Finite Group Databasebeta

← C2×#24919294 #36280751

Subgroups — C2×#24919294 #36280751

Order 21248.

2286 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128386C211yesmaximal, characteristic, complemented
2C2×#19128345C211yesmaximal, characteristic
3#24919294C2116yesmaximal, direct product factor
4C2×#19128054C211yesmaximal, characteristic, complemented
5C2×#19128023C211yesmaximal, characteristic, complemented
6C2×#19128031C211yesmaximal, characteristic, complemented
7C2×#19127999C211yesmaximal, characteristic, complemented
8C2×#19127942C211yesmaximal, characteristic, complemented
9C2×#19127929C211yesmaximal, characteristic, complemented
10C2×#19127922C211yesmaximal, characteristic, complemented
11C2×#19127864C211yesmaximal, characteristic, complemented
12C2×#19127852C211yesmaximal, characteristic, complemented
13C2×#19127792C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D83C211yesmaximal, characteristic, complemented
15C2×#19127694C211yesmaximal, characteristic, complemented
16C22×#102×C83C211yesmaximal, characteristic, complemented
17C22×#13050589C2211yescharacteristic
18C22×Dic332C2211yescharacteristic, complemented
19C22×#13050578C2211yescharacteristic
20C22×#13050578C2211yescharacteristic
21C22×C8×D83C2211yescharacteristic, complemented
22#19128386—24no—
23#19128386C2218yescomplemented
24#19128345—24no—
25#19128345C2218yes—
26C2×#14581787—21no—
27C2×#14581783C2211yescharacteristic, complemented
28C2×#14581782—21no—
29C2×#14581779C2211yescharacteristic
30C2×#14581775—21no—
31C2×#14581773—21no—
32C2×#14581772C2211yescharacteristic, complemented
33C2×#14581771C2211yescharacteristic
34C2×#14581771C2211yescharacteristic
35C2×#14581764—21no—
36C2×#14581763C2211yescharacteristic
37C2×#14581761—21no—
38C2×#14581757C2211yescharacteristic, complemented
39C2×D4×Dic83C2211yescharacteristic
40C2×C4×C22⋊D83C2211yescharacteristic
41C2×#14581751—21no—
42C2×#14581750C2211yescharacteristic, complemented
43C22×C22⋊Dic83—21no—
44#19128054C2218yescomplemented
45#19128031C2218yescomplemented
46#19128023C2218yescomplemented
47#19127999C2218yescomplemented
48#19127942C2218yescomplemented
49#19127929C2218yescomplemented
50#19127922C2218yescomplemented
51#19127864C2218yescomplemented
52#19127852C2218yescomplemented
53#19127792C2218yescomplemented
54C8×C22⋊D83C2218yescomplemented
55C2×#14581726C2211yescharacteristic, complemented
56C2×#14581723C2211yescharacteristic, complemented
57C2×#14581723C2211yescharacteristic, complemented
58C2×Dic83⋊C8C2211yescharacteristic, complemented
59#19127694C2218yescomplemented
60C2×#14581717C2211yescharacteristic, complemented
61C2×#14581717C2211yescharacteristic, complemented
62C2×#14581715C2211yescharacteristic, complemented
63C2×#14581715C2211yescharacteristic, complemented
64C2×#14581713C2211yescharacteristic
65C2×#14581713C2211yescharacteristic
66C2×C22⋊(C83⋊C8)C2211yescharacteristic
67C2×(C2×D83)⋊C8C2211yescharacteristic, complemented
