Finite Group Databasebeta

← C73×#33817 #32943221

Subgroups — C73×#33817 #32943221

Order 18688.

534 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3169C211yesmaximal, characteristic, complemented
2C73×#3168C211yesmaximal, characteristic, complemented
3C73×#2228C212yesmaximal, complemented
4C73×#2225C211yesmaximal, characteristic, complemented
5C73×#2224C211yesmaximal, characteristic, complemented
6C73×#2220C212yesmaximal, complemented
7C73×#2218C212yesmaximal, complemented
8C73×#2210C212yesmaximal, complemented
9C73×#2207C211yesmaximal, characteristic, complemented
10C73×#2206C211yesmaximal, characteristic, complemented
11C73×#2150C211yesmaximal, characteristic, complemented
12#532×C73—21no—
13#529×C73—21no—
14C2×SD32×C73C2212yes—
15C2×D16×C73C2212yes—
16C2×M32×C73C2212yes—
17#500×C73C2211yescharacteristic
18#499×C73C2211yescharacteristic
19#495×C73C2211yescharacteristic
20#493×C73C2211yescharacteristic
21#488×C73—21no—
22#486×C73—21no—
23#467×C73C2211yescharacteristic
24#466×C73—21no—
25#466×C73C2211yescharacteristic
26#466×C73C2212yes—
27#465×C73—21no—
28C4×Q16×C73C2211yescharacteristic
29C4×SD16×C73—21no—
30C4×D8×C73—21no—
31C4×D8×C73C2211yescharacteristic
32C4×D8×C73C2212yes—
33C2×C4×C8×C73C2211yescharacteristic
34#367×C73C2212yes—
35#366×C73C2212yes—
36C4⋊C16×C73C2211yescharacteristic
37C4⋊C16×C73C2211yescharacteristic
38C4⋊C16×C73C2212yes—
39#358×C73C2212yes—
40#357×C73C2212yes—
41#357×C73C2212yes—
42#357×C73C2212yes—
43C2×#41×C73—41no—
44C2×Q16×C73C2311yescharacteristic
45C2×SD16×C73—21no—
46C2×D8×C73—21no—
47C2×D8×C73C2312yes—
48C2×D8×C73C2311yescharacteristic
49C22×C8×C73D411yescharacteristic
50C22×C8×C73C2311yescharacteristic
51C4⋊Q8×C73—21no—
52#127×C73—21no—
53#126×C73—41no—
54#125×C73—21no—
55#124×C73—21no—
56#124×C73—41no—
57#123×C73—41no—
58C22⋊Q8×C73—21no—
59#121×C73—21no—
60#121×C73—22no—
61#121×C73—41no—
62C4×Q8×C73—21no—
63C4×D4×C73—22no—
64C4×D4×C73—21no—
65C4×D4×C73—41no—
66C4×D4×C73—41no—
67#117×C73—41no—
68C2×C42×C73D411yescharacteristic
69SD32×C73—42no—
70D16×C73—42no—
71M32×C73—42no—
72C2×C16×C73C2312yes—
73C2×C16×C73C2312yes—
74#107×C73—21no—
75#107×C73C2312yes—
76#107×C73C2311yescharacteristic
77#107×C73C2311yescharacteristic
78#106×C73—21no—
79#103×C73—21no—
80#103×C73—21no—
81#102×C73—22no—
82#102×C73—21no—
83#102×C73—22no—
84#102×C73—21no—
85C4×C8×C73D411yescharacteristic
86C4×C8×C73D411yescharacteristic
87C4×C8×C73C2311yescharacteristic
88C4×C8×C73C2311yescharacteristic
89#41×C73—84no—
90C2×Q8×C73—21no—
91C2×Q8×C73—41no—
92C2×D4×C73—21no—
93C2×D4×C73—22no—
94C2×D4×C73—41no—
95C2×D4×C73—42no—
96C2×D4×C73—41no—
97C2×D4×C73—41no—
98C22×C4×C73—41no—
99C22×C4×C73—42no—
100C22×C4×C73D811yescharacteristic
101C22×C4×C73D811yescharacteristic
