Finite Group Databasebeta

← C2×#24919498 #36281073

Subgroups — C2×#24919498 #36281073

Order 21248.

2254 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×#19128425C211yesmaximal, characteristic, complemented
2C2×#19128344C211yesmaximal, characteristic
3#24919498C2116yesmaximal, direct product factor
4C2×#19128041C211yesmaximal, characteristic, complemented
5C2×#19128023C211yesmaximal, characteristic, complemented
6C2×#19127988C211yesmaximal, characteristic, complemented
7C2×#19127958C211yesmaximal, characteristic, complemented
8C2×#19127929C211yesmaximal, characteristic, complemented
9C2×#19127920C211yesmaximal, characteristic, complemented
10C2×#19127866C211yesmaximal, characteristic, complemented
11C2×#19127853C211yesmaximal, characteristic, complemented
12C2×#19127803C211yesmaximal, characteristic, complemented
13C2×#19127774C211yesmaximal, characteristic, complemented
14C2×#19127704C211yesmaximal, characteristic, complemented
15C2×#19127696C211yesmaximal, characteristic, complemented
16C2×#489×C83C211yesmaximal, characteristic, complemented
17C22×#13050591C2211yescharacteristic
18C22×D4×D83C2211yescharacteristic
19C22×#13050580C2211yescharacteristic, complemented
20C22×#13050579C2211yescharacteristic
21C22×#13050578C2211yescharacteristic
22C22×#13050573C2211yescharacteristic
23C22×C8×D83C2211yescharacteristic, complemented
24#19128425—24no—
25#19128425C2218yescomplemented
26#19128344—24no—
27#19128344C2218yes—
28C2×#14581787—21no—
29C2×#14581787—21no—
30C2×#14581781—21no—
31C2×#14581774—21no—
32C2×#14581772C2211yescharacteristic
33C2×#14581772C2211yescharacteristic, complemented
34C2×#14581768C2211yescharacteristic
35C2×#14581765—21no—
36C2×#14581763C2211yescharacteristic
37C2×#14581762—21no—
38C2×Q8×Dic83—21no—
39C2×C4×Dic166C2211yescharacteristic, complemented
40C2×C4×D332C2211yescharacteristic
41C2×C4×D332C2211yescharacteristic
42C2×#14581750C2211yescharacteristic
43C2×#14581750C2211yescharacteristic, complemented
44C2×C22⋊C4×D83—21no—
45#19128041C2218yescomplemented
46#19128023C2218yescomplemented
47#19127988C2218yescomplemented
48#19127958C2218yescomplemented
49#19127929C2218yescomplemented
50#19127920C2218yescomplemented
51#19127866C2218yescomplemented
52#19127853C2218yescomplemented
53#19127803C2218yescomplemented
54#19127774C2218yescomplemented
55C2×#14581726C2211yescharacteristic, complemented
56C2×#14581723C2211yescharacteristic, complemented
57C2×#14581723C2211yescharacteristic, complemented
58C2×C4⋊(C83⋊C8)C2211yescharacteristic, complemented
59#19127704C2218yescomplemented
60#19127696C2218yescomplemented
61C2×#14581717C2211yescharacteristic, complemented
62C2×#14581716C2211yescharacteristic, complemented
63C2×#14581714C2211yescharacteristic
64C2×#14581713C2211yescharacteristic
65C2×#14581712C2211yescharacteristic
66C2×#14581712C2211yescharacteristic
