Finite Group Databasebeta

← C2×#22609572 #33073726

Subgroups — C2×#22609572 #33073726

Order 18688.

966 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988963C211yesmaximal, characteristic
2C2×#17988960C211yesmaximal, characteristic, complemented
3C2×#17988937C211yesmaximal, characteristic, complemented
4C2×#17988935C211yesmaximal, characteristic, complemented
5C2×#17988933C211yesmaximal, characteristic, complemented
6#22609572C218yesmaximal, direct product factor
7C2×#17988309C211yesmaximal, characteristic, complemented
8C2×#486×C73C211yesmaximal, characteristic, complemented
9C22×#11924017—22no—
10C22×#11924013—22no—
11C2×#14556591C2211yescharacteristic
12C2×#14556588C2211yescharacteristic
13#17988963—22no—
14#17988963C2214yes—
15#17988960—22no—
16#17988960C2214yescomplemented
17#17988937—22no—
18#17988937C2214yescomplemented
19#17988935—22no—
20#17988935C2214yescomplemented
21#17988933—22no—
22#17988933C2214yescomplemented
23C2×#14556515—22no—
24C2×#14556512—22no—
25C2×#14556511—22no—
26C2×C4×#10596831C2211yescharacteristic
27C2×C4×#10596831C2211yescharacteristic
28#17988309C2214yescomplemented
29C2×C4⋊Q8×C73C2211yescharacteristic
30C2×#127×C73C2211yescharacteristic
31#486×C73—22no—
32#486×C73C2214yescomplemented
33C2×#102×C73—22no—
34C2×C4×C8×C73C2211yescharacteristic
35C22×Dic146—21no—
36C22×D292—21no—
37C22×D292—21no—
38C22×D292—21no—
39C2×#11924017—28no—
40C2×#11924017—48no—
41C2×#11924013—28no—
42C2×#11924013—48no—
43C22×#10596831D412yes—
44C22×#10596831D412yes—
45#14556591—21no—
46#14556591—21no—
47#14556591—21no—
48#14556591C2312yes—
49#14556588—21no—
50#14556588—21no—
51#14556588—21no—
52#14556588C2312yes—
53C2×C4⋊Dic73—21no—
54C2×C4⋊Dic73—21no—
55#14556515—28no—
56#14556512—28no—
57#14556511—28no—
58C4×#10596831D412yes—
59C4×#10596831D412yes—
60C4×#10596831C2312yes—
61C4×#10596831C2312yes—
62C22×Q8×C73—21no—
63C22×D4×C73—21no—
64C22×D4×C73—21no—
65C22×D4×C73—21no—
66C22×C8×C73D412yes—
67C4⋊Q8×C73—21no—
68C4⋊Q8×C73—21no—
69C4⋊Q8×C73—21no—
70C4⋊Q8×C73C2312yes—
71#127×C73—21no—
72#127×C73—21no—
73#127×C73—21no—
74#127×C73C2312yes—
75C2×C4⋊C4×C73—21no—
76C2×C4⋊C4×C73—21no—
77C2×C42×C73C2311yescharacteristic
78#102×C73—28no—
79C4×C8×C73D412yes—
80C4×C8×C73C2312yes—
81C23×D73—41no—
82C2×Dic146—22no—
83C2×Dic146—44no—
84C2×Dic146—41no—
85C2×D292—22no—
86C2×D292—22no—
87C2×D292—22no—
88C2×D292—44no—
89C2×D292—44no—
90C2×D292—44no—
91C2×D292—41no—
92C2×D292—41no—
93C2×D292—41no—
94C22×Dic73—41no—
95#11924017—416no—
96#11924013—416no—
97C2×#10596831—24no—
98C2×#10596831—24no—
99C2×#10596831C2×D414yes—
100C2×#10596831C2×D414yes—
101C4⋊Dic73—22no—
102C4⋊Dic73—22no—
103C4⋊Dic73—41no—
104C4⋊Dic73—41no—
105C24×C73—41no—
106C2×Q8×C73—22no—
107C2×Q8×C73—41no—
108C2×Q8×C73—44no—
109C2×D4×C73—22no—
110C2×D4×C73—22no—
111C2×D4×C73—22no—
112C2×D4×C73—41no—
113C2×D4×C73—41no—
114C2×D4×C73—41no—
115C2×D4×C73—44no—
116C2×D4×C73—44no—
117C2×D4×C73—44no—
118C22×C4×C73—41no—
119C22×C4×C73C2×D411yescharacteristic
120C22×C4×C73C2×D411yescharacteristic
121C22×C4×C73C2×D411yescharacteristic
122C2×C8×C73—24no—
123C2×C8×C73C2×D414yes—
124C4⋊C4×C73—22no—
125C4⋊C4×C73—22no—
126C4⋊C4×C73—41no—
