Finite Group Databasebeta

← C2×#14540829 #17910924

Subgroups — C2×#14540829 #17910924

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×D4×Dic34C211yesmaximal, characteristic
2#14540829C2116yesmaximal, direct product factor
3C2×#11763179C211yesmaximal, characteristic, complemented
4C2×#11763150C211yesmaximal, characteristic, complemented
5C2×#11763139C211yesmaximal, characteristic, complemented
6C2×#11763113C211yesmaximal, characteristic, complemented
7C2×#11763065C211yesmaximal, characteristic, complemented
8C2×#11763048C211yesmaximal, characteristic, complemented
9C2×#11763019C211yesmaximal, characteristic, complemented
10C2×#11762964C211yesmaximal, characteristic, complemented
11C2×#11762964C211yesmaximal, characteristic, complemented
12C2×#11762914C211yesmaximal, characteristic, complemented
13C2×#11762881C211yesmaximal, characteristic
14C2×#11762817C211yesmaximal, characteristic, complemented
15C22×#10587481C211yesmaximal, characteristic, complemented
16C2×C17×#552C211yesmaximal, characteristic
17C23×Dic34C2211yescharacteristic
18C23×Dic34C2211yescharacteristic
19C22×#63231C2211yescharacteristic
20C22×#63231C2211yescharacteristic
21C22×#63231C2211yescharacteristic
22C22×#63223C2211yescharacteristic
23C23×#3622C2211yescharacteristic
24D4×Dic34—24no—
25D4×Dic34C2218yes—
26C2×#10587555C2211yescharacteristic
27C2×#10587574—21no—
28C2×#10587610C2211yescharacteristic
29C2×#10587610C2211yescharacteristic
30C2×#10587564—21no—
31C2×#10587564—21no—
32C2×C4×Dic34C2211yescharacteristic
33C2×D4×Dic17—21no—
34#11763179C2218yescomplemented
35#11763150C2218yescomplemented
36#11763139C2218yescomplemented
37#11763113C2218yescomplemented
38#11763065C2218yescomplemented
39#11763048C2218yescomplemented
40#11763019C2218yescomplemented
41#11762964C2218yescomplemented
42#11762964C2218yescomplemented
43#11762914C2218yescomplemented
44#11762881C2218yes—
45C2×#10587478C2211yescharacteristic
46C2×#10587479C2211yescharacteristic
47C2×#10587479C2211yescharacteristic
48C2×C4⋊#3622C2211yescharacteristic
49#11762817C2218yescomplemented
50C2×#10587506C2211yescharacteristic
51C2×#10587481C2211yescharacteristic
52C2×#10587481C2211yescharacteristic
53C2×#10587481C2211yescharacteristic
54C2×#10587481C2211yescharacteristic
55C2×#10587481C2211yescharacteristic
56C2×#10587481C2211yescharacteristic
57C2×#10587481C2211yescharacteristic
58C2×#10587481C2211yescharacteristic
59C2×#10587481C2211yescharacteristic
60C2×#10587481C2218yescomplemented
61C2×C22⋊#3622C2211yescharacteristic
62C2×C22⋊#3622C2211yescharacteristic
63C2×#10587474C2211yescharacteristic
64C17×#552—24no—
65C17×#552C2218yes—
66C2×C17×#126—21no—
67C2×C17×#125—21no—
68C2×C17×#125C2211yescharacteristic
69C2×C17×#123—21no—
70C2×C17×C22⋊Q8C2211yescharacteristic
71C2×C17×C22⋊Q8C2211yescharacteristic
72C2×C4×Q8×C17C2211yescharacteristic
73C2×C4×D4×C17C2211yescharacteristic
74C2×C17×#117—21no—
