Finite Group Databasebeta

← C2×#14540957 #17910948

Subgroups — C2×#14540957 #17910948

Order 4352.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763505C211yesmaximal, characteristic
2C2×D4×Dic34C211yesmaximal, characteristic, complemented
3#14540957C2116yesmaximal, direct product factor
4C2×#11763178C211yesmaximal, characteristic, complemented
5C2×#11763145C211yesmaximal, characteristic, complemented
6C2×#11763151C211yesmaximal, characteristic, complemented
7C2×#11763117C211yesmaximal, characteristic, complemented
8C2×#11763055C211yesmaximal, characteristic, complemented
9C2×#11763038C211yesmaximal, characteristic, complemented
10C2×#11763015C211yesmaximal, characteristic, complemented
11C2×#11762950C211yesmaximal, characteristic, complemented
12C2×#11762950C211yesmaximal, characteristic, complemented
13C2×#11762911C211yesmaximal, characteristic, complemented
14C2×#11762819C211yesmaximal, characteristic, complemented
15C22×#10587487C211yesmaximal, characteristic, complemented
16C2×C17×#435C211yesmaximal, characteristic, complemented
17C23×Dic34C2211yescharacteristic
18C23×Dic34C2211yescharacteristic
19C22×#63219C2211yescharacteristic
20C22×#63219C2211yescharacteristic
21C22×#63219C2211yescharacteristic
22#11763505—24no—
23#11763505C2218yes—
24D4×Dic34—24no—
25D4×Dic34C2218yescomplemented
26C2×#10587555C2211yescharacteristic
27C2×#10587574—21no—
28C2×#10587584—21no—
29C2×#10587556C2211yescharacteristic
30C2×#10587569—21no—
31C2×#10587610C2211yescharacteristic
32C2×#10587610C2211yescharacteristic
33C2×#10587564—21no—
34C2×#10587564—21no—
35C2×#10587616C2211yescharacteristic
36C2×#10587616C2211yescharacteristic
37C2×#10587625—21no—
38C2×C4×Dic34C2211yescharacteristic
39C2×C4×D68C2211yescharacteristic
40C2×D4×Dic17—21no—
41C2×#10587567—21no—
42C2×#10587612C2211yescharacteristic
43C22×C4⋊Dic17C2211yescharacteristic
44#11763178C2218yescomplemented
45#11763151C2218yescomplemented
46#11763145C2218yescomplemented
47#11763117C2218yescomplemented
48#11763055C2218yescomplemented
49#11763038C2218yescomplemented
50#11763015C2218yescomplemented
51#11762950C2218yescomplemented
52#11762950C2218yescomplemented
53#11762911C2218yescomplemented
54C2×#10587489C2211yescharacteristic
55C2×#10587489C2211yescharacteristic
56C2×#10587488C2211yescharacteristic
57#11762819C2218yescomplemented
58C2×#10587487C2211yescharacteristic
59C2×#10587487C2211yescharacteristic
60C2×#10587487C2211yescharacteristic
61C2×#10587487C2211yescharacteristic
62C2×#10587487C2211yescharacteristic
63C2×#10587487C2211yescharacteristic
64C2×#10587487C2211yescharacteristic
65C2×#10587487C2211yescharacteristic
