Finite Group Databasebeta

← C2×#22625739 #34020238

Subgroups — C2×#22625739 #34020238

Order 18688.

1062 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556662C211yesmaximal, characteristic
2C2×#17989552C212yesmaximal
3C22×#14556645C211yesmaximal, characteristic
4#22625739C218yesmaximal, direct product factor
5C2×#17989457C212yesmaximal
6C2×#17988622C211yesmaximal, characteristic
7C22×#11924038C2212yes—
8C22×#11924036C2211yescharacteristic
9C22×C4×#64408C2211yescharacteristic
10C2×#14556662C418yescomplemented
11C2×#14556662C2214yes—
12#17989552—24no—
13#17989552C2218yes—
14C2×#14556646—22no—
15C2×#14556645C418yescomplemented
16C2×#14556645C2214yes—
17C2×C4×#10596833—22no—
18#17989457C2218yes—
19C22×C8×D73C2211yescharacteristic
20C2×#14556549C2212yes—
21#17988622C414yescomplemented
22#17988622C2214yes—
23C2×#14556524C412yescomplemented
24C2×#14556523C411yescharacteristic, complemented
25C2×#106×C73C411yescharacteristic, complemented
26C23×#64408—21no—
27C2×#11924038—22no—
28C2×#11924038—24no—
29C2×#11924038C2×C418yes—
30C2×#11924038C2314yes—
31C2×#11924036C2×C414yes—
32C2×#11924036D412yes—
33C2×#11924036Q814yes—
34C2×#11924036C2312yes—
35C22×#10596833—22no—
36C22×#10596833D412yes—
37C2×C4×#64408—21no—
38C2×C4×#64408—22no—
39C2×C4×#64408C2×C414yes—
40C2×C4×#64408C2312yes—
41#14556662C2×C4116yescomplemented
42#14556646—28no—
43#14556645C2×C4116yescomplemented
44C4×#10596833—28no—
45C22×C4×D73C2311yescharacteristic
46C22×#10596831C2×C411yescharacteristic
47C2×C8×D73C2×C414yes—
48C2×C8×D73C2×C414yes—
49C2×C8×D73C2×C412yes—
50C2×C8×D73C2312yes—
51#14556549—22no—
52#14556549—22no—
53#14556549C2×C414yes—
54#14556549C2314yes—
55C2×C4⋊Dic73C2×C412yes—
56C2×#11924005—22no—
57C2×C4×Dic73—22no—
58#14556524C2×C418yescomplemented
59#14556523C2×C414yescomplemented
60C22×C8×C73C2×C411yescharacteristic
61C2×C4⋊C4×C73C2×C412yes—
62#106×C73C2×C414yescomplemented
63C22×#64408—24no—
64C22×#64408—22no—
65C22×#64408—44no—
66#11924038—28no—
67#11924038—24no—
68#11924038C22×C418yes—
69#11924036C4⋊C418yes—
70#11924036C22×C414yes—
71#11924036C2×Q814yes—
72C2×#10596833—28no—
73C2×#10596833—24no—
74C2×#10596833C4⋊C418yes—
75C2×#10596833C2×D414yes—
76C4×#64408—24no—
77C4×#64408—22no—
78C4×#64408C22×C414yes—
79C23×D73#4111yescharacteristic
80C22×Dic73—22no—
81C22×Dic73C2×D411yescharacteristic
82C2×C4×D73C22×C411yescharacteristic
83C2×C4×D73C22×C412yes—
84C2×C4×D73C22×C412yes—
85C2×C4×D73C2×D411yescharacteristic
86C2×C4×D73C2×Q812yes—
87C2×C4×D73#4111yescharacteristic
88C2×C4×D73#4112yes—
89C2×C4×D73C2411yescharacteristic
90C2×#10596831C4214yes—
91C2×#10596831C22×C412yes—
92C8×D73C4218yes—
93C8×D73C22×C414yes—
94C8×D73C22×C414yes—
95C4⋊Dic73—22no—
96C4⋊Dic73C22×C414yes—
97#11924005—24no—
98#11924005—24no—
99C4×Dic73—24no—
100C4×Dic73—24no—
101C22×C4×C73—22no—
102C22×C4×C73C22×C411yescharacteristic
