Finite Group Databasebeta

← C2×#21447946 #29834579

Subgroups — C2×#21447946 #29834579

Order 15616.

658 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840178C211yesmaximal, characteristic, complemented
2C2×#16840034C211yesmaximal, characteristic, complemented
3C2×#16840029C211yesmaximal, characteristic
4#21447946C218yesmaximal, direct product factor
5C2×#16839592C211yesmaximal, characteristic, complemented
6C2×#16839578C211yesmaximal, characteristic, complemented
7C2×#16839575C211yesmaximal, characteristic, complemented
8C22×SD32×C61C211yesmaximal, characteristic, complemented
9C2×#14519808—21no—
10C2×#14519803—21no—
11C2×#14519783C2211yescharacteristic
12#16840178—22no—
13#16840178C2214yescomplemented
14C2×#14519717C2211yescharacteristic
15C2×#14519716—21no—
16C2×C16×D61—21no—
17#16840034—22no—
18#16840034C2214yescomplemented
19#16840029—22no—
20#16840029C2214yes—
21C2×#14519713C2211yescharacteristic
22C2×#14519713C2211yescharacteristic
23C2×#14519696—21no—
24C2×#14519694—21no—
25#16839592C2214yescomplemented
26#16839578C2214yescomplemented
27#16839575C2214yescomplemented
28C22×Q16×C61C2211yescharacteristic
29C22×D8×C61C2211yescharacteristic
30C2×SD32×C61—21no—
31C2×SD32×C61—21no—
32C2×SD32×C61—22no—
33C2×SD32×C61C2214yescomplemented
34C22×C16×C61C2211yescharacteristic
35C2×#11758222D411yescharacteristic
36#14519808—24no—
37#14519808—42no—
38#14519803—24no—
39#14519803—42no—
40C2×#11758202—41no—
41C2×#11758200—41no—
42C2×#11758201—41no—
43C2×#11758199—41no—
44#14519783—21no—
45#14519783—21no—
46#14519783D412yes—
47#14519783C2312yes—
48C2×#11758194—21no—
49C2×#11758194—21no—
50C2×#11758194D411yescharacteristic
51C2×#11758189—21no—
52C2×C8×D61—21no—
53#14519717—21no—
54#14519717C2312yes—
55#14519716—24no—
56C2×#11758185—21no—
57C16×D61—24no—
58#14519713—21no—
59#14519713—21no—
60#14519713C2312yes—
61#14519713C2312yes—
62#14519696—24no—
63#14519694—24no—
64C22×Q8×C61—21no—
65C22×D4×C61—21no—
66C2×Q16×C61—21no—
67C2×Q16×C61—21no—
68C2×Q16×C61—21no—
69C2×Q16×C61—21no—
70C2×Q16×C61—21no—
71C2×Q16×C61C2312yes—
72C2×D8×C61—21no—
73C2×D8×C61—21no—
74C2×D8×C61—21no—
75C2×D8×C61—21no—
76C2×D8×C61—21no—
77C2×D8×C61C2312yes—
78C22×C8×C61C2311yescharacteristic
79SD32×C61—24no—
80SD32×C61—24no—
81C2×C16×C61D411yescharacteristic
82C2×C16×C61D411yescharacteristic
83C2×C16×C61D412yes—
84C2×C16×C61C2312yes—
85C24×C61—41no—
86C2×Q8×C61—22no—
87C2×Q8×C61—41no—
88C2×Q8×C61—41no—
89C2×Q8×C61—41no—
90C2×Q8×C61—41no—
91C2×Q8×C61—41no—
92C2×D4×C61—22no—
93C2×D4×C61—41no—
94C2×D4×C61—41no—
95C2×D4×C61—41no—
96C2×D4×C61—41no—
97C2×D4×C61—41no—
98C22×C4×C61—41no—
99C22×C4×C61C2×D411yescharacteristic
100C2×C22⋊D61—21no—
101#11758222—21no—
102#11758222—21no—
103#11758222D812yes—
104#11758222C2×D412yes—
105C2×D244D811yescharacteristic
106C2×C4×D61—21no—
107C2×Dic122D811yescharacteristic
108Q16×C61—22no—
109Q16×C61—22no—
110Q16×C61—41no—
111Q16×C61—41no—
112D8×C61—22no—
113D8×C61—22no—
114D8×C61—41no—
115D8×C61—41no—
116C2×C8×C61C2×D411yescharacteristic
117C2×C8×C61C2×D411yescharacteristic
118C2×C8×C61C2×D411yescharacteristic
119C2×C8×C61#4111yescharacteristic
120C2×C8×C61#4111yescharacteristic
121C2×C8×C61C2411yescharacteristic
122#11758202—44no—
123#11758201—44no—
124#11758200—44no—
125#11758199—44no—
126#11758194—21no—
127#11758194—22no—
