Finite Group Databasebeta

← C2×#21445389 #29662679

Subgroups — C2×#21445389 #29662679

Order 15616.

734 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840110C211yesmaximal, characteristic
2C2×#16839962C211yesmaximal, characteristic
3C2×#16839893C211yesmaximal, characteristic, complemented
4#21445389C218yesmaximal, direct product factor
5C2×#16839512C211yesmaximal, characteristic, complemented
6C2×#16839508C211yesmaximal, characteristic, complemented
7C2×#16839505C211yesmaximal, characteristic
8C2×C61×#462C211yesmaximal, characteristic, complemented
9C22×#11758201—21no—
10C2×#14519774C2211yescharacteristic
11#16840110—22no—
12#16840110C2214yes—
13#16839962—22no—
14#16839962C2214yes—
15#16839893—22no—
16#16839893C2214yescomplemented
17C2×C4⋊#92418—21no—
18C2×C4⋊#92418C2211yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20C2×#14519697—21no—
21C2×#14519697—21no—
22C2×#14519697—21no—
23C2×#14519688—21no—
24C2×C4×#92418C2211yescharacteristic
25#16839512C2214yescomplemented
26#16839508C2214yescomplemented
27#16839505C2214yes—
28C22×Q16×C61—21no—
29C2×C4⋊Q8×C61C2211yescharacteristic
30C2×C4×Q8×C61C2211yescharacteristic
31C61×#462—22no—
32C61×#462C2214yescomplemented
33C2×C4⋊C8×C61C2211yescharacteristic
34C2×#103×C61—21no—
35C22×D244—21no—
36C22×D244—21no—
37C22×D244—21no—
38C2×#11758201—24no—
39C2×#11758201—44no—
40C22×#92418—21no—
41C22×#92418—21no—
42C22×#92418D411yescharacteristic
43C22×#92418D411yescharacteristic
44#14519774—21no—
45#14519774—21no—
46#14519774—21no—
47#14519774C2312yes—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50C4⋊#92418—24no—
51C4⋊#92418C2312yes—
52C4⋊#92418C2312yes—
53#14519697—24no—
54#14519697—24no—
55#14519697—24no—
56#14519688—24no—
57C4×#92418D412yes—
58C4×#92418C2312yes—
59C22×Q8×C61—21no—
60C22×Q8×C61D411yescharacteristic
61C2×Q16×C61—24no—
62C2×Q16×C61—44no—
63C22×C8×C61—21no—
64C4⋊Q8×C61—21no—
65C4⋊Q8×C61—21no—
66C4⋊Q8×C61—21no—
67C4⋊Q8×C61C2312yes—
68C4×Q8×C61—21no—
69C4×Q8×C61—21no—
70C4×Q8×C61D412yes—
71C4×Q8×C61C2312yes—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61—21no—
74C2×C4⋊C4×C61—21no—
75C2×C4⋊C4×C61D411yescharacteristic
76C2×C42×C61—21no—
77C2×C42×C61C2311yescharacteristic
78C4⋊C8×C61—21no—
79C4⋊C8×C61C2312yes—
80#103×C61—24no—
81C23×D61—41no—
82C2×Q8×C61—21no—
83C2×Q8×C61—22no—
84C2×Q8×C61—22no—
85C2×Q8×C61—22no—
86C2×Q8×C61—41no—
87C2×Q8×C61—42no—
88C2×Q8×C61—42no—
89C2×Q8×C61C2×D412yes—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—41no—
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61#4111yescharacteristic
96C2×D244—22no—
97C2×D244—22no—
98C2×D244—22no—
99C2×D244—42no—
100C2×D244—42no—
101C2×D244—42no—
102C2×D244—42no—
103C2×D244—41no—
104C2×D244—41no—
105C2×D244—41no—
106C2×D244—82no—
107Q16×C61—48no—
108C2×C8×C61—22no—
109C2×C8×C61—42no—
110C4⋊C4×C61—22no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—22no—
113C4⋊C4×C61—22no—
114C4⋊C4×C61—22no—
115C4⋊C4×C61—41no—
116C4⋊C4×C61—41no—
117C4⋊C4×C61C2×D412yes—
118C42×C61—22no—
119C42×C61—22no—
120C42×C61C2×D411yescharacteristic
121C42×C61C2×D411yescharacteristic
122C42×C61#4111yescharacteristic
123C42×C61C2411yescharacteristic
124#11758201—48no—
