Finite Group Databasebeta

← #34030392

Subgroups — #34030392

Order 18688.

626 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626317C212yesmaximal, complemented
2#22626314C214yesmaximal, complemented
3#22626310C212yesmaximal, complemented
4#22626292C211yesmaximal, characteristic, complemented
5#22626288C211yesmaximal, characteristic, complemented
6#22626159C212yesmaximal, complemented
7#22626156C212yesmaximal, complemented
8C2×#17988652C211yesmaximal, characteristic
9C2×#14556666C2214yescomplemented
10C2×#14556664C2214yescomplemented
11C4⋊#11924031C2212yescomplemented
12C4⋊#11924031C2212yescomplemented
13#17989482C2214yescomplemented
14#17989482C2214yescomplemented
15C22⋊#11924031C2211yescharacteristic
16C22⋊#11924031C2212yes—
17C22⋊#11924031C2211yescharacteristic
18#17989475C2212yescomplemented
19C4×#11924031C2212yescomplemented
20C22×C8×D73C2212yes—
21C2×C4×D292C411yescharacteristic
22#17988652C411yescharacteristic
23#17988652C412yes—
24#17988652C411yescharacteristic
25#17988652C2211yescharacteristic
26#17988652C2212yes—
27#17988652C2211yescharacteristic
28C2×#14556503C412yes—
29C2×C4×#10596831C2211yescharacteristic
30C2×C4⋊C8×C73C411yescharacteristic
31#14556666—44no—
32#14556664—44no—
33C2×#11924031C2312yes—
34C2×#11924031C2314yes—
35C2×#11924031C2312yes—
36C22×D292C811yescharacteristic
37C22×C4×D73C2×C412yes—
38C22×#10596831C2×C411yescharacteristic
39C22×#10596831C2311yescharacteristic
40C2×C8×D73—44no—
41C2×C8×D73C2×C412yes—
42C2×C8×D73C2×C412yes—
43C2×C8×D73C2312yes—
44C2×C8×D73C2312yes—
45C4×D292C812yes—
46C4×D292C811yescharacteristic
47C4×D292C811yescharacteristic
48C4×D292C2×C412yes—
49C4×D292C2×C411yescharacteristic
50C4×D292C2×C411yescharacteristic
51C2×C4⋊Dic73C811yescharacteristic
52C2×#11924005C812yes—
53#14556503C2×C412yes—
54#14556503C2×C412yes—
55#14556503C2×C412yes—
56#14556503C2×C412yes—
57C4×#10596831C2×C411yescharacteristic
58C4×#10596831C2×C411yescharacteristic
59C4×#10596831C2311yescharacteristic
60C4×#10596831C2311yescharacteristic
61C22×C8×C73C2×C412yes—
62C2×C42×C73C2×C411yescharacteristic
63C4⋊C8×C73C2×C411yescharacteristic
64C4⋊C8×C73C2×C412yes—
65C4⋊C8×C73C2×C411yescharacteristic
66#11924031—22no—
67#11924031—24no—
68#11924031—22no—
69C23×D73C2×C812yes—
70C2×D292—24no—
71C2×D292C2×C812yes—
72C2×D292C2×C811yescharacteristic
73C2×D292C2×C811yescharacteristic
74C22×Dic73C2×C812yes—
75C2×C4×D73—42no—
76C2×C4×D73—42no—
77C2×C4×D73C2×C812yes—
78C2×C4×D73C2×C812yes—
79C2×C4×D73C22×C412yes—
80C2×C4×D73C22×C412yes—
81C2×#10596831—22no—
82C2×#10596831—41no—
83C2×#10596831C22×C411yescharacteristic
84C2×#10596831C22×C411yescharacteristic
85C2×#10596831C22×C411yescharacteristic
86C2×#10596831C2411yescharacteristic
87C8×D73—24no—
88C8×D73—24no—
89C8×D73—42no—
90C8×D73—42no—
91C4⋊Dic73C2×C812yes—
92C4⋊Dic73C2×C811yescharacteristic
93C4⋊Dic73C2×C811yescharacteristic
94#11924005C2×C812yes—
95#11924005C2×C812yes—
96#11924005C2×C812yes—
