Finite Group Databasebeta

← C73×#19211 #32928615

Subgroups — C73×#19211 #32928615

Order 18688.

570 conjugacy classes of subgroups.

The subgroup lattice has 332 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×#1692C214yesmaximal, complemented
5C73×#1676C212yesmaximal, complemented
6C73×#1674C212yesmaximal, complemented
7C2×#335×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#335×C73C2212yes—
33#335×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—22no—
119Q8×C73—22no—
120Q8×C73—42no—
121Q8×C73—42no—
122Q8×C73—42no—
123Q8×C73—82no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—22no—
127C2×C4×C73—22no—
128C2×C4×C73—41no—
129C2×C4×C73—42no—
130C2×C4×C73—42no—
131C2×C4×C73#12111yescharacteristic
132C2×C4×C73#12111yescharacteristic
133C2×C4×C73#12111yescharacteristic
134C2×C4×C73C2×Q1612yes—
135C2×C4×C73#13712yes—
136C2×C4×C73C22×D411yescharacteristic
137C2×C4×C73C22×D411yescharacteristic
138C2×C4×C73C2×#4111yescharacteristic
139C8×C73—21no—
140C8×C73—21no—
141C8×C73—42no—
142C8×C73—44no—
143C8×C73C2×Q1612yes—
144C8×C73C2×Q1612yes—
145C22×C73—21no—
146C22×C73—21no—
147C22×C73#46212yes—
148C22×C73C2×#12111yescharacteristic
149C4×C73—21no—
150C4×C73—21no—
151C4×C73—21no—
152C4×C73—42no—
153C4×C73—42no—
154C4×C73—82no—
155C4×C73—82no—
156C4×C73#46212yes—
157C4×C73C22×Q1611yescharacteristic
158C4×C73C2×#13711yescharacteristic
159C4×C73#57611yescharacteristic
160C4×C73#57811yescharacteristic
161#19211C7311yesmaximal, characteristic, direct product factor, Sylow
162C2×C73—22no—
163C2×C73C2×#46211yescharacteristic
164C2×C73#306111yescharacteristic
165C2×C73#306711yescharacteristic
166#3249C2×C7312yes—
167#3160C2×C7311yescharacteristic
168#2960C2×C7311yescharacteristic
169#1692C2×C7314yescomplemented
170#1676C2×C7312yescomplemented
171#1674C2×C7312yescomplemented
172C2×#335C2×C7311yescharacteristic
173#1550C2×C7312yes—
174C73#1921111yescharacteristic, direct product factor, Sylow
175#533C22×C7312yes—
176#533C22×C7311yescharacteristic
177#500C22×C7311yescharacteristic
178#500C22×C7311yescharacteristic
179#499—21no—
180#499—21no—
181#498C22×C7312yes—
182#477—22no—
183#477C22×C7314yes—
184#467—24no—
185#462—22no—
186#462C22×C7314yes—
187#446—21no—
188#446C22×C7312yes—
189C8×Q8—21no—
190C8×Q8C22×C7312yes—
191#427—21no—
192#427—21no—
193#424—21no—
194#423C22×C7311yescharacteristic
195C2×C4⋊C8C22×C7312yes—
196#405—21no—
197C2×C4×C8C22×C7311yescharacteristic
198#335C22×C7312yes—
199#335C22×C7312yes—
200#333C22×C7314yes—
201#332C22×C7314yes—
202C2×Q16—24no—
203C2×M16—21no—
204C22×C8—22no—
205C22×C8D4×C7311yescharacteristic
206C22×C8D4×C7311yescharacteristic
207C4⋊Q8D4×C7311yescharacteristic
208C4⋊Q8D4×C7311yescharacteristic
209C4⋊Q8C23×C7312yes—
210C4⋊Q8C23×C7312yes—
211#125—22no—
212#125—21no—
213C22⋊Q8—21no—
214C22⋊Q8—22no—
215C22⋊Q8—22no—
216C22⋊Q8D4×C7312yes—
217C4×Q8—21no—
218C4×Q8—22no—
219C4×Q8—22no—
220C4×Q8C23×C7312yes—
221#117—21no—
222#117—22no—
223C2×C42C23×C7311yescharacteristic
224#107—21no—
225#107—21no—
226#107—21no—
227#107—21no—
228#107—24no—
229#106—22no—
230#106—22no—
231C4⋊C8—22no—
232C4⋊C8—22no—
233C4⋊C8—22no—
234C4⋊C8—21no—
235C4⋊C8C23×C7312yes—
236C4⋊C8C23×C7314yes—
237#103—24no—
238#103—24no—
239#97—22no—
240C4×C8—22no—
241C4×C8D4×C7311yescharacteristic
242C4×C8D4×C7311yescharacteristic
243C4×C8C23×C7311yescharacteristic
244C4×C8C23×C7311yescharacteristic
245C2×Q8—21no—
246C2×Q8—22no—
247C2×Q8—22no—
248C2×Q8C2×D4×C7312yes—
249C22×C4C2×D4×C7311yescharacteristic
250C22×C4C2×D4×C7311yescharacteristic
251C22×C4#41×C7311yescharacteristic
252Q16—84no—
253M16—42no—
254C2×C8—22no—
255C2×C8—22no—
256C2×C8—24no—
257C2×C8—82no—
258C2×C8Q16×C7314yescomplemented
259C2×C8C2×D4×C7311yescharacteristic
260C2×C8C2×D4×C7311yescharacteristic
261C2×C8C2×D4×C7311yescharacteristic
262C2×C8C2×D4×C7311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4C2×D4×C7312yes—
275C22⋊C4—22no—
276C22⋊C4—42no—
277C42—22no—
278C42—42no—
279C42C2×D4×C7311yescharacteristic
280C42C2×D4×C7311yescharacteristic
281C42#41×C7311yescharacteristic
282C42C24×C7311yescharacteristic
283C23#121×C7311yescharacteristic
284Q8—22no—
285Q8—22no—
286Q8—42no—
287Q8—42no—
288Q8—42no—
289Q8—82no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4#121×C7311yescharacteristic
298C2×C4#121×C7311yescharacteristic
299C2×C4#121×C7311yescharacteristic
300C2×C4C2×Q16×C7312yes—
301C2×C4#137×C7312yes—
302C2×C4C22×D4×C7311yescharacteristic
303C2×C4C22×D4×C7311yescharacteristic
304C2×C4C2×#41×C7311yescharacteristic
305C8—21no—
306C8—21no—
307C8—42no—
308C8—44no—
309C8C2×Q16×C7312yes—
310C8C2×Q16×C7312yes—
311C22—21no—
312C22—21no—
313C22#462×C7312yes—
314C22C2×#121×C7311yescharacteristic
315C4—21no—
316C4—21no—
317C4—21no—
318C4—42no—
319C4—42no—
320C4—82no—
321C4—82no—
322C4#462×C7312yes—
323C4C22×Q16×C7311yescharacteristic
324C4C2×#137×C7311yescharacteristic
325C4#576×C7311yescharacteristic
326C4#578×C7311yescharacteristic
327C2—22no—
328C2C2×#462×C7311yescharacteristic
329C2C73×#306111yescharacteristic
330C2C73×#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×#1692C2semidirect
5. C73×#1676C2semidirect
6. C73×#1674C2semidirect
92. C2×C8×C73Q16semidirect
161. #19211C73direct (N × H)
169. #1692C2×C73semidirect
170. #1676C2×C73semidirect
171. #1674C2×C73semidirect
174. C73#19211direct (N × H)
258. 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×#16922
C73×#16762
C73×#16742
C2×#335×C732
C73×#15502
#1921173