Finite Group Databasebeta

← C2×#14539887 #17905713

Subgroups — C2×#14539887 #17905713

Order 4352.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763385C211yesmaximal, characteristic, complemented
2#14539887C2116yesmaximal, direct product factor
3C2×#11763204C211yesmaximal, characteristic, complemented
4C2×#11763191C211yesmaximal, characteristic, complemented
5C2×#11763171C211yesmaximal, characteristic, complemented
6C2×#11763161C211yesmaximal, characteristic, complemented
7C2×#11763031C211yesmaximal, characteristic, complemented
8C2×#11763019C211yesmaximal, characteristic, complemented
9C2×#11763024C211yesmaximal, characteristic, complemented
10C2×#11763014C211yesmaximal, characteristic, complemented
11C2×#11762969C211yesmaximal, characteristic, complemented
12C2×#11762952C211yesmaximal, characteristic
13C2×#11762964C211yesmaximal, characteristic, complemented
14C2×#11762947C211yesmaximal, characteristic, complemented
15C2×#11762870C211yesmaximal, characteristic, complemented
16C2×C17×#542C211yesmaximal, characteristic, complemented
17C22×#63252C2211yescharacteristic
18C23×Dic34C2211yescharacteristic
19C22×#63231C2211yescharacteristic
20C22×#63231C2211yescharacteristic
21C22×#63231C2211yescharacteristic
22C22×#63229C2211yescharacteristic
23C22×#63229C2211yescharacteristic
24C22×#63229C2211yescharacteristic
25C22×#63230C2211yescharacteristic
26C22×#63228C2211yescharacteristic
27#11763385—24no—
28#11763385C2218yescomplemented
29C2×#10587555C2211yescharacteristic
30C2×#10587555C2211yescharacteristic
31C2×#10587561C2211yescharacteristic
32C2×#10587561C2211yescharacteristic
33C2×#10587572—21no—
34C2×#10587572—21no—
35C2×#10587583—21no—
36C2×#10587583—21no—
37#11763204C2218yescomplemented
38#11763191C2218yescomplemented
39#11763171C2218yescomplemented
40#11763161C2218yescomplemented
41#11763031C2218yescomplemented
42#11763024C2218yescomplemented
43#11763019C2218yescomplemented
44#11763014C2218yescomplemented
45#11762969C2218yescomplemented
46#11762964C2218yescomplemented
47#11762952C2218yes—
48#11762947C2218yescomplemented
49#11762870C2218yescomplemented
50C2×C4⋊#3622C2211yescharacteristic
51C2×C4⋊#3622C2211yescharacteristic
52C2×#10587481C2211yescharacteristic
53C2×#10587481C2211yescharacteristic
54C2×#10587481C2211yescharacteristic
55C2×#10587481C2211yescharacteristic
56C2×#10587481C2211yescharacteristic
57C2×#10587481C2211yescharacteristic
58C2×#10587480C2211yescharacteristic
59C2×#10587480C2211yescharacteristic
60C2×C22⋊#3622C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×#10587474C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C17×#542—24no—
