Finite Group Databasebeta

← C2×#14537720 #17898692

Subgroups — C2×#14537720 #17898692

Order 4352.

1894 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763363C211yesmaximal, characteristic
2#14537720C2116yesmaximal, direct product factor
3C2×#11762940C211yesmaximal, characteristic, complemented
4C2×#11762939C211yesmaximal, characteristic, complemented
5C2×#11762938C211yesmaximal, characteristic, complemented
6C2×#11762938C211yesmaximal, characteristic, complemented
7C2×#11762937C211yesmaximal, characteristic, complemented
8C2×#11762937C211yesmaximal, characteristic, complemented
9C2×#11762936C211yesmaximal, characteristic, complemented
10C2×#11762834C211yesmaximal, characteristic
11C2×#11762834C211yesmaximal, characteristic
12C2×#11762831C211yesmaximal, characteristic
13C2×#11762766C211yesmaximal, characteristic
14C2×#11762763C211yesmaximal, characteristic
15C2×#97×D17C211yesmaximal, characteristic
16C2×C17×#446C211yesmaximal, characteristic, complemented
17C22×#63218C2211yescharacteristic
18C22×#63218C2211yescharacteristic
19C22×C8×D17C2211yescharacteristic
20C22×C8×D17C2211yescharacteristic
21#11763363C418yes—
22#11763363C2218yes—
23C2×#10587574C411yescharacteristic
24C2×#10587630C411yescharacteristic
25C2×#10587575C411yescharacteristic
26C2×#10587575C411yescharacteristic
27C2×#10587583C411yescharacteristic
28C2×#10587582C411yescharacteristic
29C2×#10587582C411yescharacteristic
30C2×#10587632C411yescharacteristic
31C2×C4×Dic34C2211yescharacteristic
32C2×C4×Dic34C2211yescharacteristic
33C2×C4×Dic34C2211yescharacteristic
34C2×#10587558C2211yescharacteristic
35C2×#10587558C2211yescharacteristic
36C2×C42×D17C2211yescharacteristic
37#11762940C2218yescomplemented
38#11762939C2218yescomplemented
39#11762938C2218yescomplemented
40#11762938C2218yescomplemented
41#11762937C2218yescomplemented
42#11762937C2218yescomplemented
43#11762936C2218yescomplemented
44#11762834C2218yes—
45#11762834C2218yes—
46#11762831C2218yes—
47C2×C4⋊#3622C2211yescharacteristic
48C2×C4⋊#3622C2211yescharacteristic
49C2×C4⋊#3622C2211yescharacteristic
50C2×#10587485C2211yescharacteristic
51C2×#10587485C2211yescharacteristic
52C2×#10587485C2211yescharacteristic
53C2×#10587485C2211yescharacteristic
54C2×#10587485C2211yescharacteristic
55C2×#10587485C2211yescharacteristic
56#11762766C2218yes—
57#11762763C2218yes—
58C2×#10587474C2211yescharacteristic
59C2×#10587474C2211yescharacteristic
60C2×#10587486C2211yescharacteristic
61C2×#10587486C2211yescharacteristic
62C2×#10587486C2211yescharacteristic
63C2×#10587486C2211yescharacteristic
64#97×D17C2218yes—
65C2×C4×#3622C2211yescharacteristic
66C2×C8×Dic17C2211yescharacteristic
67C2×C8×Dic17C2211yescharacteristic
68C2×C4×Q8×C17C2211yescharacteristic
69C17×#446C2218yescomplemented
70C2×C17×C4⋊C8C2211yescharacteristic
71C2×C17×C4⋊C8C2211yescharacteristic
72C2×C17×C4⋊C8C2211yescharacteristic