66C2×#10587487C2211yescharacteristic
67C2×#10587487C2218yescomplemented
68C2×#10587492C2211yescharacteristic
69C22×M16×C17C2211yescharacteristic
70C23×C8×C17C2211yescharacteristic
71C2×C4×D4×C17C2211yescharacteristic
72C17×#435C2218yescomplemented
73C2×C17×C4⋊C8C2211yescharacteristic
74C2×C17×C22⋊C8C2211yescharacteristic
75C2×C17×C22⋊C8C2211yescharacteristic
76C2×C17×#97C2211yescharacteristic
77C22×D4×C17D411yescharacteristic
78C23×C4×C17C2311yescharacteristic
79C23×C4×C17C2311yescharacteristic
80C22×C22⋊D17—21no—
81C22×C22⋊D17—21no—
82C23×Dic17—21no—
83C23×Dic17—21no—
84C23×Dic17—21no—
85C22×D68C2311yescharacteristic
86C22×C4×D17—21no—
87C22×Dic34—24no—
88C22×Dic34—24no—
89C22×Dic34—22no—
90C22×Dic34—22no—
91C22×Dic34—21no—
92C22×Dic34—21no—
93C22×Dic34—42no—
94C22×Dic34—42no—
95C22×Dic34C2311yescharacteristic
96C22×Dic34C2311yescharacteristic
97C22×Dic34C2314yes—
98C22×Dic34C2314yes—
99C22×Dic34C2311yescharacteristic
100C2×M16×C17—42no—
101C2×M16×C17C2314yes—
102C22×C8×C17—42no—
103C22×C8×C17C2311yescharacteristic
104C22×C8×C17C2311yescharacteristic
105C22×C8×C17C2311yescharacteristic
106C22×C8×C17C2311yescharacteristic
107C22×C8×C17C2314yes—
108C4×D4×C17D414yes—
109C4×D4×C17C2314yes—
110C2×C4⋊C4×C17D411yescharacteristic
111C2×C22⋊C4×C17D411yescharacteristic
112C2×C22⋊C4×C17D411yescharacteristic
113C2×C42×C17C2311yescharacteristic
114C2×C22⋊Dic17—21no—
115C2×C22⋊Dic17—21no—
116C2×C22⋊Dic17—21no—
117#10587625—28no—
118D4×Dic17—28no—
119#10587616—22no—
120#10587616—22no—
121#10587616C2314yes—
122#10587616C2314yes—
123C2×#63227—21no—
124C2×#63227—21no—
125C2×#63227—21no—
126#10587612—22no—
127#10587612C2314yes—
128C2×C4⋊Dic17—22no—
129C2×C4⋊Dic17—21no—
130C2×C4⋊Dic17—21no—
131C2×C4⋊Dic17—21no—
132C2×C4⋊Dic17C2314yes—
133C2×C4⋊Dic17C2311yescharacteristic
134C2×C4⋊Dic17C2311yescharacteristic
135C2×C4⋊Dic17C2311yescharacteristic
136C2×C4⋊Dic17C2311yescharacteristic
137#10587610—22no—
138#10587610—22no—
139#10587610C2314yes—
140#10587610C2314yes—
141C2×#63225—21no—
142C2×#63225—21no—
143C2×#63225—21no—
144C2×#63225—21no—
145C2×#63225—21no—
146C2×C4×Dic17—21no—
147C2×C4×Dic17—21no—
148C2×#63219—24no—
149C2×#63219—42no—
150C2×#63219—42no—
151C2×#63219C2314yes—
152C2×#63219C2314yes—
153C2×#63219C2314yes—
154#10587584—28no—
155#10587574—28no—
156#10587569—28no—
157#10587567—28no—
158#10587564—28no—
159#10587564—28no—
160C4×D68—22no—
161C4×D68C2314yes—
162#10587556—22no—
163#10587556C2314yes—
164#10587555—22no—
165#10587555C2314yes—
166C4×Dic34—22no—
167C4×Dic34C2314yes—
168C17×C4⋊C8C2314yes—
169C17×C22⋊C8C2314yes—
170C17×C22⋊C8C2314yes—
