Finite Group Databasebeta

← C2×#22626342 #34030294

Subgroups — C2×#22626342 #34030294

Order 18688.

710 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989633C211yesmaximal, characteristic, complemented
2C2×#17989628C211yesmaximal, characteristic, complemented
3#22626342C218yesmaximal, direct product factor
4C2×#17989512C211yesmaximal, characteristic, complemented
5C2×#17989505C211yesmaximal, characteristic, complemented
6C2×#17989504C211yesmaximal, characteristic, complemented
7C2×#17989477C211yesmaximal, characteristic, complemented
8C2×#17989024C211yesmaximal, characteristic
9C2×#14556679—21no—
10C2×D4×#64408—21no—
11C2×#14556666C2211yescharacteristic
12#17989633—22no—
13#17989633C2214yescomplemented
14#17989628—22no—
15#17989628C2214yescomplemented
16C2×#14556661C2211yescharacteristic
17C2×#14556659C2211yescharacteristic
18C2×#14556656—21no—
19C2×#14556653—21no—
20C2×#14556645C2211yescharacteristic
21#17989512C2214yescomplemented
22#17989505C2214yescomplemented
23#17989504C2214yescomplemented
24#17989477C2214yescomplemented
25C2×#14556614C2211yescharacteristic
26C2×D8×D73C2211yescharacteristic
27#17989024C414yescomplemented
28#17989024C2214yes—
29C2×#14556534C411yescharacteristic, complemented
30C2×D1168C411yescharacteristic, complemented
31C2×#14556532C411yescharacteristic, complemented
32C2×#14556530C2211yescharacteristic
33C2×SD32×C73C411yescharacteristic, complemented
34C23×#64408—41no—
35#14556679—24no—
36#14556679—42no—
37C2×#11924038—21no—
38C2×#11924038—41no—
39C2×#11924036—41no—
40C2×#11924036D411yescharacteristic
41D4×#64408—24no—
42D4×#64408—42no—
43C2×C4⋊#64408—21no—
44C2×C22⋊#64408—41no—
45C2×C4×#64408D411yescharacteristic
46#14556666—21no—
47#14556666C2312yes—
48C2×#11924031—21no—
49#14556661—21no—
50#14556661C2312yes—
51#14556659—21no—
52#14556659C2312yes—
53#14556656—24no—
54#14556653—24no—
55#14556645D412yes—
56#14556645C2312yes—
57C2×#11924029—21no—
58C2×D4×D73—21no—
59#14556614—21no—
60#14556614—21no—
61#14556614C2×C412yescomplemented
62#14556614C2312yes—
63C2×#11924015—21no—
64C2×D584C2×C411yescharacteristic
65C2×D584C2×C411yescharacteristic, complemented
66C2×#11924013—21no—
67D8×D73—21no—
68D8×D73—21no—
69D8×D73C2×C412yes—
70D8×D73C2312yes—
71C2×C8×D73C2311yescharacteristic
72#14556534C2×C414yescomplemented
73D1168C2×C414yescomplemented
74#14556532C2×C414yescomplemented
75#14556530C2×C412yescomplemented
76#14556530C2312yes—
77C2×#11924003C2×C411yescharacteristic, complemented
78C2×Q16×C73C2×C411yescharacteristic, complemented
79C2×D8×C73C2×C411yescharacteristic
80SD32×C73C2×C414yescomplemented
81C2×C16×C73C2×C411yescharacteristic, complemented
82C22×#64408—21no—
