Finite Group Databasebeta

← C2×#14537949 #17899432

Subgroups — C2×#14537949 #17899432

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×#11763337C211yesmaximal, characteristic
2#14537949C2116yesmaximal, direct product factor
3C2×#11762939C211yesmaximal, characteristic, complemented
4C2×#11762937C211yesmaximal, characteristic, complemented
5C2×#11762888C211yesmaximal, characteristic, complemented
6C2×#11762884C211yesmaximal, characteristic, complemented
7C2×#11762883C211yesmaximal, characteristic, complemented
8C2×#11762882C211yesmaximal, characteristic, complemented
9C2×#11762877C211yesmaximal, characteristic, complemented
10C2×#11762877C211yesmaximal, characteristic, complemented
11C2×#11762869C211yesmaximal, characteristic, complemented
12C2×#11762865C211yesmaximal, characteristic, complemented
13C2×#11762836C211yesmaximal, characteristic, complemented
14C2×#11762834C211yesmaximal, characteristic, complemented
15C2×#11762831C211yesmaximal, characteristic, complemented
16C2×C17×#433C211yesmaximal, characteristic, complemented
17C22×#63223C2211yescharacteristic
18C22×#63218C2211yescharacteristic
19C22×#63218C2211yescharacteristic
20C22×#63218C2211yescharacteristic
21C23×#3622C2211yescharacteristic
22C22×C8×D17C2211yescharacteristic
23#11763337C418yes—
24#11763337C2218yes—
25C2×#10587584C411yescharacteristic
26C2×#10587565C411yescharacteristic
27C2×#10587575C411yescharacteristic
28C2×#10587571C411yescharacteristic
29C2×#10587580C411yescharacteristic
30C2×#10587569C411yescharacteristic
31C2×#10587582C411yescharacteristic
32C2×#10587570C411yescharacteristic
33C2×C4×Dic34C2211yescharacteristic
34C2×C4×D68C2211yescharacteristic
35C2×C4×C22⋊D17C2211yescharacteristic
36C2×C4×C22⋊D17C2211yescharacteristic
37C2×#10587558C2211yescharacteristic
38C2×C42×D17C2211yescharacteristic
39#11762939C2218yescomplemented
40#11762937C2218yescomplemented
41#11762888C2218yescomplemented
42#11762884C2218yescomplemented
43#11762883C2218yescomplemented
44#11762882C2218yescomplemented
45#11762877C2218yescomplemented
46#11762877C2218yescomplemented
47#11762869C2218yescomplemented
48#11762865C2218yescomplemented
49#11762836C2218yescomplemented
50#11762834C2218yescomplemented
51#11762831C2218yescomplemented
52C2×C4⋊#3622C2211yescharacteristic
53C2×C4⋊#3622C2211yescharacteristic
54C2×C4⋊#3622C2211yescharacteristic
55C2×C4⋊#3622C2211yescharacteristic
56C2×#10587485C2211yescharacteristic
57C2×#10587485C2211yescharacteristic
58C2×#10587485C2211yescharacteristic
59C2×#10587485C2211yescharacteristic
60C2×#10587491C2211yescharacteristic
61C2×#10587491C2211yescharacteristic
62C2×#10587491C2211yescharacteristic
63C2×#10587491C2211yescharacteristic
64C2×#10587486C2211yescharacteristic
65C2×#10587486C2211yescharacteristic
66C2×#10587486C2211yescharacteristic
67C2×C8×Dic17C2211yescharacteristic
68C2×C17×#117C2211yescharacteristic
69C17×#433C2218yescomplemented
70C2×C17×C4⋊C8C2211yescharacteristic
71C2×C17×C4⋊C8C2211yescharacteristic
72C2×C17×C22⋊C8C2211yescharacteristic
73C2×C17×C22⋊C8C2211yescharacteristic
74C2×C17×#97C2211yescharacteristic
75C2×C4×C8×C17C2211yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C22×C22⋊D17C2×C411yescharacteristic
