Finite Group Databasebeta

← #32996725

Subgroups — #32996725

Order 18688.

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

normal subgroups only

This group has 388 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#22613199C211yesmaximal, characteristic
2#22608265C211yesmaximal, characteristic
3#22607960C212yesmaximal, complemented
4#22607957C212yesmaximal, complemented
5C73×#1822C211yesmaximal, characteristic
6C2×C4×Dic146C411yescharacteristic
7#17988644—21no—
8#17988526C2211yescharacteristic
9#17988523C411yescharacteristic
10#17988520—21no—
11#17988510—21no—
12#17988507C2211yescharacteristic
13#17988499C411yescharacteristic
14C4×#11924007—21no—
15C4×C4⋊Dic73C411yescharacteristic
16C4×C22⋊Dic73—21no—
17#17988313C2212yes—
18#17988311—21no—
19C2×#117×C73C2211yescharacteristic
20#407×C73—21no—
21#343×C73—21no—
22#343×C73C2212yes—
23C22×Dic146C2×C411yescharacteristic
24C4×Dic146—41no—
25C4×Dic146—41no—
26C2×C4⋊Dic73—21no—
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—
34C2×C4×Dic73—21no—
35C4⋊#10596831—41no—
36C22⋊#10596831—22no—
37#14556502—41no—
38#14556498—21no—
39#14556498—21no—
40#14556498—21no—
41#14556498—21no—
42#14556498C2×C411yescharacteristic
43#14556498C2×C411yescharacteristic
44C23×C4×C73D411yescharacteristic
45C2×M16×C73—22no—
46#117×C73—41no—
47#117×C73—41no—
48C2×C4⋊C4×C73D411yescharacteristic
49C2×C4⋊C4×C73C2311yescharacteristic
50C2×C22⋊C4×C73C2×C411yescharacteristic
51C2×C22⋊C4×C73D411yescharacteristic
52C2×C42×C73C2×C411yescharacteristic
53C2×C42×C73D411yescharacteristic
54C22⋊C8×C73—41no—
55C22⋊C8×C73—41no—
56C2×Dic146—41no—
57C2×Dic146—42no—
58C22×Dic73—21no—
59C22×Dic73—21no—
60C22×Dic73—21no—
61C22×Dic73—21no—
62C2×#10596831—42no—
63C4⋊Dic73—42no—
64C4⋊Dic73—41no—
65#11924007—42no—
66#11924007—42no—
67#11924007—42no—
68C22⋊Dic73—42no—
69C22⋊Dic73—42no—
70C4×Dic73—42no—
71C4×Dic73—41no—
72C4×Dic73—41no—
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
84M16×C73—42no—
85M16×C73—42no—
86C2×C8×C73—42no—
87C4⋊C4×C73—41no—
88C4⋊C4×C73—41no—
89C22⋊C4×C73—41no—
90C22⋊C4×C73—41no—
91C42×C73—21no—
92C42×C73—21no—
93C42×C73—21no—
94C42×C73—21no—
95C23×C73—21no—
96C23×C73—21no—
97C23×C73—21no—
98C23×C73—41no—
99C23×C73—41no—
100C23×C73C2×C22⋊C411yescharacteristic
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—21no—
108C2×C4×C73—21no—
109C2×C4×C73—42no—
110C2×C4×C73—42no—
111C2×C4×C73—41no—
112C2×C4×C73—41no—
113C2×C4×C73—41no—
114C2×C4×C73—41no—
115C2×C4×C73#9911yescharacteristic
116C2×C4×C73#9911yescharacteristic
117C2×C4×C73#13712yes—
118C2×Dic73—22no—
119C2×Dic73—22no—
120C2×Dic73—41no—
121C2×Dic73—41no—
122C2×Dic73—41no—
123C2×Dic73—41no—
124C2×Dic73—41no—
125C2×Dic73—41no—
126C2×Dic73—41no—
127C2×Dic73—41no—
128C2×Dic73—41no—
129C2×Dic73—41no—
130Dic146—42no—
131Dic146—42no—
132C8×C73—82no—
133#10596831—82no—
134C22×C73—21no—
135C22×C73—21no—
136C22×C73—42no—
137C22×C73—41no—
138C22×C73—41no—
139C22×C73—41no—
140C22×C73—81no—
141C22×C73C2×#9911yescharacteristic
142C22×C73#41911yescharacteristic
143C22×C73#42111yescharacteristic
144C4×C73—22no—
145C4×C73—21no—
146C4×C73—21no—
147C4×C73—41no—
148C4×C73—41no—
149C4×C73—41no—
150C4×C73—41no—
151Dic73—42no—
152Dic73—42no—
153Dic73—81no—
154Dic73—81no—
155#11816—731nomaximal, Sylow
156C2×C73—21no—
157C2×C73—21no—
158C2×C73—81no—
159C2×C73#151111yescharacteristic
160C2×C73#212011yescharacteristic
161C2×C73#213211yescharacteristic