83C22×#64408—44no—
84C22×#64408—41no—
85C22×#64408—84no—
86#11924038—22no—
87#11924038—44no—
88#11924038—41no—
89#11924036—21no—
90#11924036—44no—
91#11924036C2×D412yes—
92C2×#10596833—21no—
93C2×#10596833—41no—
94C4⋊#64408—22no—
95C4⋊#64408—41no—
96C22⋊#64408—44no—
97C4×#64408—21no—
98C4×#64408C2×D412yes—
99#11924031—22no—
100C23×D73—41no—
101#11924029—22no—
102#11924029—22no—
103#11924029—41no—
104#11924029—41no—
105C2×D292—21no—
106C2×D292—21no—
107C2×D292—41no—
108C2×C22⋊D73—41no—
109D4×D73—22no—
110D4×D73—22no—
111D4×D73—41no—
112D4×D73—41no—
113C2×C4×D73—41no—
114C2×C4×D73C2×D411yescharacteristic
115#11924015—22no—
116#11924015—22no—
117D584—21no—
118D584—21no—
119D584C22×C412yes—
120D584C22×C412yescomplemented
121#11924013—22no—
122#11924013—22no—
123C2×#10596831#4111yescharacteristic
124C8×D73C22×C411yescharacteristic
125C8×D73C2×D411yescharacteristic
126C8×D73#4111yescharacteristic
127C8×D73C2411yescharacteristic
128#11924003C22×C412yescomplemented
129C2×Q8×C73—21no—
130C2×D4×C73—21no—
131Q16×C73—21no—
132Q16×C73C22×C412yescomplemented
133D8×C73—21no—
134D8×C73C22×C412yes—
135C2×C8×C73C22×C411yescharacteristic
136C16×C73C22×C412yescomplemented
137C23×C73—41no—
138C22×D73—41no—
139C22×D73—41no—
140C22×D73—42no—
141C22×D73—42no—
142C22×D73—82no—
143C22×D73—82no—
144C22×D73AGL(1,ℤ/8)11yescharacteristic
145C2×#64408—22no—
146C2×#64408—42no—
147C2×#64408—42no—
148C2×#64408—88no—
149C2×#64408—82no—
150Q8×C73—22no—
151Q8×C73—41no—
152D4×C73—22no—
153D4×C73—41no—
154C2×C4×C73—41no—
155C2×C4×C73C4×D411yescharacteristic
156C22⋊D73—42no—
157C22⋊D73—42no—
158C2×Dic73AGL(1,ℤ/8)11yescharacteristic
159D292—22no—
160D292—22no—
161D292—42no—
162D292—42no—
163D292—41no—
164D292—41no—
165C4×D73—42no—
166C4×D73—42no—
167C4×D73C4×D411yescharacteristic
168C4×D73AGL(1,ℤ/8)11yescharacteristic
169C4×D73AGL(1,ℤ/8)11yescharacteristic
170C4×D73C22×D411yescharacteristic
171#10596833—22no—
172#10596833—42no—
173C8×C73C4×D411yescharacteristic
174C8×C73C23×C411yescharacteristic
175#10596831C4×D411yescharacteristic
176#10596831C2×#4111yescharacteristic
177C22×C73—42no—
178C22×C73—82no—
179C22×C73#44211yescharacteristic
180C2×D73—22no—
181C2×D73—42no—
182C2×D73—42no—
183C2×D73—82no—
184C2×D73—82no—
185C2×D73—84no—
186C2×D73—82no—
187C2×D73—82no—
188C2×D73#44211yescharacteristic
189C2×D73C2×AGL(1,ℤ/8)11yescharacteristic
190#64408—42no—
191#64408—82no—
192C4×C73—42no—
193C4×C73#44211yescharacteristic
194C4×C73C2×C4×D411yescharacteristic
195Dic73#44211yescharacteristic
196Dic73C2×AGL(1,ℤ/8)11yescharacteristic
197C2×AGL(1,ℤ/16)—731nomaximal, Sylow
198C2×C73—82no—
199C2×C73AGL(1,ℤ/16)12yescomplemented
200C2×C73C2×#44211yescharacteristic
