Finite Group Databasebeta

← #32976161

Subgroups — #32976161

Order 18688.

652 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988611C211yesmaximal, characteristic
2C2×C4×#11924012C211yesmaximal, characteristic
3#22607822C214yesmaximal, complemented
4C73×#2920C211yesmaximal, characteristic
5C22×#11924012—21no—
6C22×#11924012C412yes—
7#17988611—21no—
8#17988611—21no—
9#17988611C412yes—
10#17988611C2212yes—
11C2×C4⋊#10596831—21no—
12C2×C4⋊#10596831—21no—
13C4×#11924012—21no—
14C4×#11924012—21no—
15C4×#11924012C412yes—
16C4×#11924012C2212yes—
17C2×#14556502C412yes—
18C2×C4×#10596831—21no—
19C22×C42×C73C2211yescharacteristic
20#432×C73—21no—
21#432×C73C412yes—
22#431×C73—21no—
23#431×C73C2212yes—
24#423×C73C412yes—
25#407×C73—21no—
26C4×M16×C73—21no—
27C2×#11924012—28no—
28C2×#11924012—22no—
29C2×#11924012—22no—
30C2×#11924012—22no—
31C2×#11924012—44no—
32C2×#11924012C2×C414yes—
33C22×#10596831—22no—
34C22×#10596831—22no—
35C4⋊#10596831—22no—
36C4⋊#10596831—22no—
37C4⋊#10596831—22no—
38C4⋊#10596831—22no—
39#14556502—22no—
40#14556502C2×C414yes—
41C4×#10596831—22no—
42C4×#10596831—22no—
43C23×C4×C73C2×C411yescharacteristic
44C23×C4×C73D411yescharacteristic
45C23×C4×C73Q811yescharacteristic
46C2×M16×C73—22no—
47C2×C42×C73C2×C411yescharacteristic
48C2×C42×C73C2×C411yescharacteristic
49C2×C42×C73C2×C411yescharacteristic
50C2×C42×C73C2×C411yescharacteristic
51C2×C42×C73C2×C411yescharacteristic
52C2×C42×C73D411yescharacteristic
53C2×C42×C73D411yescharacteristic
54C2×C42×C73D411yescharacteristic
55C2×C42×C73D411yescharacteristic
56C2×C42×C73D411yescharacteristic
57C2×C42×C73Q811yescharacteristic
58C2×C42×C73C2311yescharacteristic
59C4⋊C8×C73—22no—
60C4⋊C8×C73C2×C414yes—
61C22⋊C8×C73—22no—
62C22⋊C8×C73—22no—
63#97×C73—22no—
64C4×C8×C73—22no—
65#11924012—28no—
66#11924012—28no—
67#11924012—44no—
68#11924012—44no—
69C2×#10596831—28no—
70C2×#10596831—24no—
71C2×#10596831—24no—
72C2×#10596831—44no—
73C24×C73C4⋊C411yescharacteristic
74C22×C4×C73—22no—
75C22×C4×C73—22no—
76C22×C4×C73—24no—
77C22×C4×C73—42no—
78C22×C4×C73C4211yescharacteristic
79C22×C4×C73C4211yescharacteristic
80C22×C4×C73C22⋊C411yescharacteristic
81C22×C4×C73C22⋊C411yescharacteristic
82C22×C4×C73C22⋊C411yescharacteristic
83C22×C4×C73C22⋊C411yescharacteristic
84C22×C4×C73C22⋊C411yescharacteristic
85C22×C4×C73C22⋊C411yescharacteristic
86C22×C4×C73C4⋊C411yescharacteristic
87C22×C4×C73C4⋊C411yescharacteristic
88C22×C4×C73C4⋊C411yescharacteristic
89C22×C4×C73C4⋊C411yescharacteristic
90C22×C4×C73C4⋊C411yescharacteristic
91C22×C4×C73C4⋊C411yescharacteristic
92C22×C4×C73C4⋊C411yescharacteristic
93C22×C4×C73C22×C411yescharacteristic
94C22×C4×C73C2×D411yescharacteristic
95C22×C4×C73C2×Q811yescharacteristic
96M16×C73—44no—
97C2×C8×C73—24no—
98C42×C73C4211yescharacteristic
99C42×C73C4211yescharacteristic
100C42×C73C22⋊C411yescharacteristic
101C42×C73C22⋊C411yescharacteristic
102C42×C73C22⋊C411yescharacteristic
103C42×C73C22⋊C411yescharacteristic
104C42×C73C22⋊C411yescharacteristic
105C42×C73C22⋊C411yescharacteristic
106C42×C73C4⋊C411yescharacteristic
107C42×C73C4⋊C411yescharacteristic
108C42×C73C4⋊C411yescharacteristic
109C42×C73C4⋊C411yescharacteristic
110C42×C73C22×C411yescharacteristic
111C42×C73C22×C411yescharacteristic