162#2396—731no—
163#1822D7311yescharacteristic
164#1464—731no—
165#1354—732no—
166#1353—732no—
167C73#1181611yescharacteristic, complemented, Sylow
168C2×C4×Q8—731no—
169C2×#117C2×D7311yescharacteristic
170#432—1461no—
171#407—21no—
172#400—731no—
173#399—731no—
174#398—1461no—
175#396—1461no—
176#395—731no—
177#393—731no—
178C4×C4⋊C4—731no—
179C4×C4⋊C4—1461no—
180C4×C22⋊C4—1461no—
181#343—21no—
182#343C2×D7312yes—
183#324—732no—
184#323—1461no—
185C22×Q8—731no—
186C23×C4C22⋊D7311yescharacteristic
187C2×M16—22no—
188C4×Q8—2921no—
189C4×Q8—2921no—
190#117—41no—
191#117—41no—
192C2×C4⋊C4—731no—
193C2×C4⋊C4—1461no—
194C2×C4⋊C4—1461no—
195C2×C4⋊C4—1461no—
196C2×C4⋊C4—1461no—
197C2×C4⋊C4C22⋊D7311yescharacteristic
198C2×C4⋊C4C22×D7311yescharacteristic
199C2×C22⋊C4—1461no—
200C2×C22⋊C4—1461no—
201C2×C22⋊C4C4×D7311yescharacteristic
202C2×C22⋊C4D29211yescharacteristic
203C2×C42—1461no—
204C2×C42—1461no—
205C2×C42C4×D7311yescharacteristic
206C2×C42D29211yescharacteristic
207C4⋊C8—2921no—
208C22⋊C8—41no—
209C22⋊C8—41no—
210C22⋊C8—1462no—
211#97—2921no—
212#95—731no—
213#95—731no—
214#95—1461no—
215#95—1461no—
216#95—1461no—
217#95—1461no—
218C24#1192400511yescharacteristic
219C2×Q8—2921no—
220C2×Q8—2922no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—41no—
225C22×C4—1461no—
226C22×C4—1461no—
227C22×C4—1461no—
228C22×C4—1461no—
229C22×C4#1192400511yescharacteristic
230C22×C4#1192400511yescharacteristic
231C22×C4#1192400511yescharacteristic
232C22×C4C2×C4×D7311yescharacteristic
233C22×C4C2×C22⋊D7311yescharacteristic
234C22×C4C2×D29211yescharacteristic
235M16—42no—
236M16—42no—
237C2×C8—42no—
238C2×C8—2922no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—2921no—
242C4⋊C4—2922no—
243C4⋊C4—2922no—
244C4⋊C4—2922no—
245C4⋊C4—2922no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—2922no—
249C22⋊C4—2922no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—2922no—
255C42—2921no—
256C42—2921no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23—41no—
261C23—41no—
262C23C2×#1192400511yescharacteristic
263Q8—2922no—
264Q8—2922no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—2921no—
280C2×C4—2921no—
281C2×C4—2921no—
282C2×C4—2921no—
283C2×C4—2921no—
284C2×C4—2921no—
285C2×C4—2921no—
286C2×C4—2921no—
287C2×C4—2921no—
288C2×C4—2921no—
289C2×C4—1462no—
290C2×C4—1462no—
291C2×C4#1455650511yescharacteristic
292C2×C4#1455650511yescharacteristic
293C2×C4#1455662112yes—
294C8—82no—
295C8—5842no—
296C22—21no—
297C22—21no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C2×#1455650511yescharacteristic
304C22#1798859511yescharacteristic
305C22#1798860511yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—2922no—
314C4—2922no—
315C4—5841no—
316C4—5841no—
317C2—21no—
318C2—21no—
319C2—81no—
320C2#2260846311yescharacteristic
321C2#2261157311yescharacteristic
322C2#2261161411yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC2×C4⋊C4C22×D73
FittingC73×#1822C2
socleC22×C73C2×#99
prime radicalC24×C73C22⋊C4
cosocleC2×C4⋊C4×C73C23
hypercenter#1822D73
hypocenterC73#11816
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1822

Complements

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

NH ≅ G/Ntype
3. #22607960C2semidirect
4. #22607957C2semidirect
167. C73#11816semidirect

Maximal subgroups

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

subgroupindex
#226131992
#226082652
#226079602
#226079572
C73×#18222
#1181673