75C2×C17×#117C2211yescharacteristic
76C22×C4⋊C4×C17C2211yescharacteristic
77C22×Q8×C17C2311yescharacteristic
78C22×D4×C17D411yescharacteristic
79C23×C4×C17—21no—
80C23×C4×C17C2311yescharacteristic
81C23×C4×C17C2311yescharacteristic
82C23×Dic17—21no—
83C23×Dic17—21no—
84C22×Dic34—24no—
85C22×Dic34—24no—
86C22×Dic34—22no—
87C22×Dic34—22no—
88C22×Dic34—21no—
89C22×Dic34—21no—
90C22×Dic34—42no—
91C22×Dic34—42no—
92C22×Dic34C2311yescharacteristic
93C22×Dic34C2311yescharacteristic
94C22×Dic34C2314yes—
95C22×Dic34C2314yes—
96C22×Dic34C2311yescharacteristic
97C17×#126—28no—
98C17×#125—28no—
99C17×#125—22no—
100C17×#125C2314yes—
101C17×#123—28no—
102C17×C22⋊Q8—22no—
103C17×C22⋊Q8—22no—
104C17×C22⋊Q8C2314yes—
105C17×C22⋊Q8C2314yes—
106C4×Q8×C17—22no—
107C4×Q8×C17C2314yes—
108C4×D4×C17D414yes—
109C4×D4×C17C2314yes—
110C17×#117—22no—
111C17×#117—28no—
112C17×#117C2314yes—
113C2×C4⋊C4×C17—21no—
114C2×C4⋊C4×C17—22no—
115C2×C4⋊C4×C17—21no—
116C2×C4⋊C4×C17—21no—
117C2×C4⋊C4×C17—21no—
118C2×C4⋊C4×C17—21no—
119C2×C4⋊C4×C17—21no—
120C2×C4⋊C4×C17D411yescharacteristic
121C2×C4⋊C4×C17C2311yescharacteristic
122C2×C4⋊C4×C17C2311yescharacteristic
123C2×C4⋊C4×C17C2314yes—
124C2×C4⋊C4×C17C2311yescharacteristic
125C2×C22⋊C4×C17—21no—
126C2×C22⋊C4×C17—21no—
127C2×C22⋊C4×C17—21no—
128C2×C22⋊C4×C17D411yescharacteristic
129C2×C22⋊C4×C17D411yescharacteristic
130C2×C42×C17—21no—
131C2×C42×C17—21no—
132C2×C42×C17C2311yescharacteristic
133C2×C22⋊Dic17—21no—
134C2×C22⋊Dic17—21no—
135C2×#63231—24no—
136C2×#63231—42no—
137C2×#63231—42no—
138C2×#63231C2314yes—
139C2×#63231C2314yes—
140C2×#63231C2314yes—
141D4×Dic17—28no—
142C2×C4⋊Dic17—21no—
143C2×C4⋊Dic17—21no—
144C2×C4⋊Dic17C2311yescharacteristic
145#10587610—22no—
146#10587610—22no—
147#10587610C2314yes—
148#10587610C2314yes—
149C2×#63225—21no—
150C2×#63225—21no—
151C2×#63225—21no—
152C2×C4×Dic17—21no—
153C2×#63223—42no—
154C2×#63223C2314yes—
155C22×#3622—42no—
156C22×#3622C2311yescharacteristic
157C22×#3622C2311yescharacteristic
158C22×#3622C2311yescharacteristic
159C22×#3622C2311yescharacteristic
160C22×#3622C2314yes—
161#10587574—28no—
162#10587564—28no—
163#10587564—28no—
164#10587555—22no—
165#10587555C2314yes—
166C4×Dic34—22no—
167C4×Dic34C2314yes—
168#10587506C2314yes—
169C22⋊#3622C2314yes—
170C22⋊#3622C2314yes—
171#10587481C2314yes—
172#10587481C2314yes—
173#10587481C2314yes—
174#10587481C2314yes—
175#10587481C2314yes—
176#10587481C2314yes—
177#10587481C2314yes—
178#10587481C2314yes—
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—22no—
189C2×Q8×C17—22no—
190C2×Q8×C17C2412yes—
191C2×D4×C17—24no—
192C2×D4×C17C2×D414yes—
193C22×C4×C17—22no—
194C22×C4×C17—22no—
195C22×C4×C17—22no—
196C22×C4×C17—22no—
197C22×C4×C17—24no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—44no—
203C22×C4×C17C2×D412yes—
204C22×C4×C17C2×D412yes—
205C22×C4×C17C2×D411yescharacteristic
206C22×C4×C17C2×D411yescharacteristic
