Finite Group Databasebeta

← #34008134

Subgroups — #34008134

Order 18688.

518 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 126 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#22625846C211yesmaximal, characteristic
2C4×#14556646C211yesmaximal, characteristic
3#22624767C212yesmaximal
4#22624767C212yesmaximal
5#22612502C211yesmaximal, characteristic
6C2×C4⋊#10596833C2212yes—
7C2×#14556646—21no—
8C2×#14556646—21no—
9C2×C4×#10596833C2212yes—
10#17989453—21no—
11#17989453—21no—
12C2×#14556590C411yescharacteristic
13C2×#14556556—21no—
14#17988491—21no—
15#17988485C411yescharacteristic
16#17988482—21no—
17#17988456C411yescharacteristic
18C4⋊C4×Dic73C2211yescharacteristic
19C4⋊C4×Dic73C2211yescharacteristic
20#17988438—21no—
21C42×Dic73C2211yescharacteristic
22#389×C73C411yescharacteristic
23C22×#10596833—22no—
24C22×#10596833—22no—
25C4⋊#10596833—24no—
26#14556646—24no—
27#14556646—24no—
28C4×#10596833—22no—
29C4×#10596833Q814yescomplemented
30C22×Dic146—21no—
31#14556590—22no—
32#14556590—22no—
33#14556556—44no—
34C2×C4⋊Dic73C2×C411yescharacteristic
35C2×C4⋊Dic73C2×C411yescharacteristic
36C2×#11924007—21no—
37C2×#11924007—21no—
38C2×#11924007—21no—
39C2×#11924007—21no—
40C2×C4×Dic73—21no—
41C2×C4×Dic73—21no—
42C2×C4×Dic73C2×C411yescharacteristic
43C2×C4×Dic73D411yescharacteristic
44C2×C4×Dic73D411yescharacteristic
45C2×C4×Dic73D411yescharacteristic
46C2×C4×Dic73D411yescharacteristic
47C2×C4×Dic73C2311yescharacteristic
48#14556498—21no—
49#14556498—21no—
50#14556498—21no—
51C2×C4⋊C4×C73—21no—
52C2×C4⋊C4×C73C2×C411yescharacteristic
53C2×C4⋊C4×C73C2×C411yescharacteristic
54C2×C42×C73C2×C411yescharacteristic
55#95×C73—21no—
56C2×#10596833—24no—
57C2×#10596833—24no—
58C2×#10596833—24no—
59C2×#10596833—42no—
60C2×#10596833—42no—
61C2×#10596833—42no—
62C2×Dic146—24no—
63C2×Dic146—42no—
64C2×Dic146—42no—
65C22×Dic73—21no—
66C22×Dic73—21no—
67C22×Dic73C22⋊C411yescharacteristic
68C22×Dic73C22⋊C411yescharacteristic
69C22×Dic73C2×D411yescharacteristic
70C22×Dic73C2×D411yescharacteristic
71C4⋊Dic73—21no—
72C4⋊Dic73—22no—
73C4⋊Dic73M1612yes—
74#11924007—24no—
75#11924007—42no—
76#11924007—42no—
77#11924007—42no—
78C4×Dic73—21no—
79C4×Dic73—21no—
80C4×Dic73—22no—
81C4×Dic73—22no—
82C4×Dic73—22no—
83C4×Dic73—22no—
84C4×Dic73—42no—
85C4×Dic73—42no—
86C4×Dic73C2×Q812yes—
87C4×Dic73#4112yes—
88C22×C4×C73—21no—
89C22×C4×C73—21no—
90C22×C4×C73C22⋊C411yescharacteristic
91C22×C4×C73C22⋊C411yescharacteristic
92C22×C4×C73C22×C411yescharacteristic
93C4⋊C4×C73—21no—
94C4⋊C4×C73—22no—
95C4⋊C4×C73—42no—
96C4⋊C4×C73M1612yes—
97C42×C73—22no—
98C23×C73C2×C22⋊C411yescharacteristic
99C2×C4×C73—22no—
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—41no—
107C2×C4×C73—41no—
108C2×C4×C73—41no—
109C2×C4×C73—41no—
110C2×C4×C73—41no—
111C2×C4×C73C4×Q812yes—
112C2×C4×C73C2×M1611yescharacteristic
113C2×C4×C73C2×M1611yescharacteristic
114C2×C4×C73#13112yes—
115C2×Dic73—21no—
116C2×Dic73—21no—
117C2×Dic73—21no—
118C2×Dic73—21no—
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73—22no—
122C2×Dic73—41no—
123C2×Dic73—41no—
124C2×Dic73—41no—
125C2×Dic73—41no—
126C2×Dic73—41no—
127C2×Dic73#10412yes—
128C2×Dic73#10412yes—
129C2×Dic73C22⋊Q812yes—
130C2×Dic73#12411yescharacteristic
131C2×Dic73C4⋊Q811yescharacteristic
132C2×Dic73AGL(1,ℤ/8)12yes—
133C2×Dic73#13712yes—
134Dic146—48no—
135#10596833—28no—
136#10596833—82no—
137C22×C73#39111yescharacteristic
138C22×C73#40711yescharacteristic
139C22×C73#40811yescharacteristic
140C22×C73#41811yescharacteristic
141C22×C73#41911yescharacteristic
142C22×C73C2×#10411yescharacteristic
143C22×C73C2×#10411yescharacteristic
144C4×C73—41no—
145C4×C73—41no—
146C4×C73—42no—
147C4×C73—81no—
148C4×C73#44612yes—
149C4×C73#44612yes—
150Dic73—22no—
151Dic73—22no—
152Dic73—22no—
153Dic73—42no—
154Dic73—81no—
155Dic73#48912yes—
