Finite Group Databasebeta

← C2×#22609443 #33068512

Subgroups — C2×#22609443 #33068512

Order 18688.

758 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988990C211yesmaximal, characteristic, complemented
2C2×#17988793C211yesmaximal, characteristic
3C2×#17988789C211yesmaximal, characteristic
4C2×#17988664C211yesmaximal, characteristic
5#22609443C218yesmaximal, direct product factor
6C2×#17988337C211yesmaximal, characteristic, complemented
7C2×#17988332C211yesmaximal, characteristic, complemented
8C2×#332×C73C211yesmaximal, characteristic, complemented
9C22×#11924017—21no—
10C22×#11924015—21no—
11C22×#11924011—21no—
12C2×#14556591C2211yescharacteristic
13C2×C4×D292C2211yescharacteristic
14#17988990—22no—
15#17988990C2214yescomplemented
16#17988793—22no—
17#17988793C2214yes—
18#17988789—22no—
19#17988789C2214yes—
20#17988664—22no—
21#17988664C2214yes—
22C2×#14556524—21no—
23C2×#14556524—21no—
24C2×C4⋊#10596831C2211yescharacteristic
25C2×#14556516—21no—
26C2×#14556515—21no—
27C2×#14556503—21no—
28C2×C4×#10596831C2211yescharacteristic
29#17988337C2214yescomplemented
30#17988332C2214yescomplemented
31C2×C4⋊Q8×C73C2211yescharacteristic
32C2×C4⋊C8×C73C2211yescharacteristic
33C2×C4⋊C8×C73C2211yescharacteristic
34#332×C73C2214yescomplemented
35C22×Dic146—21no—
36C22×D292D411yescharacteristic
37C22×C4×D73—21no—
38C2×#11924017—24no—
39C2×#11924017—44no—
40C2×#11924015—24no—
41C2×#11924015—44no—
42C2×#11924011—24no—
43C2×#11924011—44no—
44C22×#10596831—21no—
45C22×#10596831D411yescharacteristic
46C22×#10596831D411yescharacteristic
47#14556591—21no—
48#14556591—21no—
49#14556591—21no—
50#14556591C2312yes—
51C4×D292—21no—
52C4×D292—21no—
53C4×D292D412yes—
54C4×D292C2312yes—
55C2×C4⋊Dic73—21no—
56C2×C4⋊Dic73—21no—
57C2×C4⋊Dic73D411yescharacteristic
58C2×#11924005—21no—
59#14556524—24no—
60#14556524—24no—
61C4⋊#10596831—21no—
62C4⋊#10596831C2312yes—
63#14556516—24no—
64#14556515—24no—
65#14556503—24no—
66C4×#10596831D412yes—
67C4×#10596831C2312yes—
68C22×Q8×C73—21no—
69C22×C8×C73—21no—
70C22×C8×C73—21no—
71C4⋊Q8×C73—21no—
72C4⋊Q8×C73—21no—
73C4⋊Q8×C73—21no—
74C4⋊Q8×C73C2312yes—
75C2×C4⋊C4×C73—21no—
76C2×C4⋊C4×C73—21no—
77C2×C42×C73C2311yescharacteristic
78C4⋊C8×C73—21no—
79C4⋊C8×C73—21no—
80C4⋊C8×C73C2312yes—
81C4⋊C8×C73C2312yes—
82C23×D73—21no—
83C2×Dic146—22no—
84C2×Dic146—42no—
85C2×Dic146—42no—
86C2×Dic146—41no—
87C2×D292—22no—
88C2×D292—22no—
89C2×D292—21no—
90C2×D292C2×D412yes—
91C22×Dic73—21no—
92C22×Dic73—41no—
93C2×C4×D73—22no—
94C2×C4×D73—22no—
95C2×C4×D73—42no—
96C2×C4×D73—42no—
97#11924017—48no—
98#11924015—48no—
99#11924011—48no—
100C2×#10596831—22no—
101C2×#10596831—22no—
102C2×#10596831—42no—
103C2×#10596831SD1614yescomplemented
104C2×#10596831C2×D412yes—
105C2×#10596831C2×D412yes—
106C4⋊Dic73—21no—
107C4⋊Dic73—22no—
108C4⋊Dic73—22no—
109C4⋊Dic73—41no—
110C4⋊Dic73—41no—
111C4⋊Dic73C2×D412yes—
112#11924005—22no—
113#11924005—22no—
114C2×Q8×C73—22no—
115C2×Q8×C73—41no—
116C2×Q8×C73—42no—
117C2×Q8×C73—42no—
118C22×C4×C73—41no—
119C22×C4×C73C2×D411yescharacteristic
120C22×C4×C73C2×D411yescharacteristic
121C22×C4×C73#4111yescharacteristic
122C2×C8×C73—22no—
123C2×C8×C73—22no—
124C2×C8×C73—42no—
125C2×C8×C73—42no—
126C4⋊C4×C73—22no—
127C4⋊C4×C73—22no—
128C4⋊C4×C73—41no—
