Finite Group Databasebeta

← C2×#24918566 #36275793

Subgroups — C2×#24918566 #36275793

Order 21248.

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×#19128277C211yesmaximal, characteristic, complemented
2#24918566C2116yesmaximal, direct product factor
3C2×#19128096C211yesmaximal, characteristic, complemented
4C2×#19128083C211yesmaximal, characteristic, complemented
5C2×#19128063C211yesmaximal, characteristic, complemented
6C2×#19128053C211yesmaximal, characteristic, complemented
7C2×#19127923C211yesmaximal, characteristic, complemented
8C2×#19127911C211yesmaximal, characteristic, complemented
9C2×#19127916C211yesmaximal, characteristic, complemented
10C2×#19127906C211yesmaximal, characteristic, complemented
11C2×#19127861C211yesmaximal, characteristic, complemented
12C2×#19127844C211yesmaximal, characteristic
13C2×#19127856C211yesmaximal, characteristic, complemented
14C2×#19127839C211yesmaximal, characteristic, complemented
15C2×#19127762C211yesmaximal, characteristic, complemented
16C2×#542×C83C211yesmaximal, characteristic, complemented
17C22×#13050590C2211yescharacteristic
18C23×Dic166C2211yescharacteristic
19C22×#13050580C2211yescharacteristic
20C22×#13050580C2211yescharacteristic
21C22×#13050580C2211yescharacteristic
22C22×#13050578C2211yescharacteristic
23C22×#13050578C2211yescharacteristic
24C22×#13050578C2211yescharacteristic
25C22×#13050577C2211yescharacteristic
26C22×#13050575C2211yescharacteristic
27#19128277—24no—
28#19128277C2218yescomplemented
29C2×#14581792C2211yescharacteristic
30C2×#14581792C2211yescharacteristic
31C2×#14581780C2211yescharacteristic
32C2×#14581780C2211yescharacteristic
33C2×#14581776—21no—
34C2×#14581776—21no—
35C2×#14581772—21no—
36C2×#14581772—21no—
37#19128096C2218yescomplemented
38#19128083C2218yescomplemented
39#19128063C2218yescomplemented
40#19128053C2218yescomplemented
41#19127923C2218yescomplemented
42#19127916C2218yescomplemented
43#19127911C2218yescomplemented
44#19127906C2218yescomplemented
45#19127861C2218yescomplemented
46#19127856C2218yescomplemented
47#19127844C2218yes—
48#19127839C2218yescomplemented
49#19127762C2218yescomplemented
50C2×C4⋊(C83⋊C8)C2211yescharacteristic
51C2×C4⋊(C83⋊C8)C2211yescharacteristic
52C2×#14581715C2211yescharacteristic
53C2×#14581715C2211yescharacteristic
54C2×#14581715C2211yescharacteristic
55C2×#14581715C2211yescharacteristic
56C2×#14581715C2211yescharacteristic
57C2×#14581715C2211yescharacteristic
58C2×#14581712C2211yescharacteristic
59C2×#14581712C2211yescharacteristic
60C2×C22⋊(C83⋊C8)C2211yescharacteristic
61C2×C22⋊(C83⋊C8)C2211yescharacteristic
62C2×#14581703C2211yescharacteristic
63C2×C4×C83⋊C8C2211yescharacteristic