128#11758194—22no—
129#11758194—41no—
130#11758194—41no—
131#11758194C2×D412yes—
132C2×#92418—21no—
133C2×#92418—41no—
134C2×#92418—41no—
135#11758189—22no—
136#11758189—22no—
137C8×D61—22no—
138C8×D61—22no—
139C16×C61C2×D412yes—
140C16×C61C2×D412yes—
141#11758185—22no—
142C23×C61—42no—
143C23×C61—81no—
144C23×C61—81no—
145C23×C61—162no—
146C23×C61#13511yescharacteristic
147C22×D61—21no—
148Q8×C61—42no—
149Q8×C61—42no—
150Q8×C61—81no—
151Q8×C61—81no—
152D4×C61—42no—
153D4×C61—42no—
154D4×C61—81no—
155D4×C61—81no—
156C2×C4×C61—42no—
157C2×C4×C61—81no—
158C2×C4×C61—81no—
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12111yescharacteristic
161C2×C4×C61C2×D811yescharacteristic
162C2×C4×C61C2×D811yescharacteristic
163C2×C4×C61#13511yescharacteristic
164C2×C4×C61C22×D411yescharacteristic
165C22⋊D61—22no—
166C22⋊D61—22no—
167C2×Dic61—21no—
168D244—21no—
169D244C2×D812yes—
170C4×D61—22no—
171C4×D61—22no—
172Dic122—21no—
173Dic122C2×D812yes—
174C8×C61#12111yescharacteristic
175C8×C61#12111yescharacteristic
176C8×C61C22×D411yescharacteristic
177C8×C61C2×#4111yescharacteristic
178#92418—22no—
179#92418—42no—
180#92418—42no—
181C2×#2223—611nomaximal, Sylow
182C22×C61—22no—
183C22×C61—82no—
184C22×C61—162no—
185C22×C61—162no—
186C22×C61—162no—
187C22×C61#46611yescharacteristic
188C22×C61#46611yescharacteristic
189C22×C61C2×#13511yescharacteristic
190C2×D61—22no—
191C2×D61—42no—
192C4×C61—82no—
193C4×C61#46611yescharacteristic
194C4×C61#46611yescharacteristic
195C4×C61C2×#12111yescharacteristic
196C4×C61C22×D811yescharacteristic
197Dic61—22no—
198C22×SD32D6111yescharacteristic, complemented
199C2×#504—611no—
200C2×#473—611no—
201C2×#472—611no—
202#2223—618no—
203C2×#368—611no—
204C2×#362—611no—
205C2×#361—611no—
206C2×C61—21no—
207C2×C61—21no—
208C2×C61—162no—
209C2×C61#222312yescomplemented
210C2×C61C2×#46611yescharacteristic
211D61—42no—
212C2×#137—1221no—
213C2×AGL(1,ℤ/8)—1221no—
214C22×Q16C2×D6111yescharacteristic
215C22×D8C2×D6111yescharacteristic
216C2×#131—611no—
217C2×SD32—21no—
218C2×SD32—21no—
219C2×SD32—22no—
220C2×SD32C2×D6114yescomplemented
221#504—614no—
222#504—1222no—
223C2×M32—611no—
224C2×M32—1221no—
225C22×C16—1221no—
226C22×C16C2×D6111yescharacteristic
227#473—614no—
228#473—1222no—
229#472—614no—
230#472—1222no—
231C2×#108—611no—
232C2×#108—611no—
233C2×#101—1221no—
234C2×#100—1221no—
235#368—614no—
236#362—614no—
237#361—614no—
238C61C2×#222311yescharacteristic, complemented, Sylow
239C2×#41—611no—
240C22×Q8—21no—
241C22×D4—21no—
242#137—1224no—
243#137—2442no—
244AGL(1,ℤ/8)—1224no—
245AGL(1,ℤ/8)—2442no—
246C2×Q16—21no—
247C2×Q16—21no—
248C2×Q16—21no—
249C2×Q16—21no—
250C2×Q16—21no—
251C2×Q16—2441no—
252C2×Q16C22×D6112yes—
253C2×SD16—2441no—
254C2×SD16—2441no—
255C2×D8—21no—
256C2×D8—21no—
257C2×D8—21no—
258C2×D8—21no—
259C2×D8—21no—
260C2×D8—2441no—
261C2×D8C22×D6112yes—
262#131—612no—
263#131—612no—
264#131—1221no—
265#131—1221no—
266C2×M16—611no—
267C2×M16—1221no—
268C2×M16—1221no—
269C2×M16—1221no—
270C22×C8—1221no—
271C22×C8C22×D6111yescharacteristic
272SD32—24no—
273SD32—24no—
274M32—612no—
275M32—1221no—
276M32—1224no—
277C2×C16—1221no—
278C2×C16—1224no—
279C2×C16C22⋊D6111yescharacteristic
280C2×C16C22⋊D6111yescharacteristic
281C2×C16C22⋊D6112yes—
282C2×C16C22×D6112yes—
283#108—612no—
284#108—612no—