65C17×#542C2218yescomplemented
66C2×C17×C4⋊Q8C2211yescharacteristic
67C2×C17×#126—21no—
68C2×C17×#124—21no—
69C2×C17×#124C2211yescharacteristic
70C2×C17×#123—21no—
71C2×C17×C22⋊Q8—21no—
72C2×C17×C22⋊Q8C2211yescharacteristic
73C2×C17×#121C2211yescharacteristic
74C2×C4×Q8×C17C2211yescharacteristic
75C2×C4×D4×C17C2211yescharacteristic
76C2×C17×#117C2211yescharacteristic
77C22×Q8×C17—21no—
78C22×Q8×C17C2311yescharacteristic
79C22×D4×C17—21no—
80C22×D4×C17C2311yescharacteristic
81C23×C4×C17—21no—
82C23×C4×C17C2311yescharacteristic
83C22×C22⋊D17—21no—
84C23×Dic17—21no—
85C2×#63252—22no—
86C2×#63252—42no—
87C2×#63252—42no—
88C2×#63252C2314yes—
89C22×D68C2311yescharacteristic
90C22×C4×D17—21no—
91C22×Dic34—21no—
92C22×Dic34—22no—
93C22×Dic34—42no—
94C22×Dic34—42no—
95C22×Dic34C2311yescharacteristic
96C22×Dic34C2311yescharacteristic
97C22×Dic34C2311yescharacteristic
98C22×Dic34C2314yes—
99C17×C4⋊Q8—22no—
100C17×C4⋊Q8C2314yes—
101C17×#126—28no—
102C17×#124—28no—
103C17×#124—22no—
104C17×#124C2314yes—
105C17×#123—28no—
106C17×C22⋊Q8—22no—
107C17×C22⋊Q8—28no—
108C17×C22⋊Q8C2314yes—
109C17×#121—22no—
110C17×#121C2314yes—
111C4×Q8×C17—22no—
112C4×Q8×C17C2314yes—
113C4×D4×C17—22no—
114C4×D4×C17C2314yes—
115C17×#117D414yes—
116C17×#117C2314yes—
117C2×C4⋊C4×C17—21no—
118C2×C4⋊C4×C17—21no—
119C2×C4⋊C4×C17—21no—
120C2×C4⋊C4×C17D411yescharacteristic
121C2×C4⋊C4×C17D411yescharacteristic
122C2×C4⋊C4×C17C2311yescharacteristic
123C2×C4⋊C4×C17C2311yescharacteristic
124C2×C22⋊C4×C17—21no—
125C2×C22⋊C4×C17—21no—
126C2×C22⋊C4×C17—21no—
127C2×C22⋊C4×C17—21no—
128C2×C22⋊C4×C17—21no—
129C2×C22⋊C4×C17D411yescharacteristic
130C2×C22⋊C4×C17D411yescharacteristic
131C2×C42×C17—21no—
132C2×C42×C17C2311yescharacteristic
133C2×C42×C17C2311yescharacteristic
134C2×#63231—42no—
135C2×#63231—42no—
136C2×#63231—42no—
137C2×#63231C2314yes—
138C2×#63231C2314yes—
139C2×#63231C2314yes—
140C2×#63230—42no—
141C2×#63230C2314yes—
142C2×#63229—42no—
143C2×#63229—42no—
144C2×#63229—42no—
145C2×#63229C2314yes—
146C2×#63229C2314yes—
147C2×#63229C2314yes—
148C2×#63228—42no—
149C2×#63228C2314yes—
150C2×#63227—21no—
151C2×#63227—21no—
152C2×#63227—21no—
153C2×#63227—21no—
154C2×C4⋊Dic17—21no—
155C2×C4⋊Dic17—21no—
156C2×C4⋊Dic17—21no—
157C2×C4⋊Dic17—21no—
158C22×#3622C2311yescharacteristic
159C22×#3622C2311yescharacteristic
160C22×#3622C2311yescharacteristic
161C22×#3622C2311yescharacteristic
162#10587583—28no—
163#10587583—28no—
164#10587572—28no—
165#10587572—28no—
166#10587561—22no—
167#10587561—22no—
168#10587561C2314yes—
169#10587561C2314yes—
170#10587555—22no—
171#10587555—22no—
