Finite Group Databasebeta

← #32990748

Subgroups — #32990748

Order 18688.

350 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22610868C211yesmaximal, characteristic
2#22610058C211yesmaximal, characteristic
3#22609936C211yesmaximal, characteristic
4#22607815C211yesmaximal, characteristic
5#22607814C211yesmaximal, characteristic
6#22607765C211yesmaximal, characteristic
7C73×#1803C211yesmaximal, characteristic
8C2×C4⋊#10596831C2211yescharacteristic
9C2×C4⋊#10596831C2211yescharacteristic
10C2×#14556515—21no—
11C2×C4×#10596831C2211yescharacteristic
12#17988457C2211yescharacteristic
13#17988349—21no—
14#17988349—21no—
15#17988349—21no—
16#17988342—21no—
17#17988342—21no—
18C2×C4×Q8×C73C2211yescharacteristic
19C2×C4⋊C8×C73C2211yescharacteristic
20C2×#103×C73—21no—
21#384×C73C2211yescharacteristic
22#340×C73—21no—
23C22×#10596831—21no—
24C22×#10596831—21no—
25C22×#10596831D411yescharacteristic
26C22×#10596831D411yescharacteristic
27C2×C4⋊Dic73—21no—
28C2×C4⋊Dic73—21no—
29C2×C4⋊Dic73—21no—
30C4⋊#10596831—21no—
31C4⋊#10596831—21no—
32C4⋊#10596831—21no—
33C4⋊#10596831—21no—
34#14556515—42no—
35C4×#10596831—21no—
36C4×#10596831—21no—
37C22×Q8×C73D411yescharacteristic
38C22×C8×C73—21no—
39C4×Q8×C73—21no—
40C4×Q8×C73—21no—
41C4×Q8×C73—21no—
42C4×Q8×C73—21no—
43C2×C4⋊C4×C73—21no—
44C2×C4⋊C4×C73—21no—
45C2×C4⋊C4×C73—21no—
46C2×C4⋊C4×C73—21no—
47C2×C4⋊C4×C73D411yescharacteristic
48C2×C42×C73—21no—
49C2×C42×C73C2311yescharacteristic
50C4⋊C8×C73—21no—
51C4⋊C8×C73—21no—
52#103×C73—42no—
53C22×Dic73—41no—
54C2×#10596831—21no—
55C2×#10596831—21no—
56C2×#10596831—21no—
57C2×#10596831—21no—
58C2×#10596831—21no—
59C2×#10596831—21no—
60C2×#10596831—41no—
61C2×#10596831—41no—
62C2×#10596831—41no—
63C2×#10596831—41no—
64C2×#10596831—41no—
65C2×#10596831—41no—
66C4⋊Dic73—41no—
67C4⋊Dic73—41no—
68C4⋊Dic73—41no—
69C4⋊Dic73—41no—
70C4⋊Dic73—81no—
71C2×Q8×C73—21no—
72C2×Q8×C73—21no—
73C2×Q8×C73—21no—
74C2×Q8×C73—21no—
75C2×Q8×C73—21no—
76C2×Q8×C73SD1612yes—
77C22×C4×C73—21no—
78C22×C4×C73—21no—
79C22×C4×C73—41no—
80C22×C4×C73C2×D411yescharacteristic
81C22×C4×C73C2×D411yescharacteristic
82C22×C4×C73#4111yescharacteristic
83C2×C8×C73—41no—
84C2×C8×C73—41no—
85C2×C8×C73—41no—
86C4⋊C4×C73—21no—
87C4⋊C4×C73—21no—
88C4⋊C4×C73—41no—
89C4⋊C4×C73—41no—
90C4⋊C4×C73—41no—
91C4⋊C4×C73—41no—
92C4⋊C4×C73—41no—
93C4⋊C4×C73—41no—
94C4⋊C4×C73—81no—
95C42×C73—41no—
96C42×C73—41no—
97C42×C73#4111yescharacteristic
98C42×C73#4111yescharacteristic
99C42×C73#4111yescharacteristic
100C42×C73#4111yescharacteristic
101C23×C73#12111yescharacteristic
102Q8×C73—22no—
103Q8×C73—22no—
104Q8×C73—41no—
105Q8×C73—41no—
106C2×C4×C73—21no—
107C2×C4×C73—21no—
108C2×C4×C73—22no—
109C2×C4×C73—41no—
110C2×C4×C73—41no—
111C2×C4×C73—41no—
112C2×C4×C73—41no—
113C2×C4×C73—41no—
114C2×C4×C73—81no—
115C2×C4×C73—81no—
116C2×C4×C73—81no—
117C2×C4×C73#12311yescharacteristic
118C2×C4×C73#12311yescharacteristic
119C2×C4×C73#12311yescharacteristic
120C2×C4×C73#12411yescharacteristic
121C2×C4×C73#12611yescharacteristic
122C2×C4×C73#12611yescharacteristic
123C2×C4×C73C2×SD1611yescharacteristic
124C2×C4×C73#13511yescharacteristic
125C2×C4×C73#13511yescharacteristic
126C2×C4×C73#13511yescharacteristic
127C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C73#13711yescharacteristic
129C2×C4×C73#13711yescharacteristic
130C2×C4×C73#13711yescharacteristic
131C2×Dic73—81no—
132C2×Dic73—81no—
133C2×Dic73—81no—
134C8×C73—81no—
135#10596831—41no—
136#10596831—41no—
137#10596831—81no—
138#10596831—81no—
139C22×C73#39711yescharacteristic
140C22×C73#46411yescharacteristic
141C22×C73#46411yescharacteristic
142C22×C73#46511yescharacteristic
143C22×C73#46811yescharacteristic
144C22×C73#47211yescharacteristic
145C22×C73#47311yescharacteristic
146C4×C73—21no—
147C4×C73—21no—
148C4×C73—42no—
149C4×C73—81no—
150C4×C73—161no—
151C4×C73#48111yescharacteristic
152C4×C73#48211yescharacteristic
153C4×C73#48311yescharacteristic
154C4×C73#48511yescharacteristic
155C4×C73#48511yescharacteristic
156C4×C73#48511yescharacteristic
157C4×C73#48811yescharacteristic
158C4×C73#49111yescharacteristic
159Dic73—161no—
