Finite Group Databasebeta

← C73×#33632 #32943036

Subgroups — C73×#33632 #32943036

Order 18688.

520 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3164C211yesmaximal, characteristic
2C73×#2950C211yesmaximal, characteristic
3C73×#2229C212yesmaximal, complemented
4C73×#2229C212yesmaximal, complemented
5C73×#2227C212yesmaximal, complemented
6C73×#2225C212yesmaximal, complemented
7C73×#2159C211yesmaximal, characteristic
8C73×#2158C211yesmaximal, characteristic
9C73×#2151C211yesmaximal, characteristic
10C73×#2141C211yesmaximal, characteristic
11C2×#358×C73C211yesmaximal, characteristic
12C22×Q16×C73C2211yescharacteristic
13#544×C73—21no—
14#519×C73—21no—
15C2×M32×C73C2211yescharacteristic
16C22×C16×C73C2211yescharacteristic
17#501×C73—22no—
18#500×C73C2212yes—
19#499×C73C2212yes—
20#441×C73—22no—
21C4×Q16×C73C2212yes—
22C4×Q16×C73C2212yes—
23#428×C73—21no—
24#427×C73C2211yescharacteristic
25#427×C73C2211yescharacteristic
26C2×#107×C73C2211yescharacteristic
27#419×C73—21no—
28#405×C73C2211yescharacteristic
29#367×C73C2211yescharacteristic
30#367×C73C2212yes—
31#367×C73C2211yescharacteristic
32#366×C73C2211yescharacteristic
33#366×C73C2212yes—
34#366×C73C2211yescharacteristic
35C4⋊C16×C73C2212yes—
36C4⋊C16×C73C2212yes—
37#358×C73C2212yes—
38#358×C73C2212yes—
39#358×C73C2212yes—
40#358×C73C2212yes—
41C22×Q8×C73—21no—
42C2×Q16×C73—21no—
43C2×Q16×C73—22no—
44C2×Q16×C73Q814yescomplemented
45C2×Q16×C73C2312yes—
46C2×M16×C73D411yescharacteristic
47C22×C8×C73C2311yescharacteristic
48C4⋊Q8×C73—22no—
49C4⋊Q8×C73—41no—
50#125×C73—22no—
51#125×C73—41no—
52C22⋊Q8×C73—42no—
53C4×Q8×C73—22no—
54C4×Q8×C73—22no—
55C4×Q8×C73—41no—
56C4×Q8×C73—41no—
57#117×C73—21no—
58#117×C73—21no—
59#117×C73—42no—
60#117×C73D411yescharacteristic
61C2×C4⋊C4×C73—21no—
62M32×C73—22no—
63C2×C16×C73—22no—
64C2×C16×C73C2311yescharacteristic
65C2×C16×C73C2311yescharacteristic
66C2×C16×C73C2312yes—
67#107×C73—21no—
68#107×C73—22no—
69#107×C73C2312yes—
70#107×C73C2311yescharacteristic
71#107×C73C2311yescharacteristic
72#107×C73C2311yescharacteristic
73#107×C73C2311yescharacteristic
74#106×C73—21no—
75#106×C73—21no—
76#106×C73—22no—
77#103×C73—22no—
78#103×C73—22no—
79#97×C73D412yes—
80C4×C8×C73C2312yes—
81C2×Q8×C73—24no—
82C2×Q8×C73—22no—
83C2×Q8×C73—41no—
84C2×Q8×C73—42no—
85C2×Q8×C73—42no—
86C22×C4×C73—41no—
87C22×C4×C73—41no—
88C22×C4×C73C2×D411yescharacteristic
89Q16×C73—24no—
90Q16×C73—22no—
91Q16×C73C2×Q814yes—
92M16×C73—22no—
93C2×C8×C73C2×D412yes—
94C2×C8×C73C2×D411yescharacteristic
95C2×C8×C73C2×Q812yes—
96C2×C8×C73#4112yes—
97C2×C8×C73C2411yescharacteristic
98C4⋊C4×C73—21no—
99C4⋊C4×C73—21no—
100C4⋊C4×C73—21no—
101C4⋊C4×C73—22no—
102C4⋊C4×C73—21no—
103C4⋊C4×C73—41no—
104C4⋊C4×C73—42no—
105C4⋊C4×C73—42no—
106C4⋊C4×C73—42no—
107C4⋊C4×C73—42no—
108C4⋊C4×C73—42no—
