Finite Group Databasebeta

← C2×#24909137 #35557196

Subgroups — C2×#24909137 #35557196

Order 21248.

1230 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128272C211yesmaximal, characteristic
2C2×#19127675C211yesmaximal, characteristic
3#24909137C218yesmaximal, direct product factor
4C2×#19127495C214yesmaximal, complemented
5C2×#410×C83C211yesmaximal, characteristic
6C23×Dic166C411yescharacteristic, complemented
7#19128272—22no—
8#19128272—22no—
9#19128272C414yescomplemented
10#19128272C2214yes—
11C2×#14581790C412yescomplemented
12C2×#14581779C2212yes—
13C2×#14581773—21no—
14C2×#14581773—21no—
15C2×#14581771—21no—
16C2×#14581771—21no—
17C2×#14581751—21no—
18C2×#14581751C411yescharacteristic, complemented
19#19127675—22no—
20#19127675C2214yes—
21C2×#14581707—21no—
22C2×#14581707C2212yes—
23#19127495C22116yescomplemented
24C22×#41×C83C2211yescharacteristic
25C2×#117×C83—21no—
26#410×C83—22no—
27#410×C83C2214yes—
28C2×#99×C83—21no—
29C2×#99×C83C2212yes—
30C22×Dic166—21no—
31C22×Dic166—22no—
32C22×Dic166—42no—
33C22×Dic166—41no—
34C22×Dic166—41no—
35C22×Dic166C2×C412yes—
36C22×Dic166C2×C414yescomplemented
37C23×Dic83—21no—
38#14581790—24no—
39#14581790C2×C418yescomplemented
40#14581779—22no—
41#14581779—22no—
42#14581779C2×C414yes—
43#14581779C2314yes—
44#14581773—24no—
45#14581773—24no—
46#14581773—24no—
47#14581773—24no—
48#14581771—24no—
49#14581771—24no—
50#14581771—24no—
51#14581771—24no—
52#14581751—22no—
53#14581751—24no—
54#14581751—42no—
55#14581751C2×C414yescomplemented
56C2×C4⋊Dic83—21no—
57C2×C4⋊Dic83—41no—
58C2×Dic83⋊C4—22no—
59C2×Dic83⋊C4—22no—
60C2×C22⋊Dic83—21no—
61C2×C22⋊Dic83—22no—
62C2×C22⋊Dic83—22no—
63C2×C22⋊Dic83—22no—
64C2×C4×Dic83—41no—
65C2×C4×Dic83C2×C412yes—
66#14581707—24no—
67#14581707—22no—
68#14581707C2314yes—
69C2×#41×C83—41no—
70C2×#41×C83—41no—
71C2×#41×C83—42no—
72C2×#41×C83C2×C412yes—
73C2×#41×C83D412yes—
74C2×#41×C83D412yes—
75C2×#41×C83C2312yes—
76C22×Q8×C83C2×C411yescharacteristic
77C22×D4×C83D411yescharacteristic
78C22×D4×C83D411yescharacteristic
79C22×D4×C83C2311yescharacteristic
80C23×C4×C83C2×C411yescharacteristic
81C23×C4×C83D411yescharacteristic
82C23×C4×C83D411yescharacteristic
83#117×C83—24no—
84#117×C83—42no—
85C2×C4⋊C4×C83—41no—
86C2×C22⋊C4×C83—22no—
87C2×C42×C83—41no—
88#99×C83—24no—
89#99×C83—22no—
90#99×C83C2314yes—
91C2×Dic166—24no—
92C2×Dic166—22no—
93C2×Dic166—44no—
94C2×Dic166—44no—
95C2×Dic166—42no—
96C2×Dic166—41no—
97C2×Dic166—41no—
98C2×Dic166—42no—
99C2×Dic166—42no—
100C2×Dic166—44no—
101C2×Dic166—44no—
102C2×Dic166C22×C414yes—
103C22×Dic83—24no—
104C22×Dic83—22no—
105C22×Dic83—22no—
106C22×Dic83—42no—
107C22×Dic83—42no—
108C22×Dic83—42no—
109C4⋊Dic83—24no—
110C4⋊Dic83—44no—
111Dic83⋊C4—28no—
112Dic83⋊C4—28no—
113C22⋊Dic83—24no—
114C22⋊Dic83—24no—
115C22⋊Dic83—24no—
116C22⋊Dic83—24no—
117C22⋊Dic83—24no—
118C22⋊Dic83—24no—
119C22⋊Dic83—42no—
120C4×Dic83—22no—
121C4×Dic83—44no—
122C4×Dic83C22×C414yes—
123C24×C83C22⋊C411yescharacteristic
124C24×C83C2×D411yescharacteristic
125C24×C83C2×D411yescharacteristic