160#10626—731nomaximal, Sylow
161C2×C73#167811yescharacteristic
162C2×C73#168011yescharacteristic
163C2×C73#169811yescharacteristic
164C2×C73#170011yescharacteristic
165C2×C73#207411yescharacteristic
166C2×C73#207711yescharacteristic
167C2×C73#207811yescharacteristic
168#1984—731no—
169#1834—731no—
170#1803—731no—
171#1803D7311yescharacteristic
172#1296—731no—
173#1296—731no—
174#1277—731no—
175C73#1062611yescharacteristic, complemented, Sylow
176C2×C4×Q8C2×D7311yescharacteristic
177C2×C4⋊C8—731no—
178C2×C4⋊C8—731no—
179C2×C4⋊C8C2×D7311yescharacteristic
180C2×#103—21no—
181C2×#103—1461no—
182C2×C4×C8—731no—
183#384—731no—
184#384C2×D7311yescharacteristic
185#340—21no—
186#340—1461no—
187#340—1461no—
188#340—1461no—
189#336—1461no—
190#336—1461no—
191C22×Q8C22⋊D7311yescharacteristic
192C22×C8—21no—
193C22×C8—731no—
194C22×C8—731no—
195C22×C8—1461no—
196C22×C8—1461no—
197C4×Q8—21no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—1461no—
206C2×C4⋊C4—1461no—
207C2×C4⋊C4—1461no—
208C2×C4⋊C4C22⋊D7311yescharacteristic
209C2×C42—21no—
210C2×C42C22×D7311yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—1461no—
214C4⋊C8—1461no—
215C4⋊C8—1461no—
216C4⋊C8—1461no—
217#103—42no—
218#103—2922no—
219C4×C8—1461no—
220C4×C8—1461no—
221C2×Q8—21no—
222C2×Q8—21no—
223C2×Q8—21no—
224C2×Q8—21no—
225C2×Q8—21no—
226C2×Q8#1192401612yes—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—41no—
230C22×C4—2921no—
231C22×C4D4×D7311yescharacteristic
232C22×C4C2×C22⋊D7311yescharacteristic
233C22×C4#1192402711yescharacteristic
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—2921no—
238C2×C8—2921no—
239C2×C8—2921no—
240C2×C8—2921no—
241C2×C8—2921no—
242C2×C8—2921no—
243C2×C8—1461no—
244C2×C8—1461no—
245C2×C8—1461no—
246C2×C8—1461no—
247C2×C8—1461no—
248C2×C8—1461no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—81no—
258C4⋊C4—2921no—
259C4⋊C4—2921no—
260C4⋊C4—2921no—
261C4⋊C4—2921no—
262C4⋊C4—5841no—
263C42—41no—
264C42—41no—
265C42#1192402711yescharacteristic
266C42#1192402711yescharacteristic
267C42#1192402811yescharacteristic
268C42#1192402811yescharacteristic
269C23#1455656311yescharacteristic
270Q8—22no—
271Q8—22no—
272Q8—41no—
273Q8—41no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—5841no—
286C2×C4—5841no—
287C2×C4—5841no—
288C2×C4#1455657211yescharacteristic
289C2×C4#1455657311yescharacteristic
290C2×C4#1455657411yescharacteristic
291C2×C4#1455657711yescharacteristic
292C2×C4#1455658411yescharacteristic
293C2×C4#1455658411yescharacteristic
294C2×C4C2×#1192401611yescharacteristic
295C2×C4#1455661111yescharacteristic
296C2×C4#1455661211yescharacteristic
297C2×C4#1455661411yescharacteristic
298C2×C4#1455661611yescharacteristic
299C2×C4#1455662011yescharacteristic
300C2×C4#1455662211yescharacteristic
301C2×C4#1455662311yescharacteristic
302C8—81no—
303C8—2921no—
304C8—2921no—
305C8—5841no—
306C8—5841no—
307C22#1798851511yescharacteristic
308C22#1798880711yescharacteristic
309C22#1798881111yescharacteristic
310C22#1798881411yescharacteristic
311C22#1798883511yescharacteristic
312C22#1798885511yescharacteristic
313C22#1798886011yescharacteristic
314C4—21no—
315C4—21no—
316C4—42no—
317C4—81no—
318C4—161no—
319C4—11681no—
320C4#1798890311yescharacteristic
321C4#1798891111yescharacteristic
322C4#1798891711yescharacteristic
323C4#1798892511yescharacteristic
324C4#1798892611yescharacteristic
325C4#1798892711yescharacteristic
326C4#1798894311yescharacteristic
327C4#1798895411yescharacteristic
328C2#2260934511yescharacteristic
329C2#2260936311yescharacteristic
330C2#2260947311yescharacteristic
331C2#2260948311yescharacteristic
332C2#2261135211yescharacteristic
333C2#2261136711yescharacteristic
334C2#2261137411yescharacteristic
subgroupG/H
centerC23#14556563
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1803C2
socle, prime radicalC23×C73#121
hypercenter#1803D73
hypocenterC73#10626
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
175. C73#10626semidirect

Maximal subgroups

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

subgroupindex
#226108682
#226100582
#226099362
#226078152
#226078142
#226077652
C73×#18032
#1062673