Finite Group Databasebeta

← #32984349

Subgroups — #32984349

Order 18688.

382 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22610893C211yesmaximal, characteristic
2#22610689C211yesmaximal, characteristic
3C4⋊C4×#10596831C211yesmaximal, characteristic
4C2×#17988336C211yesmaximal, characteristic
5#22607815C211yesmaximal, characteristic
6#22607765C211yesmaximal, characteristic
7C73×#1987C211yesmaximal, characteristic
8C2×#14556524—21no—
9C2×C4⋊#10596831C2211yescharacteristic
10C2×C4⋊#10596831C2211yescharacteristic
11C2×C4×#10596831—21no—
12C2×C4×#10596831C2211yescharacteristic
13#17988457C2211yescharacteristic
14#17988349—21no—
15#17988349—21no—
16#17988349—21no—
17#17988342—21no—
18#17988336C414yescomplemented
19C2×C4⋊Q8×C73C2211yescharacteristic
20C2×C4⋊C8×C73C2211yescharacteristic
21C4×C4⋊C4×C73C2211yescharacteristic
22#340×C73—21no—
23#340×C73—21no—
24C22×#10596831—21no—
25C22×#10596831—21no—
26C22×#10596831D411yescharacteristic
27C22×#10596831D411yescharacteristic
28C2×C4⋊Dic73—21no—
29C2×C4⋊Dic73—21no—
30C2×C4⋊Dic73—21no—
31#14556524—42no—
32C4⋊#10596831—21no—
33C4⋊#10596831—21no—
34C4⋊#10596831C2×C412yes—
35C4⋊#10596831C2×C412yes—
36C4×#10596831—21no—
37C4×#10596831—21no—
38C4×#10596831—42no—
39C22×Q8×C73—21no—
40C22×C8×C73—21no—
41C4⋊Q8×C73—21no—
42C4⋊Q8×C73—21no—
43C4⋊Q8×C73—21no—
44C4⋊Q8×C73C2×C412yes—
45C2×C4⋊C4×C73—21no—
46C2×C4⋊C4×C73—21no—
47C2×C4⋊C4×C73D411yescharacteristic
48C2×C4⋊C4×C73D411yescharacteristic
49C2×C42×C73—21no—
50C2×C42×C73C2311yescharacteristic
51C4⋊C8×C73—21no—
52C4⋊C8×C73—21no—
53#95×C73—21no—
54C22×Dic73—41no—
55C2×#10596831—21no—
56C2×#10596831—21no—
57C2×#10596831—22no—
58C2×#10596831—22no—
59C2×#10596831—21no—
60C2×#10596831—21no—
61C2×#10596831—21no—
62C2×#10596831—41no—
63C2×#10596831—41no—
64C2×#10596831—41no—
65C2×#10596831—41no—
66C2×#10596831Q1612yes—
67C4⋊Dic73—41no—
68C4⋊Dic73—41no—
69C4⋊Dic73—41no—
70C4⋊Dic73—41no—
71C4⋊Dic73—81no—
72C2×Q8×C73—22no—
73C2×Q8×C73—41no—
74C2×Q8×C73—81no—
75C2×Q8×C73—81no—
76C22×C4×C73—21no—
77C22×C4×C73—21no—
78C22×C4×C73—41no—
79C22×C4×C73C2×D411yescharacteristic
80C22×C4×C73C2×D411yescharacteristic
81C22×C4×C73#4111yescharacteristic
82C2×C8×C73—41no—
83C2×C8×C73—41no—
84C2×C8×C73—41no—
85C4⋊C4×C73—21no—
86C4⋊C4×C73—21no—
87C4⋊C4×C73—22no—
88C4⋊C4×C73—22no—
89C4⋊C4×C73—41no—
90C4⋊C4×C73—41no—
91C4⋊C4×C73SD1612yes—
92C4⋊C4×C73Q1612yes—
93C42×C73—41no—
94C42×C73—41no—
95C42×C73C22×C411yescharacteristic
96C42×C73#4111yescharacteristic
97C42×C73#4111yescharacteristic
98C42×C73#4111yescharacteristic
99C23×C73#12111yescharacteristic
100Q8×C73—82no—
101Q8×C73—82no—
102C2×C4×C73—21no—
103C2×C4×C73—21no—
104C2×C4×C73—22no—
105C2×C4×C73—22no—
106C2×C4×C73—41no—
107C2×C4×C73—41no—
108C2×C4×C73—41no—
109C2×C4×C73—41no—
110C2×C4×C73—42no—
111C2×C4×C73—81no—
