Finite Group Databasebeta

← #32990477

Subgroups — #32990477

Order 18688.

426 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22614962C211yesmaximal, characteristic
2#22610695C211yesmaximal, characteristic
3#22610694C211yesmaximal, characteristic
4#22610059C211yesmaximal, characteristic
5#22607815C211yesmaximal, characteristic
6#22607771C211yesmaximal, characteristic
7C73×#1279C211yesmaximal, characteristic
8C2×#14556582—21no—
9C2×#14556523—21no—
10C2×#14556522—21no—
11C2×C4⋊#10596831C2211yescharacteristic
12#17988519—22no—
13#17988486—21no—
14#17988485—21no—
15#17988457—21no—
16#17988457C2211yescharacteristic
17#17988457C2211yescharacteristic
18C4×C4⋊Dic73C2211yescharacteristic
19#17988350—21no—
20#17988350—22no—
21#17988349—21no—
22C2×C4⋊C8×C73C2211yescharacteristic
23C2×C4×C8×C73C2211yescharacteristic
24C4×C4⋊C4×C73C2211yescharacteristic
25C22×#10596831—21no—
26#14556582—42no—
27#14556582—42no—
28C2×C4⋊Dic73—22no—
29C2×C4⋊Dic73—22no—
30C2×C4⋊Dic73—21no—
31C2×C4⋊Dic73—21no—
32C2×C4⋊Dic73—21no—
33C2×C4⋊Dic73—21no—
34C2×C4⋊Dic73—21no—
35C2×C4⋊Dic73D411yescharacteristic
36C2×C4⋊Dic73D411yescharacteristic
37C2×C4⋊Dic73D412yes—
38C2×#11924007—22no—
39C2×C4×Dic73—21no—
40#14556523—42no—
41#14556522—42no—
42C4⋊#10596831—21no—
43C4⋊#10596831Q812yes—
44#14556498—22no—
45#14556498—21no—
46C22×C8×C73—21no—
47C22×C8×C73—21no—
48C2×C4⋊C4×C73D411yescharacteristic
49C2×C4⋊C4×C73D411yescharacteristic
50C2×C42×C73—21no—
51C2×C42×C73C2311yescharacteristic
52C4⋊C8×C73—21no—
53C4⋊C8×C73Q812yes—
54C4×C8×C73—21no—
55C4×C8×C73Q812yes—
56#95×C73—21no—
57C22×Dic73—21no—
58C22×Dic73—21no—
59C22×Dic73—22no—
60C22×Dic73—41no—
61C2×#10596831—22no—
62C2×#10596831—41no—
63C2×#10596831—41no—
64C4⋊Dic73—21no—
65C4⋊Dic73—21no—
66C4⋊Dic73—21no—
67C4⋊Dic73—21no—
68C4⋊Dic73—44no—
69C4⋊Dic73—41no—
70C4⋊Dic73—41no—
71C4⋊Dic73—41no—
72C4⋊Dic73—41no—
73C4⋊Dic73—42no—
74C4⋊Dic73—42no—
75C4⋊Dic73—41no—
76C4⋊Dic73—41no—
77C4⋊Dic73—41no—
78C4⋊Dic73—41no—
79C4⋊Dic73—82no—
80#11924007—44no—
81C4×Dic73—41no—
82C4×Dic73—41no—
83C22×C4×C73—21no—
84C22×C4×C73—21no—
85C22×C4×C73C2×D411yescharacteristic
86C22×C4×C73C2×D411yescharacteristic
87C22×C4×C73C2×D411yescharacteristic
88C2×C8×C73—22no—
89C2×C8×C73—22no—
90C2×C8×C73—41no—
91C2×C8×C73—41no—
92C2×C8×C73—41no—
93C2×C8×C73—41no—
94C4⋊C4×C73—21no—
95C4⋊C4×C73—21no—
96C4⋊C4×C73SD1612yes—
97C4⋊C4×C73SD1612yes—
98C42×C73—41no—
99C42×C73—41no—
100C42×C73C2×Q811yescharacteristic
101C42×C73C2×Q811yescharacteristic
102C42×C73C2×Q811yescharacteristic
103C42×C73#4111yescharacteristic
104C23×C73#12011yescharacteristic
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—22no—
108C2×C4×C73—22no—
109C2×C4×C73—41no—
110C2×C4×C73—41no—
111C2×C4×C73—41no—
112C2×C4×C73—41no—
113C2×C4×C73C22⋊Q811yescharacteristic
114C2×C4×C73C22⋊Q811yescharacteristic
115C2×C4×C73C22⋊Q811yescharacteristic
