Finite Group Databasebeta

← #32975194

Subgroups — #32975194

Order 18688.

378 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22611474C211yesmaximal, characteristic
2#22611407C211yesmaximal, characteristic
3#22611339C211yesmaximal, characteristic
4#22607757C211yesmaximal, characteristic
5#22607757C211yesmaximal, characteristic
6#22607754C211yesmaximal, characteristic
7C73×#2806C211yesmaximal, characteristic
8C2×#14556522—21no—
9C2×#14556522—21no—
10C2×#14556515—21no—
11C2×#14556515—21no—
12#17988457C2211yescharacteristic
13#17988349—21no—
14#17988349—21no—
15#17988342C2211yescharacteristic
16#17988342C2211yescharacteristic
17#17988342C2211yescharacteristic
18#398×C73—21no—
19#398×C73—21no—
20#395×C73—21no—
21#391×C73—21no—
22#391×C73C2211yescharacteristic
23#391×C73C2211yescharacteristic
24#389×C73—21no—
25#389×C73C2211yescharacteristic
26#387×C73—21no—
27C22×#10596831—21no—
28C22×#10596831—21no—
29C22×#10596831—21no—
30C2×C4⋊Dic73—21no—
31C2×C4⋊Dic73—21no—
32C2×C4⋊Dic73—21no—
33#14556522—42no—
34#14556522—42no—
35#14556515—42no—
36#14556515—42no—
37C22×Q8×C73D411yescharacteristic
38C22×Q8×C73D411yescharacteristic
39C2×C4⋊C4×C73—21no—
40C2×C4⋊C4×C73—21no—
41C2×C4⋊C4×C73—21no—
42C2×C4⋊C4×C73—21no—
43C2×C4⋊C4×C73—21no—
44C2×C4⋊C4×C73D411yescharacteristic
45C2×C4⋊C4×C73D411yescharacteristic
46C2×C4⋊C4×C73D411yescharacteristic
47C2×C4⋊C4×C73D411yescharacteristic
48C2×C42×C73—21no—
49C2×C42×C73C2311yescharacteristic
50#95×C73—21no—
51#95×C73—21no—
52#95×C73—21no—
53#95×C73—21no—
54#95×C73—21no—
55#95×C73—21no—
56#95×C73—21no—
57#95×C73—21no—
58C22×Dic73—41no—
59C2×#10596831—22no—
60C2×#10596831—22no—
61C2×#10596831—41no—
62C2×#10596831—41no—
63C2×#10596831—41no—
64C2×#10596831—41no—
65C2×#10596831—41no—
66C2×#10596831—41no—
67C2×#10596831—41no—
68C4⋊Dic73—41no—
69C4⋊Dic73—41no—
70C4⋊Dic73—41no—
71C4⋊Dic73—41no—
72C4⋊Dic73—41no—
73C4⋊Dic73—41no—
74C2×Q8×C73—21no—
75C2×Q8×C73—21no—
76C2×Q8×C73—21no—
77C2×Q8×C73—41no—
78C2×Q8×C73—41no—
79C2×Q8×C73—41no—
80C2×Q8×C73—41no—
81C2×Q8×C73SD1612yes—
82C22×C4×C73—21no—
83C22×C4×C73—21no—
84C22×C4×C73—21no—
85C22×C4×C73—21no—
86C22×C4×C73—21no—
87C22×C4×C73—21no—
88C22×C4×C73C2×D411yescharacteristic
89C22×C4×C73C2×D411yescharacteristic
90C22×C4×C73C2×D411yescharacteristic
91C4⋊C4×C73—21no—
92C4⋊C4×C73—41no—
93C4⋊C4×C73—41no—
94C4⋊C4×C73—41no—
95C4⋊C4×C73—41no—
96C4⋊C4×C73—41no—
97C4⋊C4×C73—81no—
98C4⋊C4×C73—81no—
99C4⋊C4×C73—81no—
100C4⋊C4×C73—81no—
101C4⋊C4×C73SD1612yes—
102C42×C73—41no—
103C42×C73—81no—
104C23×C73#12011yescharacteristic
105Q8×C73—42no—
106Q8×C73—42no—
107Q8×C73—81no—
108Q8×C73—81no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—22no—
116C2×C4×C73—22no—
117C2×C4×C73—41no—
118C2×C4×C73—41no—
119C2×C4×C73—41no—
120C2×C4×C73—41no—
121C2×C4×C73—41no—
122C2×C4×C73—41no—
123C2×C4×C73—41no—
124C2×C4×C73—41no—
125C2×C4×C73—41no—
126C2×C4×C73—41no—
127C2×C4×C73—41no—
128C2×C4×C73—41no—
129C2×C4×C73—41no—
130C2×C4×C73—41no—
131C2×C4×C73—41no—
132C2×C4×C73—41no—
133C2×C4×C73C2×SD1611yescharacteristic
134C2×C4×C73C2×SD1611yescharacteristic
135C2×C4×C73#13511yescharacteristic
136C2×C4×C73#13711yescharacteristic
137C2×C4×C73#13711yescharacteristic
138C2×C4×C73#13711yescharacteristic
139C2×Dic73—81no—
140C2×Dic73—81no—
141C2×Dic73—81no—
142#10596831—42no—
143#10596831—42no—
144#10596831—81no—
145C22×C73#44811yescharacteristic
146C22×C73#44811yescharacteristic
147C22×C73#45211yescharacteristic
148C22×C73#45311yescharacteristic
149C22×C73#45511yescharacteristic
150C22×C73#45611yescharacteristic
151C22×C73#45811yescharacteristic
152C4×C73—21no—
153C4×C73—21no—
154C4×C73—21no—
155C4×C73—21no—
156C4×C73—21no—
157C4×C73—21no—
158C4×C73—42no—
159C4×C73—42no—