78C22×C22⋊D17C2×C411yescharacteristic
79C22×D68C2×C411yescharacteristic
80C22×C4×D17C2×C411yescharacteristic
81C22×C4×D17C2×C411yescharacteristic
82C22×C4×D17C2311yescharacteristic
83C22×C4×D17C2311yescharacteristic
84C22×Dic34C2×C411yescharacteristic
85C22×C8×C17C2311yescharacteristic
86C22×C8×C17C2311yescharacteristic
87C22×C8×C17C2311yescharacteristic
88C22×C8×C17C2311yescharacteristic
89C17×#117C2×C414yes—
90C17×#117C2314yes—
91C2×C4⋊C4×C17C2×C411yescharacteristic
92C2×C4⋊C4×C17C2×C411yescharacteristic
93C2×C22⋊C4×C17C2×C411yescharacteristic
94C2×C22⋊C4×C17C2×C411yescharacteristic
95C2×C42×C17C2311yescharacteristic
96C2×C42×C17C2311yescharacteristic
97C2×C22⋊Dic17C2×C411yescharacteristic
98C2×C22⋊Dic17C2×C411yescharacteristic
99C4×C22⋊D17C2×C414yes—
100C4×C22⋊D17C2×C414yes—
101C4×C22⋊D17C2314yes—
102C4×C22⋊D17C2314yes—
103C2×#63227C2×C411yescharacteristic
104C2×#63227C2×C411yescharacteristic
105C2×#63227C2×C411yescharacteristic
106C2×#63227C2×C411yescharacteristic
107C2×#63227C2×C411yescharacteristic
108C2×#63227C2×C411yescharacteristic
109C2×C4⋊Dic17C2×C411yescharacteristic
110C2×C4⋊Dic17C2×C411yescharacteristic
111C2×#63225C2×C411yescharacteristic
112C2×#63225C2×C411yescharacteristic
113C2×#63225C2×C411yescharacteristic
114C2×#63225C2×C411yescharacteristic
115C2×#63225C2×C411yescharacteristic
116C2×#63225C2×C411yescharacteristic
117C2×C4×Dic17C2×C411yescharacteristic
118C2×C4×Dic17C2×C411yescharacteristic
119C2×C4×Dic17C2311yescharacteristic
120C2×C4×Dic17C2311yescharacteristic
121C2×#63223—42no—
122C2×#63223C2314yes—
123C22×#3622—42no—
124C22×#3622C2311yescharacteristic
125C22×#3622C2311yescharacteristic
126C22×#3622C2311yescharacteristic
127C22×#3622C2311yescharacteristic
128C22×#3622C2314yes—
129C2×#63218—42no—
130C2×#63218—42no—
131C2×#63218—42no—
132C2×#63218C2314yes—
133C2×#63218C2314yes—
134C2×#63218C2314yes—
135C2×C8×D17—42no—
136C2×C8×D17C2314yes—
137#10587584C2×C418yes—
138#10587582C2×C418yes—
139#10587580C2×C418yes—
140#10587575C2×C418yes—
141#10587571C2×C418yes—
142#10587570C2×C418yes—
143#10587569C2×C418yes—
144#10587565C2×C418yes—
145C4×D68C2×C414yes—
146C4×D68C2314yes—
147#10587558C2×C414yes—
148#10587558C2314yes—
149C42×D17C2×C414yes—
150C42×D17C2314yes—
151C4×Dic34C2×C414yes—
152C4×Dic34C2314yes—
153C17×C4⋊C8C2314yes—
154C17×C4⋊C8C2314yes—
155C17×C22⋊C8C2314yes—
156C17×C22⋊C8C2314yes—
157C17×#97C2314yes—
158C4×C8×C17C2314yes—
159#10587491C2314yes—
160#10587491C2314yes—
161#10587491C2314yes—
162#10587491C2314yes—
163#10587486C2314yes—
164#10587486C2314yes—
165#10587486C2314yes—
166#10587485C2314yes—
167#10587485C2314yes—
168#10587485C2314yes—
169#10587485C2314yes—
170C8×Dic17C2314yes—
171C4⋊#3622C2314yes—
172C4⋊#3622C2314yes—
173C4⋊#3622C2314yes—
174C4⋊#3622C2314yes—
175C24×C17C22×C411yescharacteristic
176C23×D17C22×C411yescharacteristic
177C23×D17C22×C411yescharacteristic
178C22×C4×C17—22no—
179C22×C4×C17—22no—
180C22×C4×C17C22×C411yescharacteristic
181C22×C4×C17C22×C411yescharacteristic
182C22×C4×C17C22×C411yescharacteristic
183C22×C4×C17C22×C411yescharacteristic
184C22×C4×C17C22×C411yescharacteristic
185C22×C4×C17C22×C412yes—
186C22×C4×C17C2412yes—
187C22×C4×C17C2411yescharacteristic
188C2×C22⋊D17—42no—
