Finite Group Databasebeta

← #34033581

Subgroups — #34033581

Order 18688.

454 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#17989673C212yesmaximal
2#22626968C212yesmaximal, complemented
3#22626967C212yesmaximal, complemented
4#22626412C211yesmaximal, characteristic
5C2×C22⋊#10596842—22no—
6#17989673—22no—
7#17989673C2214yes—
8C2×#14556670C411yescharacteristic
9C22×C4⋊#64408C2211yescharacteristic
10#17989538—22no—
11#17989534—22no—
12#17989533C411yescharacteristic
13#17989533C2211yescharacteristic
14#17989531C411yescharacteristic
15#17989531C2211yescharacteristic
16#117×D73C411yescharacteristic
17C22×#10596842—42no—
18C22⋊#10596842—24no—
19C22⋊#10596842—42no—
20C23×#64408D412yes—
21#14556670—42no—
22C2×C4⋊#64408—22no—
23C2×C4⋊#64408—22no—
24C2×C4⋊#64408—42no—
25C2×C4⋊#64408C2×C411yescharacteristic
26C2×C4⋊#64408C2×C411yescharacteristic
27C2×C4⋊#64408C2×C411yescharacteristic
28C2×C4⋊#64408D412yes—
29C2×C4⋊#64408C2311yescharacteristic
30C2×C22⋊#64408—21no—
31C2×C4×#64408—21no—
32(C2×#64408)⋊C4—22no—
33(C2×#64408)⋊C4—22no—
34C22×C4×D73C2×C411yescharacteristic
35#14556550C811yescharacteristic, complemented
36#14556549—21no—
37#14556548C811yescharacteristic, complemented
38#14556548C811yescharacteristic, complemented
39#14556547—21no—
40C4⋊C4×D73—21no—
41C22⋊C4×D73—21no—
42C42×D73C2×C411yescharacteristic
43C42×D73C2×C411yescharacteristic
44#117×C73C811yescharacteristic, complemented
45C2×#10596842—44no—
46C2×#10596842—84no—
47C22×#64408—22no—
48C22×#64408—22no—
49C22×#64408—21no—
50C22×#64408—21no—
51C22×#64408—82no—
52C22×#64408C22⋊C412yes—
53C22×#64408C2×D412yes—
54C4⋊#64408—41no—
55C4⋊#64408—42no—
56C4⋊#64408—41no—
57C4⋊#64408—41no—
58C4⋊#64408—41no—
59C4⋊#64408—82no—
60C4⋊#64408—82no—
61C22⋊#64408—42no—
62C4×#64408—42no—
63C23×D73C22⋊C411yescharacteristic
64C22×Dic73M1611yescharacteristic
65C2×C4×D73—22no—
66C2×C4×D73—22no—
67C2×C4×D73—21no—
68C2×C4×D73—21no—
69C2×C4×D73C22⋊C411yescharacteristic
70C2×C4×D73C2×C811yescharacteristic
71C2×C4×D73M1611yescharacteristic
72C2×C4×D73C22×C411yescharacteristic
73C4⋊Dic73—21no—
74#11924007—21no—
75#11924007—21no—
76C22⋊Dic73—21no—
77#11924005—21no—
78#11924005—21no—
79C4×Dic73—21no—
80C4×Dic73—21no—
81C4×Dic73C2×C811yescharacteristic, complemented
82C4×Dic73C2×C811yescharacteristic, complemented
83C22×C4×C73C2×C811yescharacteristic
84C4⋊C4×C73—21no—
85C22⋊C4×C73—21no—
86C42×C73C2×C811yescharacteristic, complemented
87C42×C73C2×C811yescharacteristic, complemented
88C23×C73C22⋊C811yescharacteristic
89C22×D73—41no—
90C22×D73—41no—
91C22×D73C22⋊C811yescharacteristic
92C22×D73#9912yes—
93C22×D73#10112yes—
94C22×D73C2×C22⋊C411yescharacteristic
95C2×#64408—22no—
96C2×#64408—22no—
97C2×#64408—44no—
98C2×#64408—42no—
99C2×#64408—42no—
100C2×#64408—42no—
101C2×#64408—42no—
102C2×#64408—41no—
103C2×#64408—41no—
104C2×#64408—82no—
105#10596842—84no—
106C2×C4×C73—22no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73C22⋊C811yescharacteristic
110C2×C4×C73C22×C811yescharacteristic
111C2×Dic73—22no—
112C2×Dic73—21no—
113C2×Dic73—21no—
114C2×Dic73C22⋊C811yescharacteristic
115C2×Dic73C2×M1611yescharacteristic
116C4×D73—22no—
117C4×D73—22no—
118C4×D73—21no—
119C4×D73—21no—
120C4×D73—21no—
121C4×D73—21no—
122C4×D73—41no—
123C4×D73—41no—
124C4×D73—41no—
125C4×D73—41no—
126C22×C73—41no—
127C22×C73#32412yes—
128C22×C73C2×C22⋊C811yescharacteristic
129C2×D73—21no—
130C2×D73—22no—
131C2×D73—21no—
132C2×D73—22no—
133C2×D73—41no—
134C2×D73—42no—
135C2×D73#32412yes—
136C2×D73C2×#9911yescharacteristic
137C2×D73C2×#10111yescharacteristic
138#64408—42no—
139#64408—42no—
140#64408—81no—
141#64408—81no—
142C4×C73—21no—
143C4×C73—21no—
144C4×C73—41no—
145C4×C73—41no—
146Dic73—21no—
147Dic73—21no—
148Dic73—41no—
149Dic73—41no—
150#11448—731nomaximal, Sylow
151C2×C73—21no—