129C4⋊C4×C73—41no—
130C42×C73C2×D411yescharacteristic
131C42×C73C2×D411yescharacteristic
132C42×C73#4111yescharacteristic
133C42×C73C2411yescharacteristic
134C23×C73#12111yescharacteristic
135C22×D73—22no—
136C22×D73—42no—
137C22×D73—42no—
138C22×D73—42no—
139Q8×C73—42no—
140Q8×C73—42no—
141Q8×C73—82no—
142C2×C4×C73—22no—
143C2×C4×C73—42no—
144C2×C4×C73—82no—
145C2×C4×C73#12111yescharacteristic
146C2×C4×C73#12111yescharacteristic
147C2×C4×C73#12111yescharacteristic
148C2×C4×C73C2×SD1612yes—
149C2×C4×C73AGL(1,ℤ/8)12yes—
150C2×C4×C73AGL(1,ℤ/8)12yes—
151C2×C4×C73#13712yes—
152C2×C4×C73C22×D411yescharacteristic
153C2×C4×C73C22×D411yescharacteristic
154C2×C4×C73C2×#4111yescharacteristic
155C2×Dic73—22no—
156C2×Dic73—42no—
157C2×Dic73—42no—
158C2×Dic73—82no—
159D292—22no—
160D292—22no—
161D292—42no—
162C4×D73—42no—
163C4×D73—42no—
164C4×D73—44no—
165Dic146—42no—
166Dic146—42no—
167Dic146—82no—
168C8×C73—42no—
169C8×C73—42no—
170#10596831—22no—
171#10596831—42no—
172#10596831C2×SD1614yescomplemented
173C22×C73#46112yes—
174C22×C73#46912yes—
175C22×C73#47312yes—
176C22×C73C2×#12111yescharacteristic
177C2×D73—42no—
178C2×D73—42no—
179C2×D73—42no—
180C2×D73—84no—
181C4×C73—21no—
182C4×C73—21no—
183C4×C73—82no—
184C4×C73#46112yes—
185C4×C73#46912yes—
186C4×C73C22×SD1611yescharacteristic
187C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
188C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
189C4×C73C2×#13711yescharacteristic
190Dic73—42no—
191Dic73—82no—
192C2×#1693—731nomaximal, Sylow
193C2×C73#169314yescomplemented
194C2×C73C2×#46111yescharacteristic
195C2×C73C2×#46911yescharacteristic
196C2×C73C2×#47311yescharacteristic
197D73—82no—
198C2×#500—731no—
199C2×#461—731no—
200C2×#461—731no—
201C2×#436—731no—
202#1693—738no—
203C2×#334—731no—
204C2×#332—731no—
205C2×#332D7311yescharacteristic, complemented
206C73C2×#169311yescharacteristic, complemented, Sylow
207C22×SD16—1461no—
208C22×SD16—1461no—
209C22×M16—1461no—
210C2×C4⋊Q8—731no—
211C2×C4⋊Q8C2×D7311yescharacteristic
212C2×C4×D4—731no—
213#500—734no—
214#500—1462no—
215#461—734no—
216#461—734no—
217#461—1462no—
218#461—1462no—
219#436—734no—
220#436—1462no—
221C2×#107—1461no—
222C2×#107—1461no—
223C2×C4⋊C8—731no—
224C2×C4⋊C8C2×D7311yescharacteristic
225C2×C4⋊C8C2×D7311yescharacteristic
226C2×#103—1461no—
227C2×#103—1461no—
228C2×C22⋊C8—1461no—
229C2×C4×C8—731no—
230#334—734no—
231#332—734no—
232#332C2×D7314yescomplemented
233C22×Q8—21no—
234C22×Q8—1461no—
235C22×D4—731no—
236C23×C4—1461no—
237C2×SD16—2924no—
238C2×SD16—2924no—
239C2×SD16—1464no—
240C2×SD16—1464no—
241C2×M16—2924no—
242C2×M16—1464no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—731no—
246C22×C8—731no—
247C22×C8—1461no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—732no—
252C4⋊Q8—1461no—
253C4⋊Q8—1461no—
254C4⋊Q8—1461no—
255C4⋊Q8C22×D7312yes—
256C4×D4—732no—
257C4×D4—732no—
258C4×D4—1461no—
259C4×D4—1461no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—731no—
263C2×C4⋊C4—1461no—
264C2×C4⋊C4—1461no—
265C2×C22⋊C4—1461no—
266C2×C42C22×D7311yescharacteristic
267#107—1464no—
268#107—1464no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—732no—
272C4⋊C8—1461no—
273C4⋊C8C22×D7312yes—
274C4⋊C8C22×D7312yes—
275#103—1464no—