97#11924005C2×C812yes—
98C22×C4×C73C2×C811yescharacteristic
99C22×C4×C73C2×C811yescharacteristic
100C22×C4×C73C22×C411yescharacteristic
101C2×C8×C73—42no—
102C2×C8×C73C22×C412yes—
103C2×C8×C73C22×C412yes—
104C42×C73C2×C811yescharacteristic
105C42×C73C2×C811yescharacteristic
106C42×C73C22×C411yescharacteristic
107C42×C73C22×C411yescharacteristic
108C23×C73C22×C811yescharacteristic
109C22×D73—24no—
110C22×D73—24no—
111C22×D73—42no—
112C22×D73C22×C812yes—
113C22×D73C22×C812yes—
114C2×C4×C73—22no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—22no—
118C2×C4×C73C22×C811yescharacteristic
119C2×C4×C73C22×C811yescharacteristic
120C2×C4×C73C22×C811yescharacteristic
121C2×C4×C73C22×C811yescharacteristic
122C2×C4×C73C22×C811yescharacteristic
123C2×C4×C73C23×C411yescharacteristic
124C2×Dic73—42no—
125C2×Dic73C22×C812yes—
126C2×Dic73C22×C812yes—
127D292—24no—
128D292—22no—
129D292M3214yescomplemented
130C4×D73—22no—
131C4×D73—22no—
132C4×D73—22no—
133C4×D73—22no—
134C4×D73—42no—
135C4×D73—42no—
136C8×C73—22no—
137C8×C73—22no—
138#10596831—21no—
139#10596831—21no—
140#10596831—21no—
141#10596831H(5,𝔽2)12yes—
142C22×C73—21no—
143C22×C73—21no—
144C22×C73#50412yes—
145C22×C73C23×C811yescharacteristic
146C2×D73—22no—
147C2×D73—22no—
148C2×D73—22no—
149C2×D73—22no—
150C2×D73—22no—
151C2×D73—48no—
152C2×D73C2×M3214yes—
153C4×C73—21no—
154C4×C73—21no—
155C4×C73—21no—
156C4×C73—21no—
157C4×C73C2×M3212yes—
158C4×C73#51811yescharacteristic
159C4×C73#56811yescharacteristic
160Dic73—22no—
161Dic73—22no—
162#33488—731nomaximal, Sylow
163C2×C73—22no—
164C2×C73#297211yescharacteristic
165C2×C73C22×M3211yescharacteristic
166C2×C73C2×#50411yescharacteristic
167D73—24no—
168D73—42no—
169C2×C8×D4—731no—
170#2169—732no—
171#2168—734no—
172D4×C16—732no—
173#2163—731no—
174#2162—731no—
175#2112—732no—
176C2×C22⋊C16—732no—
177C73#3348811yescharacteristic, complemented, Sylow
178C23×C8—732no—
179C2×C4×D4—731no—
180C2×M32—734no—
181C22×C16—734no—
182C8×D4—732no—
183C8×D4—731no—
184C8×D4—731no—
185C8×D4—731no—
186C8×D4—732no—
187C8×D4—731no—
188C2×C4⋊C8#6440811yescharacteristic
189C2×C22⋊C8—732no—
190C2×C4×C8—731no—
191C4⋊C16—732no—
192C4⋊C16—732no—
193C22⋊C16—731no—
194C22⋊C16—732no—
195C22⋊C16—734no—
196C22⋊C16—731no—
197C22⋊C16—734no—
198#346—732no—
199C4×C16—732no—
200C22×D4—731no—
201C23×C4—732no—
202C22×C8—2924no—
203C22×C8—731no—
204C22×C8—732no—
205C22×C8—732no—
206C22×C8—731no—
207C22×C8—732no—
208C22×C8—732no—
209C22×C8C2×#6440812yes—
210C4×D4—731no—
211C4×D4—732no—
212C4×D4—731no—
213C4×D4—731no—
214C4×D4—732no—
215C4×D4—731no—
216C2×C4⋊C4—731no—
217C2×C22⋊C4—732no—
218C2×C42C2×#6440811yescharacteristic
219M32—2924no—
220C2×C16—2924no—
221C2×C16—732no—
222C2×C16—732no—
223C2×C16—734no—
224C4⋊C8C2×#6440811yescharacteristic
225C4⋊C8C2×#6440812yes—
226C4⋊C8C2×#6440811yescharacteristic
227C22⋊C8—732no—
228C22⋊C8—732no—
229C22⋊C8—732no—
230C22⋊C8—732no—
231C4×C8—731no—
232C4×C8—731no—