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×(C2×D83)⋊C8C2211yescharacteristic, complemented
69C2×C4⋊Q8×C83C2211yescharacteristic, complemented
70C2×#124×C83C2211yescharacteristic
71#489×C83C2218yescomplemented
72C2×#103×C83C2211yescharacteristic, complemented
73C2×#103×C83C2211yescharacteristic, complemented
74C2×#102×C83C2211yescharacteristic
75C2×#102×C83C2211yescharacteristic
76C2×#97×C83C2211yescharacteristic, complemented
77C24×D83—21no—
78C2×#13050591—22no—
79C2×#13050591—24no—
80C2×#13050591—42no—
81C2×#13050591C2314yes—
82C22×Dic166C2311yescharacteristic
83C22×D332—21no—
84C22×D332D411yescharacteristic
85C22×D332C2311yescharacteristic
86C22×C22⋊D83—21no—
87C22×C22⋊D83—21no—
88C2×D4×D83—24no—
89C2×D4×D83—22no—
90C2×D4×D83—42no—
91C2×D4×D83C2314yes—
92C22×C4×D83—21no—
93C22×C4×D83—21no—
94C22×C4×D83C2311yescharacteristic
95C22×C4×D83C2311yescharacteristic
96C2×#13050580—42no—
97C2×#13050580C2314yescomplemented
98C2×#13050579—24no—
99C2×#13050579C2314yes—
100C2×#13050578—42no—
101C2×#13050578C2314yes—
102C2×#13050573—42no—
103C2×#13050573C2314yes—
104C22×C83⋊C8C2311yescharacteristic
105C22×C83⋊C8C2311yescharacteristic
106C2×C8×D83—42no—
107C2×C8×D83C2314yescomplemented
108#14581787—28no—
109#14581787—28no—
110#14581781—28no—
111#14581774—28no—
112#14581772—22no—
113#14581772—22no—
114#14581772C2314yes—
115#14581772C2314yescomplemented
116#14581768—22no—
117#14581768C2314yes—
118#14581765—28no—
119#14581763—22no—
120#14581763C2314yes—
121#14581762—28no—
122Q8×Dic83—28no—
123C4×Dic166—22no—
124C4×Dic166C2314yescomplemented
125C4×D332—22no—
126C4×D332D414yes—
127C4×D332C2314yes—
128C4×D332C2314yes—
129#14581750—22no—
130#14581750—22no—
131#14581750C2314yes—
132#14581750C2314yescomplemented
133C2×C4⋊Dic83—21no—
134C2×C4⋊Dic83—21no—
135C2×C4⋊Dic83D411yescharacteristic
136C2×C4⋊Dic83C2311yescharacteristic
137C2×C4⋊Dic83C2311yescharacteristic
138C2×Dic83⋊C4—21no—
139C2×Dic83⋊C4—21no—
140C2×C22⋊Dic83—21no—
141C2×(C2×D83)⋊C4—21no—
142C2×(C2×D83)⋊C4—21no—
143C2×(C2×D83)⋊C4—21no—
144C2×(C2×D83)⋊C4—21no—
145C2×(C2×D83)⋊C4—21no—
146C2×(C2×D83)⋊C4—21no—
147C2×(C2×D83)⋊C4D411yescharacteristic
148C2×(C2×D83)⋊C4D411yescharacteristic
149C22⋊C4×D83—28no—
150C2×C4×Dic83—21no—
151C2×C4×Dic83—21no—
152C2×C4×Dic83—21no—
153#14581726C2314yescomplemented
154#14581723C2314yescomplemented
155#14581723C2314yescomplemented
156C4⋊(C83⋊C8)C2314yescomplemented
157#14581717C2314yescomplemented
158#14581716C2314yescomplemented
159#14581714C2314yes—
160#14581713C2314yes—
161#14581712C2314yes—
162#14581712C2314yes—
163(C2×D83)⋊C8C2314yes—
164(C2×D83)⋊C8C2314yescomplemented
165C22×Q8×C83—21no—
166C22×Q8×C83C2311yescharacteristic
167C22×D4×C83C2311yescharacteristic
168C22×C8×C83C2311yescharacteristic
169C22×C8×C83C2311yescharacteristic
170C4⋊Q8×C83—22no—
171C4⋊Q8×C83C2314yescomplemented
172#124×C83—22no—
173#124×C83C2314yes—
174C2×C4⋊C4×C83—21no—
