Finite Group Databasebeta

← #32987299

Subgroups — #32987299

Order 18688.

484 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#17988993C211yesmaximal, characteristic
2#22617998C211yesmaximal, characteristic
3#22610905C211yesmaximal, characteristic
4C2×#17988329C211yesmaximal, characteristic
5C2×#17988328C211yesmaximal, characteristic
6#22607813C211yesmaximal, characteristic
7C2×#491×C73C211yesmaximal, characteristic
8C2×#14556583C2211yescharacteristic
9#17988993—22no—
10#17988993—22no—
11C2×#14556524—21no—
12C2×#14556522—21no—
13C2×#14556502C2211yescharacteristic
14C2×#14556502C2211yescharacteristic
15#17988526—21no—
16#17988525—21no—
17#17988520—22no—
18#17988518—21no—
19#17988517—21no—
20#17988453C2211yescharacteristic
21#17988349—22no—
22#17988329—22no—
23#17988328—22no—
24C2×C4⋊Q8×C73C2211yescharacteristic
25C2×#125×C73C2211yescharacteristic
26#491×C73—22no—
27#491×C73—22no—
28C2×#103×C73—21no—
29C2×#103×C73—21no—
30C2×#97×C73C2211yescharacteristic
31C22×#10596831—21no—
32C22×#10596831—21no—
33#14556583—21no—
34#14556583—21no—
35#14556583—21no—
36#14556583—21no—
37C2×C4⋊Dic73D411yescharacteristic
38C2×C4⋊Dic73D411yescharacteristic
39C2×C4⋊Dic73D412yes—
40C2×#11924007—22no—
41C2×#11924007—21no—
42C2×#11924007—21no—
43#14556524—24no—
44#14556522—24no—
45#14556502—21no—
46#14556502—21no—
47#14556502—21no—
48#14556502D412yes—
49#14556498—22no—
50#14556498—22no—
51#14556498—22no—
52#14556498—21no—
53#14556498—21no—
54C22×Q8×C73—21no—
55C22×C8×C73—21no—
56C4⋊Q8×C73—21no—
57C4⋊Q8×C73—21no—
58C4⋊Q8×C73—21no—
59C4⋊Q8×C73D412yes—
60#125×C73—21no—
61#125×C73—21no—
62#125×C73—21no—
63#125×C73—21no—
64C2×C4⋊C4×C73—21no—
65C2×C4⋊C4×C73—21no—
66C2×C4⋊C4×C73—21no—
67C2×C4⋊C4×C73—21no—
68C2×C4⋊C4×C73D411yescharacteristic
69C2×C4⋊C4×C73D411yescharacteristic
70C2×C42×C73C2311yescharacteristic
71#103×C73—24no—
72#103×C73—24no—
73#97×C73—21no—
74#97×C73D412yes—
75C22×Dic73—22no—
76C22×Dic73—21no—
77C22×Dic73—21no—
78C2×#10596831—24no—
79C2×#10596831—22no—
80C2×#10596831—22no—
81C2×#10596831—41no—
82C2×#10596831—41no—
83C4⋊Dic73—21no—
84C4⋊Dic73—21no—
85C4⋊Dic73—21no—
86C4⋊Dic73—21no—
87C4⋊Dic73—42no—
88#11924007—41no—
89#11924007—41no—
90#11924007—41no—
91#11924007—41no—
92#11924007—82no—
93C2×Q8×C73—22no—
94C2×Q8×C73—44no—
95C2×Q8×C73—41no—
96C22×C4×C73—21no—
97C22×C4×C73—21no—
98C22×C4×C73—41no—
99C22×C4×C73C2×D411yescharacteristic
100C22×C4×C73C2×D411yescharacteristic
101C22×C4×C73C2×D411yescharacteristic
102C2×C8×C73—22no—
103C2×C8×C73—42no—
104C4⋊C4×C73—21no—
105C4⋊C4×C73—21no—
106C4⋊C4×C73—22no—
107C4⋊C4×C73—22no—
108C4⋊C4×C73—21no—
109C4⋊C4×C73—21no—
110C4⋊C4×C73—41no—
111C4⋊C4×C73—41no—
112C4⋊C4×C73—41no—
113C4⋊C4×C73—41no—
114C4⋊C4×C73—41no—
115C4⋊C4×C73—41no—
116C42×C73C2×D411yescharacteristic
117C42×C73C2×D411yescharacteristic
118C42×C73C2×D411yescharacteristic
119C42×C73#4111yescharacteristic
120C23×C73#12011yescharacteristic
121Q8×C73—44no—
122Q8×C73—82no—
123C2×C4×C73—22no—
124C2×C4×C73—21no—
125C2×C4×C73—22no—
126C2×C4×C73—21no—
127C2×C4×C73—41no—
128C2×C4×C73—41no—
129C2×C4×C73—42no—
130C2×C4×C73—41no—
131C2×C4×C73—42no—
132C2×C4×C73—41no—
133C2×C4×C73—82no—
134C2×C4×C73#12011yescharacteristic
135C2×C4×C73#12011yescharacteristic
136C2×C4×C73#12111yescharacteristic
137C2×C4×C73#12111yescharacteristic
138C2×C4×C73#12111yescharacteristic
139C2×C4×C73#12711yescharacteristic
140C2×Dic73—41no—
141C2×Dic73—41no—
142C2×Dic73—42no—
143C2×Dic73—42no—
144C2×Dic73—41no—
145C2×Dic73—42no—
146C2×Dic73—42no—
147C2×Dic73—41no—
148C8×C73—42no—
149#10596831—24no—
150#10596831—42no—
151C22×C73#39211yescharacteristic
152C22×C73#45412yes—
153C22×C73#45511yescharacteristic
154C22×C73#45611yescharacteristic
155C22×C73#45612yes—
156C4×C73—21no—
157C4×C73—21no—
158C4×C73—21no—
159C4×C73—21no—