109C4⋊C4×C73D811yescharacteristic
110C4⋊C4×C73D811yescharacteristic
111C22⋊C4×C73—41no—
112C22⋊C4×C73—41no—
113C22⋊C4×C73D812yes—
114C42×C73—41no—
115C42×C73—41no—
116C42×C73—42no—
117C42×C73—42no—
118C42×C73C2×D412yes—
119C16×C73—21no—
120C16×C73—21no—
121C16×C73—22no—
122C23×C73C2×D811yescharacteristic
123Q8×C73—24no—
124Q8×C73—42no—
125Q8×C73—44no—
126Q8×C73—162no—
127C2×C4×C73—42no—
128C2×C4×C73—44no—
129C2×C4×C73—41no—
130C2×C4×C73—41no—
131C2×C4×C73—41no—
132C2×C4×C73—41no—
133C2×C4×C73—42no—
134C2×C4×C73—161no—
135C2×C4×C73C22⋊Q812yes—
136C2×C4×C73C2×D812yes—
137C2×C4×C73C2×D812yes—
138C2×C4×C73C2×D811yescharacteristic
139C2×C4×C73#13712yes—
140C2×C4×C73C22×D411yescharacteristic
141C8×C73—22no—
142C8×C73C22⋊Q812yes—
143C8×C73C22×Q811yescharacteristic
144C8×C73C2×#4111yescharacteristic
145C22×C73—21no—
146C22×C73—21no—
147C22×C73#47412yes—
148C22×C73C22×D811yescharacteristic
149C4×C73—22no—
150C4×C73—22no—
151C4×C73—44no—
152C4×C73—81no—
153C4×C73—82no—
154C4×C73—81no—
155C4×C73—81no—
156C4×C73—81no—
157C4×C73#47412yes—
158C4×C73C2×C22⋊Q811yescharacteristic
159C4×C73C2×#13711yescharacteristic
160#33632C7311yesmaximal, characteristic, direct product factor, Sylow
161C2×C73—22no—
162C2×C73C2×#47411yescharacteristic
163C2×C73#341611yescharacteristic
164C2×C73#341711yescharacteristic
165#3164C2×C7311yescharacteristic
166#2950C2×C7311yescharacteristic
167#2229C2×C7312yescomplemented
168#2229C2×C7312yescomplemented
169#2227C2×C7312yescomplemented
170#2225C2×C7312yescomplemented
171#2159C2×C7311yescharacteristic
172#2158C2×C7311yescharacteristic
173#2151C2×C7311yescharacteristic
174#2141C2×C7311yescharacteristic
175C2×#358C2×C7311yescharacteristic
176C73#3363211yescharacteristic, direct product factor, Sylow
177C22×Q16C22×C7311yescharacteristic
178#544—21no—
179#519—21no—
180C2×M32C22×C7311yescharacteristic
181C22×C16C22×C7311yescharacteristic
182#501—22no—
183#500C22×C7312yes—
184#499C22×C7312yes—
185#441—22no—
186C4×Q16C22×C7312yes—
187C4×Q16C22×C7312yes—
188#428—21no—
189#427C22×C7311yescharacteristic
190#427C22×C7311yescharacteristic
191C2×#107C22×C7311yescharacteristic
192#419—21no—
193#405C22×C7311yescharacteristic
194#367C22×C7311yescharacteristic
195#367C22×C7311yescharacteristic
196#367C22×C7312yes—
197#366C22×C7311yescharacteristic
198#366C22×C7311yescharacteristic
199#366C22×C7312yes—
200C4⋊C16C22×C7312yes—
201C4⋊C16C22×C7312yes—
202#358C22×C7312yes—
203#358C22×C7312yes—
204#358C22×C7312yes—
205#358C22×C7312yes—
206C22×Q8—21no—
207C2×Q16—21no—
208C2×Q16—22no—
209C2×Q16Q8×C7314yescomplemented
210C2×Q16C23×C7312yes—
211C2×M16D4×C7311yescharacteristic
212C22×C8C23×C7311yescharacteristic
213C4⋊Q8—22no—
214C4⋊Q8—41no—
215#125—22no—
216#125—41no—
217C22⋊Q8—42no—
218C4×Q8—22no—
219C4×Q8—22no—
220C4×Q8—41no—
221C4×Q8—41no—
222#117—21no—
