Finite Group Databasebeta

← C2×#21445331 #29662541

Subgroups — C2×#21445331 #29662541

Order 15616.

758 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840165C211yesmaximal, characteristic, complemented
2C2×#16839968C211yesmaximal, characteristic
3C2×#16839964C211yesmaximal, characteristic
4C2×#16839839C211yesmaximal, characteristic
5#21445331C218yesmaximal, direct product factor
6C2×#16839512C211yesmaximal, characteristic, complemented
7C2×#16839507C211yesmaximal, characteristic, complemented
8C2×C61×#332C211yesmaximal, characteristic, complemented
9C22×#11758190—21no—
10C22×#11758201—21no—
11C22×#11758189—21no—
12C2×#14519777C2211yescharacteristic
13C2×C4×D244C2211yescharacteristic
14#16840165—22no—
15#16840165C2214yescomplemented
16#16839968—22no—
17#16839968C2214yes—
18#16839964—22no—
19#16839964C2214yes—
20#16839839—22no—
21#16839839C2214yes—
22C2×#14519710—21no—
23C2×#14519710—21no—
24C2×C4⋊#92418C2211yescharacteristic
25C2×#14519702—21no—
26C2×#14519701—21no—
27C2×#14519689—21no—
28C2×C4×#92418C2211yescharacteristic
29#16839512C2214yescomplemented
30#16839507C2214yescomplemented
31C2×C4⋊Q8×C61C2211yescharacteristic
32C2×C4⋊C8×C61C2211yescharacteristic
33C2×C4⋊C8×C61C2211yescharacteristic
34C61×#332C2214yescomplemented
35C22×Dic122—21no—
36C22×D244D411yescharacteristic
37C22×C4×D61—21no—
38C2×#11758190—24no—
39C2×#11758190—44no—
40C2×#11758201—24no—
41C2×#11758201—44no—
42C2×#11758189—24no—
43C2×#11758189—44no—
44C22×#92418—21no—
45C22×#92418D411yescharacteristic
46C22×#92418D411yescharacteristic
47#14519777—21no—
48#14519777—21no—
49#14519777—21no—
50#14519777C2312yes—
51C4×D244—21no—
52C4×D244—21no—
53C4×D244D412yes—
54C4×D244C2312yes—
55C2×C4⋊Dic61—21no—
56C2×C4⋊Dic61—21no—
57C2×C4⋊Dic61D411yescharacteristic
58C2×#11758198—21no—
59#14519710—24no—
60#14519710—24no—
61C4⋊#92418—21no—
62C4⋊#92418C2312yes—
63#14519702—24no—
64#14519701—24no—
65#14519689—24no—
66C4×#92418D412yes—
67C4×#92418C2312yes—
68C22×Q8×C61—21no—
69C22×C8×C61—21no—
70C22×C8×C61—21no—
71C4⋊Q8×C61—21no—
72C4⋊Q8×C61—21no—
73C4⋊Q8×C61—21no—
74C4⋊Q8×C61C2312yes—
75C2×C4⋊C4×C61—21no—
76C2×C4⋊C4×C61—21no—
77C2×C42×C61C2311yescharacteristic
78C4⋊C8×C61—21no—
79C4⋊C8×C61—21no—
80C4⋊C8×C61C2312yes—
81C4⋊C8×C61C2312yes—
82C23×D61—21no—
83C2×Q8×C61—22no—
84C2×Q8×C61—41no—
85C2×Q8×C61—42no—
86C2×Q8×C61—42no—
87C22×C4×C61—41no—
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61#4111yescharacteristic
91C22×Dic61—21no—
92C22×Dic61—41no—
93C2×D244—22no—
94C2×D244—22no—
95C2×D244—21no—
96C2×D244C2×D412yes—
97C2×C4×D61—22no—
98C2×C4×D61—22no—
99C2×C4×D61—42no—
100C2×C4×D61—42no—
101C2×Dic122—22no—
102C2×Dic122—42no—
103C2×Dic122—42no—
104C2×Dic122—41no—
105C2×C8×C61—22no—
106C2×C8×C61—22no—
107C2×C8×C61—42no—
108C2×C8×C61—42no—
109C4⋊C4×C61—22no—
110C4⋊C4×C61—22no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C42×C61#4111yescharacteristic
116C42×C61C2411yescharacteristic
117#11758201—48no—
118#11758198—22no—
119#11758198—22no—
120C4⋊Dic61—21no—
121C4⋊Dic61—22no—
122C4⋊Dic61—22no—
123C4⋊Dic61—41no—
124C4⋊Dic61—41no—
125C4⋊Dic61C2×D412yes—
126C2×#92418—22no—
127C2×#92418—22no—
128C2×#92418—42no—
129C2×#92418SD1614yescomplemented
