Finite Group Databasebeta

← C73×#19210 #32928614

Subgroups — C73×#19210 #32928614

Order 18688.

570 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3249C212yesmaximal
2C73×#3160C211yesmaximal, characteristic
3C73×#2960C211yesmaximal, characteristic
4C73×#1696C212yesmaximal, complemented
5C73×#1694C212yesmaximal, complemented
6C73×#1672C214yesmaximal, complemented
7C2×#334×C73C211yesmaximal, characteristic
8C73×#1550C212yesmaximal
9#533×C73C2212yes—
10#533×C73C2211yescharacteristic
11#500×C73C2211yescharacteristic
12#500×C73C2211yescharacteristic
13#499×C73—21no—
14#499×C73—21no—
15#498×C73C2212yes—
16#477×C73—22no—
17#477×C73C2214yes—
18#467×C73—24no—
19#462×C73—22no—
20#462×C73C2214yes—
21#446×C73—21no—
22#446×C73C2212yes—
23C8×Q8×C73—21no—
24C8×Q8×C73C2212yes—
25#427×C73—21no—
26#427×C73—21no—
27#424×C73—21no—
28#423×C73C2211yescharacteristic
29C2×C4⋊C8×C73C2212yes—
30#405×C73—21no—
31C2×C4×C8×C73C2211yescharacteristic
32#334×C73C2212yes—
33#334×C73C2212yes—
34#333×C73C2214yes—
35#332×C73C2214yes—
36C2×Q16×C73—24no—
37C2×M16×C73—21no—
38C22×C8×C73—22no—
39C22×C8×C73D411yescharacteristic
40C22×C8×C73D411yescharacteristic
41C4⋊Q8×C73D411yescharacteristic
42C4⋊Q8×C73D411yescharacteristic
43C4⋊Q8×C73C2312yes—
44C4⋊Q8×C73C2312yes—
45#125×C73—22no—
46#125×C73—21no—
47C22⋊Q8×C73—21no—
48C22⋊Q8×C73—22no—
49C22⋊Q8×C73—22no—
50C22⋊Q8×C73D412yes—
51C4×Q8×C73—21no—
52C4×Q8×C73—22no—
53C4×Q8×C73—22no—
54C4×Q8×C73C2312yes—
55#117×C73—21no—
56#117×C73—22no—
57C2×C42×C73C2311yescharacteristic
58#107×C73—21no—
59#107×C73—21no—
60#107×C73—21no—
61#107×C73—21no—
62#107×C73—24no—
63#106×C73—22no—
64#106×C73—22no—
65C4⋊C8×C73—22no—
66C4⋊C8×C73—22no—
67C4⋊C8×C73—22no—
68C4⋊C8×C73—21no—
69C4⋊C8×C73C2314yes—
70C4⋊C8×C73C2312yes—
71#103×C73—24no—
72#103×C73—24no—
73#97×C73—22no—
74C4×C8×C73—22no—
75C4×C8×C73D411yescharacteristic
76C4×C8×C73D411yescharacteristic
77C4×C8×C73C2311yescharacteristic
78C4×C8×C73C2311yescharacteristic
79C2×Q8×C73—21no—
80C2×Q8×C73—22no—
81C2×Q8×C73—22no—
82C2×Q8×C73C2×D412yes—
83C22×C4×C73C2×D411yescharacteristic
84C22×C4×C73C2×D411yescharacteristic
85C22×C4×C73#4111yescharacteristic
86Q16×C73—84no—
87M16×C73—42no—
88C2×C8×C73—22no—
89C2×C8×C73—22no—
90C2×C8×C73—24no—
91C2×C8×C73—82no—
92C2×C8×C73Q1614yescomplemented
93C2×C8×C73C2×D411yescharacteristic
94C2×C8×C73C2×D411yescharacteristic
95C2×C8×C73C2×D411yescharacteristic
96C2×C8×C73C2×D411yescharacteristic
97C4⋊C4×C73—21no—
98C4⋊C4×C73—21no—
99C4⋊C4×C73—21no—
100C4⋊C4×C73—22no—
101C4⋊C4×C73—22no—
102C4⋊C4×C73—22no—
103C4⋊C4×C73—22no—
104C4⋊C4×C73—22no—
105C4⋊C4×C73—22no—
106C4⋊C4×C73—42no—
107C4⋊C4×C73—42no—