175C2×C4⋊C4×C83C2311yescharacteristic
176C2×C4⋊C4×C83C2311yescharacteristic
177C2×C22⋊C4×C83—21no—
178C2×C22⋊C4×C83—21no—
179C2×C42×C83C2311yescharacteristic
180#103×C83C2314yescomplemented
181#103×C83C2314yescomplemented
182#102×C83C2314yes—
183#102×C83C2314yes—
184#97×C83C2314yescomplemented
185C23×D83—21no—
186C23×D83—24no—
187C23×D83—44no—
188C23×D83—44no—
189C23×D83—82no—
190C23×D83C2×D411yescharacteristic
191C23×D83C2×D411yescharacteristic
192#13050591—28no—
193#13050591—44no—
194#13050591—48no—
195C2×Dic166—22no—
196C2×Dic166—22no—
197C2×Dic166—21no—
198C2×Dic166C2412yes—
199C2×D332—21no—
200C2×D332—22no—
201C2×D332—24no—
202C2×D332—42no—
203C2×D332—44no—
204C2×D332C2×D414yes—
205C2×D332#4114yes—
206C2×D332C2412yes—
207C2×C22⋊D83—24no—
208C2×C22⋊D83—24no—
209C2×C22⋊D83—44no—
210C2×C22⋊D83—82no—
211D4×D83—28no—
212D4×D83—44no—
213D4×D83—48no—
214C22×Dic83—21no—
215C22×Dic83—21no—
216C22×Dic83—21no—
217C22×Dic83C2×D411yescharacteristic
218C22×Dic83C2×D411yescharacteristic
219C2×C4×D83—22no—
220C2×C4×D83—22no—
221C2×C4×D83—22no—
222C2×C4×D83—22no—
223C2×C4×D83—24no—
224C2×C4×D83—24no—
225C2×C4×D83—44no—
226C2×C4×D83—82no—
227C2×C4×D83C2×D412yes—
228C2×C4×D83C2×D412yes—
229C2×C4×D83C2412yes—
230C2×C4×D83C2412yes—
231#13050580—44no—
232#13050579—28no—
233#13050578—44no—
234#13050573—44no—
235C2×C83⋊C8—22no—
236C2×C83⋊C8—22no—
237C2×C83⋊C8C2412yes—
238C2×C83⋊C8C2412yes—
239C8×D83—44no—
240C4⋊Dic83—21no—
241C4⋊Dic83—21no—
242C4⋊Dic83—24no—
243C4⋊Dic83—24no—
244C4⋊Dic83C2×D414yes—
245C4⋊Dic83C2412yes—
246C4⋊Dic83C2412yes—
247Dic83⋊C4—24no—
248Dic83⋊C4—24no—
249C22⋊Dic83—24no—
250(C2×D83)⋊C4—24no—
251(C2×D83)⋊C4—24no—
252(C2×D83)⋊C4—24no—
253(C2×D83)⋊C4—24no—
254(C2×D83)⋊C4—24no—
255(C2×D83)⋊C4—24no—
256(C2×D83)⋊C4C2×D414yes—
257(C2×D83)⋊C4C2×D414yes—
258C4×Dic83—24no—
259C4×Dic83—24no—
260C4×Dic83—24no—
261C24×C83—21no—
262C2×Q8×C83—21no—
263C2×Q8×C83—24no—
264C2×Q8×C83—22no—
265C2×Q8×C83—22no—
266C2×Q8×C83—44no—
267C2×Q8×C83C2412yes—
268C2×D4×C83—21no—
269C2×D4×C83—22no—
270C2×D4×C83—22no—
271C2×D4×C83C2412yes—
272C22×C4×C83—21no—
273C22×C4×C83—21no—
274C22×C4×C83—21no—
275C22×C4×C83C2×D411yescharacteristic
276C22×C4×C83C2×D411yescharacteristic
277C22×C4×C83C2411yescharacteristic
278C2×C8×C83—22no—
279C2×C8×C83—22no—
280C2×C8×C83C2412yes—
281C2×C8×C83C2412yes—
282C4⋊C4×C83—21no—
283C4⋊C4×C83—21no—
284C4⋊C4×C83—24no—
285C4⋊C4×C83C2412yes—
286C4⋊C4×C83C2412yes—
287C22⋊C4×C83—24no—
288C22⋊C4×C83—24no—
289C42×C83C2×D412yes—
290C42×C83C2412yes—
291C23×C83—22no—
292C23×C83—42no—
293C23×C83—42no—
294C23×C83—42no—
295C23×C83C22×D411yescharacteristic
296C22×D83—22no—
297C22×D83—22no—
298C22×D83—24no—
299C22×D83—22no—
300C22×D83—22no—
301C22×D83—22no—
302C22×D83—22no—
303C22×D83—22no—
304C22×D83—48no—
305C22×D83—48no—
306C22×D83—42no—
307C22×D83—42no—
308C22×D83—84no—
309C22×D83—816no—
310C22×D83C22×D412yes—