68C2×C8×Dic83C2211yescharacteristic, complemented
69C23×D4×C83C2211yescharacteristic
70C23×C8×C83C2211yescharacteristic
71C22×C4⋊C4×C83C2211yescharacteristic
72C2×#102×C83C2211yescharacteristic
73C2×#102×C83C2211yescharacteristic
74C2×#102×C83C2211yescharacteristic
75C2×#102×C83C2211yescharacteristic
76C2×#102×C83C2218yescomplemented
77C2×#13050589—22no—
78C2×#13050589—24no—
79C2×#13050589—42no—
80C2×#13050589C2314yes—
81C22×Dic166C2311yescharacteristic
82C22×Dic166C2311yescharacteristic
83C22×C22⋊D83—21no—
84C22×C22⋊D83—21no—
85C22×C22⋊D83D411yescharacteristic
86C23×Dic83—21no—
87C23×Dic83—21no—
88C22×C4×D83C2311yescharacteristic
89C2×Dic332—42no—
90C2×Dic332C2314yescomplemented
91C2×#13050578—24no—
92C2×#13050578—42no—
93C2×#13050578C2314yes—
94C2×#13050578C2314yes—
95C22×C83⋊C8C2311yescharacteristic
96C22×C83⋊C8C2311yescharacteristic
97C2×C8×D83—42no—
98C2×C8×D83C2314yescomplemented
99#14581787—28no—
100#14581783—22no—
101#14581783C2314yescomplemented
102#14581782—28no—
103#14581779—22no—
104#14581779C2314yes—
105#14581775—28no—
106#14581773—28no—
107#14581772—22no—
108#14581772C2314yescomplemented
109#14581771—22no—
110#14581771—22no—
111#14581771C2314yes—
112#14581771C2314yes—
113#14581764—28no—
114#14581763—22no—
115#14581763C2314yes—
116#14581761—28no—
117#14581757—22no—
118#14581757C2314yescomplemented
119D4×Dic83—22no—
120D4×Dic83C2314yes—
121C4×C22⋊D83D414yes—
122C4×C22⋊D83C2314yes—
123#14581751—28no—
124#14581750—22no—
125#14581750C2314yescomplemented
126C2×C4⋊Dic83—21no—
127C2×C4⋊Dic83—21no—
128C2×C4⋊Dic83C2311yescharacteristic
129C2×C4⋊Dic83C2311yescharacteristic
130C2×Dic83⋊C4—21no—
131C2×Dic83⋊C4—21no—
132C2×Dic83⋊C4—21no—
133C2×Dic83⋊C4—21no—
134C2×Dic83⋊C4D411yescharacteristic
135C2×C22⋊Dic83—21no—
136C2×C22⋊Dic83—21no—
137C2×C22⋊Dic83—21no—
138C2×C22⋊Dic83—21no—
139C2×C22⋊Dic83—28no—
140C2×C22⋊Dic83—21no—
141C2×C22⋊Dic83—21no—
142C2×C22⋊Dic83D411yescharacteristic
143C2×(C2×D83)⋊C4—21no—
144C2×(C2×D83)⋊C4—21no—
145C2×(C2×D83)⋊C4D411yescharacteristic
146C2×C4×Dic83—21no—
147C2×C4×Dic83—21no—
148C2×C4×Dic83C2311yescharacteristic
149#14581726C2314yescomplemented
150#14581723C2314yescomplemented
151#14581723C2314yescomplemented
152Dic83⋊C8C2314yescomplemented
153#14581717C2314yescomplemented
154#14581717C2314yescomplemented
155#14581715C2314yescomplemented
156#14581715C2314yescomplemented
157#14581713C2314yes—
158#14581713C2314yes—
159C22⋊(C83⋊C8)C2314yes—
160(C2×D83)⋊C8C2314yescomplemented
161C8×Dic83C2314yescomplemented
162C25×C83—21no—
163C22×D4×C83—24no—
164C22×D4×C83—22no—
165C22×D4×C83—21no—
166C22×D4×C83—42no—
167C22×D4×C83C2311yescharacteristic
168C22×D4×C83C2314yes—
169C22×D4×C83C2311yescharacteristic
170C23×C4×C83—21no—
171C23×C4×C83C2311yescharacteristic
172C22×C8×C83—42no—
173C22×C8×C83C2311yescharacteristic
174C22×C8×C83C2311yescharacteristic
175C22×C8×C83C2314yes—
176C2×C4⋊C4×C83—22no—
