Finite Group Databasebeta

← #32975193

Subgroups — #32975193

Order 18688.

378 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 83 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#22617890C211yesmaximal, characteristic
2#22611408C211yesmaximal, characteristic
3#22611340C211yesmaximal, characteristic
4#22607757C211yesmaximal, characteristic
5#22607756C211yesmaximal, characteristic
6#22607755C211yesmaximal, characteristic
7C73×#2096C211yesmaximal, characteristic
8C2×#14556522—21no—
9C2×#14556514—21no—
10#17988521—21no—
11#17988521—21no—
12#17988506—21no—
13#17988493C2211yescharacteristic
14#17988491—21no—
15#17988485C2211yescharacteristic
16#17988482—21no—
17#17988472—21no—
18#17988349—21no—
19#17988349—21no—
20#17988342C2211yescharacteristic
21#17988342C2211yescharacteristic
22C2×#106×C73—21no—
23C2×#103×C73—21no—
24#391×C73C2211yescharacteristic
25#384×C73C2211yescharacteristic
26#336×C73C2211yescharacteristic
27C22×Dic146D411yescharacteristic
28C22×#10596831—21no—
29C22×#10596831—21no—
30C2×C4⋊Dic73D411yescharacteristic
31C2×C4⋊Dic73D411yescharacteristic
32C2×C4⋊Dic73D411yescharacteristic
33C2×#11924007—21no—
34C2×#11924007—21no—
35C2×#11924007—21no—
36C2×#11924007—21no—
37C2×#11924007—21no—
38C2×C4×Dic73—21no—
39#14556522—42no—
40#14556514—42no—
41#14556498—21no—
42#14556498—21no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47C22×Q8×C73D411yescharacteristic
48C22×C8×C73—21no—
49C2×C4⋊C4×C73—21no—
50C2×C4⋊C4×C73—21no—
51C2×C4⋊C4×C73—21no—
52C2×C4⋊C4×C73D411yescharacteristic
53C2×C42×C73C2311yescharacteristic
54#106×C73—42no—
55#103×C73—42no—
56#95×C73—21no—
57#95×C73—21no—
58C2×Dic146—21no—
59C2×Dic146—41no—
60C2×Dic146—41no—
61C2×Dic146SD1612yes—
62C22×Dic73—21no—
63C22×Dic73—21no—
64C22×Dic73—21no—
65C22×Dic73—21no—
66C2×#10596831—22no—
67C2×#10596831—41no—
68C2×#10596831—41no—
69C2×#10596831—41no—
70C2×#10596831—41no—
71C2×#10596831—41no—
72C4⋊Dic73—21no—
73C4⋊Dic73—41no—
74C4⋊Dic73—41no—
75C4⋊Dic73SD1612yes—
76#11924007—41no—
77#11924007—41no—
78#11924007—81no—
79#11924007—81no—
80#11924007—81no—
81#11924007—81no—
82C4×Dic73—81no—
83C2×Q8×C73—21no—
84C2×Q8×C73—21no—
85C2×Q8×C73—41no—
86C2×Q8×C73—41no—
87C22×C4×C73—21no—
88C22×C4×C73—21no—
89C22×C4×C73—41no—
90C22×C4×C73C2×D411yescharacteristic
91C22×C4×C73C2×D411yescharacteristic
92C22×C4×C73C2×D411yescharacteristic
93C2×C8×C73—22no—
94C2×C8×C73—41no—
95C2×C8×C73—41no—
96C4⋊C4×C73—41no—
97C4⋊C4×C73—41no—
98C4⋊C4×C73—41no—
99C4⋊C4×C73—41no—
100C4⋊C4×C73—41no—
101C4⋊C4×C73—41no—
102C4⋊C4×C73—41no—
103C42×C73—41no—
104C23×C73#12011yescharacteristic
105Q8×C73—42no—
106Q8×C73—81no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—41no—
114C2×C4×C73—41no—
115C2×C4×C73—41no—
116C2×C4×C73—41no—
117C2×C4×C73—41no—
118C2×C4×C73—41no—
119C2×C4×C73—81no—
120C2×C4×C73—81no—
121C2×C4×C73—81no—
122C2×C4×C73C2×SD1611yescharacteristic
123C2×C4×C73C2×SD1611yescharacteristic
124C2×C4×C73#13511yescharacteristic
125C2×C4×C73#13711yescharacteristic
126C2×C4×C73#13711yescharacteristic
127C2×C4×C73#13711yescharacteristic
128C2×Dic73—22no—
129C2×Dic73—22no—
130C2×Dic73—41no—
131C2×Dic73—41no—
132C2×Dic73—41no—
133C2×Dic73—41no—
134C2×Dic73—41no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C2×Dic73—41no—
138C2×Dic73—41no—
139C2×Dic73—41no—
140Dic146—42no—
141Dic146—81no—
142C8×C73—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—81no—
159C4×C73—81no—
160C4×C73—161no—
161Dic73—42no—
162Dic73—42no—
163Dic73—81no—
164Dic73—81no—
