Finite Group Databasebeta

← #34009819

Subgroups — #34009819

Order 18688.

526 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 90 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#22625165C212yesmaximal
2#22624862C212yesmaximal, complemented
3#22624861C212yesmaximal, complemented
4#22612514C211yesmaximal, characteristic
5#17989604—22no—
6#17989432C2214yes—
7#17989431—22no—
8C22×Q8×D73C411yescharacteristic
9C2×#14556549C2211yescharacteristic
10C2×#14556548C411yescharacteristic
11#17988494C2211yescharacteristic
12#17988493C2211yescharacteristic
13#17988492C411yescharacteristic
14#17988491—22no—
15#17988449—22no—
16#391×C73C411yescharacteristic
17#14556658—42no—
18C22⋊#10596833—24no—
19C4×#10596833—42no—
20C22×Dic146—21no—
21C22×Dic146C2×C411yescharacteristic
22C2×Q8×D73—22no—
23C2×Q8×D73—42no—
24C2×Q8×D73—42no—
25C2×Q8×D73C814yescomplemented
26C22×C4×D73—21no—
27C22×C4×D73C2×C411yescharacteristic
28#14556549—42no—
29#14556548—42no—
30C2×C4⋊Dic73C2311yescharacteristic
31C2×#11924007—21no—
32C2×#11924005—21no—
33C2×#11924005D412yes—
34C2×C4×Dic73C2×C411yescharacteristic
35C2×C4×Dic73D412yes—
36#14556498—22no—
37#14556498—22no—
38#14556498—22no—
39C22×Q8×C73C2×C411yescharacteristic
40C2×C4⋊C4×C73C2×C411yescharacteristic
41C2×C42×C73C2×C411yescharacteristic
42#95×C73—22no—
43C2×#10596833—44no—
44C23×D73C22⋊C411yescharacteristic
45C2×Dic146—21no—
46C2×Dic146—24no—
47C2×Dic146—42no—
48C2×Dic146—42no—
49C2×Dic146—41no—
50C2×Dic146—41no—
51C2×Dic146C2×C812yes—
52Q8×D73—48no—
53Q8×D73—48no—
54C22×Dic73—21no—
55C22×Dic73—21no—
56C22×Dic73C22⋊C411yescharacteristic
57C22×Dic73C2×D412yes—
58C2×C4×D73—22no—
59C2×C4×D73—22no—
60C2×C4×D73—24no—
61C2×C4×D73—42no—
62C2×C4×D73—42no—
63C2×C4×D73C2×C812yes—
64C2×C4×D73M1612yes—
65C4⋊Dic73—41no—
66#11924007—42no—
67#11924005—42no—
68#11924005—42no—
69C4×Dic73—22no—
70C4×Dic73—22no—
71C4×Dic73—41no—
72C2×Q8×C73—21no—
73C2×Q8×C73—41no—
74C2×Q8×C73—41no—
75C2×Q8×C73C2×C812yes—
76C22×C4×C73—21no—
77C22×C4×C73—21no—
78C22×C4×C73C22⋊C412yes—
79C22×C4×C73C22×C411yescharacteristic
80C4⋊C4×C73—41no—
81C42×C73—41no—
82C23×C73C2×C22⋊C411yescharacteristic
83C22×D73—21no—
84C22×D73—21no—
85C22×D73—41no—
86C22×D73—41no—
87C22×D73C22⋊C812yes—
88Q8×C73—42no—
89Q8×C73—42no—
90C2×C4×C73—21no—
91C2×C4×C73—21no—
92C2×C4×C73—22no—
93C2×C4×C73—22no—
94C2×C4×C73—41no—
95C2×C4×C73—41no—
96C2×C4×C73—42no—
97C2×C4×C73—41no—
98C2×C4×C73—41no—
99C2×C4×C73—41no—
100C2×C4×C73C22×C811yescharacteristic
101C2×C4×C73C2×M1611yescharacteristic
102C2×Dic73—22no—
103C2×Dic73—22no—
104C2×Dic73—41no—
105C2×Dic73—41no—
106C2×Dic73—42no—
107C2×Dic73—41no—
108C2×Dic73—41no—
109C2×Dic73—41no—
110C2×Dic73C22⋊C812yes—
111C2×Dic73#9912yes—
112C2×Dic73#10012yes—
113C4×D73—24no—
114C4×D73—24no—
115C4×D73—48no—
116Dic146—42no—
117Dic146—48no—
118Dic146—42no—
119#10596833—84no—
120C22×C73—21no—
121C22×C73—21no—
122C22×C73C2×C22⋊C811yescharacteristic
123C22×C73C2×#9911yescharacteristic
124C22×C73C2×#10011yescharacteristic
125C2×D73—22no—
126C2×D73—42no—
127C2×D73—41no—
128C2×D73—41no—
129C2×D73—42no—
130C4×C73—21no—
131C4×C73—21no—
132C4×C73—42no—
133C4×C73—42no—
134C4×C73—81no—
135Dic73—42no—
136Dic73—42no—
137Dic73—81no—
138Dic73#32314yes—
139#11434—731nomaximal, Sylow
140C2×C73—21no—
141C2×C73—21no—