130C2×#92418C2×D412yes—
131C2×#92418C2×D412yes—
132#11758190—48no—
133#11758189—48no—
134C23×C61#12111yescharacteristic
135C22×D61—22no—
136C22×D61—42no—
137C22×D61—42no—
138C22×D61—42no—
139Q8×C61—42no—
140Q8×C61—42no—
141Q8×C61—82no—
142C2×C4×C61—22no—
143C2×C4×C61—42no—
144C2×C4×C61—82no—
145C2×C4×C61#12111yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61#12111yescharacteristic
148C2×C4×C61C2×SD1612yes—
149C2×C4×C61AGL(1,ℤ/8)12yes—
150C2×C4×C61AGL(1,ℤ/8)12yes—
151C2×C4×C61#13712yes—
152C2×C4×C61C22×D411yescharacteristic
153C2×C4×C61C22×D411yescharacteristic
154C2×C4×C61C2×#4111yescharacteristic
155C2×Dic61—22no—
156C2×Dic61—42no—
157C2×Dic61—42no—
158C2×Dic61—82no—
159D244—22no—
160D244—22no—
161D244—42no—
162C4×D61—42no—
163C4×D61—42no—
164C4×D61—44no—
165Dic122—42no—
166Dic122—42no—
167Dic122—82no—
168C8×C61—42no—
169C8×C61—42no—
170#92418—22no—
171#92418—42no—
172#92418C2×SD1614yescomplemented
173C2×#1693—611nomaximal, Sylow
174C22×C61#46112yes—
175C22×C61#46912yes—
176C22×C61#47312yes—
177C22×C61C2×#12111yescharacteristic
178C2×D61—42no—
179C2×D61—42no—
180C2×D61—42no—
181C2×D61—84no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—82no—
185C4×C61#46112yes—
186C4×C61#46912yes—
187C4×C61C22×SD1611yescharacteristic
188C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
189C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
190C4×C61C2×#13711yescharacteristic
191Dic61—42no—
192Dic61—82no—
193C2×#500—611no—
194C2×#461—611no—
195C2×#461—611no—
196C2×#436—611no—
197#1693—618no—
198C2×#334—611no—
199C2×#332—611no—
200C2×#332D6111yescharacteristic, complemented
201C2×C61#169314yescomplemented
202C2×C61C2×#46111yescharacteristic
203C2×C61C2×#46911yescharacteristic
204C2×C61C2×#47311yescharacteristic
205D61—82no—
206C22×SD16—1221no—
207C22×SD16—1221no—
208C22×M16—1221no—
209C2×C4⋊Q8—611no—
210C2×C4⋊Q8C2×D6111yescharacteristic
211C2×C4×D4—611no—
212#500—614no—
213#500—1222no—
214#461—614no—
215#461—614no—
216#461—1222no—
217#461—1222no—
218#436—614no—
219#436—1222no—
220C2×#107—1221no—
221C2×#107—1221no—
222C2×C4⋊C8—611no—
223C2×C4⋊C8C2×D6111yescharacteristic
224C2×C4⋊C8C2×D6111yescharacteristic
225C2×#103—1221no—
226C2×#103—1221no—
227C2×C22⋊C8—1221no—
228C2×C4×C8—611no—
229#334—614no—
230#332—614no—
231#332C2×D6114yescomplemented
232C61C2×#169311yescharacteristic, complemented, Sylow
233C22×Q8—21no—
234C22×Q8—1221no—
235C22×D4—611no—
236C23×C4—1221no—
237C2×SD16—1224no—
238C2×SD16—1224no—
239C2×SD16—2444no—
240C2×SD16—2444no—
241C2×M16—1224no—
242C2×M16—2444no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—611no—
246C22×C8—611no—
247C22×C8—1221no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—612no—
252C4⋊Q8—1221no—
253C4⋊Q8—1221no—
254C4⋊Q8—1221no—
255C4⋊Q8C22×D6112yes—
256C4×D4—612no—
257C4×D4—612no—
258C4×D4—1221no—
259C4×D4—1221no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—611no—
263C2×C4⋊C4—1221no—
264C2×C4⋊C4—1221no—
265C2×C22⋊C4—1221no—
266C2×C42C22×D6111yescharacteristic
267#107—1224no—
268#107—1224no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—612no—
272C4⋊C8—1221no—
273C4⋊C8C22×D6112yes—
274C4⋊C8C22×D6112yes—
275#103—1224no—
276#103—1224no—
277C22⋊C8—1224no—