73C2×C17×#97C2211yescharacteristic
74C2×C17×#97C2211yescharacteristic
75C2×C4×C8×C17C2211yescharacteristic
76C22×Q8×C17C2×C411yescharacteristic
77C22×C4×D17C2×C411yescharacteristic
78C22×C4×D17C2×C411yescharacteristic
79C22×C4×D17C2311yescharacteristic
80C22×Dic34C2×C411yescharacteristic
81C22×Dic34C2×C411yescharacteristic
82C22×Dic34C2×C411yescharacteristic
83C22×C8×C17C2311yescharacteristic
84C22×C8×C17C2311yescharacteristic
85C22×C8×C17C2311yescharacteristic
86C22×C8×C17C2311yescharacteristic
87C4×Q8×C17C2×C414yes—
88C4×Q8×C17C2314yes—
89C2×C4⋊C4×C17C2×C411yescharacteristic
90C2×C4⋊C4×C17C2×C411yescharacteristic
91C2×C4⋊C4×C17C2×C411yescharacteristic
92C2×C42×C17C2311yescharacteristic
93C2×C42×C17C2311yescharacteristic
94C2×C42×C17C2311yescharacteristic
95#10587632C2×C418yes—
96#10587630C2×C418yes—
97C2×#63227C2×C411yescharacteristic
98C2×#63227C2×C411yescharacteristic
99C2×#63227C2×C411yescharacteristic
100C2×#63227C2×C411yescharacteristic
101C2×C4⋊Dic17C2×C411yescharacteristic
102C2×C4⋊Dic17C2×C411yescharacteristic
103C2×C4⋊Dic17C2×C411yescharacteristic
104C2×#63225C2×C411yescharacteristic
105C2×#63225C2×C411yescharacteristic
106C2×#63225C2×C411yescharacteristic
107C2×#63225C2×C411yescharacteristic
108C2×#63225C2×C411yescharacteristic
109C2×#63225C2×C411yescharacteristic
110C2×#63225C2×C411yescharacteristic
111C2×#63225C2×C411yescharacteristic
112C2×#63225C2×C411yescharacteristic
113C2×#63225C2×C411yescharacteristic
114C2×C4×Dic17C2×C411yescharacteristic
115C2×C4×Dic17C2×C411yescharacteristic
116C2×C4×Dic17C2311yescharacteristic
117C2×C4×Dic17C2311yescharacteristic
118C2×C4×Dic17C2311yescharacteristic
119C22×#3622C2311yescharacteristic
120C22×#3622C2311yescharacteristic
121C22×#3622C2311yescharacteristic
122C22×#3622C2311yescharacteristic
123C2×#63218—24no—
124C2×#63218—24no—
125C2×#63218C2314yes—
126C2×#63218C2314yes—
127C2×C8×D17—24no—
128C2×C8×D17Q818yescomplemented
129C2×C8×D17C2314yes—
130C2×C8×D17C2314yes—
131#10587583C2×C418yes—
132#10587582C2×C418yes—
133#10587582C2×C418yes—
134#10587575C2×C418yes—
135#10587575C2×C418yes—
136#10587574C2×C418yes—
137#10587558C2×C414yes—
138#10587558C2×C414yes—
139#10587558C2314yes—
140#10587558C2314yes—
141C42×D17C2×C414yes—
142C42×D17C2314yes—
143C4×Dic34C2×C414yes—
144C4×Dic34C2×C414yes—
145C4×Dic34C2×C414yes—
146C4×Dic34C2314yes—
147C4×Dic34C2314yes—
148C4×Dic34C2314yes—
149C17×C4⋊C8C2314yes—
150C17×C4⋊C8C2314yes—
151C17×C4⋊C8C2314yes—
152C17×#97C2314yes—
153C17×#97C2314yes—
154C4×C8×C17C2314yes—
155#10587486C2314yes—
156#10587486C2314yes—
157#10587486C2314yes—
158#10587486C2314yes—
159#10587485C2314yes—
160#10587485C2314yes—
161#10587485C2314yes—
162#10587485C2314yes—
163#10587485C2314yes—
164#10587485C2314yes—
165C8×Dic17C2314yes—
166C8×Dic17C2314yes—
167C4⋊#3622C2314yes—
168C4⋊#3622C2314yes—
169C4⋊#3622C2314yes—
170#10587474C2314yes—
171#10587474C2314yes—
172C4×#3622C2314yes—