177C2×C4⋊C4×C83—21no—
178C2×C4⋊C4×C83C2314yes—
179C2×C4⋊C4×C83C2311yescharacteristic
180C2×C4⋊C4×C83C2311yescharacteristic
181#102×C83C2314yes—
182#102×C83C2314yes—
183#102×C83C2314yes—
184#102×C83C2314yes—
185C23×D83C2×D411yescharacteristic
186#13050589—28no—
187#13050589—44no—
188#13050589—48no—
189C2×Dic166—22no—
190C2×Dic166—22no—
191C2×Dic166—22no—
192C2×Dic166—22no—
193C2×Dic166—21no—
194C2×Dic166—21no—
195C2×Dic166C2412yes—
196C2×Dic166C2412yes—
197C2×C22⋊D83—24no—
198C2×C22⋊D83—24no—
199C2×C22⋊D83—24no—
200C2×C22⋊D83—44no—
201C2×C22⋊D83—82no—
202C2×C22⋊D83C2×D414yes—
203C22×Dic83—21no—
204C22×Dic83—21no—
205C22×Dic83—21no—
206C22×Dic83—21no—
207C22×Dic83—24no—
208C22×Dic83—24no—
209C22×Dic83—44no—
210C22×Dic83—82no—
211C22×Dic83C2×D411yescharacteristic
212C22×Dic83C2×D411yescharacteristic
213C22×Dic83C2×D411yescharacteristic
214C2×C4×D83—22no—
215C2×C4×D83—22no—
216C2×C4×D83C2×D412yes—
217C2×C4×D83C2412yes—
218Dic332—44no—
219#13050578—28no—
220#13050578—44no—
221C2×C83⋊C8—22no—
222C2×C83⋊C8—22no—
223C2×C83⋊C8C2412yes—
224C2×C83⋊C8C2412yes—
225C8×D83—44no—
226C4⋊Dic83—21no—
227C4⋊Dic83—21no—
228C4⋊Dic83—24no—
229C4⋊Dic83—24no—
230C4⋊Dic83C2412yes—
231C4⋊Dic83C2412yes—
232Dic83⋊C4—24no—
233Dic83⋊C4—24no—
234Dic83⋊C4—24no—
235Dic83⋊C4—24no—
236Dic83⋊C4C2×D414yes—
237C22⋊Dic83—24no—
238C22⋊Dic83—24no—
239C22⋊Dic83—24no—
240C22⋊Dic83—24no—
241C22⋊Dic83—24no—
242C22⋊Dic83—24no—
243C22⋊Dic83C2×D414yes—
244(C2×D83)⋊C4—24no—
245(C2×D83)⋊C4—24no—
246(C2×D83)⋊C4C2×D414yes—
247C4×Dic83—24no—
248C4×Dic83—24no—
249C4×Dic83C2×D412yes—
250C4×Dic83C2412yes—
251C24×C83—21no—
252C24×C83—21no—
253C24×C83—24no—
254C24×C83—44no—
255C24×C83—44no—
256C24×C83—82no—
257C24×C83C2×D411yescharacteristic
258C2×D4×C83—28no—
259C2×D4×C83—21no—
260C2×D4×C83—21no—
261C2×D4×C83—24no—
262C2×D4×C83—22no—
263C2×D4×C83—22no—
264C2×D4×C83—22no—
265C2×D4×C83—44no—
266C2×D4×C83—48no—
267C2×D4×C83—44no—
268C2×D4×C83#4114yes—
269C2×D4×C83C2412yes—
270C2×D4×C83C2412yes—
271C22×C4×C83—22no—
272C22×C4×C83—22no—
273C22×C4×C83—24no—
274C22×C4×C83—21no—
275C22×C4×C83—21no—
276C22×C4×C83—44no—
277C22×C4×C83C2×D412yes—
278C22×C4×C83C2×D411yescharacteristic
279C22×C4×C83C2412yes—
280C22×C4×C83C2411yescharacteristic
281C2×C8×C83—22no—
282C2×C8×C83—22no—
283C2×C8×C83—44no—
284C2×C8×C83C2412yes—
285C2×C8×C83C2412yes—
286C4⋊C4×C83—21no—
287C4⋊C4×C83—24no—
288C4⋊C4×C83—21no—
289C4⋊C4×C83C2412yes—
290C4⋊C4×C83C2412yes—
291C23×C83—22no—
292C23×C83—22no—
293C23×C83—24no—
294C23×C83—22no—
295C23×C83—22no—
296C23×C83—48no—
297C23×C83—42no—
298C23×C83—42no—
299C23×C83—42no—
300C23×C83—48no—
301C23×C83—42no—
302C23×C83—42no—
303C23×C83—84no—
304C23×C83—816no—
305C23×C83#13514yes—
306C23×C83C22×D412yes—
307C23×C83C22×D411yescharacteristic
308C22×D83—22no—
309C22×D83—22no—
310C22×D83—22no—
311C22×D83C22×D412yes—
312D4×C83—24no—
313D4×C83—22no—
314D4×C83—22no—
315D4×C83—22no—
316D4×C83—48no—
317D4×C83—42no—