160C4×C73—81no—
161C4×C73—81no—
162C4×C73—81no—
163C4×C73—81no—
164Dic73—161no—
165#7814—731nomaximal, Sylow
166C2×C73#160811yescharacteristic
167C2×C73#161111yescharacteristic
168C2×C73#161811yescharacteristic
169C2×C73#162311yescharacteristic
170C2×C73#164311yescharacteristic
171C2×C73#165311yescharacteristic
172C2×C73#166111yescharacteristic
173#2806D7311yescharacteristic
174#2096—731no—
175#2084—731no—
176#2072—731no—
177#1272—731no—
178#1272—731no—
179#1271—731no—
180C73#781411yescharacteristic, complemented, Sylow
181C2×#106—1461no—
182C2×#106—1461no—
183C2×#103—1461no—
184C2×#103—1461no—
185#398—21no—
186#398—21no—
187#395—21no—
188#391—21no—
189#391C2×D7311yescharacteristic
190#391C2×D7311yescharacteristic
191#389—21no—
192#389C2×D7311yescharacteristic
193#387—21no—
194#384—731no—
195#340—1461no—
196#340—1461no—
197#336—731no—
198#336—731no—
199#336—731no—
200C22×Q8C22⋊D7311yescharacteristic
201C22×Q8C22⋊D7311yescharacteristic
202C22×C8—1461no—
203C22×C8—1461no—
204C22×C8—1461no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—1461no—
211C2×C4⋊C4—1461no—
212C2×C4⋊C4—1461no—
213C2×C4⋊C4C22⋊D7311yescharacteristic
214C2×C4⋊C4C22⋊D7311yescharacteristic
215C2×C4⋊C4C22⋊D7311yescharacteristic
216C2×C4⋊C4C22⋊D7311yescharacteristic
217C2×C42—21no—
218C2×C42C22×D7311yescharacteristic
219#106—2922no—
220#106—2922no—
221#103—2922no—
222#103—2922no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—21no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8#1192401512yes—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—2921no—
246C22×C4C2×C22⋊D7311yescharacteristic
247C22×C4C2×C22⋊D7311yescharacteristic
248C22×C4C2×C22⋊D7311yescharacteristic
249C2×C8—2921no—
250C2×C8—2921no—
251C2×C8—2921no—
252C2×C8—2921no—
253C2×C8—2921no—
254C2×C8—2921no—
255C2×C8—2921no—
256C2×C8—1462no—
257C2×C8—1462no—
258C4⋊C4—21no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—81no—
265C4⋊C4—81no—
266C4⋊C4—81no—
267C4⋊C4—81no—
268C4⋊C4—2921no—
269C4⋊C4—2921no—
270C4⋊C4—2921no—
271C4⋊C4—2921no—
272C4⋊C4—2921no—
273C4⋊C4—2921no—
274C4⋊C4#1192401512yes—
275C42—41no—
276C42—81no—
277C23#1455656011yescharacteristic
278Q8—42no—
279Q8—42no—
280Q8—81no—
281Q8—81no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—5841no—
307C2×C4—5841no—
308C2×C4—5841no—
309C2×C4C2×#1192401511yescharacteristic
310C2×C4C2×#1192401511yescharacteristic
311C2×C4#1455661111yescharacteristic
312C2×C4#1455662111yescharacteristic
313C2×C4#1455662211yescharacteristic
314C2×C4#1455662211yescharacteristic
315C8—2922no—
316C8—2922no—
317C8—5841no—
318C22#1798872611yescharacteristic
319C22#1798872611yescharacteristic
320C22#1798874911yescharacteristic
321C22#1798875511yescharacteristic
322C22#1798876511yescharacteristic
323C22#1798877011yescharacteristic
324C22#1798877711yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—42no—
332C4—42no—
333C4—81no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4—11681no—
338C2#2260892211yescharacteristic
339C2#2260893911yescharacteristic
340C2#2260897911yescharacteristic
341C2#2260900911yescharacteristic
342C2#2260913811yescharacteristic
343C2#2260920811yescharacteristic
344C2#2260924811yescharacteristic
subgroupG/H
centerC23#14556560
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2806C2
socle, prime radicalC23×C73#120
hypercenter#2806D73
hypocenterC73#7814
LCSG ▷ C2×C42×C73 ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2806

Complements

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

NH ≅ G/Ntype
180. C73#7814semidirect

Maximal subgroups

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

subgroupindex
#226114742
#226114072
#226113392
#226077572
#226077542
C73×#28062
#781473