64#542×C83—24no—
65#542×C83C2218yescomplemented
66C2×C4⋊Q8×C83C2211yescharacteristic
67C2×#126×C83—21no—
68C2×#124×C83—21no—
69C2×#124×C83C2211yescharacteristic
70C2×#123×C83—21no—
71C2×C22⋊Q8×C83—21no—
72C2×C22⋊Q8×C83C2211yescharacteristic
73C2×#121×C83C2211yescharacteristic
74C2×C4×Q8×C83C2211yescharacteristic
75C2×C4×D4×C83C2211yescharacteristic
76C2×#117×C83C2211yescharacteristic
77C2×#13050590—22no—
78C2×#13050590—42no—
79C2×#13050590—42no—
80C2×#13050590C2314yes—
81C22×Dic166—21no—
82C22×Dic166—22no—
83C22×Dic166—42no—
84C22×Dic166—42no—
85C22×Dic166C2311yescharacteristic
86C22×Dic166C2311yescharacteristic
87C22×Dic166C2311yescharacteristic
88C22×Dic166C2314yes—
89C22×D332C2311yescharacteristic
90C22×C22⋊D83—21no—
91C23×Dic83—21no—
92C22×C4×D83—21no—
93C2×#13050580—42no—
94C2×#13050580—42no—
95C2×#13050580—42no—
96C2×#13050580C2314yes—
97C2×#13050580C2314yes—
98C2×#13050580C2314yes—
99C2×#13050578—42no—
100C2×#13050578—42no—
101C2×#13050578—42no—
102C2×#13050578C2314yes—
103C2×#13050578C2314yes—
104C2×#13050578C2314yes—
105C2×#13050577—42no—
106C2×#13050577C2314yes—
107C2×#13050575—42no—
108C2×#13050575C2314yes—
109C22×C83⋊C8C2311yescharacteristic
110C22×C83⋊C8C2311yescharacteristic
111C22×C83⋊C8C2311yescharacteristic
112C22×C83⋊C8C2311yescharacteristic
113#14581792—22no—
114#14581792—22no—
115#14581792C2314yes—
116#14581792C2314yes—
117#14581780—22no—
118#14581780—22no—
119#14581780C2314yes—
120#14581780C2314yes—
121#14581776—28no—
122#14581776—28no—
123#14581772—28no—
124#14581772—28no—
125C2×C4⋊Dic83—21no—
126C2×C4⋊Dic83—21no—
127C2×C4⋊Dic83—21no—
128C2×C4⋊Dic83—21no—
129C2×(C2×D83)⋊C4—21no—
130C2×(C2×D83)⋊C4—21no—
131C2×(C2×D83)⋊C4—21no—
132C2×(C2×D83)⋊C4—21no—
133C4⋊(C83⋊C8)C2314yes—
134C4⋊(C83⋊C8)C2314yes—
135#14581715C2314yes—
136#14581715C2314yes—
137#14581715C2314yes—
138#14581715C2314yes—
139#14581715C2314yes—
140#14581715C2314yes—
141#14581712C2314yes—
142#14581712C2314yes—
143C22⋊(C83⋊C8)C2314yes—
144C22⋊(C83⋊C8)C2314yes—
145#14581703C2314yes—
146C4×C83⋊C8C2314yes—
147C22×Q8×C83—21no—
148C22×Q8×C83C2311yescharacteristic
149C22×D4×C83—21no—
150C22×D4×C83C2311yescharacteristic
151C23×C4×C83—21no—
152C23×C4×C83C2311yescharacteristic
153C4⋊Q8×C83—22no—
154C4⋊Q8×C83C2314yes—
155#126×C83—28no—
156#124×C83—28no—
157#124×C83—22no—
158#124×C83C2314yes—
159#123×C83—28no—
160C22⋊Q8×C83—22no—
161C22⋊Q8×C83—28no—
162C22⋊Q8×C83C2314yes—
163#121×C83—22no—
164#121×C83C2314yes—
165C4×Q8×C83—22no—
166C4×Q8×C83C2314yes—
167C4×D4×C83—22no—
168C4×D4×C83C2314yes—
169#117×C83D414yes—
170#117×C83C2314yes—
171C2×C4⋊C4×C83—21no—
172C2×C4⋊C4×C83—21no—
173C2×C4⋊C4×C83—21no—
174C2×C4⋊C4×C83D411yescharacteristic
