Finite Group Databasebeta

← C2×#14540835 #17910930

Subgroups — C2×#14540835 #17910930

Order 4352.

2094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763499C211yesmaximal, characteristic
2#14540835C2116yesmaximal, direct product factor
3C2×#11763177C211yesmaximal, characteristic, complemented
4C2×#11763147C211yesmaximal, characteristic, complemented
5C2×#11763137C211yesmaximal, characteristic, complemented
6C2×#11763116C211yesmaximal, characteristic, complemented
7C2×#11763065C211yesmaximal, characteristic, complemented
8C2×#11763048C211yesmaximal, characteristic, complemented
9C2×#11763016C211yesmaximal, characteristic, complemented
10C2×#11762965C211yesmaximal, characteristic, complemented
11C2×#11762965C211yesmaximal, characteristic, complemented
12C2×#11762914C211yesmaximal, characteristic, complemented
13C2×#11762881C211yesmaximal, characteristic
14C2×#11762818C211yesmaximal, characteristic, complemented
15C22×#10587506C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C17C211yesmaximal, characteristic
17C22×#63231C2211yescharacteristic
18C22×#63231C2211yescharacteristic
19C22×#63231C2211yescharacteristic
20C22×#63223C2211yescharacteristic
21C23×#3622C2211yescharacteristic
22#11763499—24no—
23#11763499C2218yes—
24C2×#10587565—21no—
25C2×#10587556C2211yescharacteristic
26C2×#10587575—21no—
27C2×#10587621—21no—
28C2×#10587610C2211yescharacteristic
29C2×#10587610C2211yescharacteristic
30C2×C4×Dic34C2211yescharacteristic
31C2×#10587612C2211yescharacteristic
32C2×#10587563—21no—
33C22×C4⋊Dic17C2211yescharacteristic
34#11763177C2218yescomplemented
35#11763147C2218yescomplemented
36#11763137C2218yescomplemented
37#11763116C2218yescomplemented
38#11763065C2218yescomplemented
39#11763048C2218yescomplemented
40#11763016C2218yescomplemented
41#11762965C2218yescomplemented
42#11762965C2218yescomplemented
43#11762914C2218yescomplemented
44#11762881C2218yes—
45C2×#10587478C2211yescharacteristic
46C2×#10587479C2211yescharacteristic
47C2×#10587479C2211yescharacteristic
48C2×C4⋊#3622C2211yescharacteristic
49#11762818C2218yescomplemented
50C2×#10587506C2211yescharacteristic
51C2×#10587506C2211yescharacteristic
52C2×#10587506C2211yescharacteristic
53C2×#10587506C2211yescharacteristic
54C2×#10587506C2211yescharacteristic
55C2×#10587506C2211yescharacteristic
56C2×#10587506C2211yescharacteristic
57C2×#10587506C2211yescharacteristic
58C2×#10587506C2211yescharacteristic
59C2×#10587506C2218yescomplemented
60C2×#10587481C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×C22⋊#3622C2211yescharacteristic
63C2×#10587474C2211yescharacteristic
64C23×Q8×C17C2211yescharacteristic
65C23×Q8×C17C2211yescharacteristic
66D4×Q8×C17—24no—
67D4×Q8×C17C2218yes—
68C2×C17×C4⋊Q8—21no—
69C2×C17×C4⋊Q8C2211yescharacteristic
70C2×C17×C22⋊Q8—21no—
71C2×C17×C22⋊Q8—21no—
72C2×C17×C22⋊Q8C2211yescharacteristic
73C2×C17×C22⋊Q8C2211yescharacteristic
74C2×C4×Q8×C17C2211yescharacteristic
75C2×C4×D4×C17—21no—