172#10587555C2314yes—
173#10587555C2314yes—
174C22⋊#3622C2314yes—
175C22⋊#3622C2314yes—
176#10587481C2314yes—
177#10587481C2314yes—
178#10587481C2314yes—
179#10587481C2314yes—
180#10587481C2314yes—
181#10587481C2314yes—
182#10587480C2314yes—
183#10587480C2314yes—
184C4⋊#3622C2314yes—
185C4⋊#3622C2314yes—
186#10587474C2314yes—
187C4×#3622C2314yes—
188C24×C17—21no—
189C24×C17C2×D411yescharacteristic
190C23×D17—21no—
191C2×Q8×C17—21no—
192C2×Q8×C17—24no—
193C2×Q8×C17—22no—
194C2×Q8×C17—22no—
195C2×Q8×C17—82no—
196C2×Q8×C17C2412yes—
197C2×D4×C17—24no—
198C2×D4×C17—21no—
199C2×D4×C17—22no—
200C2×D4×C17—22no—
201C2×D4×C17—82no—
202C2×D4×C17C2412yes—
203C22×C4×C17—22no—
204C22×C4×C17—22no—
205C22×C4×C17—21no—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—24no—
209C22×C4×C17—82no—
210C22×C4×C17C2×D412yes—
211C22×C4×C17C2×D411yescharacteristic
212C22×C4×C17C2×D411yescharacteristic
213C22×C4×C17C2×D411yescharacteristic
214C22×C4×C17C2×D411yescharacteristic
215C22×C4×C17C2×D411yescharacteristic
216C22×C4×C17C2412yes—
217C22×C4×C17C2411yescharacteristic
218C2×C22⋊D17—24no—
219C2×C22⋊D17—44no—
220C22×Dic17—24no—
221C22×Dic17—21no—
222C22×Dic17—21no—
223C22×Dic17—21no—
224C22×Dic17—44no—
225#63252—44no—
226#63252—44no—
227#63252—48no—
228C2×D68—22no—
229C2×D68—22no—
230C2×D68—21no—
231C2×D68C2412yes—
232C2×C4×D17—24no—
233C2×C4×D17—44no—
234C2×Dic34—22no—
235C2×Dic34—22no—
236C2×Dic34—22no—
237C2×Dic34—22no—
238C2×Dic34—22no—
239C2×Dic34—22no—
240C2×Dic34—21no—
241C2×Dic34—21no—
242C2×Dic34—24no—
243C2×Dic34—21no—
244C2×Dic34—44no—
245C2×Dic34—44no—
246C2×Dic34—44no—
247C2×Dic34—48no—
248C2×Dic34C2412yes—
249C2×Dic34C2412yes—
250C2×Dic34C2412yes—
251C4⋊C4×C17—24no—
252C4⋊C4×C17—24no—
253C4⋊C4×C17—21no—
254C4⋊C4×C17—24no—
255C4⋊C4×C17—21no—
256C4⋊C4×C17C2×D414yes—
257C4⋊C4×C17C2×D414yes—
258C4⋊C4×C17C2412yes—
259C4⋊C4×C17C2412yes—
260C22⋊C4×C17—24no—
261C22⋊C4×C17—24no—
262C22⋊C4×C17—24no—
263C22⋊C4×C17—24no—
264C22⋊C4×C17—24no—
265C22⋊C4×C17C2×D414yes—
266C22⋊C4×C17C2×D414yes—
267C42×C17—24no—
268C42×C17C2×D412yes—
269C42×C17C2×D412yes—
270C42×C17C2412yes—
271C42×C17C2412yes—
272#63231—44no—
273#63231—44no—
274#63231—44no—
275#63230—44no—
276#63229—44no—
277#63229—44no—
278#63229—44no—
279#63228—44no—
280#63227—24no—
281#63227—24no—
282#63227—24no—
283#63227—24no—
284C4⋊Dic17—24no—
285C4⋊Dic17—24no—
286C4⋊Dic17—24no—
287C4⋊Dic17—24no—
288C2×#3622—22no—
289C2×#3622—22no—
290C2×#3622—22no—
291C2×#3622—22no—
292C2×#3622C2412yes—
293C2×#3622C2412yes—
294C2×#3622C2412yes—
295C2×#3622C2412yes—
296C2×#3225—171nomaximal, Sylow
297C23×C17—22no—
298C23×C17—22no—
299C23×C17—22no—