102C22×C4×C73C2×D411yescharacteristic
103Q16×C73—21no—
104Q16×C73—21no—
105SD16×C73—42no—
106D8×C73—21no—
107D8×C73—22no—
108D8×C73—22no—
109D8×C73—21no—
110D8×C73—42no—
111C2×C8×C73—21no—
112C2×C8×C73—21no—
113C2×C8×C73—41no—
114C2×C8×C73C2×D411yescharacteristic
115C2×C8×C73C2×D411yescharacteristic
116C2×C8×C73C2×D411yescharacteristic
117C2×C8×C73C2411yescharacteristic
118C4⋊C4×C73—22no—
119C4⋊C4×C73—21no—
120C4⋊C4×C73—21no—
121C4⋊C4×C73—41no—
122C4⋊C4×C73—41no—
123C4⋊C4×C73—41no—
124C4⋊C4×C73—41no—
125C4⋊C4×C73—41no—
126C22⋊C4×C73—41no—
127C22⋊C4×C73—41no—
128C22⋊C4×C73—41no—
129C22⋊C4×C73—42no—
130C22⋊C4×C73—41no—
131C22⋊C4×C73—42no—
132C22⋊C4×C73—41no—
133C42×C73—41no—
134C42×C73D811yescharacteristic
135C42×C73D811yescharacteristic
136C42×C73C2×D411yescharacteristic
137C42×C73C2×D411yescharacteristic
138C16×C73—22no—
139C16×C73—22no—
140C23×C73—41no—
141C23×C73—42no—
142C23×C73C2×D811yescharacteristic
143Q8×C73—41no—
144Q8×C73—41no—
145Q8×C73—82no—
146D4×C73—41no—
147D4×C73—42no—
148D4×C73—42no—
149D4×C73—41no—
150D4×C73—82no—
151D4×C73—82no—
152D4×C73—84no—
153D4×C73—82no—
154C2×C4×C73—21no—
155C2×C4×C73—21no—
156C2×C4×C73—22no—
157C2×C4×C73—41no—
158C2×C4×C73—41no—
159C2×C4×C73—41no—
160C2×C4×C73—41no—
161C2×C4×C73—42no—
162C2×C4×C73—84no—
163C2×C4×C73—82no—
164C2×C4×C73C2×D811yescharacteristic
165C2×C4×C73C2×D811yescharacteristic
166C2×C4×C73C2×D811yescharacteristic
167C2×C4×C73C2×D811yescharacteristic
168C2×C4×C73C2×D811yescharacteristic
169C2×C4×C73C22×D411yescharacteristic
170C8×C73—21no—
171C8×C73—21no—
172C8×C73—21no—
173C8×C73H(5,𝔽2)11yescharacteristic
174C8×C732−1+411yescharacteristic
175C22×C73—21no—
176C22×C73—21no—
177C22×C73—21no—
178C22×C73—82no—
179C22×C73—81no—
180C22×C73—82no—
181C22×C73—81no—
182C22×C73—82no—
183C22×C73—81no—
184C22×C73C22×D811yescharacteristic
185C4×C73—21no—
186C4×C73—21no—
187C4×C73—21no—
188C4×C73—21no—
189C4×C73—81no—
190C4×C73—82no—
191C4×C73—81no—
192C4×C73—81no—
193C4×C73#50912yes—
194C4×C73#53711yescharacteristic
195C4×C73#57511yescharacteristic
196#33817C7311yesmaximal, characteristic, direct product factor, Sylow
197C2×C73—41no—
198C2×C73—162no—
199C2×C73—161no—
200C2×C73#324511yescharacteristic
201C2×C73C2×#50911yescharacteristic
202C2×C73#341411yescharacteristic
203#3169C2×C7311yescharacteristic, complemented
204#3168C2×C7311yescharacteristic, complemented
205#2228C2×C7312yescomplemented
206#2225C2×C7311yescharacteristic, complemented
207#2224C2×C7311yescharacteristic, complemented
208#2220C2×C7312yescomplemented
209#2218C2×C7312yescomplemented
210#2210C2×C7312yescomplemented
211#2207C2×C7311yescharacteristic, complemented
212#2206C2×C7311yescharacteristic, complemented
213#2150C2×C7311yescharacteristic, complemented
