Finite Group Databasebeta

← C2×#22609430 #33068505

Subgroups — C2×#22609430 #33068505

Order 18688.

726 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988985C211yesmaximal, characteristic, complemented
2C2×#17988877C211yesmaximal, characteristic
3C2×#17988792C211yesmaximal, characteristic
4#22609430C218yesmaximal, direct product factor
5C2×#17988340C211yesmaximal, characteristic, complemented
6C2×#17988335C211yesmaximal, characteristic, complemented
7C2×#17988332C211yesmaximal, characteristic, complemented
8C2×#436×C73C211yesmaximal, characteristic
9C22×#11924016—21no—
10C2×#14556591C2211yescharacteristic
11C2×#14556591C2211yescharacteristic
12#17988985—22no—
13#17988985C2214yescomplemented
14#17988877—22no—
15#17988877C2214yes—
16#17988792—22no—
17#17988792C2214yes—
18C2×#14556523—21no—
19C2×#14556523—21no—
20C2×#14556522—21no—
21C2×C4⋊#10596831C2211yescharacteristic
22C2×C4⋊#10596831C2211yescharacteristic
23C2×#14556514—21no—
24C2×#14556512—21no—
25#17988340C2214yescomplemented
26#17988335C2214yescomplemented
27#17988332C2214yescomplemented
28C22×M16×C73—21no—
29C2×C4×D4×C73C2211yescharacteristic
30#436×C73—22no—
31#436×C73C2214yes—
32C2×C4⋊C8×C73C2211yescharacteristic
33C2×C22⋊C8×C73—21no—
34C2×C4×C8×C73C2211yescharacteristic
35C22×Dic146—21no—
36C22×Dic146—21no—
37C2×#11924016—24no—
38C2×#11924016—44no—
39C22×#10596831—21no—
40C22×#10596831—21no—
41#14556591—21no—
42#14556591—21no—
43#14556591—21no—
44#14556591—21no—
45#14556591—21no—
46#14556591—21no—
47#14556591C2312yes—
48#14556591C2312yes—
49C2×C4⋊Dic73—21no—
50C2×C4⋊Dic73—21no—
51C2×C4⋊Dic73—21no—
52C2×C4⋊Dic73—21no—
53#14556523—24no—
54#14556523—24no—
55#14556522—24no—
56C4⋊#10596831—21no—
57C4⋊#10596831—21no—
58C4⋊#10596831C2312yes—
59C4⋊#10596831C2312yes—
60#14556514—24no—
61#14556512—24no—
62C22×D4×C73D411yescharacteristic
63C23×C4×C73—21no—
64C2×M16×C73—24no—
65C2×M16×C73—44no—
66C22×C8×C73—21no—
67C22×C8×C73D411yescharacteristic
68C22×C8×C73D411yescharacteristic
69C4×D4×C73—21no—
70C4×D4×C73—21no—
71C4×D4×C73D412yes—
72C4×D4×C73C2312yes—
73C2×C4⋊C4×C73D411yescharacteristic
74C2×C22⋊C4×C73—21no—
75C2×C42×C73C2311yescharacteristic
76C4⋊C8×C73—21no—
77C4⋊C8×C73C2312yes—
78C22⋊C8×C73—24no—
79C4×C8×C73D412yes—
80C4×C8×C73C2312yes—
81C2×Dic146—22no—
82C2×Dic146—22no—
83C2×Dic146—42no—
84C2×Dic146—42no—
85C2×Dic146—41no—
86C2×Dic146—41no—
87C2×Dic146—82no—
88C22×Dic73—41no—
89C22×Dic73—41no—
90#11924016—48no—
91C2×#10596831—22no—
92C2×#10596831—22no—
93C2×#10596831—42no—
94C2×#10596831—42no—
95C4⋊Dic73—22no—
96C4⋊Dic73—22no—
97C4⋊Dic73—22no—
98C4⋊Dic73—22no—
99C4⋊Dic73—41no—
100C4⋊Dic73—41no—
101C4⋊Dic73—41no—
102C4⋊Dic73—41no—
103C24×C73—21no—
104C2×D4×C73—21no—
105C2×D4×C73—22no—
106C2×D4×C73—22no—
107C2×D4×C73C2×D412yes—
108C22×C4×C73—21no—
109C22×C4×C73—22no—
110C22×C4×C73—22no—
111C22×C4×C73—42no—
112C22×C4×C73—42no—
113C22×C4×C73C2×D411yescharacteristic
114C22×C4×C73C2×D411yescharacteristic
115C22×C4×C73#4111yescharacteristic
116M16×C73—48no—
117C2×C8×C73—22no—
118C2×C8×C73—22no—
119C2×C8×C73—42no—
120C2×C8×C73SD1614yescomplemented
121C2×C8×C73C2×D412yes—
122C2×C8×C73C2×D412yes—
123C4⋊C4×C73—21no—
124C4⋊C4×C73C2×D412yes—