300C23×C17—22no—
301C23×C17—42no—
302C23×C17—42no—
303C23×C17—42no—
304C23×C17C22×D412yes—
305C23×C17C22×D411yescharacteristic
306C22×D17—22no—
307C22×D17—42no—
308C22×D17—42no—
309C22×D17—42no—
310Q8×C17—22no—
311Q8×C17—22no—
312Q8×C17—42no—
313Q8×C17—84no—
314D4×C17—22no—
315D4×C17—22no—
316D4×C17—42no—
317D4×C17—84no—
318C2×C4×C17—22no—
319C2×C4×C17—22no—
320C2×C4×C17—22no—
321C2×C4×C17—22no—
322C2×C4×C17—22no—
323C2×C4×C17—24no—
324C2×C4×C17—22no—
325C2×C4×C17—22no—
326C2×C4×C17—22no—
327C2×C4×C17—22no—
328C2×C4×C17—22no—
329C2×C4×C17—42no—
330C2×C4×C17—42no—
331C2×C4×C17—42no—
332C2×C4×C17—84no—
333C2×C4×C17C22×D412yes—
334C2×C4×C17C22×D412yes—
335C2×C4×C17C22×D412yes—
336C2×C4×C17C22×D412yes—
337C2×C4×C17C22×D412yes—
338C2×C4×C17C22×D411yescharacteristic
339C2×C4×C17H(5,𝔽2)12yes—
340C2×C4×C17H(5,𝔽2)12yes—
341C2×C4×C17C2511yescharacteristic
342C22⋊D17—48no—
343C2×Dic17—22no—
344C2×Dic17—22no—
345C2×Dic17—22no—
346C2×Dic17—48no—
347C2×Dic17—42no—
348C2×Dic17—42no—
349C2×Dic17—42no—
350D68—22no—
351D68—22no—
352D68—42no—
353C4×D17—48no—
354Dic34—22no—
355Dic34—22no—
356Dic34—22no—
357Dic34—22no—
358Dic34—22no—
359Dic34—22no—
360Dic34—48no—
361Dic34—42no—
362Dic34—42no—
363Dic34—42no—
364#3622—22no—
365#3622—22no—
366#3622—22no—
367#3622—22no—
368C2×#542D1711yescharacteristic, complemented
369C2×#536—171no—
370#3225—1716no—
371C2×#497—171no—
372C2×#495—171no—
373C2×#489—171no—
374C2×#487—171no—
375C2×#464—171no—
376C2×#462—171no—
377C2×#463—171no—
378C2×#461—171no—
379C2×#452—171no—
380C2×#449—171no—
381C2×#451—171no—
382C2×#448—171no—
383C2×#433—171no—
384C22×C17—22no—
385C22×C17—22no—
386C22×C17—22no—
387C22×C17—44no—
388C22×C17—42no—
389C22×C17—42no—
390C22×C17—42no—
391C22×C17—84no—
392C22×C17#53512yes—
393C22×C17#57712yes—
394C22×C17#57812yes—
395C22×C17C23×D411yescharacteristic
396C2×D17—42no—
397C2×D17—42no—
398C2×D17—42no—
399C2×D17—84no—
400C4×C17—22no—
401C4×C17—22no—
402C4×C17—22no—
403C4×C17—22no—
404C4×C17—22no—
405C4×C17—42no—
406C4×C17—42no—
407C4×C17—42no—
408C4×C17#53512yes—
409C4×C17C2×H(5,𝔽2)11yescharacteristic
410C4×C17C2×H(5,𝔽2)11yescharacteristic
411Dic17—42no—
412Dic17—42no—
413Dic17—42no—
414C22×#41—171no—
415C23×Q8—171no—
416C22×Q16—171no—
417C22×Q16—171no—
418C22×Q16—171no—
419C22×SD16—171no—
420C22×SD16—171no—
421C22×SD16—171no—
422C22×SD16—171no—
423C22×D8—171no—
424#542—24no—
425#542C2×D1718yescomplemented
426#536—178no—
427#536—344no—
428C2×C4⋊Q8—171no—
429C2×C4⋊Q8—171no—
430C2×C4⋊Q8C2×D1711yescharacteristic
431C2×#126—21no—
432C2×#124—21no—
433C2×#124—171no—
434C2×#124—171no—
435C2×#124C2×D1711yescharacteristic
