Finite Group Databasebeta

← #34001335

Subgroups — #34001335

Order 18688.

684 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 146 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
1C4×#14556658C212yesmaximal, complemented
2#22624748C212yesmaximal, complemented
3#22624747C212yesmaximal, complemented
4C4×#14556587C211yesmaximal, characteristic
5C2×#14556658—22no—
6C2×C4×#10596833—22no—
7#17989453C2214yes—
8C2×#14556587C411yescharacteristic
9C2×C4×D292C411yescharacteristic
10C2×C4×C22⋊D73—22no—
11#17988490C2211yescharacteristic
12#17988488C2211yescharacteristic
13#17988487—22no—
14#17988456C411yescharacteristic
15C42×Dic73C2211yescharacteristic
16C2×C4×D4×C73C411yescharacteristic
17C22×#10596833—24no—
18#14556658—28no—
19C4×#10596833—44no—
20C22×D292C2×C411yescharacteristic
21C22×C22⋊D73—22no—
22C22×C4×D73—21no—
23#14556587—22no—
24#14556587C814yescomplemented
25C4×D292—42no—
26C4×C22⋊D73—44no—
27C4×C22⋊D73—44no—
28C2×C4⋊Dic73C2×C411yescharacteristic
29C2×#11924007—22no—
30C2×C22⋊Dic73—22no—
31C2×#11924005—22no—
32C2×#11924005—21no—
33C2×C4×Dic73C2×C411yescharacteristic
34C2×C4×Dic73D412yes—
35C2×C4×Dic73D412yes—
36C2×C4×Dic73C2311yescharacteristic
37C22×D4×C73C2×C411yescharacteristic
38C23×C4×C73—21no—
39C4×D4×C73—42no—
40C2×C4⋊C4×C73C2×C411yescharacteristic
41C2×C22⋊C4×C73—21no—
42C2×C42×C73C2×C411yescharacteristic
43C2×#10596833—28no—
44C2×#10596833—44no—
45C2×#10596833—44no—
46C23×D73—21no—
47C2×D292—21no—
48C2×D292—41no—
49C2×D292—41no—
50C2×D292C2×C812yes—
51C2×C22⋊D73—28no—
52C2×C22⋊D73—44no—
53C2×C22⋊D73—44no—
54C22×Dic73—21no—
55C22×Dic73C22⋊C412yes—
56C22×Dic73C2×D412yes—
57C2×C4×D73—42no—
58C2×C4×D73—44no—
59C4⋊Dic73—41no—
60#11924007—44no—
61C22⋊Dic73—42no—
62C22⋊Dic73—42no—
63#11924005—42no—
64#11924005—42no—
65#11924005—42no—
66C4×Dic73—24no—
67C4×Dic73—41no—
68C4×Dic73C2×C812yes—
69C4×Dic73M1612yes—
70C4×Dic73D814yes—
71C4×Dic73SD1614yes—
72C24×C73—21no—
73C2×D4×C73—21no—
74C2×D4×C73—41no—
75C2×D4×C73—41no—
76C2×D4×C73C2×C812yes—
77C22×C4×C73—21no—
78C22×C4×C73—42no—
79C22×C4×C73—44no—
80C22×C4×C73C22⋊C411yescharacteristic
81C22×C4×C73C22⋊C411yescharacteristic
82C22×C4×C73C22×C411yescharacteristic
83C4⋊C4×C73—41no—
84C22⋊C4×C73—42no—
85C42×C73—22no—
86C23×C73—22no—
87C23×C73—41no—
88C23×C73—41no—
89C23×C73—42no—
90C23×C73—42no—
91C23×C73C2×C22⋊C411yescharacteristic
92C22×D73—22no—
93C22×D73—41no—
94C22×D73—41no—
95C22×D73—42no—
96C22×D73—42no—
97D4×C73—42no—
98D4×C73—42no—
99C2×C4×C73—21no—
100C2×C4×C73—21no—
101C2×C4×C73—21no—
102C2×C4×C73—22no—
103C2×C4×C73—41no—
104C2×C4×C73—42no—
105C2×C4×C73—84no—
106C2×C4×C73#10012yes—
107C2×C4×C73#10214yes—
108C2×C4×C73C22×C811yescharacteristic
109C2×C4×C73C2×M1611yescharacteristic
110C22⋊D73—416no—
111C2×Dic73—22no—
112C2×Dic73—22no—
113C2×Dic73—41no—
114C2×Dic73—42no—
115C2×Dic73C22⋊C814yes—
116C2×Dic73#10214yes—
117C2×Dic73#10414yes—
118C2×Dic73C2×D812yes—
119C2×Dic73C2×SD1612yes—
120D292—42no—
121D292—42no—
122C4×D73—84no—
123#10596833—48no—
124C22×C73—42no—
125C22×C73—44no—
126C22×C73—81no—
127C22×C73—82no—
128C22×C73—81no—
129C22×C73C2×C22⋊C811yescharacteristic
130C22×C73#41011yescharacteristic
131C22×C73C2×#10011yescharacteristic
132C22×C73C2×#10212yes—
133C22×C73C2×#10412yes—
134C2×D73—42no—
135C2×D73—44no—
136C2×D73—81no—
137C2×D73—82no—
138C2×D73—81no—
139C4×C73—21no—
140C4×C73—21no—
141C4×C73—41no—
142C4×C73—81no—
143C4×C73#33114yes—
144Dic73—22no—
145Dic73—22no—
146Dic73—81no—
147Dic73D4⋊C818yes—
148#7569—731nomaximal, Sylow
149C2×C73—82no—
150C2×C73#146011yescharacteristic
151C2×C73C2×D4⋊C812yes—
