Finite Group Databasebeta

← C2×#21458693 #30560451

Subgroups — C2×#21458693 #30560451

Order 15616.

1842 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840491C211yesmaximal, characteristic, complemented
2C2×#16840473C211yesmaximal, characteristic
3#21458693C2116yesmaximal, direct product factor
4C2×#16840163C212yesmaximal, complemented
5C2×#16840158C211yesmaximal, characteristic, complemented
6C2×#16840071C212yesmaximal, complemented
7C2×#16840065C212yesmaximal
8C2×#16840043C211yesmaximal, characteristic
9C2×#16839886C211yesmaximal, characteristic, complemented
10C2×C4×#11758201C211yesmaximal, characteristic
11C2×#16839847C212yesmaximal
12C2×C61×#477C211yesmaximal, characteristic, complemented
13C22×#11758201C2211yescharacteristic
14#16840491—24no—
15#16840491C2218yescomplemented
16#16840473—24no—
17#16840473C2218yes—
18C2×#14519777—21no—
19C2×#14519777C2211yescharacteristic
20C2×#14519768—22no—
21C2×#14519768C2212yes—
22C2×#14519768C2212yes—
23C2×#14519757—21no—
24C2×#14519753—22no—
25C2×Q8×Dic61C2212yes—
26C2×C4×Dic122—21no—
27C2×C4×Dic122C2211yescharacteristic
28C2×C4×D244C2211yescharacteristic
29C2×#14519739C2212yes—
30C2×C4⋊C4×D61—21no—
31#16840163C22116yescomplemented
32#16840158C2218yescomplemented
33#16840071C22116yescomplemented
34#16840065C22116yes—
35#16840043C2218yes—
36#16839886C2218yescomplemented
37C4×#11758201C2218yes—
38#16839847C22116yes—
39C2×#14519711C2212yes—
40C2×#14519708C2212yes—
41C2×#14519708C2212yes—
42C2×#14519708C2211yescharacteristic
43C2×#14519706C2212yes—
44C2×#14519701C2211yescharacteristic
45C2×#14519699C2212yes—
46C2×#14519697C2211yescharacteristic
47C2×C4×#92418C2211yescharacteristic
48C2×C8×Dic61C2212yes—
49C2×C4⋊Q8×C61C2211yescharacteristic
50C2×C4×Q8×C61C2211yescharacteristic
51C61×#477C2218yescomplemented
52C2×#107×C61C2212yes—
53C2×C4⋊C8×C61C2211yescharacteristic
54C2×#103×C61C2212yes—
55C22×Dic122—21no—
56C22×Dic122D411yescharacteristic
57C22×D244C2311yescharacteristic
58C22×C4×D61—21no—
59C22×C4×D61—22no—
60C2×#11758201Q818yescomplemented
61C2×#11758201C2314yes—
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64#14519777—28no—
65#14519777—22no—
66#14519777C2314yes—
67#14519768—216no—
68#14519768—24no—
69#14519768—24no—
70#14519768C2318yes—
71#14519768C2318yes—
72#14519757—28no—
73#14519753—216no—
74Q8×Dic61—24no—
75Q8×Dic61C2318yes—
76C4×Dic122—28no—
77C4×Dic122D414yes—
78C4×Dic122C2314yes—
79C4×D244—22no—
80C4×D244C2314yes—
81#14519739—24no—
82#14519739C2318yes—
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61—22no—
85C2×C4⋊Dic61—22no—
86C2×C4⋊Dic61—22no—
87C2×C4⋊Dic61D411yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2312yes—
90C2×#11758196—22no—
91C2×#11758196—22no—
92C2×#11758196D412yes—
93C4⋊C4×D61—28no—
94C2×#11758198—21no—
95C2×#11758198—22no—
96C2×C4×Dic61—22no—
97C2×C4×Dic61C2312yes—
98#14519711C2318yes—
99#14519708C2318yes—
100#14519708C2318yes—
101#14519708C2314yes—
102#14519706C2318yes—
103#14519701C2314yes—
104#14519699C2318yes—