436C2×#123—21no—
437C2×#123—341no—
438C2×#123—341no—
439C2×C22⋊Q8—21no—
440C2×C22⋊Q8—341no—
441C2×C22⋊Q8—341no—
442C2×C22⋊Q8C2×D1711yescharacteristic
443C2×#121C2×D1711yescharacteristic
444C2×C4×Q8C2×D1711yescharacteristic
445C2×C4×D4C2×D1711yescharacteristic
446C2×#117C2×D1711yescharacteristic
447#497—178no—
448#495—178no—
449#489—178no—
450#487—178no—
451#464—178no—
452#463—178no—
453#462—178no—
454#461—178no—
455#452—178no—
456#451—178no—
457#449—178no—
458#448—178no—
459#433—178no—
460C2×C4⋊C8—171no—
461C2×C4⋊C8—171no—
462C2×#103—171no—
463C2×#103—171no—
464C2×#103—171no—
465C2×#103—171no—
466C2×#103—171no—
467C2×#103—171no—
468C2×#102—171no—
469C2×#102—171no—
470C2×C22⋊C8—171no—
471C2×C22⋊C8—171no—
472C2×#97—171no—
473C2×C4×C8—171no—
474C2×C17—42no—
475C2×C17—82no—
476C2×C17#322514yescomplemented
477C2×C17C2×#53511yescharacteristic
478C2×C17C2×#57711yescharacteristic
479C2×C17C2×#57811yescharacteristic
480D17—82no—
481C2×#41—174no—
482C2×#41—342no—
483C2×#41—682no—
484C2×#41—682no—
485C22×Q8—21no—
486C22×Q8—171no—
487C22×Q8—171no—
488C22×Q8—171no—
489C22×Q8—174no—
490C22×Q8—341no—
491C22×Q8—342no—
492C22×Q8—682no—
493C22×Q8—682no—
494C22×Q8C22×D1711yescharacteristic
495C22×D4—21no—
496C22×D4—171no—
497C22×D4—341no—
498C22×D4C22×D1711yescharacteristic
499C23×C4—21no—
500C23×C4—341no—
501C23×C4—341no—
502C23×C4C22×D1711yescharacteristic
503C2×Q16—174no—
504C2×Q16—174no—
505C2×Q16—174no—
506C2×Q16—682no—
507C2×Q16—682no—
508C2×Q16—682no—
509C2×SD16—174no—
510C2×SD16—174no—
511C2×SD16—174no—
512C2×SD16—174no—
513C2×SD16—682no—
514C2×SD16—682no—
515C2×SD16—682no—
516C2×SD16—682no—
517C2×D8—174no—
518C2×D8—682no—
519C22×C8—171no—
520C22×C8—171no—
521C22×C8—171no—
522C22×C8—171no—
523C4⋊Q8—22no—
524C4⋊Q8—174no—
525C4⋊Q8—174no—
526C4⋊Q8—342no—
527C4⋊Q8—342no—
528C4⋊Q8C22×D1714yes—
529#126—28no—
530#124—28no—
531#124—22no—
532#124—174no—
533#124—174no—
534#124—342no—
535#124—342no—
536#124C22×D1714yes—
537#123—28no—
538#123—348no—
539#123—348no—
540C22⋊Q8—22no—
541C22⋊Q8—28no—
542C22⋊Q8—348no—
543C22⋊Q8—348no—
544C22⋊Q8C22×D1714yes—
545#121—22no—
546#121C22×D1714yes—
547C4×Q8—22no—
548C4×Q8C22×D1714yes—
549C4×D4—22no—
550C4×D4C22×D1714yes—
551#117C22⋊D1714yes—
552#117C22×D1714yes—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—341no—
557C2×C4⋊C4—341no—
558C2×C4⋊C4—341no—
559C2×C4⋊C4—341no—
560C2×C4⋊C4C22⋊D1711yescharacteristic
561C2×C4⋊C4C22⋊D1711yescharacteristic
562C2×C4⋊C4C22×D1711yescharacteristic
563C2×C4⋊C4C22×D1711yescharacteristic
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—341no—
570C2×C22⋊C4—341no—
571C2×C22⋊C4—341no—
