Finite Group Databasebeta

← C2×#21447898 #29834397

Subgroups — C2×#21447898 #29834397

Order 15616.

686 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840202C211yesmaximal, characteristic
2C2×#16840140C211yesmaximal, characteristic, complemented
3C2×#16839879C211yesmaximal, characteristic
4#21447898C218yesmaximal, direct product factor
5C2×#16839582C211yesmaximal, characteristic, complemented
6C2×#16839579C211yesmaximal, characteristic, complemented
7C2×#16839578C211yesmaximal, characteristic, complemented
8C2×C61×#510C211yesmaximal, characteristic
9C22×Dic244C2211yescharacteristic
10C22×#11758202—21no—
11C2×#14519784—21no—
12C2×#14519775—21no—
13#16840202—22no—
14#16840202C2214yes—
15C2×#14519723—21no—
16C2×#14519721—21no—
17C2×#14519717C2211yescharacteristic
18#16840140—22no—
19#16840140C2214yescomplemented
20#16839879—22no—
21#16839879C2214yes—
22C2×#14519713C2211yescharacteristic
23C2×#14519704—21no—
24C2×C8×Dic61C2211yescharacteristic
25#16839582C2214yescomplemented
26#16839579C2214yescomplemented
27#16839578C2214yescomplemented
28C2×#135×C61C2211yescharacteristic
29C22×Q16×C61C2211yescharacteristic
30C61×#510—22no—
31C61×#510C2214yes—
32C2×Q32×C61—21no—
33C2×SD32×C61—21no—
34C2×M32×C61C2211yescharacteristic
35C22×Dic122—21no—
36C2×Dic244—21no—
37C2×Dic244—21no—
38C2×Dic244—21no—
39C2×Dic244—21no—
40C2×Dic244—21no—
41C2×Dic244C2312yes—
42C2×#11758202—24no—
43C2×#11758202—41no—
44C2×#11758202—41no—
45C2×#11758202—42no—
46#14519784—24no—
47#14519784—42no—
48C2×#11758194—21no—
49C2×#11758194—41no—
50C22×#92418—41no—
51C22×#92418D411yescharacteristic
52#14519775—24no—
53#14519775—42no—
54C2×#11758196—42no—
55C2×C4×Dic61D411yescharacteristic
56#14519723—24no—
57#14519721—24no—
58#14519717—21no—
59#14519717C2312yes—
60C2×#11758185—21no—
61#14519713—21no—
62#14519713C2312yes—
63#14519704—24no—
64C8×Dic61D412yes—
65C8×Dic61C2312yes—
66C2×#41×C61—21no—
67C22×Q8×C61—21no—
68#135×C61—21no—
69#135×C61—21no—
70#135×C61D412yes—
71#135×C61C2312yes—
72C2×Q16×C61—21no—
73C2×Q16×C61—21no—
74C2×Q16×C61—21no—
75C2×Q16×C61—21no—
76C2×Q16×C61—21no—
77C2×Q16×C61D411yescharacteristic
78C2×Q16×C61C2312yes—
79C2×SD16×C61—21no—
80C2×D8×C61D411yescharacteristic
81C22×C8×C61C2311yescharacteristic
82Q32×C61—24no—
83SD32×C61—24no—
84M32×C61—21no—
85M32×C61C2312yes—
86C2×C16×C61—21no—
87#41×C61—22no—
88#41×C61—22no—
89#41×C61—41no—
90#41×C61—41no—
91C2×Q8×C61—21no—
92C2×Q8×C61—22no—
93C2×Q8×C61—41no—
94C2×Q8×C61—41no—
95C2×Q8×C61—41no—
96C2×Q8×C61—41no—
97C2×Q8×C61—41no—
98C2×D4×C61—21no—
99C2×D4×C61—41no—
100C22×C4×C61—41no—
101C22×C4×C61—41no—
102C22×C4×C61C2×D411yescharacteristic
103C22×Dic61—21no—
104C22×Dic61—41no—
105C2×Dic122—22no—
106C2×Dic122—41no—
107C2×Dic122—41no—
108C2×Dic122—41no—
109C2×Dic122—41no—
110C2×Dic122—41no—
111Q16×C61—21no—
112Q16×C61—22no—
113Q16×C61—22no—
114Q16×C61—41no—
115Q16×C61—41no—
116Q16×C61C2×D412yes—
117SD16×C61—22no—
118SD16×C61—22no—
119D8×C61—21no—
120D8×C61C2×D412yes—
121C2×C8×C61C2×D411yescharacteristic
122C2×C8×C61C2×D411yescharacteristic
123C2×C8×C61C2×D411yescharacteristic
124C2×C8×C61#4111yescharacteristic
125C2×C8×C61#4111yescharacteristic
126C2×C8×C61C2411yescharacteristic
127#11758202—44no—
128#11758202—44no—
129#11758196—48no—
130C4×Dic61—21no—