160C4×C73—21no—
161C4×C73—21no—
162C4×C73—82no—
163C4×C73—81no—
164C4×C73—81no—
165Dic73—82no—
166Dic73—81no—
167Dic73—81no—
168#10084—731nomaximal, Sylow
169C2×C73#166312yes—
170C2×C73#166412yes—
171C2×C73#200311yescharacteristic
172C2×C73#200511yescharacteristic
173C2×C73#200711yescharacteristic
174C2×#501—731no—
175C2×#491D7311yescharacteristic
176#2822—731no—
177#1993—731no—
178C2×#330—731no—
179C2×#330—731no—
180#1295—731no—
181C73#1008411yescharacteristic, complemented, Sylow
182C2×C4⋊Q8C2×D7311yescharacteristic
183C2×#125—731no—
184C2×#125C2×D7311yescharacteristic
185#501—1462no—
186#501—1462no—
187#491—22no—
188#491—22no—
189C2×#107—1461no—
190C2×#106—1461no—
191C2×#103—21no—
192C2×#103—21no—
193C2×#97—731no—
194C2×#97—731no—
195C2×#97C2×D7311yescharacteristic
196#400—1461no—
197#400—1461no—
198#398—1461no—
199#398—1462no—
200#398—1461no—
201#382—731no—
202#340—1462no—
203#330—1462no—
204#330—1462no—
205C22×Q8—21no—
206C22×C8—21no—
207C22×C8—1461no—
208C22×C8—1461no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8C22⋊D7312yes—
213#125—21no—
214#125—21no—
215#125—21no—
216#125—21no—
217#125—1461no—
218#125—1461no—
219#125—1461no—
220#125—1461no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—732no—
226C2×C4⋊C4—731no—
227C2×C4⋊C4—731no—
228C2×C4⋊C4—1461no—
229C2×C4⋊C4—1461no—
230C2×C4⋊C4—1462no—
231C2×C4⋊C4C22⋊D7311yescharacteristic
232C2×C4⋊C4C22⋊D7311yescharacteristic
233C2×C42C22×D7311yescharacteristic
234#107—1464no—
235#106—1464no—
236#103—24no—
237#103—24no—
238#97—21no—
239#97—732no—
240#97—1461no—
241#97—1461no—
242#97—1461no—
243#97C22⋊D7312yes—
244#95—1462no—
245#95—1462no—
246#95—1462no—
247#95—1461no—
248#95—1461no—
249C2×Q8—22no—
250C2×Q8—44no—
251C2×Q8—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—1462no—
256C22×C4—1461no—
257C22×C4—1461no—
258C22×C4D4×D7311yescharacteristic
259C22×C4D4×D7311yescharacteristic
260C22×C4C2×C22⋊D7311yescharacteristic
261C2×C8—22no—
262C2×C8—42no—
263C2×C8—2921no—
264C2×C8—2921no—
265C2×C8—1462no—
266C2×C8—1464no—
267C2×C8—1462no—
268C4⋊C4—22no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—2922no—
281C4⋊C4—2921no—
282C4⋊C4—2921no—
283C4⋊C4—2921no—
284C4⋊C4—2921no—
285C4⋊C4—5842no—
286C4⋊C4—1461no—
287C4⋊C4—1461no—
288C4⋊C4—1461no—
289C4⋊C4—1461no—
290C42D4×D7311yescharacteristic
291C42C2×C22⋊D7311yescharacteristic
292C42C2×C22⋊D7311yescharacteristic
293C42#1192402711yescharacteristic
294C23#1455655911yescharacteristic
295Q8—44no—
296Q8—82no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—82no—
308C2×C4—2921no—
309C2×C4—2921no—
310C2×C4—2922no—
311C2×C4—2922no—
312C2×C4—2922no—
313C2×C4—2921no—
314C2×C4—2921no—
315C2×C4—2922no—
316C2×C4#1455655911yescharacteristic
317C2×C4#1455656011yescharacteristic
318C2×C4#1455656211yescharacteristic
319C2×C4#1455656311yescharacteristic
320C2×C4#1455656311yescharacteristic
321C2×C4#1455658711yescharacteristic
322C8—42no—
323C8—2922no—
324C8—1464no—
325C22#1798849511yescharacteristic
326C22#1798875912yes—
327C22#1798876311yescharacteristic
328C22#1798876812yes—
329C22#1798876811yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—82no—
337C4—81no—
338C4—81no—
339C4—5841no—
340C4—5841no—
341C4—5842no—
342C2#2260925712yes—
343C2#2260926212yes—
344C2#2261095311yescharacteristic
345C2#2261096411yescharacteristic
346C2#2261097611yescharacteristic
subgroupG/H
centerC23#14556559
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC2×#491×C73C2
socle, prime radicalC23×C73#120
hypercenterC2×#491D73
hypocenterC73#10084
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
181. C73#10084semidirect

Maximal subgroups

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

subgroupindex
C2×#179889932
#226179982
#226109052
C2×#179883292
C2×#179883282
#226078132
C2×#491×C732
#1008473