Finite Group Databasebeta

← #32990571

Subgroups — #32990571

Order 18688.

370 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22610893C211yesmaximal, characteristic
2#22610694C211yesmaximal, characteristic
3#22610650C211yesmaximal, characteristic
4C2×#17988337C211yesmaximal, characteristic
5C2×#17988336C211yesmaximal, characteristic
6#22607815C211yesmaximal, characteristic
7C73×#1987C211yesmaximal, characteristic
8C2×#14556522—21no—
9C2×C4⋊#10596831—21no—
10C2×C4⋊#10596831C2211yescharacteristic
11C2×C4⋊#10596831C2211yescharacteristic
12C2×C4×#10596831C2211yescharacteristic
13#17988457C2211yescharacteristic
14#17988349—21no—
15#17988349—21no—
16#17988349—21no—
17#17988342—21no—
18#17988337—22no—
19#17988336—22no—
20C2×C4⋊Q8×C73C2211yescharacteristic
21C2×C4⋊C8×C73C2211yescharacteristic
22C4×C4⋊C4×C73C2211yescharacteristic
23#340×C73—21no—
24#340×C73—21no—
25C22×#10596831—21no—
26C22×#10596831—21no—
27C22×#10596831D411yescharacteristic
28C22×#10596831D411yescharacteristic
29C2×C4⋊Dic73—21no—
30C2×C4⋊Dic73—21no—
31C2×C4⋊Dic73—21no—
32#14556522—42no—
33C4⋊#10596831—21no—
34C4⋊#10596831—21no—
35C4⋊#10596831—21no—
36C4⋊#10596831—42no—
37C4⋊#10596831D412yes—
38C4×#10596831—21no—
39C4×#10596831—21no—
40C22×Q8×C73—21no—
41C22×C8×C73—21no—
42C4⋊Q8×C73—21no—
43C4⋊Q8×C73—21no—
44C4⋊Q8×C73—21no—
45C4⋊Q8×C73Q812yes—
46C2×C4⋊C4×C73—21no—
47C2×C4⋊C4×C73—21no—
48C2×C4⋊C4×C73D411yescharacteristic
49C2×C4⋊C4×C73D411yescharacteristic
50C2×C42×C73—21no—
51C2×C42×C73C2311yescharacteristic
52C4⋊C8×C73—21no—
53C4⋊C8×C73—21no—
54#95×C73—21no—
55C22×Dic73—41no—
56C2×#10596831—21no—
57C2×#10596831—21no—
58C2×#10596831—21no—
59C2×#10596831—22no—
60C2×#10596831—21no—
61C2×#10596831—21no—
62C2×#10596831—41no—
63C2×#10596831—41no—
64C2×#10596831—41no—
65C2×#10596831—41no—
66C2×#10596831—41no—
67C2×#10596831SD1612yes—
68C4⋊Dic73—41no—
69C4⋊Dic73—41no—
70C4⋊Dic73—41no—
71C4⋊Dic73—41no—
72C4⋊Dic73—81no—
73C2×Q8×C73—22no—
74C2×Q8×C73—41no—
75C2×Q8×C73—81no—
76C2×Q8×C73—81no—
77C22×C4×C73—21no—
78C22×C4×C73—21no—
79C22×C4×C73—41no—
80C22×C4×C73C2×D411yescharacteristic
81C22×C4×C73C2×D411yescharacteristic
82C22×C4×C73#4111yescharacteristic
83C2×C8×C73—41no—
84C2×C8×C73—41no—
85C2×C8×C73—41no—
86C4⋊C4×C73—21no—
87C4⋊C4×C73—22no—
88C4⋊C4×C73—22no—
89C4⋊C4×C73—21no—
90C4⋊C4×C73—21no—
91C4⋊C4×C73—41no—
92C4⋊C4×C73—41no—
93C4⋊C4×C73SD1612yes—
94C42×C73—41no—
95C42×C73—41no—
96C42×C73C2×D411yescharacteristic
97C42×C73C2×Q811yescharacteristic
98C42×C73#4111yescharacteristic
99C42×C73#4111yescharacteristic
100C23×C73#12111yescharacteristic
101Q8×C73—82no—
102Q8×C73—82no—
103C2×C4×C73—21no—
104C2×C4×C73—21no—
105C2×C4×C73—22no—
106C2×C4×C73—41no—
107C2×C4×C73—41no—
108C2×C4×C73—42no—
109C2×C4×C73—41no—
110C2×C4×C73—41no—
111C2×C4×C73—41no—
