Finite Group Databasebeta

← #34012517

Subgroups — #34012517

Order 18688.

628 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 102 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×#17989492C212yesmaximal
2C4×#14556650C212yesmaximal, complemented
3#22625025C212yesmaximal, complemented
4#22612656C211yesmaximal, characteristic
5C2×#14556650C2214yes—
6C4×C22⋊#64408—22no—
7#17989492C418yescomplemented
8#17989465—22no—
9C2×#14556588C2211yescharacteristic
10C2×C4×D292C411yescharacteristic, complemented
11C2×C4×D292C2211yescharacteristic
12#17988489C411yescharacteristic, complemented
13#17988489C2211yescharacteristic
14#17988465—22no—
15#17988465—22no—
16#17988453C411yescharacteristic, complemented
17#376×C73C411yescharacteristic, complemented
18C2×C22⋊#64408—24no—
19C2×C4×#64408—42no—
20#14556650—24no—
21#14556650C2×C418yescomplemented
22(C2×#64408)⋊C4—42no—
23C22×D292—22no—
24C22×D292C2×C411yescharacteristic
25C22×D292C2311yescharacteristic
26C22×C4×D73—21no—
27C22×C4×D73D412yes—
28#14556588—22no—
29#14556588C2×C414yes—
30C4×D292—42no—
31C4×D292—42no—
32C2×C4⋊Dic73C2×C411yescharacteristic
33C2×C4⋊Dic73C2×C411yescharacteristic
34C2×#11924005—22no—
35C2×#11924005—22no—
36C2×#11924005—21no—
37C2×#11924005D412yes—
38#14556498—22no—
39C2×C42×C73C2×C411yescharacteristic
40C2×C42×C73C2×C411yescharacteristic
41C2×C42×C73C2×C411yescharacteristic
42#95×C73—21no—
43#95×C73—21no—
44C22×#64408—44no—
45C22⋊#64408—28no—
46C22⋊#64408—44no—
47C4×#64408—84no—
48C23×D73—21no—
49C23×D73C2×D412yes—
50C2×D292—21no—
51C2×D292—28no—
52C2×D292—41no—
53C2×D292—41no—
54C2×D292—41no—
55C2×D292—41no—
56C2×D292—82no—
57C2×D292—82no—
58C2×D292C4212yescomplemented
59C2×D292C22×C412yes—
60C2×D292#4112yes—
61C22×Dic73—21no—
62C22×Dic73C22⋊C412yes—
63C2×C4×D73—22no—
64C2×C4×D73—22no—
65C2×C4×D73—42no—
66C2×C4×D73—82no—
67C2×C4×D73—82no—
68C4⋊Dic73—41no—
69C4⋊Dic73—41no—
70#11924005—42no—
71#11924005—42no—
72#11924005—82no—
73#11924005—82no—
74C22×C4×C73—21no—
75C22×C4×C73—21no—
76C22×C4×C73C22⋊C411yescharacteristic
77C22×C4×C73C22⋊C411yescharacteristic
78C22×C4×C73C22×C411yescharacteristic
79C42×C73—22no—
80C42×C73—21no—
81C42×C73—41no—
82C42×C73C4212yescomplemented
83C23×C73C2×C22⋊C411yescharacteristic
84C22×D73—22no—
85C22×D73—22no—
86C22×D73—22no—
87C22×D73—42no—
88C22×D73—42no—
89C22×D73—42no—
90C22×D73—42no—
91C22×D73—41no—
92C22×D73—41no—
93C22×D73C4×D414yes—
94C2×#64408—48no—
95C2×#64408—84no—
96C2×#64408—84no—
97C2×C4×C73—21no—
98C2×C4×C73—21no—
99C2×C4×C73—22no—
100C2×C4×C73—21no—
101C2×C4×C73—41no—
102C2×C4×C73—41no—
103C2×C4×C73—41no—
104C2×C4×C73—41no—
105C2×C4×C73—41no—
106C2×C4×C73—41no—
107C2×C4×C73—41no—
108C2×C4×C73#9912yes—
109C2×C4×C73C2×C4211yescharacteristic
110C2×C4×C73#11711yescharacteristic
111C2×Dic73—22no—
112C2×Dic73—42no—
113C2×Dic73—42no—
114C2×Dic73—41no—
115D292—42no—
116D292—42no—
117D292—42no—
118D292—42no—
119D292—88no—
120C4×D73—44no—
121C4×D73—82no—
122C4×D73—84no—
123C22×C73—21no—
124C22×C73—21no—
125C22×C73C4×C22⋊C411yescharacteristic
126C22×C73C2×#9911yescharacteristic
127C22×C73#41011yescharacteristic
128C2×D73—24no—
129C2×D73—42no—
130C2×D73—42no—
131C2×D73—44no—
132C2×D73—44no—
133C2×D73—42no—
134C2×D73—82no—
135C2×D73—82no—
136C2×D73—81no—
137C2×D73—81no—
138#64408—88no—
139C4×C73—22no—
140C4×C73—21no—
141C4×C73—21no—
142C4×C73—42no—
143C4×C73—41no—
144C4×C73—81no—
145Dic73—42no—
146Dic73—81no—
147#12628—731nomaximal, Sylow
148C2×C73—21no—
149C2×C73—21no—
150C2×C73C4×#9911yescharacteristic
151C2×C73#212711yescharacteristic
152C2×C73#212811yescharacteristic
