Finite Group Databasebeta

← C2×#22626341 #34030292

Subgroups — C2×#22626341 #34030292

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×#17989634C211yesmaximal, characteristic, complemented
2C2×#17989628C211yesmaximal, characteristic, complemented
3#22626341C218yesmaximal, direct product factor
4C2×#17989512C211yesmaximal, characteristic, complemented
5C2×#17989505C211yesmaximal, characteristic, complemented
6C2×#17989503C211yesmaximal, characteristic, complemented
7C2×#17989478C211yesmaximal, characteristic, complemented
8C2×#17989021C211yesmaximal, characteristic
9C2×#14556678—21no—
10C2×D4×#64408—21no—
11C2×#14556666C2211yescharacteristic
12#17989634—22no—
13#17989634C2214yescomplemented
14#17989628—22no—
15#17989628C2214yescomplemented
16C2×#14556661C2211yescharacteristic
17C2×#14556659C2211yescharacteristic
18C2×#14556655—21no—
19C2×#14556653—21no—
20C2×#14556645C2211yescharacteristic
21#17989512C2214yescomplemented
22#17989505C2214yescomplemented
23#17989503C2214yescomplemented
24#17989478C2214yescomplemented
25C2×#14556610C2211yescharacteristic
26C2×D8×D73C2211yescharacteristic
27#17989021C414yescomplemented
28#17989021C2214yes—
29C2×#14556536C411yescharacteristic, complemented
30C2×#14556535C411yescharacteristic, complemented
31C2×#14556532C411yescharacteristic, complemented
32C2×#14556530C2211yescharacteristic
33C2×D16×C73C411yescharacteristic, complemented
34C23×#64408—41no—
35#14556678—24no—
36#14556678—42no—
37C2×#11924038—21no—
38C2×#11924037—41no—
39C2×#11924036D411yescharacteristic
40C22×#10596833—41no—
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#14556655—24no—
54#14556653—24no—
55#14556645D412yes—
56#14556645C2312yes—
57C2×#11924027—21no—
58C2×D4×D73—21no—
59#14556610—21no—
60#14556610—21no—
61#14556610C2×C412yescomplemented
62#14556610C2312yes—
63C2×Dic292C2×C411yescharacteristic, complemented
64C2×#11924016—21no—
65C2×D584C2×C411yescharacteristic
66C2×#11924013—21no—
67D8×D73—21no—
68D8×D73—21no—
69D8×D73C2×C412yes—
70D8×D73C2312yes—
71C2×C8×D73C2311yescharacteristic
72#14556536C2×C414yescomplemented
73#14556535C2×C414yescomplemented
74#14556532C2×C414yescomplemented
75#14556530C2×C412yescomplemented
76#14556530C2312yes—
77C2×#11924003C2×C411yescharacteristic, complemented
78C2×D8×C73C2×C411yescharacteristic
79C2×D8×C73C2×C411yescharacteristic, complemented
80D16×C73C2×C414yescomplemented
81C2×C16×C73C2×C411yescharacteristic, complemented
82C22×#64408—21no—
83C22×#64408—44no—
84C22×#64408—41no—
85C22×#64408—84no—
86#11924038—22no—
87#11924038—41no—
88#11924037—44no—
89#11924036—21no—
90#11924036C2×D412yes—
91C2×#10596833—21no—
92C2×#10596833—44no—
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#11924027—22no—
102#11924027—22no—
103#11924027—41no—
104#11924027—41no—
105C2×Dic146—21no—
106C2×D292—21no—
107C2×C22⋊D73—41no—
108C2×C22⋊D73—41no—
109D4×D73—22no—
110D4×D73—22no—
111D4×D73—41no—
112D4×D73—41no—
113C22×Dic73—41no—
114C2×C4×D73C2×D411yescharacteristic
115Dic292—21no—
116Dic292C22×C412yescomplemented
117#11924016—22no—
118#11924016—22no—
119D584—21no—
120D584C22×C412yes—
121#11924013—22no—
122#11924013—22no—
123C2×#10596831#4111yescharacteristic
124C8×D73C22×C411yescharacteristic
125C8×D73C2×D411yescharacteristic
126C8×D73#4111yescharacteristic
127C8×D73C2411yescharacteristic
128#11924003C22×C412yescomplemented
129C2×D4×C73—21no—
130C2×D4×C73—21no—
131D8×C73—21no—
132D8×C73—21no—
133D8×C73C22×C412yes—
134D8×C73C22×C412yescomplemented
135C2×C8×C73C22×C411yescharacteristic
136C16×C73C22×C412yescomplemented
137C23×C73—41no—
138C23×C73—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—
150D4×C73—22no—
151D4×C73—22no—
152D4×C73—41no—
153D4×C73—41no—
154C2×C4×C73C4×D411yescharacteristic
155C22⋊D73—42no—
156C22⋊D73—42no—
157C22⋊D73—42no—
158C22⋊D73—42no—
159C2×Dic73—41no—
160C2×Dic73—42no—
161C2×Dic73—42no—
162C2×Dic73AGL(1,ℤ/8)11yescharacteristic
163D292—22no—
164D292—41no—
165C4×D73C4×D411yescharacteristic
166C4×D73AGL(1,ℤ/8)11yescharacteristic
167C4×D73AGL(1,ℤ/8)11yescharacteristic
168C4×D73C22×D411yescharacteristic
169Dic146—22no—
170Dic146—41no—
171#10596833—22no—
172#10596833—42no—
173C8×C73C4×D411yescharacteristic
174C8×C73C23×C411yescharacteristic
175#10596831C4×D411yescharacteristic