112C2×C4×C73—81no—
113C2×C4×C73—81no—
114C2×C4×C73#12111yescharacteristic
115C2×C4×C73#12111yescharacteristic
116C2×C4×C73C22⋊Q811yescharacteristic
117C2×C4×C73C22⋊Q811yescharacteristic
118C2×C4×C73C22⋊Q811yescharacteristic
119C2×C4×C73#12611yescharacteristic
120C2×C4×C73C2×SD1611yescharacteristic
121C2×C4×C73C2×SD1611yescharacteristic
122C2×C4×C73#13511yescharacteristic
123C2×C4×C73#13511yescharacteristic
124C2×C4×C73#13711yescharacteristic
125C2×C4×C73#13711yescharacteristic
126C2×C4×C73#13711yescharacteristic
127C2×C4×C73#13711yescharacteristic
128C2×Dic73—81no—
129C2×Dic73—81no—
130C2×Dic73—81no—
131C8×C73—81no—
132#10596831—22no—
133#10596831—42no—
134#10596831—41no—
135#10596831—81no—
136C22×C73#39611yescharacteristic
137C22×C73#46111yescharacteristic
138C22×C73#46411yescharacteristic
139C22×C73#46511yescharacteristic
140C22×C73#47011yescharacteristic
141C22×C73#47111yescharacteristic
142C22×C73#47211yescharacteristic
143C4×C73—21no—
144C4×C73—21no—
145C4×C73—42no—
146C4×C73—82no—
147C4×C73—81no—
148C4×C73#46111yescharacteristic
149C4×C73#46411yescharacteristic
150C4×C73#46511yescharacteristic
151C4×C73#47011yescharacteristic
152C4×C73#47511yescharacteristic
153C4×C73#47511yescharacteristic
154C4×C73#47911yescharacteristic
155C4×C73#47911yescharacteristic
156Dic73—161no—
157#10597—731nomaximal, Sylow
158C2×C73#167111yescharacteristic
159C2×C73#167811yescharacteristic
160C2×C73#169511yescharacteristic
161C2×C73#170411yescharacteristic
162C2×C73#206311yescharacteristic
163C2×C73#206611yescharacteristic
164C2×C73#206611yescharacteristic
165#1990—731no—
166#1987D7311yescharacteristic
167#1948—731no—
168#1939—731no—
169C2×#334—731no—
170C2×#333—731no—
171#1296—731no—
172C73#1059711yescharacteristic, complemented, Sylow
173C2×C4⋊Q8C2×D7311yescharacteristic
174C2×#106—1461no—
175C2×C4⋊C8—731no—
176C2×C4⋊C8—731no—
177C2×C4⋊C8—1461no—
178C2×C4⋊C8C2×D7311yescharacteristic
179C2×C4×C8—731no—
180#384—731no—
181C4×C4⋊C4C2×D7311yescharacteristic
182#340—21no—
183#340—21no—
184#340—1461no—
185#340—1461no—
186#340—1461no—
187#336—1461no—
188#334—1462no—
189#333—1462no—
190C22×Q8—21no—
191C22×C8—21no—
192C22×C8—731no—
193C22×C8—731no—
194C22×C8—1461no—
195C22×C8—1461no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8Dic14612yes—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—1461no—
203C2×C4⋊C4—1461no—
204C2×C4⋊C4—1461no—
205C2×C4⋊C4C22⋊D7311yescharacteristic
206C2×C4⋊C4C22⋊D7311yescharacteristic
207C2×C42—21no—
208C2×C42C22×D7311yescharacteristic
209#106—2922no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—2922no—
213C4⋊C8—732no—
214C4⋊C8—1461no—
215C4⋊C8—1461no—
216C4⋊C8—1461no—
217C4×C8—1461no—
218C4×C8—1461no—
219#95—21no—
220C2×Q8—22no—
221C2×Q8—41no—
222C2×Q8—81no—
