Finite Group Databasebeta

← C2×#21447708 #29833444

Subgroups — C2×#21447708 #29833444

Order 15616.

646 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840203C211yesmaximal, characteristic
2C2×#16839885C211yesmaximal, characteristic
3#21447708C218yesmaximal, direct product factor
4C2×#16839584C211yesmaximal, characteristic, complemented
5C2×#16839578C211yesmaximal, characteristic, complemented
6C2×#16839571C211yesmaximal, characteristic
7C2×#16839540C211yesmaximal, characteristic, complemented
8C2×C61×#441C211yesmaximal, characteristic, complemented
9C2×#14519799C2211yescharacteristic
10C2×#14519783—21no—
11#16840203C414yescomplemented
12#16840203C2214yes—
13C2×#14519723C412yescomplemented
14C2×#14519720C412yescomplemented
15C2×#14519717C2211yescharacteristic
16C2×#14519717C2211yescharacteristic
17#16839885—22no—
18#16839885C2214yes—
19C2×#14519713C2211yescharacteristic
20C2×#14519705—21no—
21#16839584C2214yescomplemented
22#16839578C2214yescomplemented
23#16839571C2214yes—
24#16839540C2214yescomplemented
25C22×Q16×C61C2211yescharacteristic
26C2×C4×Q8×C61—21no—
27C61×#441—22no—
28C61×#441C2214yescomplemented
29C2×#106×C61C2211yescharacteristic
30C2×#103×C61—21no—
31C2×#97×C61C2211yescharacteristic
32C2×#11758222—21no—
33#14519799—21no—
34#14519799—21no—
35#14519799C2×C412yes—
36#14519799C2312yes—
37C2×Dic244C2×C411yescharacteristic
38C2×#11758190—21no—
39C2×D488C2×C411yescharacteristic
40#14519783—24no—
41#14519783—42no—
42C2×#11758194—21no—
43C2×#11758189—41no—
44C2×C8×D61—41no—
45#14519723C2×C418yescomplemented
46#14519720C2×C418yescomplemented
47#14519717—21no—
48#14519717C2×C412yes—
49#14519717C2312yes—
50#14519717C2312yes—
51C2×#11758185—21no—
52C2×#11758185C2×C412yes—
53#14519713—21no—
54#14519713C2312yes—
55#14519705—24no—
56C22×Q8×C61—21no—
57C2×Q16×C61—21no—
58C2×Q16×C61—21no—
59C2×Q16×C61—21no—
60C2×Q16×C61C2×C412yes—
61C2×Q16×C61C2×C412yes—
62C2×Q16×C61C2312yes—
63C22×C8×C61D411yescharacteristic
64C22×C8×C61C2311yescharacteristic
65C4×Q8×C61—24no—
66C4×Q8×C61—42no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—41no—
69C2×C42×C61—41no—
70C2×C42×C61D411yescharacteristic
71#106×C61—21no—
72#106×C61C2312yes—
73#103×C61—24no—
74#97×C61D412yes—
75#97×C61C2312yes—
76C2×Q8×C61—22no—
77C2×Q8×C61—22no—
78C2×Q8×C61—22no—
79C2×Q8×C61—41no—
80C2×Q8×C61—41no—
81C2×Q8×C61—41no—
82C22×C4×C61—21no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61C2×D411yescharacteristic
86C2×C22⋊D61—41no—
87#11758222—22no—
88#11758222—22no—
89#11758222—41no—
90#11758222—41no—
91C2×D244—21no—
92C2×C4×D61—41no—
93C2×Dic122—21no—
94Q16×C61—22no—
95Q16×C61—22no—
96Q16×C61—22no—
97Q16×C61C22×C414yes—
98C2×C8×C61—21no—
99C2×C8×C61—21no—
100C2×C8×C61C22×C411yescharacteristic
101C2×C8×C61C22×C411yescharacteristic
102C2×C8×C61C2×D412yes—
103C2×C8×C61C2×D411yescharacteristic
104C2×C8×C61#4111yescharacteristic
105C2×C8×C61#4111yescharacteristic
106C2×C8×C61C2411yescharacteristic
107C4⋊C4×C61—22no—
108C4⋊C4×C61—44no—
109C4⋊C4×C61—41no—
110C42×C61—21no—
111C42×C61—44no—
112C42×C61C2×D412yes—