126#41×C83—42no—
127#41×C83—42no—
128#41×C83—42no—
129#41×C83—42no—
130#41×C83—42no—
131#41×C83—42no—
132#41×C83—42no—
133#41×C83—42no—
134C2×Q8×C83—41no—
135C2×Q8×C83—41no—
136C2×Q8×C83C22⋊C412yes—
137C2×Q8×C83C22×C412yes—
138C2×D4×C83—41no—
139C2×D4×C83—41no—
140C2×D4×C83—41no—
141C2×D4×C83—41no—
142C2×D4×C83—41no—
143C2×D4×C83—41no—
144C2×D4×C83C22⋊C412yes—
145C2×D4×C83C22⋊C412yes—
146C2×D4×C83C22×C411yescharacteristic
147C2×D4×C83C2×D412yes—
148C2×D4×C83C2×D411yescharacteristic
149C2×D4×C83C2×D412yes—
150C2×D4×C83C2×D411yescharacteristic
151C2×D4×C83C2411yescharacteristic
152C22×C4×C83—22no—
153C22×C4×C83—21no—
154C22×C4×C83—21no—
155C22×C4×C83—21no—
156C22×C4×C83—21no—
157C22×C4×C83—22no—
158C22×C4×C83—21no—
159C22×C4×C83—21no—
160C22×C4×C83—22no—
161C22×C4×C83—42no—
162C22×C4×C83C22⋊C412yes—
163C22×C4×C83C22⋊C412yes—
164C22×C4×C83C22⋊C412yes—
165C22×C4×C83C22⋊C411yescharacteristic
166C22×C4×C83C22⋊C411yescharacteristic
167C22×C4×C83C22⋊C411yescharacteristic
168C22×C4×C83C22×C411yescharacteristic
169C22×C4×C83C22×C412yes—
170C22×C4×C83C2×D412yes—
171C22×C4×C83C2×D412yes—
172C4⋊C4×C83—44no—
173C22⋊C4×C83—24no—
174C22⋊C4×C83—42no—
175C42×C83—44no—
176C23×C83—21no—
177C23×C83—21no—
178C23×C83—21no—
179C23×C83—21no—
180C23×C83—21no—
181C23×C83—21no—
182C23×C83—42no—
183C23×C83—42no—
184C23×C83—42no—
185C23×C83C2×C22⋊C411yescharacteristic
186C23×C83C2×C22⋊C411yescharacteristic
187C23×C83C2×C22⋊C411yescharacteristic
188C23×C83C2×C22⋊C412yes—
189C23×C83C22×D411yescharacteristic
190C23×C83C22×D411yescharacteristic
191Q8×C83—42no—
192Q8×C83—42no—
193D4×C83—42no—
194D4×C83—42no—
195D4×C83—41no—
196D4×C83—41no—
197D4×C83—42no—
198D4×C83—41no—
199D4×C83—42no—
200D4×C83—41no—
201C2×C4×C83—21no—
202C2×C4×C83—21no—
203C2×C4×C83—21no—
204C2×C4×C83—21no—
205C2×C4×C83—21no—
206C2×C4×C83—21no—
207C2×C4×C83—22no—
208C2×C4×C83—22no—
209C2×C4×C83—22no—
210C2×C4×C83—22no—
211C2×C4×C83—22no—
212C2×C4×C83—22no—
213C2×C4×C83—22no—
214C2×C4×C83—22no—
215C2×C4×C83—22no—
216C2×C4×C83—22no—
217C2×C4×C83—22no—
218C2×C4×C83—22no—
219C2×C4×C83—44no—
220C2×C4×C83—84no—
221C2×C4×C83#9912yes—
222C2×C4×C83#9911yescharacteristic
223C2×C4×C83#9911yescharacteristic
224C2×C4×C83C2×C22⋊C411yescharacteristic
225C2×C4×C83C2×C22⋊C412yes—
226C2×C4×C83C2×C22⋊C412yes—
227C2×C4×C83C2×C22⋊C412yes—
228C2×C4×C83C23×C411yescharacteristic
229C2×Dic83—24no—
230C2×Dic83—24no—
231C2×Dic83—44no—
232C2×Dic83—48no—
233C2×Dic83—42no—
234C2×Dic83—42no—
235C2×Dic83—44no—
236C2×Dic83—84no—
237Dic166—44no—
238Dic166—44no—
239Dic166—44no—
240Dic166—44no—
241C22×C83—22no—
242C22×C83—22no—
243C22×C83—21no—
244C22×C83—21no—
245C22×C83—21no—
246C22×C83—21no—
247C22×C83—42no—
248C22×C83—41no—
249C22×C83—41no—
250C22×C83—41no—
251C22×C83—41no—
252C22×C83—42no—
253C22×C83—42no—
254C22×C83—42no—
255C22×C83—42no—
256C22×C83—81no—
257C22×C83—81no—
258C22×C83C2×#9911yescharacteristic
259C22×C83C2×#9911yescharacteristic
260C22×C83C22×C22⋊C411yescharacteristic
261C4×C83—21no—
262C4×C83—21no—
263C4×C83—22no—