131C4×Dic61C2×D412yes—
132#11758194—22no—
133#11758194—41no—
134#11758194—44no—
135C2×#92418—41no—
136C2×#92418—44no—
137C2×#92418D811yescharacteristic
138C2×#92418D811yescharacteristic
139C2×#92418D812yes—
140C2×#92418C2×D412yes—
141Dic244—22no—
142Dic244—22no—
143Dic244—41no—
144Dic244—41no—
145C16×C61—22no—
146#11758185—22no—
147C23×C61—41no—
148C23×C61AGL(1,ℤ/8)11yescharacteristic
149Q8×C61—22no—
150Q8×C61—41no—
151Q8×C61—42no—
152Q8×C61—42no—
153Q8×C61—81no—
154Q8×C61—81no—
155D4×C61—22no—
156D4×C61—42no—
157D4×C61—42no—
158D4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—42no—
161C2×C4×C61—42no—
162C2×C4×C61—42no—
163C2×C4×C61—81no—
164C2×C4×C61—81no—
165C2×C4×C61#12111yescharacteristic
166C2×C4×C61#12111yescharacteristic
167C2×C4×C61C2×D811yescharacteristic
168C2×C4×C61C2×D811yescharacteristic
169C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C61C22×D411yescharacteristic
171C2×Dic61—24no—
172C2×Dic61—22no—
173C2×Dic61—42no—
174C2×Dic61—81no—
175C2×Dic61—81no—
176Dic122—42no—
177Dic122—42no—
178Dic122—81no—
179Dic122—81no—
180C8×C61#12111yescharacteristic
181C8×C61#12111yescharacteristic
182C8×C61C22×D411yescharacteristic
183C8×C61C2×#4111yescharacteristic
184#92418—42no—
185#92418C2×D812yes—
186#92418C2×D812yes—
187C2×#2214—611nomaximal, Sylow
188C22×C61—22no—
189C22×C61—42no—
190C22×C61—82no—
191C22×C61#45911yescharacteristic
192C22×C61#45911yescharacteristic
193C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
194C4×C61—42no—
195C4×C61—82no—
196C4×C61#45911yescharacteristic
197C4×C61#45911yescharacteristic
198C4×C61C2×#12111yescharacteristic
199C4×C61C22×D811yescharacteristic
200Dic61—24no—
201Dic61—82no—
202C2×#510—611no—
203C2×#510D6111yescharacteristic
204C2×#494—611no—
205C2×#443—611no—
206#2214—618no—
207C2×#364—611no—
208C2×#362—611no—
209C2×#362—611no—
210C2×C61—21no—
211C2×C61—21no—
212C2×C61—82no—
213C2×C61#221412yescomplemented
214C2×C61C2×#45911yescharacteristic
215C2×#135C2×D6111yescharacteristic
216C22×Q16—611no—
217C22×Q16—1221no—
218C22×Q16C2×D6111yescharacteristic
219C2×#131—1221no—
220C2×C4⋊Q8—1221no—
221#510—22no—
222#510—614no—
223#510—1222no—
224#510C2×D6114yes—
225C2×Q32—21no—
226C2×Q32—1221no—
227C2×SD32—21no—
228C2×SD32—1221no—
229C2×M32—611no—
230C2×M32C2×D6111yescharacteristic
231#494—614no—
232#494—1222no—
233#443—614no—
234#443—1222no—
235C2×#108—611no—
236C2×#104—1221no—
237C2×C4×C8—611no—
238#364—614no—
239#362—614no—
240#362—614no—
241C61C2×#221411yescharacteristic, complemented, Sylow
242C2×#41—21no—
243C22×Q8—21no—
244C22×Q8—1221no—
245#135—21no—
246#135—21no—
247#135C22⋊D6112yes—
248#135C22×D6112yes—
249C2×Q16—21no—
250C2×Q16—21no—
251C2×Q16—21no—
252C2×Q16—21no—
253C2×Q16—21no—
254C2×Q16—612no—
255C2×Q16—1224no—
256C2×Q16—1221no—
257C2×Q16—1221no—
258C2×Q16—1221no—
259C2×Q16—1221no—
260C2×Q16—1221no—
261C2×Q16—2441no—
262C2×Q16—2441no—
263C2×Q16—2442no—
264C2×Q16C22⋊D6111yescharacteristic
265C2×Q16C22×D6112yes—
266C2×SD16—21no—
267C2×D8C22⋊D6111yescharacteristic
268#131—1224no—
269#131—2442no—
270C2×M16—1221no—
271C2×M16—2441no—
272C22×C8—611no—
273C22×C8—2441no—
274C22×C8C22×D6111yescharacteristic
275C4⋊Q8—1224no—
276C4⋊Q8—2442no—
277C2×C4⋊C4—2442no—
278C2×C42—611no—
279Q32—24no—
280Q32—1224no—
281SD32—24no—