103C2×C8×C73C4214yes—
104C2×C8×C73C22×C412yes—
105C4⋊C4×C73—22no—
106C4⋊C4×C73C22×C414yes—
107C23×C73C4×D411yescharacteristic
108C22×D73—24no—
109C22×D73#11712yes—
110C22×D73C4×D411yescharacteristic
111C22×D73C4×Q812yes—
112C22×D73C2×#4111yescharacteristic
113C2×#64408—24no—
114C2×#64408—44no—
115C2×#64408—48no—
116C2×C4×C73—24no—
117C2×C4×C73—44no—
118C2×C4×C73C2×C4212yes—
119C2×C4×C73C4×D411yescharacteristic
120C2×C4×C73C4×Q812yes—
121C2×C4×C73C23×C411yescharacteristic
122C2×Dic73—24no—
123C2×Dic73—44no—
124C2×Dic73C2×C4⋊C412yes—
125C2×Dic73C4×D412yes—
126C2×Dic73C4×D411yescharacteristic
127C2×Dic73C22×D411yescharacteristic
128C4×D73C2×C4212yes—
129C4×D73C2×C4⋊C412yes—
130C4×D73#11712yes—
131C4×D73C4×D412yes—
132C4×D73C4×Q812yes—
133C4×D73C4×Q812yes—
134C4×D73C23×C411yescharacteristic
135C4×D73C23×C411yescharacteristic
136C4×D73C22×Q811yescharacteristic
137C4×D73C2×#4111yescharacteristic
138#10596833—28no—
139#10596833C2×C4⋊C418yes—
140C8×C73C2×C4214yes—
141#10596831C2×C4214yes—
142C22×C73C4×C4⋊C412yes—
143C22×C73#44414yes—
144C22×C73C2×C4×D411yescharacteristic
145C2×D73—22no—
146C2×D73—22no—
147C2×D73—24no—
148C2×D73—24no—
149C2×D73C4×C4⋊C412yes—
150C2×D73C2×#11711yescharacteristic
151C2×D73C2×C4×Q811yescharacteristic
152#64408—44no—
153C4×C73—44no—
154C4×C73C4×C4⋊C412yes—
155C4×C73C22×C4211yescharacteristic
156C4×C73C2×C4×Q811yescharacteristic
157Dic73—44no—
158Dic73C4×C4⋊C412yes—
159Dic73C22×C4⋊C411yescharacteristic
160Dic73C2×C4×D411yescharacteristic
161C2×#1773—731nomaximal, Sylow
162C2×C73#177314yescomplemented
163C2×C73C2×C4×C4⋊C411yescharacteristic
164C2×C73C2×#44412yes—
165D73—21no—
166D73—21no—
167D73—22no—
168C22×#108—731no—
169C2×#427—731no—
170C2×#405—732no—
171C22×#97—731no—
172#1773—738no—
173C2×#339—732no—
174C73C2×#177311yescharacteristic, complemented, Sylow
175C22×M16—732no—
176C23×C8—731no—
177C23×C8—731no—
178C2×#117—732no—
179C22×C42—731no—
180C2×#108—738no—
181C2×#108—734no—
182#427—734no—
183#427—734no—
184C2×#107—732no—
185C2×#106—731no—
186C2×#106#6440811yescharacteristic, complemented
187#405—738no—
188#405—1464no—
189C2×#97—738no—
190C2×#97—734no—
191C2×#97—1462no—
192C2×C4×C8—1462no—
193#339—738no—
194C23×C4—731no—
195C23×C4—1461no—
196C2×M16—738no—
197C2×M16—734no—
198C2×M16—1464no—
199C2×M16—1462no—
200C22×C8—732no—
201C22×C8—734no—
202C22×C8—732no—
203C22×C8—734no—
204C22×C8—732no—
205C22×C8—731no—
206C22×C8—734no—
207C22×C8—734no—
208C22×C8—732no—
209C22×C8—732no—
210C22×C8—1462no—
211C22×C8C2×#6440811yescharacteristic
212#117—734no—
213#117—734no—
214#117—1462no—
215#117—1462no—
216C2×C4⋊C4—732no—
217C2×C4⋊C4C2×#6440812yes—
218C2×C22⋊C4—1462no—
219C2×C42—732no—
220C2×C42—734no—
221C2×C42—1462no—
222C2×C42—1462no—
223C2×C42—1461no—
224#108—7316no—
225#107—738no—
226#106—734no—
227#106C2×#6440814yescomplemented
228#97—7316no—
