435—171no—
336C2×#435—171no—
337C2×#435—171no—
338C2×#435D1711yescharacteristic, complemented
339C2×#433—171no—
340C2×#433—171no—
341C2×#432—171no—
342C2×#424—171no—
343C2×#424—171no—
344C2×#423—171no—
345C22×C17—22no—
346C22×C17—22no—
347C22×C17—22no—
348C22×C17—22no—
349C22×C17—22no—
350C22×C17—22no—
351C22×C17—44no—
352C22×C17—44no—
353C22×C17#52012yes—
354C22×C17#56812yes—
355C22×C17#56812yes—
356C22×C17C24×C411yescharacteristic
357C2×D17—22no—
358C2×D17—22no—
359C2×D17—22no—
360C2×D17—44no—
361C4×C17—22no—
362C4×C17—22no—
363C4×C17—22no—
364C4×C17—22no—
365C4×C17#52012yes—
366C4×C17C2×H(5,𝔽2)11yescharacteristic
367C4×C17C2×2−1+411yescharacteristic
368Dic17—22no—
369Dic17—22no—
370Dic17—22no—
371Dic17—22no—
372Dic17—22no—
373Dic17—22no—
374Dic17—22no—
375C22×M16—171no—
376C22×M16—171no—
377C22×M16—171no—
378C22×M16C2×D1711yescharacteristic
379C23×C8—171no—
380C23×C8C2×D1711yescharacteristic
381#529—178no—
382#529—178no—
383C2×#126—171no—
384C2×#126—171no—
385C2×#125—171no—
386C2×#124—171no—
387C2×#123—171no—
388C2×#123—171no—
389C2×C22⋊Q8—171no—
390C2×#121—171no—
391C2×C4×Q8—171no—
392C2×C4×D4—171no—
393C2×C4×D4—171no—
394C2×C4×D4C2×D1711yescharacteristic
395C2×#117—171no—
396C2×#117—171no—
397C22×C42—171no—
398#446—178no—
399#446—178no—
400#436—178no—
401#436—178no—
402#435—178no—
403#435—178no—
404#435—178no—
405#435C2×D1718yescomplemented
406#433—178no—
407#433—178no—
408#432—178no—
409#424—178no—
410#424—178no—
411#423—178no—
412C2×C4⋊C8—171no—
413C2×C4⋊C8—171no—
414C2×C4⋊C8—171no—
415C2×C4⋊C8—171no—
416C2×C4⋊C8—171no—
417C2×C4⋊C8—171no—
418C2×C4⋊C8—171no—
419C2×C4⋊C8—171no—
420C2×C4⋊C8—171no—
421C2×C4⋊C8C2×D1711yescharacteristic
422C2×C22⋊C8—171no—
423C2×C22⋊C8—171no—
424C2×C22⋊C8—171no—
425C2×C22⋊C8—171no—
426C2×C22⋊C8C2×D1711yescharacteristic
427C2×C22⋊C8C2×D1711yescharacteristic
428C2×#97—171no—
429C2×#97—171no—
430C2×#97—171no—
431C2×#97C2×D1711yescharacteristic
432C2×C4×C8—171no—
433C2×C4×C8—171no—
434C2×C17—42no—
435C2×C17—42no—
436C2×C17#299514yescomplemented
437C2×C17C2×#52011yescharacteristic
438C2×C17C2×#56811yescharacteristic
439C2×C17C2×#56811yescharacteristic
440D17—42no—
441C22×Q8—171no—
442C22×D4—171no—
443C22×D4—171no—
444C22×D4C4×D1711yescharacteristic
445C23×C4—171no—
446C23×C4—171no—
447C23×C4—171no—
448C23×C4C22×D1711yescharacteristic
449C23×C4C22×D1711yescharacteristic
450C2×M16—42no—
451C2×M16—174no—
452C2×M16—174no—
453C2×M16—174no—
454C2×M16—682no—
455C2×M16—682no—
456C2×M16—682no—
457C2×M16C22×D1714yes—
458C22×C8—42no—
459C22×C8—171no—
460C22×C8—171no—
461C22×C8—171no—
462C22×C8—171no—
463C22×C8—174no—
464C22×C8—682no—
465C22×C8C22×D1711yescharacteristic
466C22×C8C22×D1711yescharacteristic
467C22×C8C22×D1711yescharacteristic
468C22×C8C22×D1711yescharacteristic
469C22×C8C22×D1714yes—
470#126—178no—
471#126—178no—
472#125—178no—
473#124—178no—
474#123—178no—
475#123—178no—
476C22⋊Q8—178no—
477#121—178no—
478C4×Q8—174no—
479C4×Q8—174no—