318D4×C83C2×#4114yes—
319C2×C4×C83—22no—
320C2×C4×C83—24no—
321C2×C4×C83—22no—
322C2×C4×C83—22no—
323C2×C4×C83—22no—
324C2×C4×C83—22no—
325C2×C4×C83—48no—
326C2×C4×C83—42no—
327C2×C4×C83—42no—
328C2×C4×C83C22×D412yes—
329C2×C4×C83C22×D411yescharacteristic
330C2×C4×C83C2×#4112yes—
331C2×C4×C83H(5,𝔽2)12yes—
332C2×C4×C83C2511yescharacteristic
333C22⋊D83—28no—
334C22⋊D83—48no—
335C22⋊D83—84no—
336C2×Dic83—22no—
337C2×Dic83—22no—
338C2×Dic83—22no—
339C2×Dic83—22no—
340C2×Dic83—22no—
341C2×Dic83—22no—
342C2×Dic83—22no—
343C2×Dic83—48no—
344C2×Dic83—42no—
345C2×Dic83—42no—
346C2×Dic83—42no—
347C2×Dic83—42no—
348C2×Dic83—84no—
349C2×Dic83C22×D412yes—
350C2×Dic83C22×D412yes—
351C2×Dic83C22×D412yes—
352C4×D83—24no—
353C4×D83—22no—
354C4×D83—22no—
355Dic166—22no—
356Dic166—22no—
357Dic166—22no—
358Dic166—22no—
359Dic166—42no—
360Dic166—42no—
361C8×C83—22no—
362C8×C83—22no—
363C83⋊C8—22no—
364C83⋊C8—22no—
365C22×C83—22no—
366C22×C83—28no—
367C22×C83—22no—
368C22×C83—24no—
369C22×C83—48no—
370C22×C83—42no—
371C22×C83—42no—
372C22×C83—42no—
373C22×C83—42no—
374C22×C83—42no—
375C22×C83—816no—
376C22×C83—84no—
377C22×C83#54612yes—
378C22×C83C2×#13514yes—
379C22×C83C2×#13512yes—
380C22×C83#57712yes—
381C22×C83C23×D411yescharacteristic
382C2×D83—22no—
383C2×D83—22no—
384C2×D83—22no—
385C2×D83—44no—
386C4×C83—22no—
387C4×C83—42no—
388C4×C83—42no—
389C4×C83#54612yes—
390C4×C83C22×#4111yescharacteristic
391C4×C83C2×H(5,𝔽2)11yescharacteristic
392Dic83—22no—
393Dic83—22no—
394Dic83—22no—
395Dic83—42no—
396Dic83—42no—
397Dic83—42no—
398Dic83—42no—
399C2×#3296—831nomaximal, Sylow
400C2×C83—24no—
401C2×C83—44no—
402C2×C83—82no—
403C2×C83#329614yescomplemented
404C2×C83C2×#54611yescharacteristic
405C2×C83C22×#13511yescharacteristic
406C2×C83C2×#57711yescharacteristic
407D83—42no—
408C2×#552—831no—
409C2×#546—831no—
410#3296—8316no—
411C2×#488—831no—
412C2×#482—831no—
413C2×#483—831no—
414C2×#478—831no—
415C2×#467—831no—
416C2×#465—831no—
417C2×#464—831no—
418C2×#452—831no—
419C2×#450—831no—
420C2×C4×SD16—831no—
421C2×C8×D4—831no—
422C2×#416—831no—
423C22×#102D8311yescharacteristic, complemented
424C83C2×#329611yescharacteristic, complemented, Sylow
425C22×#41—831no—
426C23×D4C2×D8311yescharacteristic
427C22×Q16—831no—
428C22×SD16—831no—
429C22×SD16—831no—
430C23×C8—831no—
431C23×C8C2×D8311yescharacteristic
432#552—838no—
433#552—1664no—
434#546—838no—
435#546—1664no—
436C2×#126—1661no—
437C2×#125—831no—
438C2×#125—1661no—
439C2×#124—831no—
440C2×#123—1661no—
441C2×#123—1661no—
442C2×C22⋊Q8—831no—
443C2×C22⋊Q8—831no—
444C2×C22⋊Q8—831no—
445C2×#121—831no—
446C2×#121—1661no—
447C2×#120—1661no—
448C2×C4×Q8—831no—
449C2×C4×D4—831no—
450C2×C4×D4—831no—
451C2×#117—831no—
452C2×#117—1661no—
453C22×C4⋊C4C2×D8311yescharacteristic
454C22×C22⋊C4—1661no—
455#488—838no—
456#483—838no—
457#482—838no—
458#478—838no—
459#467—838no—
460#465—838no—
461#464—838no—
462#452—838no—
463#450—838no—
