Finite Group Databasebeta

← #32984533

Subgroups — #32984533

Order 18688.

382 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22610649C211yesmaximal, characteristic
2C4×#14556522C211yesmaximal, characteristic
3C2×#17988339C211yesmaximal, characteristic
4C2×#17988309C211yesmaximal, characteristic
5#22607772C211yesmaximal, characteristic
6#22607770C211yesmaximal, characteristic
7C73×#1939C211yesmaximal, characteristic
8C2×#14556522C411yescharacteristic
9C2×#14556522C411yescharacteristic
10C2×C4⋊#10596831C2211yescharacteristic
11C2×#14556520—21no—
12C2×C4×#10596831C2211yescharacteristic
13C2×C4×#10596831C2211yescharacteristic
14C4×C4⋊Dic73C2211yescharacteristic
15#17988349C411yescharacteristic
16#17988349C411yescharacteristic
17#17988341—21no—
18#17988339—22no—
19#17988309—22no—
20C2×C4⋊C8×C73—21no—
21C2×C4⋊C8×C73C2211yescharacteristic
22C2×C4×C8×C73C2211yescharacteristic
23C4×C4⋊C4×C73C2211yescharacteristic
24#336×C73—21no—
25C22×#10596831—21no—
26C22×#10596831—21no—
27C22×#10596831C2×C411yescharacteristic
28C22×#10596831C2×C411yescharacteristic
29C2×C4⋊Dic73C2×C411yescharacteristic
30C2×C4⋊Dic73C2×C411yescharacteristic
31C2×C4×Dic73—21no—
32#14556522—22no—
33#14556522C814yescomplemented
34C4⋊#10596831—21no—
35C4⋊#10596831—21no—
36#14556520—42no—
37C4×#10596831—21no—
38C4×#10596831D412yes—
39C4×#10596831Q812yes—
40C4×#10596831Q812yes—
41#14556498—21no—
42C22×C8×C73—21no—
43C22×C8×C73D411yescharacteristic
44C22×C8×C73D411yescharacteristic
45C2×C4⋊C4×C73C2×C411yescharacteristic
46C2×C4⋊C4×C73C2×C411yescharacteristic
47C2×C42×C73—21no—
48C2×C42×C73C2311yescharacteristic
49C4⋊C8×C73—21no—
50C4⋊C8×C73—21no—
51C4⋊C8×C73—42no—
52C4×C8×C73—21no—
53C4×C8×C73—21no—
54#95×C73—21no—
55C22×Dic73—21no—
56C22×Dic73—21no—
57C2×#10596831—21no—
58C2×#10596831—21no—
59C2×#10596831—22no—
60C2×#10596831—41no—
61C2×#10596831—41no—
62C2×#10596831—41no—
63C2×#10596831—41no—
64C2×#10596831—41no—
65C2×#10596831C4⋊C412yes—
66C2×#10596831C4⋊C412yes—
67C2×#10596831C2×C812yes—
68C2×#10596831M1612yes—
69C4⋊Dic73—21no—
70C4⋊Dic73—21no—
71C4⋊Dic73—21no—
72C4⋊Dic73C2×C812yes—
73C4×Dic73—41no—
74C4×Dic73—41no—
75C22×C4×C73—21no—
76C22×C4×C73—21no—
77C22×C4×C73C22×C411yescharacteristic
78C22×C4×C73C2×D411yescharacteristic
79C22×C4×C73#4111yescharacteristic
80C2×C8×C73—21no—
81C2×C8×C73—21no—
82C2×C8×C73—21no—
83C2×C8×C73—21no—
84C2×C8×C73—21no—
85C2×C8×C73—21no—
86C2×C8×C73—41no—
87C2×C8×C73—41no—
88C2×C8×C73—41no—
89C4⋊C4×C73—21no—
90C4⋊C4×C73—21no—
91C4⋊C4×C73—21no—
92C4⋊C4×C73C2×C812yes—
93C42×C73—41no—
94C42×C73—41no—
95C42×C73C2×D411yescharacteristic
96C42×C73C2×Q811yescharacteristic
97C42×C73C2×Q811yescharacteristic
98C42×C73#4111yescharacteristic
99C23×C73C4×D411yescharacteristic
100C2×C4×C73—21no—
101C2×C4×C73—21no—
102C2×C4×C73—22no—
103C2×C4×C73—41no—
104C2×C4×C73—41no—
105C2×C4×C73—41no—
106C2×C4×C73—41no—
107C2×C4×C73—41no—