76C2×C4×D4×C17C2211yescharacteristic
77C22×Q8×C17—21no—
78C22×Q8×C17—21no—
79C22×Q8×C17—22no—
80C22×Q8×C17—22no—
81C22×Q8×C17—24no—
82C22×Q8×C17—24no—
83C22×Q8×C17—42no—
84C22×Q8×C17—42no—
85C22×Q8×C17C2311yescharacteristic
86C22×Q8×C17C2311yescharacteristic
87C22×Q8×C17C2314yes—
88C22×Q8×C17C2314yes—
89C22×Q8×C17C2311yescharacteristic
90C22×D4×C17D411yescharacteristic
91C23×C4×C17—21no—
92C23×C4×C17—21no—
93C23×C4×C17C2311yescharacteristic
94C23×C4×C17C2311yescharacteristic
95C23×Dic17—21no—
96C22×Dic34C2311yescharacteristic
97C17×C4⋊Q8—28no—
98C17×C4⋊Q8—22no—
99C17×C4⋊Q8C2314yes—
100C17×C22⋊Q8—22no—
101C17×C22⋊Q8—22no—
102C17×C22⋊Q8—28no—
103C17×C22⋊Q8—28no—
104C17×C22⋊Q8C2314yes—
105C17×C22⋊Q8C2314yes—
106C4×Q8×C17—22no—
107C4×Q8×C17C2314yes—
108C4×D4×C17—28no—
109C4×D4×C17D414yes—
110C4×D4×C17C2314yes—
111C2×C4⋊C4×C17—21no—
112C2×C4⋊C4×C17—21no—
113C2×C4⋊C4×C17—21no—
114C2×C4⋊C4×C17—21no—
115C2×C4⋊C4×C17—21no—
116C2×C4⋊C4×C17D411yescharacteristic
117C2×C4⋊C4×C17C2311yescharacteristic
118C2×C22⋊C4×C17—21no—
119C2×C22⋊C4×C17—21no—
120C2×C22⋊C4×C17D411yescharacteristic
121C2×C22⋊C4×C17D411yescharacteristic
122C2×C42×C17—21no—
123C2×C42×C17C2311yescharacteristic
124C2×C22⋊Dic17—21no—
125C2×C22⋊Dic17—21no—
126C2×C22⋊Dic17—21no—
127C2×#63231—24no—
128C2×#63231—42no—
129C2×#63231—42no—
130C2×#63231C2314yes—
131C2×#63231C2314yes—
132C2×#63231C2314yes—
133#10587621—28no—
134#10587612—22no—
135#10587612C2314yes—
136C2×C4⋊Dic17—22no—
137C2×C4⋊Dic17—21no—
138C2×C4⋊Dic17C2314yes—
139C2×C4⋊Dic17C2311yescharacteristic
140C2×C4⋊Dic17C2311yescharacteristic
141C2×C4⋊Dic17C2311yescharacteristic
142#10587610—22no—
143#10587610—22no—
144#10587610C2314yes—
145#10587610C2314yes—
146C2×#63225—21no—
147C2×#63225—21no—
148C2×#63225—21no—
149C2×#63225—21no—
150C2×#63225—21no—
151C2×C4×Dic17—21no—
152C2×C4×Dic17—21no—
153C2×#63223—42no—
154C2×#63223C2314yes—
155C22×#3622—42no—
156C22×#3622C2311yescharacteristic
157C22×#3622C2311yescharacteristic
158C22×#3622C2311yescharacteristic
159C22×#3622C2311yescharacteristic
160C22×#3622C2314yes—
161#10587575—28no—
162#10587565—28no—
163#10587563—28no—
164#10587556—22no—
165#10587556C2314yes—
166C4×Dic34—22no—
167C4×Dic34C2314yes—
168#10587506C2314yes—
169#10587506C2314yes—
170#10587506C2314yes—
171#10587506C2314yes—
172#10587506C2314yes—
173#10587506C2314yes—
174#10587506C2314yes—
175#10587506C2314yes—
176#10587506C2314yes—
177C22⋊#3622C2314yes—
178C22⋊#3622C2314yes—
179#10587481C2314yes—
180#10587479C2314yes—
181#10587479C2314yes—
182#10587478C2314yes—
183C4⋊#3622C2314yes—
184#10587474C2314yes—
185C24×C17C2×D411yescharacteristic
186C24×C17C2×D411yescharacteristic
187C2×Q8×C17—21no—
188C2×Q8×C17—24no—
189C2×Q8×C17—24no—
190C2×Q8×C17—21no—
191C2×Q8×C17—21no—
192C2×Q8×C17—22no—
193C2×Q8×C17—28no—
194C2×Q8×C17—28no—
195C2×Q8×C17—22no—
196C2×Q8×C17—22no—
197C2×Q8×C17—22no—
198C2×Q8×C17—22no—
199C2×Q8×C17—44no—
200C2×Q8×C17—44no—
201C2×Q8×C17—44no—