201D73—21no—
202D73—21no—
203D73—82no—
204D73—82no—
205C2×#509—731no—
206C2×#444—731no—
207C2×#442—731no—
208AGL(1,ℤ/16)—738no—
209C2×#365—731no—
210C2×#361—731no—
211C2×#360—731no—
212C2×#347—731no—
213C73C2×AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
214C2×#135—731no—
215C22×D8—731no—
216C2×#131—1461no—
217C2×C4×D4—1461no—
218#509—734no—
219#509—734no—
220C2×SD32—731no—
221C2×SD32#6440811yescharacteristic, complemented
222C2×D16—731no—
223C2×D16—731no—
224C2×M32—731no—
225C2×M32—731no—
226#444—734no—
227#444—1462no—
228#442—734no—
229#442—1462no—
230C2×#108—731no—
231C2×#106—731no—
232C2×#104—1461no—
233C2×#102—1461no—
234C2×#97—731no—
235#365—734no—
236#361—734no—
237#360—734no—
238#347—734no—
239C2×#41—1461no—
240C22×D4—1461no—
241C23×C4—2921no—
242#135—732no—
243#135—732no—
244#135—1461no—
245#135—1461no—
246C2×Q16C2×#6440811yescharacteristic, complemented
247C2×SD16—1461no—
248C2×D8—732no—
249C2×D8—732no—
250C2×D8—731no—
251C2×D8—731no—
252C2×D8—1461no—
253C2×D8—1461no—
254C2×D8—1461no—
255C2×D8C2×#6440811yescharacteristic
256#131—2922no—
257#131—1464no—
258C2×M16—2921no—
259C2×M16—1461no—
260C22×C8—2921no—
261C22×C8—731no—
262C22×C8—731no—
263C4×D4—2922no—
264C4×D4—1464no—
265C2×C4⋊C4—1461no—
266C2×C22⋊C4—2921no—
267C2×C42—731no—
268SD32—734no—
269SD32C2×#6440814yescomplemented
270D16—734no—
271D16—734no—
272M32—732no—
273M32—732no—
274M32—732no—
275M32—1461no—
276C2×C16—731no—
277C2×C16—1461no—
278C2×C16C2×#6440811yescharacteristic, complemented
279#108—732no—
280#108—1461no—
281#106—732no—
282#106—1461no—
283#104—1464no—
284#102—1464no—
285#97—732no—
286#97—732no—
287C24—2921no—
288#41—2921no—
289#41—2921no—
290#41—1462no—
291#41—1462no—
292C2×Q8—21no—
293C2×D4—21no—
294C2×D4—2921no—
295C2×D4—2921no—
296C2×D4—2921no—
297C2×D4—2921no—
298C2×D4—1462no—
299C2×D4—1462no—
300C2×D4—1461no—
301C2×D4—1461no—
302C22×C4—2921no—
303C22×C4—2921no—
304C22×C4—2924no—
305C22×C4—5844no—
306C22×C4—731no—
307C22×C4—1461no—
308Q16—21no—
309Q16C22×#6440812yescomplemented
310SD16—1462no—
311SD16—1462no—
312D8—21no—
313D8—732no—
314D8—732no—
315D8—1462no—
316D8—1462no—
317D8—1461no—
318D8—1461no—
319D8C22×#6440812yes—
320M16—2921no—
321M16—2924no—
322M16—1462no—
323C2×C8—2921no—
324C2×C8—2924no—
325C2×C8—731no—
326C2×C8—731no—
327C2×C8—731no—
328C2×C8—731no—
329C2×C8—731no—
330C2×C8—732no—
331C2×C8—1461no—
332C2×C8—1461no—
333C2×C8C22×#6440811yescharacteristic
334C4⋊C4—2921no—
335C4⋊C4—1462no—
336C22⋊C4—2924no—
337C42—732no—
338C42—1461no—
339C16—732no—
340C16—1462no—
341C16C22×#6440812yescomplemented
342C23—41no—
343C23—2922no—
344C23—2922no—
345C23—2921no—
346C23—2921no—
347C23—5842no—
348C23—5842no—
