Finite Group Databasebeta

← C2×#22609573 #33073727

Subgroups — C2×#22609573 #33073727

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×#17988964C211yesmaximal, characteristic
2C2×#17988961C211yesmaximal, characteristic, complemented
3C2×#17988935C211yesmaximal, characteristic, complemented
4C2×#17988935C211yesmaximal, characteristic, complemented
5C2×#17988935C211yesmaximal, characteristic, complemented
6#22609573C218yesmaximal, direct product factor
7C2×#17988309C211yesmaximal, characteristic, complemented
8C2×#487×C73C211yesmaximal, characteristic, complemented
9C22×#11924015—22no—
10C22×D584—22no—
11C2×#14556588C2211yescharacteristic
12C2×#14556588C2211yescharacteristic
13#17988964—22no—
14#17988964C2214yes—
15#17988961—22no—
16#17988961C2214yescomplemented
17#17988935—22no—
18#17988935—22no—
19#17988935—22no—
20#17988935C2214yescomplemented
21#17988935C2214yescomplemented
22#17988935C2214yescomplemented
23C2×#14556511—22no—
24C2×#14556511—22no—
25C2×#14556511—22no—
26C2×C4×#10596831C2211yescharacteristic
27C2×C4×#10596831C2211yescharacteristic
28#17988309C2214yescomplemented
29C2×C4⋊Q8×C73C2211yescharacteristic
30C2×C4⋊Q8×C73C2211yescharacteristic
31#487×C73—22no—
32#487×C73C2214yescomplemented
33C2×#103×C73—22no—
34C2×C4×C8×C73C2211yescharacteristic
35C22×D292—21no—
36C22×D292—21no—
37C22×D292—21no—
38C22×D292—21no—
39C22×D292—21no—
40C22×D292—21no—
41C2×#11924015—28no—
42C2×#11924015—48no—
43C2×D584—28no—
44C2×D584—48no—
45C22×#10596831D412yes—
46C22×#10596831D412yes—
47#14556588—21no—
48#14556588—21no—
49#14556588—21no—
50#14556588—21no—
51#14556588—21no—
52#14556588—21no—
53#14556588C2312yes—
54#14556588C2312yes—
55#14556511—28no—
56#14556511—28no—
57#14556511—28no—
58C4×#10596831D412yes—
59C4×#10596831D412yes—
60C4×#10596831C2312yes—
61C4×#10596831C2312yes—
62C22×Q8×C73—21no—
63C22×Q8×C73—21no—
64C22×C8×C73D412yes—
65C4⋊Q8×C73—21no—
66C4⋊Q8×C73—21no—
67C4⋊Q8×C73—21no—
68C4⋊Q8×C73—21no—
69C4⋊Q8×C73—21no—
70C4⋊Q8×C73—21no—
71C4⋊Q8×C73C2312yes—
72C4⋊Q8×C73C2312yes—
73C2×C4⋊C4×C73—21no—
74C2×C4⋊C4×C73—21no—
75C2×C4⋊C4×C73—21no—
76C2×C4⋊C4×C73—21no—
77C2×C42×C73C2311yescharacteristic
78#103×C73—28no—
79C4×C8×C73D412yes—
80C4×C8×C73C2312yes—
81C23×D73—41no—
82C23×D73—41no—
83C2×D292—22no—
84C2×D292—22no—
85C2×D292—22no—
86C2×D292—22no—
87C2×D292—22no—
88C2×D292—22no—
89C2×D292—44no—
90C2×D292—44no—
91C2×D292—44no—
92C2×D292—44no—
93C2×D292—44no—
94C2×D292—44no—
95C2×D292—41no—
96C2×D292—41no—
97C2×D292—41no—
98C2×D292—41no—
99C2×D292—41no—
100C2×D292—41no—
101#11924015—416no—
102D584—416no—
103C2×#10596831—24no—
104C2×#10596831—24no—
105C2×#10596831C2×D414yes—
106C2×#10596831C2×D414yes—
107C2×Q8×C73—22no—
108C2×Q8×C73—22no—
109C2×Q8×C73—41no—
110C2×Q8×C73—41no—
111C2×Q8×C73—44no—
112C2×Q8×C73—44no—
113C22×C4×C73—41no—
114C22×C4×C73—41no—
115C22×C4×C73C2×D411yescharacteristic
116C22×C4×C73C2×D411yescharacteristic
117C22×C4×C73C2×D411yescharacteristic
118C2×C8×C73—24no—
