Finite Group Databasebeta

← C2×#22626967 #34033578

Subgroups — C2×#22626967 #34033578

Order 18688.

510 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 93 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#22626967C214yesmaximal, direct product factor
3C2×#17989531C211yesmaximal, characteristic
4C2×C22⋊#10596842—22no—
5#17989673—22no—
6#17989673C2214yes—
7C22×C4⋊#64408C411yescharacteristic
8C22×C4⋊#64408C2211yescharacteristic
9#17989531—22no—
10#17989531C412yes—
11#17989531C2212yes—
12C2×(C2×#64408)⋊C4—22no—
13C2×C42×D73C411yescharacteristic
14C22×#10596842—42no—
15C22⋊#10596842—24no—
16C22⋊#10596842—42no—
17C23×#64408—21no—
18C23×#64408D412yes—
19C2×C4⋊#64408—21no—
20C2×C4⋊#64408—41no—
21C2×C4⋊#64408—41no—
22C2×C4⋊#64408—41no—
23C2×C4⋊#64408—41no—
24C2×C4⋊#64408C2×C412yes—
25C2×C4⋊#64408C2×C411yescharacteristic
26C2×C4⋊#64408D412yes—
27C2×C4⋊#64408C2311yescharacteristic
28(C2×#64408)⋊C4—24no—
29(C2×#64408)⋊C4—24no—
30C22×C4×D73—21no—
31C22×C4×D73C2×C411yescharacteristic
32C2×C4×Dic73—21no—
33C2×C4×Dic73C811yescharacteristic, complemented
34C42×D73—21no—
35C42×D73—21no—
36C42×D73C812yescomplemented
37C42×D73C2×C412yes—
38C2×C42×C73C811yescharacteristic, complemented
39C2×#10596842—44no—
40C2×#10596842—84no—
41C22×#64408—22no—
42C22×#64408—22no—
43C22×#64408—22no—
44C22×#64408—44no—
45C22×#64408—44no—
46C22×#64408—41no—
47C22×#64408—41no—
48C22×#64408C22⋊C412yes—
49C22×#64408C2×D412yes—
50C4⋊#64408—41no—
51C4⋊#64408—42no—
52C4⋊#64408—41no—
53C4⋊#64408—42no—
54C4⋊#64408—42no—
55C23×D73C22⋊C411yescharacteristic
56C22×Dic73—21no—
57C22×Dic73M1611yescharacteristic
58C2×C4×D73—21no—
59C2×C4×D73—21no—
60C2×C4×D73—21no—
61C2×C4×D73—21no—
62C2×C4×D73—22no—
63C2×C4×D73—22no—
64C2×C4×D73—42no—
65C2×C4×D73—42no—
66C2×C4×D73C22⋊C411yescharacteristic
67C2×C4×D73C2×C811yescharacteristic
68C2×C4×D73M1611yescharacteristic
69C2×C4×D73C22×C411yescharacteristic
70C4×Dic73—21no—
71C4×Dic73—22no—
72C4×Dic73—22no—
73C4×Dic73C2×C812yescomplemented
74C22×C4×C73—21no—
75C22×C4×C73C2×C811yescharacteristic
76C42×C73—21no—
77C42×C73C2×C812yescomplemented
78C23×C73C22⋊C811yescharacteristic
79C22×D73—22no—
80C22×D73—22no—
81C22×D73C22⋊C811yescharacteristic
82C22×D73#9911yescharacteristic
83C22×D73#9911yescharacteristic
84C22×D73#10111yescharacteristic
85C22×D73#10111yescharacteristic
86C22×D73C2×C22⋊C411yescharacteristic
87C2×#64408—22no—
88C2×#64408—22no—
89C2×#64408—44no—
90C2×#64408—42no—
91C2×#64408—42no—
92C2×#64408—44no—
93C2×#64408—42no—
94C2×#64408—82no—
95C2×#64408—82no—
96C2×#64408—82no—
97#10596842—84no—
98C2×C4×C73—21no—
99C2×C4×C73—21no—
100C2×C4×C73—22no—
101C2×C4×C73—42no—
102C2×C4×C73C22⋊C811yescharacteristic
103C2×C4×C73C22×C811yescharacteristic
104C2×Dic73—21no—
105C2×Dic73—21no—
106C2×Dic73—22no—
107C2×Dic73—42no—
108C2×Dic73C22⋊C811yescharacteristic
109C2×Dic73C2×M1611yescharacteristic
110C4×D73—21no—
111C4×D73—21no—
112C4×D73—21no—
113C4×D73—21no—
114C4×D73—21no—
115C4×D73—21no—
116C4×D73—21no—
117C4×D73—21no—
118C4×D73—44no—
119C4×D73—42no—
120C4×D73—42no—
121C22×C73—22no—
122C22×C73#32411yescharacteristic
123C22×C73#32411yescharacteristic
124C22×C73C2×C22⋊C811yescharacteristic
125C2×D73—22no—
126C2×D73—22no—
127C2×D73—22no—
128C2×D73—21no—
129C2×D73—21no—
130C2×D73—21no—
131C2×D73—21no—
132C2×D73#32411yescharacteristic
133C2×D73#32411yescharacteristic
134C2×D73#35412yes—
135C2×D73#35512yes—
136C2×D73C2×#9911yescharacteristic
137C2×D73C2×#10111yescharacteristic
138#64408—42no—
139#64408—42no—
140#64408—82no—
141C4×C73—21no—
142C4×C73—21no—
143C4×C73—42no—
144Dic73—21no—
145Dic73—21no—
146Dic73—42no—
147C2×#1324—731nomaximal, Sylow
148C2×C73—21no—
149C2×C73—21no—
150C2×C73#132412yescomplemented