202C2×Q8×C17—44no—
203C2×Q8×C17—48no—
204C2×Q8×C17—48no—
205C2×Q8×C17#4114yes—
206C2×Q8×C17C2412yes—
207C2×Q8×C17C2412yes—
208C2×Q8×C17C2412yes—
209C2×D4×C17—24no—
210C2×D4×C17C2×D414yes—
211C22×C4×C17—21no—
212C22×C4×C17—22no—
213C22×C4×C17—22no—
214C22×C4×C17—22no—
215C22×C4×C17—22no—
216C22×C4×C17—24no—
217C22×C4×C17—24no—
218C22×C4×C17—21no—
219C22×C4×C17—21no—
220C22×C4×C17—21no—
221C22×C4×C17—44no—
222C22×C4×C17—44no—
223C22×C4×C17C2×D412yes—
224C22×C4×C17C2×D412yes—
225C22×C4×C17C2×D411yescharacteristic
226C22×C4×C17C2×D411yescharacteristic
227C22×C4×C17C2×D411yescharacteristic
228C22×C4×C17C2×D411yescharacteristic
229C22×C4×C17C2412yes—
230C22×C4×C17C2412yes—
231C22×C4×C17C2411yescharacteristic
232C22×Dic17—21no—
233C22×Dic17—24no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—44no—
238C2×Dic34—22no—
239C2×Dic34—22no—
240C2×Dic34—21no—
241C2×Dic34C2412yes—
242C4⋊C4×C17—24no—
243C4⋊C4×C17—24no—
244C4⋊C4×C17—21no—
245C4⋊C4×C17—24no—
246C4⋊C4×C17—24no—
247C4⋊C4×C17—24no—
248C4⋊C4×C17C2×D414yes—
249C4⋊C4×C17C2412yes—
250C22⋊C4×C17—24no—
251C22⋊C4×C17—24no—
252C22⋊C4×C17C2×D414yes—
253C22⋊C4×C17C2×D414yes—
254C42×C17—24no—
255C42×C17C2×D412yes—
256C42×C17C2412yes—
257C22⋊Dic17—24no—
258C22⋊Dic17—24no—
259C22⋊Dic17—24no—
260#63231—28no—
261#63231—44no—
262#63231—44no—
263C4⋊Dic17—21no—
264C4⋊Dic17—21no—
265C4⋊Dic17—21no—
266C4⋊Dic17—24no—
267C4⋊Dic17C2412yes—
268C4⋊Dic17C2412yes—
269C4⋊Dic17C2412yes—
270#63225—24no—
271#63225—24no—
272#63225—24no—
273#63225—24no—
274#63225—24no—
275C4×Dic17—24no—
276C4×Dic17—24no—
277#63223—44no—
278C2×#3622—22no—
279C2×#3622—22no—
280C2×#3622—22no—
281C2×#3622—22no—
282C2×#3622—44no—
283C2×#3622C2412yes—
284C2×#3622C2412yes—
285C2×#3622C2412yes—
286C2×#3622C2412yes—
287C2×#3312—171nomaximal, Sylow
288C23×C17—22no—
289C23×C17—22no—
290C23×C17—22no—
291C23×C17—22no—
292C23×C17—22no—
293C23×C17#13714yes—
294C23×C17C22×D412yes—
295C23×C17C22×D412yes—
296C23×C17C22×D411yescharacteristic
297Q8×C17—24no—
298Q8×C17—22no—
299Q8×C17—22no—
300Q8×C17—22no—
301Q8×C17—22no—
302Q8×C17—22no—
303Q8×C17—48no—
304Q8×C17—48no—
305Q8×C17—42no—
306Q8×C17—42no—
307Q8×C17C2×#4114yes—
308D4×C17—28no—
309C2×C4×C17—22no—
310C2×C4×C17—22no—
311C2×C4×C17—24no—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—22no—
315C2×C4×C17—24no—
316C2×C4×C17—24no—
317C2×C4×C17—22no—
318C2×C4×C17—22no—
319C2×C4×C17—22no—
320C2×C4×C17—22no—
321C2×C4×C17—22no—
322C2×C4×C17—22no—
323C2×C4×C17—22no—
324C2×C4×C17—48no—
325C2×C4×C17—48no—
326C2×C4×C17—42no—
327C2×C4×C17—42no—
328C2×C4×C17—42no—
329C2×C4×C17C22×D412yes—
330C2×C4×C17C22×D412yes—
331C2×C4×C17C22×D412yes—
332C2×C4×C17C22×D412yes—
333C2×C4×C17C22×D411yescharacteristic
334C2×C4×C17C2×#4112yes—
335C2×C4×C17H(5,𝔽2)12yes—
336C2×C4×C17C2511yescharacteristic
337C2×Dic17—22no—
338C2×Dic17—22no—
339C2×Dic17—22no—
340C2×Dic17—22no—
341C2×Dic17—42no—
342C2×Dic17—48no—
343C2×Dic17—42no—
344C2×Dic17—42no—
345C2×Dic17—42no—
