Finite Group Databasebeta

← #32979039

Subgroups — #32979039

Order 18688.

542 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×D292C211yesmaximal, characteristic
2#22610091C211yesmaximal, characteristic, complemented
3#22609932C212yesmaximal
4#22607815C212yesmaximal, complemented
5C2×#335×C73C211yesmaximal, characteristic, complemented
6C22×C8×D73—21no—
7C2×C4×D292C2211yescharacteristic
8C8×D292—22no—
9C8×D292C414yescomplemented
10C2×#14556525—21no—
11C2×#14556525—21no—
12C2×C4⋊#10596831C2211yescharacteristic
13C2×#14556513—22no—
14C2×#14556503—21no—
15#17988457C2212yes—
16#17988350—22no—
17C2×C4⋊C8×C73C2212yes—
18C2×C4×C8×C73C2211yescharacteristic
19#335×C73—22no—
20C22×D292D411yescharacteristic
21C22×C4×D73—21no—
22C22×#10596831—21no—
23C2×C8×D73—24no—
24C2×C8×D73—42no—
25C2×C8×D73—42no—
26C4×D292—21no—
27C4×D292—21no—
28C4×D292C2×C412yes—
29C4×D292Q812yes—
30C2×C4⋊Dic73—22no—
31C2×C4⋊Dic73—22no—
32C2×C4⋊Dic73—22no—
33C2×C4⋊Dic73D411yescharacteristic
34C2×#11924005—21no—
35#14556525—42no—
36#14556525—42no—
37C4⋊#10596831—21no—
38C4⋊#10596831C2×C412yes—
39#14556513—44no—
40#14556503—24no—
41C22×C8×C73—22no—
42C22×C8×C73D411yescharacteristic
43C22×C8×C73D411yescharacteristic
44C2×C42×C73C2311yescharacteristic
45C4⋊C8×C73—22no—
46C4⋊C8×C73—22no—
47C4×C8×C73C2×C412yes—
48C4×C8×C73D412yes—
49C23×D73—21no—
50C2×D292—21no—
51C2×D292—21no—
52C2×D292—21no—
53C2×D292C4⋊C412yes—
54C2×D292D812yes—
55C2×D292Q1612yes—
56C22×Dic73—21no—
57C22×Dic73—42no—
58C2×C4×D73—22no—
59C2×C4×D73—22no—
60C2×C4×D73—41no—
61C2×C4×D73—41no—
62C2×C4×D73—41no—
63C2×C4×D73—41no—
64C2×#10596831—22no—
65C2×#10596831—41no—
66C2×#10596831—41no—
67C8×D73—48no—
68C4⋊Dic73—21no—
69C4⋊Dic73—42no—
70C4⋊Dic73—42no—
71C4⋊Dic73—42no—
72C4⋊Dic73—42no—
73C4⋊Dic73—82no—
74C4⋊Dic73C4⋊C412yes—
75#11924005—22no—
76#11924005—22no—
77C22×C4×C73C2×D411yescharacteristic
78C22×C4×C73C2×D411yescharacteristic
79C22×C4×C73#4111yescharacteristic
80C2×C8×C73—21no—
81C2×C8×C73—21no—
82C2×C8×C73—42no—
83C2×C8×C73—42no—
84C2×C8×C73—42no—
85C2×C8×C73C22⋊C412yes—
86C2×C8×C73C22⋊C412yes—
87C2×C8×C73D812yes—
88C2×C8×C73SD1612yes—
89C42×C73C22×C411yescharacteristic
90C42×C73C2×D411yescharacteristic
91C42×C73C2×Q811yescharacteristic
92C42×C73#4111yescharacteristic
93C23×C73#12111yescharacteristic
94C22×D73—22no—
95C22×D73—22no—
96C22×D73—22no—
97C22×D73—41no—
98C22×D73—41no—
99C22×D73—41no—
100C22×D73—41no—
101C2×C4×C73—21no—
102C2×C4×C73—21no—
103C2×C4×C73C2×C22⋊C411yescharacteristic
104C2×C4×C73C2×C4⋊C411yescharacteristic
105C2×C4×C73#11711yescharacteristic
106C2×C4×C73#12111yescharacteristic
107C2×C4×C73C22⋊Q811yescharacteristic
108C2×C4×C73C22⋊Q811yescharacteristic
109C2×C4×C73C2×D811yescharacteristic
110C2×C4×C73C2×D811yescharacteristic
111C2×C4×C73C2×SD1611yescharacteristic
112C2×C4×C73C2×Q1611yescharacteristic
113C2×C4×C73#13511yescharacteristic
114C2×C4×C73#13511yescharacteristic