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#2806—731no—
174#2096D7311yescharacteristic
175#2084—731no—
176#2072—731no—
177#1272—731no—
178#1272—731no—
179#1271—731no—
180C73#781411yescharacteristic, complemented, Sylow
181C2×#106—21no—
182C2×#106—1461no—
183C2×#103—21no—
184C2×#103—1461no—
185#398—1461no—
186#398—1461no—
187#395—1461no—
188#391—731no—
189#391—1461no—
190#391C2×D7311yescharacteristic
191#389—731no—
192#389—1461no—
193#387—1461no—
194#384C2×D7311yescharacteristic
195#340—1461no—
196#340—1461no—
197#336—731no—
198#336—731no—
199#336C2×D7311yescharacteristic
200C22×Q8—731no—
201C22×Q8C22⋊D7311yescharacteristic
202C22×C8—21no—
203C22×C8—1461no—
204C22×C8—1461no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—731no—
209C2×C4⋊C4—731no—
210C2×C4⋊C4—731no—
211C2×C4⋊C4—1461no—
212C2×C4⋊C4—1461no—
213C2×C4⋊C4—1461no—
214C2×C4⋊C4—1461no—
215C2×C4⋊C4—1461no—
216C2×C4⋊C4C22⋊D7311yescharacteristic
217C2×C42—1461no—
218C2×C42C22×D7311yescharacteristic
219#106—42no—
220#106—2922no—
221#103—42no—
222#103—2922no—
223#95—21no—
224#95—21no—
225#95—1461no—
226#95—1461no—
227#95—1461no—
228#95—1461no—
229#95—1461no—
230#95—1461no—
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—2921no—
236C2×Q8—2921no—
237C2×Q8—732no—
238C2×Q8—1461no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—41no—
242C22×C4—1461no—
243C22×C4—1461no—
244C22×C4—1461no—
245C22×C4—1461no—
246C22×C4D4×D7311yescharacteristic
247C22×C4D4×D7311yescharacteristic
248C22×C4C2×C22⋊D7311yescharacteristic
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—2921no—
253C2×C8—2921no—
254C2×C8—2921no—
255C2×C8—2921no—
256C2×C8—2921no—
257C2×C8—1462no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—2921no—
266C4⋊C4—2921no—
267C4⋊C4—2921no—
268C4⋊C4—2921no—
269C4⋊C4—5841no—
270C4⋊C4—5841no—
271C4⋊C4—5841no—
272C4⋊C4—5841no—
273C4⋊C4—732no—
274C4⋊C4—1461no—
275C42—41no—
276C42—5841no—
277C23#1455655911yescharacteristic
278Q8—42no—
279Q8—81no—
280Q8—2922no—
281Q8—5841no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—2921no—
298C2×C4—2921no—
299C2×C4—2921no—
300C2×C4—2921no—
301C2×C4—2921no—
302C2×C4—2921no—
303C2×C4—2921no—
304C2×C4—2921no—
305C2×C4—2921no—
306C2×C4—2921no—
307C2×C4—1462no—
308C2×C4—1462no—
309C2×C4SD16×D7311yescharacteristic
310C2×C4SD16×D7311yescharacteristic
311C2×C4#1455661111yescharacteristic
312C2×C4#1455662011yescharacteristic
313C2×C4#1455662011yescharacteristic
314C2×C4#1455662211yescharacteristic
315C8—42no—
316C8—2922no—
317C8—5841no—
318C22#1798872411yescharacteristic
319C22#1798872411yescharacteristic
320C22#1798874711yescharacteristic
321C22#1798875411yescharacteristic
322C22#1798876311yescharacteristic
323C22#1798876811yescharacteristic
324C22#1798877611yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—81no—
332C4—81no—
333C4—161no—
334C4—2922no—
335C4—2922no—
336C4—5841no—
337C4—5841no—
338C2#2260892011yescharacteristic
339C2#2260893711yescharacteristic
340C2#2260897711yescharacteristic
341C2#2260900711yescharacteristic
342C2#2260913711yescharacteristic
343C2#2260920711yescharacteristic
344C2#2260924511yescharacteristic
subgroupG/H
centerC23#14556559
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2096C2
socle, prime radicalC23×C73#120
hypercenter#2096D73
hypocenterC73#7814
LCSG ▷ C2×C42×C73 ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2096

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
#226178902
#226114082
#226113402
#226077572
#226077562
#226077552
C73×#20962
#781473