311C22×D83C22×D412yes—
312Q8×C83—22no—
313Q8×C83—22no—
314Q8×C83—48no—
315Q8×C83—42no—
316D4×C83—22no—
317D4×C83—22no—
318D4×C83—42no—
319C2×C4×C83—22no—
320C2×C4×C83—22no—
321C2×C4×C83—22no—
322C2×C4×C83—22no—
323C2×C4×C83—22no—
324C2×C4×C83—42no—
325C2×C4×C83—42no—
326C2×C4×C83—42no—
327C2×C4×C83C22×D412yes—
328C2×C4×C83C22×D412yes—
329C2×C4×C83C22×D411yescharacteristic
330C2×C4×C83C2×#4112yes—
331C2×C4×C83H(5,𝔽2)12yes—
332C2×C4×C83C2511yescharacteristic
333C22⋊D83—48no—
334C22⋊D83—84no—
335C2×Dic83—22no—
336C2×Dic83—22no—
337C2×Dic83—22no—
338C2×Dic83—22no—
339C2×Dic83—22no—
340C2×Dic83—42no—
341C2×Dic83—42no—
342C2×Dic83—42no—
343C2×Dic83C22×D412yes—
344C2×Dic83C22×D412yes—
345D332—24no—
346D332—22no—
347D332—44no—
348D332—48no—
349D332C2×#4114yes—
350C4×D83—24no—
351C4×D83—24no—
352C4×D83—22no—
353C4×D83—22no—
354C4×D83—22no—
355C4×D83—22no—
356C4×D83—48no—
357C4×D83—84no—
358Dic166—22no—
359Dic166—22no—
360Dic166—42no—
361C8×C83—22no—
362C8×C83—22no—
363C83⋊C8—22no—
364C83⋊C8—22no—
365C22×C83—42no—
366C22×C83—42no—
367C22×C83—42no—
368C22×C83—84no—
369C22×C83#54612yes—
370C22×C83#57512yes—
371C22×C83#57712yes—
372C22×C83C23×D411yescharacteristic
373C2×D83—22no—
374C2×D83—22no—
375C2×D83—24no—
376C2×D83—22no—
377C2×D83—22no—
378C2×D83—22no—
379C2×D83—22no—
380C2×D83—44no—
381C2×D83—44no—
382C2×D83—48no—
383C2×D83—42no—
384C2×D83—42no—
385C2×D83—816no—
386C4×C83—22no—
387C4×C83—22no—
388C4×C83—42no—
389C4×C83—42no—
390C4×C83—42no—
391C4×C83#54612yes—
392C4×C83C22×#4111yescharacteristic
393C4×C83C2×H(5,𝔽2)11yescharacteristic
394Dic83—22no—
395Dic83—22no—
396Dic83—42no—
397Dic83—42no—
398Dic83—42no—
399C2×#3311—831nomaximal, Sylow
400C2×C83—82no—
401C2×C83#331114yescomplemented
402C2×C83C2×#54611yescharacteristic
403C2×C83C2×#57511yescharacteristic
404C2×C83C2×#57711yescharacteristic
405D83—42no—
406D83—42no—
407D83—44no—
408C2×#556—831no—
409C2×#546—831no—
410#3311—8316no—
411C2×#489D8311yescharacteristic, complemented
412C2×#485—831no—
413C2×#482—831no—
414C2×#476—831no—
415C2×#470—831no—
416C2×#465—831no—
417C2×#464—831no—
418C2×#452—831no—
419C2×#450—831no—
420C2×#440—831no—
421C2×#435—831no—
422C2×#418—831no—
423C2×#416—831no—
424C83C2×#331111yescharacteristic, complemented, Sylow
425C22×#41—831no—
426C23×D4—831no—
427C22×Q16—831no—
428C22×SD16—831no—
429C22×SD16—831no—
430C22×M16—831no—
431C23×C8—831no—
432#556—838no—
433#556—1664no—
434#546—838no—
435#546—1664no—
436C2×C4⋊Q8C2×D8311yescharacteristic, complemented
437C2×#126—1661no—
438C2×#126—1661no—
439C2×#124—1661no—
440C2×#124C2×D8311yescharacteristic
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×Q8—1661no—
450C2×C4×D4—831no—
451C2×C4×D4—831no—
452C2×#117—831no—
453C2×#117—831no—
454C22×C22⋊C4—1661no—
455#489C2×D8318yescomplemented
456#485—838no—
457#482—838no—
458#476—838no—
459#470—838no—
460#465—838no—
461#464—838no—