108C2×C4×C73C2×C4⋊C411yescharacteristic
109C2×C4×C73C4×Q811yescharacteristic
110C2×C4×C73#12111yescharacteristic
111C2×C4×C73C22⋊Q811yescharacteristic
112C2×C4×C73#12511yescharacteristic
113C2×C4×C73C4⋊Q811yescharacteristic
114C2×C4×C73C22×C811yescharacteristic
115C2×C4×C73C2×M1611yescharacteristic
116C2×C4×C73#13111yescharacteristic
117C2×C4×C73#13111yescharacteristic
118C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C73#13711yescharacteristic
121C2×C4×C73#13711yescharacteristic
122C2×Dic73—22no—
123C2×Dic73—41no—
124C2×Dic73—41no—
125C2×Dic73—41no—
126C2×Dic73—41no—
127C2×Dic73—41no—
128C8×C73—41no—
129C8×C73—41no—
130C8×C73—81no—
131#10596831—22no—
132#10596831—42no—
133#10596831—81no—
134#10596831C4⋊C814yescomplemented
135C22×C73#38911yescharacteristic
136C22×C73C8×D411yescharacteristic
137C22×C73#43611yescharacteristic
138C22×C73#44011yescharacteristic
139C22×C73#44011yescharacteristic
140C22×C73#44411yescharacteristic
141C22×C73#44411yescharacteristic
142C4×C73—21no—
143C4×C73—21no—
144C4×C73—42no—
145C4×C73—81no—
146C4×C73C2×C4⋊C811yescharacteristic
147C4×C73#42411yescharacteristic
148C4×C73C8×Q811yescharacteristic
149C4×C73#44611yescharacteristic
150C4×C73#46911yescharacteristic
151C4×C73#47011yescharacteristic
152C4×C73#50111yescharacteristic
153C4×C73#50111yescharacteristic
154Dic73—42no—
155Dic73—81no—
156#9596—731nomaximal, Sylow
157C2×C73SD16⋊C811yescharacteristic
158C2×C73SD16⋊C811yescharacteristic
159C2×C73#159211yescharacteristic
160C2×C73#159211yescharacteristic
161C2×C73#193911yescharacteristic
162C2×C73#194411yescharacteristic
163C2×C73#194611yescharacteristic
164#1939—731no—
165#1939D7311yescharacteristic
166C4×#106—731no—
167C2×#335—731no—
168C2×#322—731no—
169#1279—731no—
170#1279—731no—
171C73#959611yescharacteristic, complemented, Sylow
172C2×#106—731no—
173C2×#106—731no—
174C2×C4⋊C8—21no—
175C2×C4⋊C8—731no—
176C2×C4⋊C8—1461no—
177C2×C4⋊C8C2×D7311yescharacteristic
178C2×C4×C8—731no—
179C2×C4×C8—731no—
180C2×C4×C8C2×D7311yescharacteristic
181C4×C4⋊C4—731no—
182C4×C4⋊C4C2×D7311yescharacteristic
183#340—731no—
184#340—731no—
185#336—21no—
186#336—1461no—
187#335—1462no—
188#322—1462no—
189C22×C8—21no—
190C22×C8—731no—
191C22×C8—731no—
192C22×C8—1461no—
193C22×C8—1461no—
194C22×C8C22⋊D7311yescharacteristic
195C22×C8C22⋊D7311yescharacteristic
196C2×C4⋊C4—731no—
197C2×C4⋊C4—731no—
198C2×C4⋊C4C4×D7311yescharacteristic
199C2×C4⋊C4C4×D7311yescharacteristic
200C2×C42—21no—
201C2×C42—1461no—
202C2×C42C22×D7311yescharacteristic
203#106—734no—
204#106—1462no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—42no—
208C4⋊C8—2922no—
209C4⋊C8—1461no—
210C4⋊C8—1461no—
211C4×C8—21no—
212C4×C8—21no—
213C4×C8—732no—
214C4×C8—732no—
215C4×C8—732no—
216C4×C8—1461no—
217#95—21no—
218#95—1461no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—1461no—
222C22×C4—1461no—
223C22×C4C2×C4×D7311yescharacteristic