115C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C73#13711yescharacteristic
117C2×Dic73—22no—
118C2×Dic73—41no—
119C2×Dic73—41no—
120C2×Dic73—82no—
121C2×Dic73—82no—
122C2×Dic73—82no—
123D292—22no—
124D292—22no—
125D292—22no—
126D292#10714yescomplemented
127C4×D73—42no—
128C4×D73—42no—
129C4×D73—42no—
130C4×D73—42no—
131C8×C73—22no—
132C8×C73—82no—
133C8×C73#10214yescomplemented
134#10596831—42no—
135C22×C73#38011yescharacteristic
136C22×C73#45911yescharacteristic
137C22×C73#46111yescharacteristic
138C22×C73#46611yescharacteristic
139C22×C73#46711yescharacteristic
140C22×C73#47211yescharacteristic
141C22×C73#47311yescharacteristic
142C2×D73—24no—
143C2×D73—42no—
144C2×D73—42no—
145C2×D73—42no—
146C2×D73—42no—
147C2×D73—42no—
148C2×D73—42no—
149C4×C73—21no—
150C4×C73—21no—
151C4×C73C2×#10211yescharacteristic
152C4×C73#41711yescharacteristic
153C4×C73C2×#10711yescharacteristic
154C4×C73#42711yescharacteristic
155C4×C73#46611yescharacteristic
156C4×C73#46711yescharacteristic
157C4×C73#47411yescharacteristic
158C4×C73#47611yescharacteristic
159Dic73—42no—
160Dic73—162no—
161#8644—731nomaximal, Sylow
162C2×C73#166711yescharacteristic
163C2×C73#166911yescharacteristic
164C2×C73#167311yescharacteristic
165C2×C73#167511yescharacteristic
166C2×C73#180211yescharacteristic
167C2×C73#180811yescharacteristic
168C2×C73#181611yescharacteristic
169D73—44no—
170C2×C8×D4—731no—
171#1845—731no—
172#1802—732no—
173C2×#335D7311yescharacteristic, complemented
174#1296—732no—
175C73#864411yescharacteristic, complemented, Sylow
176C23×C8—1461no—
177C2×C4×D4—731no—
178C8×D4—734no—
179C8×D4—1462no—
180C2×#107—1461no—
181C2×#107—1461no—
182C2×C4⋊C8—731no—
183C2×C4⋊C8C2×D7312yes—
184C2×#102—1462no—
185C2×C22⋊C8—1461no—
186C2×C4×C8C2×D7311yescharacteristic
187#384—732no—
188#340—1462no—
189#335—22no—
190C22×D4—731no—
191C23×C4—1461no—
192C22×C8—22no—
193C22×C8—2922no—
194C22×C8—2922no—
195C22×C8—1461no—
196C22×C8—1464no—
197C22×C8D29211yescharacteristic
198C22×C8D29211yescharacteristic
199C4×D4—732no—
200C4×D4—732no—
201C4×D4—1461no—
202C4×D4—1461no—
203C2×C4⋊C4—731no—
204C2×C4⋊C4—1462no—
205C2×C4⋊C4—1462no—
206C2×C4⋊C4—1462no—
207C2×C22⋊C4—1461no—
208C2×C42C22×D7311yescharacteristic
209#107—2922no—
210#107—2922no—
211C4⋊C8—22no—
212C4⋊C8—22no—
213C4⋊C8—732no—
214C4⋊C8—1461no—
215#102—2924no—
216C22⋊C8—1464no—
217C4×C8C4×D7312yes—
218C4×C8C22⋊D7312yes—
219C24—1461no—
220C2×D4—732no—
221C2×D4—732no—
222C2×D4—732no—
223C2×D4—1461no—
224C2×D4—1461no—
225C2×D4—1461no—
226C22×C4—2921no—
227C22×C4—2921no—
228C22×C4—2921no—
229C22×C4—2921no—
230C22×C4—2922no—
231C22×C4—1461no—
232C22×C4—1462no—
233C22×C4—1462no—
234C22×C4D4×D7311yescharacteristic
235C22×C4C2×D29211yescharacteristic
236C22×C4#1192402911yescharacteristic
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—2921no—
243C2×C8—2921no—
244C2×C8—2928no—
245C2×C8—1462no—
246C2×C8#1192400512yes—
247C2×C8#1192400512yes—