116C2×C4×C73C4⋊Q811yescharacteristic
117C2×C4×C73C4⋊Q811yescharacteristic
118C2×C4×C73C4⋊Q811yescharacteristic
119C2×C4×C73C2×SD1611yescharacteristic
120C2×C4×C73C2×SD1611yescharacteristic
121C2×C4×C73#13511yescharacteristic
122C2×C4×C73#13511yescharacteristic
123C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C73#13711yescharacteristic
126C2×C4×C73#13711yescharacteristic
127C2×Dic73—41no—
128C2×Dic73—42no—
129C2×Dic73—41no—
130C2×Dic73—41no—
131C2×Dic73—42no—
132C2×Dic73—41no—
133C2×Dic73—41no—
134C2×Dic73—42no—
135C2×Dic73—41no—
136C2×Dic73—81no—
137C2×Dic73—81no—
138C2×Dic73—81no—
139C8×C73—42no—
140C8×C73—42no—
141#10596831—42no—
142C22×C73#39511yescharacteristic
143C22×C73#44811yescharacteristic
144C22×C73#44911yescharacteristic
145C22×C73#45011yescharacteristic
146C22×C73#45211yescharacteristic
147C22×C73#45411yescharacteristic
148C22×C73#45511yescharacteristic
149C4×C73—21no—
150C4×C73—21no—
151C4×C73—42no—
152C4×C73—42no—
153C4×C73#47511yescharacteristic
154C4×C73#47611yescharacteristic
155C4×C73#47811yescharacteristic
156C4×C73#47911yescharacteristic
157C4×C73#49811yescharacteristic
158C4×C73#49911yescharacteristic
159C4×C73#50111yescharacteristic
160C4×C73#50111yescharacteristic
161Dic73—81no—
162Dic73—81no—
163Dic73—82no—
164Dic73—161no—
165#10582—731nomaximal, Sylow
166C2×C73#162611yescharacteristic
167C2×C73#163511yescharacteristic
168C2×C73#164211yescharacteristic
169C2×C73#164311yescharacteristic
170C2×C73#205811yescharacteristic
171C2×C73#205911yescharacteristic
172C2×C73#206111yescharacteristic
173#2552—731no—
174#1948—731no—
175#1948—731no—
176#1834—731no—
177#1296—731no—
178#1279—731no—
179#1279D7311yescharacteristic
180C73#1058211yescharacteristic, complemented, Sylow
181C2×#125—1461no—
182C2×#106—1461no—
183C2×#106—1461no—
184C2×C4⋊C8—731no—
185C2×C4⋊C8C2×D7311yescharacteristic
186C2×C4×C8C2×D7311yescharacteristic
187#398—1462no—
188#389—1461no—
189#389—1461no—
190#384—731no—
191#384—731no—
192#384—1461no—
193C4×C4⋊C4—731no—
194C4×C4⋊C4C2×D7311yescharacteristic
195#340—1462no—
196#340—1461no—
197#340—1461no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—1461no—
201#125—2922no—
202#125—2922no—
203C2×C4⋊C4—732no—
204C2×C4⋊C4—731no—
205C2×C4⋊C4—731no—
206C2×C4⋊C4—1462no—
207C2×C4⋊C4—1462no—
208C2×C4⋊C4—1461no—
209C2×C4⋊C4—1461no—
210C2×C4⋊C4—1461no—
211C2×C4⋊C4—1461no—
212C2×C4⋊C4—1461no—
213C2×C4⋊C4—1462no—
214C2×C4⋊C4D29211yescharacteristic
215C2×C4⋊C4D29211yescharacteristic
216C2×C42—21no—
217C2×C42—1461no—
218C2×C42C22×D7311yescharacteristic
219#106—2922no—
220#106—2922no—
221C4⋊C8—21no—
222C4⋊C8—732no—
223C4⋊C8—1461no—
224C4⋊C8Dic14612yes—
225C4×C8—21no—
226C4×C8Dic14612yes—
227#95—21no—
228#95—1462no—
229#95—1461no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—2921no—
233C22×C4—1461no—
234C22×C4—1461no—
235C22×C4—1462no—
236C22×C4D4×D7311yescharacteristic