346Dic34—22no—
347Dic34—22no—
348Dic34—42no—
349#3622—22no—
350#3622—22no—
351#3622—22no—
352#3622—22no—
353C2×#552—171no—
354C2×D4×Q8D1711yescharacteristic
355#3312—1716no—
356C2×#491—171no—
357C2×#485—171no—
358C2×#483—171no—
359C2×#479—171no—
360C2×#470—171no—
361C2×#467—171no—
362C2×#462—171no—
363C2×#451—171no—
364C2×#451—171no—
365C2×#441—171no—
366C2×#435—171no—
367C2×#419—171no—
368C22×#103—171no—
369C22×C17—22no—
370C22×C17—28no—
371C22×C17—22no—
372C22×C17—22no—
373C22×C17—22no—
374C22×C17—22no—
375C22×C17—44no—
376C22×C17#54612yes—
377C22×C17C2×#13714yes—
378C22×C17C2×#13712yes—
379C22×C17#57812yes—
380C22×C17C23×D411yescharacteristic
381C4×C17—22no—
382C4×C17—22no—
383C4×C17—24no—
384C4×C17—22no—
385C4×C17—22no—
386C4×C17—42no—
387C4×C17—42no—
388C4×C17—42no—
389C4×C17#54612yes—
390C4×C17C22×#4111yescharacteristic
391C4×C17C2×H(5,𝔽2)11yescharacteristic
392Dic17—42no—
393Dic17—42no—
394Dic17—42no—
395Dic17—42no—
396C23×Q8C2×D1711yescharacteristic
397C23×Q8C2×D1711yescharacteristic
398C22×Q16—171no—
399C22×Q16—171no—
400C22×Q16—171no—
401C22×M16—171no—
402C23×C8—171no—
403#552—178no—
404#552—344no—
405D4×Q8—24no—
406D4×Q8C2×D1718yes—
407C2×C4⋊Q8—21no—
408C2×C4⋊Q8C2×D1711yescharacteristic
409C2×#126—341no—
410C2×#125—171no—
411C2×#125—341no—
412C2×#123—341no—
413C2×C22⋊Q8—21no—
414C2×C22⋊Q8—21no—
415C2×C22⋊Q8—171no—
416C2×C22⋊Q8—171no—
417C2×C22⋊Q8C2×D1711yescharacteristic
418C2×C22⋊Q8C2×D1711yescharacteristic
419C2×C4×Q8—171no—
420C2×C4×Q8C2×D1711yescharacteristic
421C2×C4×D4—21no—
422C2×C4×D4C2×D1711yescharacteristic
423C2×#117—171no—
424C2×#117—341no—
425C22×C4⋊C4—171no—
426#491—178no—
427#485—178no—
428#483—178no—
429#479—178no—
430#470—178no—
431#467—178no—
432#462—178no—
433#451—178no—
434#451—178no—
435#441—178no—
436#435—178no—
437C2×#107—171no—
438C2×#106—171no—
439C2×#106—171no—
440C2×C4⋊C8—171no—
441#419—178no—
442C2×#103—171no—
443C2×#103—171no—
444C2×#103—171no—
445C2×#103—171no—
446C2×#103—171no—
447C2×#103—171no—
448C2×#103—171no—
449C2×#103—171no—
450C2×#103—171no—
451C2×#103—178no—
452C2×#103—171no—
453C2×C22⋊C8—171no—
454C2×C22⋊C8—171no—
455C2×#97—171no—
456C2×C17—24no—
457C2×C17—42no—
458C2×C17#331214yescomplemented
459C2×C17C2×#54611yescharacteristic
460C2×C17C22×#13711yescharacteristic
461C2×C17C2×#57811yescharacteristic
462C22×Q8—21no—
463C22×Q8—21no—
464C22×Q8—22no—
465C22×Q8—22no—
466C22×Q8—24no—
467C22×Q8—24no—
468C22×Q8—42no—
469C22×Q8—42no—
470C22×Q8—171no—
471C22×Q8C22×D1711yescharacteristic
472C22×Q8C22×D1711yescharacteristic
473C22×Q8C22×D1714yes—
474C22×Q8C22×D1714yes—
475C22×Q8C22×D1711yescharacteristic
476C22×D4C22⋊D1711yescharacteristic
477C23×C4—21no—
478C23×C4—21no—
479C23×C4—341no—
480C23×C4C22×D1711yescharacteristic
481C23×C4C22×D1711yescharacteristic
482C2×Q16—174no—
483C2×Q16—174no—
484C2×Q16—174no—
485C2×Q16—344no—
486C2×Q16—682no—
487C2×Q16—682no—
488C2×M16—174no—
489C2×M16—682no—
490C22×C8—171no—
491C22×C8—171no—
492C22×C8—171no—
