Finite Group Databasebeta

← #32996893

Subgroups — #32996893

Order 18688.

376 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 79 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#22615508C211yesmaximal, characteristic
2#22610014C211yesmaximal, characteristic
3#22607962C212yesmaximal, complemented
4#22607938C212yesmaximal, complemented
5C73×#1458C211yesmaximal, characteristic
6C2×C4×Dic146C411yescharacteristic
7#17988551—21no—
8#17988517C2211yescharacteristic
9#17988512C411yescharacteristic
10#17988507C2211yescharacteristic
11#17988499C411yescharacteristic
12#17988475—21no—
13#17988471—21no—
14#17988468—21no—
15#17988460—21no—
16#17988455C411yescharacteristic
17#17988356—21no—
18#17988356C2212yes—
19C2×#117×C73C2211yescharacteristic
20#431×C73—21no—
21#324×C73C2212yes—
22#323×C73—21no—
23C22×Dic146C2×C411yescharacteristic
24C2×#11924012—22no—
25C4×Dic146—41no—
26C4×Dic146—41no—
27C2×C4⋊Dic73C2×C411yescharacteristic
28C2×#11924007—21no—
29C2×#11924007—21no—
30C2×#11924007—21no—
31C2×C22⋊Dic73—21no—
32C2×C22⋊Dic73—21no—
33C2×C4×Dic73—21no—
34C22⋊#10596831—41no—
35C22⋊#10596831—41no—
36#14556498—21no—
37#14556498—21no—
38#14556498—21no—
39#14556498—21no—
40#14556498—21no—
41#14556498—21no—
42#14556498C2×C411yescharacteristic
43#14556498C2×C411yescharacteristic
44C23×C4×C73D411yescharacteristic
45#117×C73—41no—
46#117×C73—41no—
47C2×C4⋊C4×C73D411yescharacteristic
48C2×C4⋊C4×C73C2311yescharacteristic
49C2×C22⋊C4×C73C2×C411yescharacteristic
50C2×C22⋊C4×C73D411yescharacteristic
51C2×C42×C73C2×C411yescharacteristic
52C2×C42×C73D411yescharacteristic
53C4⋊C8×C73—41no—
54C22⋊C8×C73—22no—
55C4×C8×C73—41no—
56C2×Dic146—41no—
57C2×Dic146—42no—
58C22×Dic73—21no—
59C22×Dic73—21no—
60C22×Dic73—21no—
61C22×Dic73—21no—
62#11924012—42no—
63#11924012—42no—
64C2×#10596831—42no—
65C4⋊Dic73—41no—
66#11924007—42no—
67#11924007—41no—
68#11924007—41no—
69#11924007—42no—
70C22⋊Dic73—42no—
71C22⋊Dic73—42no—
72C4×Dic73—42no—
73C24×C73C22⋊C411yescharacteristic
74C22×C4×C73—21no—
75C22×C4×C73—21no—
76C22×C4×C73—22no—
77C22×C4×C73—41no—
78C22×C4×C73C22⋊C411yescharacteristic
79C22×C4×C73C22⋊C411yescharacteristic
80C22×C4×C73C22⋊C411yescharacteristic
81C22×C4×C73C22×C411yescharacteristic
82C22×C4×C73C2×D411yescharacteristic
83C22×C4×C73C2×D411yescharacteristic
84C2×C8×C73—42no—
85C4⋊C4×C73—41no—
86C4⋊C4×C73—41no—
87C22⋊C4×C73—41no—
88C22⋊C4×C73—41no—
89C42×C73—21no—
90C42×C73—21no—
91C42×C73—21no—
92C42×C73—21no—
93C23×C73—21no—
94C23×C73—21no—
95C23×C73—21no—
96C23×C73—41no—
97C23×C73—41no—
98C23×C73C2×C22⋊C411yescharacteristic
99C2×C4×C73—21no—
100C2×C4×C73—21no—
101C2×C4×C73—21no—
102C2×C4×C73—21no—
103C2×C4×C73—21no—
104C2×C4×C73—21no—
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—42no—
108C2×C4×C73—42no—
109C2×C4×C73—41no—
110C2×C4×C73—41no—
111C2×C4×C73—41no—
112C2×C4×C73—41no—
113C2×C4×C73#9911yescharacteristic
114C2×C4×C73#9911yescharacteristic
115C2×C4×C73#13512yes—
116C2×Dic73—22no—
117C2×Dic73—41no—
118C2×Dic73—41no—
119C2×Dic73—41no—
120C2×Dic73—41no—
121C2×Dic73—41no—
122C2×Dic73—41no—
123C2×Dic73—41no—
124C2×Dic73—41no—
125C2×Dic73—41no—
126C2×Dic73—41no—
127C2×Dic73—41no—
128Dic146—42no—
129Dic146—42no—
130C8×C73—82no—
131#10596831—82no—
132C22×C73—21no—
133C22×C73—21no—
134C22×C73—42no—
135C22×C73—41no—
136C22×C73—41no—
137C22×C73—41no—
138C22×C73—81no—
139C22×C73C2×#9911yescharacteristic
140C22×C73#41611yescharacteristic
141C22×C73#42111yescharacteristic
142C4×C73—22no—
143C4×C73—21no—
144C4×C73—21no—
145C4×C73—41no—
146C4×C73—41no—
147C4×C73—41no—
