Finite Group Databasebeta

← #34007592

Subgroups — #34007592

Order 18688.

530 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 134 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#22625848C211yesmaximal, characteristic
2#22625645C211yesmaximal, characteristic
3C2×#17989437C212yesmaximal
4C2×Q8⋊#10596833C212yesmaximal
5#22612500C211yesmaximal, characteristic
6C2×C4⋊#10596833C2212yes—
7C2×C4×#10596833C2212yes—
8#17989453—22no—
9#17989453—22no—
10#17989437—24no—
11Q8⋊#10596833—24no—
12C2×#14556589C411yescharacteristic
13C2×Q8×Dic73C2211yescharacteristic
14C2×#14556556C2211yescharacteristic
15#17988493C411yescharacteristic
16#17988484—22no—
17#17988456C411yescharacteristic
18#17988438—22no—
19C42×Dic73C2211yescharacteristic
20#391×C73C411yescharacteristic
21C22×#10596833—22no—
22C22×#10596833—22no—
23C4⋊#10596833—22no—
24C4⋊#10596833—22no—
25C4×#10596833—22no—
26C4×#10596833D414yes—
27C22×Dic146C2×C411yescharacteristic
28#14556589—22no—
29#14556589C814yescomplemented
30Q8×Dic73—22no—
31Q8×Dic73—22no—
32#14556556—22no—
33#14556556—22no—
34C2×C4⋊Dic73—21no—
35C2×C4⋊Dic73C2×C411yescharacteristic
36C2×#11924007—22no—
37C2×#11924007—22no—
38C2×#11924007—21no—
39C2×C4×Dic73—21no—
40C2×C4×Dic73—21no—
41C2×C4×Dic73C2×C411yescharacteristic
42C2×C4×Dic73D412yes—
43C2×C4×Dic73D412yes—
44C2×C4×Dic73C2311yescharacteristic
45#14556498—22no—
46C22×Q8×C73C2×C411yescharacteristic
47C2×C4⋊C4×C73C2×C411yescharacteristic
48C2×C42×C73C2×C411yescharacteristic
49#95×C73—22no—
50C2×#10596833—24no—
51C2×#10596833—44no—
52C2×#10596833—42no—
53C2×#10596833—44no—
54C2×Dic146—22no—
55C2×Dic146—22no—
56C2×Dic146—21no—
57C2×Dic146C2×C812yes—
58C22×Dic73—21no—
59C22×Dic73—21no—
60C22×Dic73C22⋊C412yes—
61C22×Dic73C2×D411yescharacteristic
62C22×Dic73C2×D411yescharacteristic
63C4⋊Dic73—22no—
64C4⋊Dic73—42no—
65#11924007—28no—
66#11924007—44no—
67#11924007—42no—
68C4×Dic73—24no—
69C4×Dic73—42no—
70C4×Dic73—41no—
71C4×Dic73—41no—
72C4×Dic73—41no—
73C4×Dic73—41no—
74C4×Dic73C2×C812yes—
75C4×Dic73M1612yes—
76C4×Dic73C2×D412yes—
77C4×Dic73#4112yes—
78C2×Q8×C73—21no—
79C2×Q8×C73—22no—
80C2×Q8×C73—22no—
81C2×Q8×C73C2×C812yes—
82C22×C4×C73—21no—
83C22×C4×C73—21no—
84C22×C4×C73C22⋊C412yes—
85C22×C4×C73C22×C411yescharacteristic
86C4⋊C4×C73—22no—
87C42×C73—22no—
88C23×C73C2×C22⋊C411yescharacteristic
89Q8×C73—24no—
90Q8×C73—42no—
91C2×C4×C73—22no—
92C2×C4×C73—22no—
93C2×C4×C73—22no—
94C2×C4×C73—22no—
95C2×C4×C73—41no—
96C2×C4×C73—41no—
97C2×C4×C73—41no—
98C2×C4×C73—42no—
99C2×C4×C73C4×D412yes—
100C2×C4×C73C22×C811yescharacteristic
101C2×C4×C73C2×M1611yescharacteristic
102C2×C4×C73#13112yes—
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73—41no—
108C2×Dic73—41no—
109C2×Dic73—41no—
110C2×Dic73—42no—
111C2×Dic73C22⋊C814yes—
112C2×Dic73#12112yes—
113C2×Dic73#12411yescharacteristic
114C2×Dic73#12711yescharacteristic
115C2×Dic73#13714yes—
116Dic146—24no—
117Dic146—42no—
118#10596833—44no—
119#10596833—82no—
120C22×C73#39011yescharacteristic
121C22×C73C2×C22⋊C811yescharacteristic
122C22×C73#40811yescharacteristic
123C22×C73#41912yes—
124C22×C73#42112yes—
125C4×C73—42no—
126C4×C73—42no—
127C4×C73—81no—
128C4×C73C8×D412yes—
129C4×C73#43612yes—
130Dic73—22no—
131Dic73—24no—
132Dic73—42no—
133Dic73—81no—
134Dic73#49112yes—