189C2×C22⋊D17—42no—
190C2×C22⋊D17C22×C414yes—
191C2×C22⋊D17C22×C414yes—
192C22×Dic17C22×C411yescharacteristic
193C22×Dic17C22×C411yescharacteristic
194C22×Dic17C22×C411yescharacteristic
195C22×Dic17C22×C411yescharacteristic
196C22×Dic17C22×C411yescharacteristic
197C22×Dic17C22×C411yescharacteristic
198C2×D68—42no—
199C2×D68C22×C414yes—
200C2×C4×D17—22no—
201C2×C4×D17—22no—
202C2×C4×D17—22no—
203C2×C4×D17—22no—
204C2×C4×D17—42no—
205C2×C4×D17—42no—
206C2×C4×D17C22×C412yes—
207C2×C4×D17C22×C412yes—
208C2×C4×D17C22×C414yes—
209C2×C4×D17C22×C414yes—
210C2×C4×D17C2412yes—
211C2×C4×D17C2412yes—
212C2×Dic34—42no—
213C2×Dic34C22×C414yes—
214C2×C8×C17—22no—
215C2×C8×C17—22no—
216C2×C8×C17—22no—
217C2×C8×C17—22no—
218C2×C8×C17C2412yes—
219C2×C8×C17C2412yes—
220C2×C8×C17C2412yes—
221C2×C8×C17C2412yes—
222C4⋊C4×C17C22×C414yes—
223C4⋊C4×C17C22×C414yes—
224C22⋊C4×C17C22×C414yes—
225C22⋊C4×C17C22×C414yes—
226C42×C17C22×C412yes—
227C42×C17C22×C412yes—
228C42×C17C2412yes—
229C42×C17C2412yes—
230C22⋊Dic17C22×C414yes—
231C22⋊Dic17C22×C414yes—
232#63227C22×C414yes—
233#63227C22×C414yes—
234#63227C22×C414yes—
235#63227C22×C414yes—
236#63227C22×C414yes—
237#63227C22×C414yes—
238C4⋊Dic17C22×C414yes—
239C4⋊Dic17C22×C414yes—
240#63225C22×C414yes—
241#63225C22×C414yes—
242#63225C22×C414yes—
243#63225C22×C414yes—
244#63225C22×C414yes—
245#63225C22×C414yes—
246C4×Dic17C22×C412yes—
247C4×Dic17C22×C412yes—
248C4×Dic17C22×C414yes—
249C4×Dic17C22×C414yes—
250C4×Dic17C2412yes—
251C4×Dic17C2412yes—
252#63223—44no—
253C2×#3622—22no—
254C2×#3622—22no—
255C2×#3622—22no—
256C2×#3622—22no—
257C2×#3622—44no—
258C2×#3622C2412yes—
259C2×#3622C2412yes—
260C2×#3622C2412yes—
261C2×#3622C2412yes—
262#63218—44no—
263#63218—44no—
264#63218—44no—
265C8×D17—44no—
266C2×#2995—171nomaximal, Sylow
267C23×C17—22no—
268C23×C17—22no—
269C23×C17—22no—
270C23×C17C23×C412yes—
271C23×C17C23×C411yescharacteristic
272C22×D17—22no—
273C22×D17—22no—
274C22×D17—22no—
275C22×D17—22no—
276C22×D17—22no—
277C22×D17—22no—
278C22×D17C23×C412yes—
279C22×D17C23×C412yes—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—24no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17C23×C412yes—
289C2×C4×C17C23×C412yes—
290C2×C4×C17C23×C412yes—
291C2×C4×C17C23×C412yes—
292C2×C4×C17C23×C412yes—
293C2×C4×C17C23×C411yescharacteristic
294C2×C4×C17H(5,𝔽2)12yes—
295C2×C4×C172−1+412yes—
296C2×C4×C17C2511yescharacteristic
297C22⋊D17—44no—
298C22⋊D17—44no—
299C2×Dic17—22no—
300C2×Dic17—22no—
301C2×Dic17—22no—
302C2×Dic17—22no—
303C2×Dic17—22no—
304C2×Dic17—22no—
305C2×Dic17C23×C412yes—
306C2×Dic17C23×C412yes—
307C2×Dic17C23×C412yes—
308C2×Dic17C23×C412yes—
309C2×Dic17C23×C412yes—
310C2×Dic17C23×C412yes—
311D68—44no—
312C4×D17—24no—
313C4×D17—24no—
314C4×D17—22no—
315C4×D17—22no—
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×#435—171no—
339C2×#433—171no—
340C2×#433D1711yescharacteristic, complemented
341C2×#432—171no—
342C2×#424—171no—
343C2×#424—171no—
344C2×#423—171no—
345C22×C17—22no—
346C22×C17—22no—
347C22×C17—22no—
348C22×C17—44no—
349C22×C17#52012yes—
350C22×C17#56812yes—
351C22×C17#56812yes—
352C22×C17C24×C411yescharacteristic
353C2×D17—22no—
354C2×D17—22no—
355C2×D17—22no—
356C2×D17—22no—