105#14519697C2314yes—
106C4×#92418C2314yes—
107C8×Dic61C2318yes—
108C22×Q8×C61—21no—
109C22×Q8×C61C2311yescharacteristic
110C22×C8×C61C2312yes—
111C4⋊Q8×C61—22no—
112C4⋊Q8×C61C2314yes—
113C4×Q8×C61—22no—
114C4×Q8×C61C2314yes—
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61C2312yes—
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C42×C61—21no—
120C2×C42×C61C2311yescharacteristic
121#107×C61C2318yes—
122C4⋊C8×C61C2314yes—
123#103×C61C2318yes—
124C23×D61—21no—
125C2×Q8×C61—21no—
126C2×Q8×C61—24no—
127C2×Q8×C61—22no—
128C2×Q8×C61—82no—
129C2×Q8×C61C2×Q814yes—
130C2×Q8×C61C2412yes—
131C22×C4×C61—21no—
132C22×C4×C61—22no—
133C22×C4×C61—21no—
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2411yescharacteristic
137C22×Dic61—21no—
138C22×Dic61—22no—
139C22×Dic61C2×D412yes—
140C22×Dic61C2×D412yes—
141C2×D244—21no—
142C2×D244—22no—
143C2×D244C2×Q814yes—
144C2×D244C2412yes—
145C2×C4×D61—24no—
146C2×C4×D61—28no—
147C2×C4×D61—44no—
148C2×C4×D61—84no—
149C2×Dic122—24no—
150C2×Dic122—24no—
151C2×Dic122—44no—
152C2×Dic122C2×D414yes—
153C2×C8×C61—24no—
154C2×C8×C61C2414yes—
155C4⋊C4×C61—24no—
156C4⋊C4×C61—24no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—22no—
159C4⋊C4×C61C2414yes—
160C4⋊C4×C61C2412yes—
161C42×C61—24no—
162C42×C61C2×D412yes—
163C42×C61C2412yes—
164#11758201C2×Q8116yescomplemented
165#11758198—24no—
166#11758198—28no—
167C4⋊Dic61—24no—
168C4⋊Dic61—21no—
169C4⋊Dic61—22no—
170C4⋊Dic61—28no—
171C4⋊Dic61—28no—
172C4⋊Dic61—28no—
173C4⋊Dic61C2×D414yes—
174C4⋊Dic61C2414yes—
175C4⋊Dic61C2412yes—
176#11758196—28no—
177#11758196—28no—
178#11758196C2×D418yes—
179C4×Dic61—28no—
180C4×Dic61C2×D414yes—
181C4×Dic61C2414yes—
182C2×#92418—22no—
183C2×#92418C2×Q814yes—
184C2×#92418C2412yes—
185C2×#92418C2412yes—
186C23×C61C22×D411yescharacteristic
187C22×D61—24no—
188C22×D61—22no—
189C22×D61—42no—
190C22×D61—42no—
191Q8×C61—24no—
192Q8×C61—22no—
193Q8×C61—84no—
194Q8×C61C22×Q814yes—
195C2×C4×C61—24no—
196C2×C4×C61—22no—
197C2×C4×C61—22no—
198C2×C4×C61—22no—
199C2×C4×C61—24no—
200C2×C4×C61—44no—
201C2×C4×C61—42no—
202C2×C4×C61#13514yes—
203C2×C4×C61C22×D412yes—
204C2×C4×C61C22×D411yescharacteristic
205C2×C4×C61C22×D412yes—
206C2×C4×C61C22×Q812yes—
207C2×C4×C612−1+412yes—
208C2×C4×C61C2511yescharacteristic
209C2×Dic61—24no—
210C2×Dic61—24no—
211C2×Dic61—24no—
212C2×Dic61—22no—
213C2×Dic61—44no—
214C2×Dic61—42no—
215C2×Dic61C22×D414yes—
216C2×Dic61C22×D414yes—
217D244—24no—
218D244—22no—
219D244C22×Q814yes—
220C4×D61—48no—
221C4×D61—88no—
222Dic122—28no—
223Dic122—48no—
224C8×C61—24no—
225#92418—22no—
226#92418C22×Q814yes—
227C2×#3381—611nomaximal, Sylow
228C22×C61D4×Q812yes—
229C22×C61C2×#13512yes—
230C22×C61#57712yes—
231C22×C61C23×D411yescharacteristic
232C2×D61—24no—
233C2×D61—48no—
234C2×D61—42no—
235C2×D61—42no—
236C4×C61—24no—
237C4×C61—22no—
238C4×C61—44no—
239C4×C61—42no—
240C4×C61D4×Q812yes—
241C4×C61C2×#13514yes—
242C4×C61C23×Q811yescharacteristic
243C4×C61C2×2−1+411yescharacteristic
244Dic61—24no—
