Finite Group Databasebeta

← C2×#21447707 #29833443

Subgroups — C2×#21447707 #29833443

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×#16840202C211yesmaximal, characteristic
2C2×#16839884C211yesmaximal, characteristic
3C2×#16839868C211yesmaximal, characteristic, complemented
4#21447707C218yesmaximal, direct product factor
5C2×#16839584C211yesmaximal, characteristic, complemented
6C2×#16839579C211yesmaximal, characteristic, complemented
7C2×#16839539C211yesmaximal, characteristic, complemented
8C2×C61×#360C211yesmaximal, characteristic
9C22×Dic244C2211yescharacteristic
10C2×#14519784—21no—
11C2×#14519742—21no—
12#16840202C414yescomplemented
13#16840202C2214yes—
14C2×#14519723C412yescomplemented
15C2×#14519721C412yescomplemented
16C2×#14519717C2211yescharacteristic
17#16839884—22no—
18#16839884C2214yes—
19#16839868—22no—
20#16839868C2214yescomplemented
21C2×#14519713C2211yescharacteristic
22C2×#14519704—21no—
23C2×#14519700—21no—
24C2×#14519687C2211yescharacteristic
25#16839584C2214yescomplemented
26#16839579C2214yescomplemented
27#16839539C2214yescomplemented
28C2×#135×C61C2211yescharacteristic
29C2×M32×C61C2211yescharacteristic
30C2×#106×C61C2211yescharacteristic
31C61×#360C2214yes—
32C22×Dic122—21no—
33C2×Dic244—21no—
34C2×Dic244—21no—
35C2×Dic244—21no—
36C2×Dic244C2×C412yes—
37C2×Dic244C2×C412yes—
38C2×Dic244C2312yes—
39#14519784—24no—
40#14519784—42no—
41C2×#11758194—21no—
42C2×#11758194—41no—
43C22×#92418—41no—
44C22×#92418D411yescharacteristic
45#14519742—24no—
46#14519742—42no—
47C2×#11758196—41no—
48C2×C4×Dic61—41no—
49C2×C4×Dic61D411yescharacteristic
50#14519723C2×C418yescomplemented
51#14519721C2×C418yescomplemented
52#14519717C2×C412yes—
53#14519717C2312yes—
54C2×#11758185C2×C412yes—
55#14519713—21no—
56#14519713C2312yes—
57#14519704—24no—
58#14519700—24no—
59#14519687D412yes—
60#14519687C2312yes—
61C2×#41×C61—21no—
62#135×C61—21no—
63#135×C61—21no—
64#135×C61C2×C412yes—
65#135×C61C2312yes—
66C2×Q16×C61C2×C411yescharacteristic
67C2×SD16×C61—21no—
68C2×D8×C61C2×C411yescharacteristic
69C22×C8×C61C2311yescharacteristic
70C2×C4⋊C4×C61—21no—
71M32×C61—21no—
72M32×C61C2312yes—
73C2×C16×C61—21no—
74#106×C61—21no—
75#106×C61C2312yes—
76#41×C61—22no—
77#41×C61—22no—
78#41×C61—41no—
79#41×C61—41no—
80C2×Q8×C61—21no—
81C2×D4×C61—21no—
82C2×D4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61C2×D411yescharacteristic
86C22×Dic61—21no—
87C22×Dic61—41no—
88C2×Dic122—22no—
89C2×Dic122—22no—
90C2×Dic122—22no—
91C2×Dic122—41no—
92C2×Dic122—41no—
93C2×Dic122—41no—
94Q16×C61—21no—
95Q16×C61C22×C412yes—
96SD16×C61—22no—
97SD16×C61—22no—
98D8×C61—21no—
99D8×C61C22×C412yes—
100C2×C8×C61C22×C411yescharacteristic
101C2×C8×C61C22×C411yescharacteristic
102C2×C8×C61C2×D411yescharacteristic
103C2×C8×C61#4111yescharacteristic
104C2×C8×C61#4111yescharacteristic
105C2×C8×C61C2411yescharacteristic
106C4⋊C4×C61—22no—
107C4⋊C4×C61—41no—
108#11758196—44no—
109C4×Dic61—21no—
110C4×Dic61—44no—
111C4×Dic61C2×D412yes—