248C2×C8D58412yes—
249C2×C8#1192401712yes—
250C4⋊C4—2922no—
251C4⋊C4—2922no—
252C4⋊C4—2922no—
253C4⋊C4—2922no—
254C4⋊C4—5842no—
255C4⋊C4—732no—
256C4⋊C4—1461no—
257C22⋊C4—1462no—
258C22⋊C4—1462no—
259C42C2×C4×D7311yescharacteristic
260C42C2×C22⋊D7311yescharacteristic
261C42Q8×D7311yescharacteristic
262C42#1192402711yescharacteristic
263C23—2921no—
264C23—2921no—
265C23—2921no—
266C23—2921no—
267C23—1462no—
268C23—1462no—
269C23—1462no—
270C23#1455656611yescharacteristic
271D4—734no—
272D4—1462no—
273D4—1462no—
274D4—1462no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—2921no—
278C2×C4—2921no—
279C2×C4—2922no—
280C2×C4—2922no—
281C2×C4—2922no—
282C2×C4—2922no—
283C2×C4—5842no—
284C2×C4—5842no—
285C2×C4—5842no—
286C2×C4—1462no—
287C2×C4C2×#1192400511yescharacteristic
288C2×C4C4⋊C4×D7311yescharacteristic
289C2×C4#1455654911yescharacteristic
290C2×C4#1455656211yescharacteristic
291C2×C4#1455656711yescharacteristic
292C2×C4#1455657111yescharacteristic
293C2×C4D8×D7311yescharacteristic
294C2×C4C2×D58411yescharacteristic
295C2×C4C2×#1192401711yescharacteristic
296C2×C4Q16×D7311yescharacteristic
297C2×C4#1455661011yescharacteristic
298C2×C4#1455661411yescharacteristic
299C2×C4#1455661911yescharacteristic
300C2×C4#1455662411yescharacteristic
301C8—22no—
302C8—82no—
303C8—2922no—
304C8#1455651314yescomplemented
305C22—2922no—
306C22—2922no—
307C22—2922no—
308C22—2922no—
309C22—2922no—
310C22—2922no—
311C22—1464no—
312C22#1798844411yescharacteristic
313C22#1798878311yescharacteristic
314C22#1798879311yescharacteristic
315C22#1798882411yescharacteristic
316C22#1798882911yescharacteristic
317C22#1798885811yescharacteristic
318C22#1798886311yescharacteristic
319C4—21no—
320C4—21no—
321C4—2922no—
322C4—11682no—
323C4C2×#1455651311yescharacteristic
324C4#1798858911yescharacteristic
325C4#107×D7311yescharacteristic
326C4#1798862411yescharacteristic
327C4#1798882011yescharacteristic
328C4#1798882511yescharacteristic
329C4#1798886811yescharacteristic
330C4#1798887811yescharacteristic
331C2—2924no—
332C2#2260928711yescharacteristic
333C2#2260929711yescharacteristic
334C2#2260932111yescharacteristic
335C2#2260933111yescharacteristic
336C2#2260993211yescharacteristic
337C2#2260995711yescharacteristic
338C2#2260999211yescharacteristic
subgroupG/H
centerC23#14556566
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC2×#335×C73C2
socleC23×C73#121
prime radicalC22×D292D4
cosocleC2×C42×C73C23
hypercenterC2×#335D73
hypocenterC73#8644
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
2. #22610091C2semidirect
4. #22607815C2semidirect
5. C2×#335×C73C2semidirect
9. C8×D292C4semidirect
126. D292#107semidirect
133. C8×C73#102semidirect
173. C2×#335D73semidirect
175. C73#8644semidirect
304. C8#14556513semidirect

Maximal subgroups

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

subgroupindex
C2×C8×D2922
#226100912
#226099322
#226078152
C2×#335×C732
#864473