Finite Group Databasebeta

← C2×#14537876 #17899277

Subgroups — C2×#14537876 #17899277

Order 4352.

1750 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763362C211yesmaximal, characteristic
2#14537876C2116yesmaximal, direct product factor
3C2×#11762939C211yesmaximal, characteristic, complemented
4C2×#11762938C211yesmaximal, characteristic, complemented
5C2×#11762938C211yesmaximal, characteristic, complemented
6C2×#11762937C211yesmaximal, characteristic, complemented
7C2×#11762937C211yesmaximal, characteristic, complemented
8C2×#11762936C211yesmaximal, characteristic, complemented
9C2×C8×Dic34C211yesmaximal, characteristic, complemented
10C2×#11762933C211yesmaximal, characteristic, complemented
11C2×#11762870C211yesmaximal, characteristic
12C2×#11762867C211yesmaximal, characteristic
13C2×#11762867C211yesmaximal, characteristic
14C2×#11762863C211yesmaximal, characteristic
15C2×#11762859C211yesmaximal, characteristic
16C2×C17×#433C211yesmaximal, characteristic
17#11763362C418yes—
18#11763362C2218yes—
19C2×#10587574C411yescharacteristic
20C2×#10587574C411yescharacteristic
21C2×#10587576C411yescharacteristic
22C2×#10587576C411yescharacteristic
23C2×#10587564C411yescharacteristic
24C2×#10587564C411yescharacteristic
25C2×#10587564C411yescharacteristic
26C2×#10587564C411yescharacteristic
27C2×C4×Dic34C2211yescharacteristic
28C2×C4×Dic34C2211yescharacteristic
29C2×C4×Dic34C2211yescharacteristic
30C2×C4×Dic34C2211yescharacteristic
31C2×#10587612C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33#11762939C2218yescomplemented
34#11762938C2218yescomplemented
35#11762938C2218yescomplemented
36#11762937C2218yescomplemented
37#11762937C2218yescomplemented
38#11762936C2218yescomplemented
39C8×Dic34C2218yescomplemented
40#11762933C2218yescomplemented
41#11762870C2218yes—
42#11762867C2218yes—
43#11762867C2218yes—
44#11762863C2218yes—
45#11762859C2218yes—
46C2×C4⋊#3622C2211yescharacteristic
47C2×C4⋊#3622C2211yescharacteristic
48C2×#10587485C2211yescharacteristic
49C2×#10587485C2211yescharacteristic
50C2×#10587485C2211yescharacteristic
51C2×#10587485C2211yescharacteristic
52C2×#10587485C2211yescharacteristic
53C2×#10587485C2211yescharacteristic
54C2×#10587485C2211yescharacteristic
55C2×#10587485C2211yescharacteristic
56C2×C22⋊#3622C2211yescharacteristic
57C2×C22⋊#3622C2211yescharacteristic
58C2×#10587474C2211yescharacteristic
59C2×#10587486C2211yescharacteristic
60C2×#10587486C2211yescharacteristic
61C2×#10587486C2211yescharacteristic
62C2×#10587486C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C2×C8×Dic17C2211yescharacteristic
65C2×C8×Dic17C2211yescharacteristic
66C2×C8×Dic17C2211yescharacteristic
67C2×C8×Dic17C2211yescharacteristic
68C2×C17×#117C2211yescharacteristic