112#11758194—22no—
113#11758194—44no—
114#11758194—41no—
115C2×#92418—21no—
116C2×#92418—21no—
117C2×#92418—44no—
118C2×#92418—41no—
119C2×#92418C2×D412yes—
120Dic244—22no—
121Dic244—22no—
122Dic244—22no—
123Dic244C22×C414yes—
124C16×C61—22no—
125#11758185C22×C414yes—
126C23×C61—41no—
127C23×C61AGL(1,ℤ/8)11yescharacteristic
128Q8×C61—22no—
129Q8×C61—41no—
130D4×C61—22no—
131D4×C61—42no—
132D4×C61—42no—
133D4×C61—41no—
134C2×C4×C61—41no—
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
145C2×Dic61—22no—
146C2×Dic61—42no—
147C2×Dic61—42no—
148C2×Dic61—42no—
149C2×Dic61—42no—
150Dic122—24no—
151Dic122—42no—
152Dic122—42no—
153Dic122—42no—
154C8×C61C4×D411yescharacteristic
155C8×C61C4×D411yescharacteristic
156C8×C61C23×C411yescharacteristic
157C8×C61C2×#4111yescharacteristic
158#92418—22no—
159#92418—42no—
160C2×#2180—611nomaximal, Sylow
161C22×C61—22no—
162C22×C61—42no—
163C22×C61—82no—
164C22×C61#44211yescharacteristic
165C22×C61#44211yescharacteristic
166C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
167C4×C61—42no—
168C4×C61—82no—
169C4×C61#44211yescharacteristic
170C4×C61#44211yescharacteristic
171C4×C61C2×C4×D411yescharacteristic
172C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
173Dic61—42no—
174Dic61—44no—
175C2×#510—611no—
176C2×#444—611no—
177C2×#441—611no—
178#2180—618no—
179C2×#365—611no—
180C2×#362—611no—
181C2×#360D6111yescharacteristic
182C2×#347—611no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61—82no—
186C2×C61#218012yescomplemented
187C2×C61C2×#44211yescharacteristic
188C2×#135C2×D6111yescharacteristic
189C22×Q16—611no—
190C2×#131—1221no—
191C2×C4×Q8—1221no—
192#510—614no—
193#510—614no—
194C2×Q32—612no—
195C2×SD32—612no—
196C2×M32—611no—
197C2×M32C2×D6111yescharacteristic
198#444—614no—
199#444—1222no—
200#441—614no—
201#441—1222no—
202C2×#108—611no—
203C2×#106C2×D6111yescharacteristic
204C2×#104—1221no—
205C2×#103—1221no—
206C2×#97—611no—
207#365—614no—
208#362—614no—
209#360C2×D6114yes—
210#347—614no—
211C61C2×#218011yescharacteristic, complemented, Sylow
212C2×#41—21no—
213C22×Q8—1221no—
214#135—21no—
215#135—21no—
216#135C4×D6112yes—
217#135C22×D6112yes—
218C2×Q16—612no—
219C2×Q16—612no—
220C2×Q16—612no—
221C2×Q16—1221no—
222C2×Q16—1221no—
223C2×Q16—1221no—
224C2×Q16C4×D6111yescharacteristic
225C2×SD16—21no—
226C2×D8C4×D6111yescharacteristic
227#131—1224no—
228#131—2442no—
229C2×M16—1221no—
230C2×M16—2441no—
231C22×C8—611no—
232C22×C8—2441no—
233C22×C8C22×D6111yescharacteristic
234C4×Q8—1224no—
235C4×Q8—2442no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—2441no—
238C2×C42—611no—
239C2×C42—2441no—
240Q32—618no—
241SD32—618no—
242M32—21no—
243M32—612no—
244M32—612no—
245M32C22×D6112yes—
246C2×C16—21no—
247C2×C16—612no—
248#108—612no—
249#108—1221no—
250#106—21no—
251#106C22×D6112yes—
252#104—1224no—
253#103—1224no—
254#97—612no—
255#97—612no—
256#41—22no—
257#41—22no—
258#41—41no—
259#41—41no—
260C2×Q8—21no—
261C2×Q8—1222no—
262C2×Q8—1222no—
263C2×Q8—1222no—