224C22×C4C2×C22⋊D7311yescharacteristic
225C22×C4#1192402811yescharacteristic
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—2921no—
236C2×C8—2921no—
237C2×C8—2921no—
238C2×C8—2921no—
239C2×C8—2921no—
240C2×C8—732no—
241C2×C8—732no—
242C2×C8—732no—
243C2×C8—732no—
244C2×C8—1462no—
245C2×C8—1461no—
246C2×C8—1461no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—732no—
251C4⋊C4—1461no—
252C4⋊C4—1461no—
253C4⋊C4—1461no—
254C4⋊C4C8×D7312yes—
255C42—41no—
256C42—41no—
257C42—2921no—
258C42—2921no—
259C42D4×D7311yescharacteristic
260C42Q8×D7311yescharacteristic
261C42Q8×D7311yescharacteristic
262C42#1192402711yescharacteristic
263C23C4×C22⋊D7311yescharacteristic
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—2921no—
273C2×C4—2921no—
274C2×C4—2921no—
275C2×C4—2921no—
276C2×C4—2921no—
277C2×C4—1462no—
278C2×C4C4⋊C4×D7311yescharacteristic
279C2×C4#1455655611yescharacteristic
280C2×C4#1455656311yescharacteristic
281C2×C4#1455656911yescharacteristic
282C2×C4#1455658111yescharacteristic
283C2×C4#1455658911yescharacteristic
284C2×C4C2×C8×D7311yescharacteristic
285C2×C4M16×D7311yescharacteristic
286C2×C4#1455659711yescharacteristic
287C2×C4#1455659911yescharacteristic
288C2×C4#1455661611yescharacteristic
289C2×C4#1455661711yescharacteristic
290C2×C4#1455662111yescharacteristic
291C2×C4#1455662211yescharacteristic
292C8—41no—
293C8—41no—
294C8—81no—
295C8—2922no—
296C8—5841no—
297C8—734no—
298C8—1462no—
299C22#1798848211yescharacteristic
300C22C8×C22⋊D7311yescharacteristic
301C22#1798866311yescharacteristic
302C22#1798868511yescharacteristic
303C22#1798868711yescharacteristic
304C22#1798870711yescharacteristic
305C22#1798870711yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—81no—
310C4—2922no—
311C4—5841no—
312C4C4⋊C8×D7311yescharacteristic
313C4#1798861211yescharacteristic
314C4#1798871111yescharacteristic
315C4#1798871611yescharacteristic
316C4#1798883811yescharacteristic
317C4#1798884311yescharacteristic
318C4#1798899311yescharacteristic
319C4#1798899711yescharacteristic
320C2#2260874111yescharacteristic
321C2#2260874311yescharacteristic
322C2#2260883111yescharacteristic
323C2#2260883311yescharacteristic
324C2#2261064611yescharacteristic
325C2#2261067111yescharacteristic
326C2#2261068111yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D73
commutatorC2×C4×C73C22×C8
FrattiniC2×C42C22×D73
FittingC73×#1939C2
socle, prime radicalC23×C73C4×D4
cosocleC2×C42×C73C23
hypercenter#1939D73
hypocenterC73#9596
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1939

Complements

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

NH ≅ G/Ntype
33. #14556522C8semidirect
134. #10596831C4⋊C8semidirect
171. C73#9596semidirect

Maximal subgroups

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

subgroupindex
#226106492
C4×#145565222
C2×#179883392
C2×#179883092
#226077722
#226077702
C73×#19392
#959673