493C22×C8—171no—
494C22×C8—174no—
495C22×C8—682no—
496C4⋊Q8—28no—
497C4⋊Q8—22no—
498C4⋊Q8C22×D1714yes—
499#126—348no—
500#125—174no—
501#125—348no—
502#125—342no—
503#123—348no—
504C22⋊Q8—22no—
505C22⋊Q8—22no—
506C22⋊Q8—28no—
507C22⋊Q8—28no—
508C22⋊Q8—174no—
509C22⋊Q8—174no—
510C22⋊Q8—342no—
511C22⋊Q8—342no—
512C22⋊Q8C22×D1714yes—
513C22⋊Q8C22×D1714yes—
514C4×Q8—22no—
515C4×Q8—174no—
516C4×Q8—342no—
517C4×Q8C22×D1714yes—
518C4×D4—28no—
519C4×D4C22⋊D1714yes—
520C4×D4C22×D1714yes—
521#117—174no—
522#117—342no—
523#117—348no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—171no—
530C2×C4⋊C4—171no—
531C2×C4⋊C4—174no—
532C2×C4⋊C4—171no—
533C2×C4⋊C4—341no—
534C2×C4⋊C4—342no—
535C2×C4⋊C4—341no—
536C2×C4⋊C4—341no—
537C2×C4⋊C4—341no—
538C2×C4⋊C4—341no—
539C2×C4⋊C4—341no—
540C2×C4⋊C4C22⋊D1711yescharacteristic
541C2×C4⋊C4C22×D1711yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—341no—
545C2×C22⋊C4—341no—
546C2×C22⋊C4—341no—
547C2×C22⋊C4C22⋊D1711yescharacteristic
548C2×C22⋊C4C22⋊D1711yescharacteristic
549C2×C42—21no—
550C2×C42—341no—
551C2×C42—341no—
552C2×C42C22×D1711yescharacteristic
553#107—174no—
554#106—174no—
555#106—174no—
556C4⋊C8—174no—
557#103—174no—
558#103—174no—
559#103—174no—
560#103—174no—
561#103—174no—
562#103—174no—
563#103—174no—
564#103—174no—
565#103—174no—
566#103—174no—
567C22⋊C8—174no—
568C22⋊C8—174no—
569#97—174no—
570C17C2×#331211yescharacteristic, complemented, Sylow
571C24C2×C22⋊D1711yescharacteristic
572C24C2×C22⋊D1711yescharacteristic
573C2×Q8—22no—
574C2×Q8—21no—
575C2×Q8—24no—
576C2×Q8—24no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—28no—
580C2×Q8—28no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—44no—
586C2×Q8—44no—
587C2×Q8—44no—
588C2×Q8—44no—
589C2×Q8—48no—
590C2×Q8—48no—
591C2×Q8—172no—
592C2×Q8—341no—
593C2×Q8—342no—
594C2×Q8—342no—
595C2×Q8#6325414yes—
596C2×Q8C23×D1712yes—
597C2×Q8C23×D1712yes—
598C2×Q8C23×D1712yes—
599C2×D4—24no—
600C2×D4C2×C22⋊D1714yes—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—344no—
614C22×C4—341no—
615C22×C4—341no—
616C22×C4—341no—
617C22×C4—341no—
618C22×C4—684no—
619C22×C4C2×C22⋊D1712yes—
620C22×C4C2×C22⋊D1712yes—
621C22×C4C2×C22⋊D1711yescharacteristic
622C22×C4C2×C22⋊D1711yescharacteristic
623C22×C4C2×C22⋊D1711yescharacteristic
624C22×C4C2×C22⋊D1711yescharacteristic
625C22×C4C23×D1712yes—
626C22×C4C23×D1712yes—
627C22×C4C23×D1711yescharacteristic
628Q16—348no—
629Q16—684no—
630Q16—684no—
631M16—684no—
632C2×C8—172no—
633C2×C8—172no—
634C2×C8—172no—
635C2×C8—172no—
636C2×C8—342no—
637C2×C8—342no—
638C2×C8—342no—
639C2×C8—342no—
640C2×C8—684no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—172no—
648C4⋊C4—172no—
649C4⋊C4—172no—
650C4⋊C4—341no—
651C4⋊C4—341no—
652C4⋊C4—344no—
653C4⋊C4—341no—
654C4⋊C4—344no—
655C4⋊C4—344no—
656C4⋊C4—344no—
657C4⋊C4—344no—
658C4⋊C4—344no—
659C4⋊C4C2×C22⋊D1714yes—
660C4⋊C4C23×D1712yes—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—344no—
