Finite Group Databasebeta

← C73×#11760 #32921164

Subgroups — C73×#11760 #32921164

Order 18688.

436 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C73×#2611C211yesmaximal, characteristic
2C73×#1740C211yesmaximal, characteristic
3C73×#1464C211yesmaximal, characteristic
4C73×#1352C212yesmaximal
5C73×#1344C212yesmaximal
6C2×#125×C73C411yescharacteristic, complemented
7C2×#117×C73—21no—
8C2×#117×C73C2211yescharacteristic
9#432×C73—21no—
10#400×C73C411yescharacteristic, complemented
11#399×C73C2211yescharacteristic
12#398×C73C411yescharacteristic, complemented
13#397×C73C2211yescharacteristic
14#389×C73—21no—
15#388×C73—21no—
16#387×C73—21no—
17#385×C73—21no—
18#376×C73C411yescharacteristic, complemented
19#342×C73—21no—
20#342×C73C2212yes—
21#324×C73—21no—
22#323×C73C2212yes—
23C23×C4×C73D411yescharacteristic
24#125×C73—41no—
25#125×C73—41no—
26#117×C73—24no—
27#117×C73—41no—
28#117×C73—41no—
29#117×C73—42no—
30C2×C4⋊C4×C73—21no—
31C2×C4⋊C4×C73—21no—
32C2×C4⋊C4×C73—21no—
33C2×C4⋊C4×C73—21no—
34C2×C4⋊C4×C73—41no—
35C2×C4⋊C4×C73C2×C411yescharacteristic
36C2×C4⋊C4×C73C2×C411yescharacteristic
37C2×C4⋊C4×C73C2×C411yescharacteristic
38C2×C4⋊C4×C73D411yescharacteristic
39C2×C22⋊C4×C73—22no—
40C2×C22⋊C4×C73—21no—
41C2×C22⋊C4×C73—21no—
42C2×C22⋊C4×C73D411yescharacteristic
43C2×C22⋊C4×C73C2311yescharacteristic
44C2×C42×C73—21no—
45C2×C42×C73—41no—
46C2×C42×C73C2×C411yescharacteristic
47C2×C42×C73D411yescharacteristic
48C4⋊C8×C73—41no—
49C22⋊C8×C73—22no—
50#97×C73—41no—
51#95×C73—21no—
52#95×C73—21no—
53#95×C73—21no—
54#95×C73—21no—
55#95×C73—21no—
56#95×C73C2×C411yescharacteristic
57#95×C73C2×C411yescharacteristic
58C24×C73C2×D411yescharacteristic
59C22×C4×C73—21no—
60C22×C4×C73—21no—
61C22×C4×C73—21no—
62C22×C4×C73—21no—
63C22×C4×C73—22no—
64C22×C4×C73—21no—
65C22×C4×C73—21no—
66C22×C4×C73—21no—
67C22×C4×C73—21no—
68C22×C4×C73—42no—
69C22×C4×C73C22⋊C411yescharacteristic
70C22×C4×C73C22⋊C411yescharacteristic
71C22×C4×C73C22⋊C411yescharacteristic
72C22×C4×C73C22⋊C411yescharacteristic
73C22×C4×C73C22×C411yescharacteristic
74C22×C4×C73C2×D411yescharacteristic
75C2×C8×C73—42no—
76C4⋊C4×C73—41no—
77C4⋊C4×C73—41no—
78C4⋊C4×C73—41no—
79C4⋊C4×C73—41no—
80C4⋊C4×C73—42no—
81C4⋊C4×C73—42no—
82C4⋊C4×C73—44no—
83C4⋊C4×C73—41no—
84C4⋊C4×C73—41no—
85C4⋊C4×C73—42no—
86C22⋊C4×C73—24no—
87C22⋊C4×C73—41no—
88C22⋊C4×C73—41no—
89C22⋊C4×C73—42no—
90C22⋊C4×C73—41no—
91C22⋊C4×C73—42no—
92C22⋊C4×C73—41no—
93C42×C73—21no—
94C42×C73—21no—
95C42×C73—21no—
96C42×C73—21no—
97C42×C73—42no—
98C42×C73—44no—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73—41no—
102C23×C73—41no—
103C23×C73C2×C22⋊C411yescharacteristic
104C23×C73AGL(1,ℤ/8)11yescharacteristic
105C23×C73#13711yescharacteristic
106C2×C4×C73—22no—
107C2×C4×C73—22no—
108C2×C4×C73—22no—
109C2×C4×C73—22no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—22no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—41no—
120C2×C4×C73—41no—
121C2×C4×C73—41no—
122C2×C4×C73—41no—
123C2×C4×C73—41no—
124C2×C4×C73—41no—
125C2×C4×C73—44no—
126C2×C4×C73—41no—
127C2×C4×C73—41no—
128C2×C4×C73—41no—
129C2×C4×C73—41no—
130C2×C4×C73—41no—
131C2×C4×C73—41no—
132C2×C4×C73—41no—
133C2×C4×C73—41no—
134C2×C4×C73—41no—
135C2×C4×C73—82no—
136C2×C4×C73—82no—
137C2×C4×C73#9911yescharacteristic
138C2×C4×C73#9911yescharacteristic
139C2×C4×C73#10412yes—
140C8×C73—82no—
141C22×C73—21no—
142C22×C73—21no—
143C22×C73—21no—
144C22×C73—21no—
145C22×C73—41no—
146C22×C73—41no—
147C22×C73—41no—
148C22×C73—41no—
149C22×C73—81no—
150C22×C73C2×#9911yescharacteristic
151C22×C73#41711yescharacteristic
152C22×C73C2×#10411yescharacteristic
153C4×C73—21no—
154C4×C73—21no—
155C4×C73—22no—
156C4×C73—42no—
157C4×C73—41no—
158C4×C73—41no—
159C4×C73—41no—
160C4×C73—41no—
161C4×C73—81no—
162C4×C73—84no—