223C2×Q8—81no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—41no—
227C22×C4—2921no—
228C22×C4D4×D7311yescharacteristic
229C22×C4C2×C22⋊D7311yescharacteristic
230C22×C4#1192402711yescharacteristic
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—2921no—
235C2×C8—2921no—
236C2×C8—2921no—
237C2×C8—2921no—
238C2×C8—2921no—
239C2×C8—732no—
240C2×C8—1462no—
241C2×C8—1461no—
242C2×C8—1461no—
243C2×C8—1461no—
244C2×C8—1461no—
245C2×C8—1461no—
246C4⋊C4—21no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—2921no—
254C4⋊C4—2921no—
255C4⋊C4—2921no—
256C4⋊C4—2921no—
257C4⋊C4—5841no—
258C4⋊C4#1192401512yes—
259C42—41no—
260C42—41no—
261C42D4×D7311yescharacteristic
262C42C2×Dic14611yescharacteristic
263C42#1192402711yescharacteristic
264C42#1192402811yescharacteristic
265C23#1455656311yescharacteristic
266Q8—82no—
267Q8—82no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—5841no—
280C2×C4—5841no—
281C2×C4—5841no—
282C2×C4#1455656211yescharacteristic
283C2×C4#1455656411yescharacteristic
284C2×C4#1455656811yescharacteristic
285C2×C4#1455656811yescharacteristic
286C2×C4#1455657011yescharacteristic
287C2×C4#1455658411yescharacteristic
288C2×C4SD16×D7311yescharacteristic
289C2×C4C2×#1192401511yescharacteristic
290C2×C4#1455661111yescharacteristic
291C2×C4#1455661411yescharacteristic
292C2×C4#1455662011yescharacteristic
293C2×C4#1455662111yescharacteristic
294C2×C4#1455662211yescharacteristic
295C2×C4#1455662311yescharacteristic
296C8—81no—
297C8—2922no—
298C8—2921no—
299C8—5841no—
300C8—1462no—
301C22#1798851011yescharacteristic
302C22#1798879011yescharacteristic
303C22#1798881111yescharacteristic
304C22#1798881811yescharacteristic
305C22#1798884311yescharacteristic
306C22#1798884811yescharacteristic
307C22#1798885511yescharacteristic
308C4—21no—
309C4—21no—
310C4—42no—
311C4—81no—
312C4—82no—
313C4—11681no—
314C4#1798878911yescharacteristic
315C4#1798880611yescharacteristic
316C4#1798881911yescharacteristic
317C4#1798884411yescharacteristic
318C4#1798887011yescharacteristic
319C4#1798887211yescharacteristic
320C4#1798889411yescharacteristic
321C4#1798889611yescharacteristic
322C2#2260930811yescharacteristic
323C2#2260934911yescharacteristic
324C2#2260945211yescharacteristic
325C2#2260951511yescharacteristic
326C2#2261129111yescharacteristic
327C2#2261130811yescharacteristic
328C2#2261131211yescharacteristic
subgroupG/H
centerC23#14556563
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1987C2
socle, prime radicalC23×C73#121
hypercenter#1987D73
hypocenterC73#10597
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
172. C73#10597semidirect

Maximal subgroups

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

subgroupindex
#226108932
#226106942
#226106502
C2×#179883372
C2×#179883362
#226078152
C73×#19872
#1059773