276#103—1464no—
277C22⋊C8—1464no—
278C4×C8—732no—
279C4×C8—732no—
280C24—1461no—
281C2×Q8—22no—
282C2×Q8—41no—
283C2×Q8—42no—
284C2×Q8—42no—
285C2×Q8—2921no—
286C2×Q8—2922no—
287C2×Q8—2922no—
288C2×Q8—1462no—
289C2×D4—732no—
290C2×D4—1461no—
291C2×D4—1462no—
292C2×D4—1462no—
293C22×C4—41no—
294C22×C4—2922no—
295C22×C4—2922no—
296C22×C4—2921no—
297C22×C4—1461no—
298C22×C4—1462no—
299C22×C4—1462no—
300C22×C4D4×D7311yescharacteristic
301C22×C4D4×D7311yescharacteristic
302C22×C4#1192402811yescharacteristic
303SD16—2928no—
304SD16—2928no—
305M16—2928no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—42no—
309C2×C8—42no—
310C2×C8—2922no—
311C2×C8—734no—
312C2×C8—732no—
313C2×C8—732no—
314C2×C8—1462no—
315C2×C8—1462no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—2921no—
321C4⋊C4—2921no—
322C4⋊C4—732no—
323C4⋊C4—1462no—
324C4⋊C4—1462no—
325C4⋊C4—1461no—
326C22⋊C4—1462no—
327C22⋊C4—1462no—
328C42D4×D7311yescharacteristic
329C42D4×D7311yescharacteristic
330C42#1192402811yescharacteristic
331C42C23×D7311yescharacteristic
332C23—2922no—
333C23—2922no—
334C23—2922no—
335C23—1462no—
336C23#1455656411yescharacteristic
337Q8—42no—
338Q8—42no—
339Q8—82no—
340Q8—2922no—
341Q8—2922no—
342Q8—5842no—
343D4—2922no—
344D4—1462no—
345D4—1462no—
346C2×C4—22no—
347C2×C4—42no—
348C2×C4—82no—
349C2×C4—2922no—
350C2×C4—2922no—
351C2×C4—2924no—
352C2×C4—2922no—
353C2×C4—2922no—
354C2×C4—5842no—
355C2×C4—1462no—
356C2×C4#1455656411yescharacteristic
357C2×C4#1455656411yescharacteristic
358C2×C4#1455656411yescharacteristic
359C2×C4SD16×D7312yes—
360C2×C4#1455661512yes—
361C2×C4#1455661812yes—
362C2×C4#1455662312yes—
363C2×C4C2×D4×D7311yescharacteristic
364C2×C4C2×D4×D7311yescharacteristic
365C2×C4C2×#1192402811yescharacteristic
366C8—42no—
367C8—42no—
368C8—2922no—
369C8—734no—
370C8—1462no—
371C22—2922no—
372C22—2922no—
373C22—2922no—
374C22—5844no—
375C22#1798879112yes—
376C22#1798883912yes—
377C22#1798886112yes—
378C22C2×#1455656411yescharacteristic
379C4—21no—
380C4—21no—
381C4—82no—
382C4—2922no—
383C4—5842no—
384C4#1798879112yes—
385C4#1798883912yes—
386C4C2×SD16×D7311yescharacteristic
387C4C2×#1455661511yescharacteristic
388C4C2×#1455661811yescharacteristic
389C4C2×#1455662311yescharacteristic
390C2—5842no—
391C2#2260944314yesdirect product factor
392C2C2×#1798879111yescharacteristic
393C2C2×#1798883911yescharacteristic
394C2C2×#1798886111yescharacteristic
subgroupG/H
centerC23#14556564
commutator, cosocleC42×C73C24
FrattiniC42C23×D73
FittingC2×#332×C73C2
socleC23×C73#121
prime radicalC22×D292D4
hypercenterC2×#332D73
hypocenterC73C2×#1693
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
1. C2×#17988990C2semidirect
5. #22609443C2direct (N × H)
6. C2×#17988337C2semidirect
7. C2×#17988332C2semidirect
8. C2×#332×C73C2semidirect
15. #17988990C22semidirect
29. #17988337C22semidirect
30. #17988332C22semidirect
34. #332×C73C22semidirect
103. C2×#10596831SD16semidirect
172. #10596831C2×SD16semidirect
193. C2×C73#1693semidirect
205. C2×#332D73semidirect
206. C73C2×#1693semidirect
232. #332C2×D73semidirect
391. C2#22609443direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179889902
C2×#179887932
C2×#179887892
C2×#179886642
#226094432
C2×#179883372
C2×#179883322
C2×#332×C732
C2×#169373