Finite Group Databasebeta

← C2×#14539893 #17905719

Subgroups — C2×#14539893 #17905719

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×#11763430C211yesmaximal, characteristic, complemented
2#14539893C2116yesmaximal, direct product factor
3C2×#11763201C211yesmaximal, characteristic, complemented
4C2×#11763191C211yesmaximal, characteristic, complemented
5C2×#11763168C211yesmaximal, characteristic, complemented
6C2×#11763159C211yesmaximal, characteristic, complemented
7C2×#11763028C211yesmaximal, characteristic, complemented
8C2×#11763016C211yesmaximal, characteristic, complemented
9C2×#11763021C211yesmaximal, characteristic, complemented
10C2×#11763011C211yesmaximal, characteristic, complemented
11C2×#11762971C211yesmaximal, characteristic, complemented
12C2×#11762954C211yesmaximal, characteristic
13C2×#11762965C211yesmaximal, characteristic, complemented
14C2×#11762948C211yesmaximal, characteristic, complemented
15C2×#11762870C211yesmaximal, characteristic, complemented
16C2×C17×#536C211yesmaximal, characteristic, complemented
17C22×#63231C2211yescharacteristic
18C22×#63231C2211yescharacteristic
19C22×#63231C2211yescharacteristic
20C22×#63229C2211yescharacteristic
21C22×#63230C2211yescharacteristic
22C22×#63230C2211yescharacteristic
23C22×#63230C2211yescharacteristic
24C22×#63228C2211yescharacteristic
25#11763430—24no—
26#11763430C2218yescomplemented
27C2×#10587555C2211yescharacteristic
28C2×#10587584—21no—
29C2×#10587561C2211yescharacteristic
30C2×#10587571—21no—
31C2×#10587569—21no—
32C2×#10587610C2211yescharacteristic
33C2×#10587582—21no—
34C2×#10587616C2211yescharacteristic
35C2×C4×Dic34C2211yescharacteristic
36C2×C4×D68C2211yescharacteristic
37#11763201C2218yescomplemented
38#11763191C2218yescomplemented
39#11763168C2218yescomplemented
40#11763159C2218yescomplemented
41#11763028C2218yescomplemented
42#11763021C2218yescomplemented
43#11763016C2218yescomplemented
44#11763011C2218yescomplemented
45#11762971C2218yescomplemented
46#11762965C2218yescomplemented
47#11762954C2218yes—
48#11762948C2218yescomplemented
49#11762870C2218yescomplemented
50C2×C4⋊#3622C2211yescharacteristic
51C2×C4⋊#3622C2211yescharacteristic
52C2×#10587506C2211yescharacteristic
53C2×#10587506C2211yescharacteristic
54C2×#10587506C2211yescharacteristic
55C2×#10587506C2211yescharacteristic
56C2×#10587506C2211yescharacteristic
57C2×#10587506C2211yescharacteristic
58C2×#10587503C2211yescharacteristic
59C2×#10587503C2211yescharacteristic
60C2×C22⋊#3622C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×#10587474C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C22×#41×C17C2211yescharacteristic
65C23×Q8×C17C2211yescharacteristic
66C17×#536—24no—
67C17×#536C2218yescomplemented
68C2×C17×C4⋊Q8C2211yescharacteristic
69C2×C17×C4⋊Q8C2211yescharacteristic
70C2×C17×#124C2211yescharacteristic