572C2×C22⋊C4—341no—
573C2×C22⋊C4C22⋊D1711yescharacteristic
574C2×C22⋊C4C22⋊D1711yescharacteristic
575C2×C42—21no—
576C2×C42C22×D1711yescharacteristic
577C2×C42C22×D1711yescharacteristic
578C4⋊C8—174no—
579C4⋊C8—174no—
580#103—174no—
581#103—174no—
582#103—174no—
583#103—174no—
584#103—174no—
585#103—174no—
586#102—174no—
587#102—174no—
588C22⋊C8—174no—
589C22⋊C8—174no—
590#97—174no—
591C4×C8—174no—
592C17C2×#322511yescharacteristic, complemented, Sylow
593C24—21no—
594C24—341no—
595C24C2×C22⋊D1711yescharacteristic
596#41—684no—
597#41—684no—
598#41—688no—
599C2×Q8—21no—
600C2×Q8—24no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—82no—
604C2×Q8—172no—
605C2×Q8—172no—
606C2×Q8—172no—
607C2×Q8—344no—
608C2×Q8—341no—
609C2×Q8—341no—
610C2×Q8—341no—
611C2×Q8—342no—
612C2×Q8—342no—
613C2×Q8—342no—
614C2×Q8—342no—
615C2×Q8—342no—
616C2×Q8—342no—
617C2×Q8—684no—
618C2×Q8—684no—
619C2×Q8—684no—
620C2×Q8—688no—
621C2×Q8C23×D1712yes—
622C2×D4—24no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—21no—
626C2×D4—82no—
627C2×D4—172no—
628C2×D4—344no—
629C2×D4—342no—
630C2×D4—342no—
631C2×D4—341no—
632C2×D4—684no—
633C2×D4C23×D1712yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—82no—
641C22×C4—344no—
642C22×C4—341no—
643C22×C4—341no—
644C22×C4—341no—
645C22×C4—344no—
646C22×C4—684no—
647C22×C4—684no—
648C22×C4C2×C22⋊D1712yes—
649C22×C4C2×C22⋊D1711yescharacteristic
650C22×C4C2×C22⋊D1711yescharacteristic
651C22×C4C2×C22⋊D1711yescharacteristic
652C22×C4C2×C22⋊D1711yescharacteristic
653C22×C4C2×C22⋊D1711yescharacteristic
654C22×C4C23×D1712yes—
655C22×C4C23×D1711yescharacteristic
656Q16—684no—
657Q16—684no—
658Q16—684no—
659SD16—684no—
660SD16—684no—
661SD16—684no—
662SD16—684no—
663D8—684no—
664C2×C8—172no—
665C2×C8—172no—
666C2×C8—172no—
667C2×C8—172no—
668C2×C8—342no—
669C2×C8—342no—
670C2×C8—342no—
671C2×C8—342no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—344no—
678C4⋊C4—344no—
679C4⋊C4—344no—
680C4⋊C4—344no—
681C4⋊C4C2×C22⋊D1714yes—
682C4⋊C4C2×C22⋊D1714yes—
683C4⋊C4C23×D1712yes—
684C4⋊C4C23×D1712yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—344no—
691C22⋊C4—344no—
692C22⋊C4—344no—
693C22⋊C4—344no—
694C22⋊C4C2×C22⋊D1714yes—
695C22⋊C4C2×C22⋊D1714yes—
696C42—24no—
697C42C2×C22⋊D1712yes—
698C42C2×C22⋊D1712yes—
699C42C23×D1712yes—
700C42C23×D1712yes—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—342no—
709C23—682no—
710C23—682no—
711C23—682no—
712C23C22×C22⋊D1712yes—
713C23C22×C22⋊D1711yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—84no—
718Q8—342no—
719Q8—342no—
720Q8—342no—
721Q8—342no—
722Q8—342no—
723Q8—342no—
724Q8—688no—
