Finite Group Databasebeta

← C2×#20291117 #28328381

Subgroups — C2×#20291117 #28328381

Order 13568.

654 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811667C211yesmaximal, characteristic, complemented
2C2×#16811665C211yesmaximal, characteristic, complemented
3#20291117C218yesmaximal, direct product factor
4C2×#16811551C211yesmaximal, characteristic, complemented
5C2×#16811538C211yesmaximal, characteristic, complemented
6C2×#16811537C211yesmaximal, characteristic, complemented
7C2×#16811510C211yesmaximal, characteristic, complemented
8C2×#16811054C211yesmaximal, characteristic
9C2×#13133305—21no—
10C2×#13133304—21no—
11C2×D53⋊C16C2211yescharacteristic
12#16811667—22no—
13#16811667C2214yescomplemented
14#16811665—22no—
15#16811665C2214yescomplemented
16C2×#13133288C2211yescharacteristic
17C2×#13133288C2211yescharacteristic
18C2×#13133282—21no—
19C2×#13133281—21no—
20C2×C8×#6157C2211yescharacteristic
21#16811551C2214yescomplemented
22#16811538C2214yescomplemented
23#16811537C2214yescomplemented
24#16811510C2214yescomplemented
25C2×#13133240C2211yescharacteristic
26C2×#13133236C2211yescharacteristic
27#16811054C414yescomplemented
28#16811054C2214yes—
29C2×#13133163C411yescharacteristic, complemented
30C2×#13133162C411yescharacteristic, complemented
31C2×#13133158C411yescharacteristic, complemented
32C2×C16×D53C2211yescharacteristic
33C2×SD32×C53C411yescharacteristic, complemented
34#13133305—24no—
35#13133305—42no—
36#13133304—24no—
37#13133304—42no—
38C2×#11719936—21no—
39C2×#11719936—21no—
40C2×#11719936—41no—
41C2×#11719940—41no—
42C2×D53⋊C8—41no—
43C2×D53⋊C8D411yescharacteristic
44C22×#88324—41no—
45C2×C4×#6157D411yescharacteristic
46D53⋊C16—21no—
47D53⋊C16C2312yes—
48C2×#11719910—21no—
49#13133288—21no—
50#13133288—21no—
51#13133288C2312yes—
52#13133288C2312yes—
53#13133282—24no—
54#13133281—24no—
55C8×#6157D412yes—
56C8×#6157C2312yes—
57C2×#11719949—21no—
58C2×#11719947—21no—
59#13133240—21no—
60#13133240—21no—
61#13133240C2×C412yes—
62#13133240C2312yes—
63#13133236—21no—
64#13133236—21no—
65#13133236C2×C412yes—
66#13133236C2312yes—
67C2×Dic212C2×C411yescharacteristic
68C2×#11719923—21no—
69C2×#11719924—21no—
70C2×D424C2×C411yescharacteristic
71C2×C8×D53C2311yescharacteristic
72#13133163C2×C414yescomplemented
73#13133162C2×C414yescomplemented
74#13133158C2×C414yescomplemented
75C2×#11719908C2×C411yescharacteristic
76C16×D53C2×C412yes—
77C16×D53C2312yes—
78C2×Q16×C53C2×C411yescharacteristic
79C2×D8×C53C2×C411yescharacteristic
80SD32×C53C2×C414yescomplemented
81C2×C16×C53C2×C411yescharacteristic
82C22×#6157—21no—
83C2×Q8×C53—21no—
84C2×D4×C53—21no—
85C2×C22⋊D53—41no—
86C22×Dic53—41no—
87#11719949—22no—
88#11719949—22no—
89#11719949—41no—
90#11719949—41no—
91#11719947—22no—
92#11719947—22no—
93#11719947—41no—
94#11719947—41no—
95C2×D212—21no—
96C2×D212—41no—
97C2×C4×D53—41no—
98C2×C4×D53C2×D411yescharacteristic
99C2×Dic106—21no—
100#11719940—44no—
101C2×#88324—41no—
102C2×#88324—41no—
103C2×#88324—44no—
104C2×#88324D811yescharacteristic
105C2×#88324D811yescharacteristic
106C4×#6157—21no—
107C4×#6157C2×D412yes—
108#11719936—22no—
109#11719936—22no—
110#11719936—41no—
111#11719936—41no—
112#11719936—44no—
113D53⋊C8—44no—
114D53⋊C8D812yes—
115D53⋊C8C2×D412yes—