108C4⋊C4×C73C2×D412yes—
109C22⋊C4×C73—22no—
110C22⋊C4×C73—42no—
111C42×C73—22no—
112C42×C73—42no—
113C42×C73C2×D411yescharacteristic
114C42×C73C2×D411yescharacteristic
115C42×C73#4111yescharacteristic
116C42×C73C2411yescharacteristic
117C23×C73#12111yescharacteristic
118Q8×C73—24no—
119Q8×C73—42no—
120Q8×C73—42no—
121Q8×C73—42no—
122Q8×C73—82no—
123C2×C4×C73—22no—
124C2×C4×C73—22no—
125C2×C4×C73—22no—
126C2×C4×C73—41no—
127C2×C4×C73—42no—
128C2×C4×C73—42no—
129C2×C4×C73#12111yescharacteristic
130C2×C4×C73#12111yescharacteristic
131C2×C4×C73#12111yescharacteristic
132C2×C4×C73C2×Q1612yes—
133C2×C4×C73#13712yes—
134C2×C4×C73C22×D411yescharacteristic
135C2×C4×C73C22×D411yescharacteristic
136C2×C4×C73C2×#4111yescharacteristic
137C8×C73—21no—
138C8×C73—21no—
139C8×C73—42no—
140C8×C73—44no—
141C8×C73C2×Q1612yes—
142C8×C73C2×Q1612yes—
143C22×C73—21no—
144C22×C73—21no—
145C22×C73#46212yes—
146C22×C73C2×#12111yescharacteristic
147C4×C73—21no—
148C4×C73—21no—
149C4×C73—21no—
150C4×C73—42no—
151C4×C73—42no—
152C4×C73—82no—
153C4×C73—82no—
154C4×C73#46212yes—
155C4×C73C22×Q1611yescharacteristic
156C4×C73C2×#13711yescharacteristic
157C4×C73#57712yes—
158#19210C7311yesmaximal, characteristic, direct product factor, Sylow
159C2×C73—22no—
160C2×C73C2×#46211yescharacteristic
161C2×C73#306011yescharacteristic
162C2×C73#306711yescharacteristic
163#3249C2×C7312yes—
164#3160C2×C7311yescharacteristic
165#2960C2×C7311yescharacteristic
166#1696C2×C7312yescomplemented
167#1694C2×C7312yescomplemented
168#1672C2×C7314yescomplemented
169C2×#334C2×C7311yescharacteristic
170#1550C2×C7312yes—
171C73#1921011yescharacteristic, direct product factor, Sylow
172#533C22×C7312yes—
173#533C22×C7311yescharacteristic
174#500C22×C7311yescharacteristic
175#500C22×C7311yescharacteristic
176#499—21no—
177#499—21no—
178#498C22×C7312yes—
179#477—22no—
180#477C22×C7314yes—
181#467—24no—
182#462—22no—
183#462C22×C7314yes—
184#446—21no—
185#446C22×C7312yes—
186C8×Q8—21no—
187C8×Q8C22×C7312yes—
188#427—21no—
189#427—21no—
190#424—21no—
191#423C22×C7311yescharacteristic
192C2×C4⋊C8C22×C7312yes—
193#405—21no—
194C2×C4×C8C22×C7311yescharacteristic
195#334C22×C7312yes—
196#334C22×C7312yes—
197#333C22×C7314yes—
198#332C22×C7314yes—
199C2×Q16—24no—
200C2×M16—21no—
201C22×C8—22no—
202C22×C8D4×C7311yescharacteristic
203C22×C8D4×C7311yescharacteristic
204C4⋊Q8D4×C7311yescharacteristic
205C4⋊Q8D4×C7311yescharacteristic
206C4⋊Q8C23×C7312yes—
207C4⋊Q8C23×C7312yes—
208#125—22no—
209#125—21no—
210C22⋊Q8—21no—
211C22⋊Q8—22no—
212C22⋊Q8—22no—
213C22⋊Q8D4×C7312yes—
214C4×Q8—21no—
215C4×Q8—22no—
216C4×Q8—22no—
217C4×Q8C23×C7312yes—