464C4×SD16—838no—
465C8×D4—838no—
466C2×#107—831no—
467C2×#106—831no—
468C2×#106—831no—
469C2×C4⋊C8—831no—
470#416—838no—
471C2×#103—831no—
472C2×#103—831no—
473C2×#103—831no—
474C2×#103—831no—
475C2×#102—831no—
476C2×#102—831no—
477C2×#102C2×D8311yescharacteristic
478C2×#102C2×D8311yescharacteristic
479C2×#102C2×D8311yescharacteristic
480C2×#102C2×D8311yescharacteristic
481C2×#102C2×D8318yescomplemented
482C2×C22⋊C8—831no—
483C2×C22⋊C8—831no—
484C2×C4×C8—831no—
485C25—21no—
486C2×#41—3322no—
487C2×#41—834no—
488C2×#41—1664no—
489C2×#41—1662no—
490C22×Q8—831no—
491C22×Q8—831no—
492C22×D4—24no—
493C22×D4—21no—
494C22×D4—22no—
495C22×D4—42no—
496C22×D4—831no—
497C22×D4—1661no—
498C22×D4—1661no—
499C22×D4C22×D8311yescharacteristic
500C22×D4C22×D8314yes—
501C22×D4C22×D8311yescharacteristic
502C23×C4—21no—
503C23×C4—831no—
504C23×C4—1661no—
505C23×C4—1661no—
506C23×C4C22×D8311yescharacteristic
507C2×Q16—3322no—
508C2×Q16—834no—
509C2×SD16—3322no—
510C2×SD16—834no—
511C2×SD16—834no—
512C2×SD16—1664no—
513C22×C8—42no—
514C22×C8—3322no—
515C22×C8—834no—
516C22×C8—831no—
517C22×C8—831no—
518C22×C8C22×D8311yescharacteristic
519C22×C8C22×D8311yescharacteristic
520C22×C8C22×D8314yes—
521#126—1668no—
522#125—834no—
523#125—1662no—
524#125—1668no—
525#124—834no—
526#124—1662no—
527#123—1668no—
528#123—1668no—
529C22⋊Q8—834no—
530C22⋊Q8—834no—
531C22⋊Q8—834no—
532C22⋊Q8—1662no—
533C22⋊Q8—1662no—
534C22⋊Q8—1662no—
535#121—834no—
536#121—1668no—
537#121—1662no—
538#120—1668no—
539C4×Q8—834no—
540C4×Q8—1662no—
541C4×D4—834no—
542C4×D4—834no—
543C4×D4—834no—
544C4×D4—1662no—
545#117—834no—
546#117—1668no—
547#117—1662no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—831no—
551C2×C4⋊C4—831no—
552C2×C4⋊C4—831no—
553C2×C4⋊C4—1661no—
554C2×C4⋊C4—1661no—
555C2×C4⋊C4—1661no—
556C2×C4⋊C4—1661no—
557C2×C4⋊C4—1661no—
558C2×C4⋊C4—1661no—
559C2×C4⋊C4C22×D8311yescharacteristic
560C2×C4⋊C4C22×D8311yescharacteristic
561C2×C4⋊C4C22×D8314yes—
562C2×C22⋊C4—831no—
563C2×C22⋊C4—831no—
564C2×C22⋊C4—1668no—
565C2×C22⋊C4—1661no—
566C2×C22⋊C4—1661no—
567C2×C22⋊C4—1661no—
568C2×C22⋊C4—1661no—
569C2×C22⋊C4—1661no—
570C2×C22⋊C4—1661no—
571C2×C22⋊C4—1661no—
572C2×C22⋊C4—1661no—
573C2×C42—831no—
574C2×C42—1661no—
575C2×C42—1661no—
576#107—834no—
577#106—834no—
578#106—834no—
579C4⋊C8—834no—
580#103—834no—
581#103—834no—
582#103—834no—
583#103—834no—
584#102—834no—
585#102—834no—
586#102C22×D8314yes—
587#102C22×D8314yes—
588#102C22×D8314yes—
589#102C22×D8314yes—
590C22⋊C8—834no—
591C22⋊C8—834no—
592C4×C8—834no—
593C24—21no—
594C24—21no—
595C24—24no—
596C24—44no—
597C24—44no—
598C24—82no—
599C24—831no—
600C24D4×D8311yescharacteristic
601#41—3328no—
602#41—3324no—
603#41—1668no—
604C2×Q8—832no—
605C2×Q8—832no—
606C2×Q8—1662no—
607C2×Q8—1662no—
608C2×Q8—1662no—
609C2×Q8—1662no—
610C2×Q8—1661no—
611C2×Q8—1661no—
612C2×D4—28no—
613C2×D4—21no—
614C2×D4—24no—