116Q16×C53—21no—
117Q16×C53C22×C412yes—
118D8×C53—21no—
119D8×C53C22×C412yes—
120C2×C8×C53C22×C411yescharacteristic
121#11719924—22no—
122#11719924—22no—
123#11719923—22no—
124#11719923—22no—
125C2×#88322#4111yescharacteristic
126Dic212—21no—
127Dic212C22×C412yes—
128D424—21no—
129D424C22×C412yes—
130C8×D53C22×C411yescharacteristic
131C8×D53C2×D411yescharacteristic
132C8×D53#4111yescharacteristic
133C8×D53C2411yescharacteristic
134#11719910—22no—
135C16×C53C22×C412yes—
136#11719908C22×C412yes—
137C23×C53—41no—
138C22×D53—41no—
139C22×D53#13511yescharacteristic
140C2×#6157—22no—
141C2×#6157—42no—
142Q8×C53—22no—
143Q8×C53—41no—
144D4×C53—22no—
145D4×C53—41no—
146C2×C4×C53—41no—
147C2×C4×C53C4×D411yescharacteristic
148C22⋊D53—42no—
149C22⋊D53—42no—
150C2×Dic53—41no—
151C2×Dic53—42no—
152C2×Dic53—42no—
153C2×Dic53C2×D811yescharacteristic
154D212—22no—
155D212—42no—
156D212—42no—
157D212—41no—
158C4×D53—42no—
159C4×D53—42no—
160C4×D53C4×D411yescharacteristic
161C4×D53C2×D811yescharacteristic
162C4×D53#13511yescharacteristic
163C4×D53C22×D411yescharacteristic
164Dic106—22no—
165Dic106—41no—
166#88324—42no—
167#88324—42no—
168#88324C2×D812yes—
169#88324C2×D812yes—
170C8×C53C4×D411yescharacteristic
171C8×C53C23×C411yescharacteristic
172#88322C4×D411yescharacteristic
173#88322C2×#4111yescharacteristic
174C2×#2179—531nomaximal, Sylow
175C22×C53—42no—
176C22×C53—82no—
177C22×C53C4×D811yescharacteristic
178C2×D53—22no—
179C2×D53—42no—
180C2×D53—82no—
181C2×D53C4×D811yescharacteristic
182C2×D53C2×#13511yescharacteristic
183#6157—42no—
184C4×C53—42no—
185C4×C53C4×D811yescharacteristic
186C4×C53C2×C4×D411yescharacteristic
187Dic53—42no—
188Dic53C4×D811yescharacteristic
189Dic53C22×D811yescharacteristic
190C2×#508—531no—
191C2×#443—531no—
192C2×#443—531no—
193#2179—538no—
194C2×#368—531no—
195C2×#359—531no—
196C2×#359—531no—
197C2×#346—531no—
198C2×C53—82no—
199C2×C53#217912yescomplemented
200C2×C53C2×C4×D811yescharacteristic
201D53—21no—
202D53—21no—
203D53—82no—
204C2×#135—531no—
205C2×#135—531no—
206C2×#131—1061no—
207C2×#131—1061no—
208#508—534no—
209#508—534no—
210C2×Q32—531no—
211C2×SD32—531no—
212C2×SD32#615711yescharacteristic, complemented
213C2×D16—531no—
214C22×C16—531no—
215C22×C16—531no—
216#443—534no—
217#443—534no—
218#443—1062no—
219#443—1062no—
220C2×#108—531no—
221C2×#108—531no—
222C2×#104—1061no—
223C2×#104—1061no—
224C2×C4×C8—531no—
225#368—534no—
226#359—534no—
227#359—534no—
228#346—534no—
229C53C2×#217911yescharacteristic, complemented, Sylow
230C2×#41—1061no—
231C2×#41—1061no—
232#135—532no—
233#135—532no—
234#135—532no—
235#135—532no—
236#135—1061no—
237#135—1061no—
238#135—1061no—
239#135—1061no—
240C2×Q16—531no—
241C2×Q16C2×#615711yescharacteristic
242C2×SD16—1061no—
243C2×SD16—1061no—
244C2×D8—531no—
245C2×D8C2×#615711yescharacteristic
246#131—1064no—
247#131—1064no—
248#131—2122no—
249#131—2122no—
250C2×M16—1061no—
251C2×M16—1061no—
252C2×M16—2121no—
253C2×M16—2121no—
254C22×C8—531no—
255C22×C8—531no—
256C22×C8—2121no—
257C22×C8—2121no—
258C2×C42—531no—
259Q32—534no—
260SD32—534no—
261SD32C2×#615714yescomplemented
262D16—534no—
263C2×C16—531no—
264C2×C16—532no—
265C2×C16—532no—
266C2×C16—532no—
267C2×C16—1061no—
268C2×C16—1061no—
