Finite Group Databasebeta

← C2×#21445243 #29662299

Subgroups — C2×#21445243 #29662299

Order 15616.

758 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840113C211yesmaximal, characteristic, complemented
2C2×#16840043C211yesmaximal, characteristic
3C2×#16839968C211yesmaximal, characteristic
4C2×C8×D244C211yesmaximal, characteristic
5#21445243C218yesmaximal, direct product factor
6C2×#16839509C211yesmaximal, characteristic, complemented
7C2×#16839507C211yesmaximal, characteristic, complemented
8C2×C61×#334C211yesmaximal, characteristic, complemented
9C22×#11758190—21no—
10C22×C8×D61—21no—
11C2×#14519777C2211yescharacteristic
12C2×#14519777C2211yescharacteristic
13C2×C4×D244C2211yescharacteristic
14#16840113—22no—
15#16840113C2214yescomplemented
16#16840043—22no—
17#16840043C2214yes—
18#16839968—22no—
19#16839968C2214yes—
20C8×D244—22no—
21C8×D244C2214yes—
22C2×#14519711—21no—
23C2×C4⋊#92418C2211yescharacteristic
24C2×#14519702—21no—
25C2×#14519702—21no—
26C2×#14519702—21no—
27C2×#14519699—21no—
28C2×#14519689—21no—
29#16839509C2214yescomplemented
30#16839507C2214yescomplemented
31C2×C4⋊C8×C61C2211yescharacteristic
32C2×C4⋊C8×C61C2211yescharacteristic
33C2×C4×C8×C61C2211yescharacteristic
34C61×#334C2214yescomplemented
35C22×Dic122—21no—
36C22×Dic122—21no—
37C22×D244D411yescharacteristic
38C22×C4×D61—21no—
39C2×#11758190—24no—
40C2×#11758190—44no—
41C22×#92418—21no—
42C2×C8×D61—24no—
43C2×C8×D61—44no—
44#14519777—21no—
45#14519777—21no—
46#14519777—21no—
47#14519777—21no—
48#14519777—21no—
49#14519777—21no—
50#14519777C2312yes—
51#14519777C2312yes—
52C4×D244—21no—
53C4×D244—21no—
54C4×D244D412yes—
55C4×D244C2312yes—
56C2×C4⋊Dic61—21no—
57C2×C4⋊Dic61—21no—
58C2×C4⋊Dic61—21no—
59C2×C4⋊Dic61—21no—
60C2×C4⋊Dic61D411yescharacteristic
61C2×#11758198—21no—
62#14519711—24no—
63C4⋊#92418—21no—
64C4⋊#92418C2312yes—
65#14519702—24no—
66#14519702—24no—
67#14519702—24no—
68#14519699—24no—
69#14519689—24no—
70C22×C8×C61—21no—
71C22×C8×C61—21no—
72C22×C8×C61D411yescharacteristic
73C22×C8×C61D411yescharacteristic
74C2×C42×C61C2311yescharacteristic
75C4⋊C8×C61—21no—
76C4⋊C8×C61—21no—
77C4⋊C8×C61C2312yes—
78C4⋊C8×C61C2312yes—
79C4×C8×C61D412yes—
80C4×C8×C61C2312yes—
81C23×D61—21no—
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61#4111yescharacteristic
85C22×Dic61—21no—
86C22×Dic61—41no—
87C22×Dic61—41no—
88C2×D244—21no—
89C2×D244—22no—
90C2×D244SD1614yes—
91C2×D244C2×D412yes—
92C2×C4×D61—22no—
93C2×C4×D61—22no—
94C2×C4×D61—42no—
95C2×C4×D61—42no—
96C2×Dic122—22no—
97C2×Dic122—22no—
98C2×Dic122—42no—
99C2×Dic122—42no—
100C2×Dic122—42no—
101C2×Dic122—42no—
102C2×Dic122—41no—
103C2×Dic122—41no—
104C2×C8×C61—22no—
105C2×C8×C61—22no—
106C2×C8×C61—22no—
107C2×C8×C61—22no—
108C2×C8×C61—42no—
109C2×C8×C61—42no—
110C2×C8×C61C2×D412yes—
111C2×C8×C61C2×D412yes—
112C42×C61C2×D411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C42×C61#4111yescharacteristic
115C42×C61C2411yescharacteristic
116#11758198—22no—
117#11758198—22no—
118C4⋊Dic61—21no—
119C4⋊Dic61—22no—
120C4⋊Dic61—22no—
121C4⋊Dic61—22no—
122C4⋊Dic61—22no—
123C4⋊Dic61—41no—
124C4⋊Dic61—41no—
125C4⋊Dic61—41no—
126C4⋊Dic61—41no—
127C4⋊Dic61C2×D412yes—