112C42×C73C2×D411yescharacteristic
113C42×C73C2×D411yescharacteristic
114C23×C73—22no—
115C23×C73—22no—
116C23×C73—41no—
117C23×C73#9511yescharacteristic
118C23×C73#9511yescharacteristic
119C23×C73C2×C4⋊C411yescharacteristic
120C2×C4×C73—22no—
121C2×C4×C73—22no—
122C2×C4×C73—22no—
123C2×C4×C73—22no—
124C2×C4×C73—22no—
125C2×C4×C73—22no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—22no—
131C2×C4×C73—22no—
132C2×C4×C73—22no—
133C2×C4×C73—22no—
134C2×C4×C73—22no—
135C2×C4×C73—41no—
136C2×C4×C73—41no—
137C2×C4×C73—41no—
138C2×C4×C73#9511yescharacteristic
139C2×C4×C73#9511yescharacteristic
140C2×C4×C73#9511yescharacteristic
141C2×C4×C73#9511yescharacteristic
142C2×C4×C73#9511yescharacteristic
143C2×C4×C73#9511yescharacteristic
144C2×C4×C73#10012yes—
145C2×C4×C73#10112yes—
146C2×C4×C73#10414yes—
147C2×C4×C73C2×C4211yescharacteristic
148C2×C4×C73C2×C22⋊C411yescharacteristic
149C2×C4×C73C2×C22⋊C411yescharacteristic
150C2×C4×C73C2×C22⋊C411yescharacteristic
151C2×C4×C73C2×C4⋊C411yescharacteristic
152C2×C4×C73C2×C4⋊C411yescharacteristic
153C8×C73—44no—
154#10596831—28no—
155#10596831—44no—
156C22×C73—21no—
157C22×C73—21no—
158C22×C73—21no—
159C22×C73—21no—
160C22×C73—21no—
161C22×C73—21no—
162C22×C73—21no—
163C22×C73—44no—
164C22×C73#33912yes—
165C22×C73#34312yes—
166C22×C73C2×#9511yescharacteristic
167C4×C73—21no—
168C4×C73—21no—
169C4×C73—21no—
170C4×C73—21no—
171C4×C73—21no—
172C4×C73—21no—
173C4×C73—21no—
174C4×C73#33912yes—
175C4×C73#34312yes—
176C4×C73C2×#10011yescharacteristic
177C4×C73C2×#10111yescharacteristic
178C4×C73C2×#10412yes—
179C4×C73#43012yes—
180#8063—731nomaximal, Sylow
181C2×C73—22no—
182C2×C73—22no—
183C2×C73—41no—
184C2×C73C2×#33911yescharacteristic
185C2×C73#173811yescharacteristic
186C2×C73C2×#34311yescharacteristic
187#2920D7311yescharacteristic
188C2×#423—731no—
189C2×C4×M16—731no—
190#1299—734no—
191C73#806311yescharacteristic, complemented, Sylow
192C22×M16—732no—
193C22×M16—1461no—
194C22×C42C2×D7311yescharacteristic
195#432—21no—
196#432Dic7312yes—
197#431—21no—
198#431C2×D7312yes—
199#423—732no—
200#423—732no—
201#423—1461no—
202#423—1461no—
203#423Dic7312yes—
204C2×C4⋊C8—1461no—
205C2×C4⋊C8—1461no—
206#407—21no—
207C4×M16—21no—
208C4×M16—732no—
209C4×M16—732no—
210C4×M16—1461no—
211C4×M16—1461no—
212C2×#97—732no—
213C2×C4×C8—1461no—
214C23×C4Dic14611yescharacteristic
215C23×C4C4×D7311yescharacteristic
216C23×C4C22⋊D7311yescharacteristic
217C2×M16—22no—
218C2×M16—2924no—
219C2×M16—734no—
220C2×M16—1462no—
221C2×M16—1468no—
222C2×M16—1462no—
223C2×M16—1462no—
224C22×C8—1462no—
225C22×C8—1462no—
226C2×C42Dic14611yescharacteristic
227C2×C42C4×D7311yescharacteristic
228C2×C42C4×D7311yescharacteristic
229C2×C42C4×D7311yescharacteristic
230C2×C42D29211yescharacteristic
231C2×C42D29211yescharacteristic
232C2×C42C2×Dic7311yescharacteristic
233C2×C42C2×Dic7311yescharacteristic
234C2×C42C22⋊D7311yescharacteristic
235C2×C42C22⋊D7311yescharacteristic
236C2×C42C22⋊D7311yescharacteristic
237C2×C42C22×D7311yescharacteristic
238C4⋊C8—22no—
239C4⋊C8—1462no—
240C4⋊C8—1462no—
241C4⋊C8—1462no—
242C4⋊C8—1462no—
243C4⋊C8C2×Dic7314yes—
244C22⋊C8—22no—
245C22⋊C8—22no—
246#97—22no—
247#97—734no—
248#97—1462no—
249C4×C8—22no—
250C4×C8—1462no—
251C4×C8—1462no—