69C17×#433C2218yes—
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
77C23×Dic17C2×C411yescharacteristic
78C23×Dic17C2×C411yescharacteristic
79C22×Dic34C2×C411yescharacteristic
80C22×Dic34C2×C411yescharacteristic
81C22×Dic34C2×C411yescharacteristic
82C22×Dic34C2×C411yescharacteristic
83C22×C8×C17C2311yescharacteristic
84C22×C8×C17C2311yescharacteristic
85C22×C8×C17C2311yescharacteristic
86C22×C8×C17C2311yescharacteristic
87C17×#117C2×C414yes—
88C17×#117C2314yes—
89C2×C4⋊C4×C17C2×C411yescharacteristic
90C2×C4⋊C4×C17C2×C411yescharacteristic
91C2×C22⋊C4×C17C2×C411yescharacteristic
92C2×C22⋊C4×C17C2×C411yescharacteristic
93C2×C42×C17C2311yescharacteristic
94C2×C42×C17C2311yescharacteristic
95C2×C22⋊Dic17C2×C411yescharacteristic
96C2×C22⋊Dic17C2×C411yescharacteristic
97#10587612C2×C414yes—
98#10587612C2314yes—
99C2×C4⋊Dic17C2×C411yescharacteristic
100C2×C4⋊Dic17C2×C411yescharacteristic
101C2×C4⋊Dic17C2×C411yescharacteristic
102C2×C4⋊Dic17C2×C411yescharacteristic
103C2×C4⋊Dic17C2×C411yescharacteristic
104C2×C4⋊Dic17C2×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×C4×Dic17C2×C411yescharacteristic
114C2×C4×Dic17C2×C411yescharacteristic
115C2×C4×Dic17C2×C414yes—
116C2×C4×Dic17C2311yescharacteristic
117C2×C4×Dic17C2311yescharacteristic
118C2×C4×Dic17C2314yes—
119C2×C4×Dic17C2311yescharacteristic
120C2×C4×Dic17C2311yescharacteristic
121C22×#3622C2311yescharacteristic
122C22×#3622C2311yescharacteristic
123C22×#3622C2311yescharacteristic
124C22×#3622C2311yescharacteristic
125#10587576C2×C418yes—
126#10587576C2×C418yes—
127#10587574C2×C418yes—
128#10587574C2×C418yes—
129#10587564C2×C418yes—
130#10587564C2×C418yes—
131#10587564C2×C418yes—
132#10587564C2×C418yes—
133C4×Dic34C2×C414yes—
134C4×Dic34C2×C414yes—
135C4×Dic34C2×C414yes—
136C4×Dic34C2×C414yes—
137C4×Dic34C2314yes—
138C4×Dic34C2314yes—
139C4×Dic34C2314yes—
140C4×Dic34C2314yes—
141C17×C4⋊C8C2314yes—
142C17×C4⋊C8C2314yes—
143C17×C22⋊C8C2314yes—
144C17×C22⋊C8C2314yes—
145C17×#97C2314yes—
146C4×C8×C17C2314yes—
147C22⋊#3622C2314yes—
148C22⋊#3622C2314yes—
149#10587486C2314yes—
150#10587486C2314yes—
151#10587486C2314yes—
152#10587486C2314yes—
153#10587485C2314yes—
154#10587485C2314yes—
155#10587485C2314yes—
156#10587485C2314yes—
157#10587485C2314yes—
158#10587485C2314yes—
159#10587485C2314yes—
160#10587485C2314yes—
161C8×Dic17C2314yes—
162C8×Dic17C2314yes—
163C8×Dic17C2314yes—
164C8×Dic17C2314yes—
165C4⋊#3622C2314yes—
166C4⋊#3622C2314yes—
167#10587474C2314yes—
168C4×#3622C2314yes—
169C24×C17C22×C411yescharacteristic
170C22×C4×C17—22no—
171C22×C4×C17—22no—
172C22×C4×C17C22×C411yescharacteristic
173C22×C4×C17C22×C411yescharacteristic
174C22×C4×C17C22×C411yescharacteristic
175C22×C4×C17C22×C411yescharacteristic