152C2×C73—22no—
153C2×C73C2×#32411yescharacteristic
154D73—22no—
155D73—21no—
156D73#212711yescharacteristic
157D73#213311yescharacteristic
158#2317—731no—
159C2×#324—732no—
160#1325—732no—
161#1324—732no—
162C73#1144811yescharacteristic, complemented, Sylow
163C2×#117—731no—
164C2×#117—731no—
165C22×C4⋊C4—731no—
166C2×C22⋊C8—1462no—
167#389—1462no—
168#385—1462no—
169#384—731no—
170#384—731no—
171#382—731no—
172#382—731no—
173#324—734no—
174#324—1462no—
175C23×C4—732no—
176C23×C4—731no—
177C22×C8—2922no—
178#117—2922no—
179#117—731no—
180#117—731no—
181#117—731no—
182#117—1461no—
183#117—1461no—
184#117#1059684211yescharacteristic, complemented
185C2×C4⋊C4—2922no—
186C2×C4⋊C4—731no—
187C2×C4⋊C4—732no—
188C2×C4⋊C4—731no—
189C2×C4⋊C4—731no—
190C2×C4⋊C4—731no—
191C2×C4⋊C4—1461no—
192C2×C4⋊C4—1462no—
193C2×C4⋊C4—1462no—
194C2×C22⋊C4—1461no—
195C2×C22⋊C4—1461no—
196C2×C42—731no—
197C2×C42—731no—
198C2×C42—1461no—
199C22⋊C8—2922no—
200C22⋊C8—1464no—
201#95—1462no—
202#95—1462no—
203C24—731no—
204C22×C4—5842no—
205C22×C4—732no—
206C22×C4—732no—
207C22×C4—731no—
208C22×C4—731no—
209C22×C4—731no—
210C22×C4—731no—
211C22×C4—731no—
212C22×C4—1461no—
213C22×C4—1461no—
214C22×C4—1462no—
215C22×C4—1462no—
216C22×C4—1461no—
217C22×C4—1461no—
218C22×C4—1462no—
219C22×C4—1462no—
220C22×C4C2×#1059684211yescharacteristic
221C2×C8—2924no—
222C2×C8—5844no—
223C4⋊C4—21no—
224C4⋊C4—2921no—
225C4⋊C4—2921no—
226C4⋊C4—2922no—
227C4⋊C4—2921no—
228C4⋊C4—2921no—
229C4⋊C4—5842no—
230C4⋊C4—5842no—
231C4⋊C4—1461no—
232C4⋊C4—1461no—
233C4⋊C4—1461no—
234C22⋊C4—21no—
235C22⋊C4—2922no—
236C22⋊C4—1461no—
237C22⋊C4—1461no—
238C22⋊C4—1461no—
239C42—2922no—
240C42—731no—
241C42—731no—
242C42—1461no—
243C42—1461no—
244C42C2×#1059684211yescharacteristic, complemented
245C42C2×#1059684211yescharacteristic, complemented
246C23—2921no—
247C23—2921no—
248C23—732no—
249C23—731no—
250C23—732no—
251C23—731no—
252C23C22⋊#1059684211yescharacteristic
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—2921no—
257C2×C4—2921no—
258C2×C4—2921no—
259C2×C4—2921no—
260C2×C4—2924no—
261C2×C4—2922no—
262C2×C4—2922no—
263C2×C4—2921no—
264C2×C4—2921no—
265C2×C4—2922no—
266C2×C4—2922no—
267C2×C4—5842no—
268C2×C4—731no—
269C2×C4—731no—
270C2×C4—1461no—
271C2×C4—1461no—
272C2×C4—1462no—
273C2×C4—1461no—
274C2×C4—1462no—
275C2×C4—1461no—
276C2×C4—1462no—
277C2×C4—1462no—
278C2×C4—1461no—
279C2×C4—1461no—
280C2×C4—1462no—
281C2×C4C22⋊#1059684211yescharacteristic
282C2×C4C22×#1059684211yescharacteristic
283C8—5844no—
284C22—41no—
285C22—2921no—
286C22—2922no—
287C22—731no—
288C22—732no—
289C22—731no—
290C22—1461no—
291C22—1461no—
292C22—1462no—
293C22—1462no—
294C22#1798967312yes—
295C22C2×C22⋊#1059684211yescharacteristic
296C4—21no—
297C4—21no—
298C4—41no—
299C4—41no—
300C4—2921no—
301C4—2921no—
302C4—2922no—
303C4—2922no—
304C4—5841no—
305C4—5841no—
306C4—1461no—
307C4—1461no—
308C2—21no—
309C2—22no—
310C2—731no—
311C2—731no—
312C2—1462no—
313C2—1461no—
314C2C2×#1798967311yescharacteristic
subgroupG/H
centerC2C2×#17989673
commutatorC2×C4×C73C22×C8
FrattiniC2×C4C22×#10596842
Fitting#117×C73C8
socleC2×C73C2×#324
prime radicalC23×D73C22⋊C4
cosocleC2×C4⋊#64408C23
hypercenter#117#10596842
hypocenterC73#11448
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #22626968C2semidirect
3. #22626967C2semidirect
35. #14556550C8semidirect
37. #14556548C8semidirect
38. #14556548C8semidirect
44. #117×C73C8semidirect
81. C4×Dic73C2×C8semidirect
82. C4×Dic73C2×C8semidirect
86. C42×C73C2×C8semidirect
87. C42×C73C2×C8semidirect
162. C73#11448semidirect
184. #117#10596842semidirect
244. C42C2×#10596842semidirect
245. C42C2×#10596842semidirect

Maximal subgroups

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

subgroupindex
C2×#179896732
#226269682
#226269672
#226264122
#1144873