Finite Group Databasebeta

← #32974103

Subgroups — #32974103

Order 18688.

608 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 111 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#22612495C211yesmaximal, characteristic
2#22610073C212yesmaximal, complemented
3#22607752C211yesmaximal, characteristic, complemented
4#22607751C212yesmaximal, complemented
5C73×#1270C211yesmaximal, characteristic, complemented
6C2×#14556587C411yescharacteristic
7C2×D4×Dic73C411yescharacteristic
8C2×#14556553C411yescharacteristic
9C2×#14556551—22no—
10#17988489C2211yescharacteristic
11#17988487—22no—
12#17988456C411yescharacteristic
13C42×Dic73C2211yescharacteristic
14#17988342C2212yes—
15#17988341—22no—
16#17988341—22no—
17#390×C73C2211yescharacteristic
18#336×C73C2212yes—
19C22×D292C2×C411yescharacteristic
20C22×C22⋊D73—22no—
21C23×Dic73—21no—
22C22×C4×D73—21no—
23C22×#10596831—22no—
24#14556587—22no—
25#14556587C814yescomplemented
26D4×Dic73—42no—
27#14556553—42no—
28#14556551—44no—
29#14556551—44no—
30C2×C4⋊Dic73C2×C411yescharacteristic
31C2×#11924007—22no—
32C2×C22⋊Dic73—21no—
33C2×#11924005—21no—
34C2×#11924005—22no—
35C2×C4×Dic73C2×C411yescharacteristic
36C2×C4×Dic73C2×C411yescharacteristic
37C2×C4×Dic73D412yes—
38C2×C4×Dic73D412yes—
39C22×D4×C73C2×C411yescharacteristic
40C22×C8×C73—22no—
41C2×C4⋊C4×C73C2×C411yescharacteristic
42C2×C22⋊C4×C73—22no—
43C2×C42×C73C2311yescharacteristic
44C23×D73—21no—
45C2×D292—21no—
46C2×D292—41no—
47C2×D292—41no—
48C2×D292C2×C812yes—
49C2×C22⋊D73—28no—
50C2×C22⋊D73—44no—
51C2×C22⋊D73—44no—
52C22×Dic73—21no—
53C22×Dic73—44no—
54C22×Dic73—42no—
55C22×Dic73C22⋊C411yescharacteristic
56C22×Dic73C22⋊C412yes—
57C22×Dic73C22⋊C411yescharacteristic
58C2×C4×D73—44no—
59C2×C4×D73—42no—
60C2×#10596831—42no—
61C2×#10596831—42no—
62C2×#10596831—42no—
63C4⋊Dic73—41no—
64#11924007—44no—
65C22⋊Dic73—42no—
66#11924005—42no—
67#11924005—42no—
68#11924005—42no—
69C4×Dic73—22no—
70C4×Dic73—22no—
71C4×Dic73—22no—
72C4×Dic73—42no—
73C4×Dic73C2×C812yes—
74C4×Dic73M1612yes—
75C24×C73—21no—
76C2×D4×C73—21no—
77C2×D4×C73—41no—
78C2×D4×C73—41no—
79C2×D4×C73C2×C812yes—
80C22×C4×C73—21no—
81C22×C4×C73C22×C411yescharacteristic
82C22×C4×C73C2×D412yes—
83C2×C8×C73—42no—
84C2×C8×C73—42no—
85C2×C8×C73—42no—
86C4⋊C4×C73—41no—
87C22⋊C4×C73—42no—
88C22⋊C4×C73—42no—
89C42×C73—41no—
90C23×C73—22no—
91C23×C73—41no—
92C23×C73—41no—
93C23×C73—42no—
94C23×C73—42no—
95C23×C73C2×C22⋊C411yescharacteristic
96C22×D73—22no—
97C22×D73—41no—
98C22×D73—41no—
99C22×D73—42no—
100C22×D73—42no—
101D4×C73—42no—
102D4×C73—42no—
103C2×C4×C73—22no—
104C2×C4×C73—21no—
105C2×C4×C73—21no—
106C2×C4×C73—22no—
107C2×C4×C73—41no—
108C2×C4×C73—42no—
109C2×C4×C73C22×C811yescharacteristic
110C2×C4×C73C2×M1611yescharacteristic
111C2×C4×C73AGL(1,ℤ/8)12yes—
112C2×C4×C73AGL(1,ℤ/8)12yes—
113C22⋊D73—416no—
114C2×Dic73—22no—
115C2×Dic73—22no—
116C2×Dic73—22no—
117C2×Dic73—21no—
118C2×Dic73—22no—
119C2×Dic73—41no—
120C2×Dic73—42no—
121C2×Dic73—84no—
122C2×Dic73C22⋊C814yes—
123C2×Dic73#10012yes—
124D292—42no—
125D292—42no—
126C4×D73—84no—
127C8×C73—82no—
128#10596831—82no—
129C22×C73—42no—
130C22×C73—44no—
131C22×C73—81no—
132C22×C73—81no—
133C22×C73—82no—
134C22×C73C2×C22⋊C811yescharacteristic
135C22×C73#41011yescharacteristic
136C22×C73C2×#10011yescharacteristic
137C22×C73#41812yes—
138C22×C73#42112yes—
139C2×D73—42no—
140C2×D73—44no—
141C2×D73—81no—
142C2×D73—81no—
143C2×D73—82no—
144C4×C73—21no—
145C4×C73—21no—
146C4×C73—22no—
147C4×C73—22no—
148C4×C73—81no—
149Dic73—22no—
150Dic73—24no—
151Dic73—41no—
152Dic73—81no—
153#7603—731nomaximal, Sylow
154C2×C73—82no—
155C2×C73#146011yescharacteristic