71C2×C17×#124C2211yescharacteristic
72C2×C17×#123—21no—
73C2×C17×#123—21no—
74C2×C17×C22⋊Q8—21no—
75C2×C17×C22⋊Q8—21no—
76C2×C17×#117C2211yescharacteristic
77C2×#41×C17—22no—
78C2×#41×C17—42no—
79C2×#41×C17—42no—
80C2×#41×C17C2314yes—
81C22×Q8×C17—21no—
82C22×Q8×C17—22no—
83C22×Q8×C17—42no—
84C22×Q8×C17—42no—
85C22×Q8×C17C2311yescharacteristic
86C22×Q8×C17C2311yescharacteristic
87C22×Q8×C17C2311yescharacteristic
88C22×Q8×C17C2314yes—
89C22×D4×C17—21no—
90C22×D4×C17C2311yescharacteristic
91C23×C4×C17—21no—
92C23×C4×C17—21no—
93C23×C4×C17C2311yescharacteristic
94C22×C22⋊D17—21no—
95C22×D68C2311yescharacteristic
96C22×C4×D17—21no—
97C22×Dic34—21no—
98C22×Dic34C2311yescharacteristic
99C17×C4⋊Q8—22no—
100C17×C4⋊Q8—22no—
101C17×C4⋊Q8C2314yes—
102C17×C4⋊Q8C2314yes—
103C17×#124—22no—
104C17×#124—22no—
105C17×#124C2314yes—
106C17×#124C2314yes—
107C17×#123—28no—
108C17×#123—28no—
109C17×C22⋊Q8—28no—
110C17×C22⋊Q8—28no—
111C17×#117D414yes—
112C17×#117C2314yes—
113C2×C4⋊C4×C17—21no—
114C2×C4⋊C4×C17—21no—
115C2×C4⋊C4×C17—21no—
116C2×C4⋊C4×C17—21no—
117C2×C4⋊C4×C17D411yescharacteristic
118C2×C4⋊C4×C17D411yescharacteristic
119C2×C22⋊C4×C17—21no—
120C2×C22⋊C4×C17—21no—
121C2×C22⋊C4×C17—21no—
122C2×C22⋊C4×C17—21no—
123C2×C22⋊C4×C17D411yescharacteristic
124C2×C22⋊C4×C17D411yescharacteristic
125C2×C42×C17C2311yescharacteristic
126C2×C42×C17C2311yescharacteristic
127C2×C22⋊Dic17—21no—
128C2×#63231—42no—
129C2×#63231—42no—
130C2×#63231—42no—
131C2×#63231C2314yes—
132C2×#63231C2314yes—
133C2×#63231C2314yes—
134C2×#63230—42no—
135C2×#63230—42no—
136C2×#63230—42no—
137C2×#63230C2314yes—
138C2×#63230C2314yes—
139C2×#63230C2314yes—
140C2×#63229—42no—
141C2×#63229C2314yes—
142C2×#63228—42no—
143C2×#63228C2314yes—
144#10587616—22no—
145#10587616C2314yes—
146C2×#63227—21no—
147C2×#63227—21no—
148C2×#63227—21no—
149C2×#63227—21no—
150C2×C4⋊Dic17—21no—
151C2×C4⋊Dic17C2311yescharacteristic
152C2×C4⋊Dic17C2311yescharacteristic
153#10587610—22no—
154#10587610C2314yes—
155C2×#63225—21no—
156C2×#63225—21no—
157C2×C4×Dic17—21no—
158C22×#3622C2311yescharacteristic
159C22×#3622C2311yescharacteristic
160C22×#3622C2311yescharacteristic
161C22×#3622C2311yescharacteristic
162#10587584—28no—
163#10587582—28no—
164#10587571—28no—
165#10587569—28no—
166#10587561—22no—
167#10587561C2314yes—
168C4×D68—22no—
169C4×D68C2314yes—
170#10587555—22no—
171#10587555C2314yes—
172C4×Dic34—22no—
173C4×Dic34C2314yes—
174#10587506C2314yes—
175#10587506C2314yes—
176#10587506C2314yes—
177#10587506C2314yes—
178#10587506C2314yes—
179#10587506C2314yes—
180#10587503C2314yes—
181#10587503C2314yes—
182C22⋊#3622C2314yes—
183C22⋊#3622C2314yes—
184C4⋊#3622C2314yes—
185C4⋊#3622C2314yes—
186#10587474C2314yes—
187C4×#3622C2314yes—
188C24×C17—21no—
189C24×C17C2×D411yescharacteristic
190C23×D17—21no—
191#41×C17—44no—
192#41×C17—44no—
193#41×C17—48no—
194C2×Q8×C17—24no—