664C22⋊C4—344no—
665C22⋊C4—344no—
666C22⋊C4C2×C22⋊D1714yes—
667C22⋊C4C2×C22⋊D1714yes—
668C42—24no—
669C42—344no—
670C42—344no—
671C42C2×C22⋊D1712yes—
672C42C23×D1712yes—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23#1058762814yes—
679C23C22×C22⋊D1712yes—
680C23C22×C22⋊D1712yes—
681C23C22×C22⋊D1711yescharacteristic
682Q8—22no—
683Q8—24no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—22no—
688Q8—48no—
689Q8—48no—
690Q8—42no—
691Q8—42no—
692Q8—342no—
693Q8—342no—
694Q8—682no—
695Q8C2×#6325414yes—
696D4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—48no—
713C2×C4—48no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—342no—
718C2×C4—342no—
719C2×C4—342no—
720C2×C4—342no—
721C2×C4—688no—
722C2×C4—682no—
723C2×C4—682no—
724C2×C4—682no—
725C2×C4—682no—
726C2×C4C2×#6325412yes—
727C2×C4#1058769112yes—
728C2×C4C22×C22⋊D1712yes—
729C2×C4C22×C22⋊D1712yes—
730C2×C4C22×C22⋊D1712yes—
731C2×C4C22×C22⋊D1712yes—
732C2×C4C22×C22⋊D1711yescharacteristic
733C2×C4C24×D1711yescharacteristic
734C8—342no—
735C8—342no—
736C8—342no—
737C8—342no—
738C22—28no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—44no—
745C22#1176345312yes—
746C22C2×#1058762814yes—
747C22C2×#1058762812yes—
748C22#1176362412yes—
749C22C23×C22⋊D1711yescharacteristic
750C4—22no—
751C4—22no—
752C4—24no—
753C4—22no—
754C4—22no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—682no—
759C4—682no—
760C4—682no—
761C4—682no—
762C4#1176345312yes—
763C4C22×#6325411yescharacteristic
764C4C2×#1058769111yescharacteristic
765C2—24no—
766C2—42no—
767C2#1454083514yesdirect product factor
768C2C2×#1176345311yescharacteristic
769C2C22×#1058762811yescharacteristic
770C2C2×#1176362411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×D4×Q8×C17C2
socleC23×C17C22×D4
prime radicalC22×D4×C17D4
hypercenterC2×D4×Q8D17
hypocenterC17C2×#3312
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
2. #14540835C2direct (N × H)
3. C2×#11763177C2semidirect
4. C2×#11763147C2semidirect
5. C2×#11763137C2semidirect
6. C2×#11763116C2semidirect
7. C2×#11763065C2semidirect
8. C2×#11763048C2semidirect
9. C2×#11763016C2semidirect
10. C2×#11762965C2semidirect
11. C2×#11762965C2semidirect
12. C2×#11762914C2semidirect
14. C2×#11762818C2semidirect
15. C22×#10587506C2semidirect
34. #11763177C22semidirect
35. #11763147C22semidirect
36. #11763137C22semidirect
37. #11763116C22semidirect
38. #11763065C22semidirect
39. #11763048C22semidirect
40. #11763016C22semidirect
41. #11762965C22semidirect
42. #11762965C22semidirect
43. #11762914C22semidirect
49. #11762818C22semidirect
59. C2×#10587506C22semidirect
458. C2×C17#3312semidirect
570. C17C2×#3312semidirect
767. C2#14540835direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634992
#145408352
C2×#117631772
C2×#117631472
C2×#117631372
C2×#117631162
C2×#117630652
C2×#117630482
C2×#117630162
C2×#117629652
C2×#117629142
C2×#117628812
C2×#117628182
C22×#105875062
C2×D4×Q8×C172
C2×#331217