Finite Group Databasebeta

← #34018166

Subgroups — #34018166

Order 18688.

610 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626627C212yesmaximal
2#22625502C214yesmaximal, complemented
3#22625499C212yesmaximal, complemented
4#22625491C212yesmaximal, complemented
5#22625490C211yesmaximal, characteristic, complemented
6#22625480C212yesmaximal, complemented
7#22625476C211yesmaximal, characteristic, complemented
8C8×#11924027C211yesmaximal, characteristic
9#17989611—24no—
10#17989608C2214yes—
11#17989603C2214yes—
12#17989591C2212yes—
13#17989588C2212yes—
14#17989561—22no—
15#17989552—22no—
16#17989451C2211yescharacteristic
17#17989451C2211yescharacteristic
18#17989451C2212yes—
19#17989451C2212yes—
20#17989450C2212yes—
21#17989449C2214yes—
22#17989448C2214yes—
23C4×#11924027C2211yescharacteristic
24C8×Dic146C411yescharacteristic
25#17988711C411yescharacteristic
26D4×#10596831C411yescharacteristic
27C8×C22⋊D73C412yes—
28#17988650C412yes—
29#17988639C2211yescharacteristic
30#17988637C2212yes—
31C2×C8×Dic73C2212yes—
32C4×C8×D73C2211yescharacteristic
33C8×D4×C73C411yescharacteristic
34C2×#11924038—22no—
35C2×#11924036—22no—
36#14556658—22no—
37C4⋊#10596833—22no—
38C4⋊#10596833C2312yes—
39C4⋊#10596833C2314yes—
40C4⋊#10596833C2312yes—
41C22⋊#10596833—24no—
42C22⋊#10596833—24no—
43#14556646—24no—
44C4×#10596833—24no—
45C2×#11924027D411yescharacteristic
46C22×#10596831C2×C412yes—
47C2×C8×D73C2×C411yescharacteristic
48C2×C8×D73C2×C411yescharacteristic
49C4×Dic146C2×C411yescharacteristic
50#14556556Q811yescharacteristic
51D4×Dic73Q811yescharacteristic
52C4×C22⋊D73C2×C412yes—
53#14556551Q812yes—
54#14556549D411yescharacteristic
55#14556547D412yes—
56C2×C4×Dic73C2312yes—
57C42×D73C2311yescharacteristic
58C4⋊#10596831C2×C411yescharacteristic
59#14556520C2×C412yes—
60#14556520C2×C412yes—
61C22⋊#10596831C2×C412yes—
62#14556503C2×C412yes—
63C4×#10596831C2×C411yescharacteristic
64C8×Dic73C2×C412yes—
65C8×Dic73C2×C412yes—
66C8×Dic73C2311yescharacteristic
67C8×Dic73C2312yes—
68C8×Dic73C2311yescharacteristic
69C22×C8×C73C2×C412yes—
70C4×D4×C73C2×C411yescharacteristic
71C4⋊C8×C73C2×C411yescharacteristic
72C22⋊C8×C73C2×C412yes—
73C4×C8×C73C2×C411yescharacteristic
74#11924038—44no—
75#11924036—44no—
76C2×#10596833—22no—
77C2×#10596833—22no—
78C2×#10596833—24no—
79#11924027—22no—
80#11924027—22no—
81C2×Dic146C4⋊C411yescharacteristic
82C2×C22⋊D73C4⋊C412yes—
83C22×Dic73C2×D412yes—
84C22×Dic73C2×Q812yes—
85C2×C4×D73C22×C411yescharacteristic
86C2×C4×D73C2×D411yescharacteristic
87C2×C4×D73C2×Q811yescharacteristic
88C2×#10596831—24no—
89C2×#10596831C22×C412yes—
90C2×#10596831C22×C411yescharacteristic
91C2×#10596831C22×C411yescharacteristic
92C8×D73—22no—
93C8×D73—41no—
94C4⋊Dic73C4⋊C411yescharacteristic
95#11924007C4⋊C412yes—
96#11924007C4⋊C412yes—
97C22⋊Dic73C4⋊C412yes—