480C4×D4—174no—
481C4×D4—174no—
482C4×D4—174no—
483C4×D4—174no—
484C4×D4C4×D1714yes—
485C4×D4C22×D1714yes—
486#117—174no—
487#117—174no—
488#117—174no—
489#117—174no—
490C2×C4⋊C4—171no—
491C2×C4⋊C4—171no—
492C2×C4⋊C4—171no—
493C2×C4⋊C4—171no—
494C2×C4⋊C4—171no—
495C2×C4⋊C4—171no—
496C2×C4⋊C4—171no—
497C2×C4⋊C4—171no—
498C2×C4⋊C4—171no—
499C2×C4⋊C4C4×D1711yescharacteristic
500C2×C22⋊C4—171no—
501C2×C22⋊C4—171no—
502C2×C22⋊C4—171no—
503C2×C22⋊C4—171no—
504C2×C22⋊C4—171no—
505C2×C22⋊C4—171no—
506C2×C22⋊C4—171no—
507C2×C22⋊C4—171no—
508C2×C22⋊C4C4×D1711yescharacteristic
509C2×C22⋊C4C4×D1711yescharacteristic
510C2×C42—171no—
511C2×C42—171no—
512C2×C42—171no—
513C2×C42—171no—
514C2×C42—171no—
515C2×C42—174no—
516C2×C42—174no—
517C2×C42C22×D1711yescharacteristic
518C4⋊C8—174no—
519C4⋊C8—174no—
520C4⋊C8—174no—
521C4⋊C8—174no—
522C4⋊C8—174no—
523C4⋊C8—174no—
524C4⋊C8—174no—
525C4⋊C8—174no—
526C4⋊C8—174no—
527C4⋊C8C22×D1714yes—
528C22⋊C8—174no—
529C22⋊C8—174no—
530C22⋊C8—174no—
531C22⋊C8—174no—
532C22⋊C8C22×D1714yes—
533C22⋊C8C22×D1714yes—
534#97—174no—
535#97—174no—
536#97—174no—
537#97C22×D1714yes—
538C4×C8—174no—
539C4×C8—174no—
540C17C2×#299511yescharacteristic, complemented, Sylow
541C24—171no—
542C24C2×C4×D1711yescharacteristic
543C24C2×C4×D1711yescharacteristic
544C2×Q8—174no—
545C2×Q8—682no—
546C2×D4—42no—
547C2×D4—174no—
548C2×D4—174no—
549C2×D4—682no—
550C2×D4—682no—
551C2×D4C2×C4×D1714yes—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—171no—
557C22×C4—171no—
558C22×C4—171no—
559C22×C4—171no—
560C22×C4—171no—
561C22×C4—171no—
562C22×C4—171no—
563C22×C4—172no—
564C22×C4—172no—
565C22×C4—174no—
566C22×C4—174no—
567C22×C4—342no—
568C22×C4—342no—
569C22×C4—682no—
570C22×C4—682no—
571C22×C4C2×C4×D1711yescharacteristic
572C22×C4C2×C4×D1711yescharacteristic
573C22×C4C2×C4×D1711yescharacteristic
574C22×C4C2×C4×D1711yescharacteristic
575C22×C4C2×C4×D1712yes—
576C22×C4C2×C4×D1712yes—
577C22×C4C23×D1712yes—
578C22×C4C23×D1712yes—
579C22×C4C23×D1711yescharacteristic
580M16—44no—
581M16—684no—
582M16—684no—
583M16—684no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—44no—
589C2×C8—172no—
590C2×C8—172no—
591C2×C8—172no—
592C2×C8—172no—
593C2×C8—342no—
594C2×C8—342no—
595C2×C8—342no—
596C2×C8—342no—
597C2×C8—684no—
598C2×C8C23×D1712yes—
599C2×C8C23×D1712yes—
600C2×C8C23×D1712yes—
601C2×C8C23×D1712yes—
602C4⋊C4—174no—
603C4⋊C4—174no—
604C4⋊C4—174no—
605C4⋊C4—174no—
606C4⋊C4—174no—
607C4⋊C4—174no—
608C4⋊C4—174no—
609C4⋊C4—174no—
610C4⋊C4—174no—
611C4⋊C4C2×C4×D1714yes—
612C22⋊C4—174no—
613C22⋊C4—174no—
614C22⋊C4—174no—
615C22⋊C4—174no—
616C22⋊C4—174no—
617C22⋊C4—174no—
618C22⋊C4—174no—
619C22⋊C4—174no—
620C22⋊C4C2×C4×D1714yes—
621C22⋊C4C2×C4×D1714yes—
622C42—172no—
623C42—174no—
624C42—174no—
625C42—172no—
626C42—172no—
627C42—172no—
628C42—172no—
629C42—172no—
630C42C2×C4×D1712yes—
631C42C23×D1712yes—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—172no—
639C23—342no—
