Finite Group Databasebeta

← #34008105

Subgroups — #34008105

Order 18688.

460 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22625717C211yesmaximal, characteristic
2C4×#14556658C211yesmaximal, characteristic
3#22624767C212yesmaximal
4#22624767C212yesmaximal
5#125×Dic73C211yesmaximal, characteristic
6C2×#14556658—21no—
7C2×C4⋊#10596833C2212yes—
8C2×#14556646—21no—
9C2×C4×#10596833C2212yes—
10#17989453—21no—
11#17989453—21no—
12#17988486C411yescharacteristic
13#17988486C411yescharacteristic
14#17988473—21no—
15#17988473—21no—
16#17988453C411yescharacteristic
17C4⋊C4×Dic73—21no—
18C4⋊C4×Dic73—21no—
19C4⋊C4×Dic73C2211yescharacteristic
20C4⋊C4×Dic73C2211yescharacteristic
21C42×Dic73C2211yescharacteristic
22C2×#125×C73C411yescharacteristic
23C22×#10596833—22no—
24C22×#10596833—22no—
25#14556658—24no—
26C4⋊#10596833—22no—
27C4⋊#10596833Q814yes—
28#14556646—42no—
29C4×#10596833—24no—
30C2×C4⋊Dic73—21no—
31C2×C4⋊Dic73—21no—
32C2×C4⋊Dic73C2×C411yescharacteristic
33C2×C4⋊Dic73C2×C411yescharacteristic
34C2×C4×Dic73—21no—
35C2×C4×Dic73—21no—
36C2×C4×Dic73C2×C411yescharacteristic
37C2×C4×Dic73D411yescharacteristic
38C2×C4×Dic73D411yescharacteristic
39C2×C4×Dic73D411yescharacteristic
40C2×C4×Dic73D411yescharacteristic
41C2×C4×Dic73C2311yescharacteristic
42#14556498—21no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48#125×C73—22no—
49#125×C73—22no—
50C2×C4⋊C4×C73—21no—
51C2×C4⋊C4×C73—21no—
52C2×C4⋊C4×C73C2×C411yescharacteristic
53C2×C4⋊C4×C73C2×C411yescharacteristic
54C2×C42×C73C2×C411yescharacteristic
55C2×#10596833—24no—
56C2×#10596833—24no—
57C2×#10596833—42no—
58C2×#10596833—42no—
59C2×#10596833—42no—
60C2×#10596833—42no—
61C22×Dic73—21no—
62C22×Dic73—21no—
63C22×Dic73C22⋊C411yescharacteristic
64C22×Dic73C22⋊C411yescharacteristic
65C22×Dic73C2×D411yescharacteristic
66C22×Dic73C2×D411yescharacteristic
67C4⋊Dic73—22no—
68C4⋊Dic73—22no—
69C4⋊Dic73—42no—
70C4⋊Dic73—42no—
71C4×Dic73—22no—
72C4×Dic73—22no—
73C4×Dic73—22no—
74C4×Dic73—21no—
75C4×Dic73—21no—
76C4×Dic73—41no—
77C4×Dic73—42no—
78C4×Dic73—41no—
79C4×Dic73—41no—
80C4×Dic73C2×Q812yes—
81C4×Dic73#4112yes—
82C22×C4×C73—21no—
83C22×C4×C73—21no—
84C22×C4×C73C22⋊C411yescharacteristic
85C22×C4×C73C22⋊C411yescharacteristic
86C22×C4×C73C22×C411yescharacteristic
87C4⋊C4×C73—24no—
88C4⋊C4×C73—24no—
89C4⋊C4×C73—21no—
90C4⋊C4×C73—21no—
91C4⋊C4×C73M1612yes—
92C4⋊C4×C73M1612yes—
93C42×C73—21no—
94C42×C73—21no—
95C23×C73C2×C22⋊C411yescharacteristic
96C2×C4×C73—21no—
97C2×C4×C73—21no—
98C2×C4×C73—22no—
99C2×C4×C73—22no—
100C2×C4×C73—21no—
101C2×C4×C73—21no—
102C2×C4×C73—21no—
103C2×C4×C73—21no—
104C2×C4×C73—41no—
105C2×C4×C73—41no—
106C2×C4×C73—41no—
107C2×C4×C73—41no—
108C2×C4×C73C4×Q812yes—
109C2×C4×C73C2×M1611yescharacteristic
110C2×C4×C73C2×M1611yescharacteristic
111C2×C4×C73#13112yes—
112C2×Dic73—21no—
113C2×Dic73—21no—
114C2×Dic73—21no—
115C2×Dic73—21no—
116C2×Dic73—21no—
117C2×Dic73—21no—
118C2×Dic73—21no—
119C2×Dic73—41no—
120C2×Dic73—41no—
121C2×Dic73—41no—
122C2×Dic73—41no—
123C2×Dic73—41no—
124C2×Dic73—41no—
125C2×Dic73#10412yes—
126C2×Dic73C22⋊Q812yes—
127C2×Dic73#12411yescharacteristic
128C2×Dic73C4⋊Q811yescharacteristic
129C2×Dic73#13512yes—
130C2×Dic73AGL(1,ℤ/8)11yescharacteristic
131C2×Dic73#13711yescharacteristic
132#10596833—44no—
133#10596833—44no—
134C22×C73#39111yescharacteristic
135C22×C73#40711yescharacteristic
136C22×C73#40811yescharacteristic
137C22×C73#41611yescharacteristic
138C22×C73#41711yescharacteristic
139C22×C73C2×#10411yescharacteristic
140C22×C73#42111yescharacteristic
141C4×C73—41no—
142C4×C73—42no—
143C4×C73—41no—
144C4×C73—42no—
145C4×C73#44612yes—
146C4×C73#44612yes—
147Dic73—21no—
148Dic73—21no—
149Dic73—22no—
150Dic73—41no—
151Dic73—81no—
152Dic73—81no—
153Dic73#47812yes—