173C23×D17C22×C411yescharacteristic
174C2×Q8×C17—42no—
175C2×Q8×C17C22×C414yes—
176C22×C4×C17C22×C411yescharacteristic
177C22×C4×C17C22×C411yescharacteristic
178C22×C4×C17C22×C411yescharacteristic
179C22×C4×C17C22×C411yescharacteristic
180C22×C4×C17C22×C411yescharacteristic
181C22×C4×C17C22×C411yescharacteristic
182C22×C4×C17C2411yescharacteristic
183C22×Dic17C22×C411yescharacteristic
184C22×Dic17C22×C411yescharacteristic
185C22×Dic17C22×C411yescharacteristic
186C22×Dic17C22×C411yescharacteristic
187C22×Dic17C22×C411yescharacteristic
188C22×Dic17C22×C411yescharacteristic
189C22×Dic17C22×C411yescharacteristic
190C2×C4×D17—42no—
191C2×C4×D17—42no—
192C2×C4×D17C22×C414yes—
193C2×C4×D17C22×C414yes—
194C2×C4×D17C22×C412yes—
195C2×C4×D17C2×Q814yes—
196C2×C4×D17#4114yes—
197C2×C4×D17C2412yes—
198C2×Dic34—42no—
199C2×Dic34—42no—
200C2×Dic34—42no—
201C2×Dic34C22×C414yes—
202C2×Dic34C22×C414yes—
203C2×Dic34C22×C414yes—
204C2×C8×C17—22no—
205C2×C8×C17—22no—
206C2×C8×C17—22no—
207C2×C8×C17C2×Q814yes—
208C2×C8×C17C2412yes—
209C2×C8×C17C2412yes—
210C2×C8×C17C2412yes—
211C2×C8×C17C2412yes—
212C4⋊C4×C17C22×C414yes—
213C4⋊C4×C17C22×C414yes—
214C4⋊C4×C17C22×C414yes—
215C42×C17C22×C412yes—
216C42×C17C22×C412yes—
217C42×C17C22×C412yes—
218C42×C17C2412yes—
219C42×C17C2412yes—
220C42×C17C2412yes—
221#63227C22×C414yes—
222#63227C22×C414yes—
223#63227C22×C414yes—
224#63227C22×C414yes—
225C4⋊Dic17C22×C414yes—
226C4⋊Dic17C22×C414yes—
227C4⋊Dic17C22×C414yes—
228#63225C22×C414yes—
229#63225C22×C414yes—
230#63225C22×C414yes—
231#63225C22×C414yes—
232#63225C22×C414yes—
233#63225C22×C414yes—
234#63225C22×C414yes—
235#63225C22×C414yes—
236#63225C22×C414yes—
237#63225C22×C414yes—
238C4×Dic17C22×C412yes—
239C4×Dic17C22×C412yes—
240C4×Dic17C22×C412yes—
241C4×Dic17C22×C414yes—
242C4×Dic17C22×C414yes—
243C4×Dic17C2412yes—
244C4×Dic17C2412yes—
245C4×Dic17C2412yes—
246C2×#3622—22no—
247C2×#3622—22no—
248C2×#3622—22no—
249C2×#3622C2×Q814yes—
250C2×#3622C2412yes—
251C2×#3622C2412yes—
252C2×#3622C2412yes—
253C2×#3622C2412yes—
254#63218—28no—
255#63218—28no—
256C8×D17—28no—
257C8×D17C2×Q8116yescomplemented
258C2×#2961—171nomaximal, Sylow
259C23×C17C23×C411yescharacteristic
260C22×D17—22no—
261C22×D17—22no—
262C22×D17C4×Q814yes—
263C22×D17C23×C412yes—
264Q8×C17—44no—
265C2×C4×C17—22no—
266C2×C4×C17—22no—
267C2×C4×C17—22no—
268C2×C4×C17—22no—
269C2×C4×C17—22no—
270C2×C4×C17—22no—
271C2×C4×C17C23×C412yes—
272C2×C4×C17C23×C412yes—
273C2×C4×C17C23×C412yes—
274C2×C4×C17C23×C412yes—
275C2×C4×C17C23×C412yes—
276C2×C4×C17C23×C412yes—
277C2×C4×C17C23×C411yescharacteristic
278C2×C4×C17C22×Q812yes—
279C2×C4×C17C2×#4112yes—
280C2×C4×C17C2511yescharacteristic
281C2×Dic17—22no—
282C2×Dic17—22no—
283C2×Dic17—22no—
284C2×Dic17—22no—
285C2×Dic17—22no—
286C2×Dic17—22no—
287C2×Dic17C4×Q814yes—
288C2×Dic17C23×C412yes—
289C2×Dic17C23×C412yes—
290C2×Dic17C23×C412yes—