285#108—1221no—
286#108—1221no—
287#101—1224no—
288#100—1224no—
289C24—41no—
290#41—612no—
291#41—612no—
292#41—1221no—
293#41—1221no—
294C2×Q8—22no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—611no—
301C2×D4—22no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—611no—
308C2×D4—1221no—
309C22×C4—41no—
310C22×C4—1221no—
311C22×C4D4×D6111yescharacteristic
312Q16—22no—
313Q16—22no—
314Q16—41no—
315Q16—41no—
316Q16—2444no—
317SD16—2444no—
318SD16—2444no—
319D8—22no—
320D8—22no—
321D8—41no—
322D8—41no—
323D8—2444no—
324M16—612no—
325M16—1221no—
326M16—1222no—
327M16—1222no—
328M16—1222no—
329M16—1222no—
330M16—2441no—
331M16—2441no—
332C2×C8—1221no—
333C2×C8—1222no—
334C2×C8—1222no—
335C2×C8—2441no—
336C2×C8—2441no—
337C2×C8D4×D6111yescharacteristic
338C2×C8#1175822411yescharacteristic
339C2×C8#1175822411yescharacteristic
340C2×C8C2×C22⋊D6111yescharacteristic
341C2×C8C2×C22⋊D6111yescharacteristic
342C2×C8C23×D6111yescharacteristic
343C16—1222no—
344C16C2×C22⋊D6112yes—
345C16C2×C22⋊D6112yes—
346C23—42no—
347C23—81no—
348C23—81no—
349C23—162no—
350C23—1221no—
351C23#1451979611yescharacteristic
352Q8—42no—
353Q8—42no—
354Q8—81no—
355Q8—81no—
356Q8—612no—
357Q8—1221no—
358D4—42no—
359D4—42no—
360D4—81no—
361D4—81no—
362D4—612no—
363D4—1222no—
364D4—1222no—
365D4—1221no—
366C2×C4—42no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—1221no—
370C2×C4—1222no—
371C2×C4—1222no—
372C2×C4#1451974811yescharacteristic
373C2×C4#1451974811yescharacteristic
374C2×C4D8×D6111yescharacteristic
375C2×C4D8×D6111yescharacteristic
376C2×C4#1451979611yescharacteristic
377C2×C4C2×D4×D6111yescharacteristic
378C8—1222no—
379C8—2442no—
380C8—2442no—
381C8#1451974811yescharacteristic
382C8#1451974811yescharacteristic
383C8C22×C22⋊D6111yescharacteristic
384C8C2×#1175822411yescharacteristic
385C22—22no—
386C22—82no—
387C22—162no—
388C22—162no—
389C22—162no—
390C22—1222no—
391C22—2442no—
392C22#1683999511yescharacteristic
393C22#1683999511yescharacteristic
394C22C2×#1451979611yescharacteristic
395C4—82no—
396C4—1222no—
397C4#1683999511yescharacteristic
398C4#1683999511yescharacteristic
399C4C2×#1451974811yescharacteristic
400C4C2×D8×D6111yescharacteristic
401C2—21no—
402C2—21no—
403C2—162no—
404C2—2442no—
405C2#2144794612yesdirect product factor
406C2C2×#1683999511yescharacteristic
subgroupG/H
centerC22#16839995
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC22×SD32×C61C2
socleC22×C61#466
prime radicalC2×#16840029C2
hypercenterC22×SD32D61
hypocenterC61C2×#2223
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×SD32

Complements

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

NH ≅ G/Ntype
1. C2×#16840178C2semidirect
2. C2×#16840034C2semidirect
4. #21447946C2direct (N × H)
5. C2×#16839592C2semidirect
6. C2×#16839578C2semidirect
7. C2×#16839575C2semidirect
8. C22×SD32×C61C2semidirect
13. #16840178C22semidirect
18. #16840034C22semidirect
25. #16839592C22semidirect
26. #16839578C22semidirect
27. #16839575C22semidirect
33. C2×SD32×C61C22semidirect
198. C22×SD32D61semidirect
209. C2×C61#2223semidirect
220. C2×SD32C2×D61semidirect
238. C61C2×#2223semidirect
405. C2#21447946direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401782
C2×#168400342
C2×#168400292
#214479462
C2×#168395922
C2×#168395782
C2×#168395752
C22×SD32×C612
C2×#222361