195C2×Q8×C17—21no—
196C2×Q8×C17—21no—
197C2×Q8×C17—21no—
198C2×Q8×C17—22no—
199C2×Q8×C17—22no—
200C2×Q8×C17—22no—
201C2×Q8×C17—22no—
202C2×Q8×C17—22no—
203C2×Q8×C17—22no—
204C2×Q8×C17—44no—
205C2×Q8×C17—44no—
206C2×Q8×C17—44no—
207C2×Q8×C17—48no—
208C2×Q8×C17C2412yes—
209C2×Q8×C17C2412yes—
210C2×Q8×C17C2412yes—
211C2×D4×C17—24no—
212C2×D4×C17—21no—
213C2×D4×C17—22no—
214C2×D4×C17—22no—
215C2×D4×C17—44no—
216C2×D4×C17C2412yes—
217C22×C4×C17—22no—
218C22×C4×C17—22no—
219C22×C4×C17—24no—
220C22×C4×C17—21no—
221C22×C4×C17—21no—
222C22×C4×C17—21no—
223C22×C4×C17—24no—
224C22×C4×C17—44no—
225C22×C4×C17—44no—
226C22×C4×C17C2×D411yescharacteristic
227C22×C4×C17C2×D411yescharacteristic
228C22×C4×C17C2×D411yescharacteristic
229C22×C4×C17C2×D412yes—
230C22×C4×C17C2×D411yescharacteristic
231C22×C4×C17C2×D411yescharacteristic
232C22×C4×C17C2412yes—
233C22×C4×C17C2411yescharacteristic
234C2×C22⋊D17—24no—
235C2×C22⋊D17—82no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—21no—
239C2×D68—22no—
240C2×D68—22no—
241C2×D68—21no—
242C2×D68C2412yes—
243C2×C4×D17—24no—
244C2×C4×D17—82no—
245C2×Dic34—22no—
246C2×Dic34—22no—
247C2×Dic34—21no—
248C2×Dic34—24no—
249C2×Dic34—82no—
250C2×Dic34C2412yes—
251C4⋊C4×C17—24no—
252C4⋊C4×C17—24no—
253C4⋊C4×C17—24no—
254C4⋊C4×C17—24no—
255C4⋊C4×C17C2×D414yes—
256C4⋊C4×C17C2×D414yes—
257C22⋊C4×C17—24no—
258C22⋊C4×C17—24no—
259C22⋊C4×C17—24no—
260C22⋊C4×C17—24no—
261C22⋊C4×C17C2×D414yes—
262C22⋊C4×C17C2×D414yes—
263C42×C17C2×D412yes—
264C42×C17C2×D412yes—
265C42×C17C2412yes—
266C42×C17C2412yes—
267C22⋊Dic17—24no—
268#63231—44no—
269#63231—44no—
270#63231—44no—
271#63230—44no—
272#63230—44no—
273#63230—44no—
274#63229—44no—
275#63228—44no—
276#63227—24no—
277#63227—24no—
278#63227—24no—
279#63227—24no—
280C4⋊Dic17—21no—
281C4⋊Dic17—21no—
282C4⋊Dic17—24no—
283C4⋊Dic17C2412yes—
284C4⋊Dic17C2412yes—
285#63225—24no—
286#63225—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—22no—
313Q8×C17—22no—
314Q8×C17—22no—
315Q8×C17—22no—
316Q8×C17—48no—
317Q8×C17—42no—
318Q8×C17—42no—
319Q8×C17—42no—
320D4×C17—22no—
321D4×C17—22no—
322D4×C17—48no—
323D4×C17—42no—
324C2×C4×C17—22no—
325C2×C4×C17—22no—
326C2×C4×C17—22no—
327C2×C4×C17—22no—
328C2×C4×C17—22no—
329C2×C4×C17—24no—
330C2×C4×C17—22no—
331C2×C4×C17—22no—
332C2×C4×C17—22no—
333C2×C4×C17—22no—
334C2×C4×C17—22no—
335C2×C4×C17—48no—
336C2×C4×C17—48no—
337C2×C4×C17—42no—
338C2×C4×C17—42no—
339C2×C4×C17—42no—
340C2×C4×C17C22×D412yes—
341C2×C4×C17C22×D412yes—
342C2×C4×C17C22×D412yes—
343C2×C4×C17C22×D412yes—
344C2×C4×C17C22×D412yes—
345C2×C4×C17C22×D411yescharacteristic
346C2×C4×C17H(5,𝔽2)12yes—
347C2×C4×C17H(5,𝔽2)12yes—
348C2×C4×C17C2511yescharacteristic
349C22⋊D17—84no—
350C2×Dic17—22no—
351C2×Dic17—22no—
352C2×Dic17—22no—
353C2×Dic17—42no—
354C2×Dic17—42no—
355C2×Dic17—42no—
356D68—22no—
357D68—22no—
358D68—42no—
359C4×D17—84no—