171C17×#97C2314yes—
172#10587492C2314yes—
173#10587489C2314yes—
174#10587489C2314yes—
175#10587488C2314yes—
176#10587487C2314yes—
177#10587487C2314yes—
178#10587487C2314yes—
179#10587487C2314yes—
180#10587487C2314yes—
181#10587487C2314yes—
182#10587487C2314yes—
183#10587487C2314yes—
184#10587487C2314yes—
185C24×C17C2×D411yescharacteristic
186C24×C17C2×D411yescharacteristic
187C23×D17—21no—
188C2×D4×C17—24no—
189C2×D4×C17C2×D414yes—
190C22×C4×C17—22no—
191C22×C4×C17—22no—
192C22×C4×C17—22no—
193C22×C4×C17—22no—
194C22×C4×C17C2×D411yescharacteristic
195C22×C4×C17C2×D411yescharacteristic
196C22×C4×C17C2×D412yes—
197C22×C4×C17C2×D412yes—
198C22×C4×C17C2×D411yescharacteristic
199C22×C4×C17C2×D411yescharacteristic
200C22×C4×C17C2412yes—
201C22×C4×C17C2412yes—
202C22×C4×C17C2411yescharacteristic
203C2×C22⋊D17—24no—
204C2×C22⋊D17—24no—
205C2×C22⋊D17—44no—
206C2×C22⋊D17—82no—
207C22×Dic17—21no—
208C22×Dic17—24no—
209C22×Dic17—24no—
210C22×Dic17—21no—
211C22×Dic17—21no—
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C22×Dic17—24no—
217C22×Dic17—44no—
218C22×Dic17—44no—
219C22×Dic17—82no—
220C2×D68—22no—
221C2×D68—22no—
222C2×D68—21no—
223C2×D68C2412yes—
224C2×C4×D17—24no—
225C2×C4×D17—82no—
226C2×Dic34—21no—
227C2×Dic34—22no—
228C2×Dic34—22no—
229C2×Dic34—22no—
230C2×Dic34—22no—
231C2×Dic34—22no—
232C2×Dic34—28no—
233C2×Dic34—28no—
234C2×Dic34—21no—
235C2×Dic34—21no—
236C2×Dic34—24no—
237C2×Dic34—24no—
238C2×Dic34—44no—
239C2×Dic34—44no—
240C2×Dic34—48no—
241C2×Dic34—48no—
242C2×Dic34—44no—
243C2×Dic34—44no—
244C2×Dic34#4114yes—
245C2×Dic34C2412yes—
246C2×Dic34C2412yes—
247C2×Dic34C2412yes—
248M16×C17—44no—
249C2×C8×C17—22no—
250C2×C8×C17—22no—
251C2×C8×C17—22no—
252C2×C8×C17—22no—
253C2×C8×C17—44no—
254C2×C8×C17C2412yes—
255C2×C8×C17C2412yes—
256C2×C8×C17C2412yes—
257C2×C8×C17C2412yes—
258C4⋊C4×C17C2×D414yes—
259C22⋊C4×C17C2×D414yes—
260C22⋊C4×C17C2×D414yes—
261C42×C17C2×D412yes—
262C42×C17C2412yes—
263C22⋊Dic17—24no—
264C22⋊Dic17—24no—
265C22⋊Dic17—24no—
266#63227—24no—
267#63227—24no—
268#63227—24no—
269C4⋊Dic17—21no—
270C4⋊Dic17—24no—
271C4⋊Dic17—24no—
272C4⋊Dic17—21no—
273C4⋊Dic17—21no—
274C4⋊Dic17—21no—
275C4⋊Dic17—24no—
276C4⋊Dic17C2412yes—
277C4⋊Dic17C2412yes—
278C4⋊Dic17C2412yes—
279C4⋊Dic17C2412yes—
280#63225—24no—
281#63225—24no—
282#63225—24no—
283#63225—24no—
284#63225—24no—
285C4×Dic17—24no—
286C4×Dic17—24no—
287#63219—28no—
288#63219—44no—
289#63219—44no—
290C2×#3320—171nomaximal, Sylow
291C23×C17—22no—
292C23×C17—22no—
293C23×C17—22no—
294C23×C17—22no—
295C23×C17—22no—
296C23×C17#13714yes—
297C23×C17C22×D412yes—
298C23×C17C22×D412yes—