278C4×C8—612no—
279C4×C8—612no—
280C24—1221no—
281C2×Q8—22no—
282C2×Q8—41no—
283C2×Q8—42no—
284C2×Q8—42no—
285C2×Q8—1222no—
286C2×Q8—2442no—
287C2×Q8—2442no—
288C2×Q8—2441no—
289C2×D4—612no—
290C2×D4—1221no—
291C2×D4—1222no—
292C2×D4—1222no—
293C22×C4—41no—
294C22×C4—1221no—
295C22×C4—1222no—
296C22×C4—1222no—
297C22×C4—2441no—
298C22×C4—2442no—
299C22×C4—2442no—
300C22×C4#1175822211yescharacteristic
301C22×C4D4×D6111yescharacteristic
302C22×C4D4×D6111yescharacteristic
303SD16—2448no—
304SD16—2448no—
305M16—2448no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—42no—
309C2×C8—42no—
310C2×C8—612no—
311C2×C8—614no—
312C2×C8—612no—
313C2×C8—1222no—
314C2×C8—1222no—
315C2×C8—2442no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—612no—
321C4⋊C4—1221no—
322C4⋊C4—1222no—
323C4⋊C4—1222no—
324C4⋊C4—2441no—
325C4⋊C4—2441no—
326C22⋊C4—1222no—
327C22⋊C4—1222no—
328C42#1175822211yescharacteristic
329C42D4×D6111yescharacteristic
330C42D4×D6111yescharacteristic
331C42C23×D6111yescharacteristic
332C23—1222no—
333C23—2442no—
334C23—2442no—
335C23—2442no—
336C23#1451975011yescharacteristic
337Q8—42no—
338Q8—42no—
339Q8—82no—
340Q8—4882no—
341Q8—2442no—
342Q8—2442no—
343D4—1222no—
344D4—1222no—
345D4—2442no—
346C2×C4—22no—
347C2×C4—42no—
348C2×C4—82no—
349C2×C4—1222no—
350C2×C4—4882no—
351C2×C4—2442no—
352C2×C4—2442no—
353C2×C4—2444no—
354C2×C4—2442no—
355C2×C4—2442no—
356C2×C4#1451975011yescharacteristic
357C2×C4#1451975011yescharacteristic
358C2×C4#1451975011yescharacteristic
359C2×C4SD16×D6112yes—
360C2×C4#1451980112yes—
361C2×C4#1451980412yes—
362C2×C4#1451980912yes—
363C2×C4C2×D4×D6111yescharacteristic
364C2×C4C2×D4×D6111yescharacteristic
365C2×C4C2×#1175822211yescharacteristic
366C8—42no—
367C8—42no—
368C8—614no—
369C8—1222no—
370C8—2442no—
371C22—4884no—
372C22—2442no—
373C22—2442no—
374C22—2442no—
375C22#1683996612yes—
376C22#1684001412yes—
377C22#1684003612yes—
378C22C2×#1451975011yescharacteristic
379C4—21no—
380C4—21no—
381C4—82no—
382C4—4882no—
383C4—2442no—
384C4#1683996612yes—
385C4#1684001412yes—
386C4C2×SD16×D6111yescharacteristic
387C4C2×#1451980111yescharacteristic
388C4C2×#1451980411yescharacteristic
389C4C2×#1451980911yescharacteristic
390C2—4882no—
391C2#2144533114yesdirect product factor
392C2C2×#1683996611yescharacteristic
393C2C2×#1684001411yescharacteristic
394C2C2×#1684003611yescharacteristic
subgroupG/H
centerC23#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#332C2
socleC23×C61#121
prime radicalC22×D244D4
hypercenterC2×#332D61
hypocenterC61C2×#1693
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
1. C2×#16840165C2semidirect
5. #21445331C2direct (N × H)
6. C2×#16839512C2semidirect
7. C2×#16839507C2semidirect
8. C2×C61×#332C2semidirect
15. #16840165C22semidirect
29. #16839512C22semidirect
30. #16839507C22semidirect
34. C61×#332C22semidirect
129. C2×#92418SD16semidirect
172. #92418C2×SD16semidirect
200. C2×#332D61semidirect
201. C2×C61#1693semidirect
231. #332C2×D61semidirect
232. C61C2×#1693semidirect
391. C2#21445331direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401652
C2×#168399682
C2×#168399642
C2×#168398392
#214453312
C2×#168395122
C2×#168395072
C2×C61×#3322
C2×#169361