127C4⋊C4×C73—41no—
128C42×C73C2×D411yescharacteristic
129C42×C73C2×D411yescharacteristic
130C42×C73C2×D411yescharacteristic
131C42×C73C2411yescharacteristic
132C23×C73—42no—
133C23×C73—82no—
134C23×C73—82no—
135C23×C73—82no—
136C23×C73#12711yescharacteristic
137C22×D73—42no—
138C22×D73—82no—
139C22×D73—82no—
140C22×D73—82no—
141Q8×C73—44no—
142Q8×C73—82no—
143D4×C73—44no—
144D4×C73—44no—
145D4×C73—44no—
146D4×C73—82no—
147D4×C73—82no—
148D4×C73—82no—
149C2×C4×C73—42no—
150C2×C4×C73—82no—
151C2×C4×C73#12711yescharacteristic
152C2×C4×C73#12711yescharacteristic
153C2×C4×C73#12711yescharacteristic
154C2×C4×C73#13514yes—
155C2×C4×C73AGL(1,ℤ/8)14yes—
156C2×C4×C73AGL(1,ℤ/8)14yes—
157C2×C4×C73C22×D411yescharacteristic
158C2×C4×C73C22×D411yescharacteristic
159C2×C4×C73C22×D411yescharacteristic
160C2×Dic73—42no—
161C2×Dic73—82no—
162D292—44no—
163D292—44no—
164D292—44no—
165D292—82no—
166D292—82no—
167D292—82no—
168Dic146—44no—
169Dic146—82no—
170C8×C73—24no—
171#10596831—24no—
172#10596831—24no—
173C22×C73—82no—
174C22×C73—82no—
175C22×C73—82no—
176C22×C73—164no—
177C22×C73#49512yes—
178C22×C73#49612yes—
179C22×C73#49612yes—
180C22×C73C2×#12711yescharacteristic
181C2×D73—82no—
182C2×D73—82no—
183C2×D73—82no—
184C2×D73—164no—
185C4×C73—82no—
186C4×C73#49512yes—
187C4×C73#49612yes—
188C4×C73#49612yes—
189C4×C73C2×#13512yes—
190C4×C73C2×AGL(1,ℤ/8)12yes—
191C4×C73C2×AGL(1,ℤ/8)12yes—
192Dic73—82no—
193C2×#1717—731nomaximal, Sylow
194C2×C73—162no—
195C2×C73#171714yescomplemented
196C2×C73C2×#49511yescharacteristic
197C2×C73C2×#49611yescharacteristic
198C2×C73C2×#49611yescharacteristic
199D73—162no—
200C2×#493—731no—
201C2×#492—731no—
202C2×#487—731no—
203C2×#486—731no—
204C2×#486—731no—
205C2×#486D7311yescharacteristic, complemented
206#1717—738no—
207C2×#322—731no—
208C73C2×#171711yescharacteristic, complemented, Sylow
209C22×SD16—1462no—
210C22×D8—1462no—
211C2×C4⋊Q8—731no—
212C2×C4⋊Q8C2×D7311yescharacteristic
213C2×#127—731no—
214C2×#127C2×D7311yescharacteristic
215#493—734no—
216#493—1462no—
217#492—734no—
218#492—1462no—
219#487—734no—
220#487—1462no—
221#486—22no—
222#486—734no—
223#486—734no—
224#486—1462no—
225#486—1462no—
226#486C2×D7314yescomplemented
227C2×#103—1462no—
228C2×#102—22no—
229C2×#102—1462no—
230C2×#102—1462no—
231C2×C4×C8—731no—
232C2×C4×C8—731no—
233C2×C4×C8C2×D7311yescharacteristic
234#322—734no—
235C22×Q8—21no—
236C22×Q8—1461no—
237C22×D4—21no—
238C22×D4—21no—
239C22×D4—21no—
240C22×D4—1461no—
241C22×D4—1461no—
242C22×D4—1461no—
243C2×SD16—2928no—
244C2×SD16—1468no—
245C2×D8—2928no—
246C2×D8—1468no—
247C22×C8—732no—
248C22×C8—732no—
249C22×C8C22⋊D7312yes—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—732no—
254C4⋊Q8—1461no—
255C4⋊Q8—1461no—
256C4⋊Q8—1461no—
257C4⋊Q8C22×D7312yes—
258#127—21no—
259#127—21no—
260#127—21no—
261#127—732no—
262#127—1461no—
263#127—1461no—
264#127—1461no—
265#127C22×D7312yes—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—1461no—
269C2×C4⋊C4—1461no—
270C2×C42C22×D7311yescharacteristic
271#103—1468no—
272#102—28no—
273#102—1468no—
274#102—1468no—
275C4×C8—732no—
276C4×C8—732no—
277C4×C8—732no—
278C4×C8—732no—
279C4×C8C22⋊D7312yes—