156C2×C73#147812yes—
157C2×C73#151412yes—
158C2×C73#153611yescharacteristic
159C2×C73#155511yescharacteristic
160D73—82no—
161C4×#127—731no—
162#1839—732no—
163#1270—731no—
164#1270—732no—
165#1270D7311yescharacteristic, complemented
166C73#760311yescharacteristic, complemented, Sylow
167C2×#127—731no—
168C2×C4×D4—731no—
169C2×C4×D4—731no—
170C2×C4×D4—1462no—
171#390—731no—
172#390—1462no—
173#390C2×D7311yescharacteristic
174#384—731no—
175C43—731no—
176#336—732no—
177#336—1462no—
178#336—1462no—
179#336C2×D7312yes—
180C22×D4—731no—
181C22×D4—1462no—
182C22×D4C4×D7311yescharacteristic
183C23×C4—1461no—
184C23×C4—1461no—
185C22×C8—22no—
186C22×C8—1462no—
187#127—734no—
188#127—1462no—
189C4×D4—2924no—
190C4×D4—2924no—
191C4×D4—2922no—
192C4×D4—2922no—
193C2×C4⋊C4—731no—
194C2×C4⋊C4—1462no—
195C2×C4⋊C4C4×D7311yescharacteristic
196C2×C22⋊C4—22no—
197C2×C22⋊C4—1461no—
198C2×C22⋊C4—1461no—
199C2×C22⋊C4—1462no—
200C2×C42—732no—
201C2×C42—731no—
202C2×C42—731no—
203C2×C42—732no—
204C2×C42C22×D7311yescharacteristic
205C24—21no—
206C24—1461no—
207C2×D4—21no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—2921no—
211C2×D4—2921no—
212C2×D4—2924no—
213C2×D4—2924no—
214C2×D4—732no—
215C2×D4—1468no—
216C2×D4—1461no—
217C2×D4C8×D7312yes—
218C22×C4—21no—
219C22×C4—2922no—
220C22×C4—2924no—
221C22×C4—2922no—
222C22×C4—2924no—
223C22×C4—732no—
224C22×C4—731no—
225C22×C4—731no—
226C22×C4—1461no—
227C22×C4C2×C4×D7311yescharacteristic
228C22×C4D4×D7312yes—
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—2922no—
233C2×C8—2922no—
234C2×C8—2922no—
235C4⋊C4—41no—
236C4⋊C4—2921no—
237C4⋊C4—2924no—
238C22⋊C4—42no—
239C22⋊C4—42no—
240C22⋊C4—2922no—
241C22⋊C4—2922no—
242C22⋊C4—2922no—
243C22⋊C4—2922no—
244C42—41no—
245C42—2922no—
246C42—732no—
247C42—732no—
248C42—1462no—
249C42—1462no—
250C42—1462no—
251C23—22no—
252C23—41no—
253C23—41no—
254C23—42no—
255C23—42no—
256C23—2921no—
257C23—2921no—
258C23—2922no—
259C23—2922no—
260C23—1462no—
261C23C22⋊C4×D7311yescharacteristic
262D4—42no—
263D4—42no—
264D4—2922no—
265D4—2922no—
266D4—29216no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—2921no—
274C2×C4—2922no—
275C2×C4—5844no—
276C2×C4—5844no—
277C2×C4—734no—
278C2×C4—732no—
279C2×C4—1461no—
280C2×C4—1462no—
281C2×C4—1462no—
282C2×C4—1462no—
283C2×C4—1462no—
284C2×C4C2×C8×D7311yescharacteristic
285C2×C4M16×D7311yescharacteristic
286C2×C4#1455661512yes—
287C2×C4#1455661812yes—
288C8—82no—
289C8—5842no—
290C22—42no—
291C22—44no—
292C22—81no—
293C22—82no—
294C22—81no—
295C22—2922no—
296C22—2924no—
297C22—5841no—
298C22—5842no—
299C22—5841no—
300C22C22⋊C8×D7311yescharacteristic
301C22#1798855911yescharacteristic
302C22#100×D7311yescharacteristic
303C22#1798859012yes—
304C22#1798860212yes—
305C4—22no—
306C4—22no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—2921no—
311C4—5841no—
312C4—1462no—
313C4—1464no—
314C2—82no—
315C2—5842no—
316C2#2260825011yescharacteristic
317C2#2260832012yes—
318C2#2260847612yes—
319C2#2260856411yescharacteristic
320C2#2260864311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D73
commutatorC2×C4×C73C22×C8
FrattiniC2×C42C22×D73
FittingC73×#1270C2
socleC23×C73C2×C22⋊C4
prime radicalC2×#14556587C4
cosocleC2×C42×C73C23
hypercenter#1270D73
hypocenterC73#7603
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #22610073C2semidirect
3. #22607752C2semidirect
4. #22607751C2semidirect
5. C73×#1270C2semidirect
25. #14556587C8semidirect
165. #1270D73semidirect
166. C73#7603semidirect

Maximal subgroups

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

subgroupindex
#226124952
#226100732
#226077522
#226077512
C73×#12702
#760373