125C22⋊C4×C73—22no—
126C22⋊C4×C73—22no—
127C42×C73C2×D411yescharacteristic
128C42×C73C2×D411yescharacteristic
129C42×C73#4111yescharacteristic
130C42×C73C2411yescharacteristic
131C23×C73—22no—
132C23×C73—42no—
133C23×C73—42no—
134C23×C73—42no—
135C23×C73#12111yescharacteristic
136D4×C73—22no—
137D4×C73—22no—
138D4×C73—42no—
139C2×C4×C73—22no—
140C2×C4×C73—22no—
141C2×C4×C73—42no—
142C2×C4×C73—42no—
143C2×C4×C73—42no—
144C2×C4×C73—44no—
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×C73#13712yes—
151C2×C4×C73#13712yes—
152C2×C4×C73C22×D411yescharacteristic
153C2×C4×C73C22×D411yescharacteristic
154C2×C4×C73C2×#4111yescharacteristic
155C2×Dic73—42no—
156C2×Dic73—42no—
157C2×Dic73—82no—
158C2×Dic73—82no—
159Dic146—42no—
160Dic146—42no—
161Dic146—82no—
162Dic146—82no—
163Dic146—82no—
164C8×C73—22no—
165C8×C73—42no—
166C8×C73C2×SD1614yescomplemented
167#10596831—42no—
168#10596831—42no—
169C22×C73—42no—
170C22×C73—42no—
171C22×C73—42no—
172C22×C73—84no—
173C22×C73#46112yes—
174C22×C73#46812yes—
175C22×C73#47112yes—
176C22×C73C2×#12111yescharacteristic
177C4×C73—21no—
178C4×C73—21no—
179C4×C73—42no—
180C4×C73#46112yes—
181C4×C73#46812yes—
182C4×C73C22×SD1611yescharacteristic
183C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
184C4×C73C2×#13711yescharacteristic
185C4×C73C2×#13711yescharacteristic
186Dic73—82no—
187Dic73—82no—
188C2×#1691—731nomaximal, Sylow
189C2×C73—82no—
190C2×C73#169114yescomplemented
191C2×C73C2×#46111yescharacteristic
192C2×C73C2×#46811yescharacteristic
193C2×C73C2×#47111yescharacteristic
194C2×#498—731no—
195C2×#476—731no—
196C2×#461—731no—
197C2×#436D7311yescharacteristic
198#1691—738no—
199C2×#335—731no—
200C2×#333—731no—
201C2×#332—731no—
202C73C2×#169111yescharacteristic, complemented, Sylow
203C22×SD16—1461no—
204C22×M16—21no—
205C2×C4⋊Q8—731no—
206C2×C4⋊Q8—731no—
207C2×C4×D4C2×D7311yescharacteristic
208#498—734no—
209#498—1462no—
210#476—734no—
211#476—1462no—
212#461—734no—
213#461—1462no—
214#436—22no—
215#436C2×D7314yes—
216C2×#106—1461no—
217C2×#106—1461no—
218C2×#106—1461no—
219C2×C4⋊C8—731no—
220C2×C4⋊C8—731no—
221C2×C4⋊C8C2×D7311yescharacteristic
222C2×#103—1461no—
223C2×#102—1461no—
224C2×C22⋊C8—21no—
225C2×C4×C8C2×D7311yescharacteristic
226#335—734no—
227#333—734no—
228#332—734no—
229C22×Q8—1461no—
230C22×Q8—1461no—
231C22×D4D29211yescharacteristic
232C23×C4—21no—
233C2×SD16—2924no—
234C2×SD16—1464no—
235C2×M16—24no—
236C2×M16—44no—
237C22×C8—21no—
238C22×C8—1461no—
239C22×C8—1461no—
240C22×C8C22⋊D7311yescharacteristic
241C22×C8C22⋊D7311yescharacteristic
242C4⋊Q8—732no—
243C4⋊Q8—732no—
244C4⋊Q8—1461no—
245C4⋊Q8—1461no—
246C4⋊Q8—1461no—
247C4⋊Q8—1461no—
248C4⋊Q8—1461no—
249C4⋊Q8—1461no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4D29212yes—
253C4×D4C22×D7312yes—
254C2×C4⋊C4—1461no—
255C2×C4⋊C4—1461no—
256C2×C4⋊C4—1461no—
257C2×C4⋊C4—1461no—
258C2×C4⋊C4D29211yescharacteristic
259C2×C22⋊C4—21no—
260C2×C42C22×D7311yescharacteristic
261#106—1464no—
262#106—1464no—
263#106—1464no—
264C4⋊C8—21no—
265C4⋊C8—732no—
266C4⋊C8—732no—
267C4⋊C8—1461no—
268C4⋊C8—1461no—
269C4⋊C8C22×D7312yes—
270#103—1464no—
271#102—1464no—
272C22⋊C8—24no—
273C4×C8C22⋊D7312yes—
274C4×C8C22×D7312yes—