264C2×Q8—2441no—
265C2×Q8—2441no—
266C2×Q8—2441no—
267C2×D4—21no—
268C2×D4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—1221no—
272C22×C4—2441no—
273C22×C4D4×D6111yescharacteristic
274Q16—21no—
275Q16—614no—
276Q16—1222no—
277Q16—1222no—
278Q16—1222no—
279Q16C2×C4×D6112yes—
280SD16—22no—
281SD16—22no—
282D8—21no—
283D8C2×C4×D6112yes—
284M16—1222no—
285M16—2444no—
286M16—2441no—
287C2×C8—612no—
288C2×C8—1221no—
289C2×C8—1221no—
290C2×C8—2444no—
291C2×C8—2441no—
292C2×C8C2×C4×D6111yescharacteristic
293C2×C8C2×C4×D6111yescharacteristic
294C2×C8D4×D6111yescharacteristic
295C2×C8#1175822411yescharacteristic
296C2×C8#1175822411yescharacteristic
297C2×C8C23×D6111yescharacteristic
298C4⋊C4—22no—
299C4⋊C4—41no—
300C4⋊C4—2444no—
301C42—612no—
302C42—1221no—
303C42—2444no—
304C16—22no—
305C16—614no—
306C23—41no—
307C23#1451980111yescharacteristic
308Q8—22no—
309Q8—41no—
310Q8—1224no—
311Q8—2442no—
312Q8—2442no—
313Q8—2442no—
314D4—22no—
315D4—42no—
316D4—42no—
317D4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—82no—
323C2×C4—1222no—
324C2×C4—2442no—
325C2×C4—2442no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4#1451973711yescharacteristic
329C2×C4#1451973711yescharacteristic
330C2×C4#1451980111yescharacteristic
331C2×C4#1451980411yescharacteristic
332C2×C4#1451980411yescharacteristic
333C2×C4C2×D4×D6111yescharacteristic
334C8—1222no—
335C8—2442no—
336C8#1451973711yescharacteristic
337C8#1451973711yescharacteristic
338C8C22×C4×D6111yescharacteristic
339C8C2×#1175822411yescharacteristic
340C22—22no—
341C22—42no—
342C22—82no—
343C22#1683987111yescharacteristic
344C22#1683987111yescharacteristic
345C22C2×#1451980111yescharacteristic
346C4—42no—
347C4—82no—
348C4—2442no—
349C4—2444no—
350C4#1683987111yescharacteristic
351C4#1683987111yescharacteristic
352C4C2×#1451973711yescharacteristic
353C4C2×#1451980411yescharacteristic
354C2—21no—
355C2—21no—
356C2—82no—
357C2#2144770712yesdirect product factor
358C2C2×#1683987111yescharacteristic
subgroupG/H
centerC22#16839871
commutatorC8×C61C23×C4
FrattiniC2×C8C23×D61
FittingC2×C61×#360C2
socleC22×C61#442
prime radicalC2×#135×C61C22
cosocleC2×C8×C61C24
hypercenterC2×#360D61
hypocenterC61C2×#2180
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#360

Complements

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

NH ≅ G/Ntype
3. C2×#16839868C2semidirect
4. #21447707C2direct (N × H)
5. C2×#16839584C2semidirect
6. C2×#16839579C2semidirect
7. C2×#16839539C2semidirect
12. #16840202C4semidirect
14. C2×#14519723C4semidirect
15. C2×#14519721C4semidirect
20. #16839868C22semidirect
25. #16839584C22semidirect
26. #16839579C22semidirect
27. #16839539C22semidirect
50. #14519723C2×C4semidirect
51. #14519721C2×C4semidirect
186. C2×C61#2180semidirect
211. C61C2×#2180semidirect
357. C2#21447707direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402022
C2×#168398842
C2×#168398682
#214477072
C2×#168395842
C2×#168395792
C2×#168395392
C2×C61×#3602
C2×#218061