357C2×D17—22no—
358C2×D17—22no—
359C2×D17—44no—
360C2×D17—44no—
361C4×C17—22no—
362C4×C17—22no—
363C4×C17—22no—
364C4×C17—22no—
365C4×C17—22no—
366C4×C17#52012yes—
367C4×C17C2×H(5,𝔽2)11yescharacteristic
368C4×C17C2×2−1+411yescharacteristic
369Dic17—22no—
370Dic17—22no—
371Dic17—22no—
372Dic17—22no—
373Dic17—22no—
374Dic17—22no—
375C22×M16—171no—
376C22×M16—171no—
377C22×M16—171no—
378C22×M16—171no—
379C23×C8—171no—
380C23×C8—171no—
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×D4—171no—
395C2×#117—171no—
396C2×#117C2×D1711yescharacteristic
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#435—178no—
406#433—178no—
407#433C2×D1718yescomplemented
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⋊C8C2×D1711yescharacteristic
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×C8C2×D1711yescharacteristic
434C2×C17—42no—
435C2×C17#299514yescomplemented
436C2×C17C2×#52011yescharacteristic
437C2×C17C2×#56811yescharacteristic
438C2×C17C2×#56811yescharacteristic
439D17—42no—
440D17—42no—
441C22×Q8—171no—
442C22×D4—171no—
443C22×D4—171no—
444C22×D4—171no—
445C23×C4—171no—
446C23×C4—171no—
447C23×C4—171no—
448C23×C4—171no—
449C23×C4C22×D1711yescharacteristic
450C2×M16—174no—
451C2×M16—174no—
452C2×M16—174no—
453C2×M16—174no—
454C2×M16—682no—
455C2×M16—682no—
456C2×M16—682no—
457C2×M16—682no—
458C22×C8—171no—
459C22×C8—171no—
460C22×C8—171no—
461C22×C8—171no—
462C22×C8—174no—
463C22×C8—174no—
464C22×C8—682no—
465C22×C8—682no—
466C22×C8C22×D1711yescharacteristic
467C22×C8C22×D1711yescharacteristic
468C22×C8C22×D1711yescharacteristic
469C22×C8C22×D1711yescharacteristic
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×D4—174no—
485C4×D4—174no—
486#117—174no—
487#117—174no—
488#117C4×D1714yes—
489#117C22×D1714yes—
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⋊C4C4×D1711yescharacteristic
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—174no—
515C2×C42—174no—
516C2×C42C22×D1711yescharacteristic
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⋊C8C22×D1714yes—
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×C8C22×D1714yes—
540C17C2×#299511yescharacteristic, complemented, Sylow
541C24—171no—
542C24—171no—
543C24C2×C4×D1711yescharacteristic
544C2×Q8—174no—
545C2×Q8—682no—
546C2×D4—174no—
547C2×D4—174no—
548C2×D4—174no—
549C2×D4—682no—
550C2×D4—682no—
551C2×D4—682no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—171no—
555C22×C4—171no—
556C22×C4—171no—
557C22×C4—171no—
558C22×C4—171no—
559C22×C4—171no—
560C22×C4—172no—
561C22×C4—172no—
562C22×C4—172no—
563C22×C4—172no—
564C22×C4—174no—
565C22×C4—174no—
566C22×C4—342no—
567C22×C4—342no—
568C22×C4—342no—
569C22×C4—342no—
570C22×C4—682no—
571C22×C4—682no—
572C22×C4C2×C4×D1711yescharacteristic
573C22×C4C2×C4×D1711yescharacteristic
574C22×C4C2×C4×D1711yescharacteristic
575C22×C4C2×C4×D1711yescharacteristic
576C22×C4C2×C4×D1711yescharacteristic
577C22×C4C2×C4×D1712yes—
578C22×C4C23×D1712yes—
579C22×C4C23×D1711yescharacteristic
580M16—684no—
581M16—684no—
582M16—684no—
583M16—684no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—172no—
589C2×C8—172no—
590C2×C8—172no—
591C2×C8—172no—
592C2×C8—342no—
593C2×C8—342no—
594C2×C8—342no—