175C2×C4⋊C4×C83D411yescharacteristic
176C2×C4⋊C4×C83C2311yescharacteristic
177C2×C4⋊C4×C83C2311yescharacteristic
178C2×C22⋊C4×C83—21no—
179C2×C22⋊C4×C83—21no—
180C2×C22⋊C4×C83—21no—
181C2×C22⋊C4×C83—21no—
182C2×C22⋊C4×C83—21no—
183C2×C22⋊C4×C83D411yescharacteristic
184C2×C22⋊C4×C83D411yescharacteristic
185C2×C42×C83—21no—
186C2×C42×C83C2311yescharacteristic
187C2×C42×C83C2311yescharacteristic
188C23×D83—21no—
189#13050590—44no—
190#13050590—44no—
191#13050590—48no—
192C2×Dic166—22no—
193C2×Dic166—22no—
194C2×Dic166—22no—
195C2×Dic166—22no—
196C2×Dic166—22no—
197C2×Dic166—22no—
198C2×Dic166—24no—
199C2×Dic166—21no—
200C2×Dic166—21no—
201C2×Dic166—21no—
202C2×Dic166—44no—
203C2×Dic166—44no—
204C2×Dic166—44no—
205C2×Dic166—48no—
206C2×Dic166C2412yes—
207C2×Dic166C2412yes—
208C2×Dic166C2412yes—
209C2×D332—22no—
210C2×D332—22no—
211C2×D332—21no—
212C2×D332C2412yes—
213C2×C22⋊D83—24no—
214C2×C22⋊D83—44no—
215C22×Dic83—24no—
216C22×Dic83—21no—
217C22×Dic83—21no—
218C22×Dic83—21no—
219C22×Dic83—44no—
220C2×C4×D83—24no—
221C2×C4×D83—44no—
222#13050580—44no—
223#13050580—44no—
224#13050580—44no—
225#13050578—44no—
226#13050578—44no—
227#13050578—44no—
228#13050577—44no—
229#13050575—44no—
230C2×C83⋊C8—22no—
231C2×C83⋊C8—22no—
232C2×C83⋊C8—22no—
233C2×C83⋊C8—22no—
234C2×C83⋊C8C2412yes—
235C2×C83⋊C8C2412yes—
236C2×C83⋊C8C2412yes—
237C2×C83⋊C8C2412yes—
238C4⋊Dic83—24no—
239C4⋊Dic83—24no—
240C4⋊Dic83—24no—
241C4⋊Dic83—24no—
242(C2×D83)⋊C4—24no—
243(C2×D83)⋊C4—24no—
244(C2×D83)⋊C4—24no—
245(C2×D83)⋊C4—24no—
246C24×C83—21no—
247C24×C83C2×D411yescharacteristic
248C2×Q8×C83—21no—
249C2×Q8×C83—24no—
250C2×Q8×C83—22no—
251C2×Q8×C83—22no—
252C2×Q8×C83—82no—
253C2×Q8×C83C2412yes—
254C2×D4×C83—24no—
255C2×D4×C83—21no—
256C2×D4×C83—22no—
257C2×D4×C83—22no—
258C2×D4×C83—82no—
259C2×D4×C83C2412yes—
260C22×C4×C83—22no—
261C22×C4×C83—22no—
262C22×C4×C83—21no—
263C22×C4×C83—21no—
264C22×C4×C83—21no—
265C22×C4×C83—24no—
266C22×C4×C83—82no—
267C22×C4×C83C2×D411yescharacteristic
268C22×C4×C83C2×D412yes—
269C22×C4×C83C2×D411yescharacteristic
270C22×C4×C83C2×D411yescharacteristic
271C22×C4×C83C2×D411yescharacteristic
272C22×C4×C83C2×D411yescharacteristic
273C22×C4×C83C2412yes—
274C22×C4×C83C2411yescharacteristic
275C4⋊C4×C83—24no—
276C4⋊C4×C83—24no—
277C4⋊C4×C83—24no—
278C4⋊C4×C83—21no—
279C4⋊C4×C83—21no—
280C4⋊C4×C83C2×D414yes—
281C4⋊C4×C83C2×D414yes—
282C4⋊C4×C83C2412yes—
283C4⋊C4×C83C2412yes—
284C22⋊C4×C83—24no—
285C22⋊C4×C83—24no—
286C22⋊C4×C83—24no—
287C22⋊C4×C83—24no—
288C22⋊C4×C83—24no—
289C22⋊C4×C83C2×D414yes—
290C22⋊C4×C83C2×D414yes—
291C42×C83—24no—
292C42×C83C2×D412yes—
293C42×C83C2×D412yes—