615C2×D4—21no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—44no—
620C2×D4—48no—
621C2×D4—44no—
622C2×D4—3324no—
623C2×D4—834no—
624C2×D4—6642no—
625C2×D4—1664no—
626C2×D4—1664no—
627C2×D4—1664no—
628C2×D4#1305059014yes—
629C2×D4C23×D8312yes—
630C2×D4C23×D8312yes—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—24no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—44no—
637C22×C4—3324no—
638C22×C4—831no—
639C22×C4—831no—
640C22×C4—831no—
641C22×C4—832no—
642C22×C4—832no—
643C22×C4—6642no—
644C22×C4—1664no—
645C22×C4—1661no—
646C22×C4—1661no—
647C22×C4—1661no—
648C22×C4—1661no—
649C22×C4—1664no—
650C22×C4—1662no—
651C22×C4—1662no—
652C22×C4D4×D8312yes—
653C22×C4D4×D8311yescharacteristic
654C22×C4C23×D8312yes—
655C22×C4C23×D8311yescharacteristic
656Q16—3324no—
657SD16—3324no—
658SD16—1668no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—44no—
662C2×C8—3324no—
663C2×C8—832no—
664C2×C8—832no—
665C2×C8—1662no—
666C2×C8—1662no—
667C2×C8C23×D8312yes—
668C2×C8C23×D8312yes—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—834no—
673C4⋊C4—832no—
674C4⋊C4—832no—
675C4⋊C4—1664no—
676C4⋊C4—1664no—
677C4⋊C4—1664no—
678C4⋊C4—1664no—
679C4⋊C4—1661no—
680C4⋊C4—1661no—
681C4⋊C4—1664no—
682C4⋊C4—1664no—
683C4⋊C4C23×D8312yes—
684C4⋊C4C23×D8312yes—
685C22⋊C4—834no—
686C22⋊C4—834no—
687C22⋊C4—1664no—
688C22⋊C4—1664no—
689C22⋊C4—1664no—
690C22⋊C4—1664no—
691C22⋊C4—1664no—
692C22⋊C4—1664no—
693C22⋊C4—1664no—
694C22⋊C4—1664no—
695C42—832no—
696C42—832no—
697C42—1664no—
698C42—1664no—
699C23—22no—
700C23—22no—
701C23—24no—
702C23—22no—
703C23—22no—
704C23—48no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—48no—
709C23—42no—
710C23—42no—
711C23—84no—
712C23—816no—
713C23—832no—
714C23—1662no—
715C23—1662no—
716C23—1662no—
717C23#1458181114yes—
718C23C2×D4×D8312yes—
719C23C2×D4×D8311yescharacteristic
720Q8—3322no—
721Q8—3322no—
722Q8—1662no—
723Q8—1662no—
724Q8—1662no—
725Q8—1662no—
726D4—24no—
727D4—22no—
728D4—22no—
729D4—22no—
730D4—48no—
731D4—42no—
732D4—3328no—
733D4—6644no—
734D4—1668no—
735D4C2×#1305059014yes—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—48no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—3322no—
746C2×C4—3322no—
747C2×C4—3322no—
748C2×C4—3322no—
749C2×C4—3328no—
750C2×C4—832no—
751C2×C4—832no—
752C2×C4—832no—
753C2×C4—6644no—
754C2×C4—1662no—
755C2×C4—1662no—
756C2×C4—1662no—
757C2×C4—1662no—
758C2×C4—1662no—
759C2×C4—1662no—
760C2×C4—1662no—
761C2×C4—1664no—
762C2×C4—1662no—
763C2×C4—1662no—
764C2×C4C2×D4×D8312yes—
765C2×C4C2×D4×D8311yescharacteristic
766C2×C4C2×#1305059012yes—
767C2×C4#1458183712yes—
768C2×C4C24×D8311yescharacteristic
769C8—22no—
770C8—22no—
771C8—1662no—
772C8—1662no—
773C22—22no—
774C22—22no—
775C22—28no—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—48no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—816no—
784C22—84no—
785C22—3324no—
786C22—1662no—
787C22—1662no—
788C22—1662no—