640C23—342no—
641C23—342no—
642C23C22×C4×D1712yes—
643C23C22×C4×D1712yes—
644C23C22×C4×D1711yescharacteristic
645Q8—684no—
646D4—44no—
647D4—684no—
648D4—684no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—172no—
660C2×C4—172no—
661C2×C4—172no—
662C2×C4—172no—
663C2×C4—172no—
664C2×C4—172no—
665C2×C4—172no—
666C2×C4—342no—
667C2×C4—342no—
668C2×C4—342no—
669C2×C4—342no—
670C2×C4—342no—
671C2×C4—342no—
672C2×C4—342no—
673C2×C4—344no—
674C2×C4—342no—
675C2×C4—342no—
676C2×C4—684no—
677C2×C4—684no—
678C2×C4C22×C4×D1712yes—
679C2×C4C22×C4×D1712yes—
680C2×C4C22×C4×D1712yes—
681C2×C4C22×C4×D1712yes—
682C2×C4C22×C4×D1711yescharacteristic
683C2×C4#1058769112yes—
684C2×C4#1058769712yes—
685C2×C4C24×D1711yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—22no—
690C8—342no—
691C8—342no—
692C8—342no—
693C8—342no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—44no—
701C22—44no—
702C22—342no—
703C22—342no—
704C22—342no—
705C22—684no—
706C22#1176328812yes—
707C22#1176357412yes—
708C22#1176357512yes—
709C22C23×C4×D1711yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—342no—
715C4—342no—
716C4—342no—
717C4—342no—
718C4—342no—
719C4—342no—
720C4—342no—
721C4#1176328812yes—
722C4C2×#1058769111yescharacteristic
723C4C2×#1058769711yescharacteristic
724C2—42no—
725C2—42no—
726C2—682no—
727C2#1453795014yesdirect product factor
728C2C2×#1176328811yescharacteristic
729C2C2×#1176357411yescharacteristic
730C2C2×#1176357511yescharacteristic
subgroupG/H
centerC22×C4C23×D17
commutatorC22×C17C24×C4
FrattiniC2×C4C24×D17
FittingC2×C17×#435C2
socleC23×C17C23×C4
prime radicalC2×#10587624C4
cosocleC2×C4×C17C25
hypercenterC2×#435D17
hypocenterC17C2×#2995
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #14537950C2direct (N × H)
3. C2×#11762938C2semidirect
4. C2×#11762937C2semidirect
5. C2×#11762885C2semidirect
6. C2×#11762884C2semidirect
7. C2×#11762881C2semidirect
8. C2×#11762880C2semidirect
9. C2×#11762877C2semidirect
10. C2×#11762867C2semidirect
11. C2×#11762867C2semidirect
12. C2×#11762864C2semidirect
13. C2×#11762837C2semidirect
14. C2×#11762835C2semidirect
15. C2×#11762831C2semidirect
16. C2×C17×#435C2semidirect
37. #11762938C22semidirect
38. #11762937C22semidirect
39. #11762885C22semidirect
40. #11762884C22semidirect
41. #11762881C22semidirect
42. #11762880C22semidirect
43. #11762877C22semidirect
44. #11762867C22semidirect
45. #11762867C22semidirect
46. #11762864C22semidirect
47. #11762837C22semidirect
48. #11762835C22semidirect
49. #11762831C22semidirect
71. C17×#435C22semidirect
338. C2×#435D17semidirect
405. #435C2×D17semidirect
436. C2×C17#2995semidirect
540. C17C2×#2995semidirect
727. C2#14537950direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117633412
#145379502
C2×#117629382
C2×#117629372
C2×#117628852
C2×#117628842
C2×#117628812
C2×#117628802
C2×#117628772
C2×#117628672
C2×#117628642
C2×#117628372
C2×#117628352
C2×#117628312
C2×C17×#4352
C2×#299517