269C2×C16C2×#615711yescharacteristic
270#108—532no—
271#108—532no—
272#108—1061no—
273#108—1061no—
274#104—1064no—
275#104—1064no—
276C4×C8—532no—
277C4×C8—532no—
278#41—1062no—
279#41—1062no—
280#41—1062no—
281#41—1062no—
282#41—2121no—
283#41—2121no—
284#41—2121no—
285#41—2121no—
286C2×Q8—21no—
287C2×Q8—1061no—
288C2×D4—21no—
289C2×D4—1061no—
290C2×D4—2121no—
291C2×D4—2121no—
292C22×C4—531no—
293C22×C4—1061no—
294C22×C4—2121no—
295C22×C4—2121no—
296Q16—21no—
297Q16—532no—
298Q16—1061no—
299Q16C22×#615712yes—
300SD16—1062no—
301SD16—1062no—
302SD16—1062no—
303SD16—1062no—
304D8—21no—
305D8—532no—
306D8—1061no—
307D8C22×#615712yes—
308M16—1062no—
309M16—1062no—
310M16—2124no—
311M16—2124no—
312M16—2121no—
313M16—2121no—
314C2×C8—531no—
315C2×C8—531no—
316C2×C8—532no—
317C2×C8—532no—
318C2×C8—531no—
319C2×C8—531no—
320C2×C8—531no—
321C2×C8—531no—
322C2×C8—531no—
323C2×C8—2124no—
324C2×C8—2124no—
325C2×C8—2121no—
326C2×C8—2121no—
327C2×C8C22×#615711yescharacteristic
328C42—532no—
329C42—1061no—
330C16—532no—
331C16—1062no—
332C16C22×#615712yes—
333C23—41no—
334C23—531no—
335C23—2121no—
336Q8—22no—
337Q8—41no—
338Q8—1062no—
339Q8—2121no—
340D4—22no—
341D4—41no—
342D4—1062no—
343D4—2122no—
344D4—2122no—
345D4—2122no—
346D4—2122no—
347D4—2121no—
348C2×C4—41no—
349C2×C4—531no—
350C2×C4—531no—
351C2×C4—531no—
352C2×C4—531no—
353C2×C4—531no—
354C2×C4—1062no—
355C2×C4—2122no—
356C2×C4—2122no—
357C2×C4—2122no—
358C2×C4—2122no—
359C2×C4—2122no—
360C2×C4—2121no—
361C2×C4D4×#615711yescharacteristic
362C8—532no—
363C8—532no—
364C8—531no—
365C8—531no—
366C8—2122no—
367C8—2122no—
368C8D4×#615711yescharacteristic
369C8C23×#615711yescharacteristic
370C22—42no—
371C22—82no—
372C22—531no—
373C22—531no—
374C22—1062no—
375C22—4242no—
376C22—2122no—
377C22D8×#615711yescharacteristic
378C4—42no—
379C4—531no—
380C4—531no—
381C4—2122no—
382C4—2122no—
383C4D8×#615711yescharacteristic
384C4C2×D4×#615711yescharacteristic
385C2—82no—
386C2—1061no—
387C2—1061no—
388C2—4242no—
389C2#2029111712yesdirect product factor
390C2C2×D8×#615711yescharacteristic
subgroupG/H
centerC22D8×#6157
commutatorC8×C53C23×C4
FrattiniC8C23×#6157
FittingC2×SD32×C53C4
socleC22×C53C4×D8
prime radicalC2×#16811054C2
cosocleC8×D53C24
hypercenterC2×SD32#6157
hypocenterC53C2×#2179
LCSG ▷ C8×C53 ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. C2×#16811667C2semidirect
2. C2×#16811665C2semidirect
3. #20291117C2direct (N × H)
4. C2×#16811551C2semidirect
5. C2×#16811538C2semidirect
6. C2×#16811537C2semidirect
7. C2×#16811510C2semidirect
13. #16811667C22semidirect
15. #16811665C22semidirect
21. #16811551C22semidirect
22. #16811538C22semidirect
23. #16811537C22semidirect
24. #16811510C22semidirect
27. #16811054C4semidirect
29. C2×#13133163C4semidirect
30. C2×#13133162C4semidirect
31. C2×#13133158C4semidirect
33. C2×SD32×C53C4semidirect
72. #13133163C2×C4semidirect
73. #13133162C2×C4semidirect
74. #13133158C2×C4semidirect
80. SD32×C53C2×C4semidirect
199. C2×C53#2179semidirect
212. C2×SD32#6157semidirect
229. C53C2×#2179semidirect
261. SD32C2×#6157semidirect
389. C2#20291117direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168116672
C2×#168116652
#202911172
C2×#168115512
C2×#168115382
C2×#168115372
C2×#168115102
C2×#168110542
C2×#217953