245Dic61—24no—
246Dic61—44no—
247Dic61—42no—
248C2×#557—611no—
249C2×#554—611no—
250#3381—6116no—
251C2×#499—612no—
252C2×#498—611no—
253C2×#479—612no—
254C2×#477D6111yescharacteristic, complemented
255C2×#478—612no—
256C2×#474—611no—
257C2×C8×Q8—611no—
258C2×C4×SD16—612no—
259C2×C4×SD16—611no—
260C2×C61#338114yescomplemented
261C2×C61C2×D4×Q811yescharacteristic
262C2×C61C22×#13511yescharacteristic
263C2×C61C2×#57711yescharacteristic
264D61—44no—
265C22×SD16—611no—
266#557—618no—
267#557—1224no—
268#554—618no—
269#554—1224no—
270C2×C4⋊Q8—611no—
271C2×C4⋊Q8—1221no—
272C2×C4⋊Q8C2×D6111yescharacteristic
273C2×#125—612no—
274C2×#125—612no—
275C2×#125—1222no—
276C2×C22⋊Q8—1221no—
277C2×C22⋊Q8—1222no—
278C2×C4×Q8—611no—
279C2×C4×Q8—612no—
280C2×C4×Q8—1221no—
281C2×C4×Q8C2×D6111yescharacteristic
282C2×C4×D4—612no—
283C2×C4×D4—611no—
284C22×C4⋊C4—1221no—
285#499—6116no—
286#498—618no—
287#479—6116no—
288#478—6116no—
289#477C2×D6118yescomplemented
290#474—618no—
291C8×Q8—618no—
292C4×SD16—618no—
293C4×SD16—6116no—
294C2×#107—612no—
295C2×#107C2×D6112yes—
296C2×#106—612no—
297C2×#106—612no—
298C2×#106—611no—
299C2×C4⋊C8—612no—
300C2×C4⋊C8C2×D6111yescharacteristic
301C2×#103—611no—
302C2×#103C2×D6112yes—
303C2×#102—612no—
304C2×#102—611no—
305C2×C4×C8—612no—
306C2×C4×C8—611no—
307C61C2×#338111yescharacteristic, complemented, Sylow
308C22×Q8—21no—
309C22×Q8—611no—
310C22×Q8—1221no—
311C22×Q8C22×D6111yescharacteristic
312C22×D4—611no—
313C23×C4—1222no—
314C23×C4—1221no—
315C2×SD16—618no—
316C2×SD16—614no—
317C22×C8—611no—
318C22×C8—611no—
319C22×C8C22×D6112yes—
320C4⋊Q8—22no—
321C4⋊Q8—614no—
322C4⋊Q8—1228no—
323C4⋊Q8—1222no—
324C4⋊Q8C22×D6114yes—
325#125—618no—
326#125—618no—
327#125—1224no—
328#125—1224no—
329#125—12216no—
330C22⋊Q8—1228no—
331C22⋊Q8—12216no—
332C4×Q8—22no—
333C4×Q8—614no—
334C4×Q8—614no—
335C4×Q8—618no—
336C4×Q8—1228no—
337C4×Q8—1224no—
338C4×Q8C22×D6114yes—
339C4×D4—618no—
340C4×D4—614no—
341C4×D4—1224no—
342C4×D4—1222no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—611no—
346C2×C4⋊C4—612no—
347C2×C4⋊C4—611no—
348C2×C4⋊C4—612no—
349C2×C4⋊C4—1228no—
350C2×C4⋊C4—1222no—
351C2×C4⋊C4—1222no—
352C2×C4⋊C4—1222no—
353C2×C4⋊C4—1222no—
354C2×C4⋊C4—1222no—
355C2×C4⋊C4—1221no—
356C2×C4⋊C4C22×D6112yes—
357C2×C4⋊C4C22×D6111yescharacteristic
358C2×C22⋊C4—1222no—
359C2×C22⋊C4—1221no—
360C2×C42—21no—
361C2×C42—612no—
362C2×C42—1222no—
363C2×C42C22×D6111yescharacteristic
364#107—618no—
365#107C22×D6118yes—
366#106—618no—
367#106—614no—
368#106—618no—
369C4⋊C8—618no—
370C4⋊C8C22×D6114yes—
371#103—614no—
372#103C22×D6118yes—
373#102—618no—
374#102—614no—
375C4×C8—618no—
376C4×C8—614no—
377C24—1221no—
378C2×Q8—21no—
379C2×Q8—24no—
380C2×Q8—22no—
381C2×Q8—82no—
382C2×Q8—614no—
383C2×Q8—1224no—
384C2×Q8—1224no—
385C2×Q8—2444no—
386C2×Q8Q8×D6114yes—
387C2×Q8C23×D6112yes—
388C2×D4—614no—
389C2×D4—612no—
390C2×D4—1221no—
391C2×D4—1222no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—612no—
396C22×C4—612no—