294C42×C83C2412yes—
295C42×C83C2412yes—
296C23×C83—22no—
297C23×C83—22no—
298C23×C83—22no—
299C23×C83—22no—
300C23×C83—42no—
301C23×C83—42no—
302C23×C83—42no—
303C23×C83C22×D412yes—
304C23×C83C22×D411yescharacteristic
305C22×D83—22no—
306C22×D83—42no—
307C22×D83—42no—
308C22×D83—42no—
309Q8×C83—22no—
310Q8×C83—22no—
311Q8×C83—42no—
312Q8×C83—84no—
313D4×C83—22no—
314D4×C83—22no—
315D4×C83—42no—
316D4×C83—84no—
317C2×C4×C83—22no—
318C2×C4×C83—22no—
319C2×C4×C83—22no—
320C2×C4×C83—22no—
321C2×C4×C83—22no—
322C2×C4×C83—24no—
323C2×C4×C83—22no—
324C2×C4×C83—22no—
325C2×C4×C83—22no—
326C2×C4×C83—22no—
327C2×C4×C83—22no—
328C2×C4×C83—42no—
329C2×C4×C83—42no—
330C2×C4×C83—42no—
331C2×C4×C83—84no—
332C2×C4×C83C22×D412yes—
333C2×C4×C83C22×D412yes—
334C2×C4×C83C22×D412yes—
335C2×C4×C83C22×D412yes—
336C2×C4×C83C22×D412yes—
337C2×C4×C83C22×D411yescharacteristic
338C2×C4×C83H(5,𝔽2)12yes—
339C2×C4×C83H(5,𝔽2)12yes—
340C2×C4×C83C2511yescharacteristic
341C22⋊D83—48no—
342C2×Dic83—22no—
343C2×Dic83—22no—
344C2×Dic83—22no—
345C2×Dic83—48no—
346C2×Dic83—42no—
347C2×Dic83—42no—
348C2×Dic83—42no—
349D332—22no—
350D332—22no—
351D332—42no—
352C4×D83—48no—
353Dic166—22no—
354Dic166—22no—
355Dic166—22no—
356Dic166—22no—
357Dic166—22no—
358Dic166—22no—
359Dic166—48no—
360Dic166—42no—
361Dic166—42no—
362Dic166—42no—
363C83⋊C8—22no—
364C83⋊C8—22no—
365C83⋊C8—22no—
366C83⋊C8—22no—
367C22×C83—22no—
368C22×C83—22no—
369C22×C83—22no—
370C22×C83—44no—
371C22×C83—42no—
372C22×C83—42no—
373C22×C83—42no—
374C22×C83—84no—
375C22×C83#53512yes—
376C22×C83#57712yes—
377C22×C83#57812yes—
378C22×C83C23×D411yescharacteristic
379C2×D83—42no—
380C2×D83—42no—
381C2×D83—42no—
382C2×D83—84no—
383C4×C83—22no—
384C4×C83—22no—
385C4×C83—22no—
386C4×C83—22no—
387C4×C83—22no—
388C4×C83—42no—
389C4×C83—42no—
390C4×C83—42no—
391C4×C83#53512yes—
392C4×C83C2×H(5,𝔽2)11yescharacteristic
393C4×C83C2×H(5,𝔽2)11yescharacteristic
394Dic83—42no—
395Dic83—42no—
396Dic83—42no—
397C2×#3225—831nomaximal, Sylow
398C2×C83—42no—
399C2×C83—82no—
400C2×C83#322514yescomplemented
401C2×C83C2×#53511yescharacteristic
402C2×C83C2×#57711yescharacteristic
403C2×C83C2×#57811yescharacteristic
404D83—82no—
405C2×#542D8311yescharacteristic, complemented
406C2×#536—831no—
407#3225—8316no—
408C2×#497—831no—
409C2×#495—831no—
410C2×#489—831no—
411C2×#487—831no—
412C2×#464—831no—
413C2×#462—831no—
414C2×#463—831no—
415C2×#461—831no—
416C2×#452—831no—
417C2×#449—831no—
418C2×#451—831no—
419C2×#448—831no—
420C2×#433—831no—
421C83C2×#322511yescharacteristic, complemented, Sylow
422C22×#41—831no—
423C23×Q8—831no—
424C22×Q16—831no—
425C22×Q16—831no—
426C22×Q16—831no—
427C22×SD16—831no—
428C22×SD16—831no—