299C23×C17C22×D411yescharacteristic
300C22×D17—22no—
301C22×D17—42no—
302C22×D17—42no—
303C22×D17—42no—
304D4×C17—28no—
305C2×C4×C17—22no—
306C2×C4×C17—22no—
307C2×C4×C17—22no—
308C2×C4×C17—22no—
309C2×C4×C17—24no—
310C2×C4×C17—24no—
311C2×C4×C17—22no—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—22no—
315C2×C4×C17C22×D412yes—
316C2×C4×C17C22×D412yes—
317C2×C4×C17C22×D412yes—
318C2×C4×C17C22×D412yes—
319C2×C4×C17C22×D411yescharacteristic
320C2×C4×C17C2×#4112yes—
321C2×C4×C17H(5,𝔽2)12yes—
322C2×C4×C17C2511yescharacteristic
323C22⋊D17—48no—
324C22⋊D17—84no—
325C2×Dic17—24no—
326C2×Dic17—22no—
327C2×Dic17—22no—
328C2×Dic17—22no—
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—
338C2×Dic17—42no—
339C2×Dic17—42no—
340C2×Dic17—42no—
341C2×Dic17—84no—
342D68—22no—
343D68—22no—
344D68—42no—
345C4×D17—84no—
346Dic34—24no—
347Dic34—22no—
348Dic34—22no—
349Dic34—22no—
350Dic34—22no—
351Dic34—22no—
352Dic34—48no—
353Dic34—48no—
354Dic34—42no—
355Dic34—42no—
356Dic34C2×#4114yes—
357C8×C17—22no—
358C8×C17—22no—
359C8×C17—22no—
360C8×C17—22no—
361C2×#553—171no—
362C2×D4×Q8—171no—
363#3320—1716no—
364C2×#491—171no—
365C2×#484—171no—
366C2×#485—171no—
367C2×#479—171no—
368C2×#468—171no—
369C2×#465—171no—
370C2×#461—171no—
371C2×#448—171no—
372C2×#448—171no—
373C2×#440—171no—
374C2×#435D1711yescharacteristic, complemented
375C2×#419—171no—
376C22×#103—171no—
377C22×C17—22no—
378C22×C17—28no—
379C22×C17—22no—
380C22×C17—22no—
381C22×C17—22no—
382C22×C17—22no—
383C22×C17—44no—
384C22×C17#54612yes—
385C22×C17C2×#13714yes—
386C22×C17C2×#13712yes—
387C22×C17#57712yes—
388C22×C17C23×D411yescharacteristic
389C2×D17—42no—
390C2×D17—42no—
391C2×D17—42no—
392C2×D17—84no—
393C4×C17—22no—
394C4×C17—22no—
395C4×C17—22no—
396C4×C17—22no—
397C4×C17#54612yes—
398C4×C17C22×#4111yescharacteristic
399C4×C17C2×H(5,𝔽2)11yescharacteristic
400Dic17—24no—
401Dic17—42no—
402Dic17—42no—
403Dic17—42no—
404Dic17—42no—
405Dic17—42no—
406Dic17—42no—
407C23×Q8—171no—
408C23×Q8—171no—
409C22×SD16—171no—
410C22×SD16—171no—
411C22×SD16—171no—
412C22×M16C2×D1711yescharacteristic
413C23×C8C2×D1711yescharacteristic
414#553—178no—
415#553—344no—
416D4×Q8—178no—
417D4×Q8—344no—
418C2×C4⋊Q8—171no—
419C2×C4⋊Q8—341no—
420C2×#126—341no—
421C2×#125—171no—
422C2×#123—341no—
423C2×C22⋊Q8—171no—
424C2×C22⋊Q8—171no—
425C2×C22⋊Q8—341no—
426C2×C22⋊Q8—341no—
427C2×#121—171no—
428C2×#121—171no—
429C2×#121—341no—
430C2×C4×Q8—171no—
431C2×C4×D4—171no—
432C2×C4×D4—341no—
433C2×C4×D4—341no—
434C2×C4×D4C2×D1711yescharacteristic
435C2×#117—171no—
436C22×C4⋊C4—171no—
437#491—178no—
438#485—178no—
439#484—178no—
440#479—178no—