113#11758194—22no—
114#11758194—41no—
115C2×#92418—41no—
116Dic244—21no—
117Dic244C22×C412yes—
118D488—21no—
119D488C22×C412yes—
120#11758190—22no—
121#11758190—22no—
122#11758189—44no—
123C8×D61—44no—
124#11758185—22no—
125#11758185C22×C414yes—
126C23×C61AGL(1,ℤ/8)11yescharacteristic
127C22×D61—41no—
128Q8×C61—24no—
129Q8×C61—42no—
130Q8×C61—42no—
131Q8×C61—42no—
132C2×C4×C61—22no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61—42no—
136C2×C4×C61—42no—
137C2×C4×C61—42no—
138C2×C4×C61—82no—
139C2×C4×C61C4×D411yescharacteristic
140C2×C4×C61C4×D411yescharacteristic
141C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C61C22×D411yescharacteristic
145C22⋊D61—42no—
146C22⋊D61—42no—
147C2×Dic61—41no—
148D244—22no—
149D244—41no—
150C4×D61—42no—
151C4×D61—42no—
152Dic122—22no—
153Dic122—41no—
154C8×C61—22no—
155C8×C61C4×D411yescharacteristic
156C8×C61C4×D411yescharacteristic
157C8×C61C23×C411yescharacteristic
158C8×C61C2×#4111yescharacteristic
159#92418—42no—
160C2×#2180—611nomaximal, Sylow
161C22×C61—22no—
162C22×C61#44211yescharacteristic
163C22×C61#44211yescharacteristic
164C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
165C2×D61—42no—
166C2×D61—82no—
167C4×C61—42no—
168C4×C61—44no—
169C4×C61—82no—
170C4×C61#44211yescharacteristic
171C4×C61#44211yescharacteristic
172C4×C61C2×C4×D411yescharacteristic
173C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
174Dic61—42no—
175C2×#510—611no—
176C2×#444—611no—
177C2×#441D6111yescharacteristic, complemented
178#2180—618no—
179C2×#365—611no—
180C2×#362—611no—
181C2×#360—611no—
182C2×#347—611no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61#218012yescomplemented
186C2×C61C2×#44211yescharacteristic
187D61—82no—
188C2×#135—611no—
189C22×Q16C2×D6111yescharacteristic
190C2×#131—1221no—
191C2×C4×Q8—21no—
192#510—614no—
193#510—614no—
194C2×Q32—612no—
195C2×SD32—612no—
196C2×M32—611no—
197C2×M32—611no—
198#444—614no—
199#444—1222no—
200#441—22no—
201#441C2×D6114yescomplemented
202C2×#108—611no—
203C2×#106C2×D6111yescharacteristic
204C2×#104—1221no—
205C2×#103—21no—
206C2×#97C2×D6111yescharacteristic
207#365—614no—
208#362—614no—
209#360—614no—
210#347—614no—
211C61C2×#218011yescharacteristic, complemented, Sylow
212C2×#41—1221no—
213C22×Q8—21no—
214#135—612no—
215#135—612no—
216#135—1221no—
217#135—1221no—
218C2×Q16—21no—
219C2×Q16—21no—
220C2×Q16—21no—
221C2×Q16—611no—
222C2×Q16C4×D6112yes—
223C2×Q16C4×D6112yes—
224C2×Q16C22×D6112yes—
225C2×SD16—1221no—
226C2×D8—611no—
227#131—1224no—
228#131—2442no—
229C2×M16—1221no—
230C2×M16—2441no—
231C22×C8—2441no—
232C22×C8C22⋊D6111yescharacteristic
233C22×C8C22×D6111yescharacteristic
234C4×Q8—24no—
235C4×Q8—42no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—41no—
238C2×C42—41no—
239C2×C42C22⋊D6111yescharacteristic
240Q32—618no—
241SD32—618no—
242M32—612no—
243M32—612no—
244M32—612no—
245M32—1221no—
246C2×C16—612no—
247C2×C16—1221no—
248#108—612no—
249#108—1221no—
250#106—21no—
251#106C22×D6112yes—
252#104—1224no—
253#103—24no—
254#97C22⋊D6112yes—
255#97C22×D6112yes—