135Dic73#49712yes—
136#9641—731nomaximal, Sylow
137C2×C73#147912yes—
138C2×C73#149712yes—
139C2×C73#195411yescharacteristic
140C2×C73#196011yescharacteristic
141C2×C73#196311yescharacteristic
142C4×C4⋊Q8—731no—
143#1831—731no—
144#1744—731no—
145C2×Q8⋊C8—732no—
146C2×Q8⋊C8—732no—
147C73#964111yescharacteristic, complemented, Sylow
148C2×C4⋊Q8—731no—
149C2×C4×Q8—731no—
150C2×C4×Q8—731no—
151C2×C4⋊C8—732no—
152C2×C4×C8—732no—
153#391—731no—
154#391#6440811yescharacteristic
155#389—1462no—
156#384—731no—
157C4×C4⋊C4—1462no—
158C43—731no—
159#336—1462no—
160#336—1462no—
161Q8⋊C8—1464no—
162Q8⋊C8—1464no—
163C22×Q8—731no—
164C22×Q8C2×#6440811yescharacteristic
165C22×C8—1462no—
166C22×C8—1462no—
167C4⋊Q8—734no—
168C4⋊Q8—1462no—
169C4×Q8—1462no—
170C4×Q8—1462no—
171C4×Q8—1462no—
172C4×Q8—1462no—
173C2×C4⋊C4—731no—
174C2×C4⋊C4—1461no—
175C2×C4⋊C4—1461no—
176C2×C4⋊C4—1462no—
177C2×C4⋊C4—1462no—
178C2×C4⋊C4C2×#6440811yescharacteristic
179C2×C42—732no—
180C2×C42—731no—
181C2×C42—731no—
182C2×C42—732no—
183C2×C42—1461no—
184C2×C42—1461no—
185C2×C42C2×#6440811yescharacteristic
186C4⋊C8—1462no—
187C4⋊C8—1462no—
188C4×C8—734no—
189C4×C8—1462no—
190#95—22no—
191#95—1462no—
192C2×Q8—21no—
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—732no—
196C2×Q8—1462no—
197C2×Q8—1462no—
198C2×Q8—1461no—
199C2×Q8#1192403612yes—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—731no—
203C22×C4—732no—
204C22×C4—731no—
205C22×C4—1461no—
206C22×C4—1461no—
207C22×C4C22⋊#6440812yes—
208C22×C4C22×#6440811yescharacteristic
209C2×C8—2924no—
210C2×C8—2922no—
211C2×C8—2924no—
212C2×C8—1464no—
213C4⋊C4—22no—
214C4⋊C4—2922no—
215C4⋊C4—2922no—
216C4⋊C4—2924no—
217C4⋊C4—1468no—
218C4⋊C4—1462no—
219C42—22no—
220C42—2922no—
221C42—2921no—
222C42—2921no—
223C42—2921no—
224C42—2921no—
225C42—732no—
226C42—732no—
227C42—732no—
228C42—732no—
229C42—1464no—
230C23C2×C22⋊#6440811yescharacteristic
231Q8—24no—
232Q8—42no—
233Q8—2922no—
234Q8—1464no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—42no—
243C2×C4—2921no—
244C2×C4—2921no—
245C2×C4—2921no—
246C2×C4—2922no—
247C2×C4—731no—
248C2×C4—731no—
249C2×C4—734no—
250C2×C4—732no—
251C2×C4—734no—
252C2×C4—1462no—
253C2×C4—1462no—
254C2×C4—1462no—
255C2×C4—1462no—
256C2×C4D4×#6440812yes—
257C2×C4C2×#1192403611yescharacteristic
258C2×C4D73⋊M1611yescharacteristic
259C2×C4#1455667812yes—
260C8—2924no—
261C8—5842no—
262C22#1798953911yescharacteristic
263C22#1798955511yescharacteristic
264C22#1798956011yescharacteristic
265C22#1798958012yes—
266C22#1798958412yes—
267C4—42no—
268C4—42no—
269C4—81no—
270C4—2922no—
271C4—5841no—
272C4—732no—
273C4—732no—
274C4—1462no—
275C4—1464no—
276C4#1798961412yes—
277C4#1798962012yes—
278C2#2262523412yes—
279C2#2262529312yes—
280C2#2262605411yescharacteristic
281C2#2262606211yescharacteristic
282C2#2262606811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
Fitting#391×C73C4
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4×Dic73C23
hypercenter#391#64408
hypocenterC73#9641
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
29. #14556589C8semidirect
147. C73#9641semidirect

Maximal subgroups

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

subgroupindex
#226258482
#226256452
C2×#179894372
C2×Q8⋊#105968332
#226125002
#964173