142C2×C73C2×#32311yescharacteristic
143C2×C73#212911yescharacteristic
144C2×C73#213511yescharacteristic
145D73—42no—
146#2310—731no—
147#1458—732no—
148#1319—732no—
149#1319—732no—
150C73#1143411yescharacteristic, complemented, Sylow
151C23×Q8—731no—
152C2×#117—731no—
153C2×#117—731no—
154#431—1462no—
155#391—731no—
156#391—731no—
157#391—731no—
158#391—1462no—
159#391#6440811yescharacteristic
160#381—1462no—
161#324—734no—
162#323—1462no—
163C22×Q8—2922no—
164C22×Q8—2922no—
165C22×Q8—734no—
166C22×Q8—731no—
167C22×Q8—1461no—
168C22×Q8—1462no—
169C22×Q8C2×#6440811yescharacteristic
170C23×C4—731no—
171C23×C4—1461no—
172#117—2922no—
173#117—2922no—
174C2×C4⋊C4—731no—
175C2×C4⋊C4—1461no—
176C2×C4⋊C4C2×#6440811yescharacteristic
177C2×C22⋊C4—732no—
178C2×C22⋊C4—1461no—
179C2×C42—731no—
180C2×C42—732no—
181C2×C42C2×#6440811yescharacteristic
182C4⋊C8—2922no—
183C22⋊C8—1464no—
184C4×C8—2922no—
185#95—22no—
186#95—1462no—
187#95—1462no—
188#95—1462no—
189C24—731no—
190C2×Q8—21no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8—2921no—
194C2×Q8—2921no—
195C2×Q8—2922no—
196C2×Q8—2922no—
197C2×Q8—2928no—
198C2×Q8—2928no—
199C2×Q8—732no—
200C2×Q8—1464no—
201C2×Q8—1461no—
202C2×Q8#1192403612yes—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—2922no—
206C22×C4—2922no—
207C22×C4—732no—
208C22×C4—731no—
209C22×C4—732no—
210C22×C4—732no—
211C22×C4—1464no—
212C22×C4—1462no—
213C22×C4—1462no—
214C22×C4—1461no—
215C22×C4—1461no—
216C22×C4C22⋊#6440812yes—
217C22×C4C22×#6440811yescharacteristic
218C2×C8—2924no—
219C4⋊C4—41no—
220C4⋊C4—2921no—
221C4⋊C4—2922no—
222C22⋊C4—2922no—
223C22⋊C4—2922no—
224C42—41no—
225C42—2921no—
226C42—1462no—
227C42—1462no—
228C23—2921no—
229C23—2921no—
230C23—732no—
231C23—1461no—
232C23—1461no—
233C23C2×C22⋊#6440811yescharacteristic
234Q8—42no—
235Q8—42no—
236Q8—2922no—
237Q8—2922no—
238Q8—2928no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—2928no—
250C2×C4—2921no—
251C2×C4—2921no—
252C2×C4—2922no—
253C2×C4—2921no—
254C2×C4—2921no—
255C2×C4—2921no—
256C2×C4—732no—
257C2×C4—732no—
258C2×C4—732no—
259C2×C4—1464no—
260C2×C4—1464no—
261C2×C4—1462no—
262C2×C4—1462no—
263C2×C4C2×#1192403611yescharacteristic
264C2×C4D73⋊M1611yescharacteristic
265C8—5844no—
266C22—21no—
267C22—21no—
268C22—2922no—
269C22—2922no—
270C22—2921no—
271C22—2921no—
272C22—1462no—
273C22#1798955511yescharacteristic
274C22D73⋊#9911yescharacteristic
275C22D73⋊#10011yescharacteristic
276C4—21no—
277C4—21no—
278C4—42no—
279C4—42no—
280C4—81no—
281C4—2922no—
282C4—2922no—
283C4—5841no—
284C4—734no—
285C2—21no—
286C2—21no—
287C2—2922no—
288C2#2262515711yescharacteristic
289C2#2262621411yescharacteristic
290C2#2262623411yescharacteristic
subgroupG/H
centerC22D73⋊#99
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
Fitting#391×C73C4
socleC22×C73C2×#99
prime radicalC23×D73C22⋊C4
cosocleC2×C4⋊Dic73C23
hypercenter#391#64408
hypocenterC73#11434
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #391

Complements

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

NH ≅ G/Ntype
2. #22624862C2semidirect
3. #22624861C2semidirect
25. C2×Q8×D73C8semidirect
150. C73#11434semidirect

Maximal subgroups

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

subgroupindex
#226251652
#226248622
#226248612
#226125142
#1143473