237C22×C4D4×D7311yescharacteristic
238C22×C4C2×D29211yescharacteristic
239C2×C8—22no—
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—2921no—
246C2×C8—2921no—
247C2×C8—1462no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—2922no—
251C4⋊C4—2924no—
252C4⋊C4—2924no—
253C4⋊C4—2922no—
254C4⋊C4—2921no—
255C4⋊C4—2921no—
256C4⋊C4—2921no—
257C4⋊C4—2921no—
258C4⋊C4—2921no—
259C4⋊C4—2921no—
260C4⋊C4—2921no—
261C4⋊C4—2921no—
262C4⋊C4—5842no—
263C4⋊C4—1461no—
264C4⋊C4—1461no—
265C4⋊C4—1461no—
266C4⋊C4—1461no—
267C4⋊C4#1192401712yes—
268C4⋊C4#1192401712yes—
269C42—41no—
270C42—41no—
271C42—2921no—
272C42—2921no—
273C42Q8×D7311yescharacteristic
274C42C2×Dic14611yescharacteristic
275C42C2×Dic14611yescharacteristic
276C42#1192402711yescharacteristic
277C23#1455656111yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—2922no—
287C2×C4—2921no—
288C2×C4—2921no—
289C2×C4—2921no—
290C2×C4—2922no—
291C2×C4—2921no—
292C2×C4—2921no—
293C2×C4—2922no—
294C2×C4—2921no—
295C2×C4—5841no—
296C2×C4—5841no—
297C2×C4—5841no—
298C2×C4#1455656811yescharacteristic
299C2×C4#1455656811yescharacteristic
300C2×C4#1455657111yescharacteristic
301C2×C4#1455659011yescharacteristic
302C2×C4#1455659011yescharacteristic
303C2×C4#1455659111yescharacteristic
304C2×C4C2×#1192401711yescharacteristic
305C2×C4C2×#1192401711yescharacteristic
306C2×C4#1455661011yescharacteristic
307C2×C4#1455661411yescharacteristic
308C2×C4#1455661811yescharacteristic
309C2×C4#1455661911yescharacteristic
310C2×C4#1455662011yescharacteristic
311C2×C4#1455662411yescharacteristic
312C8—42no—
313C8—42no—
314C8—2922no—
315C22#1798850811yescharacteristic
316C22#1798872811yescharacteristic
317C22#1798873511yescharacteristic
318C22#1798874011yescharacteristic
319C22#1798875011yescharacteristic
320C22#1798876111yescharacteristic
321C22#1798876611yescharacteristic
322C4—21no—
323C4—21no—
324C4—42no—
325C4—42no—
326C4—5841no—
327C4—5842no—
328C4—5841no—
329C4—11681no—
330C4#1798887311yescharacteristic
331C4#1798887811yescharacteristic
332C4#1798888511yescharacteristic
333C4#1798889611yescharacteristic
334C4#1798898511yescharacteristic
335C4#1798898811yescharacteristic
336C4#1798899411yescharacteristic
337C4#1798899611yescharacteristic
338C2#2260903011yescharacteristic
339C2#2260908411yescharacteristic
340C2#2260913411yescharacteristic
341C2#2260914011yescharacteristic
342C2#2261126511yescharacteristic
343C2#2261127211yescharacteristic
344C2#2261128011yescharacteristic
subgroupG/H
centerC23#14556561
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1279C2
socle, prime radicalC23×C73#120
hypercenter#1279D73
hypocenterC73#10582
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
180. C73#10582semidirect

Maximal subgroups

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

subgroupindex
#226149622
#226106952
#226106942
#226100592
#226078152
#226077712
C73×#12792
#1058273