207C22×C4×C17C2×D411yescharacteristic
208C22×C4×C17C2×D411yescharacteristic
209C22×C4×C17C2412yes—
210C22×C4×C17C2412yes—
211C22×C4×C17C2411yescharacteristic
212C22×Dic17—21no—
213C22×Dic17—24no—
214C22×Dic17—24no—
215C22×Dic17—21no—
216C22×Dic17—21no—
217C22×Dic17—21no—
218C22×Dic17—44no—
219C22×Dic17—44no—
220C2×Dic34—21no—
221C2×Dic34—22no—
222C2×Dic34—22no—
223C2×Dic34—22no—
224C2×Dic34—22no—
225C2×Dic34—22no—
226C2×Dic34—28no—
227C2×Dic34—28no—
228C2×Dic34—21no—
229C2×Dic34—21no—
230C2×Dic34—24no—
231C2×Dic34—24no—
232C2×Dic34—44no—
233C2×Dic34—44no—
234C2×Dic34—48no—
235C2×Dic34—48no—
236C2×Dic34—44no—
237C2×Dic34—44no—
238C2×Dic34#4114yes—
239C2×Dic34C2412yes—
240C2×Dic34C2412yes—
241C2×Dic34C2412yes—
242C4⋊C4×C17—21no—
243C4⋊C4×C17—21no—
244C4⋊C4×C17—24no—
245C4⋊C4×C17—24no—
246C4⋊C4×C17—24no—
247C4⋊C4×C17—24no—
248C4⋊C4×C17—24no—
249C4⋊C4×C17—24no—
250C4⋊C4×C17—21no—
251C4⋊C4×C17C2×D414yes—
252C4⋊C4×C17C2412yes—
253C4⋊C4×C17C2412yes—
254C4⋊C4×C17C2412yes—
255C22⋊C4×C17—24no—
256C22⋊C4×C17—24no—
257C22⋊C4×C17—24no—
258C22⋊C4×C17C2×D414yes—
259C22⋊C4×C17C2×D414yes—
260C42×C17—24no—
261C42×C17—24no—
262C42×C17C2×D412yes—
263C42×C17C2412yes—
264C22⋊Dic17—24no—
265C22⋊Dic17—24no—
266#63231—28no—
267#63231—44no—
268#63231—44no—
269C4⋊Dic17—21no—
270C4⋊Dic17—24no—
271C4⋊Dic17—24no—
272C4⋊Dic17C2412yes—
273#63225—24no—
274#63225—24no—
275#63225—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—22no—
298Q8×C17—22no—
299Q8×C17—42no—
300D4×C17—28no—
301C2×C4×C17—22no—
302C2×C4×C17—22no—
303C2×C4×C17—22no—
304C2×C4×C17—22no—
305C2×C4×C17—24no—
306C2×C4×C17—24no—
307C2×C4×C17—22no—
308C2×C4×C17—22no—
309C2×C4×C17—22no—
310C2×C4×C17—22no—
311C2×C4×C17—22no—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—22no—
315C2×C4×C17—42no—
316C2×C4×C17—48no—
317C2×C4×C17—42no—
318C2×C4×C17—42no—
319C2×C4×C17—42no—
320C2×C4×C17C22×D412yes—
321C2×C4×C17C22×D412yes—
322C2×C4×C17C22×D412yes—
323C2×C4×C17C22×D412yes—
324C2×C4×C17C22×D411yescharacteristic
325C2×C4×C17C2×#4112yes—
326C2×C4×C17H(5,𝔽2)12yes—
327C2×C4×C17C2511yescharacteristic
328C2×Dic17—24no—
329C2×Dic17—22no—
330C2×Dic17—22no—
331C2×Dic17—22no—
332C2×Dic17—22no—
333C2×Dic17—48no—
334C2×Dic17—48no—
335C2×Dic17—42no—
336C2×Dic17—42no—
337C2×Dic17—42no—
338Dic34—24no—
339Dic34—22no—
340Dic34—22no—
341Dic34—22no—
342Dic34—22no—
343Dic34—22no—
344Dic34—48no—
345Dic34—48no—
346Dic34—42no—
347Dic34—42no—
348Dic34C2×#4114yes—
349#3622—22no—
350#3622—22no—
351#3622—22no—
352#3622—22no—
353C2×#552D1711yescharacteristic
354C2×D4×Q8—171no—
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—22no—
384C4×C17—22no—
385C4×C17—42no—
386C4×C17—42no—
387C4×C17—42no—
388C4×C17—42no—
389C4×C17#54612yes—
390C4×C17C22×#4111yescharacteristic
391C4×C17C2×H(5,𝔽2)11yescharacteristic
392Dic17—24no—
393Dic17—42no—
394Dic17—42no—
395Dic17—42no—
396C23×Q8—171no—
397C23×Q8—171no—
398C22×Q16—171no—
399C22×Q16—171no—