98#11924005C4⋊C412yes—
99C4×Dic73C22×C412yes—
100C4×Dic73C2×D411yescharacteristic
101C4×Dic73C2×D412yes—
102C4×Dic73C2×Q811yescharacteristic
103C4×Dic73C2×Q812yes—
104C4×Dic73C2411yescharacteristic
105C2×D4×C73C4⋊C411yescharacteristic
106C22×C4×C73C22×C412yes—
107C2×C8×C73—42no—
108C2×C8×C73C22×C411yescharacteristic
109C2×C8×C73C22×C411yescharacteristic
110C2×C8×C73C22×C412yes—
111C4⋊C4×C73C4⋊C411yescharacteristic
112C22⋊C4×C73C4⋊C412yes—
113C42×C73C22×C411yescharacteristic
114C23×C73C2×C4⋊C412yes—
115C22×D73C2×C4⋊C411yescharacteristic
116D4×C73—22no—
117C2×C4×C73—22no—
118C2×C4×C73—22no—
119C2×C4×C73C2×C4⋊C411yescharacteristic
120C2×C4×C73C2×C4⋊C412yes—
121C2×C4×C73C2×C4⋊C411yescharacteristic
122C2×C4×C73C23×C411yescharacteristic
123C22⋊D73—24no—
124C2×Dic73—22no—
125C2×Dic73—22no—
126C2×Dic73—42no—
127C2×Dic73C2×C4⋊C412yes—
128C2×Dic73C2×C4⋊C412yes—
129C2×Dic73C2×C4⋊C411yescharacteristic
130C2×Dic73C22×D411yescharacteristic
131C2×Dic73C22×Q811yescharacteristic
132C4×D73—21no—
133C4×D73—21no—
134C4×D73—41no—
135C4×D73#13512yes—
136C4×D73#13512yes—
137Dic146—22no—
138#10596833—42no—
139#10596833—42no—
140#10596833—44no—
141C8×C73—21no—
142C8×C73—21no—
143C8×C73—22no—
144#10596831—22no—
145#10596831—21no—
146#10596831#13112yes—
147C22×C73—22no—
148C22×C73—22no—
149C22×C73—22no—
150C22×C73C22×C4⋊C411yescharacteristic
151C2×D73—21no—
152C2×D73—21no—
153C2×D73#42712yes—
154C4×C73—22no—
155C4×C73—21no—
156C4×C73#42712yes—
157C4×C73C2×#13111yescharacteristic
158C4×C73#56811yescharacteristic
159Dic73—21no—
160Dic73—22no—
161Dic73—21no—
162Dic73—22no—
163Dic73C2×#13511yescharacteristic
164Dic73C2×#13511yescharacteristic
165#17829—731nomaximal, Sylow
166C2×C73—42no—
167C2×C73#290611yescharacteristic
168C2×C73C2×#42711yescharacteristic
169C2×C73#291611yescharacteristic
170D73—22no—
171C8×#41—731no—
172#2925—732no—
173#1572—734no—
174#1570—732no—
175#1568—732no—
176#1567—731no—
177#1564—732no—
178C2×#335—731no—
179C73#1782911yescharacteristic, complemented, Sylow
180C4×#41—731no—
181C8×Q8—731no—
182C8×Q8—731no—
183C8×D4—732no—
184C8×D4—731no—
185C8×D4—732no—
186C8×D4#6440811yescharacteristic
187#433—1464no—
188#432—734no—
189#431—731no—
190#431—732no—
191#431—734no—
192#423—732no—
193C2×C4⋊C8—732no—
194#408—1462no—
195#405—1462no—
196C2×C4×C8—732no—
197C2×C4×C8—731no—
198#335—731no—
199#335—731no—
200#335—732no—
201#335—732no—
202#335—732no—
203#334—734no—
204#334—734no—
205C2×#41—731no—
206C2×M16—1462no—
207C22×C8—731no—
208C22×C8—732no—
209C22×C8—731no—
210C22×C8—1462no—
211C22×C8C2×#6440812yes—
212C4×Q8—731no—
213C4×Q8—731no—
214C4×D4—731no—
215C4×D4—732no—
216C4×D4—732no—
217C4×D4C2×#6440811yescharacteristic
218#117—731no—
219#117—732no—
220C2×C42—732no—
221C2×C42—731no—
222C4⋊C8—732no—
223C4⋊C8—732no—
224C4⋊C8—732no—
225C4⋊C8—732no—
226C4⋊C8—734no—