264C4×C83—22no—
265C4×C83—84no—
266C4×C83C2×#9912yes—
267C4×C83C2×#9912yes—
268Dic83—44no—
269Dic83—44no—
270Dic83—84no—
271C2×#2129—831nomaximal, Sylow
272C2×C83—21no—
273C2×C83—21no—
274C2×C83—41no—
275C2×C83—41no—
276C2×C83—42no—
277C2×C83—41no—
278C2×C83—41no—
279C2×C83#212912yescomplemented
280C2×C83C22×#9911yescharacteristic
281C2×#536—831no—
282C2×#410—831no—
283C2×#410D8311yescharacteristic
284#2129—838no—
285C2×#354—834no—
286C83C2×#212911yescharacteristic, complemented, Sylow
287C22×#41C2×D8311yescharacteristic
288C23×Q8—831no—
289#536—834no—
290#536—834no—
291#536—1662no—
292#536—1662no—
293C2×C4⋊Q8—832no—
294C2×#124—832no—
295C2×#123—1661no—
296C2×#123—1661no—
297C2×C22⋊Q8—1661no—
298C2×C22⋊Q8—1661no—
299C2×#117—21no—
300C2×#117—831no—
301C2×#117—1661no—
302#410—22no—
303#410—834no—
304#410—1662no—
305#410C2×D8314yes—
306C2×#99—21no—
307C2×#99—832no—
308C2×#99—1661no—
309C2×#99C2×D8312yes—
310#354—8316no—
311C2×#41—41no—
312C2×#41—41no—
313C2×#41—42no—
314C2×#41C4×D8312yes—
315C2×#41D33212yes—
316C2×#41C22⋊D8312yes—
317C2×#41C22×D8312yes—
318C22×Q8—3322no—
319C22×Q8—3321no—
320C22×Q8—3321no—
321C22×Q8—832no—
322C22×Q8—834no—
323C22×Q8—1662no—
324C22×Q8—1661no—
325C22×Q8C4×D8311yescharacteristic
326C22×D4D33211yescharacteristic
327C22×D4C22⋊D8311yescharacteristic
328C22×D4C22×D8311yescharacteristic
329C23×C4—1661no—
330C23×C4C4×D8311yescharacteristic
331C23×C4D33211yescharacteristic
332C23×C4C22⋊D8311yescharacteristic
333C4⋊Q8—838no—
334C4⋊Q8—1664no—
335#124—834no—
336#124—834no—
337#124—1662no—
338#124—1662no—
339#123—1664no—
340#123—1664no—
341#123—1664no—
342#123—1664no—
343C22⋊Q8—1664no—
344C22⋊Q8—1664no—
345C22⋊Q8—1664no—
346C22⋊Q8—1664no—
347#117—24no—
348#117—42no—
349#117—3322no—
350#117—834no—
351#117—1664no—
352#117—1662no—
353C2×C4⋊C4—41no—
354C2×C4⋊C4—3321no—
355C2×C4⋊C4—1662no—
356C2×C4⋊C4—1662no—
357C2×C4⋊C4—1661no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—1662no—
360C2×C22⋊C4—1661no—
361C2×C22⋊C4—1662no—
362C2×C22⋊C4—1662no—
363C2×C42—41no—
364C2×C42—3321no—
365C2×C42—832no—
366#99—24no—
367#99—22no—
368#99—834no—
369#99—1662no—
370#99—1664no—
371#99C22×D8314yes—
372C24(C2×D83)⋊C411yescharacteristic
373C24C2×C22⋊D8311yescharacteristic
374C24C2×D33211yescharacteristic
375#41—42no—
376#41—42no—
377#41—42no—
378#41—42no—
379#41—42no—
380#41—42no—
381#41—42no—
382#41—42no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×Q8—3324no—
386C2×Q8—3324no—
387C2×Q8—3324no—
388C2×Q8—3324no—
389C2×Q8—3322no—
390C2×Q8—3322no—
391C2×Q8—3322no—
392C2×Q8—3321no—
393C2×Q8—3321no—
394C2×Q8—834no—
395C2×Q8—1664no—
396C2×Q8—1662no—
397C2×Q8(C2×D83)⋊C412yes—
398C2×Q8C2×C4×D8312yes—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4(C2×D83)⋊C412yes—
406C2×D4(C2×D83)⋊C412yes—
407C2×D4C2×C4×D8311yescharacteristic
408C2×D4C2×C22⋊D8312yes—
409C2×D4C2×C22⋊D8311yescharacteristic
410C2×D4C2×D33212yes—
411C2×D4C2×D33211yescharacteristic
412C2×D4C23×D8311yescharacteristic
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—42no—
423C22×C4—3322no—