282SD32—1224no—
283M32—21no—
284M32—612no—
285M32—1221no—
286M32C22×D6112yes—
287C2×C16—21no—
288C2×C16—1221no—
289#108—612no—
290#108—1221no—
291#104—1224no—
292C4×C8—612no—
293C4×C8—612no—
294#41—22no—
295#41—22no—
296#41—41no—
297#41—41no—
298C2×Q8—22no—
299C2×Q8—21no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—1222no—
306C2×Q8—2441no—
307C2×Q8—2441no—
308C2×Q8—2441no—
309C2×Q8—2441no—
310C2×Q8—2441no—
311C2×D4—21no—
312C2×D4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—1221no—
316C22×C4—2441no—
317C22×C4D4×D6111yescharacteristic
318Q16—22no—
319Q16—22no—
320Q16—21no—
321Q16—41no—
322Q16—41no—
323Q16—1222no—
324Q16—1222no—
325Q16—2444no—
326Q16—2444no—
327Q16—2441no—
328Q16—2441no—
329Q16C2×C22⋊D6112yes—
330SD16—22no—
331SD16—22no—
332D8—21no—
333D8C2×C22⋊D6112yes—
334M16—1222no—
335M16—2444no—
336M16—2441no—
337C2×C8—612no—
338C2×C8—611no—
339C2×C8—611no—
340C2×C8—612no—
341C2×C8—2444no—
342C2×C8—2441no—
343C2×C8D4×D6111yescharacteristic
344C2×C8#1175822411yescharacteristic
345C2×C8#1175822411yescharacteristic
346C2×C8C2×C22⋊D6111yescharacteristic
347C2×C8C2×C22⋊D6111yescharacteristic
348C2×C8C23×D6111yescharacteristic
349C4⋊C4—2448no—
350C42—612no—
351C42—1221no—
352C16—22no—
353C16—1222no—
354C23—41no—
355C23#1451980111yescharacteristic
356Q8—22no—
357Q8—41no—
358Q8—42no—
359Q8—42no—
360Q8—81no—
361Q8—81no—
362Q8—4881no—
363Q8—4881no—
364Q8—2442no—
365Q8—2442no—
366D4—22no—
367D4—42no—
368D4—42no—
369D4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—1224no—
377C2×C4—1222no—
378C2×C4—4881no—
379C2×C4—4881no—
380C2×C4—2442no—
381C2×C4#1451974911yescharacteristic
382C2×C4#1451974911yescharacteristic
383C2×C4D8×D6111yescharacteristic
384C2×C4D8×D6111yescharacteristic
385C2×C4#1451980111yescharacteristic
386C2×C4C2×D4×D6111yescharacteristic
387C8—612no—
388C8—612no—
389C8—2442no—
390C8#1451974911yescharacteristic
391C8#1451974911yescharacteristic
392C8C22×C22⋊D6111yescharacteristic
393C8C2×#1175822411yescharacteristic
394C22—22no—
395C22—42no—
396C22—82no—
397C22#1683995511yescharacteristic
398C22#1683995511yescharacteristic
399C22C2×#1451980111yescharacteristic
400C4—42no—
401C4—82no—
402C4—1224no—
403C4—4882no—
404C4#1683995511yescharacteristic
405C4#1683995511yescharacteristic
406C4C2×#1451974911yescharacteristic
407C4C2×D8×D6111yescharacteristic
408C2—21no—
409C2—21no—
410C2—82no—
411C2#2144789812yesdirect product factor
412C2C2×#1683995511yescharacteristic
subgroupG/H
centerC22#16839955
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#510C2
socleC22×C61#459
prime radicalC2×#135×C61C22
hypercenterC2×#510D61
hypocenterC61C2×#2214
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#510

Complements

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

NH ≅ G/Ntype
2. C2×#16840140C2semidirect
4. #21447898C2direct (N × H)
5. C2×#16839582C2semidirect
6. C2×#16839579C2semidirect
7. C2×#16839578C2semidirect
19. #16840140C22semidirect
25. #16839582C22semidirect
26. #16839579C22semidirect
27. #16839578C22semidirect
213. C2×C61#2214semidirect
241. C61C2×#2214semidirect
411. C2#21447898direct (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×#168401402
C2×#168398792
#214478982
C2×#168395822
C2×#168395792
C2×#168395782
C2×C61×#5102
C2×#221461