441#468—178no—
442#465—178no—
443#461—178no—
444#448—178no—
445#448—178no—
446#440—178no—
447#435C2×D1718yescomplemented
448C2×#107—171no—
449C2×#107—171no—
450C2×#106—171no—
451C2×C4⋊C8C2×D1711yescharacteristic
452#419—178no—
453C2×#103—171no—
454C2×#103—171no—
455C2×#103—171no—
456C2×#103—171no—
457C2×#103—171no—
458C2×#103—171no—
459C2×#103—171no—
460C2×#103—171no—
461C2×#103—171no—
462C2×#103—178no—
463C2×#102—171no—
464C2×C22⋊C8C2×D1711yescharacteristic
465C2×C22⋊C8C2×D1711yescharacteristic
466C2×#97C2×D1711yescharacteristic
467C2×C17—24no—
468C2×C17—42no—
469C2×C17#332014yescomplemented
470C2×C17C2×#54611yescharacteristic
471C2×C17C22×#13711yescharacteristic
472C2×C17C2×#57711yescharacteristic
473D17—82no—
474C22×Q8—171no—
475C22×Q8—171no—
476C22×Q8—171no—
477C22×Q8—174no—
478C22×Q8—174no—
479C22×Q8—344no—
480C22×Q8—344no—
481C22×Q8—341no—
482C22×Q8—341no—
483C22×Q8—342no—
484C22×Q8—342no—
485C22×Q8—682no—
486C22×Q8—682no—
487C22×D4—171no—
488C22×D4—341no—
489C22×D4—341no—
490C22×D4D6811yescharacteristic
491C23×C4—341no—
492C23×C4—341no—
493C23×C4—341no—
494C23×C4—341no—
495C23×C4C22×D1711yescharacteristic
496C23×C4C22×D1711yescharacteristic
497C2×SD16—174no—
498C2×SD16—174no—
499C2×SD16—174no—
500C2×SD16—344no—
501C2×SD16—682no—
502C2×SD16—682no—
503C2×M16—42no—
504C2×M16C22×D1714yes—
505C22×C8—42no—
506C22×C8C22×D1711yescharacteristic
507C22×C8C22×D1711yescharacteristic
508C22×C8C22×D1711yescharacteristic
509C22×C8C22×D1711yescharacteristic
510C22×C8C22×D1714yes—
511C4⋊Q8—174no—
512C4⋊Q8—348no—
513C4⋊Q8—342no—
514#126—348no—
515#125—174no—
516#125—342no—
517#123—348no—
518C22⋊Q8—174no—
519C22⋊Q8—174no—
520C22⋊Q8—342no—
521C22⋊Q8—342no—
522C22⋊Q8—348no—
523C22⋊Q8—348no—
524#121—174no—
525#121—174no—
526#121—348no—
527#121—342no—
528#121—342no—
529C4×Q8—174no—
530C4×Q8—342no—
531C4×D4—174no—
532C4×D4—348no—
533C4×D4—348no—
534C4×D4—342no—
535C4×D4D6814yes—
536C4×D4C22×D1714yes—
537#117—174no—
538#117—342no—
539C2×C4⋊C4—171no—
540C2×C4⋊C4—171no—
541C2×C4⋊C4—174no—
542C2×C4⋊C4—171no—
543C2×C4⋊C4—171no—
544C2×C4⋊C4—341no—
545C2×C4⋊C4—342no—
546C2×C4⋊C4—341no—
547C2×C4⋊C4—341no—
548C2×C4⋊C4—341no—
549C2×C4⋊C4—341no—
550C2×C4⋊C4—341no—
551C2×C4⋊C4—341no—
552C2×C4⋊C4—341no—
553C2×C4⋊C4D6811yescharacteristic
554C2×C22⋊C4—341no—
555C2×C22⋊C4—341no—
556C2×C22⋊C4—341no—
557C2×C22⋊C4—341no—
558C2×C22⋊C4—341no—
559C2×C22⋊C4—341no—
560C2×C22⋊C4D6811yescharacteristic
561C2×C22⋊C4D6811yescharacteristic
562C2×C42—341no—
563C2×C42—341no—
564C2×C42C22×D1711yescharacteristic
565#107—174no—
566#107—174no—
567#106—174no—
568C4⋊C8C22×D1714yes—
569#103—174no—