256#41—1222no—
257#41—1222no—
258#41—2441no—
259#41—2441no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—1221no—
267C2×D4—1221no—
268C2×D4—2441no—
269C22×C4—21no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—2441no—
273C22×C4C2×C22⋊D6111yescharacteristic
274Q16—22no—
275Q16—22no—
276Q16—22no—
277Q16—612no—
278Q16—1221no—
279Q16C2×C4×D6114yes—
280SD16—1222no—
281SD16—1222no—
282D8—612no—
283D8—1221no—
284M16—1222no—
285M16—2444no—
286M16—2441no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—2444no—
290C2×C8—2441no—
291C2×C8C2×C4×D6111yescharacteristic
292C2×C8C2×C4×D6111yescharacteristic
293C2×C8#1175822211yescharacteristic
294C2×C8#1175822211yescharacteristic
295C2×C8C2×C22⋊D6112yes—
296C2×C8C2×C22⋊D6111yescharacteristic
297C2×C8C23×D6111yescharacteristic
298C4⋊C4—22no—
299C4⋊C4—44no—
300C4⋊C4—41no—
301C42—21no—
302C42—44no—
303C42C2×C22⋊D6112yes—
304C16—614no—
305C16—1222no—
306C23—2441no—
307C23#1451980311yescharacteristic
308Q8—24no—
309Q8—42no—
310Q8—42no—
311Q8—42no—
312Q8—1222no—
313Q8—2441no—
314D4—1222no—
315D4—2442no—
316D4—2442no—
317D4—2441no—
318C2×C4—22no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—82no—
325C2×C4—2441no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4C4×C22⋊D6111yescharacteristic
329C2×C4C4×C22⋊D6111yescharacteristic
330C2×C4#1451980211yescharacteristic
331C2×C4#1451980211yescharacteristic
332C2×C4#1451980311yescharacteristic
333C2×C4C22×C22⋊D6111yescharacteristic
334C8—22no—
335C8—2442no—
336C8C4×C22⋊D6111yescharacteristic
337C8C4×C22⋊D6111yescharacteristic
338C8C22×C4×D6111yescharacteristic
339C8C2×#1175822211yescharacteristic
340C22—22no—
341C22—4882no—
342C22—2442no—
343C22#1683987211yescharacteristic
344C22#1683987211yescharacteristic
345C22C2×#1451980311yescharacteristic
346C4—42no—
347C4—44no—
348C4—82no—
349C4—2442no—
350C4#1683987211yescharacteristic
351C4#1683987211yescharacteristic
352C4C2×C4×C22⋊D6111yescharacteristic
353C4C2×#1451980211yescharacteristic
354C2—21no—
355C2—21no—
356C2—4882no—
357C2#2144770812yesdirect product factor
358C2C2×#1683987211yescharacteristic
subgroupG/H
centerC22#16839872
commutatorC8×C61C23×C4
FrattiniC2×C8C23×D61
FittingC2×C61×#441C2
socleC22×C61#442
prime radicalC2×#14519799C22
cosocleC2×C8×C61C24
hypercenterC2×#441D61
hypocenterC61C2×#2180
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. #21447708C2direct (N × H)
4. C2×#16839584C2semidirect
5. C2×#16839578C2semidirect
7. C2×#16839540C2semidirect
8. C2×C61×#441C2semidirect
11. #16840203C4semidirect
13. C2×#14519723C4semidirect
14. C2×#14519720C4semidirect
21. #16839584C22semidirect
22. #16839578C22semidirect
24. #16839540C22semidirect
28. C61×#441C22semidirect
45. #14519723C2×C4semidirect
46. #14519720C2×C4semidirect
177. C2×#441D61semidirect
185. C2×C61#2180semidirect
201. #441C2×D61semidirect
211. C61C2×#2180semidirect
357. C2#21447708direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402032
C2×#168398852
#214477082
C2×#168395842
C2×#168395782
C2×#168395712
C2×#168395402
C2×C61×#4412
C2×#218061