125C2×#92418—22no—
126C2×#92418—22no—
127C2×#92418—22no—
128C2×#92418—22no—
129C2×#92418—42no—
130C2×#92418—42no—
131C2×#92418C2×D412yes—
132C2×#92418C2×D412yes—
133C23×C61#12111yescharacteristic
134C22×D61—42no—
135C22×D61—82no—
136C22×D61—82no—
137C22×D61—82no—
138Q8×C61—22no—
139Q8×C61—22no—
140Q8×C61—42no—
141Q8×C61—42no—
142Q8×C61—42no—
143Q8×C61—82no—
144C2×C4×C61—22no—
145C2×C4×C61—22no—
146C2×C4×C61—22no—
147C2×C4×C61—42no—
148C2×C4×C61—42no—
149C2×C4×C61—42no—
150C2×C4×C61—82no—
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12111yescharacteristic
153C2×C4×C61#12111yescharacteristic
154C2×C4×C61#13512yes—
155C2×C4×C61AGL(1,ℤ/8)12yes—
156C2×C4×C61AGL(1,ℤ/8)12yes—
157C2×C4×C61#13712yes—
158C2×C4×C61C22×D411yescharacteristic
159C2×C4×C61C22×D411yescharacteristic
160C2×C4×C61C2×#4111yescharacteristic
161D244—42no—
162D244—42no—
163D244—42no—
164D244—42no—
165D244—82no—
166D244—82no—
167D244—82no—
168D244—82no—
169C8×C61—42no—
170#92418—22no—
171#92418—22no—
172#92418—42no—
173#92418—42no—
174C2×#1702—611nomaximal, Sylow
175C22×C61#46412yes—
176C22×C61#46912yes—
177C22×C61#47112yes—
178C22×C61C2×#12111yescharacteristic
179C2×D61—82no—
180C2×D61—82no—
181C2×D61—82no—
182C2×D61—164no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—42no—
186C4×C61—42no—
187C4×C61—82no—
188C4×C61#46412yes—
189C4×C61#46912yes—
190C4×C61C2×#13511yescharacteristic
191C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
192C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
193C4×C61C2×#13711yescharacteristic
194C2×#486—611no—
195C2×#462D6111yescharacteristic, complemented
196C2×#460—611no—
197C2×#446—611no—
198#1702—618no—
199C2×#334—611no—
200C2×#332—611no—
201C2×#331—611no—
202C2×C61#170214yescomplemented
203C2×C61C2×#46411yescharacteristic
204C2×C61C2×#46911yescharacteristic
205C2×C61C2×#47111yescharacteristic
206D61—162no—
207C22×Q16—21no—
208C22×SD16—1221no—
209C2×C4⋊Q8C2×D6111yescharacteristic
210C2×#127—611no—
211C2×C4×Q8C2×D6111yescharacteristic
212#486—614no—
213#486—1222no—
214#462—22no—
215#462C2×D6114yescomplemented
216#460—614no—
217#460—1222no—
218#446—614no—
219#446—1222no—
220C2×C4⋊C8—611no—
221C2×C4⋊C8—611no—
222C2×C4⋊C8—1221no—
223C2×C4⋊C8C2×D6111yescharacteristic
224C2×#103—21no—
225C2×#102—1221no—
226C2×#102—1221no—
227C2×#102—1221no—
228C2×#97—1221no—
229C2×C4×C8—611no—
230#334—614no—
231#332—614no—
232#331—614no—
233C61C2×#170211yescharacteristic, complemented, Sylow
234C22×Q8—21no—
235C22×Q8C22⋊D6111yescharacteristic
236C22×D4—1221no—
237C22×D4—1221no—
238C22×D4—1221no—
239C2×Q16—24no—
240C2×Q16—44no—
241C2×SD16—1224no—
242C2×SD16—2444no—
243C22×C8—21no—
244C22×C8—611no—
245C22×C8—611no—
246C22×C8—1221no—
247C22×C8—1221no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8C22×D6112yes—
252#127—612no—
253#127—1221no—
254#127—1221no—
255#127—1221no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8C22⋊D6112yes—
259C4×Q8C22×D6112yes—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4C22⋊D6111yescharacteristic
264C2×C42—21no—
265C2×C42C22×D6111yescharacteristic
266C4⋊C8—21no—
267C4⋊C8—612no—
268C4⋊C8—612no—
269C4⋊C8—1224no—
270C4⋊C8—1221no—
271C4⋊C8—1221no—