462#452—838no—
463#450—838no—
464#440—838no—
465#435—838no—
466C2×#107—831no—
467C2×#106—831no—
468C2×#106—831no—
469C2×C4⋊C8—831no—
470#418—838no—
471#416—838no—
472C2×#103—831no—
473C2×#103—831no—
474C2×#103C2×D8311yescharacteristic, complemented
475C2×#103C2×D8311yescharacteristic, complemented
476C2×#102—831no—
477C2×#102—831no—
478C2×#102—831no—
479C2×#102—831no—
480C2×#102C2×D8311yescharacteristic
481C2×#102C2×D8311yescharacteristic
482C2×C22⋊C8—831no—
483C2×C22⋊C8—831no—
484C2×#97C2×D8311yescharacteristic, complemented
485C25—1661no—
486C2×#41—3322no—
487C2×#41—834no—
488C2×#41—1664no—
489C2×#41—1662no—
490C22×Q8—21no—
491C22×Q8—831no—
492C22×Q8C22×D8311yescharacteristic
493C22×D4—3322no—
494C22×D4—834no—
495C22×D4—831no—
496C22×D4—831no—
497C22×D4—1661no—
498C22×D4—1662no—
499C22×D4—1661no—
500C22×D4—1664no—
501C22×D4—1661no—
502C22×D4C22×D8311yescharacteristic
503C23×C4—831no—
504C23×C4—831no—
505C23×C4—1661no—
506C23×C4—1661no—
507C2×Q16—3322no—
508C2×Q16—834no—
509C2×SD16—3322no—
510C2×SD16—834no—
511C2×SD16—834no—
512C2×SD16—1664no—
513C2×M16—3322no—
514C2×M16—834no—
515C22×C8—3322no—
516C22×C8—834no—
517C22×C8—831no—
518C22×C8—831no—
519C22×C8C22×D8311yescharacteristic
520C22×C8C22×D8311yescharacteristic
521C4⋊Q8—22no—
522C4⋊Q8C22×D8314yescomplemented
523#126—1668no—
524#126—1668no—
525#124—22no—
526#124—1668no—
527#124C22×D8314yes—
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—1668no—
541C4×Q8—1662no—
542C4×D4—834no—
543C4×D4—834no—
544C4×D4—834no—
545C4×D4—1662no—
546#117—834no—
547#117—834no—
548#117—1662no—
549#117—1662no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—831no—
552C2×C4⋊C4—831no—
553C2×C4⋊C4—831no—
554C2×C4⋊C4—1661no—
555C2×C4⋊C4—1661no—
556C2×C4⋊C4—1661no—
557C2×C4⋊C4—1661no—
558C2×C4⋊C4C22×D8311yescharacteristic
559C2×C4⋊C4C22×D8311yescharacteristic
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
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×C42—1661no—
573C2×C42—1661no—
574C2×C42—1661no—
575C2×C42C22×D8311yescharacteristic
576#107—834no—
577#106—834no—
578#106—834no—
579C4⋊C8—834no—
580#103—834no—
581#103—834no—
582#103C22×D8314yescomplemented
583#103C22×D8314yescomplemented
584#102—834no—
585#102—834no—
586#102—834no—
587#102—834no—
588#102C22×D8314yes—
589#102C22×D8314yes—
590C22⋊C8—834no—
591C22⋊C8—834no—
592#97C22×D8314yescomplemented
593C24—21no—
594C24—3324no—
595C24—3324no—
596C24—831no—
597C24—831no—
598C24—6642no—
599C24—1664no—
600C24—1661no—
601#41—3324no—
602#41—3328no—
603#41—1668no—
604C2×Q8—24no—
605C2×Q8—21no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—44no—
609C2×Q8—832no—
610C2×Q8—1662no—
611C2×Q8—1662no—
612C2×Q8—1661no—
613C2×Q8C23×D8312yes—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—3322no—
618C2×D4—3324no—
619C2×D4—3324no—
620C2×D4—3328no—
621C2×D4—3324no—
622C2×D4—834no—
623C2×D4—834no—
624C2×D4—832no—