176C22×C4×C17C22×C411yescharacteristic
177C22×C4×C17C22×C412yes—
178C22×C4×C17C2412yes—
179C22×C4×C17C2411yescharacteristic
180C22×Dic17—24no—
181C22×Dic17—42no—
182C22×Dic17C22×C411yescharacteristic
183C22×Dic17C22×C411yescharacteristic
184C22×Dic17C22×C411yescharacteristic
185C22×Dic17C22×C411yescharacteristic
186C22×Dic17C22×C411yescharacteristic
187C22×Dic17C22×C414yes—
188C22×Dic17C22×C411yescharacteristic
189C22×Dic17C22×C411yescharacteristic
190C22×Dic17C22×C414yes—
191C22×Dic17C22×C411yescharacteristic
192C2×Dic34—24no—
193C2×Dic34—24no—
194C2×Dic34—42no—
195C2×Dic34—42no—
196C2×Dic34C22×C414yes—
197C2×Dic34C22×C414yes—
198C2×Dic34C22×C414yes—
199C2×Dic34C22×C414yes—
200C2×C8×C17—22no—
201C2×C8×C17—22no—
202C2×C8×C17—22no—
203C2×C8×C17—22no—
204C2×C8×C17C2412yes—
205C2×C8×C17C2412yes—
206C2×C8×C17C2412yes—
207C2×C8×C17C2412yes—
208C4⋊C4×C17C22×C414yes—
209C4⋊C4×C17C22×C414yes—
210C22⋊C4×C17C22×C414yes—
211C22⋊C4×C17C22×C414yes—
212C42×C17C22×C412yes—
213C42×C17C22×C412yes—
214C42×C17C2412yes—
215C42×C17C2412yes—
216C22⋊Dic17C22×C414yes—
217C22⋊Dic17C22×C414yes—
218C4⋊Dic17C22×C414yes—
219C4⋊Dic17C22×C414yes—
220C4⋊Dic17C22×C414yes—
221C4⋊Dic17C22×C414yes—
222C4⋊Dic17C22×C414yes—
223C4⋊Dic17C22×C414yes—
224#63225C22×C414yes—
225#63225C22×C414yes—
226#63225C22×C414yes—
227#63225C22×C414yes—
228#63225C22×C414yes—
229#63225C22×C414yes—
230#63225C22×C414yes—
231#63225C22×C414yes—
232C4×Dic17C22×C412yes—
233C4×Dic17C22×C412yes—
234C4×Dic17C22×C412yes—
235C4×Dic17C22×C412yes—
236C4×Dic17C22×C414yes—
237C4×Dic17C22×C414yes—
238C4×Dic17C2412yes—
239C4×Dic17C2412yes—
240C4×Dic17C2412yes—
241C4×Dic17C2412yes—
242C2×#3622—22no—
243C2×#3622—22no—
244C2×#3622—22no—
245C2×#3622—22no—
246C2×#3622C2412yes—
247C2×#3622C2412yes—
248C2×#3622C2412yes—
249C2×#3622C2412yes—
250C2×#2985—171nomaximal, Sylow
251C23×C17—22no—
252C23×C17—22no—
253C23×C17—22no—
254C23×C17C23×C412yes—
255C23×C17C23×C411yescharacteristic
256C2×C4×C17—22no—
257C2×C4×C17—22no—
258C2×C4×C17—22no—
259C2×C4×C17—22no—
260C2×C4×C17—22no—
261C2×C4×C17—24no—
262C2×C4×C17—22no—
263C2×C4×C17—22no—
264C2×C4×C17C23×C412yes—
265C2×C4×C17C23×C412yes—
266C2×C4×C17C23×C412yes—
267C2×C4×C17C23×C412yes—
268C2×C4×C17C23×C412yes—
269C2×C4×C17C23×C411yescharacteristic
270C2×C4×C172−1+412yes—
271C2×C4×C172−1+412yes—
272C2×C4×C17C2511yescharacteristic
273C2×Dic17—22no—
274C2×Dic17—22no—
275C2×Dic17—22no—
276C2×Dic17—22no—
277C2×Dic17—22no—
278C2×Dic17—22no—
279C2×Dic17—22no—
280C2×Dic17—28no—
281C2×Dic17—44no—
282C2×Dic17#13114yes—
283C2×Dic17C23×C412yes—
284C2×Dic17C23×C412yes—
285C2×Dic17C23×C412yes—
286C2×Dic17C23×C412yes—
287C2×Dic17C23×C412yes—
288C2×Dic17C23×C412yes—
289C2×Dic17C23×C412yes—
290C2×Dic17C23×C412yes—
291Dic34—28no—
292Dic34—28no—