291C2×Dic17C23×C412yes—
292C2×Dic17C23×C412yes—
293C2×Dic17C23×C412yes—
294C2×Dic17C23×C412yes—
295C4×D17—44no—
296C4×D17—44no—
297C4×D17C4×Q818yes—
298C4×D17C22×Q814yes—
299C4×D17C2×#4114yes—
300Dic34—44no—
301Dic34—44no—
302Dic34—44no—
303C8×C17—22no—
304C8×C17—22no—
305C8×C17—22no—
306C8×C17C22×Q814yes—
307#3622—22no—
308#3622—22no—
309#3622—22no—
310#3622C22×Q814yes—
311C2×#533—171no—
312#2961—1716no—
313C2×#446—171no—
314C2×#446—171no—
315C2×#446—171no—
316C2×#446—171no—
317C2×#446—171no—
318C2×#446—171no—
319C2×#446—171no—
320C2×#446D1711yescharacteristic, complemented
321C2×#424—171no—
322C2×#424—171no—
323C2×#423—171no—
324C2×#405—171no—
325C2×#405—171no—
326C22×#97—171no—
327C22×C17C2×C4×Q812yes—
328C22×C17#56812yes—
329C22×C17#56812yes—
330C22×C17C24×C411yescharacteristic
331C2×D17—28no—
332C2×D17—22no—
333C2×D17—22no—
334C2×D17C2×C4×Q814yes—
335C4×C17—22no—
336C4×C17—22no—
337C4×C17—22no—
338C4×C17—22no—
339C4×C17—22no—
340C4×C17—22no—
341C4×C17C2×C4×Q812yes—
342C4×C17C23×Q811yescharacteristic
343C4×C17C22×#4111yescharacteristic
344Dic17—22no—
345Dic17—22no—
346Dic17—22no—
347Dic17—22no—
348Dic17—22no—
349Dic17—22no—
350Dic17C2×C4×Q814yes—
351C22×M16—171no—
352C22×M16—171no—
353C23×C8—171no—
354C23×C8—171no—
355#533—178no—
356#533—178no—
357C2×C4⋊Q8—171no—
358C2×C4⋊Q8—171no—
359C2×#125—171no—
360C2×#125—171no—
361C2×C22⋊Q8—171no—
362C2×C22⋊Q8—171no—
363C2×C22⋊Q8—171no—
364C2×C22⋊Q8—171no—
365C2×C4×Q8—171no—
366C2×C4×Q8—171no—
367C2×C4×Q8—171no—
368C2×C4×Q8C2×D1711yescharacteristic
369C2×#117—171no—
370C2×#117—171no—
371C22×C42—171no—
372#446—178no—
373#446—178no—
374#446—178no—
375#446—178no—
376#446—178no—
377#446—178no—
378#446—178no—
379#446C2×D1718yescomplemented
380#424—178no—
381#424—178no—
382#423—178no—
383C2×C4⋊C8—171no—
384C2×C4⋊C8—171no—
385C2×C4⋊C8—171no—
386C2×C4⋊C8—171no—
387C2×C4⋊C8—171no—
388C2×C4⋊C8—171no—
389C2×C4⋊C8—171no—
390C2×C4⋊C8—171no—
391C2×C4⋊C8—171no—
392C2×C4⋊C8C2×D1711yescharacteristic
393C2×C4⋊C8C2×D1711yescharacteristic
394C2×C4⋊C8C2×D1711yescharacteristic
395#405—178no—
396#405—178no—
397C2×#97—171no—
398C2×#97—171no—
399C2×#97—171no—
400C2×#97—171no—
401C2×#97—171no—
402C2×#97—171no—
403C2×#97—178no—
404C2×#97C2×D1711yescharacteristic
405C2×#97C2×D1711yescharacteristic
406C2×C4×C8—171no—
407C2×C4×C8—171no—
408C2×C4×C8—171no—
409C2×C4×C8C2×D1711yescharacteristic
410C2×C17#296114yescomplemented
411C2×C17C22×C4×Q811yescharacteristic
412C2×C17C2×#56811yescharacteristic
413C2×C17C2×#56811yescharacteristic
414D17—24no—
415C22×Q8—171no—
416C22×Q8—171no—
417C22×Q8—171no—
418C22×Q8C4×D1711yescharacteristic
419C23×C4—171no—
420C23×C4—171no—
421C23×C4—171no—
422C2×M16—174no—
423C2×M16—174no—
424C2×M16—344no—
425C2×M16—344no—
426C22×C8—171no—
427C22×C8—178no—
428C22×C8—174no—
429C22×C8—171no—
430C22×C8—171no—
431C22×C8—171no—
432C22×C8—174no—
433C22×C8—344no—