397C22×C4—1228no—
398C22×C4—1222no—
399C22×C4—1221no—
400C22×C4—1224no—
401C22×C4—4884no—
402C22×C4—2444no—
403C22×C4D4×D6111yescharacteristic
404C22×C4D4×D6111yescharacteristic
405C22×C4C23×D6111yescharacteristic
406SD16—6116no—
407C2×C8—24no—
408C2×C8—614no—
409C2×C8—612no—
410C2×C8—612no—
411C2×C8—1222no—
412C2×C8C23×D6114yes—
413C4⋊C4—24no—
414C4⋊C4—24no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—614no—
418C4⋊C4—618no—
419C4⋊C4—614no—
420C4⋊C4—612no—
421C4⋊C4—1228no—
422C4⋊C4—1228no—
423C4⋊C4—1228no—
424C4⋊C4—1228no—
425C4⋊C4—1228no—
426C4⋊C4—1221no—
427C4⋊C4—1222no—
428C4⋊C4—1224no—
429C4⋊C4C23×D6112yes—
430C4⋊C4C23×D6114yes—
431C22⋊C4—1228no—
432C22⋊C4—1224no—
433C42—24no—
434C42—614no—
435C42—614no—
436C42—1228no—
437C42D4×D6112yes—
438C42C23×D6112yes—
439C23—1222no—
440C23—1224no—
441C23—2442no—
442C23—2442no—
443C23C2×D4×D6111yescharacteristic
444Q8—22no—
445Q8—24no—
446Q8—84no—
447Q8—1228no—
448Q8—2448no—
449Q8C2×Q8×D6114yes—
450D4—614no—
451D4—1222no—
452D4—1224no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—24no—
458C2×C4—42no—
459C2×C4—44no—
460C2×C4—614no—
461C2×C4—614no—
462C2×C4—1224no—
463C2×C4—1224no—
464C2×C4—1224no—
465C2×C4—1222no—
466C2×C4—4888no—
467C2×C4—2442no—
468C2×C4—2444no—
469C2×C4—2448no—
470C2×C4#1451980014yes—
471C2×C4C2×D4×D6112yes—
472C2×C4C2×D4×D6112yes—
473C2×C4C2×D4×D6111yescharacteristic
474C2×C4C2×Q8×D6112yes—
475C2×C4#1451982412yes—
476C2×C4C24×D6111yescharacteristic
477C8—24no—
478C8—614no—
479C8—1222no—
480C22—1224no—
481C22—2448no—
482C22—2442no—
483C22—2442no—
484C22#1684042512yes—
485C22C2×#1451980012yes—
486C22#1684057212yes—
487C22C22×D4×D6111yescharacteristic
488C4—24no—
489C4—22no—
490C4—42no—
491C4—44no—
492C4—1224no—
493C4—1224no—
494C4—2442no—
495C4—2444no—
496C4#1684042512yes—
497C4C2×#1451980014yes—
498C4C22×Q8×D6111yescharacteristic
499C4C2×#1451982411yescharacteristic
500C2—2444no—
501C2#2145869314yesdirect product factor
502C2C2×#1684042511yescharacteristic
503C2C22×#1451980011yescharacteristic
504C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#477C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenterC2×#477D61
hypocenterC61C2×#3381
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#16840491C2semidirect
3. #21458693C2direct (N × H)
4. C2×#16840163C2semidirect
5. C2×#16840158C2semidirect
6. C2×#16840071C2semidirect
9. C2×#16839886C2semidirect
12. C2×C61×#477C2semidirect
15. #16840491C22semidirect
31. #16840163C22semidirect
32. #16840158C22semidirect
33. #16840071C22semidirect
36. #16839886C22semidirect
51. C61×#477C22semidirect
60. C2×#11758201Q8semidirect
164. #11758201C2×Q8semidirect
254. C2×#477D61semidirect
260. C2×C61#3381semidirect
289. #477C2×D61semidirect
307. C61C2×#3381semidirect
501. C2#21458693direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404912
C2×#168404732
#214586932
C2×#168401632
C2×#168401582
C2×#168400712
C2×#168400652
C2×#168400432
C2×#168398862
C2×C4×#117582012
C2×#168398472
C2×C61×#4772
C2×#338161