789C22#1912834112yes—
790C22C2×#1458181114yes—
791C22C2×#1458181112yes—
792C22#1912850712yes—
793C22C22×D4×D8311yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—3322no—
798C4—3322no—
799C4—3322no—
800C4—3322no—
801C4—1662no—
802C4—1662no—
803C4—1662no—
804C4#1912834112yes—
805C4C22×#1305059011yescharacteristic
806C4C2×#1458183711yescharacteristic
807C2—24no—
808C2—44no—
809C2—82no—
810C2—3322no—
811C2#2491929414yesdirect product factor
812C2C2×#1912834111yescharacteristic
813C2C22×#1458181111yescharacteristic
814C2C2×#1912850711yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC22×#102×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128345C2
hypercenterC22×#102D83
hypocenterC83C2×#3296
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
1. C2×#19128386C2semidirect
3. #24919294C2direct (N × H)
4. C2×#19128054C2semidirect
5. C2×#19128023C2semidirect
6. C2×#19128031C2semidirect
7. C2×#19127999C2semidirect
8. C2×#19127942C2semidirect
9. C2×#19127929C2semidirect
10. C2×#19127922C2semidirect
11. C2×#19127864C2semidirect
12. C2×#19127852C2semidirect
13. C2×#19127792C2semidirect
14. C2×C8×C22⋊D83C2semidirect
15. C2×#19127694C2semidirect
16. C22×#102×C83C2semidirect
18. C22×Dic332C22semidirect
21. C22×C8×D83C22semidirect
23. #19128386C22semidirect
27. C2×#14581783C22semidirect
32. C2×#14581772C22semidirect
38. C2×#14581757C22semidirect
42. C2×#14581750C22semidirect
44. #19128054C22semidirect
45. #19128031C22semidirect
46. #19128023C22semidirect
47. #19127999C22semidirect
48. #19127942C22semidirect
49. #19127929C22semidirect
50. #19127922C22semidirect
51. #19127864C22semidirect
52. #19127852C22semidirect
53. #19127792C22semidirect
54. C8×C22⋊D83C22semidirect
55. C2×#14581726C22semidirect
56. C2×#14581723C22semidirect
57. C2×#14581723C22semidirect
58. C2×Dic83⋊C8C22semidirect
59. #19127694C22semidirect
60. C2×#14581717C22semidirect
61. C2×#14581717C22semidirect
62. C2×#14581715C22semidirect
63. C2×#14581715C22semidirect
67. C2×(C2×D83)⋊C8C22semidirect
68. C2×C8×Dic83C22semidirect
76. C2×#102×C83C22semidirect
90. C2×Dic332C23semidirect
98. C2×C8×D83C23semidirect
101. #14581783C23semidirect
108. #14581772C23semidirect
118. #14581757C23semidirect
125. #14581750C23semidirect
149. #14581726C23semidirect
150. #14581723C23semidirect
151. #14581723C23semidirect
152. Dic83⋊C8C23semidirect
153. #14581717C23semidirect
154. #14581717C23semidirect
155. #14581715C23semidirect
156. #14581715C23semidirect
160. (C2×D83)⋊C8C23semidirect
161. C8×Dic83C23semidirect
403. C2×C83#3296semidirect
423. C22×#102D83semidirect
424. C83C2×#3296semidirect
481. C2×#102C2×D83semidirect
811. C2#24919294direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283862
C2×#191283452
#249192942
C2×#191280542
C2×#191280232
C2×#191280312
C2×#191279992
C2×#191279422
C2×#191279292
C2×#191279222
C2×#191278642
C2×#191278522
C2×#191277922
C2×C8×C22⋊D832
C2×#191276942
C22×#102×C832
C2×#329683