725Q8—682no—
726Q8—682no—
727Q8—682no—
728D4—22no—
729D4—22no—
730D4—42no—
731D4—84no—
732D4—342no—
733D4—342no—
734D4—688no—
735D4—682no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—84no—
751C2×C4—342no—
752C2×C4—342no—
753C2×C4—342no—
754C2×C4—688no—
755C2×C4—688no—
756C2×C4—682no—
757C2×C4—682no—
758C2×C4—682no—
759C2×C4#1058769612yes—
760C2×C4#1058769612yes—
761C2×C4C22×C22⋊D1712yes—
762C2×C4C22×C22⋊D1712yes—
763C2×C4C22×C22⋊D1712yes—
764C2×C4C22×C22⋊D1712yes—
765C2×C4C22×C22⋊D1712yes—
766C2×C4C22×C22⋊D1711yescharacteristic
767C2×C4C24×D1711yescharacteristic
768C8—342no—
769C8—342no—
770C8—342no—
771C8—342no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—84no—
780C22—682no—
781C22—682no—
782C22—682no—
783C22—1364no—
784C22#1176337312yes—
785C22#1176362012yes—
786C22#1176362412yes—
787C22C23×C22⋊D1711yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—682no—
797C4—682no—
798C4—682no—
799C4#1176337312yes—
800C4C2×#1058769611yescharacteristic
801C4C2×#1058769611yescharacteristic
802C2—42no—
803C2—82no—
804C2—1362no—
805C2#1453988714yesdirect product factor
806C2C2×#1176337311yescharacteristic
807C2C2×#1176362011yescharacteristic
808C2C2×#1176362411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#542C2
socleC23×C17C22×D4
prime radicalC2×#11762952C2
hypercenterC2×#542D17
hypocenterC17C2×#3225
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#11763385C2semidirect
2. #14539887C2direct (N × H)
3. C2×#11763204C2semidirect
4. C2×#11763191C2semidirect
5. C2×#11763171C2semidirect
6. C2×#11763161C2semidirect
7. C2×#11763031C2semidirect
8. C2×#11763019C2semidirect
9. C2×#11763024C2semidirect
10. C2×#11763014C2semidirect
11. C2×#11762969C2semidirect
13. C2×#11762964C2semidirect
14. C2×#11762947C2semidirect
15. C2×#11762870C2semidirect
16. C2×C17×#542C2semidirect
28. #11763385C22semidirect
37. #11763204C22semidirect
38. #11763191C22semidirect
39. #11763171C22semidirect
40. #11763161C22semidirect
41. #11763031C22semidirect
42. #11763024C22semidirect
43. #11763019C22semidirect
44. #11763014C22semidirect
45. #11762969C22semidirect
46. #11762964C22semidirect
48. #11762947C22semidirect
49. #11762870C22semidirect
65. C17×#542C22semidirect
368. C2×#542D17semidirect
425. #542C2×D17semidirect
476. C2×C17#3225semidirect
592. C17C2×#3225semidirect
805. C2#14539887direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117633852
#145398872
C2×#117632042
C2×#117631912
C2×#117631712
C2×#117631612
C2×#117630312
C2×#117630192
C2×#117630242
C2×#117630142
C2×#117629692
C2×#117629522
C2×#117629642
C2×#117629472
C2×#117628702
C2×C17×#5422
C2×#322517