119C2×C8×C73C2×D414yes—
120C4⋊C4×C73—22no—
121C4⋊C4×C73—22no—
122C4⋊C4×C73—22no—
123C4⋊C4×C73—22no—
124C4⋊C4×C73—41no—
125C4⋊C4×C73—41no—
126C4⋊C4×C73—41no—
127C4⋊C4×C73—41no—
128C42×C73C2×D411yescharacteristic
129C42×C73C2×D411yescharacteristic
130C42×C73C2×D411yescharacteristic
131C42×C73C2411yescharacteristic
132C23×C73#12711yescharacteristic
133C22×D73—42no—
134C22×D73—42no—
135C22×D73—82no—
136C22×D73—82no—
137C22×D73—82no—
138C22×D73—82no—
139C22×D73—82no—
140C22×D73—82no—
141Q8×C73—44no—
142Q8×C73—44no—
143Q8×C73—82no—
144Q8×C73—82no—
145C2×C4×C73—42no—
146C2×C4×C73—42no—
147C2×C4×C73—82no—
148C2×C4×C73—82no—
149C2×C4×C73#12711yescharacteristic
150C2×C4×C73#12711yescharacteristic
151C2×C4×C73#12711yescharacteristic
152C2×C4×C73#13514yes—
153C2×C4×C73AGL(1,ℤ/8)14yes—
154C2×C4×C73AGL(1,ℤ/8)14yes—
155C2×C4×C73C22×D411yescharacteristic
156C2×C4×C73C22×D411yescharacteristic
157C2×C4×C73C22×D411yescharacteristic
158D292—44no—
159D292—44no—
160D292—44no—
161D292—44no—
162D292—44no—
163D292—44no—
164D292—82no—
165D292—82no—
166D292—82no—
167D292—82no—
168D292—82no—
169D292—82no—
170C8×C73—24no—
171#10596831—24no—
172#10596831—24no—
173C22×C73#49512yes—
174C22×C73#49612yes—
175C22×C73#49612yes—
176C22×C73C2×#12711yescharacteristic
177C2×D73—82no—
178C2×D73—82no—
179C2×D73—82no—
180C2×D73—82no—
181C2×D73—82no—
182C2×D73—82no—
183C2×D73—164no—
184C2×D73—164no—
185C4×C73—82no—
186C4×C73—82no—
187C4×C73#49512yes—
188C4×C73#49612yes—
189C4×C73#49612yes—
190C4×C73C2×#13512yes—
191C4×C73C2×AGL(1,ℤ/8)12yes—
192C4×C73C2×AGL(1,ℤ/8)12yes—
193C2×#1717—731nomaximal, Sylow
194C2×C73#171714yescomplemented
195C2×C73C2×#49511yescharacteristic
196C2×C73C2×#49611yescharacteristic
197C2×C73C2×#49611yescharacteristic
198D73—162no—
199D73—162no—
200C2×#493—731no—
201C2×#492—731no—
202C2×#487D7311yescharacteristic, complemented
203C2×#486—731no—
204C2×#486—731no—
205C2×#486—731no—
206#1717—738no—
207C2×#322—731no—
208C73C2×#171711yescharacteristic, complemented, Sylow
209C22×SD16—1462no—
210C22×D8—1462no—
211C2×C4⋊Q8C2×D7311yescharacteristic
212C2×C4⋊Q8C2×D7311yescharacteristic
213C2×#127—731no—
214C2×#127—731no—
215#493—734no—
216#493—1462no—
217#492—734no—
218#492—1462no—
219#487—22no—
220#487C2×D7314yescomplemented
221#486—734no—
222#486—734no—
223#486—734no—
224#486—1462no—
225#486—1462no—
226#486—1462no—
227C2×#103—22no—
228C2×#102—1462no—
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—21no—
237C22×D4—1461no—
238C22×D4—1461no—
239C22×D4—1461no—
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—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8C22×D7312yes—
257C4⋊Q8C22×D7312yes—
258#127—732no—
259#127—732no—
260#127—1461no—
261#127—1461no—
262#127—1461no—
263#127—1461no—
264#127—1461no—
265#127—1461no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C42C22×D7311yescharacteristic
271#103—28no—
272#102—1468no—
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—2921no—