112C2×C4×C73—81no—
113C2×C4×C73#11711yescharacteristic
114C2×C4×C73C4×D411yescharacteristic
115C2×C4×C73C4×D411yescharacteristic
116C2×C4×C73#12311yescharacteristic
117C2×C4×C73#12411yescharacteristic
118C2×C4×C73#12611yescharacteristic
119C2×C4×C73C2×SD1611yescharacteristic
120C2×C4×C73C2×Q1611yescharacteristic
121C2×C4×C73C2×Q1611yescharacteristic
122C2×C4×C73#13511yescharacteristic
123C2×C4×C73#13511yescharacteristic
124C2×C4×C73#13511yescharacteristic
125C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C73#13711yescharacteristic
127C2×Dic73—81no—
128C2×Dic73—81no—
129C2×Dic73—81no—
130C8×C73—81no—
131#10596831—22no—
132#10596831—42no—
133#10596831—42no—
134#10596831—41no—
135C22×C73#38811yescharacteristic
136C22×C73#46211yescharacteristic
137C22×C73#46311yescharacteristic
138C22×C73#46511yescharacteristic
139C22×C73#46711yescharacteristic
140C22×C73#47111yescharacteristic
141C22×C73#47211yescharacteristic
142C4×C73—21no—
143C4×C73—21no—
144C4×C73—42no—
145C4×C73—42no—
146C4×C73—82no—
147C4×C73C4×SD1611yescharacteristic
148C4×C73C4×Q1611yescharacteristic
149C4×C73C4×Q1611yescharacteristic
150C4×C73#44011yescharacteristic
151C4×C73#48411yescharacteristic
152C4×C73#48511yescharacteristic
153C4×C73#48711yescharacteristic
154C4×C73#48811yescharacteristic
155Dic73—161no—
156#9568—731nomaximal, Sylow
157C2×C73#167211yescharacteristic
158C2×C73#167611yescharacteristic
159C2×C73#167711yescharacteristic
160C2×C73#168311yescharacteristic
161C2×C73#192811yescharacteristic
162C2×C73#193111yescharacteristic
163C2×C73#193311yescharacteristic
164#1990—731no—
165#1987D7311yescharacteristic
166#1947—731no—
167C8×C4⋊C4—731no—
168C2×#333—731no—
169#1296—731no—
170#1277—731no—
171C73#956811yescharacteristic, complemented, Sylow
172C2×C4⋊Q8C2×D7311yescharacteristic
173C2×#107—1461no—
174C2×C4⋊C8—731no—
175C2×C4⋊C8—731no—
176C2×C4⋊C8C2×D7311yescharacteristic
177C2×C4×C8—731no—
178C2×C4×C8—1461no—
179#384—731no—
180C4×C4⋊C4C2×D7311yescharacteristic
181#340—21no—
182#340—21no—
183#340—1461no—
184#340—1461no—
185#340—1461no—
186#336—1461no—
187#333—734no—
188C22×Q8—21no—
189C22×C8—21no—
190C22×C8—731no—
191C22×C8—731no—
192C22×C8—1461no—
193C22×C8—1461no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8C4×D7312yes—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—1461no—
201C2×C4⋊C4—1461no—
202C2×C4⋊C4—1461no—
203C2×C4⋊C4C22⋊D7311yescharacteristic
204C2×C4⋊C4C22⋊D7311yescharacteristic
205C2×C42—21no—
206C2×C42C22×D7311yescharacteristic
207#107—2922no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—732no—
211C4⋊C8—732no—
212C4⋊C8—1461no—
213C4⋊C8—1461no—
214C4×C8—2922no—
215C4×C8—1461no—
216C4×C8—1461no—
217#95—21no—
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—81no—
221C2×Q8—81no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4—2921no—