293Dic34—44no—
294Dic34—44no—
295C8×C17—22no—
296C8×C17—22no—
297C8×C17—22no—
298C8×C17—22no—
299#3622—22no—
300#3622—22no—
301#3622—22no—
302#3622—22no—
303C2×#533—171no—
304#2985—1716no—
305C2×#446—171no—
306C2×#446—171no—
307C2×#446—171no—
308C2×#446—171no—
309C2×#446—171no—
310C2×#446—171no—
311C2×C8×Q8—171no—
312C2×C8×Q8—171no—
313C2×#433—171no—
314C2×#433—171no—
315C2×#433—171no—
316C2×#433D1711yescharacteristic
317C2×#432—171no—
318C2×#431—171no—
319C22×C17—22no—
320C22×C17—22no—
321C22×C17—22no—
322C22×C17—44no—
323C22×C17#51912yes—
324C22×C17C2×#13112yes—
325C22×C17#56812yes—
326C22×C17C24×C411yescharacteristic
327C4×C17—22no—
328C4×C17—22no—
329C4×C17—22no—
330C4×C17—22no—
331C4×C17—22no—
332C4×C17#51912yes—
333C4×C17C2×2−1+411yescharacteristic
334C4×C17C2×2−1+411yescharacteristic
335Dic17—22no—
336Dic17—22no—
337Dic17—22no—
338Dic17—22no—
339Dic17—22no—
340Dic17—22no—
341Dic17—22no—
342Dic17C2×#13114yes—
343#533—178no—
344#533—178no—
345C2×C4⋊Q8—171no—
346C2×C4⋊Q8—171no—
347C2×#125—171no—
348C2×#125—171no—
349C2×C22⋊Q8—171no—
350C2×C22⋊Q8—171no—
351C2×C22⋊Q8—171no—
352C2×C22⋊Q8—171no—
353C2×C4×Q8—171no—
354C2×C4×Q8—171no—
355C2×C4×Q8—171no—
356C2×C4×Q8—171no—
357C2×#117—171no—
358C2×#117C2×D1711yescharacteristic
359C22×C42—171no—
360#446—178no—
361#446—178no—
362#446—178no—
363#446—178no—
364#446—178no—
365#446—178no—
366C8×Q8—178no—
367C8×Q8—178no—
368#433—178no—
369#433—178no—
370#433—178no—
371#433C2×D1718yes—
372#432—178no—
373#431—178no—
374C2×C4⋊C8—171no—
375C2×C4⋊C8—171no—
376C2×C4⋊C8—171no—
377C2×C4⋊C8—171no—
378C2×C4⋊C8—171no—
379C2×C4⋊C8—171no—
380C2×C4⋊C8—171no—
381C2×C4⋊C8—171no—
382C2×C4⋊C8—171no—
383C2×C4⋊C8—171no—
384C2×C4⋊C8C2×D1711yescharacteristic
385C2×C4⋊C8C2×D1711yescharacteristic
386C2×C22⋊C8—171no—
387C2×C22⋊C8—171no—
388C2×C22⋊C8C2×D1711yescharacteristic
389C2×C22⋊C8C2×D1711yescharacteristic
390C2×#97—171no—
391C2×#97—171no—
392C2×#97—171no—
393C2×#97—171no—
394C2×#97—171no—
395C2×#97C2×D1711yescharacteristic
396C2×C4×C8—171no—
397C2×C4×C8—171no—
398C2×C4×C8—171no—
399C2×C4×C8—171no—
400C2×C4×C8—171no—
401C2×C4×C8C2×D1711yescharacteristic
402C2×C17—42no—
403C2×C17#298514yescomplemented
404C2×C17C2×#51911yescharacteristic
405C2×C17C22×#13111yescharacteristic
406C2×C17C2×#56811yescharacteristic
407C22×Q8—171no—
408C22×Q8—171no—
409C22×Q8—171no—
410C22×Q8—171no—
411C23×C4—171no—
412C23×C4—171no—
413C23×C4C22×D1711yescharacteristic
414C22×C8—171no—
415C22×C8—171no—
416C22×C8—171no—
417C22×C8—171no—
418C22×C8C22×D1711yescharacteristic
419C22×C8C22×D1711yescharacteristic
420C22×C8C22×D1711yescharacteristic
421C22×C8C22×D1711yescharacteristic
422C4⋊Q8—178no—
423C4⋊Q8—178no—
424#125—178no—
425#125—178no—
426C22⋊Q8—178no—
427C22⋊Q8—178no—
428C22⋊Q8—178no—