280C4×C8C22×D7312yes—
281C24—41no—
282C24—2921no—
283C2×Q8—22no—
284C2×Q8—41no—
285C2×Q8—44no—
286C2×Q8—2921no—
287C2×Q8—2924no—
288C2×Q8—1462no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—44no—
296C2×D4—44no—
297C2×D4—44no—
298C2×D4—2921no—
299C2×D4—2921no—
300C2×D4—2921no—
301C2×D4—2924no—
302C2×D4—2924no—
303C2×D4—2924no—
304C2×D4—1462no—
305C2×D4—1462no—
306C2×D4—1462no—
307C22×C4—41no—
308C22×C4—2921no—
309C22×C4D4×D7311yescharacteristic
310C22×C4D4×D7311yescharacteristic
311C22×C4C2×C22⋊D7311yescharacteristic
312SD16—29216no—
313D8—29216no—
314C2×C8—24no—
315C2×C8—734no—
316C2×C8—734no—
317C2×C8—1464no—
318C2×C8—1464no—
319C2×C8C2×C22⋊D7314yes—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—2921no—
325C4⋊C4—2921no—
326C4⋊C4—1462no—
327C4⋊C4—1462no—
328C42D4×D7311yescharacteristic
329C42D4×D7311yescharacteristic
330C42C2×C22⋊D7311yescharacteristic
331C42C23×D7311yescharacteristic
332C23—42no—
333C23—82no—
334C23—82no—
335C23—82no—
336C23—2922no—
337C23—5842no—
338C23—5842no—
339C23—5842no—
340C23#1455658711yescharacteristic
341Q8—44no—
342Q8—82no—
343Q8—2924no—
344Q8—5842no—
345D4—44no—
346D4—44no—
347D4—44no—
348D4—82no—
349D4—82no—
350D4—82no—
351D4—2924no—
352D4—2924no—
353D4—2924no—
354D4—5842no—
355D4—5842no—
356D4—5842no—
357C2×C4—42no—
358C2×C4—82no—
359C2×C4—2922no—
360C2×C4—5842no—
361C2×C4#1455658711yescharacteristic
362C2×C4#1455658711yescharacteristic
363C2×C4#1455658711yescharacteristic
364C2×C4#1455661214yes—
365C2×C4#1455661514yes—
366C2×C4#1455661614yes—
367C2×C4C2×D4×D7311yescharacteristic
368C2×C4C2×D4×D7311yescharacteristic
369C2×C4C22×C22⋊D7311yescharacteristic
370C8—24no—
371C8—1464no—
372C8—1464no—
373C22—82no—
374C22—82no—
375C22—82no—
376C22—164no—
377C22—5842no—
378C22—5842no—
379C22—5842no—
380C22—11684no—
381C22#1798896812yes—
382C22#1798897512yes—
383C22#1798897712yes—
384C22C2×#1455658711yescharacteristic
385C4—82no—
386C4—5842no—
387C4#1798896812yes—
388C4#1798897512yes—
389C4#1798897712yes—
390C4C2×#1455661212yes—
391C4C2×#1455661512yes—
392C4C2×#1455661612yes—
393C2—162no—
394C2—11682no—
395C2#2260957214yesdirect product factor
396C2C2×#1798896811yescharacteristic
397C2C2×#1798897511yescharacteristic
398C2C2×#1798897711yescharacteristic
subgroupG/H
centerC23#14556587
commutator, cosocleC42×C73C24
FrattiniC42C23×D73
FittingC2×#486×C73C2
socleC23×C73#127
prime radicalC2×#17988963C2
hypercenterC2×#486D73
hypocenterC73C2×#1717
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
2. C2×#17988960C2semidirect
3. C2×#17988937C2semidirect
4. C2×#17988935C2semidirect
5. C2×#17988933C2semidirect
6. #22609572C2direct (N × H)
7. C2×#17988309C2semidirect
8. C2×#486×C73C2semidirect
16. #17988960C22semidirect
18. #17988937C22semidirect
20. #17988935C22semidirect
22. #17988933C22semidirect
28. #17988309C22semidirect
32. #486×C73C22semidirect
195. C2×C73#1717semidirect
205. C2×#486D73semidirect
208. C73C2×#1717semidirect
226. #486C2×D73semidirect
395. C2#22609572direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179889632
C2×#179889602
C2×#179889372
C2×#179889352
C2×#179889332
#226095722
C2×#179883092
C2×#486×C732
C2×#171773