154Dic73#47912yes—
155#9867—731nomaximal, Sylow
156C2×C73#148811yescharacteristic
157C2×C73#148911yescharacteristic
158C2×C73#149411yescharacteristic
159C2×C73#149511yescharacteristic
160C2×C73#198511yescharacteristic
161C2×C73#198611yescharacteristic
162C2×C73#198911yescharacteristic
163C4×#125—731no—
164#1767—731no—
165C4×C4⋊C8—731no—
166#1279—732no—
167#1279—732no—
168C73#986711yescharacteristic, complemented, Sylow
169C2×#125#6440811yescharacteristic
170C2×C4⋊C8—732no—
171C2×C4⋊C8—1461no—
172C2×#97—1461no—
173C2×C4×C8—732no—
174#389—731no—
175#389—731no—
176#387—1461no—
177#387—1461no—
178#382—731no—
179C4×C4⋊C4—731no—
180C4×C4⋊C4—731no—
181C4×C4⋊C4—1461no—
182C4×C4⋊C4—1461no—
183C43—731no—
184#336—1461no—
185#336—1461no—
186C22×C8—1462no—
187C22×C8—1462no—
188#125—22no—
189#125—22no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—731no—
193C2×C4⋊C4—731no—
194C2×C4⋊C4—1461no—
195C2×C4⋊C4—1461no—
196C2×C4⋊C4C2×#6440811yescharacteristic
197C2×C4⋊C4C2×#6440811yescharacteristic
198C2×C42—731no—
199C2×C42—731no—
200C2×C42—731no—
201C2×C42—731no—
202C2×C42—731no—
203C2×C42—731no—
204C2×C42—1461no—
205C2×C42—1461no—
206C2×C42C2×#6440811yescharacteristic
207C4⋊C8—734no—
208C4⋊C8—1462no—
209C4⋊C8—1464no—
210#97—2922no—
211C4×C8—1464no—
212#95—1461no—
213#95—1461no—
214#95—1461no—
215#95—1461no—
216#95—1461no—
217#95—1461no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—731no—
221C22×C4—731no—
222C22×C4—731no—
223C22×C4—731no—
224C22×C4—1461no—
225C22×C4—1461no—
226C22×C4C22⋊#6440811yescharacteristic
227C22×C4C22⋊#6440811yescharacteristic
228C22×C4C22×#6440811yescharacteristic
229C2×C8—2922no—
230C2×C8—2922no—
231C2×C8—2922no—
232C2×C8—2922no—
233C2×C8—1464no—
234C2×C8—1464no—
235C4⋊C4—24no—
236C4⋊C4—24no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—2922no—
240C4⋊C4—2922no—
241C4⋊C4—1462no—
242C4⋊C4—1462no—
243C4⋊C4#1192403712yes—
244C4⋊C4#1192403712yes—
245C42—21no—
246C42—21no—
247C42—2921no—
248C42—2922no—
249C42—2921no—
250C42—2921no—
251C42—732no—
252C42—732no—
253C42—1461no—
254C42—1462no—
255C42—1462no—
256C42—1461no—
257C42—1462no—
258C23C2×C22⋊#6440811yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—2921no—
272C2×C4—2921no—
273C2×C4—2921no—
274C2×C4—2921no—
275C2×C4—2921no—
276C2×C4—2921no—
277C2×C4—732no—
278C2×C4—732no—
279C2×C4—731no—
280C2×C4—731no—
281C2×C4—731no—
282C2×C4—731no—
283C2×C4—732no—
284C2×C4—1461no—
285C2×C4—1461no—
286C2×C4—1461no—
287C2×C4—1461no—
288C2×C4—1461no—
289C2×C4—1461no—
290C2×C4—1461no—
291C2×C4Q8×#6440812yes—
292C2×C4C2×#1192403711yescharacteristic
293C2×C4C2×#1192403711yescharacteristic
294C2×C4#1455667912yes—
295C8—2924no—
296C8—2924no—
297C22(C2×#64408)⋊Q811yescharacteristic
298C22#1798955711yescharacteristic
299C22#1798956211yescharacteristic
300C22#1798957711yescharacteristic
301C22#1798957811yescharacteristic
302C22D73⋊#10411yescharacteristic
303C22#1798958411yescharacteristic
304C4—41no—
305C4—42no—
306C4—41no—
307C4—42no—
308C4—2921no—
309C4—5841no—
310C4—5841no—
311C4—732no—
312C4—732no—
313C4—1462no—
314C4—1461no—
315C4—1461no—
316C4#1798963812yes—
317C4#1798963812yes—
318C2#2262526211yescharacteristic
319C2#2262526611yescharacteristic
320C2#2262528511yescharacteristic
321C2#2262528911yescharacteristic
322C2#2262610511yescharacteristic
323C2#2262610811yescharacteristic
324C2#2262611111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
FittingC2×#125×C73C4
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4×Dic73C23
hypercenterC2×#125#64408
hypocenterC73#9867
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
168. C73#9867semidirect

Maximal subgroups

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

subgroupindex
#226257172
C4×#145566582
#226247672
#125×Dic732
#986773