429C22×SD16—831no—
430C22×SD16—831no—
431C22×D8—831no—
432#542—24no—
433#542C2×D8318yescomplemented
434#536—838no—
435#536—1664no—
436C2×C4⋊Q8—831no—
437C2×C4⋊Q8—831no—
438C2×C4⋊Q8C2×D8311yescharacteristic
439C2×#126—21no—
440C2×#124—21no—
441C2×#124—831no—
442C2×#124—831no—
443C2×#124C2×D8311yescharacteristic
444C2×#123—21no—
445C2×#123—1661no—
446C2×#123—1661no—
447C2×C22⋊Q8—21no—
448C2×C22⋊Q8—1661no—
449C2×C22⋊Q8—1661no—
450C2×C22⋊Q8C2×D8311yescharacteristic
451C2×#121C2×D8311yescharacteristic
452C2×C4×Q8C2×D8311yescharacteristic
453C2×C4×D4C2×D8311yescharacteristic
454C2×#117C2×D8311yescharacteristic
455#497—838no—
456#495—838no—
457#489—838no—
458#487—838no—
459#464—838no—
460#463—838no—
461#462—838no—
462#461—838no—
463#452—838no—
464#451—838no—
465#449—838no—
466#448—838no—
467#433—838no—
468C2×C4⋊C8—831no—
469C2×C4⋊C8—831no—
470C2×#103—831no—
471C2×#103—831no—
472C2×#103—831no—
473C2×#103—831no—
474C2×#103—831no—
475C2×#103—831no—
476C2×#102—831no—
477C2×#102—831no—
478C2×C22⋊C8—831no—
479C2×C22⋊C8—831no—
480C2×#97—831no—
481C2×C4×C8—831no—
482C2×#41—3322no—
483C2×#41—3322no—
484C2×#41—834no—
485C2×#41—1662no—
486C22×Q8—21no—
487C22×Q8—3322no—
488C22×Q8—3322no—
489C22×Q8—834no—
490C22×Q8—831no—
491C22×Q8—831no—
492C22×Q8—831no—
493C22×Q8—1661no—
494C22×Q8—1662no—
495C22×Q8C22×D8311yescharacteristic
496C22×D4—21no—
497C22×D4—831no—
498C22×D4—1661no—
499C22×D4C22×D8311yescharacteristic
500C23×C4—21no—
501C23×C4—1661no—
502C23×C4—1661no—
503C23×C4C22×D8311yescharacteristic
504C2×Q16—3322no—
505C2×Q16—3322no—
506C2×Q16—3322no—
507C2×Q16—834no—
508C2×Q16—834no—
509C2×Q16—834no—
510C2×SD16—3322no—
511C2×SD16—3322no—
512C2×SD16—3322no—
513C2×SD16—3322no—
514C2×SD16—834no—
515C2×SD16—834no—
516C2×SD16—834no—
517C2×SD16—834no—
518C2×D8—3322no—
519C2×D8—834no—
520C22×C8—831no—
521C22×C8—831no—
522C22×C8—831no—
523C22×C8—831no—
524C4⋊Q8—22no—
525C4⋊Q8—834no—
526C4⋊Q8—834no—
527C4⋊Q8—1662no—
528C4⋊Q8—1662no—
529C4⋊Q8C22×D8314yes—
530#126—28no—
531#124—28no—
532#124—22no—
533#124—834no—
534#124—834no—
535#124—1662no—
536#124—1662no—
537#124C22×D8314yes—
538#123—28no—
539#123—1668no—
540#123—1668no—
541C22⋊Q8—22no—
542C22⋊Q8—28no—
543C22⋊Q8—1668no—
544C22⋊Q8—1668no—
545C22⋊Q8C22×D8314yes—
546#121—22no—
547#121C22×D8314yes—
548C4×Q8—22no—
549C4×Q8C22×D8314yes—
550C4×D4—22no—
551C4×D4C22×D8314yes—
552#117C22⋊D8314yes—
553#117C22×D8314yes—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—1661no—
558C2×C4⋊C4—1661no—
559C2×C4⋊C4—1661no—
560C2×C4⋊C4—1661no—
561C2×C4⋊C4C22⋊D8311yescharacteristic
562C2×C4⋊C4C22⋊D8311yescharacteristic
563C2×C4⋊C4C22×D8311yescharacteristic