128C2×#92418—22no—
129C2×#92418—42no—
130#11758190—48no—
131C8×D61—48no—
132C23×C61#12111yescharacteristic
133C22×D61—22no—
134C22×D61—24no—
135C22×D61—42no—
136C22×D61—42no—
137C2×C4×C61—22no—
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61#12111yescharacteristic
140C2×C4×C61#12111yescharacteristic
141C2×C4×C61C2×SD1612yes—
142C2×C4×C61#13512yes—
143C2×C4×C61#13512yes—
144C2×C4×C61AGL(1,ℤ/8)12yes—
145C2×C4×C61C22×D411yescharacteristic
146C2×C4×C61C22×D411yescharacteristic
147C2×C4×C61C2×#4111yescharacteristic
148C2×Dic61—22no—
149C2×Dic61—42no—
150C2×Dic61—42no—
151C2×Dic61—42no—
152C2×Dic61—82no—
153C2×Dic61—82no—
154D244—22no—
155D244—24no—
156D244C2×SD1614yes—
157C4×D61—42no—
158C4×D61—42no—
159C4×D61—44no—
160Dic122—42no—
161Dic122—42no—
162Dic122—42no—
163Dic122—42no—
164Dic122—82no—
165Dic122—82no—
166C8×C61—22no—
167C8×C61—22no—
168C8×C61—42no—
169C8×C61—42no—
170#92418—42no—
171C2×#1679—611nomaximal, Sylow
172C22×C61#46312yes—
173C22×C61#46512yes—
174C22×C61#47312yes—
175C22×C61C2×#12111yescharacteristic
176C2×D61—24no—
177C2×D61—48no—
178C2×D61—42no—
179C2×D61—42no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61#46312yes—
183C4×C61#46512yes—
184C4×C61C22×SD1611yescharacteristic
185C4×C61C2×#13511yescharacteristic
186C4×C61C2×#13511yescharacteristic
187C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
188Dic61—42no—
189Dic61—82no—
190Dic61—82no—
191C2×#487—611no—
192C2×#474—611no—
193C2×#461—611no—
194C2×C8×D4—611no—
195#1679—618no—
196C2×#334D6111yescharacteristic, complemented
197C2×#332—611no—
198C2×#332—611no—
199C2×C61#167914yescomplemented
200C2×C61C2×#46311yescharacteristic
201C2×C61C2×#46511yescharacteristic
202C2×C61C2×#47311yescharacteristic
203D61—44no—
204C22×SD16—1221no—
205C23×C8—1221no—
206C2×C4⋊Q8—611no—
207C2×C4⋊Q8—611no—
208C2×C4×D4—611no—
209#487—614no—
210#487—1222no—
211#474—614no—
212#474—1222no—
213#461—614no—
214#461—1222no—
215C8×D4—614no—
216C8×D4—1222no—
217C2×#107—1221no—
218C2×C4⋊C8—611no—
219C2×C4⋊C8C2×D6111yescharacteristic
220C2×C4⋊C8C2×D6111yescharacteristic
221C2×#103—1221no—
222C2×#103—1221no—
223C2×#103—1221no—
224C2×#102—1221no—
225C2×C22⋊C8—1221no—
226C2×C4×C8C2×D6111yescharacteristic
227#334C2×D6114yescomplemented
228#332—614no—
229#332—614no—
230C61C2×#167911yescharacteristic, complemented, Sylow
231C22×Q8—1221no—
232C22×Q8—1221no—
233C22×D4—611no—
234C23×C4—1221no—
235C2×SD16—1224no—
236C2×SD16—2444no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—1221no—
240C22×C8—1224no—
241C22×C8—2444no—
242C22×C8D24411yescharacteristic
243C22×C8D24411yescharacteristic
244C4⋊Q8—612no—
245C4⋊Q8—612no—
246C4⋊Q8—1221no—
247C4⋊Q8—1221no—
248C4⋊Q8—1221no—
249C4⋊Q8—1221no—
250C4⋊Q8—1221no—
251C4⋊Q8—1221no—
252C4×D4—612no—
253C4×D4—612no—
254C4×D4—1221no—
255C4×D4—1221no—
256C2×C4⋊C4—611no—
257C2×C4⋊C4—1221no—
258C2×C4⋊C4—1221no—
259C2×C4⋊C4—1221no—
260C2×C4⋊C4—1221no—
261C2×C22⋊C4—1221no—
262C2×C42C22×D6111yescharacteristic
263#107—1224no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—612no—
267C4⋊C8—1221no—
268C4⋊C8C22×D6112yes—
269C4⋊C8C22×D6112yes—
270#103—1224no—
271#103—1224no—
272#103—1224no—
273#102—1224no—
274C22⋊C8—1224no—
