Finite Group Databasebeta

← #32998908

Subgroups — #32998908

Order 18688.

324 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 59 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#22611276C211yesmaximal, characteristic
2#22608972C211yesmaximal, characteristic
3#22608938C211yesmaximal, characteristic
4#22607958C211yesmaximal, characteristic
5#22607937C211yesmaximal, characteristic
6#22607877C211yesmaximal, characteristic
7C73×#2794C211yesmaximal, characteristic
8#17989218C2211yescharacteristic
9#17988922—21no—
10#17988917—21no—
11#17988627—21no—
12#17988356C2211yescharacteristic
13#17988347—21no—
14#17988323—21no—
15#17988323—21no—
16#17988313C2211yescharacteristic
17#17988313C2211yescharacteristic
18#400×C73—21no—
19#400×C73—21no—
20#400×C73C2211yescharacteristic
21#398×C73C2211yescharacteristic
22#387×C73—21no—
23#387×C73—21no—
24#387×C73—21no—
25#387×C73—21no—
26#384×C73C2211yescharacteristic
27C2×#11924012—21no—
28#14556590—41no—
29#14556582—41no—
30#14556570—21no—
31#14556570—21no—
32#14556550—21no—
33#14556524—41no—
34#14556524—41no—
35#14556522—41no—
36#14556522—41no—
37#14556514—41no—
38#14556514—41no—
39C22⋊#10596831—21no—
40C22⋊#10596831—21no—
41C2×C4⋊C4×C73—21no—
42C2×C4⋊C4×C73—21no—
43C2×C4⋊C4×C73—21no—
44C2×C4⋊C4×C73—21no—
45C2×C4⋊C4×C73D411yescharacteristic
46C2×C4⋊C4×C73D411yescharacteristic
47C2×C4⋊C4×C73D411yescharacteristic
48C2×C4⋊C4×C73C2311yescharacteristic
49C2×C42×C73—21no—
50C2×C42×C73D411yescharacteristic
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—
58#95×C73—21no—
59#95×C73—21no—
60#95×C73D411yescharacteristic
61#95×C73D411yescharacteristic
62C2×Dic146—21no—
63C2×Dic146—21no—
64#11924012—22no—
65#11924012—41no—
66C2×#10596831—41no—
67C2×#10596831—41no—
68C2×#10596831—41no—
69C4⋊Dic73—21no—
70C4⋊Dic73—21no—
71C4⋊Dic73—21no—
72C4⋊Dic73—21no—
73#11924007—41no—
74#11924007—41no—
75C22⋊Dic73—41no—
76C4×Dic73—41no—
77C22×C4×C73—21no—
78C22×C4×C73—21no—
79C22×C4×C73—21no—
80C22×C4×C73—21no—
81C22×C4×C73—21no—
82C22×C4×C73—21no—
83C22×C4×C73C2×D411yescharacteristic
84C22×C4×C73C2×D411yescharacteristic
85C22×C4×C73C2×D411yescharacteristic
86C4⋊C4×C73—41no—
87C4⋊C4×C73—41no—
88C4⋊C4×C73—41no—
89C4⋊C4×C73—41no—
90C4⋊C4×C73—42no—
91C4⋊C4×C73—42no—
92C4⋊C4×C73—42no—
93C4⋊C4×C73—41no—
94C4⋊C4×C73—41no—
95C42×C73—21no—
96C42×C73—21no—
97C42×C73—81no—
98C23×C73#12011yescharacteristic
99C2×C4×C73—21no—
100C2×C4×C73—21no—
101C2×C4×C73—22no—
102C2×C4×C73—21no—
103C2×C4×C73—21no—
104C2×C4×C73—41no—
105C2×C4×C73—41no—
106C2×C4×C73—41no—
107C2×C4×C73—41no—
108C2×C4×C73—41no—
109C2×C4×C73—41no—
110C2×C4×C73—41no—
111C2×C4×C73—41no—
112C2×C4×C73—41no—
113C2×C4×C73—41no—
114C2×C4×C73—42no—
115C2×C4×C73—41no—
116C2×C4×C73—41no—
117C2×C4×C73—41no—
118C2×C4×C73—41no—
119C2×C4×C73—41no—
120C2×C4×C73—41no—
121C2×C4×C73—41no—
122C2×C4×C73#13511yescharacteristic
123C2×C4×C73#13711yescharacteristic
124C2×Dic73—41no—
125C2×Dic73—41no—
126Dic146—81no—
127Dic146—81no—
128#10596831—42no—
129#10596831—81no—
130#10596831—81no—
131C22×C73—21no—
132C22×C73—21no—
133C22×C73#45211yescharacteristic
134C22×C73#45611yescharacteristic
135C22×C73B(4,𝔽2)11yescharacteristic
136C4×C73—21no—