625C2×D4—6642no—
626C2×D4—1664no—
627C2×D4—1664no—
628C2×D4—1668no—
629C2×D4—1664no—
630C2×D4—1661no—
631C2×D4—1662no—
632C2×D4C23×D8312yes—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—3324no—
637C22×C4—831no—
638C22×C4—831no—
639C22×C4—832no—
640C22×C4—832no—
641C22×C4—832no—
642C22×C4—832no—
643C22×C4—6642no—
644C22×C4—1664no—
645C22×C4—1661no—
646C22×C4—1661no—
647C22×C4—1661no—
648C22×C4—1664no—
649C22×C4—1662no—
650C22×C4—1662no—
651C22×C4—1662no—
652C22×C4—1662no—
653C22×C4D4×D8311yescharacteristic
654C22×C4D4×D8311yescharacteristic
655C22×C4C23×D8311yescharacteristic
656Q16—3324no—
657SD16—3324no—
658SD16—1668no—
659M16—3324no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—3324no—
663C2×C8—832no—
664C2×C8—832no—
665C2×C8—1662no—
666C2×C8—1662no—
667C2×C8C23×D8312yes—
668C2×C8C23×D8312yes—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—834no—
673C4⋊C4—832no—
674C4⋊C4—832no—
675C4⋊C4—1664no—
676C4⋊C4—1664no—
677C4⋊C4—1664no—
678C4⋊C4—1661no—
679C4⋊C4—1661no—
680C4⋊C4—1664no—
681C4⋊C4C23×D8312yes—
682C4⋊C4C23×D8312yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
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—
694C42—1664no—
695C42—1664no—
696C42—1664no—
697C42D4×D8312yes—
698C42C23×D8312yes—
699C23—22no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—3328no—
704C23—3328no—
705C23—3322no—
706C23—3322no—
707C23—832no—
708C23—832no—
709C23—6644no—
710C23—66416no—
711C23—1664no—
712C23—1662no—
713C23—1662no—
714C23—1662no—
715C23—1662no—
716C23—1662no—
717C23—1662no—
718C23—1662no—
719C23C2×D4×D8311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—48no—
723Q8—42no—
724Q8—3322no—
725Q8—1662no—
726Q8—1662no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—3324no—
731D4—3328no—
732D4—3328no—
733D4—834no—
734D4—6644no—
735D4—1664no—
736D4—1662no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—3328no—
746C2×C4—3322no—
747C2×C4—3322no—
748C2×C4—3322no—
749C2×C4—832no—
750C2×C4—832no—
751C2×C4—6644no—
752C2×C4—1662no—
753C2×C4—1662no—
754C2×C4—1662no—
755C2×C4—1662no—
756C2×C4—1662no—
757C2×C4—1664no—
758C2×C4—1664no—
759C2×C4—1662no—
760C2×C4—1662no—
761C2×C4—1662no—
762C2×C4—1662no—
763C2×C4C2×D4×D8312yes—
764C2×C4C2×D4×D8312yes—
765C2×C4C2×D4×D8311yescharacteristic
766C2×C4#41×D8312yes—
767C2×C4#1458183812yes—
768C2×C4C24×D8311yescharacteristic
769C8—22no—
770C8—22no—
771C8—1662no—
772C8—1662no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—84no—
777C22—3322no—
778C22—3322no—
779C22—3328no—
780C22—3324no—
781C22—3324no—
782C22—66416no—
783C22—1664no—
784C22—1662no—
785C22—1662no—
786C22—1662no—
787C22—1662no—
788C22—1662no—
789C22—1662no—
790C22#1912834412yes—
791C22#1912849712yes—
792C22#1912851012yes—
793C22C22×D4×D8311yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—3322no—
800C4—3322no—
801C4—3322no—
802C4—1662no—
803C4—1662no—