176#10596831C2×#4111yescharacteristic
177C22×C73—42no—
178C22×C73—42no—
179C22×C73—82no—
180C22×C73—82no—
181C22×C73#44211yescharacteristic
182C2×D73—22no—
183C2×D73—42no—
184C2×D73—82no—
185C2×D73—82no—
186C2×D73—84no—
187C2×D73—82no—
188C2×D73#44211yescharacteristic
189C2×D73C2×AGL(1,ℤ/8)11yescharacteristic
190#64408—42no—
191#64408—82no—
192C4×C73#44211yescharacteristic
193C4×C73C2×C4×D411yescharacteristic
194Dic73—42no—
195Dic73#44211yescharacteristic
196Dic73C2×AGL(1,ℤ/8)11yescharacteristic
197C2×AGL(1,ℤ/16)—731nomaximal, Sylow
198C2×C73—82no—
199C2×C73—82no—
200C2×C73AGL(1,ℤ/16)12yescomplemented
201C2×C73C2×#44211yescharacteristic
202D73—21no—
203D73—21no—
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—731no—
222C2×D16—731no—
223C2×D16#6440811yescharacteristic, complemented
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×Q16—731no—
247C2×SD16—1461no—
248C2×D8—732no—
249C2×D8—732no—
250C2×D8—731no—
251C2×D8—1461no—
252C2×D8—1461no—
253C2×D8—1461no—
254C2×D8C2×#6440811yescharacteristic
255C2×D8C2×#6440811yescharacteristic, complemented
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—
269SD32—734no—
270D16—734no—
271D16C2×#6440814yescomplemented
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—1461no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—2921no—
296C2×D4—2921no—
297C2×D4—2921no—
298C2×D4—2921no—
299C2×D4—1462no—
300C2×D4—1462no—
301C2×D4—1461no—
302C22×C4—2921no—
303C22×C4—2921no—
304C22×C4—2924no—
305C22×C4—5844no—
306C22×C4—731no—
307C22×C4—1461no—
308Q16—732no—
309Q16—1461no—
310SD16—1462no—
311SD16—1462no—
312D8—21no—
313D8—21no—
314D8—732no—
315D8—1462no—
316D8—1462no—
317D8—1461no—
318D8C22×#6440812yes—
319D8C22×#6440812yescomplemented
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—41no—
344C23—2922no—
345C23—2922no—
346C23—2921no—
347C23—5842no—
348C23—5842no—
349C23—731no—
350Q8—2921no—
351Q8—1462no—
352D4—22no—
353D4—22no—
354D4—41no—
355D4—41no—
356D4—2922no—
357D4—2922no—
358D4—2922no—
359D4—2922no—
360D4—2921no—
361D4—1462no—
362C2×C4—2922no—
363C2×C4—2921no—
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—42no—
384C22—82no—
385C22—82no—
386C22—2922no—
387C22—5842no—
388C22—5842no—
389C22—5844no—
390C22—5842no—
391C22—731no—
392C22—731no—
393C22—1462no—
394C22#1798962811yescharacteristic
395C4—2922no—
396C4—2922no—
397C4—5842no—
398C4—731no—
399C4—731no—
400C4#1798962811yescharacteristic
401C4C2×D4×#6440811yescharacteristic
402C2—82no—
403C2—82no—
404C2—5842no—
405C2—1461no—
406C2—1461no—
407C2#2262634112yesdirect product factor
408C2C2×#1798962811yescharacteristic
subgroupG/H
centerC22#17989628
commutatorC8×C73C23×C4
FrattiniC8C23×#64408
FittingC2×D16×C73C4
socleC22×C73#442
prime radicalC2×#17989021C2
cosocleC8×D73C24
hypercenterC2×D16#64408
hypocenterC73C2×AGL(1,ℤ/16)
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. C2×#17989634C2semidirect
2. C2×#17989628C2semidirect
3. #22626341C2direct (N × H)
4. C2×#17989512C2semidirect
5. C2×#17989505C2semidirect
6. C2×#17989503C2semidirect
7. C2×#17989478C2semidirect
13. #17989634C22semidirect
15. #17989628C22semidirect
21. #17989512C22semidirect
22. #17989505C22semidirect
23. #17989503C22semidirect
24. #17989478C22semidirect
27. #17989021C4semidirect
29. C2×#14556536C4semidirect
30. C2×#14556535C4semidirect
31. C2×#14556532C4semidirect
33. C2×D16×C73C4semidirect
61. #14556610C2×C4semidirect
63. C2×Dic292C2×C4semidirect
72. #14556536C2×C4semidirect
73. #14556535C2×C4semidirect
74. #14556532C2×C4semidirect
75. #14556530C2×C4semidirect
77. C2×#11924003C2×C4semidirect
79. C2×D8×C73C2×C4semidirect
80. D16×C73C2×C4semidirect
81. C2×C16×C73C2×C4semidirect
116. Dic292C22×C4semidirect
128. #11924003C22×C4semidirect
134. D8×C73C22×C4semidirect
136. C16×C73C22×C4semidirect
200. C2×C73AGL(1,ℤ/16)semidirect
213. C73C2×AGL(1,ℤ/16)semidirect
223. C2×D16#64408semidirect
255. C2×D8C2×#64408semidirect
271. D16C2×#64408semidirect
278. C2×C16C2×#64408semidirect
319. D8C22×#64408semidirect
341. C16C22×#64408semidirect
407. C2#22626341direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179896342
C2×#179896282
#226263412
C2×#179895122
C2×#179895052
C2×#179895032
C2×#179894782
C2×#179890212
C2×AGL(1,ℤ/16)73