282C24—2921no—
283C2×Q8—22no—
284C2×Q8—22no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—44no—
288C2×Q8—44no—
289C2×D4—2921no—
290C2×D4—2921no—
291C2×D4—2921no—
292C2×D4—2921no—
293C2×D4—2921no—
294C2×D4—2921no—
295C2×D4—2924no—
296C2×D4—2924no—
297C2×D4—2924no—
298C2×D4—2924no—
299C2×D4—2924no—
300C2×D4—2924no—
301C2×D4—1462no—
302C2×D4—1462no—
303C2×D4—1462no—
304C2×D4—1462no—
305C2×D4—1462no—
306C2×D4—1462no—
307C22×C4—41no—
308C22×C4—41no—
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—22no—
323C4⋊C4—22no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C42D4×D7311yescharacteristic
329C42D4×D7311yescharacteristic
330C42C2×C22⋊D7311yescharacteristic
331C42C23×D7311yescharacteristic
332C23—2922no—
333C23—2922no—
334C23—5842no—
335C23—5842no—
336C23—5842no—
337C23—5842no—
338C23—5842no—
339C23—5842no—
340C23#1455658711yescharacteristic
341Q8—44no—
342Q8—44no—
343Q8—82no—
344Q8—82no—
345D4—2924no—
346D4—2924no—
347D4—2924no—
348D4—2924no—
349D4—2924no—
350D4—2924no—
351D4—5842no—
352D4—5842no—
353D4—5842no—
354D4—5842no—
355D4—5842no—
356D4—5842no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—82no—
360C2×C4—82no—
361C2×C4#1455658711yescharacteristic
362C2×C4#1455658711yescharacteristic
363C2×C4#1455658711yescharacteristic
364C2×C4#1455661414yes—
365C2×C4#1455661614yes—
366C2×C4#1455661814yes—
367C2×C4C2×D4×D7311yescharacteristic
368C2×C4C2×D4×D7311yescharacteristic
369C2×C4C22×C22⋊D7311yescharacteristic
370C8—24no—
371C8—1464no—
372C8—1464no—
373C22—5842no—
374C22—5842no—
375C22—5842no—
376C22—5842no—
377C22—5842no—
378C22—5842no—
379C22—11684no—
380C22—11684no—
381C22#1798897212yes—
382C22#1798897312yes—
383C22#1798897712yes—
384C22C2×#1455658711yescharacteristic
385C4—82no—
386C4—82no—
387C4#1798897212yes—
388C4#1798897312yes—
389C4#1798897712yes—
390C4C2×#1455661412yes—
391C4C2×#1455661612yes—
392C4C2×#1455661812yes—
393C2—11682no—
394C2—11682no—
395C2#2260957314yesdirect product factor
396C2C2×#1798897211yescharacteristic
397C2C2×#1798897311yescharacteristic
398C2C2×#1798897711yescharacteristic
subgroupG/H
centerC23#14556587
commutator, cosocleC42×C73C24
FrattiniC42C23×D73
FittingC2×#487×C73C2
socleC23×C73#127
prime radicalC2×#17988964C2
hypercenterC2×#487D73
hypocenterC73C2×#1717
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
2. C2×#17988961C2semidirect
3. C2×#17988935C2semidirect
4. C2×#17988935C2semidirect
5. C2×#17988935C2semidirect
6. #22609573C2direct (N × H)
7. C2×#17988309C2semidirect
8. C2×#487×C73C2semidirect
16. #17988961C22semidirect
20. #17988935C22semidirect
21. #17988935C22semidirect
22. #17988935C22semidirect
28. #17988309C22semidirect
32. #487×C73C22semidirect
194. C2×C73#1717semidirect
202. C2×#487D73semidirect
208. C73C2×#1717semidirect
220. #487C2×D73semidirect
395. C2#22609573direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179889642
C2×#179889612
C2×#179889352
#226095732
C2×#179883092
C2×#487×C732
C2×#171773