275C4×C8D24412yes—
276C4×C8C22×D6112yes—
277C24—1221no—
278C2×Q8—1222no—
279C2×Q8—1222no—
280C2×Q8—2442no—
281C2×Q8—2442no—
282C2×Q8—2442no—
283C2×Q8—2442no—
284C2×Q8—2441no—
285C2×Q8—2441no—
286C2×D4—612no—
287C2×D4—614no—
288C2×D4—1221no—
289C2×D4—1222no—
290C22×C4—1221no—
291C22×C4—1222no—
292C22×C4—1222no—
293C22×C4—2441no—
294C22×C4—2441no—
295C22×C4—2442no—
296C22×C4—2442no—
297C22×C4C2×D24411yescharacteristic
298C22×C4D4×D6111yescharacteristic
299C22×C4#1175822611yescharacteristic
300SD16—2448no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—42no—
306C2×C8—42no—
307C2×C8—1222no—
308C2×C8—2448no—
309C2×C8—2442no—
310C2×C8C2×D24412yes—
311C2×C8C2×D24412yes—
312C4⋊C4—612no—
313C4⋊C4—1221no—
314C4⋊C4—1222no—
315C4⋊C4—1222no—
316C4⋊C4—1222no—
317C4⋊C4—1222no—
318C4⋊C4—2441no—
319C4⋊C4—2441no—
320C4⋊C4—2441no—
321C4⋊C4—2441no—
322C22⋊C4—1222no—
323C22⋊C4—1222no—
324C42C2×D24411yescharacteristic
325C42D4×D6111yescharacteristic
326C42#1175822611yescharacteristic
327C42C23×D6111yescharacteristic
328C23—1224no—
329C23—1222no—
330C23—2442no—
331C23—2442no—
332C23#1451975211yescharacteristic
333Q8—4882no—
334Q8—4882no—
335Q8—2442no—
336Q8—2442no—
337Q8—2442no—
338Q8—2442no—
339D4—614no—
340D4—1224no—
341D4—1222no—
342C2×C4—22no—
343C2×C4—1222no—
344C2×C4—4882no—
345C2×C4—4882no—
346C2×C4—2442no—
347C2×C4—2442no—
348C2×C4—2442no—
349C2×C4—2444no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4#1451975211yescharacteristic
353C2×C4#1451975211yescharacteristic
354C2×C4#1451975211yescharacteristic
355C2×C4SD16×D6112yes—
356C2×C4#1451979812yes—
357C2×C4#1451979912yes—
358C2×C4#1451980512yes—
359C2×C4C2×D4×D6111yescharacteristic
360C2×C4C22×D24411yescharacteristic
361C2×C4C2×#1175822611yescharacteristic
362C8—22no—
363C8—22no—
364C8—42no—
365C8—42no—
366C8—2442no—
367C22—1224no—
368C22—2448no—
369C22—2442no—
370C22—2442no—
371C22#1683997812yes—
372C22#1683999212yes—
373C22#1684003812yes—
374C22C2×#1451975211yescharacteristic
375C4—21no—
376C4—21no—
377C4—4882no—
378C4—4882no—
379C4—2442no—
380C4#1683997812yes—
381C4#1683999212yes—
382C4C2×SD16×D6111yescharacteristic
383C4C2×#1451979811yescharacteristic
384C4C2×#1451979911yescharacteristic
385C4C2×#1451980511yescharacteristic
386C2—2444no—
387C2#2144524314yesdirect product factor
388C2C2×#1683997811yescharacteristic
389C2C2×#1683999211yescharacteristic
390C2C2×#1684003811yescharacteristic
subgroupG/H
centerC23#14519752
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#334C2
socleC23×C61#121
prime radicalC22×D244D4
hypercenterC2×#334D61
hypocenterC61C2×#1679
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
1. C2×#16840113C2semidirect
5. #21445243C2direct (N × H)
6. C2×#16839509C2semidirect
7. C2×#16839507C2semidirect
8. C2×C61×#334C2semidirect
15. #16840113C22semidirect
29. #16839509C22semidirect
30. #16839507C22semidirect
34. C61×#334C22semidirect
196. C2×#334D61semidirect
199. C2×C61#1679semidirect
227. #334C2×D61semidirect
230. C61C2×#1679semidirect
387. C2#21445243direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401132
C2×#168400432
C2×#168399682
C2×C8×D2442
#214452432
C2×#168395092
C2×#168395072
C2×C61×#3342
C2×#167961