151C2×C73C2×#32411yescharacteristic
152D73—21no—
153D73—21no—
154D73#132412yescomplemented
155D73C2×#35411yescharacteristic
156D73C2×#35511yescharacteristic
157C2×#382—731no—
158C2×#324—732no—
159#1324—734no—
160C73C2×#132411yescharacteristic, complemented, Sylow
161C22×C4⋊C4—731no—
162C22×C4⋊C4—731no—
163C22×C42—731no—
164C2×C22⋊C8—1462no—
165#382—732no—
166#382—732no—
167#382—1462no—
168C2×#95—1462no—
169#324—734no—
170#324—1462no—
171C23×C4—732no—
172C23×C4—731no—
173C23×C4—1461no—
174C23×C4—1461no—
175C22×C8—2922no—
176C2×C4⋊C4—2921no—
177C2×C4⋊C4—2921no—
178C2×C4⋊C4—2921no—
179C2×C4⋊C4—2921no—
180C2×C4⋊C4—731no—
181C2×C4⋊C4—732no—
182C2×C4⋊C4—731no—
183C2×C4⋊C4—732no—
184C2×C4⋊C4—1461no—
185C2×C42—731no—
186C2×C42—732no—
187C2×C42—732no—
188C2×C42—1461no—
189C2×C42—1461no—
190C2×C42—1461no—
191C2×C42#1059684211yescharacteristic, complemented
192C22⋊C8—2922no—
193C22⋊C8—1464no—
194#95—1464no—
195#95—1464no—
196C24—731no—
197C22×C4—21no—
198C22×C4—2922no—
199C22×C4—2922no—
200C22×C4—2924no—
201C22×C4—2921no—
202C22×C4—2921no—
203C22×C4—2924no—
204C22×C4—732no—
205C22×C4—732no—
206C22×C4—731no—
207C22×C4—731no—
208C22×C4—731no—
209C22×C4—731no—
210C22×C4—731no—
211C22×C4—1462no—
212C22×C4—1462no—
213C22×C4—1461no—
214C22×C4—1461no—
215C22×C4—1461no—
216C22×C4—1461no—
217C22×C4—1462no—
218C22×C4—1462no—
219C22×C4—1461no—
220C22×C4—1462no—
221C22×C4C2×#1059684211yescharacteristic
222C2×C8—2924no—
223C2×C8—5844no—
224C4⋊C4—2922no—
225C4⋊C4—2922no—
226C4⋊C4—2921no—
227C4⋊C4—2922no—
228C4⋊C4—2921no—
229C42—21no—
230C42—732no—
231C42—1462no—
232C42—1462no—
233C42—1461no—
234C42C2×#1059684212yescomplemented
235C23—731no—
236C23—731no—
237C23—731no—
238C23—731no—
239C23—731no—
240C23—731no—
241C23—1462no—
242C23—1462no—
243C23C22⋊#1059684211yescharacteristic
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—42no—
248C2×C4—2922no—
249C2×C4—2922no—
250C2×C4—2924no—
251C2×C4—2922no—
252C2×C4—2924no—
253C2×C4—2922no—
254C2×C4—2922no—
255C2×C4—2922no—
256C2×C4—2924no—
257C2×C4—5842no—
258C2×C4—5842no—
259C2×C4—5842no—
260C2×C4—731no—
261C2×C4—731no—
262C2×C4—1461no—
263C2×C4—1461no—
264C2×C4—1461no—
265C2×C4—1461no—
266C2×C4—1461no—
267C2×C4—1461no—
268C2×C4—1461no—
269C2×C4—1461no—
270C2×C4—1462no—
271C2×C4—1462no—
272C2×C4—1462no—
273C2×C4—1461no—
274C2×C4—1461no—
275C2×C4C22⋊#1059684211yescharacteristic
276C2×C4C22×#1059684211yescharacteristic
277C8—5844no—
278C22—22no—
279C22—732no—
280C22—732no—
281C22—731no—
282C22—731no—
283C22—731no—
284C22—731no—
285C22—1461no—
286C22—1461no—
287C22—1462no—
288C22—1461no—
289C22—1461no—
290C22—1462no—
291C22—1462no—
292C22#1798967311yescharacteristic
293C22#1798967311yescharacteristic
294C22C2×C22⋊#1059684211yescharacteristic
295C4—21no—
296C4—21no—
297C4—42no—
298C4—2922no—
299C4—2922no—
300C4—2922no—
301C4—5842no—
302C4—1461no—
303C4—1461no—
304C2—21no—
305C2—21no—
306C2—731no—
307C2—731no—
308C2—732no—
309C2—1461no—
310C2—1461no—
311C2#2262696712yesdirect product factor
312C2C2×#1798967311yescharacteristic
subgroupG/H
centerC22#17989673
commutatorC2×C4×C73C22×C8
FrattiniC2×C4C22×#10596842
FittingC2×C42×C73C8
socleC22×C73#324
prime radicalC23×D73C22⋊C4
cosocleC2×C4⋊#64408C23
hypercenterC2×C42#10596842
hypocenterC73C2×#1324
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #22626967C2direct (N × H)
33. C2×C4×Dic73C8semidirect
36. C42×D73C8semidirect
38. C2×C42×C73C8semidirect
73. C4×Dic73C2×C8semidirect
77. C42×C73C2×C8semidirect
150. C2×C73#1324semidirect
154. D73#1324semidirect
160. C73C2×#1324semidirect
191. C2×C42#10596842semidirect
234. C42C2×#10596842semidirect
311. C2#22626967direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179896732
#226269672
C2×#179895312
C2×#132473