272C4⋊C8C22×D6112yes—
273#103—24no—
274#102—1224no—
275#102—1224no—
276#102—1224no—
277#97—1224no—
278C4×C8—612no—
279C4×C8—612no—
280C24—2441no—
281C2×Q8—21no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8—22no—
285C2×Q8—41no—
286C2×Q8—42no—
287C2×Q8—42no—
288C2×Q8C2×C22⋊D6112yes—
289C2×D4—1222no—
290C2×D4—1222no—
291C2×D4—1222no—
292C2×D4—4882no—
293C2×D4—2442no—
294C2×D4—2441no—
295C2×D4—2441no—
296C2×D4—2441no—
297C2×D4—2442no—
298C2×D4—2442no—
299C2×D4—2442no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—41no—
303C22×C4D4×D6111yescharacteristic
304C22×C4#1175822411yescharacteristic
305C22×C4C2×C22⋊D6111yescharacteristic
306Q16—48no—
307SD16—2448no—
308C2×C8—22no—
309C2×C8—42no—
310C2×C8—612no—
311C2×C8—612no—
312C2×C8—1222no—
313C2×C8—1222no—
314C2×C8—1222no—
315C2×C8—1222no—
316C2×C8—2442no—
317C2×C8—2442no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4C2×C22⋊D6112yes—
326C42—22no—
327C42—22no—
328C42D4×D6111yescharacteristic
329C42#1175822411yescharacteristic
330C42C2×C22⋊D6111yescharacteristic
331C42C23×D6111yescharacteristic
332C23—4882no—
333C23—4882no—
334C23—4882no—
335C23—2442no—
336C23#1451974911yescharacteristic
337Q8—22no—
338Q8—22no—
339Q8—42no—
340Q8—42no—
341Q8—42no—
342Q8—82no—
343D4—4882no—
344D4—4882no—
345D4—4882no—
346D4—4882no—
347D4—2442no—
348D4—2442no—
349D4—2442no—
350D4—2442no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—82no—
358C2×C4#1451974911yescharacteristic
359C2×C4#1451974911yescharacteristic
360C2×C4#1451974911yescharacteristic
361C2×C4#1451980012yes—
362C2×C4#1451980212yes—
363C2×C4#1451980312yes—
364C2×C4#1451980912yes—
365C2×C4C2×D4×D6111yescharacteristic
366C2×C4C22×C22⋊D6111yescharacteristic
367C2×C4C2×#1175822411yescharacteristic
368C8—42no—
369C8—1222no—
370C8—1222no—
371C8—2442no—
372C8—2442no—
373C22—9764no—
374C22—4882no—
375C22—4882no—
376C22—4882no—
377C22#1683998612yes—
378C22#1684001312yes—
379C22#1684002712yes—
380C22C2×#1451974911yescharacteristic
381C4—21no—
382C4—21no—
383C4—42no—
384C4—42no—
385C4—82no—
386C4#1683998612yes—
387C4#1684001312yes—
388C4C2×#1451980011yescharacteristic
389C4C2×#1451980211yescharacteristic
390C4C2×#1451980311yescharacteristic
391C4C2×#1451980911yescharacteristic
392C2—9762no—
393C2#2144538914yesdirect product factor
394C2C2×#1683998611yescharacteristic
395C2C2×#1684001311yescharacteristic
396C2C2×#1684002711yescharacteristic
subgroupG/H
centerC23#14519749
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#462C2
socleC23×C61#121
prime radicalC2×#14519774C22
hypercenterC2×#462D61
hypocenterC61C2×#1702
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. C2×#16839893C2semidirect
4. #21445389C2direct (N × H)
5. C2×#16839512C2semidirect
6. C2×#16839508C2semidirect
8. C2×C61×#462C2semidirect
16. #16839893C22semidirect
25. #16839512C22semidirect
26. #16839508C22semidirect
32. C61×#462C22semidirect
195. C2×#462D61semidirect
202. C2×C61#1702semidirect
215. #462C2×D61semidirect
233. C61C2×#1702semidirect
393. C2#21445389direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401102
C2×#168399622
C2×#168398932
#214453892
C2×#168395122
C2×#168395082
C2×#168395052
C2×C61×#4622
C2×#170261