564C2×C4⋊C4C22×D8311yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—1661no—
571C2×C22⋊C4—1661no—
572C2×C22⋊C4—1661no—
573C2×C22⋊C4—1661no—
574C2×C22⋊C4C22⋊D8311yescharacteristic
575C2×C22⋊C4C22⋊D8311yescharacteristic
576C2×C42—21no—
577C2×C42C22×D8311yescharacteristic
578C2×C42C22×D8311yescharacteristic
579C4⋊C8—834no—
580C4⋊C8—834no—
581#103—834no—
582#103—834no—
583#103—834no—
584#103—834no—
585#103—834no—
586#103—834no—
587#102—834no—
588#102—834no—
589C22⋊C8—834no—
590C22⋊C8—834no—
591#97—834no—
592C4×C8—834no—
593C24—21no—
594C24—1661no—
595C24C2×C22⋊D8311yescharacteristic
596#41—3328no—
597#41—3324no—
598#41—3324no—
599C2×Q8—21no—
600C2×Q8—24no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—82no—
604C2×Q8—3324no—
605C2×Q8—3328no—
606C2×Q8—3324no—
607C2×Q8—3324no—
608C2×Q8—832no—
609C2×Q8—832no—
610C2×Q8—832no—
611C2×Q8—1662no—
612C2×Q8—1662no—
613C2×Q8—1662no—
614C2×Q8—1662no—
615C2×Q8—1662no—
616C2×Q8—1662no—
617C2×Q8—1664no—
618C2×Q8—1661no—
619C2×Q8—1661no—
620C2×Q8—1661no—
621C2×Q8C23×D8312yes—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—82no—
627C2×D4—3324no—
628C2×D4—832no—
629C2×D4—1664no—
630C2×D4—1661no—
631C2×D4—1662no—
632C2×D4—1662no—
633C2×D4C23×D8312yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—82no—
641C22×C4—3324no—
642C22×C4—3324no—
643C22×C4—1664no—
644C22×C4—1661no—
645C22×C4—1661no—
646C22×C4—1661no—
647C22×C4—1664no—
648C22×C4C2×C22⋊D8312yes—
649C22×C4C2×C22⋊D8311yescharacteristic
650C22×C4C2×C22⋊D8311yescharacteristic
651C22×C4C2×C22⋊D8311yescharacteristic
652C22×C4C2×C22⋊D8311yescharacteristic
653C22×C4C2×C22⋊D8311yescharacteristic
654C22×C4C23×D8312yes—
655C22×C4C23×D8311yescharacteristic
656Q16—3324no—
657Q16—3324no—
658Q16—3324no—
659SD16—3324no—
660SD16—3324no—
661SD16—3324no—
662SD16—3324no—
663D8—3324no—
664C2×C8—832no—
665C2×C8—832no—
666C2×C8—832no—
667C2×C8—832no—
668C2×C8—1662no—
669C2×C8—1662no—
670C2×C8—1662no—
671C2×C8—1662no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—1664no—
678C4⋊C4—1664no—
679C4⋊C4—1664no—
680C4⋊C4—1664no—
681C4⋊C4C2×C22⋊D8314yes—
682C4⋊C4C2×C22⋊D8314yes—
683C4⋊C4C23×D8312yes—
684C4⋊C4C23×D8312yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—1664no—
691C22⋊C4—1664no—
692C22⋊C4—1664no—
693C22⋊C4—1664no—
694C22⋊C4C2×C22⋊D8314yes—
695C22⋊C4C2×C22⋊D8314yes—
696C42—24no—
697C42C2×C22⋊D8312yes—
698C42C2×C22⋊D8312yes—
699C42C23×D8312yes—
700C42C23×D8312yes—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—3322no—
709C23—3322no—
710C23—3322no—
711C23—1662no—
712C23C22×C22⋊D8312yes—
713C23C22×C22⋊D8311yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—84no—
718Q8—3328no—
719Q8—3322no—
720Q8—3322no—
721Q8—3322no—