223#117—21no—
224#117—42no—
225#117D4×C7311yescharacteristic
226C2×C4⋊C4—21no—
227M32—22no—
228C2×C16—22no—
229C2×C16C23×C7311yescharacteristic
230C2×C16C23×C7312yes—
231C2×C16C23×C7311yescharacteristic
232#107—21no—
233#107—22no—
234#107C23×C7312yes—
235#107C23×C7311yescharacteristic
236#107C23×C7311yescharacteristic
237#107C23×C7311yescharacteristic
238#107C23×C7311yescharacteristic
239#106—21no—
240#106—21no—
241#106—22no—
242#103—22no—
243#103—22no—
244#97D4×C7312yes—
245C4×C8C23×C7312yes—
246C2×Q8—24no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8—42no—
250C2×Q8—42no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4C2×D4×C7311yescharacteristic
254Q16—24no—
255Q16—22no—
256Q16C2×Q8×C7314yes—
257M16—22no—
258C2×C8C2×D4×C7312yes—
259C2×C8C2×D4×C7311yescharacteristic
260C2×C8C2×Q8×C7312yes—
261C2×C8#41×C7312yes—
262C2×C8C24×C7311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—22no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4D8×C7311yescharacteristic
275C4⋊C4D8×C7311yescharacteristic
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4D8×C7312yes—
279C42—41no—
280C42—41no—
281C42—42no—
282C42—42no—
283C42C2×D4×C7312yes—
284C16—21no—
285C16—21no—
286C16—22no—
287C23C2×D8×C7311yescharacteristic
288Q8—24no—
289Q8—44no—
290Q8—42no—
291Q8—162no—
292C2×C4—44no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—161no—
300C2×C4C22⋊Q8×C7312yes—
301C2×C4C2×D8×C7312yes—
302C2×C4C2×D8×C7312yes—
303C2×C4C2×D8×C7311yescharacteristic
304C2×C4#137×C7312yes—
305C2×C4C22×D4×C7311yescharacteristic
306C8—22no—
307C8C22⋊Q8×C7312yes—
308C8C22×Q8×C7311yescharacteristic
309C8C2×#41×C7311yescharacteristic
310C22—21no—
311C22—21no—
312C22#474×C7312yes—
313C22C22×D8×C7311yescharacteristic
314C4—22no—
315C4—22no—
316C4—44no—
317C4—82no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—81no—
322C4#474×C7312yes—
323C4C2×C22⋊Q8×C7311yescharacteristic
324C4C2×#137×C7311yescharacteristic
325C2—22no—
326C2C2×#474×C7311yescharacteristic
327C2C73×#341611yescharacteristic
328C2C73×#341711yescharacteristic
subgroupG/H
center, socleC22×C73C22×D8
commutator, Frattini, cosocleC2×C8C24×C73
prime radicalC23×C73C2×D8
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ #117×C73 ◁ #405×C73 ◁ G

Complements

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

NH ≅ G/Ntype
3. C73×#2229C2semidirect
4. C73×#2229C2semidirect
5. C73×#2227C2semidirect
6. C73×#2225C2semidirect
44. C2×Q16×C73Q8semidirect
160. #33632C73direct (N × H)
167. #2229C2×C73semidirect
168. #2229C2×C73semidirect
169. #2227C2×C73semidirect
170. #2225C2×C73semidirect
176. C73#33632direct (N × H)
209. C2×Q16Q8×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#31642
C73×#29502
C73×#22292
C73×#22272
C73×#22252
C73×#21592
C73×#21582
C73×#21512
C73×#21412
C2×#358×C732
#3363273