148C4×C73—41no—
149Dic73—42no—
150Dic73—81no—
151Dic73—81no—
152Dic73—81no—
153#11849—731nomaximal, Sylow
154C2×C73—21no—
155C2×C73—21no—
156C2×C73—81no—
157C2×C73#151611yescharacteristic
158C2×C73#212011yescharacteristic
159C2×C73#213511yescharacteristic
160#2599—731no—
161#1822—731no—
162#1458D7311yescharacteristic
163#1354—732no—
164#1346—732no—
165C73#1184911yescharacteristic, complemented, Sylow
166C2×C4×Q8—731no—
167C2×#117C2×D7311yescharacteristic
168#431—21no—
169#407—1461no—
170#398—731no—
171#397—731no—
172#395—731no—
173#393—731no—
174#388—1461no—
175#387—1461no—
176#387—1461no—
177#385—1461no—
178#383—731no—
179#343—732no—
180#343—1461no—
181#324C2×D7312yes—
182#323—21no—
183C22×Q8—731no—
184C23×C4D29211yescharacteristic
185C2×M16—1462no—
186C4×Q8—2921no—
187C4×Q8—2921no—
188#117—41no—
189#117—41no—
190C2×C4⋊C4—731no—
191C2×C4⋊C4—1461no—
192C2×C4⋊C4—1461no—
193C2×C4⋊C4—1461no—
194C2×C4⋊C4D29211yescharacteristic
195C2×C4⋊C4C22×D7311yescharacteristic
196C2×C22⋊C4—1461no—
197C2×C22⋊C4—1461no—
198C2×C22⋊C4C4×D7311yescharacteristic
199C2×C22⋊C4C22⋊D7311yescharacteristic
200C2×C42—1461no—
201C2×C42C4×D7311yescharacteristic
202C2×C42C22⋊D7311yescharacteristic
203C4⋊C8—41no—
204C22⋊C8—22no—
205C22⋊C8—2921no—
206C22⋊C8—2921no—
207C4×C8—41no—
208#95—731no—
209#95—731no—
210#95—1461no—
211#95—1461no—
212#95—1461no—
213#95—1461no—
214#95—1461no—
215#95—1461no—
216C24#1192400511yescharacteristic
217C2×Q8—2921no—
218C2×Q8—2922no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—22no—
222C22×C4—41no—
223C22×C4—1461no—
224C22×C4—1461no—
225C22×C4—1461no—
226C22×C4—1461no—
227C22×C4#1192400511yescharacteristic
228C22×C4#1192400511yescharacteristic
229C22×C4#1192400511yescharacteristic
230C22×C4C2×C4×D7311yescharacteristic
231C22×C4C2×C22⋊D7311yescharacteristic
232C22×C4C2×D29211yescharacteristic
233M16—2922no—
234M16—2922no—
235C2×C8—42no—
236C2×C8—2922no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—2921no—
240C4⋊C4—2922no—
241C4⋊C4—2921no—
242C4⋊C4—2921no—
243C4⋊C4—2922no—
244C22⋊C4—41no—
245C22⋊C4—41no—
246C22⋊C4—2922no—
247C22⋊C4—2922no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—2922no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23C2×#1192400511yescharacteristic
259Q8—2922no—
260Q8—2922no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—2921no—
276C2×C4—2921no—
277C2×C4—2921no—
278C2×C4—2921no—
279C2×C4—2921no—
280C2×C4—2921no—
281C2×C4—2921no—
282C2×C4—2921no—
283C2×C4—2921no—
284C2×C4—2921no—
285C2×C4—2921no—
286C2×C4—1462no—
287C2×C4#1455650511yescharacteristic
288C2×C4#1455650511yescharacteristic
289C2×C4#1455661312yes—
290C8—82no—
291C8—5842no—
292C22—21no—
293C22—21no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—81no—
299C22C2×#1455650511yescharacteristic
300C22#1798858411yescharacteristic
301C22#1798860311yescharacteristic
302C4—22no—
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—2922no—
310C4—5841no—
311C4—5841no—
312C4—5841no—
313C2—21no—
314C2—21no—
315C2—81no—
316C2#2260848811yescharacteristic
317C2#2261157011yescharacteristic
318C2#2261162511yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC2×C4⋊C4C22×D73
FittingC73×#1458C2
socleC22×C73C2×#99
prime radicalC24×C73C22⋊C4
cosocleC2×C4⋊C4×C73C23
hypercenter#1458D73
hypocenterC73#11849
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #22607962C2semidirect
4. #22607938C2semidirect
165. C73#11849semidirect

Maximal subgroups

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

subgroupindex
#226155082
#226100142
#226079622
#226079382
C73×#14582
#1184973