722Q8—1662no—
723Q8—1662no—
724Q8—1662no—
725Q8—1662no—
726Q8—1662no—
727Q8—1662no—
728D4—22no—
729D4—22no—
730D4—42no—
731D4—84no—
732D4—3328no—
733D4—3322no—
734D4—1662no—
735D4—1662no—
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—3328no—
752C2×C4—3328no—
753C2×C4—3322no—
754C2×C4—3322no—
755C2×C4—3322no—
756C2×C4—1662no—
757C2×C4—1662no—
758C2×C4—1662no—
759C2×C4C22×C22⋊D8312yes—
760C2×C4C22×C22⋊D8312yes—
761C2×C4C22×C22⋊D8312yes—
762C2×C4C22×C22⋊D8312yes—
763C2×C4C22×C22⋊D8312yes—
764C2×C4C22×C22⋊D8311yescharacteristic
765C2×C4#1458183812yes—
766C2×C4#1458183812yes—
767C2×C4C24×D8311yescharacteristic
768C8—1662no—
769C8—1662no—
770C8—1662no—
771C8—1662no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—84no—
780C22—3322no—
781C22—3322no—
782C22—3322no—
783C22—6644no—
784C22#1912826512yes—
785C22#1912851212yes—
786C22#1912851612yes—
787C22C23×C22⋊D8311yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—3322no—
797C4—3322no—
798C4—3322no—
799C4#1912826512yes—
800C4C2×#1458183811yescharacteristic
801C4C2×#1458183811yescharacteristic
802C2—42no—
803C2—82no—
804C2—6642no—
805C2#2491856614yesdirect product factor
806C2C2×#1912826511yescharacteristic
807C2C2×#1912851211yescharacteristic
808C2C2×#1912851611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#542×C83C2
socleC23×C83C22×D4
prime radicalC2×#19127844C2
hypercenterC2×#542D83
hypocenterC83C2×#3225
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#19128277C2semidirect
2. #24918566C2direct (N × H)
3. C2×#19128096C2semidirect
4. C2×#19128083C2semidirect
5. C2×#19128063C2semidirect
6. C2×#19128053C2semidirect
7. C2×#19127923C2semidirect
8. C2×#19127911C2semidirect
9. C2×#19127916C2semidirect
10. C2×#19127906C2semidirect
11. C2×#19127861C2semidirect
13. C2×#19127856C2semidirect
14. C2×#19127839C2semidirect
15. C2×#19127762C2semidirect
16. C2×#542×C83C2semidirect
28. #19128277C22semidirect
37. #19128096C22semidirect
38. #19128083C22semidirect
39. #19128063C22semidirect
40. #19128053C22semidirect
41. #19127923C22semidirect
42. #19127916C22semidirect
43. #19127911C22semidirect
44. #19127906C22semidirect
45. #19127861C22semidirect
46. #19127856C22semidirect
48. #19127839C22semidirect
49. #19127762C22semidirect
65. #542×C83C22semidirect
400. C2×C83#3225semidirect
405. C2×#542D83semidirect
421. C83C2×#3225semidirect
433. #542C2×D83semidirect
805. C2#24918566direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191282772
#249185662
C2×#191280962
C2×#191280832
C2×#191280632
C2×#191280532
C2×#191279232
C2×#191279112
C2×#191279162
C2×#191279062
C2×#191278612
C2×#191278442
C2×#191278562
C2×#191278392
C2×#191277622
C2×#542×C832
C2×#322583