804C4#1912834412yes—
805C4C2×#41×D8311yescharacteristic
806C4C2×#1458183811yescharacteristic
807C2—82no—
808C2—3324no—
809C2—3322no—
810C2—3322no—
811C2#2491949814yesdirect product factor
812C2C2×#1912834411yescharacteristic
813C2C2×#1912849711yescharacteristic
814C2C2×#1912851011yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#489×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128344C2
hypercenterC2×#489D83
hypocenterC83C2×#3311
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#19128425C2semidirect
3. #24919498C2direct (N × H)
4. C2×#19128041C2semidirect
5. C2×#19128023C2semidirect
6. C2×#19127988C2semidirect
7. C2×#19127958C2semidirect
8. C2×#19127929C2semidirect
9. C2×#19127920C2semidirect
10. C2×#19127866C2semidirect
11. C2×#19127853C2semidirect
12. C2×#19127803C2semidirect
13. C2×#19127774C2semidirect
14. C2×#19127704C2semidirect
15. C2×#19127696C2semidirect
16. C2×#489×C83C2semidirect
19. C22×#13050580C22semidirect
23. C22×C8×D83C22semidirect
25. #19128425C22semidirect
33. C2×#14581772C22semidirect
39. C2×C4×Dic166C22semidirect
43. C2×#14581750C22semidirect
45. #19128041C22semidirect
46. #19128023C22semidirect
47. #19127988C22semidirect
48. #19127958C22semidirect
49. #19127929C22semidirect
50. #19127920C22semidirect
51. #19127866C22semidirect
52. #19127853C22semidirect
53. #19127803C22semidirect
54. #19127774C22semidirect
55. C2×#14581726C22semidirect
56. C2×#14581723C22semidirect
57. C2×#14581723C22semidirect
58. C2×C4⋊(C83⋊C8)C22semidirect
59. #19127704C22semidirect
60. #19127696C22semidirect
61. C2×#14581717C22semidirect
62. C2×#14581716C22semidirect
68. C2×(C2×D83)⋊C8C22semidirect
69. C2×C4⋊Q8×C83C22semidirect
71. #489×C83C22semidirect
72. C2×#103×C83C22semidirect
73. C2×#103×C83C22semidirect
76. C2×#97×C83C22semidirect
97. C2×#13050580C23semidirect
107. C2×C8×D83C23semidirect
115. #14581772C23semidirect
124. C4×Dic166C23semidirect
132. #14581750C23semidirect
153. #14581726C23semidirect
154. #14581723C23semidirect
155. #14581723C23semidirect
156. C4⋊(C83⋊C8)C23semidirect
157. #14581717C23semidirect
158. #14581716C23semidirect
164. (C2×D83)⋊C8C23semidirect
171. C4⋊Q8×C83C23semidirect
180. #103×C83C23semidirect
181. #103×C83C23semidirect
184. #97×C83C23semidirect
401. C2×C83#3311semidirect
411. C2×#489D83semidirect
424. C83C2×#3311semidirect
436. C2×C4⋊Q8C2×D83semidirect
455. #489C2×D83semidirect
474. C2×#103C2×D83semidirect
475. C2×#103C2×D83semidirect
484. C2×#97C2×D83semidirect
522. C4⋊Q8C22×D83semidirect
582. #103C22×D83semidirect
583. #103C22×D83semidirect
592. #97C22×D83semidirect
811. C2#24919498direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284252
C2×#191283442
#249194982
C2×#191280412
C2×#191280232
C2×#191279882
C2×#191279582
C2×#191279292
C2×#191279202
C2×#191278662
C2×#191278532
C2×#191278032
C2×#191277742
C2×#191277042
C2×#191276962
C2×#489×C832
C2×#331183