218#117—21no—
219#117—22no—
220C2×C42C23×C7311yescharacteristic
221#107—21no—
222#107—21no—
223#107—21no—
224#107—21no—
225#107—24no—
226#106—22no—
227#106—22no—
228C4⋊C8—22no—
229C4⋊C8—22no—
230C4⋊C8—22no—
231C4⋊C8—21no—
232C4⋊C8C23×C7312yes—
233C4⋊C8C23×C7314yes—
234#103—24no—
235#103—24no—
236#97—22no—
237C4×C8—22no—
238C4×C8D4×C7311yescharacteristic
239C4×C8D4×C7311yescharacteristic
240C4×C8C23×C7311yescharacteristic
241C4×C8C23×C7311yescharacteristic
242C2×Q8—21no—
243C2×Q8—22no—
244C2×Q8—22no—
245C2×Q8C2×D4×C7312yes—
246C22×C4C2×D4×C7311yescharacteristic
247C22×C4C2×D4×C7311yescharacteristic
248C22×C4#41×C7311yescharacteristic
249Q16—84no—
250M16—42no—
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—24no—
254C2×C8—82no—
255C2×C8Q16×C7314yescomplemented
256C2×C8C2×D4×C7311yescharacteristic
257C2×C8C2×D4×C7311yescharacteristic
258C2×C8C2×D4×C7311yescharacteristic
259C2×C8C2×D4×C7311yescharacteristic
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4C2×D4×C7312yes—
272C22⋊C4—22no—
273C22⋊C4—42no—
274C42—22no—
275C42—42no—
276C42C2×D4×C7311yescharacteristic
277C42C2×D4×C7311yescharacteristic
278C42#41×C7311yescharacteristic
279C42C24×C7311yescharacteristic
280C23#121×C7311yescharacteristic
281Q8—24no—
282Q8—42no—
283Q8—42no—
284Q8—42no—
285Q8—82no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4#121×C7311yescharacteristic
293C2×C4#121×C7311yescharacteristic
294C2×C4#121×C7311yescharacteristic
295C2×C4C2×Q16×C7312yes—
296C2×C4#137×C7312yes—
297C2×C4C22×D4×C7311yescharacteristic
298C2×C4C22×D4×C7311yescharacteristic
299C2×C4C2×#41×C7311yescharacteristic
300C8—21no—
301C8—21no—
302C8—42no—
303C8—44no—
304C8C2×Q16×C7312yes—
305C8C2×Q16×C7312yes—
306C22—21no—
307C22—21no—
308C22#462×C7312yes—
309C22C2×#121×C7311yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—42no—
314C4—42no—
315C4—82no—
316C4—82no—
317C4#462×C7312yes—
318C4C22×Q16×C7311yescharacteristic
319C4C2×#137×C7311yescharacteristic
320C4#577×C7312yes—
321C2—22no—
322C2C2×#462×C7311yescharacteristic
323C2C73×#306011yescharacteristic
324C2C73×#306711yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC42C24×C73
prime radicalC23×C73#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
4. C73×#1696C2semidirect
5. C73×#1694C2semidirect
6. C73×#1672C2semidirect
92. C2×C8×C73Q16semidirect
158. #19210C73direct (N × H)
166. #1696C2×C73semidirect
167. #1694C2×C73semidirect
168. #1672C2×C73semidirect
171. C73#19210direct (N × H)
255. C2×C8Q16×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#32492
C73×#31602
C73×#29602
C73×#16962
C73×#16942
C73×#16722
C2×#334×C732
C73×#15502
#1921073