233C4×C8—731no—
234C4×C8—731no—
235C24—732no—
236C2×D4—731no—
237C2×D4—732no—
238C2×D4—731no—
239C2×D4—1464no—
240C22×C4—2922no—
241C22×C4—2922no—
242C22×C4—732no—
243C22×C4—732no—
244C22×C4—732no—
245C22×C4—732no—
246C22×C4—732no—
247C22×C4#1192403611yescharacteristic
248C22×C4#1192403611yescharacteristic
249C22×C4C22×#6440811yescharacteristic
250C2×C8—42no—
251C2×C8—2922no—
252C2×C8—2922no—
253C2×C8—2921no—
254C2×C8—731no—
255C2×C8—731no—
256C2×C8—731no—
257C2×C8—731no—
258C2×C8—1464no—
259C2×C8—1464no—
260C2×C8—1462no—
261C2×C8C22×#6440812yes—
262C2×C8C22×#6440812yes—
263C4⋊C4—732no—
264C4⋊C4—731no—
265C4⋊C4—731no—
266C22⋊C4—732no—
267C22⋊C4—732no—
268C22⋊C4—732no—
269C22⋊C4—732no—
270C42#1192403611yescharacteristic
271C42#1192403611yescharacteristic
272C42C22×#6440811yescharacteristic
273C42C22×#6440811yescharacteristic
274C16—1462no—
275C16—1464no—
276C16—1462no—
277C23—2922no—
278C23—732no—
279C23—732no—
280C23—1464no—
281C23—1464no—
282C23C2×#1192403611yescharacteristic
283D4—734no—
284D4—1464no—
285D4—1462no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—2922no—
291C2×C4—2922no—
292C2×C4—2922no—
293C2×C4—732no—
294C2×C4—732no—
295C2×C4—1462no—
296C2×C4—1462no—
297C2×C4—1462no—
298C2×C4—1462no—
299C2×C4C2×#1192403611yescharacteristic
300C2×C4C2×#1192403611yescharacteristic
301C2×C4C2×#1192403611yescharacteristic
302C2×C4C2×#1192403611yescharacteristic
303C2×C4C2×#1192403611yescharacteristic
304C2×C4C23×#6440811yescharacteristic
305C8—22no—
306C8—22no—
307C8—732no—
308C8—1461no—
309C8—1461no—
310C8—1461no—
311C22—21no—
312C22—21no—
313C22—2928no—
314C22—734no—
315C22—1462no—
316C22—1462no—
317C22—1462no—
318C22—1462no—
319C22—1462no—
320C22#1798964612yes—
321C22C22×#1192403611yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—1462no—
327C4—1462no—
328C4#1798964312yes—
329C4#1798965411yescharacteristic
330C4#1798966711yescharacteristic
331C2—22no—
332C2—2922no—
333C2—1464no—
334C2#2262678111yescharacteristic
335C2C2×#1798964311yescharacteristic
336C2C2×#1798964611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×#64408
commutator, socleC22×C73C23×C8
FittingC2×C4⋊C8×C73C4
prime radicalC22×D292C8
cosocleC2×#10596831C24
hypercenterC2×C4⋊C8#64408
hypocenterC73#33488
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #22626317C2semidirect
2. #22626314C2semidirect
3. #22626310C2semidirect
4. #22626292C2semidirect
5. #22626288C2semidirect
6. #22626159C2semidirect
7. #22626156C2semidirect
9. C2×#14556666C22semidirect
10. C2×#14556664C22semidirect
11. C4⋊#11924031C22semidirect
12. C4⋊#11924031C22semidirect
13. #17989482C22semidirect
14. #17989482C22semidirect
18. #17989475C22semidirect
19. C4×#11924031C22semidirect
129. D292M32semidirect
177. C73#33488semidirect

Maximal subgroups

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

subgroupindex
#226263172
#226263142
#226263102
#226262922
#226262882
#226261592
#226261562
C2×#179886522
#3348873