360Dic34—22no—
361Dic34—22no—
362Dic34—42no—
363Dic34—84no—
364#3622—22no—
365#3622—22no—
366#3622—22no—
367#3622—22no—
368C2×#542—171no—
369C2×#536D1711yescharacteristic, complemented
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×#41C2×D1711yescharacteristic
415C23×Q8C2×D1711yescharacteristic
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—178no—
425#542—344no—
426#536—24no—
427#536C2×D1718yescomplemented
428C2×C4⋊Q8—171no—
429C2×C4⋊Q8C2×D1711yescharacteristic
430C2×C4⋊Q8C2×D1711yescharacteristic
431C2×#126—341no—
432C2×#124—171no—
433C2×#124—341no—
434C2×#124C2×D1711yescharacteristic
435C2×#124C2×D1711yescharacteristic
436C2×#123—21no—
437C2×#123—21no—
438C2×#123—341no—
439C2×C22⋊Q8—21no—
440C2×C22⋊Q8—21no—
441C2×C22⋊Q8—171no—
442C2×C22⋊Q8—341no—
443C2×#121—171no—
444C2×C4×Q8—171no—
445C2×C4×D4—171no—
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—22no—
482C2×#41—42no—
483C2×#41—42no—
484C2×#41C22×D1714yes—
485C22×Q8—21no—
486C22×Q8—22no—
487C22×Q8—42no—
488C22×Q8—42no—
489C22×Q8—171no—
490C22×Q8—341no—
491C22×Q8C22×D1711yescharacteristic
492C22×Q8C22×D1711yescharacteristic
493C22×Q8C22×D1711yescharacteristic
494C22×Q8C22×D1714yes—
495C22×D4—21no—
496C22×D4—171no—
497C22×D4—341no—
498C22×D4C22×D1711yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
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—22no—
525C4⋊Q8—174no—
526C4⋊Q8—342no—
527C4⋊Q8C22×D1714yes—
528C4⋊Q8C22×D1714yes—
529#126—348no—
530#124—22no—
531#124—22no—
532#124—174no—
533#124—348no—
534#124—342no—
535#124C22×D1714yes—
536#124C22×D1714yes—
537#123—28no—
538#123—28no—
539#123—348no—
540C22⋊Q8—28no—
541C22⋊Q8—28no—
542C22⋊Q8—174no—
543C22⋊Q8—342no—
544C22⋊Q8—348no—
545#121—174no—
546#121—342no—
547C4×Q8—174no—
548C4×Q8—342no—
549C4×D4—174no—
550C4×D4—342no—
551#117C22⋊D1714yes—
552#117C22×D1714yes—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—171no—
558C2×C4⋊C4—171no—
559C2×C4⋊C4—341no—
560C2×C4⋊C4—341no—
561C2×C4⋊C4—341no—
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—341no—
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—341no—
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—44no—
597#41—44no—
598#41—48no—
599C2×Q8—24no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—44no—
610C2×Q8—44no—
611C2×Q8—44no—
612C2×Q8—48no—
613C2×Q8—172no—
614C2×Q8—341no—
615C2×Q8—344no—
616C2×Q8—342no—
617C2×Q8—342no—
618C2×Q8—1362no—
619C2×Q8C23×D1712yes—
620C2×Q8C23×D1712yes—
621C2×Q8C23×D1712yes—
622C2×D4—24no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—21no—
626C2×D4—44no—
627C2×D4—172no—
628C2×D4—344no—
629C2×D4—342no—
630C2×D4—342no—
631C2×D4—341no—
632C2×D4—1362no—
633C2×D4C23×D1712yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—24no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—341no—
644C22×C4—341no—
645C22×C4—341no—
646C22×C4—344no—
