Finite Group Databasebeta

← C73×#3321 #22607474

Subgroups — C73×#3321 #22607474

Order 9344.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#555×C73C211yesmaximal, characteristic, complemented
2#548×C73C211yesmaximal, characteristic, complemented
3#489×C73C211yesmaximal, characteristic, complemented
4#485×C73C211yesmaximal, characteristic, complemented
5#482×C73C211yesmaximal, characteristic, complemented
6#475×C73C211yesmaximal, characteristic, complemented
7#469×C73C211yesmaximal, characteristic, complemented
8#465×C73C211yesmaximal, characteristic, complemented
9#463×C73C211yesmaximal, characteristic, complemented
10#449×C73C211yesmaximal, characteristic, complemented
11#448×C73C211yesmaximal, characteristic, complemented
12#440×C73C211yesmaximal, characteristic, complemented
13#435×C73C211yesmaximal, characteristic, complemented
14#419×C73C211yesmaximal, characteristic, complemented
15#416×C73C211yesmaximal, characteristic, complemented
16C2×#41×C73C2211yescharacteristic
17C22×Q8×C73C2211yescharacteristic
18C2×SD16×C73C2211yescharacteristic
19C2×SD16×C73C2211yescharacteristic
20C2×D8×C73C2211yescharacteristic
21C2×M16×C73C2211yescharacteristic
22C22×C8×C73C2211yescharacteristic
23C4⋊Q8×C73C2211yescharacteristic
24#124×C73—21no—
25#124×C73—21no—
26#124×C73—21no—
27#124×C73C2211yescharacteristic
28C22⋊Q8×C73—21no—
29C22⋊Q8×C73C2211yescharacteristic
30#121×C73—21no—
31#121×C73—21no—
32#121×C73C2211yescharacteristic
33#121×C73C2211yescharacteristic
34#121×C73C2211yescharacteristic
35C4×Q8×C73C2211yescharacteristic
36C4×D4×C73—21no—
37C4×D4×C73C2211yescharacteristic
38C4×D4×C73C2211yescharacteristic
39#117×C73—21no—
40#117×C73C2211yescharacteristic
41#117×C73C2211yescharacteristic
42#107×C73C2211yescharacteristic
43#106×C73C2211yescharacteristic
44#106×C73C2211yescharacteristic
45C4⋊C8×C73C2211yescharacteristic
46#103×C73C2211yescharacteristic
47#103×C73C2211yescharacteristic
48#103×C73C2211yescharacteristic
49#103×C73C2211yescharacteristic
50#103×C73C2211yescharacteristic
51#103×C73C2211yescharacteristic
52#102×C73C2211yescharacteristic
53#102×C73C2211yescharacteristic
54#102×C73C2211yescharacteristic
55#102×C73C2211yescharacteristic
56C22⋊C8×C73C2211yescharacteristic
57C22⋊C8×C73C2211yescharacteristic
58#97×C73C2211yescharacteristic
59#41×C73—22no—
60#41×C73—41no—
61C2×Q8×C73—21no—
62C2×Q8×C73—21no—
63C2×Q8×C73—22no—
64C2×Q8×C73—41no—
65C2×Q8×C73C2311yescharacteristic
66C2×Q8×C73C2311yescharacteristic
67C2×D4×C73—21no—
68C2×D4×C73—21no—
69C2×D4×C73—21no—
70C2×D4×C73—21no—
71C2×D4×C73D411yescharacteristic
72C2×D4×C73C2311yescharacteristic
73C2×D4×C73C2311yescharacteristic
74C22×C4×C73—21no—
75C22×C4×C73—21no—
76C22×C4×C73—21no—
77C22×C4×C73C2311yescharacteristic
78C22×C4×C73C2311yescharacteristic
79SD16×C73—22no—
80SD16×C73—41no—
81D8×C73—41no—
82M16×C73—41no—
83C2×C8×C73—41no—
84C2×C8×C73C2311yescharacteristic
85C2×C8×C73C2311yescharacteristic
86C2×C8×C73C2311yescharacteristic
87C2×C8×C73C2311yescharacteristic
88C4⋊C4×C73—21no—
89C4⋊C4×C73—21no—
90C4⋊C4×C73—21no—
91C4⋊C4×C73D411yescharacteristic
92C4⋊C4×C73C2311yescharacteristic
93C4⋊C4×C73C2311yescharacteristic
94C4⋊C4×C73C2311yescharacteristic
95C4⋊C4×C73C2311yescharacteristic
96C22⋊C4×C73—21no—
97C22⋊C4×C73—21no—
98C22⋊C4×C73—21no—
99C22⋊C4×C73—21no—
100C22⋊C4×C73—21no—
101C22⋊C4×C73—21no—
102C22⋊C4×C73—21no—
103C22⋊C4×C73—21no—
104C22⋊C4×C73—21no—