227C4⋊C8—731no—
228C4⋊C8—1462no—
229C4⋊C8—1462no—
230C4⋊C8C2×#6440811yescharacteristic
231C22⋊C8—732no—
232C22⋊C8—732no—
233C22⋊C8—1464no—
234C22⋊C8—1464no—
235C22⋊C8C2×#6440812yes—
236#97—1464no—
237C4×C8—732no—
238C4×C8—731no—
239C4×C8—731no—
240C4×C8—732no—
241C4×C8—732no—
242C4×C8—731no—
243C4×C8—1464no—
244C4×C8C2×#6440811yescharacteristic
245#41—1462no—
246#41—1462no—
247C2×Q8—731no—
248C2×D4—732no—
249C2×D4C4⋊#6440811yescharacteristic
250C22×C4—732no—
251C22×C4—731no—
252C22×C4—731no—
253C22×C4—732no—
254C22×C4—731no—
255C22×C4C22×#6440812yes—
256M16—2924no—
257C2×C8—42no—
258C2×C8—2921no—
259C2×C8—2924no—
260C2×C8—731no—
261C2×C8—732no—
262C2×C8—731no—
263C2×C8—1462no—
264C2×C8—1462no—
265C2×C8—1464no—
266C2×C8—1462no—
267C2×C8—1464no—
268C2×C8C22×#6440811yescharacteristic
269C2×C8C22×#6440812yes—
270C2×C8C22×#6440811yescharacteristic
271C4⋊C4—732no—
272C4⋊C4—732no—
273C4⋊C4—731no—
274C4⋊C4C4⋊#6440811yescharacteristic
275C22⋊C4—732no—
276C22⋊C4—732no—
277C22⋊C4C4⋊#6440812yes—
278C42—732no—
279C42—731no—
280C42—732no—
281C42—731no—
282C42—731no—
283C42—732no—
284C42C22×#6440811yescharacteristic
285C23—731no—
286C23C2×C4⋊#6440812yes—
287Q8—1462no—
288D4—22no—
289D4—1464no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—2921no—
293C2×C4—2922no—
294C2×C4—731no—
295C2×C4—732no—
296C2×C4—732no—
297C2×C4—731no—
298C2×C4—731no—
299C2×C4—732no—
300C2×C4—732no—
301C2×C4—1462no—
302C2×C4—1462no—
303C2×C4—1461no—
304C2×C4—1461no—
305C2×C4C2×C4⋊#6440812yes—
306C2×C4C2×C4⋊#6440811yescharacteristic
307C2×C4C2×C4⋊#6440811yescharacteristic
308C2×C4C23×#6440811yescharacteristic
309C8—21no—
310C8—21no—
311C8—22no—
312C8—2922no—
313C8—2922no—
314C8—2924no—
315C8—732no—
316C8—1462no—
317C8—1461no—
318C22—22no—
319C22—22no—
320C22—22no—
321C22—732no—
322C22—1461no—
323C22—1461no—
324C22C22×C4⋊#6440811yescharacteristic
325C4—22no—
326C4—21no—
327C4—731no—
328C4—731no—
329C4—1461no—
330C4—1462no—
331C4—1461no—
332C4—1462no—
333C4#1798959712yes—
334C4D73⋊#13111yescharacteristic
335C4#1798966511yescharacteristic
336C2—42no—
337C2—1462no—
338C2#2262657811yescharacteristic
339C2C2×#1798959711yescharacteristic
340C2#2262659211yescharacteristic
subgroupG/H
centerC22C22×C4⋊#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
FittingC8×D4×C73C4
socleC22×C73C22×C4⋊C4
prime radicalC2×#11924027D4
cosocleC4×Dic73C24
hypercenterC8×D4#64408
hypocenterC73#17829
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
2. #22625502C2semidirect
3. #22625499C2semidirect
4. #22625491C2semidirect
5. #22625490C2semidirect
6. #22625480C2semidirect
7. #22625476C2semidirect
179. C73#17829semidirect

Maximal subgroups

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

subgroupindex
#226266272
#226255022
#226254992
#226254912
#226254902
#226254802
#226254762
C8×#119240272
#1782973