647C22×C4—1362no—
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—24no—
676C4⋊C4—172no—
677C4⋊C4—172no—
678C4⋊C4—341no—
679C4⋊C4—341no—
680C4⋊C4—344no—
681C4⋊C4—344no—
682C4⋊C4—344no—
683C4⋊C4C2×C22⋊D1714yes—
684C4⋊C4C2×C22⋊D1714yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—344no—
690C22⋊C4—344no—
691C22⋊C4—344no—
692C22⋊C4—344no—
693C22⋊C4—344no—
694C22⋊C4C2×C22⋊D1714yes—
695C22⋊C4C2×C22⋊D1714yes—
696C42—344no—
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—22no—
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—48no—
721Q8—42no—
722Q8—42no—
723Q8—42no—
724Q8—342no—
725Q8—342no—
726Q8—682no—
727Q8—1364no—
728D4—22no—
729D4—22no—
730D4—48no—
731D4—42no—
732D4—342no—
733D4—342no—
734D4—682no—
735D4—1364no—
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—48no—
748C2×C4—48no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—342no—
753C2×C4—342no—
754C2×C4—342no—
755C2×C4—682no—
756C2×C4—682no—
757C2×C4—682no—
758C2×C4—1364no—
759C2×C4#1058769112yes—
760C2×C4#1058769112yes—
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#1176337612yes—
785C22#1176361712yes—
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#1176337612yes—
800C4C2×#1058769111yescharacteristic
801C4C2×#1058769111yescharacteristic
802C2—42no—
803C2—82no—
804C2—1362no—
805C2#1453989314yesdirect product factor
806C2C2×#1176337611yescharacteristic
807C2C2×#1176361711yescharacteristic
808C2C2×#1176362411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#536C2
socleC23×C17C22×D4
prime radicalC2×#11762954C2
hypercenterC2×#536D17
hypocenterC17C2×#3225
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C2×#11763430C2semidirect
2. #14539893C2direct (N × H)
3. C2×#11763201C2semidirect
4. C2×#11763191C2semidirect
5. C2×#11763168C2semidirect
6. C2×#11763159C2semidirect
7. C2×#11763028C2semidirect
8. C2×#11763016C2semidirect
9. C2×#11763021C2semidirect
10. C2×#11763011C2semidirect
11. C2×#11762971C2semidirect
13. C2×#11762965C2semidirect
14. C2×#11762948C2semidirect
15. C2×#11762870C2semidirect
16. C2×C17×#536C2semidirect
26. #11763430C22semidirect
37. #11763201C22semidirect
38. #11763191C22semidirect
39. #11763168C22semidirect
40. #11763159C22semidirect
41. #11763028C22semidirect
42. #11763021C22semidirect
43. #11763016C22semidirect
44. #11763011C22semidirect
45. #11762971C22semidirect
46. #11762965C22semidirect
48. #11762948C22semidirect
49. #11762870C22semidirect
67. C17×#536C22semidirect
369. C2×#536D17semidirect
427. #536C2×D17semidirect
476. C2×C17#3225semidirect
592. C17C2×#3225semidirect
805. C2#14539893direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634302
#145398932
C2×#117632012
C2×#117631912
C2×#117631682
C2×#117631592
C2×#117630282
C2×#117630162
C2×#117630212
C2×#117630112
C2×#117629712
C2×#117629542
C2×#117629652
C2×#117629482
C2×#117628702
C2×C17×#5362
C2×#322517