275C24—21no—
276C2×Q8—2921no—
277C2×Q8—2921no—
278C2×Q8—2922no—
279C2×Q8—2922no—
280C2×Q8—5842no—
281C2×Q8—1462no—
282C2×Q8—1462no—
283C2×D4—21no—
284C2×D4—22no—
285C2×D4—22no—
286C2×D4C2×D29212yes—
287C22×C4—21no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—2921no—
293C22×C4—2921no—
294C22×C4C2×C22⋊D7311yescharacteristic
295C22×C4C2×D29211yescharacteristic
296C22×C4#1192402811yescharacteristic
297SD16—2928no—
298M16—48no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—42no—
302C2×C8—2922no—
303C2×C8—2922no—
304C2×C8—1462no—
305C2×C8—1462no—
306C2×C8#1192401614yescomplemented
307C2×C8C2×C22⋊D7312yes—
308C2×C8C2×C22⋊D7312yes—
309C4⋊C4—21no—
310C4⋊C4—2921no—
311C4⋊C4—2921no—
312C4⋊C4—2921no—
313C4⋊C4—2921no—
314C4⋊C4—1462no—
315C4⋊C4—1462no—
316C4⋊C4—1462no—
317C4⋊C4—1462no—
318C4⋊C4C2×D29212yes—
319C22⋊C4—22no—
320C22⋊C4—22no—
321C42C2×C22⋊D7311yescharacteristic
322C42C2×D29211yescharacteristic
323C42#1192402811yescharacteristic
324C42C23×D7311yescharacteristic
325C23—22no—
326C23—42no—
327C23—42no—
328C23—42no—
329C23#1455656511yescharacteristic
330Q8—2922no—
331Q8—2922no—
332Q8—5842no—
333Q8—5842no—
334Q8—5842no—
335D4—22no—
336D4—22no—
337D4—42no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—44no—
343C2×C4—42no—
344C2×C4—2922no—
345C2×C4—2922no—
346C2×C4—5842no—
347C2×C4—5842no—
348C2×C4#1455656511yescharacteristic
349C2×C4#1455656511yescharacteristic
350C2×C4#1455656511yescharacteristic
351C2×C4C2×#1192401612yes—
352C2×C4#1455661912yes—
353C2×C4#1455662112yes—
354C2×C4#1455662412yes—
355C2×C4C22×C22⋊D7311yescharacteristic
356C2×C4C22×D29211yescharacteristic
357C2×C4C2×#1192402811yescharacteristic
358C8—22no—
359C8—42no—
360C8—2922no—
361C8—2922no—
362C8C2×#1192401614yescomplemented
363C22—42no—
364C22—42no—
365C22—42no—
366C22—84no—
367C22#1798879212yes—
368C22#1798883312yes—
369C22#1798885012yes—
370C22C2×#1455656511yescharacteristic
371C4—21no—
372C4—21no—
373C4—42no—
374C4—5842no—
375C4—5842no—
376C4#1798879212yes—
377C4#1798883312yes—
378C4C22×#1192401611yescharacteristic
379C4C2×#1455661911yescharacteristic
380C4C2×#1455662111yescharacteristic
381C4C2×#1455662411yescharacteristic
382C2—82no—
383C2#2260943014yesdirect product factor
384C2C2×#1798879211yescharacteristic
385C2C2×#1798883311yescharacteristic
386C2C2×#1798885011yescharacteristic
subgroupG/H
centerC23#14556565
commutator, cosocleC42×C73C24
FrattiniC42C23×D73
FittingC2×#436×C73C2
socleC23×C73#121
prime radicalC22×D4×C73D4
hypercenterC2×#436D73
hypocenterC73C2×#1691
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#17988985C2semidirect
4. #22609430C2direct (N × H)
5. C2×#17988340C2semidirect
6. C2×#17988335C2semidirect
7. C2×#17988332C2semidirect
13. #17988985C22semidirect
25. #17988340C22semidirect
26. #17988335C22semidirect
27. #17988332C22semidirect
120. C2×C8×C73SD16semidirect
166. C8×C73C2×SD16semidirect
190. C2×C73#1691semidirect
202. C73C2×#1691semidirect
306. C2×C8#11924016semidirect
362. C8C2×#11924016semidirect
383. C2#22609430direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179889852
C2×#179888772
C2×#179887922
#226094302
C2×#179883402
C2×#179883352
C2×#179883322
C2×#436×C732
C2×#169173