424C22×C4—3322no—
425C22×C4—3322no—
426C22×C4—1662no—
427C22×C4—1662no—
428C22×C4—1664no—
429C22×C4(C2×D83)⋊C411yescharacteristic
430C22×C4(C2×D83)⋊C411yescharacteristic
431C22×C4(C2×D83)⋊C412yes—
432C22×C4(C2×D83)⋊C412yes—
433C22×C4(C2×D83)⋊C412yes—
434C22×C4(C2×D83)⋊C411yescharacteristic
435C22×C4C2×C4×D8311yescharacteristic
436C22×C4C2×C4×D8312yes—
437C22×C4C2×C22⋊D8312yes—
438C22×C4C2×D33212yes—
439C4⋊C4—44no—
440C4⋊C4—3324no—
441C4⋊C4—1664no—
442C4⋊C4—1668no—
443C4⋊C4—1668no—
444C22⋊C4—24no—
445C22⋊C4—42no—
446C22⋊C4—3322no—
447C22⋊C4—1664no—
448C22⋊C4—1664no—
449C22⋊C4—1664no—
450C22⋊C4—1664no—
451C22⋊C4—1664no—
452C22⋊C4—1664no—
453C42—44no—
454C42—3324no—
455C42—834no—
456C42—1662no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23C2×(C2×D83)⋊C411yescharacteristic
467C23C2×(C2×D83)⋊C411yescharacteristic
468C23C2×(C2×D83)⋊C411yescharacteristic
469C23C2×(C2×D83)⋊C412yes—
470C23C22×C22⋊D8311yescharacteristic
471C23C22×D33211yescharacteristic
472Q8—42no—
473Q8—42no—
474Q8—3324no—
475Q8—3324no—
476Q8—3324no—
477Q8—3324no—
478D4—42no—
479D4—42no—
480D4—41no—
481D4—41no—
482D4—42no—
483D4—41no—
484D4—42no—
485D4—41no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—44no—
505C2×C4—84no—
506C2×C4—3328no—
507C2×C4—3324no—
508C2×C4—3322no—
509C2×C4—3322no—
510C2×C4—3324no—
511C2×C4—6644no—
512C2×C4—1664no—
513C2×C4—1664no—
514C2×C4#1458170612yes—
515C2×C4#1458170611yescharacteristic
516C2×C4#1458170611yescharacteristic
517C2×C4C2×(C2×D83)⋊C411yescharacteristic
518C2×C4C2×(C2×D83)⋊C412yes—
519C2×C4C2×(C2×D83)⋊C412yes—
520C2×C4C2×(C2×D83)⋊C412yes—
521C2×C4C22×C4×D8311yescharacteristic
522C22—22no—
523C22—21no—
524C22—21no—
525C22—22no—
526C22—21no—
527C22—21no—
528C22—41no—
529C22—41no—
530C22—42no—
531C22—41no—
532C22—41no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—81no—
538C22—81no—
539C22C2×#1458170611yescharacteristic
540C22C2×#1458170611yescharacteristic
541C22C22×(C2×D83)⋊C411yescharacteristic
542C4—21no—
543C4—21no—
544C4—22no—
545C4—22no—
546C4—84no—
547C4—3324no—
548C4—3324no—
549C4—6644no—
550C4C2×#1458170612yes—
551C4C2×#1458170612yes—
552C2—21no—
553C2—21no—
554C2—41no—
555C2—41no—
556C2—42no—
557C2—41no—
558C2—41no—
559C2#2490913712yesdirect product factor
560C2C22×#1458170611yescharacteristic
subgroupG/H
centerC22C2×#14581706
commutatorC2×C4×C83C23×C4
FrattiniC2×D4C23×D83
FittingC2×#410×C83C2
socleC22×C83C2×#99
prime radicalC22×#41×C83C22
cosocleC2×D4×C83C24
hypercenterC2×#410D83
hypocenterC83C2×#2129
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
3. #24909137C2direct (N × H)
4. C2×#19127495C2semidirect
6. C23×Dic166C4semidirect
9. #19128272C4semidirect
11. C2×#14581790C4semidirect
18. C2×#14581751C4semidirect
23. #19127495C22semidirect
36. C22×Dic166C2×C4semidirect
39. #14581790C2×C4semidirect
55. #14581751C2×C4semidirect
279. C2×C83#2129semidirect
286. C83C2×#2129semidirect
559. C2#24909137direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191282722
C2×#191276752
#249091372
C2×#191274952
C2×#410×C832
C2×#212983