570#103—174no—
571#103—174no—
572#103—174no—
573#103—174no—
574#103—174no—
575#103—174no—
576#103—174no—
577#103—174no—
578#102—174no—
579C22⋊C8C22×D1714yes—
580C22⋊C8C22×D1714yes—
581#97C22×D1714yes—
582C17C2×#332011yescharacteristic, complemented, Sylow
583C24—341no—
584C24C2×D6811yescharacteristic
585C24C2×D6811yescharacteristic
586C2×Q8—174no—
587C2×Q8—172no—
588C2×Q8—172no—
589C2×Q8—172no—
590C2×Q8—348no—
591C2×Q8—348no—
592C2×Q8—341no—
593C2×Q8—344no—
594C2×Q8—344no—
595C2×Q8—341no—
596C2×Q8—341no—
597C2×Q8—342no—
598C2×Q8—342no—
599C2×Q8—342no—
600C2×Q8—342no—
601C2×Q8—342no—
602C2×Q8—684no—
603C2×Q8—684no—
604C2×Q8—684no—
605C2×Q8—684no—
606C2×Q8—688no—
607C2×Q8—688no—
608C2×D4—24no—
609C2×D4—172no—
610C2×D4—344no—
611C2×D4—344no—
612C2×D4—341no—
613C2×D4—342no—
614C2×D4—342no—
615C2×D4—684no—
616C2×D4—1362no—
617C2×D4C2×D6814yes—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—341no—
623C22×C4—344no—
624C22×C4—344no—
625C22×C4—341no—
626C22×C4—341no—
627C22×C4—341no—
628C22×C4—341no—
629C22×C4—341no—
630C22×C4—341no—
631C22×C4—344no—
632C22×C4—344no—
633C22×C4—684no—
634C22×C4—684no—
635C22×C4—1362no—
636C22×C4—1362no—
637C22×C4C2×D6812yes—
638C22×C4C2×D6812yes—
639C22×C4C2×D6811yescharacteristic
640C22×C4C2×D6811yescharacteristic
641C22×C4C2×D6811yescharacteristic
642C22×C4C2×D6811yescharacteristic
643C22×C4C23×D1712yes—
644C22×C4C23×D1712yes—
645C22×C4C23×D1711yescharacteristic
646SD16—348no—
647SD16—684no—
648SD16—684no—
649M16—44no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—44no—
655C2×C8C23×D1712yes—
656C2×C8C23×D1712yes—
657C2×C8C23×D1712yes—
658C2×C8C23×D1712yes—
659C4⋊C4—172no—
660C4⋊C4—172no—
661C4⋊C4—172no—
662C4⋊C4—172no—
663C4⋊C4—341no—
664C4⋊C4—341no—
665C4⋊C4—344no—
666C4⋊C4—341no—
667C4⋊C4—341no—
668C4⋊C4—344no—
669C4⋊C4—344no—
670C4⋊C4—344no—
671C4⋊C4—344no—
672C4⋊C4—344no—
673C4⋊C4—344no—
674C4⋊C4—344no—
675C4⋊C4C2×D6814yes—
676C22⋊C4—344no—
677C22⋊C4—344no—
678C22⋊C4—344no—
679C22⋊C4—344no—
680C22⋊C4—344no—
681C22⋊C4—344no—
682C22⋊C4C2×D6814yes—
683C22⋊C4C2×D6814yes—
684C42—344no—
685C42—344no—
686C42C2×D6812yes—
687C42C23×D1712yes—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—342no—
694C23—682no—
695C23—682no—
696C23—682no—
697C23#1058759514yes—
698C23C22×D6812yes—
699C23C22×D6812yes—
700C23C22×D6811yescharacteristic
701Q8—174no—
702Q8—342no—
703Q8—344no—
704Q8—342no—
705Q8—342no—
706Q8—342no—
707Q8—342no—
708Q8—688no—
709Q8—688no—
710Q8—682no—
711Q8—682no—
712D4—28no—
713D4—342no—
714D4—342no—
715D4—688no—
716D4—682no—
717D4—1364no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—342no—
729C2×C4—344no—