229#97—1468no—
230C4×C8—1468no—
231C24—731no—
232C22×C4—22no—
233C22×C4—2924no—
234C22×C4—731no—
235C22×C4—732no—
236C22×C4—732no—
237C22×C4—731no—
238C22×C4—731no—
239C22×C4—732no—
240C22×C4—732no—
241C22×C4—731no—
242C22×C4—731no—
243C22×C4—1462no—
244C22×C4—1464no—
245C22×C4—1462no—
246C22×C4C22×#6440811yescharacteristic
247M16—738no—
248M16—1464no—
249M16—1468no—
250C2×C8—738no—
251C2×C8—734no—
252C2×C8—738no—
253C2×C8—734no—
254C2×C8—734no—
255C2×C8—732no—
256C2×C8—734no—
257C2×C8—738no—
258C2×C8—734no—
259C2×C8—734no—
260C2×C8—1464no—
261C2×C8—1468no—
262C2×C8C4×#6440814yes—
263C2×C8C22×#6440812yes—
264C4⋊C4—22no—
265C4⋊C4—734no—
266C4⋊C4—1462no—
267C4⋊C4C22×#6440814yes—
268C22⋊C4—1464no—
269C22⋊C4—1464no—
270C42—734no—
271C42—1464no—
272C42—1464no—
273C42—1462no—
274C42—1464no—
275C23—731no—
276C23—731no—
277C23—732no—
278C23—732no—
279C23—1464no—
280C23D4×#6440811yescharacteristic
281C2×C4—24no—
282C2×C4—44no—
283C2×C4—2924no—
284C2×C4—2928no—
285C2×C4—2924no—
286C2×C4—731no—
287C2×C4—731no—
288C2×C4—732no—
289C2×C4—732no—
290C2×C4—731no—
291C2×C4—731no—
292C2×C4—732no—
293C2×C4—731no—
294C2×C4—731no—
295C2×C4—732no—
296C2×C4—732no—
297C2×C4—732no—
298C2×C4—732no—
299C2×C4—732no—
300C2×C4—1464no—
301C2×C4—1464no—
302C2×C4C2×C4×#6440812yes—
303C2×C4D4×#6440811yescharacteristic
304C2×C4Q8×#6440812yes—
305C2×C4C23×#6440811yescharacteristic
306C8—738no—
307C8—734no—
308C8—1468no—
309C8C2×C4×#6440814yes—
310C22—731no—
311C22—731no—
312C22—732no—
313C22—1462no—
314C22—1462no—
315C22—1464no—
316C22—1464no—
317C22C4⋊C4×#6440812yes—
318C22#1798963214yes—
319C22C2×D4×#6440811yescharacteristic
320C4—44no—
321C4—2924no—
322C4—2924no—
323C4—731no—
324C4—731no—
325C4—732no—
326C4C4⋊C4×#6440812yes—
327C4C22×C4×#6440811yescharacteristic
328C4C2×Q8×#6440811yescharacteristic
329C2—1461no—
330C2—1461no—
331C2—1462no—
332C2#2262573914yesdirect product factor
333C2C2×C4⋊C4×#6440811yescharacteristic
334C2C2×#1798963212yes—
subgroupG/H
centerC23D4×#64408
commutatorC4×C73C22×C42
FrattiniC2×C4C23×#64408
FittingC2×#106×C73C4
socleC23×C73C4×D4
prime radicalC23×D73#41
cosocleC2×C4×D73C24
hypercenterC2×#106#64408
hypocenterC73C2×#1773
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
4. #22625739C2direct (N × H)
10. C2×#14556662C4semidirect
15. C2×#14556645C4semidirect
21. #17988622C4semidirect
23. C2×#14556524C4semidirect
24. C2×#14556523C4semidirect
25. C2×#106×C73C4semidirect
41. #14556662C2×C4semidirect
43. #14556645C2×C4semidirect
58. #14556524C2×C4semidirect
59. #14556523C2×C4semidirect
62. #106×C73C2×C4semidirect
162. C2×C73#1773semidirect
174. C73C2×#1773semidirect
186. C2×#106#64408semidirect
227. #106C2×#64408semidirect
332. C2#22625739direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145566622
C2×#179895522
C22×#145566452
#226257392
C2×#179894572
C2×#179886222
C2×#177373