400C22×Q16—171no—
401C22×M16—171no—
402C23×C8—171no—
403#552—24no—
404#552C2×D1718yes—
405D4×Q8—178no—
406D4×Q8—344no—
407C2×C4⋊Q8—171no—
408C2×C4⋊Q8—341no—
409C2×#126—21no—
410C2×#125—21no—
411C2×#125C2×D1711yescharacteristic
412C2×#123—21no—
413C2×C22⋊Q8—171no—
414C2×C22⋊Q8—171no—
415C2×C22⋊Q8—341no—
416C2×C22⋊Q8—341no—
417C2×C22⋊Q8C2×D1711yescharacteristic
418C2×C22⋊Q8C2×D1711yescharacteristic
419C2×C4×Q8—171no—
420C2×C4×Q8C2×D1711yescharacteristic
421C2×C4×D4—341no—
422C2×C4×D4C2×D1711yescharacteristic
423C2×#117—21no—
424C2×#117C2×D1711yescharacteristic
425C22×C4⋊C4C2×D1711yescharacteristic
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—171no—
452C2×#103—178no—
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—171no—
463C22×Q8—171no—
464C22×Q8—171no—
465C22×Q8—174no—
466C22×Q8—174no—
467C22×Q8—344no—
468C22×Q8—344no—
469C22×Q8—341no—
470C22×Q8—341no—
471C22×Q8—342no—
472C22×Q8—342no—
473C22×Q8—682no—
474C22×Q8—682no—
475C22×Q8C22×D1711yescharacteristic
476C22×D4C22⋊D1711yescharacteristic
477C23×C4—21no—
478C23×C4—341no—
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—174no—
497C4⋊Q8—348no—
498C4⋊Q8—342no—
499#126—28no—
500#125—28no—
501#125—22no—
502#125C22×D1714yes—
503#123—28no—
504C22⋊Q8—22no—
505C22⋊Q8—22no—
506C22⋊Q8—174no—
507C22⋊Q8—174no—
508C22⋊Q8—342no—
509C22⋊Q8—342no—
510C22⋊Q8—348no—
511C22⋊Q8—348no—
512C22⋊Q8C22×D1714yes—
513C22⋊Q8C22×D1714yes—
514C4×Q8—22no—
515C4×Q8—174no—
516C4×Q8—342no—
517C4×Q8C22×D1714yes—
518C4×D4—348no—
519C4×D4C22⋊D1714yes—
520C4×D4C22×D1714yes—
521#117—22no—
522#117—28no—
523#117C22×D1714yes—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—171no—
532C2×C4⋊C4—341no—
533C2×C4⋊C4—341no—
534C2×C4⋊C4—341no—
535C2×C4⋊C4—341no—
536C2×C4⋊C4—341no—
537C2×C4⋊C4C22⋊D1711yescharacteristic
538C2×C4⋊C4C22×D1711yescharacteristic
539C2×C4⋊C4C22×D1711yescharacteristic
540C2×C4⋊C4C22×D1714yes—
541C2×C4⋊C4C22×D1711yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—341no—
546C2×C22⋊C4—341no—
547C2×C22⋊C4C22⋊D1711yescharacteristic
548C2×C22⋊C4C22⋊D1711yescharacteristic
549C2×C42—21no—
550C2×C42—21no—
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—21no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—174no—
577C2×Q8—172no—
578C2×Q8—172no—
579C2×Q8—172no—
580C2×Q8—348no—
581C2×Q8—348no—
582C2×Q8—342no—
583C2×Q8—341no—
584C2×Q8—344no—
585C2×Q8—344no—
586C2×Q8—341no—
587C2×Q8—341no—
588C2×Q8—342no—
589C2×Q8—342no—
590C2×Q8—342no—
591C2×Q8—342no—
592C2×Q8—684no—
593C2×Q8—684no—
594C2×Q8—684no—
595C2×Q8—684no—
596C2×Q8—688no—
597C2×Q8—688no—
598C2×Q8C23×D1712yes—
599C2×D4—24no—
600C2×D4C2×C22⋊D1714yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—44no—
611C22×C4—341no—
612C22×C4—344no—
613C22×C4—344no—
614C22×C4—341no—
615C22×C4—341no—
616C22×C4—341no—
617C22×C4—684no—
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—21no—
642C4⋊C4—21no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—24no—