152C2×C73#150212yes—
153C2×C73#152511yescharacteristic
154C2×C73C2×#33111yescharacteristic
155D73—82no—
156C4×#127—731no—
157C4×C4⋊C8—732no—
158#1270—732no—
159#1270—732no—
160C73#756911yescharacteristic, complemented, Sylow
161C2×#127—731no—
162C2×C4×D4—731no—
163C2×C4×D4—1462no—
164C2×C4×D4#6440811yescharacteristic
165C2×C4⋊C8—1462no—
166C2×C4×C8—1462no—
167#390—731no—
168#390—731no—
169#390—1462no—
170#384—731no—
171C43—731no—
172#336—734no—
173C22×D4—731no—
174C22×D4—1462no—
175C22×D4C2×#6440811yescharacteristic
176C23×C4—21no—
177C23×C4—1461no—
178C22×C8—1464no—
179#127—734no—
180#127—1462no—
181C4×D4—42no—
182C4×D4—2922no—
183C4×D4—2924no—
184C4×D4—2924no—
185C2×C4⋊C4—731no—
186C2×C4⋊C4—1462no—
187C2×C4⋊C4C2×#6440811yescharacteristic
188C2×C22⋊C4—21no—
189C2×C22⋊C4—1462no—
190C2×C22⋊C4—1462no—
191C2×C22⋊C4—1461no—
192C2×C42—731no—
193C2×C42—732no—
194C2×C42—731no—
195C2×C42—732no—
196C2×C42C2×#6440811yescharacteristic
197C4⋊C8—1468no—
198C4×C8—2924no—
199C24—21no—
200C24—1461no—
201C2×D4—21no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4—2921no—
205C2×D4—2921no—
206C2×D4—2924no—
207C2×D4—2924no—
208C2×D4—732no—
209C2×D4—1468no—
210C2×D4—1461no—
211C2×D4#1192403612yes—
212C22×C4—21no—
213C22×C4—42no—
214C22×C4—44no—
215C22×C4—2922no—
216C22×C4—2924no—
217C22×C4—732no—
218C22×C4—732no—
219C22×C4—1461no—
220C22×C4C22⋊#6440811yescharacteristic
221C22×C4C22⋊#6440811yescharacteristic
222C22×C4C22×#6440811yescharacteristic
223C2×C8—2924no—
224C2×C8—2924no—
225C2×C8—1468no—
226C4⋊C4—41no—
227C4⋊C4—2921no—
228C4⋊C4—2924no—
229C22⋊C4—42no—
230C22⋊C4—2922no—
231C22⋊C4—2922no—
232C22⋊C4—2922no—
233C22⋊C4—2922no—
234C22⋊C4—2922no—
235C42—22no—
236C42—2921no—
237C42—732no—
238C42—732no—
239C42—734no—
240C42—734no—
241C42—1464no—
242C23—22no—
243C23—41no—
244C23—41no—
245C23—42no—
246C23—42no—
247C23—2921no—
248C23—2921no—
249C23—2922no—
250C23—2922no—
251C23—1462no—
252C23C2×C22⋊#6440811yescharacteristic
253D4—42no—
254D4—42no—
255D4—2922no—
256D4—2922no—
257D4—29216no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—84no—
265C2×C4—2921no—
266C2×C4—2922no—
267C2×C4—5844no—
268C2×C4—734no—
269C2×C4—734no—
270C2×C4—734no—
271C2×C4—732no—
272C2×C4—732no—
273C2×C4—1462no—
274C2×C4—1462no—
275C2×C4#1455665112yes—
276C2×C4#1455665314yes—
277C2×C4C2×#1192403611yescharacteristic
278C2×C4D73⋊M1611yescharacteristic
279C8—2928no—
280C22—42no—
281C22—44no—
282C22—82no—
283C22—81no—
284C22—81no—
285C22—2922no—
286C22—2924no—
287C22—5842no—
288C22—5841no—
289C22—5841no—
290C22#1798955511yescharacteristic
291C22#1798956611yescharacteristic
292C22C2×#1455665111yescharacteristic
293C22C2×#1455665312yes—
294C22D73⋊#10412yes—
295C4—21no—
296C4—21no—
297C4—41no—
298C4—81no—
299C4—5841no—
300C4—738no—
301C4—1462no—
302C4—1462no—
303C4#1798944514yes—
304C2—82no—
305C2—5842no—
306C2#2262517011yescharacteristic
307C2#2262521712yes—
308C2#2262531012yes—
309C2#2262538511yescharacteristic
310C2C2×#1798944511yescharacteristic
subgroupG/H
centerC22×C4C22⋊#64408
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
FittingC2×C4×D4×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC2×#14556587C4
cosocleC2×C4×Dic73C23
hypercenterC2×C4×D4#64408
hypocenterC73#7569
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C4×#14556658C2semidirect
2. #22624748C2semidirect
3. #22624747C2semidirect
24. #14556587C8semidirect
160. C73#7569semidirect

Maximal subgroups

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

subgroupindex
C4×#145566582
#226247482
#226247472
C4×#145565872
#756973