349C23—731no—
350Q8—22no—
351Q8—41no—
352D4—22no—
353D4—41no—
354D4—2922no—
355D4—2922no—
356D4—2922no—
357D4—2922no—
358D4—2921no—
359D4—2921no—
360D4—1462no—
361D4—1462no—
362C2×C4—41no—
363C2×C4—2922no—
364C2×C4—2922no—
365C2×C4—2922no—
366C2×C4—2922no—
367C2×C4—5848no—
368C2×C4—5842no—
369C2×C4—731no—
370C2×C4—731no—
371C2×C4—731no—
372C2×C4—731no—
373C2×C4—731no—
374C2×C4—1462no—
375C2×C4D4×#6440811yescharacteristic
376C8—2922no—
377C8—731no—
378C8—731no—
379C8—1462no—
380C8D4×#6440811yescharacteristic
381C8C23×#6440811yescharacteristic
382C22—42no—
383C22—82no—
384C22—2922no—
385C22—2922no—
386C22—5842no—
387C22—5842no—
388C22—5844no—
389C22—5842no—
390C22—5842no—
391C22—731no—
392C22—731no—
393C22—1462no—
394C22#1798962811yescharacteristic
395C4—42no—
396C4—2922no—
397C4—5842no—
398C4—731no—
399C4—731no—
400C4#1798962811yescharacteristic
401C4C2×D4×#6440811yescharacteristic
402C2—82no—
403C2—5842no—
404C2—5842no—
405C2—1461no—
406C2—1461no—
407C2#2262634212yesdirect product factor
408C2C2×#1798962811yescharacteristic
subgroupG/H
centerC22#17989628
commutatorC8×C73C23×C4
FrattiniC8C23×#64408
FittingC2×SD32×C73C4
socleC22×C73#442
prime radicalC2×#17989024C2
cosocleC8×D73C24
hypercenterC2×SD32#64408
hypocenterC73C2×AGL(1,ℤ/16)
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. C2×#17989633C2semidirect
2. C2×#17989628C2semidirect
3. #22626342C2direct (N × H)
4. C2×#17989512C2semidirect
5. C2×#17989505C2semidirect
6. C2×#17989504C2semidirect
7. C2×#17989477C2semidirect
13. #17989633C22semidirect
15. #17989628C22semidirect
21. #17989512C22semidirect
22. #17989505C22semidirect
23. #17989504C22semidirect
24. #17989477C22semidirect
27. #17989024C4semidirect
29. C2×#14556534C4semidirect
30. C2×D1168C4semidirect
31. C2×#14556532C4semidirect
33. C2×SD32×C73C4semidirect
61. #14556614C2×C4semidirect
65. C2×D584C2×C4semidirect
72. #14556534C2×C4semidirect
73. D1168C2×C4semidirect
74. #14556532C2×C4semidirect
75. #14556530C2×C4semidirect
77. C2×#11924003C2×C4semidirect
78. C2×Q16×C73C2×C4semidirect
80. SD32×C73C2×C4semidirect
81. C2×C16×C73C2×C4semidirect
120. D584C22×C4semidirect
128. #11924003C22×C4semidirect
132. Q16×C73C22×C4semidirect
136. C16×C73C22×C4semidirect
199. C2×C73AGL(1,ℤ/16)semidirect
213. C73C2×AGL(1,ℤ/16)semidirect
221. C2×SD32#64408semidirect
246. C2×Q16C2×#64408semidirect
269. SD32C2×#64408semidirect
278. C2×C16C2×#64408semidirect
309. Q16C22×#64408semidirect
341. C16C22×#64408semidirect
407. C2#22626342direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179896332
C2×#179896282
#226263422
C2×#179895122
C2×#179895052
C2×#179895042
C2×#179894772
C2×#179890242
C2×AGL(1,ℤ/16)73