226C22×C4D4×D7311yescharacteristic
227C22×C4C2×C22⋊D7311yescharacteristic
228C22×C4#1192402711yescharacteristic
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—2921no—
233C2×C8—2921no—
234C2×C8—2921no—
235C2×C8—2921no—
236C2×C8—732no—
237C2×C8—1462no—
238C2×C8—1462no—
239C2×C8—1461no—
240C2×C8—1461no—
241C2×C8—1461no—
242C2×C8—1461no—
243C2×C8—1461no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—2921no—
251C4⋊C4—2921no—
252C4⋊C4—2921no—
253C4⋊C4—2921no—
254C4⋊C4—5841no—
255C4⋊C4#1192401512yes—
256C4⋊C4#1192401812yes—
257C42—41no—
258C42—41no—
259C42C2×C4×D7311yescharacteristic
260C42#1192402711yescharacteristic
261C42#1192402711yescharacteristic
262C42#1192402811yescharacteristic
263C23#1455656311yescharacteristic
264Q8—82no—
265Q8—82no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—5841no—
278C2×C4—5841no—
279C2×C4—5841no—
280C2×C4#1455654711yescharacteristic
281C2×C4#1455655111yescharacteristic
282C2×C4C4×C22⋊D7311yescharacteristic
283C2×C4#1455657311yescharacteristic
284C2×C4#1455657811yescharacteristic
285C2×C4#1455658411yescharacteristic
286C2×C4C2×#1192401511yescharacteristic
287C2×C4Q16×D7311yescharacteristic
288C2×C4C2×#1192401811yescharacteristic
289C2×C4#1455661111yescharacteristic
290C2×C4#1455661111yescharacteristic
291C2×C4#1455661211yescharacteristic
292C2×C4#1455661811yescharacteristic
293C2×C4#1455662311yescharacteristic
294C8—81no—
295C8—2921no—
296C8—2922no—
297C8—2922no—
298C8—1462no—
299C22#1798848111yescharacteristic
300C22#1798879511yescharacteristic
301C22#1798880411yescharacteristic
302C22#1798881811yescharacteristic
303C22#1798882611yescharacteristic
304C22#1798884811yescharacteristic
305C22#1798885511yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—42no—
310C4—82no—
311C4—11681no—
312C4C4×#1192401511yescharacteristic
313C4#1798867911yescharacteristic
314C4C4×#1192401811yescharacteristic
315C4#1798869011yescharacteristic
316C4#1798892111yescharacteristic
317C4#1798892611yescharacteristic
318C4#1798893711yescharacteristic
319C4#1798894111yescharacteristic
320C2#2260931511yescharacteristic
321C2#2260933311yescharacteristic
322C2#2260934211yescharacteristic
323C2#2260938411yescharacteristic
324C2#2261057511yescharacteristic
325C2#2261059611yescharacteristic
326C2#2261061011yescharacteristic
subgroupG/H
centerC23#14556563
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1987C2
socle, prime radicalC23×C73#121
cosocleC2×C42×C73C23
hypercenter#1987D73
hypocenterC73#9568
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
18. #17988336C4semidirect
171. C73#9568semidirect

Maximal subgroups

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

subgroupindex
#226108932
#226106892
C4⋊C4×#105968312
C2×#179883362
#226078152
#226077652
C73×#19872
#956873