163C4×C73—81no—
164C4×C73—81no—
165#11760C7311yesmaximal, characteristic, direct product factor, Sylow
166C2×C73—21no—
167C2×C73—21no—
168C2×C73—41no—
169C2×C73—41no—
170C2×C73#150411yescharacteristic
171C2×C73#212311yescharacteristic
172C2×C73#212611yescharacteristic
173#2611C2×C7311yescharacteristic
174#1740C2×C7311yescharacteristic
175#1464C2×C7311yescharacteristic
176#1352C2×C7312yes—
177#1344C2×C7312yes—
178C73#1176011yescharacteristic, direct product factor, Sylow
179C2×#125C4×C7311yescharacteristic, complemented
180C2×#117—21no—
181C2×#117C22×C7311yescharacteristic
182#432—21no—
183#400C4×C7311yescharacteristic, complemented
184#399C22×C7311yescharacteristic
185#398C4×C7311yescharacteristic, complemented
186#397C22×C7311yescharacteristic
187#389—21no—
188#388—21no—
189#387—21no—
190#385—21no—
191#376C4×C7311yescharacteristic, complemented
192#342—21no—
193#342C22×C7312yes—
194#324—21no—
195#323C22×C7312yes—
196C23×C4D4×C7311yescharacteristic
197#125—41no—
198#125—41no—
199#117—24no—
200#117—41no—
201#117—41no—
202#117—42no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—41no—
208C2×C4⋊C4C2×C4×C7311yescharacteristic
209C2×C4⋊C4C2×C4×C7311yescharacteristic
210C2×C4⋊C4C2×C4×C7311yescharacteristic
211C2×C4⋊C4D4×C7311yescharacteristic
212C2×C22⋊C4—22no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4D4×C7311yescharacteristic
216C2×C22⋊C4C23×C7311yescharacteristic
217C2×C42—21no—
218C2×C42—41no—
219C2×C42C2×C4×C7311yescharacteristic
220C2×C42D4×C7311yescharacteristic
221C4⋊C8—41no—
222C22⋊C8—22no—
223#97—41no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95C2×C4×C7311yescharacteristic
230#95C2×C4×C7311yescharacteristic
231C24C2×D4×C7311yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—42no—
242C22×C4C22⋊C4×C7311yescharacteristic
243C22×C4C22⋊C4×C7311yescharacteristic
244C22×C4C22⋊C4×C7311yescharacteristic
245C22×C4C22⋊C4×C7311yescharacteristic
246C22×C4C22×C4×C7311yescharacteristic
247C22×C4C2×D4×C7311yescharacteristic
248C2×C8—42no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—44no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—42no—
259C22⋊C4—24no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—42no—
263C22⋊C4—41no—
264C22⋊C4—42no—
265C22⋊C4—41no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—42no—
271C42—44no—
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23C2×C22⋊C4×C7311yescharacteristic
277C23AGL(1,ℤ/8)×C7311yescharacteristic
278C23#137×C7311yescharacteristic
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—44no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4#99×C7311yescharacteristic
311C2×C4#99×C7311yescharacteristic
312C2×C4#104×C7312yes—
313C8—82no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—81no—
323C22C2×#99×C7311yescharacteristic
324C22#417×C7311yescharacteristic
325C22C2×#104×C7311yescharacteristic
326C4—21no—
327C4—21no—
328C4—22no—
329C4—42no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—81no—
335C4—84no—
336C4—81no—
337C4—81no—
338C2—21no—
339C2—21no—
340C2—41no—
341C2—41no—
342C2C73×#150411yescharacteristic
343C2C73×#212311yescharacteristic
344C2C73×#212611yescharacteristic
subgroupG/H
center, socleC22×C73C2×#99
commutatorC22×C4C22×C4×C73
Frattini, cosocleC2×C22⋊C4C23×C73
prime radicalC24×C73C2×D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C22×C4×C73 ◁ C2×#117×C73 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×#125×C73C4semidirect
10. #400×C73C4semidirect
12. #398×C73C4semidirect
18. #376×C73C4semidirect
165. #11760C73direct (N × H)
178. C73#11760direct (N × H)
179. C2×#125C4×C73semidirect
183. #400C4×C73semidirect
185. #398C4×C73semidirect
191. #376C4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#26112
C73×#17402
C73×#14642
C73×#13522
C73×#13442
#1176073