105C22⋊C4×C73D411yescharacteristic
106C22⋊C4×C73D411yescharacteristic
107C42×C73—21no—
108C42×C73—21no—
109C42×C73—21no—
110C42×C73C2311yescharacteristic
111C23×C73—21no—
112C23×C73—21no—
113C23×C73C2×D411yescharacteristic
114C23×C73C2×D411yescharacteristic
115Q8×C73—21no—
116Q8×C73—21no—
117Q8×C73—21no—
118Q8×C73—42no—
119Q8×C73—81no—
120Q8×C73#4112yes—
121D4×C73—21no—
122D4×C73—21no—
123D4×C73—21no—
124D4×C73—21no—
125D4×C73—41no—
126D4×C73—42no—
127D4×C73—42no—
128D4×C73—81no—
129D4×C73—81no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73—21no—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C2×C4×C73—21no—
140C2×C4×C73—42no—
141C2×C4×C73—42no—
142C2×C4×C73—42no—
143C2×C4×C73C2×D411yescharacteristic
144C2×C4×C73C2×D411yescharacteristic
145C2×C4×C73C2×D411yescharacteristic
146C2×C4×C73C2×D411yescharacteristic
147C2×C4×C73C2411yescharacteristic
148C8×C73—21no—
149C8×C73—21no—
150C8×C73—21no—
151C8×C73—21no—
152C22×C73—21no—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—21no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73C22×D411yescharacteristic
165C4×C73—21no—
166C4×C73—21no—
167C4×C73—22no—
168C4×C73—21no—
169C4×C73—21no—
170C4×C73—41no—
171C4×C73—41no—
172C4×C73—41no—
173C4×C73—41no—
174C4×C73—41no—
175C4×C73C2×#4111yescharacteristic
176C4×C73H(5,𝔽2)11yescharacteristic
177C2×C73—41no—
178C2×C73—41no—
179C2×C73—81no—
180C2×C73—81no—
181C2×C73#54611yescharacteristic
182C2×C73#57511yescharacteristic
183C2×C73#57711yescharacteristic
184#3321C7311yesmaximal, characteristic, direct product factor, Sylow
185C73#332111yescharacteristic, direct product factor, Sylow
186#555C2×C7311yescharacteristic, complemented
187#548C2×C7311yescharacteristic, complemented
188#489C2×C7311yescharacteristic, complemented
189#485C2×C7311yescharacteristic, complemented
190#482C2×C7311yescharacteristic, complemented
191#475C2×C7311yescharacteristic, complemented
192#469C2×C7311yescharacteristic, complemented
193#465C2×C7311yescharacteristic, complemented
194#463C2×C7311yescharacteristic, complemented
195#449C2×C7311yescharacteristic, complemented
196#448C2×C7311yescharacteristic, complemented
197#440C2×C7311yescharacteristic, complemented
198#435C2×C7311yescharacteristic, complemented
199#419C2×C7311yescharacteristic, complemented
200#416C2×C7311yescharacteristic, complemented
201C2×#41C22×C7311yescharacteristic
202C22×Q8C22×C7311yescharacteristic
203C2×SD16C22×C7311yescharacteristic
204C2×SD16C22×C7311yescharacteristic
205C2×D8C22×C7311yescharacteristic
206C2×M16C22×C7311yescharacteristic
207C22×C8C22×C7311yescharacteristic
208C4⋊Q8C22×C7311yescharacteristic
209#124—21no—
210#124—21no—
211#124—21no—
212#124C22×C7311yescharacteristic
213C22⋊Q8—21no—
214C22⋊Q8C22×C7311yescharacteristic
215#121—21no—
216#121—21no—
217#121C22×C7311yescharacteristic
218#121C22×C7311yescharacteristic
219#121C22×C7311yescharacteristic
220C4×Q8C22×C7311yescharacteristic
221C4×D4—21no—
222C4×D4C22×C7311yescharacteristic
223C4×D4C22×C7311yescharacteristic
224#117—21no—
225#117C22×C7311yescharacteristic
226#117C22×C7311yescharacteristic
227#107C22×C7311yescharacteristic
228#106C22×C7311yescharacteristic
229#106C22×C7311yescharacteristic
230C4⋊C8C22×C7311yescharacteristic
231#103C22×C7311yescharacteristic
232#103C22×C7311yescharacteristic
233#103C22×C7311yescharacteristic
234#103C22×C7311yescharacteristic
235#103C22×C7311yescharacteristic