252C24#1192400711yescharacteristic
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—24no—
256C22×C4—42no—
257C22×C4C4×Dic7311yescharacteristic
258C22×C4C4×Dic7311yescharacteristic
259C22×C4#1192400511yescharacteristic
260C22×C4#1192400511yescharacteristic
261C22×C4#1192400511yescharacteristic
262C22×C4#1192400511yescharacteristic
263C22×C4C22⋊Dic7311yescharacteristic
264C22×C4C22⋊Dic7311yescharacteristic
265C22×C4#1192400711yescharacteristic
266C22×C4#1192400711yescharacteristic
267C22×C4#1192400711yescharacteristic
268C22×C4#1192400711yescharacteristic
269C22×C4#1192400711yescharacteristic
270C22×C4C4⋊Dic7311yescharacteristic
271C22×C4C4⋊Dic7311yescharacteristic
272C22×C4C2×C4×D7311yescharacteristic
273C22×C4C2×C22⋊D7311yescharacteristic
274C22×C4C2×Dic14611yescharacteristic
275M16—44no—
276M16—2924no—
277M16—2924no—
278M16—1468no—
279M16—1468no—
280C2×C8—24no—
281C2×C8—2924no—
282C2×C8—1464no—
283C2×C8—1468no—
284C2×C8—1464no—
285C42C4×Dic7311yescharacteristic
286C42C4×Dic7311yescharacteristic
287C42#1192400511yescharacteristic
288C42#1192400511yescharacteristic
289C42#1192400511yescharacteristic
290C42#1192400511yescharacteristic
291C42C22⋊Dic7311yescharacteristic
292C42C22⋊Dic7311yescharacteristic
293C42#1192400711yescharacteristic
294C42#1192400711yescharacteristic
295C42C4⋊Dic7311yescharacteristic
296C42C4⋊Dic7311yescharacteristic
297C42C2×C4×D7311yescharacteristic
298C42C22×Dic7311yescharacteristic
299C42C2×C22⋊D7311yescharacteristic
300C42C2×D29211yescharacteristic
301C23—22no—
302C23—22no—
303C23—41no—
304C23#1455649811yescharacteristic
305C23#1455649811yescharacteristic
306C23C2×#1192400711yescharacteristic
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4#1455649811yescharacteristic
326C2×C4#1455649811yescharacteristic
327C2×C4#1455649811yescharacteristic
328C2×C4#1455649811yescharacteristic
329C2×C4#1455649811yescharacteristic
330C2×C4#1455649811yescharacteristic
331C2×C4#1455650712yes—
332C2×C4#1455650912yes—
333C2×C4#1455651814yes—
334C2×C4C2×C4×Dic7311yescharacteristic
335C2×C4C2×#1192400511yescharacteristic
336C2×C4C2×#1192400511yescharacteristic
337C2×C4C2×C22⋊Dic7311yescharacteristic
338C2×C4C2×#1192400711yescharacteristic
339C2×C4C2×C4⋊Dic7311yescharacteristic
340C8—44no—
341C8—2924no—
342C8—1468no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—44no—
351C22#1798834612yes—
352C22#1798835512yes—
353C22C2×#1455649811yescharacteristic
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4#1798834612yes—
362C4#1798835512yes—
363C4C2×#1455650711yescharacteristic
364C4C2×#1455650911yescharacteristic
365C4C2×#1455651812yes—
366C4#1798863612yes—
367C2—22no—
368C2—22no—
369C2—41no—
370C2C2×#1798834611yescharacteristic
371C2#2260965811yescharacteristic
372C2C2×#1798835511yescharacteristic
subgroupG/H
centerC2×C4C2×#11924005
commutatorC2×C4×C73C2×C42
FrattiniC2×C42C22×D73
FittingC73×#2920C2
socleC22×C73C2×#95
prime radicalC24×C73C4⋊C4
cosocleC2×C42×C73C23
hypercenter#2920D73
hypocenterC73#8063
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
3. #22607822C2semidirect
191. C73#8063semidirect

Maximal subgroups

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

subgroupindex
C2×#179886112
C2×C4×#119240122
#226078222
C73×#29202
#806373