429C22⋊Q8—178no—
430C4×Q8—174no—
431C4×Q8—174no—
432C4×Q8—174no—
433C4×Q8—174no—
434C4×Q8—174no—
435C4×Q8—174no—
436C4×Q8—174no—
437C4×Q8—174no—
438#117—174no—
439#117—174no—
440#117C4×D1714yes—
441#117C22×D1714yes—
442C2×C4⋊C4—171no—
443C2×C4⋊C4—171no—
444C2×C4⋊C4—171no—
445C2×C4⋊C4—171no—
446C2×C4⋊C4—171no—
447C2×C4⋊C4—171no—
448C2×C4⋊C4—171no—
449C2×C4⋊C4—171no—
450C2×C4⋊C4—171no—
451C2×C4⋊C4—171no—
452C2×C4⋊C4—171no—
453C2×C4⋊C4—171no—
454C2×C4⋊C4—171no—
455C2×C4⋊C4—171no—
456C2×C4⋊C4C4×D1711yescharacteristic
457C2×C4⋊C4C4×D1711yescharacteristic
458C2×C22⋊C4—171no—
459C2×C22⋊C4—171no—
460C2×C22⋊C4C4×D1711yescharacteristic
461C2×C22⋊C4C4×D1711yescharacteristic
462C2×C42—171no—
463C2×C42—171no—
464C2×C42—174no—
465C2×C42—174no—
466C2×C42—171no—
467C2×C42—171no—
468C2×C42—171no—
469C2×C42—171no—
470C2×C42C22×D1711yescharacteristic
471C2×C42C22×D1711yescharacteristic
472C4⋊C8—174no—
473C4⋊C8—174no—
474C4⋊C8—174no—
475C4⋊C8—174no—
476C4⋊C8—174no—
477C4⋊C8—174no—
478C4⋊C8—174no—
479C4⋊C8—174no—
480C4⋊C8—174no—
481C4⋊C8—174no—
482C4⋊C8C22×D1714yes—
483C4⋊C8C22×D1714yes—
484C22⋊C8—174no—
485C22⋊C8—174no—
486C22⋊C8C22×D1714yes—
487C22⋊C8C22×D1714yes—
488#97—174no—
489#97—174no—
490#97—174no—
491#97—174no—
492#97—174no—
493#97C22×D1714yes—
494C4×C8—174no—
495C4×C8—174no—
496C4×C8—174no—
497C4×C8—174no—
498C4×C8—174no—
499C4×C8C22×D1714yes—
500C17C2×#298511yescharacteristic, complemented, Sylow
501C24C2×C4×D1711yescharacteristic
502C2×Q8—174no—
503C2×Q8—174no—
504C2×Q8—174no—
505C2×Q8—174no—
506C2×Q8—344no—
507C2×Q8—344no—
508C2×Q8—682no—
509C2×Q8—682no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—171no—
513C22×C4—171no—
514C22×C4—171no—
515C22×C4—171no—
516C22×C4—174no—
517C22×C4—171no—
518C22×C4—171no—
519C22×C4—171no—
520C22×C4—171no—
521C22×C4—174no—
522C22×C4—344no—
523C22×C4—682no—
524C22×C4C2×C4×D1711yescharacteristic
525C22×C4C2×C4×D1712yes—
526C22×C4C2×C4×D1711yescharacteristic
527C22×C4C2×C4×D1711yescharacteristic
528C22×C4C2×C4×D1711yescharacteristic
529C22×C4C2×C4×D1711yescharacteristic
530C22×C4C23×D1712yes—
531C22×C4C23×D1711yescharacteristic
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—172no—
537C2×C8—172no—
538C2×C8—172no—
539C2×C8—172no—
540C2×C8—342no—
541C2×C8—342no—
542C2×C8—342no—
543C2×C8—342no—
544C2×C8C23×D1712yes—
545C2×C8C23×D1712yes—
546C2×C8C23×D1712yes—
547C2×C8C23×D1712yes—
548C4⋊C4—174no—
549C4⋊C4—174no—
550C4⋊C4—174no—
551C4⋊C4—174no—
552C4⋊C4—174no—
553C4⋊C4—174no—
554C4⋊C4—174no—
555C4⋊C4—174no—
556C4⋊C4—174no—
557C4⋊C4—174no—
558C4⋊C4—174no—
559C4⋊C4—174no—
560C4⋊C4—174no—
561C4⋊C4—174no—
562C4⋊C4C2×C4×D1714yes—
563C4⋊C4C2×C4×D1714yes—
564C22⋊C4—174no—
565C22⋊C4—174no—
566C22⋊C4C2×C4×D1714yes—
567C22⋊C4C2×C4×D1714yes—