236#103C22×C7311yescharacteristic
237#102C22×C7311yescharacteristic
238#102C22×C7311yescharacteristic
239#102C22×C7311yescharacteristic
240#102C22×C7311yescharacteristic
241C22⋊C8C22×C7311yescharacteristic
242C22⋊C8C22×C7311yescharacteristic
243#97C22×C7311yescharacteristic
244#41—22no—
245#41—41no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—22no—
249C2×Q8—41no—
250C2×Q8C23×C7311yescharacteristic
251C2×Q8C23×C7311yescharacteristic
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4D4×C7311yescharacteristic
257C2×D4C23×C7311yescharacteristic
258C2×D4C23×C7311yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4C23×C7311yescharacteristic
263C22×C4C23×C7311yescharacteristic
264SD16—22no—
265SD16—41no—
266D8—41no—
267M16—41no—
268C2×C8—41no—
269C2×C8C23×C7311yescharacteristic
270C2×C8C23×C7311yescharacteristic
271C2×C8C23×C7311yescharacteristic
272C2×C8C23×C7311yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4D4×C7311yescharacteristic
277C4⋊C4C23×C7311yescharacteristic
278C4⋊C4C23×C7311yescharacteristic
279C4⋊C4C23×C7311yescharacteristic
280C4⋊C4C23×C7311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4D4×C7311yescharacteristic
291C22⋊C4D4×C7311yescharacteristic
292C42—21no—
293C42—21no—
294C42—21no—
295C42C23×C7311yescharacteristic
296C23—21no—
297C23—21no—
298C23C2×D4×C7311yescharacteristic
299C23C2×D4×C7311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8—81no—
305Q8#41×C7312yes—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—21no—
310D4—41no—
311D4—42no—
312D4—42no—
313D4—81no—
314D4—81no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4C2×D4×C7311yescharacteristic
329C2×C4C2×D4×C7311yescharacteristic
330C2×C4C2×D4×C7311yescharacteristic
331C2×C4C2×D4×C7311yescharacteristic
332C2×C4C24×C7311yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22C22×D4×C7311yescharacteristic
350C4—21no—
351C4—21no—
352C4—22no—
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4C2×#41×C7311yescharacteristic
361C4H(5,𝔽2)×C7311yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—81no—
366C2#546×C7311yescharacteristic
367C2#575×C7311yescharacteristic
368C2#577×C7311yescharacteristic
subgroupG/H
center, socleC22×C73C22×D4
commutator, Frattini, cosocleC2×C4C24×C73
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C4×D4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. #555×C73C2semidirect
2. #548×C73C2semidirect
3. #489×C73C2semidirect
4. #485×C73C2semidirect
5. #482×C73C2semidirect
6. #475×C73C2semidirect
7. #469×C73C2semidirect
8. #465×C73C2semidirect
9. #463×C73C2semidirect
10. #449×C73C2semidirect
11. #448×C73C2semidirect
12. #440×C73C2semidirect
13. #435×C73C2semidirect
14. #419×C73C2semidirect
15. #416×C73C2semidirect
184. #3321C73direct (N × H)
185. C73#3321direct (N × H)
186. #555C2×C73semidirect
187. #548C2×C73semidirect
188. #489C2×C73semidirect
189. #485C2×C73semidirect
190. #482C2×C73semidirect
191. #475C2×C73semidirect
192. #469C2×C73semidirect
193. #465C2×C73semidirect
194. #463C2×C73semidirect
195. #449C2×C73semidirect
196. #448C2×C73semidirect
197. #440C2×C73semidirect
198. #435C2×C73semidirect
199. #419C2×C73semidirect
200. #416C2×C73semidirect

Maximal subgroups

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

subgroupindex
#555×C732
#548×C732
#489×C732
#485×C732
#482×C732
#475×C732
#469×C732
#465×C732
#463×C732
#449×C732
#448×C732
#440×C732
#435×C732
#419×C732
#416×C732
#332173