Finite Group Databasebeta

← C73×#8762 #32918166

Subgroups — C73×#8762 #32918166

Order 18688.

472 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2353C211yesmaximal, characteristic
2C73×#1799C211yesmaximal, characteristic
3C73×#1459C211yesmaximal, characteristic
4C73×#1294C212yesmaximal, complemented
5C73×#1289C212yesmaximal, complemented
6C2×C4×D4×C73C2211yescharacteristic
7C2×#99×C73—21no—
8C2×C22⋊C8×C73C2212yes—
9#388×C73—21no—
10#387×C73—21no—
11#386×C73—21no—
12#383×C73C411yescharacteristic, complemented
13#381×C73C411yescharacteristic, complemented
14#380×C73C2212yes—
15#380×C73C2211yescharacteristic
16C4×C22⋊C4×C73—21no—
17C4×C22⋊C4×C73C411yescharacteristic, complemented
18#376×C73C411yescharacteristic, complemented
19C2×#95×C73C2211yescharacteristic
20#342×C73—21no—
21#324×C73—21no—
22#323×C73—21no—
23C22×D4×C73D411yescharacteristic
24C23×C4×C73—21no—
25C23×C4×C73C2×C411yescharacteristic
26C23×C4×C73C2311yescharacteristic
27C22×C8×C73—22no—
28C4×D4×C73—22no—
29C4×D4×C73—22no—
30C2×C4⋊C4×C73—21no—
31C2×C4⋊C4×C73—22no—
32C2×C4⋊C4×C73D411yescharacteristic
33C2×C22⋊C4×C73—21no—
34C2×C22⋊C4×C73—21no—
35C2×C22⋊C4×C73—22no—
36C2×C22⋊C4×C73—21no—
37C2×C22⋊C4×C73D411yescharacteristic
38C2×C22⋊C4×C73D411yescharacteristic
39C2×C42×C73—21no—
40C2×C42×C73—21no—
41C2×C42×C73C2×C411yescharacteristic
42#99×C73—42no—
43C22⋊C8×C73—22no—
44C22⋊C8×C73—22no—
45#95×C73—21no—
46#95×C73—21no—
47#95×C73—21no—
48#95×C73—21no—
49#95×C73—21no—
50#95×C73—22no—
51#95×C73C2×C411yescharacteristic
52#95×C73C2×C411yescharacteristic
53#95×C73C2×C411yescharacteristic
54#95×C73C2×C411yescharacteristic
55C24×C73C22⋊C411yescharacteristic
56C24×C73C2×D411yescharacteristic
57C2×D4×C73—22no—
58C2×D4×C73—22no—
59C2×D4×C73—21no—
60C2×D4×C73—21no—
61C22×C4×C73—21no—
62C22×C4×C73—21no—
63C22×C4×C73—21no—
64C22×C4×C73—21no—
65C22×C4×C73—21no—
66C22×C4×C73—21no—
67C22×C4×C73—42no—
68C22×C4×C73—41no—
69C22×C4×C73—41no—
70C22×C4×C73—42no—
71C22×C4×C73—81no—
72C22×C4×C73—81no—
73C22×C4×C73—81no—
74C22×C4×C73C22⋊C411yescharacteristic
75C22×C4×C73C22⋊C411yescharacteristic
76C22×C4×C73C22⋊C411yescharacteristic
77C22×C4×C73C22×C411yescharacteristic
78C22×C4×C73C2×D411yescharacteristic
79C22×C4×C73#4112yes—
80C22×C4×C73#4112yes—
81C2×C8×C73—42no—
82C2×C8×C73—82no—
83C4⋊C4×C73—22no—
84C4⋊C4×C73—81no—
85C4⋊C4×C73—82no—
86C22⋊C4×C73—22no—
87C22⋊C4×C73—22no—
88C22⋊C4×C73—42no—
89C22⋊C4×C73—42no—
90C22⋊C4×C73—42no—
91C22⋊C4×C73—42no—
92C22⋊C4×C73—81no—
93C42×C73—21no—
94C42×C73—21no—
95C42×C73—42no—
96C42×C73—81no—
97C23×C73—21no—
98C23×C73—21no—
99C23×C73—21no—
100C23×C73—41no—
101C23×C73—41no—
102C23×C73—41no—
103C23×C73—41no—
104C23×C73C2×C22⋊C411yescharacteristic
105C23×C73#12312yes—
106C23×C73#13512yes—
107C23×C73AGL(1,ℤ/8)11yescharacteristic
108C23×C73#13711yescharacteristic
109D4×C73—42no—
110D4×C73—42no—
111C2×C4×C73—22no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—41no—
118C2×C4×C73—42no—
119C2×C4×C73—42no—
120C2×C4×C73—41no—
121C2×C4×C73—41no—
122C2×C4×C73—41no—
123C2×C4×C73—41no—
124C2×C4×C73—41no—
125C2×C4×C73—41no—
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—81no—
135C2×C4×C73—81no—
136C2×C4×C73—82no—
137C2×C4×C73—82no—
138C2×C4×C73—82no—
139C2×C4×C73—82no—
140C2×C4×C73—82no—
141C2×C4×C73#11711yescharacteristic
142C2×C4×C73#11711yescharacteristic
143C2×C4×C73#12312yes—
144C8×C73—82no—
145C22×C73—21no—
146C22×C73—22no—
147C22×C73—21no—
148C22×C73—22no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73—42no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73—81no—
156C22×C73—81no—
157C22×C73#38111yescharacteristic
158C22×C73#41611yescharacteristic
159C22×C73#41711yescharacteristic
160C22×C73#48212yes—
161C22×C73#48512yes—
162C4×C73—22no—
163C4×C73—21no—
164C4×C73—21no—
165C4×C73—42no—
166C4×C73—41no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73—81no—
170C4×C73—81no—
171C4×C73—81no—
172C4×C73—162no—
173#8762C7311yesmaximal, characteristic, direct product factor, Sylow