568C42—172no—
569C42—172no—
570C42—174no—
571C42—174no—
572C42—172no—
573C42—172no—
574C42—172no—
575C42—172no—
576C42—172no—
577C42—172no—
578C42C2×C4×D1712yes—
579C42C2×C4×D1712yes—
580C42C23×D1712yes—
581C42C23×D1712yes—
582C23—22no—
583C23—22no—
584C23—22no—
585C23C22×C4×D1712yes—
586C23C22×C4×D1711yescharacteristic
587Q8—348no—
588Q8—348no—
589Q8—684no—
590Q8—684no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—24no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—174no—
600C2×C4—172no—
601C2×C4—172no—
602C2×C4—172no—
603C2×C4—172no—
604C2×C4—172no—
605C2×C4—172no—
606C2×C4—172no—
607C2×C4—172no—
608C2×C4—348no—
609C2×C4—342no—
610C2×C4—342no—
611C2×C4—342no—
612C2×C4—342no—
613C2×C4—342no—
614C2×C4—342no—
615C2×C4—342no—
616C2×C4—684no—
617C2×C4C22×C4×D1712yes—
618C2×C4C22×C4×D1712yes—
619C2×C4C22×C4×D1712yes—
620C2×C4C22×C4×D1712yes—
621C2×C4C22×C4×D1712yes—
622C2×C4C22×C4×D1711yescharacteristic
623C2×C4#1058769712yes—
624C2×C4#1058769712yes—
625C2×C4C24×D1711yescharacteristic
626C8—22no—
627C8—22no—
628C8—22no—
629C8—22no—
630C8—342no—
631C8—342no—
632C8—342no—
633C8—342no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—44no—
638C22#1176328612yes—
639C22#131×D1712yes—
640C22#1176357412yes—
641C22C23×C4×D1711yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—22no—
646C4—22no—
647C4—174no—
648C4—342no—
649C4—342no—
650C4—342no—
651C4—342no—
652C4—342no—
653C4—342no—
654C4—342no—
655C4#1176328612yes—
656C4C2×#1058769711yescharacteristic
657C4C2×#1058769711yescharacteristic
658C2—42no—
659C2#1453787614yesdirect product factor
660C2C2×#1176328611yescharacteristic
661C2C2×#131×D1711yescharacteristic
662C2C2×#1176357411yescharacteristic
subgroupG/H
centerC22×C4C23×D17
commutatorC22×C17C24×C4
FrattiniC2×C4C24×D17
FittingC2×C17×#433C2
socleC23×C17C23×C4
prime radicalC24×C17C22×C4
cosocleC2×C4×C17C25
hypercenterC2×#433D17
hypocenterC17C2×#2985
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #14537876C2direct (N × H)
3. C2×#11762939C2semidirect
4. C2×#11762938C2semidirect
5. C2×#11762938C2semidirect
6. C2×#11762937C2semidirect
7. C2×#11762937C2semidirect
8. C2×#11762936C2semidirect
9. C2×C8×Dic34C2semidirect
10. C2×#11762933C2semidirect
33. #11762939C22semidirect
34. #11762938C22semidirect
35. #11762938C22semidirect
36. #11762937C22semidirect
37. #11762937C22semidirect
38. #11762936C22semidirect
39. C8×Dic34C22semidirect
40. #11762933C22semidirect
403. C2×C17#2985semidirect
500. C17C2×#2985semidirect
659. C2#14537876direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117633622
#145378762
C2×#117629392
C2×#117629382
C2×#117629372
C2×#117629362
C2×C8×Dic342
C2×#117629332
C2×#117628702
C2×#117628672
C2×#117628632
C2×#117628592
C2×C17×#4332
C2×#298517