730C2×C4—342no—
731C2×C4—342no—
732C2×C4—342no—
733C2×C4—342no—
734C2×C4—342no—
735C2×C4—342no—
736C2×C4—688no—
737C2×C4—688no—
738C2×C4—682no—
739C2×C4—682no—
740C2×C4—682no—
741C2×C4—682no—
742C2×C4—682no—
743C2×C4—682no—
744C2×C4—1364no—
745C2×C4—1364no—
746C2×C4C22×D6812yes—
747C2×C4C22×D6812yes—
748C2×C4C22×D6812yes—
749C2×C4C22×D6812yes—
750C2×C4C22×D6811yescharacteristic
751C2×C4#1058769112yes—
752C2×C4#41×D1712yes—
753C2×C4C24×D1711yescharacteristic
754C8—22no—
755C8—22no—
756C8—22no—
757C8—22no—
758C22—22no—
759C22—28no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—682no—
766C22—682no—
767C22—682no—
768C22—1364no—
769C22#1176345412yes—
770C22C2×#1058759514yes—
771C22C2×#1058759512yes—
772C22#1176362112yes—
773C22C23×D6811yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—344no—
779C4—682no—
780C4—682no—
781C4—682no—
782C4—682no—
783C4—682no—
784C4—682no—
785C4#1176345412yes—
786C4C2×#41×D1711yescharacteristic
787C4C2×#1058769111yescharacteristic
788C2—24no—
789C2—42no—
790C2—1362no—
791C2#1454095714yesdirect product factor
792C2C2×#1176345411yescharacteristic
793C2C22×#1058759511yescharacteristic
794C2C2×#1176362111yescharacteristic
subgroupG/H
centerC23C22×D68
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#435C2
socleC23×C17C22×D4
prime radicalC2×#11763505C2
hypercenterC2×#435D17
hypocenterC17C2×#3320
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic34C2semidirect
3. #14540957C2direct (N × H)
4. C2×#11763178C2semidirect
5. C2×#11763145C2semidirect
6. C2×#11763151C2semidirect
7. C2×#11763117C2semidirect
8. C2×#11763055C2semidirect
9. C2×#11763038C2semidirect
10. C2×#11763015C2semidirect
11. C2×#11762950C2semidirect
12. C2×#11762950C2semidirect
13. C2×#11762911C2semidirect
14. C2×#11762819C2semidirect
15. C22×#10587487C2semidirect
16. C2×C17×#435C2semidirect
25. D4×Dic34C22semidirect
44. #11763178C22semidirect
45. #11763151C22semidirect
46. #11763145C22semidirect
47. #11763117C22semidirect
48. #11763055C22semidirect
49. #11763038C22semidirect
50. #11763015C22semidirect
51. #11762950C22semidirect
52. #11762950C22semidirect
53. #11762911C22semidirect
57. #11762819C22semidirect
67. C2×#10587487C22semidirect
72. C17×#435C22semidirect
374. C2×#435D17semidirect
447. #435C2×D17semidirect
469. C2×C17#3320semidirect
582. C17C2×#3320semidirect
791. C2#14540957direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635052
C2×D4×Dic342
#145409572
C2×#117631782
C2×#117631452
C2×#117631512
C2×#117631172
C2×#117630552
C2×#117630382
C2×#117630152
C2×#117629502
C2×#117629112
C2×#117628192
C22×#105874872
C2×C17×#4352
C2×#332017