595C2×C8—342no—
596C2×C8—684no—
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⋊C4C2×C4×D1714yes—
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—
628C42C2×C4×D1712yes—
629C42C2×C4×D1712yes—
630C42C23×D1712yes—
631C42C23×D1712yes—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—172no—
636C23—172no—
637C23—342no—
638C23—342no—
639C23—342no—
640C23—342no—
641C23—342no—
642C23—342no—
643C23C22×C4×D1712yes—
644C23C22×C4×D1711yescharacteristic
645Q8—684no—
646D4—684no—
647D4—684no—
648D4—684no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—172no—
658C2×C4—172no—
659C2×C4—172no—
660C2×C4—172no—
661C2×C4—172no—
662C2×C4—172no—
663C2×C4—342no—
664C2×C4—342no—
665C2×C4—342no—
666C2×C4—342no—
667C2×C4—342no—
668C2×C4—342no—
669C2×C4—344no—
670C2×C4—344no—
671C2×C4—342no—
672C2×C4—342no—
673C2×C4—342no—
674C2×C4—342no—
675C2×C4—684no—
676C2×C4—684no—
677C2×C4C22×C4×D1712yes—
678C2×C4C22×C4×D1712yes—
679C2×C4C22×C4×D1712yes—
680C2×C4C22×C4×D1712yes—
681C2×C4C22×C4×D1712yes—
682C2×C4C22×C4×D1711yescharacteristic
683C2×C4#1058769612yes—
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—44no—
698C22—342no—
699C22—342no—
700C22—342no—
701C22—342no—
702C22—342no—
703C22—342no—
704C22—684no—
705C22—684no—
706C22#1176328912yes—
707C22#1176357412yes—
708C22#1176357412yes—
709C22C23×C4×D1711yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—342no—
716C4—342no—
717C4—342no—
718C4—342no—
719C4—342no—
720C4—342no—
721C4#1176328912yes—
722C4C2×#1058769611yescharacteristic
723C4C2×#1058769711yescharacteristic
724C2—42no—
725C2—682no—
726C2—682no—
727C2#1453794914yesdirect product factor
728C2C2×#1176328911yescharacteristic
729C2C2×#1176357411yescharacteristic
730C2C2×#1176357411yescharacteristic
subgroupG/H
centerC22×C4C23×D17
commutatorC22×C17C24×C4
FrattiniC2×C4C24×D17
FittingC2×C17×#433C2
socleC23×C17C23×C4
prime radicalC2×#10587570C4
cosocleC2×C4×C17C25
hypercenterC2×#433D17
hypocenterC17C2×#2995
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #14537949C2direct (N × H)
3. C2×#11762939C2semidirect
4. C2×#11762937C2semidirect
5. C2×#11762888C2semidirect
6. C2×#11762884C2semidirect
7. C2×#11762883C2semidirect
8. C2×#11762882C2semidirect
9. C2×#11762877C2semidirect
10. C2×#11762877C2semidirect
11. C2×#11762869C2semidirect
12. C2×#11762865C2semidirect
13. C2×#11762836C2semidirect
14. C2×#11762834C2semidirect
15. C2×#11762831C2semidirect
16. C2×C17×#433C2semidirect
39. #11762939C22semidirect
40. #11762937C22semidirect
41. #11762888C22semidirect
42. #11762884C22semidirect
43. #11762883C22semidirect
44. #11762882C22semidirect
45. #11762877C22semidirect
46. #11762877C22semidirect
47. #11762869C22semidirect
48. #11762865C22semidirect
49. #11762836C22semidirect
50. #11762834C22semidirect
51. #11762831C22semidirect
69. C17×#433C22semidirect
340. C2×#433D17semidirect
407. #433C2×D17semidirect
435. C2×C17#2995semidirect
540. C17C2×#2995semidirect
727. C2#14537949direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117633372
#145379492
C2×#117629392
C2×#117629372
C2×#117628882
C2×#117628842
C2×#117628832
C2×#117628822
C2×#117628772
C2×#117628692
C2×#117628652
C2×#117628362
C2×#117628342
C2×#117628312
C2×C17×#4332
C2×#299517