434C22×C8C22×D1711yescharacteristic
435C22×C8C22×D1711yescharacteristic
436C22×C8C22×D1711yescharacteristic
437C22×C8C22×D1711yescharacteristic
438C4⋊Q8—178no—
439C4⋊Q8—178no—
440#125—178no—
441#125—178no—
442C22⋊Q8—178no—
443C22⋊Q8—178no—
444C22⋊Q8—178no—
445C22⋊Q8—178no—
446C4×Q8—174no—
447C4×Q8—174no—
448C4×Q8—174no—
449C4×Q8—174no—
450C4×Q8—174no—
451C4×Q8—174no—
452C4×Q8C4×D1714yes—
453C4×Q8C22×D1714yes—
454#117—174no—
455#117—174no—
456#117—174no—
457#117—174no—
458C2×C4⋊C4—171no—
459C2×C4⋊C4—171no—
460C2×C4⋊C4—171no—
461C2×C4⋊C4—171no—
462C2×C4⋊C4—171no—
463C2×C4⋊C4—171no—
464C2×C4⋊C4—171no—
465C2×C4⋊C4—171no—
466C2×C4⋊C4—171no—
467C2×C4⋊C4—171no—
468C2×C4⋊C4—171no—
469C2×C4⋊C4—171no—
470C2×C4⋊C4—171no—
471C2×C4⋊C4C4×D1711yescharacteristic
472C2×C4⋊C4C4×D1711yescharacteristic
473C2×C4⋊C4C4×D1711yescharacteristic
474C2×C22⋊C4—171no—
475C2×C22⋊C4—171no—
476C2×C22⋊C4—171no—
477C2×C22⋊C4—171no—
478C2×C42—171no—
479C2×C42—171no—
480C2×C42—171no—
481C2×C42—171no—
482C2×C42—171no—
483C2×C42—174no—
484C2×C42—174no—
485C2×C42C22×D1711yescharacteristic
486C2×C42C22×D1711yescharacteristic
487C2×C42C22×D1711yescharacteristic
488C4⋊C8—174no—
489C4⋊C8—174no—
490C4⋊C8—174no—
491C4⋊C8—174no—
492C4⋊C8—174no—
493C4⋊C8—174no—
494C4⋊C8—174no—
495C4⋊C8—174no—
496C4⋊C8—174no—
497C4⋊C8C22×D1714yes—
498C4⋊C8C22×D1714yes—
499C4⋊C8C22×D1714yes—
500#97—174no—
501#97—174no—
502#97—174no—
503#97—174no—
504#97—174no—
505#97—174no—
506#97C22×D1714yes—
507#97C22×D1714yes—
508C4×C8—174no—
509C4×C8—174no—
510C4×C8—174no—
511C4×C8C22×D1714yes—
512C17C2×#296111yescharacteristic, complemented, Sylow
513C24—171no—
514C2×Q8—42no—
515C2×Q8—174no—
516C2×Q8—174no—
517C2×Q8—174no—
518C2×Q8—682no—
519C2×Q8—682no—
520C2×Q8—682no—
521C2×Q8C2×C4×D1714yes—
522C22×C4—171no—
523C22×C4—172no—
524C22×C4—174no—
525C22×C4—174no—
526C22×C4—172no—
527C22×C4—171no—
528C22×C4—171no—
529C22×C4—171no—
530C22×C4—171no—
531C22×C4—171no—
532C22×C4—171no—
533C22×C4—174no—
534C22×C4—174no—
535C22×C4—682no—
536C22×C4—682no—
537C22×C4C2×C4×D1711yescharacteristic
538C22×C4C2×C4×D1711yescharacteristic
539C22×C4C2×C4×D1711yescharacteristic
540C22×C4C2×C4×D1711yescharacteristic
541C22×C4C2×C4×D1711yescharacteristic
542C22×C4C2×C4×D1711yescharacteristic
543C22×C4C23×D1711yescharacteristic
544M16—348no—
545M16—348no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—174no—
550C2×C8—172no—
551C2×C8—1716no—
552C2×C8—172no—
553C2×C8—172no—
554C2×C8—172no—
555C2×C8—348no—
556C2×C8—342no—
557C2×C8—342no—
558C2×C8—342no—
559C2×C8Q8×D1714yes—
560C2×C8C23×D1712yes—
561C2×C8C23×D1712yes—
562C2×C8C23×D1712yes—
563C2×C8C23×D1712yes—
564C4⋊C4—174no—
565C4⋊C4—174no—
566C4⋊C4—174no—
567C4⋊C4—174no—
568C4⋊C4—174no—
569C4⋊C4—174no—
570C4⋊C4—174no—
571C4⋊C4—174no—
572C4⋊C4—174no—
573C4⋊C4—174no—
574C4⋊C4—174no—
575C4⋊C4—174no—
576C4⋊C4—174no—
577C4⋊C4C2×C4×D1714yes—
578C4⋊C4C2×C4×D1714yes—
579C4⋊C4C2×C4×D1714yes—