137C4×C73—21no—
138C4×C73—42no—
139C4×C73—41no—
140C4×C73—41no—
141C4×C73—81no—
142C4×C73—81no—
143C4×C73—81no—
144C4×C73—81no—
145C4×C73—81no—
146Dic73—81no—
147Dic73—81no—
148#12236—731nomaximal, Sylow
149C2×C73—21no—
150C2×C73—21no—
151C2×C73#160311yescharacteristic
152C2×C73#219811yescharacteristic
153C2×C73#220311yescharacteristic
154#2794D7311yescharacteristic
155#2060—731no—
156#1617—731no—
157#1611—731no—
158#1353—731no—
159#1346—731no—
160#1325—731no—
161C73#1223611yescharacteristic, complemented, Sylow
162#544—731no—
163#484—1461no—
164#483—1461no—
165#428—1461no—
166#400—21no—
167#400—21no—
168#400C2×D7311yescharacteristic
169#398C2×D7311yescharacteristic
170#387—21no—
171#387—21no—
172#387—21no—
173#387—21no—
174#384C2×D7311yescharacteristic
175#343—731no—
176#339—1461no—
177#328—1461no—
178#328—1461no—
179#324—731no—
180#324—731no—
181C2×M16—1461no—
182C4⋊Q8—2921no—
183#125—2921no—
184C22⋊Q8—1461no—
185C22⋊Q8—1461no—
186#117—1461no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4C22⋊D7311yescharacteristic
192C2×C4⋊C4C22⋊D7311yescharacteristic
193C2×C4⋊C4C22⋊D7311yescharacteristic
194C2×C4⋊C4C22×D7311yescharacteristic
195C2×C42—21no—
196C2×C42C22⋊D7311yescharacteristic
197#107—2921no—
198#107—2921no—
199#106—2921no—
200#106—2921no—
201#103—2921no—
202#103—2921no—
203C22⋊C8—1461no—
204C22⋊C8—1461no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95C22⋊D7311yescharacteristic
215#95C22⋊D7311yescharacteristic
216C2×Q8—1461no—
217C2×Q8—1461no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4C2×C22⋊D7311yescharacteristic
225C22×C4C2×C22⋊D7311yescharacteristic
226C22×C4C2×C22⋊D7311yescharacteristic
227M16—2921no—
228M16—1462no—
229C2×C8—2921no—
230C2×C8—2921no—
231C2×C8—2921no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—2921no—
242C4⋊C4—2921no—
243C4⋊C4—1461no—
244C4⋊C4—1461no—
245C4⋊C4—1461no—
246C4⋊C4—1461no—
247C22⋊C4—2921no—
248C42—21no—
249C42—21no—
250C42—81no—
251C42—2921no—
252C23#1455656011yescharacteristic
253Q8—5841no—
254Q8—5841no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—2921no—
279C2×C4—2921no—
280C2×C4#1455661111yescharacteristic
281C2×C4#1455662111yescharacteristic
282C8—2922no—
283C8—5841no—
284C8—5841no—
285C22—21no—
286C22—21no—
287C22#1798874911yescharacteristic
288C22#1798877011yescharacteristic
289C22#1798877411yescharacteristic
290C4—21no—
291C4—21no—
292C4—42no—
293C4—41no—
294C4—41no—
295C4—81no—
296C4—81no—
297C4—81no—
298C4—81no—
299C4—81no—
300C4—5841no—
301C4—5841no—
302C2—21no—
303C2—21no—
304C2#2260889411yescharacteristic
305C2#2261192711yescharacteristic
306C2#2261195211yescharacteristic
subgroupG/H
centerC22#17988774
commutator, cosocleC2×C4⋊C4×C73C23
FrattiniC2×C4⋊C4C22×D73
FittingC73×#2794C2
socleC22×C73B(4,𝔽2)
prime radicalC23×C73#120
hypercenter#2794D73
hypocenterC73#12236
LCSG ▷ C2×C4⋊C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2794

Complements

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

NH ≅ G/Ntype
161. C73#12236semidirect

Maximal subgroups

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

subgroupindex
#226112762
#226089722
#226089382
#226079582
#226079372
#226078772
C73×#27942
#1223673