649C4⋊C4—21no—
650C4⋊C4—172no—
651C4⋊C4—341no—
652C4⋊C4—344no—
653C4⋊C4—344no—
654C4⋊C4—344no—
655C4⋊C4—344no—
656C4⋊C4—344no—
657C4⋊C4C2×C22⋊D1714yes—
658C4⋊C4C23×D1712yes—
659C4⋊C4C23×D1712yes—
660C4⋊C4C23×D1712yes—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—24no—
664C22⋊C4—344no—
665C22⋊C4—344no—
666C22⋊C4C2×C22⋊D1714yes—
667C22⋊C4C2×C22⋊D1714yes—
668C42—24no—
669C42—24no—
670C42—344no—
671C42C2×C22⋊D1712yes—
672C42C23×D1712yes—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23#1058763714yes—
679C23C22×C22⋊D1712yes—
680C23C22×C22⋊D1712yes—
681C23C22×C22⋊D1711yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—42no—
685Q8—174no—
686Q8—342no—
687Q8—344no—
688Q8—342no—
689Q8—342no—
690Q8—342no—
691Q8—342no—
692Q8—688no—
693Q8—688no—
694Q8—682no—
695Q8—682no—
696D4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—48no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—342no—
717C2×C4—344no—
718C2×C4—342no—
719C2×C4—342no—
720C2×C4—342no—
721C2×C4—688no—
722C2×C4—688no—
723C2×C4—682no—
724C2×C4—682no—
725C2×C4—682no—
726C2×C4#41×D1712yes—
727C2×C4#1058769612yes—
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#1176344712yes—
746C22C2×#1058763714yes—
747C22C2×#1058763712yes—
748C22#1176362412yes—
749C22C23×C22⋊D1711yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—344no—
759C4—682no—
760C4—682no—
761C4—682no—
762C4#1176344712yes—
763C4C2×#41×D1711yescharacteristic
764C4C2×#1058769611yescharacteristic
765C2—24no—
766C2—42no—
767C2#1454082914yesdirect product factor
768C2C2×#1176344711yescharacteristic
769C2C22×#1058763711yescharacteristic
770C2C2×#1176362411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#552C2
socleC23×C17C22×D4
prime radicalC22×D4×C17D4
hypercenterC2×#552D17
hypocenterC17C2×#3312
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #14540829C2direct (N × H)
3. C2×#11763179C2semidirect
4. C2×#11763150C2semidirect
5. C2×#11763139C2semidirect
6. C2×#11763113C2semidirect
7. C2×#11763065C2semidirect
8. C2×#11763048C2semidirect
9. C2×#11763019C2semidirect
10. C2×#11762964C2semidirect
11. C2×#11762964C2semidirect
12. C2×#11762914C2semidirect
14. C2×#11762817C2semidirect
15. C22×#10587481C2semidirect
34. #11763179C22semidirect
35. #11763150C22semidirect
36. #11763139C22semidirect
37. #11763113C22semidirect
38. #11763065C22semidirect
39. #11763048C22semidirect
40. #11763019C22semidirect
41. #11762964C22semidirect
42. #11762964C22semidirect
43. #11762914C22semidirect
49. #11762817C22semidirect
60. C2×#10587481C22semidirect
458. C2×C17#3312semidirect
570. C17C2×#3312semidirect
767. C2#14540829direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Dic342
#145408292
C2×#117631792
C2×#117631502
C2×#117631392
C2×#117631132
C2×#117630652
C2×#117630482
C2×#117630192
C2×#117629642
C2×#117629142
C2×#117628812
C2×#117628172
C22×#105874812
C2×C17×#5522
C2×#331217