174C2×C73—21no—
175C2×C73—21no—
176C2×C73—22no—
177C2×C73—22no—
178C2×C73—81no—
179C2×C73#182511yescharacteristic
180C2×C73#182711yescharacteristic
181C2×C73#182811yescharacteristic
182#2353C2×C7311yescharacteristic
183#1799C2×C7311yescharacteristic
184#1459C2×C7311yescharacteristic
185#1294C2×C7312yescomplemented
186#1289C2×C7312yescomplemented
187C73#876211yescharacteristic, direct product factor, Sylow
188C2×C4×D4C22×C7311yescharacteristic
189C2×#99—21no—
190C2×C22⋊C8C22×C7312yes—
191#388—21no—
192#387—21no—
193#386—21no—
194#383C4×C7311yescharacteristic, complemented
195#381C4×C7311yescharacteristic, complemented
196#380C22×C7312yes—
197#380C22×C7311yescharacteristic
198C4×C22⋊C4—21no—
199C4×C22⋊C4C4×C7311yescharacteristic, complemented
200#376C4×C7311yescharacteristic, complemented
201C2×#95C22×C7311yescharacteristic
202#342—21no—
203#324—21no—
204#323—21no—
205C22×D4D4×C7311yescharacteristic
206C23×C4—21no—
207C23×C4C2×C4×C7311yescharacteristic
208C23×C4C23×C7311yescharacteristic
209C22×C8—22no—
210C4×D4—22no—
211C4×D4—22no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4D4×C7311yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4D4×C7311yescharacteristic
220C2×C22⋊C4D4×C7311yescharacteristic
221C2×C42—21no—
222C2×C42—21no—
223C2×C42C2×C4×C7311yescharacteristic
224#99—42no—
225C22⋊C8—22no—
226C22⋊C8—22no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—22no—
233#95C2×C4×C7311yescharacteristic
234#95C2×C4×C7311yescharacteristic
235#95C2×C4×C7311yescharacteristic
236#95C2×C4×C7311yescharacteristic
237C24C22⋊C4×C7311yescharacteristic
238C24C2×D4×C7311yescharacteristic
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—21no—
242C2×D4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—42no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—42no—
253C22×C4—81no—
254C22×C4—81no—
255C22×C4—81no—
256C22×C4C22⋊C4×C7311yescharacteristic
257C22×C4C22⋊C4×C7311yescharacteristic
258C22×C4C22⋊C4×C7311yescharacteristic
259C22×C4C22×C4×C7311yescharacteristic
260C22×C4C2×D4×C7311yescharacteristic
261C22×C4#41×C7312yes—
262C22×C4#41×C7312yes—
263C2×C8—42no—
264C2×C8—82no—
265C4⋊C4—22no—
266C4⋊C4—81no—
267C4⋊C4—82no—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—42no—
274C22⋊C4—81no—
275C42—21no—
276C42—21no—
277C42—42no—
278C42—81no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23C2×C22⋊C4×C7311yescharacteristic
287C23#123×C7312yes—
288C23#135×C7312yes—
289C23AGL(1,ℤ/8)×C7311yescharacteristic
290C23#137×C7311yescharacteristic
291D4—42no—
292D4—42no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—82no—
321C2×C4—82no—
322C2×C4—82no—
323C2×C4#117×C7311yescharacteristic
324C2×C4#117×C7311yescharacteristic
325C2×C4#123×C7312yes—
326C8—82no—
327C22—21no—
328C22—22no—
329C22—21no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—42no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22—81no—
339C22#381×C7311yescharacteristic
340C22#416×C7311yescharacteristic
341C22#417×C7311yescharacteristic
342C22#482×C7312yes—
343C22#485×C7312yes—
344C4—22no—
345C4—21no—
346C4—21no—
347C4—42no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—81no—
352C4—81no—
353C4—81no—
354C4—162no—
355C2—21no—
356C2—21no—
357C2—22no—
358C2—22no—
359C2—81no—
360C2C73×#182511yescharacteristic
361C2C73×#182711yescharacteristic
362C2C73×#182811yescharacteristic
subgroupG/H
center, socleC22×C73#381
commutatorC22×C4C22×C4×C73
Frattini, cosocleC23×C4C23×C73
prime radicalC22×D4×C73D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
4. C73×#1294C2semidirect
5. C73×#1289C2semidirect
12. #383×C73C4semidirect
13. #381×C73C4semidirect
17. C4×C22⋊C4×C73C4semidirect
18. #376×C73C4semidirect
173. #8762C73direct (N × H)
185. #1294C2×C73semidirect
186. #1289C2×C73semidirect
187. C73#8762direct (N × H)
194. #383C4×C73semidirect
195. #381C4×C73semidirect
199. C4×C22⋊C4C4×C73semidirect
200. #376C4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#23532
C73×#17992
C73×#14592
C73×#12942
C73×#12892
#876273