156Dic73#50112yes—
157#9877—731nomaximal, Sylow
158C2×C73#148411yescharacteristic
159C2×C73#148511yescharacteristic
160C2×C73#149011yescharacteristic
161C2×C73#149111yescharacteristic
162C2×C73#198511yescharacteristic
163C2×C73#199311yescharacteristic
164C2×C73#199411yescharacteristic
165C4×C4⋊Q8—731no—
166#1831—731no—
167C4×#97—731no—
168#1279—732no—
169#1279—732no—
170C73#987711yescharacteristic, complemented, Sylow
171C2×C4⋊Q8—731no—
172C2×C4×Q8—1461no—
173C2×C4⋊C8—732no—
174C2×#97—1461no—
175C2×#97—1461no—
176C2×C4×C8—732no—
177#391—1461no—
178#389—731no—
179#389—1461no—
180#389#6440811yescharacteristic
181#384—731no—
182C4×C4⋊C4—731no—
183C4×C4⋊C4—731no—
184C4×C4⋊C4—1461no—
185C43—731no—
186#336—1461no—
187#336—1461no—
188C22×Q8—1461no—
189C22×C8—1462no—
190C22×C8—1462no—
191C4⋊Q8—1462no—
192C4⋊Q8—1462no—
193C4×Q8—2924no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—731no—
196C2×C4⋊C4—731no—
197C2×C4⋊C4—1461no—
198C2×C4⋊C4—1461no—
199C2×C4⋊C4—1461no—
200C2×C4⋊C4—1461no—
201C2×C4⋊C4C2×#6440811yescharacteristic
202C2×C4⋊C4C2×#6440811yescharacteristic
203C2×C42—731no—
204C2×C42—731no—
205C2×C42—731no—
206C2×C42—731no—
207C2×C42—731no—
208C2×C42—731no—
209C2×C42—1461no—
210C2×C42—1461no—
211C2×C42C2×#6440811yescharacteristic
212C4⋊C8—1464no—
213#97—1464no—
214#97—1464no—
215C4×C8—734no—
216C4×C8—1462no—
217#95—21no—
218#95—1461no—
219#95—1461no—
220#95—1461no—
221C2×Q8—2922no—
222C2×Q8—2922no—
223C2×Q8—1464no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—731no—
227C22×C4—731no—
228C22×C4—731no—
229C22×C4—731no—
230C22×C4—1461no—
231C22×C4—1461no—
232C22×C4C22⋊#6440811yescharacteristic
233C22×C4C22⋊#6440811yescharacteristic
234C22×C4C22×#6440811yescharacteristic
235C2×C8—2922no—
236C2×C8—2922no—
237C2×C8—2922no—
238C2×C8—1464no—
239C2×C8—1464no—
240C2×C8—1464no—
241C4⋊C4—21no—
242C4⋊C4—22no—
243C4⋊C4—42no—
244C4⋊C4—2922no—
245C4⋊C4—2922no—
246C4⋊C4—2922no—
247C4⋊C4—732no—
248C4⋊C4—1464no—
249C4⋊C4—1462no—
250C4⋊C4—1461no—
251C4⋊C4#1192403812yes—
252C42—22no—
253C42—2922no—
254C42—2922no—
255C42—732no—
256C42—732no—
257C42—1462no—
258C42—1462no—
259C42—1462no—
260C42—1462no—
261C42—1461no—
262C42—1461no—
263C23C2×C22⋊#6440811yescharacteristic
264Q8—2928no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—2921no—
278C2×C4—2921no—
279C2×C4—2921no—
280C2×C4—2921no—
281C2×C4—2921no—
282C2×C4—731no—
283C2×C4—731no—
284C2×C4—732no—
285C2×C4—732no—
286C2×C4—732no—
287C2×C4—732no—
288C2×C4—732no—
289C2×C4—1462no—
290C2×C4—1461no—
291C2×C4—1461no—
292C2×C4—1461no—
293C2×C4—1461no—
294C2×C4—1461no—
295C2×C4—1461no—
296C2×C4Q8×#6440812yes—
297C2×C4D73⋊M1611yescharacteristic
298C2×C4C2×#1192403811yescharacteristic
299C2×C4#1455667812yes—
300C8—5842no—
301C8—1468no—
302C22(C2×#64408)⋊Q811yescharacteristic
303C22#1798955811yescharacteristic
304C22#1798956011yescharacteristic
305C22#1798957911yescharacteristic
306C22#1798958011yescharacteristic
307C22D73⋊#10411yescharacteristic
308C22D73⋊#10411yescharacteristic
309C4—41no—
310C4—41no—
311C4—42no—
312C4—81no—
313C4—2922no—
314C4—5841no—
315C4—732no—
316C4—732no—
317C4—1462no—
318C4—1462no—
319C4—1462no—
320C4#1798963712yes—
321C4#1798963912yes—
322C2#2262525011yescharacteristic
323C2#2262525311yescharacteristic
324C2#2262527111yescharacteristic
325C2#2262527411yescharacteristic
326C2#2262610411yescharacteristic
327C2#2262611511yescharacteristic
328C2#2262611711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
Fitting#389×C73C4
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4×Dic73C23
hypercenter#389#64408
hypocenterC73#9877
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
29. C4×#10596833Q8semidirect
170. C73#9877semidirect

Maximal subgroups

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

subgroupindex
#226258462
C4×#145566462
#226247672
#226125022
#987773