580C22⋊C4—174no—
581C22⋊C4—174no—
582C22⋊C4—174no—
583C22⋊C4—174no—
584C42—172no—
585C42—174no—
586C42—174no—
587C42—172no—
588C42—172no—
589C42—172no—
590C42—172no—
591C42—172no—
592C42C2×C4×D1712yes—
593C42C2×C4×D1712yes—
594C42C2×C4×D1712yes—
595C42C23×D1712yes—
596C42C23×D1712yes—
597C42C23×D1712yes—
598C23—174no—
599C23—172no—
600C23—342no—
601C23—342no—
602C23C22×C4×D1711yescharacteristic
603Q8—44no—
604Q8—684no—
605Q8—684no—
606Q8—684no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—174no—
614C2×C4—172no—
615C2×C4—178no—
616C2×C4—174no—
617C2×C4—174no—
618C2×C4—172no—
619C2×C4—172no—
620C2×C4—172no—
621C2×C4—172no—
622C2×C4—172no—
623C2×C4—172no—
624C2×C4—342no—
625C2×C4—342no—
626C2×C4—342no—
627C2×C4—342no—
628C2×C4—342no—
629C2×C4—342no—
630C2×C4—684no—
631C2×C4—684no—
632C2×C4C22×C4×D1712yes—
633C2×C4C22×C4×D1712yes—
634C2×C4C22×C4×D1712yes—
635C2×C4C22×C4×D1712yes—
636C2×C4C22×C4×D1712yes—
637C2×C4C22×C4×D1712yes—
638C2×C4C22×C4×D1711yescharacteristic
639C2×C4C2×Q8×D1712yes—
640C2×C4#41×D1712yes—
641C2×C4C24×D1711yescharacteristic
642C8—22no—
643C8—22no—
644C8—22no—
645C8—174no—
646C8—342no—
647C8—342no—
648C8—342no—
649C8C2×Q8×D1714yes—
650C22—174no—
651C22—342no—
652C22—342no—
653C22—348no—
654C22C4×Q8×D1712yes—
655C22#1176357412yes—
656C22#1176357512yes—
657C22C23×C4×D1711yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—174no—
665C4—342no—
666C4—342no—
667C4—342no—
668C4—342no—
669C4—342no—
670C4—342no—
671C4C4×Q8×D1712yes—
672C4C22×Q8×D1711yescharacteristic
673C4C2×#41×D1711yescharacteristic
674C2—344no—
675C2#1453772014yesdirect product factor
676C2C2×C4×Q8×D1711yescharacteristic
677C2C2×#1176357411yescharacteristic
678C2C2×#1176357511yescharacteristic
subgroupG/H
centerC22×C4C23×D17
commutatorC22×C17C24×C4
FrattiniC2×C4C24×D17
FittingC2×C17×#446C2
socleC23×C17C23×C4
prime radicalC23×D17C22×C4
cosocleC2×C4×C17C25
hypercenterC2×#446D17
hypocenterC17C2×#2961
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #14537720C2direct (N × H)
3. C2×#11762940C2semidirect
4. C2×#11762939C2semidirect
5. C2×#11762938C2semidirect
6. C2×#11762938C2semidirect
7. C2×#11762937C2semidirect
8. C2×#11762937C2semidirect
9. C2×#11762936C2semidirect
16. C2×C17×#446C2semidirect
37. #11762940C22semidirect
38. #11762939C22semidirect
39. #11762938C22semidirect
40. #11762938C22semidirect
41. #11762937C22semidirect
42. #11762937C22semidirect
43. #11762936C22semidirect
69. C17×#446C22semidirect
128. C2×C8×D17Q8semidirect
257. C8×D17C2×Q8semidirect
320. C2×#446D17semidirect
379. #446C2×D17semidirect
410. C2×C17#2961semidirect
512. C17C2×#2961semidirect
675. C2#14537720direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117633632
#145377202
C2×#117629402
C2×#117629392
C2×#117629382
C2×#117629372
C2×#117629362
C2×#117628342
C2×#117628312
C2×#117627662
C2×#117627632
C2×#97×D172
C2×C17×#4462
C2×#296117