153D73—44no—
154D73—82no—
155#2328—731no—
156C2×#353—732no—
157C4×#99—732no—
158#1393—732no—
159C73#1262811yescharacteristic, complemented, Sylow
160C2×#127—731no—
161C2×C4×D4—731no—
162C2×C4×D4—731no—
163C2×#99—734no—
164#390—731no—
165#390—731no—
166#386—1462no—
167#386—1462no—
168#382—731no—
169C4×C22⋊C4—1462no—
170#376#6440811yescharacteristic, complemented
171#353—738no—
172#342—1462no—
173C22×D4—731no—
174C22×D4—731no—
175C22×D4—1462no—
176C23×C4—732no—
177C23×C4—1461no—
178#127—734no—
179#127—1462no—
180C4×D4—2922no—
181C4×D4—2922no—
182C2×C4⋊C4—731no—
183C2×C4⋊C4—731no—
184C2×C22⋊C4—732no—
185C2×C22⋊C4—1461no—
186C2×C22⋊C4—1464no—
187C2×C22⋊C4—1462no—
188C2×C22⋊C4—1462no—
189C2×C42—2922no—
190C2×C42C2×#6440811yescharacteristic
191C2×C42C2×#6440811yescharacteristic
192C2×C42C2×#6440811yescharacteristic
193#99—738no—
194#99—1464no—
195#95—21no—
196#95—21no—
197#95—2922no—
198#95—1462no—
199C24—732no—
200C24—1461no—
201C2×D4—2921no—
202C2×D4—2921no—
203C2×D4—2921no—
204C2×D4—2921no—
205C2×D4—5842no—
206C2×D4—5842no—
207C2×D4—732no—
208C2×D4—732no—
209C2×D4—732no—
210C2×D4—1468no—
211C2×D4—1461no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—2922no—
215C22×C4—2924no—
216C22×C4—5842no—
217C22×C4—5842no—
218C22×C4—732no—
219C22×C4—1461no—
220C22×C4—1462no—
221C22×C4—1462no—
222C22×C4C22⋊#6440811yescharacteristic
223C22×C4C22⋊#6440811yescharacteristic
224C22×C4C22×#6440811yescharacteristic
225C4⋊C4—2921no—
226C4⋊C4—2921no—
227C22⋊C4—2922no—
228C22⋊C4—2924no—
229C22⋊C4—2922no—
230C22⋊C4—5842no—
231C22⋊C4—5842no—
232C22⋊C4—1468no—
233C42—22no—
234C42—21no—
235C42—41no—
236C42—5844no—
237C42C4×#6440812yescomplemented
238C23—2922no—
239C23—2922no—
240C23—2922no—
241C23—2922no—
242C23—2921no—
243C23—2921no—
244C23—734no—
245C23—1462no—
246C23—1462no—
247C23—1462no—
248C23C2×C22⋊#6440811yescharacteristic
249D4—2922no—
250D4—2922no—
251D4—2922no—
252D4—2922no—
253D4—5848no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—2924no—
266C2×C4—2922no—
267C2×C4—2922no—
268C2×C4—2928no—
269C2×C4—2921no—
270C2×C4—5842no—
271C2×C4—5844no—
272C2×C4—5844no—
273C2×C4—5844no—
274C2×C4—1462no—
275C2×C4#1455665012yes—
276C2×C4C2×C4×#6440811yescharacteristic
277C2×C4#1455667011yescharacteristic
278C22—21no—
279C22—21no—
280C22—2924no—
281C22—2924no—
282C22—2922no—
283C22—2922no—
284C22—2922no—
285C22—5842no—
286C22—5842no—
287C22—5841no—
288C22—5841no—
289C22—1464no—
290C22C4×C22⋊#6440811yescharacteristic
291C22C2×#1455665011yescharacteristic
292C22#1798956611yescharacteristic
293C4—21no—
294C4—21no—
295C4—22no—
296C4—42no—
297C4—41no—
298C4—81no—
299C4—2922no—
300C4—5848no—
301C4—5841no—
302C2—21no—
303C2—21no—
304C2—2924no—
305C2—5842no—
306C2C4×#1455665011yescharacteristic
307C2#2262620811yescharacteristic
308C2#2262621211yescharacteristic
subgroupG/H
centerC22C2×#14556650
commutatorC2×C4×C73C2×C42
FrattiniC22×C4C22×#64408
Fitting#376×C73C4
socleC22×C73C2×#99
prime radicalC2×#14556588C22
cosocleC22×D292C23
hypercenter#376#64408
hypocenterC73#12628
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
2. C4×#14556650C2semidirect
3. #22625025C2semidirect
7. #17989492C4semidirect
10. C2×C4×D292C4semidirect
12. #17988489C4semidirect
16. #17988453C4semidirect
17. #376×C73C4semidirect
21. #14556650C2×C4semidirect
58. C2×D292C42semidirect
82. C42×C73C42semidirect
159. C73#12628semidirect
170. #376#64408semidirect
237. C42C4×#64408semidirect

Maximal subgroups

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

subgroupindex
C2×#179894922
C4×#145566502
#226250252
#226126562
#1262873