214C73#3381711yescharacteristic, direct product factor, Sylow
215#532—21no—
216#529—21no—
217C2×SD32C22×C7312yes—
218C2×D16C22×C7312yes—
219C2×M32C22×C7312yes—
220#500C22×C7311yescharacteristic
221#499C22×C7311yescharacteristic
222#495C22×C7311yescharacteristic
223#493C22×C7311yescharacteristic
224#488—21no—
225#486—21no—
226#467C22×C7311yescharacteristic
227#466—21no—
228#466C22×C7311yescharacteristic
229#466C22×C7312yes—
230#465—21no—
231C4×Q16C22×C7311yescharacteristic
232C4×SD16—21no—
233C4×D8—21no—
234C4×D8C22×C7311yescharacteristic
235C4×D8C22×C7312yes—
236C2×C4×C8C22×C7311yescharacteristic
237#367C22×C7312yes—
238#366C22×C7312yes—
239C4⋊C16C22×C7311yescharacteristic
240C4⋊C16C22×C7311yescharacteristic
241C4⋊C16C22×C7312yes—
242#358C22×C7312yes—
243#357C22×C7312yes—
244#357C22×C7312yes—
245#357C22×C7312yes—
246C2×#41—41no—
247C2×Q16C23×C7311yescharacteristic
248C2×SD16—21no—
249C2×D8—21no—
250C2×D8C23×C7312yes—
251C2×D8C23×C7311yescharacteristic
252C22×C8D4×C7311yescharacteristic
253C22×C8C23×C7311yescharacteristic
254C4⋊Q8—21no—
255#127—21no—
256#126—41no—
257#125—21no—
258#124—21no—
259#124—41no—
260#123—41no—
261C22⋊Q8—21no—
262#121—21no—
263#121—22no—
264#121—41no—
265C4×Q8—21no—
266C4×D4—21no—
267C4×D4—22no—
268C4×D4—41no—
269C4×D4—41no—
270#117—41no—
271C2×C42D4×C7311yescharacteristic
272SD32—42no—
273D16—42no—
274M32—42no—
275C2×C16C23×C7312yes—
276C2×C16C23×C7312yes—
277#107—21no—
278#107C23×C7311yescharacteristic
279#107C23×C7311yescharacteristic
280#107C23×C7312yes—
281#106—21no—
282#103—21no—
283#103—21no—
284#102—22no—
285#102—21no—
286#102—22no—
287#102—21no—
288C4×C8D4×C7311yescharacteristic
289C4×C8D4×C7311yescharacteristic
290C4×C8C23×C7311yescharacteristic
291C4×C8C23×C7311yescharacteristic
292#41—84no—
293C2×Q8—21no—
294C2×Q8—41no—
295C2×D4—21no—
296C2×D4—22no—
297C2×D4—41no—
298C2×D4—42no—
299C2×D4—41no—
300C2×D4—41no—
301C22×C4—41no—
302C22×C4—42no—
303C22×C4D8×C7311yescharacteristic
304C22×C4D8×C7311yescharacteristic
305C22×C4C2×D4×C7311yescharacteristic
306Q16—21no—
307Q16—21no—
308SD16—42no—
309D8—21no—
310D8—22no—
311D8—22no—
312D8—21no—
313D8—42no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—41no—
317C2×C8C2×D4×C7311yescharacteristic
318C2×C8C2×D4×C7311yescharacteristic
319C2×C8C2×D4×C7311yescharacteristic
320C2×C8C24×C7311yescharacteristic
321C4⋊C4—22no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—42no—
333C22⋊C4—41no—
334C22⋊C4—42no—
335C22⋊C4—41no—
336C42—41no—
337C42D8×C7311yescharacteristic
338C42D8×C7311yescharacteristic
339C42C2×D4×C7311yescharacteristic
340C42C2×D4×C7311yescharacteristic
341C16—22no—
342C16—22no—
343C23—41no—
344C23—42no—
345C23C2×D8×C7311yescharacteristic
346Q8—41no—
347Q8—41no—
348Q8—82no—
349D4—41no—
350D4—42no—
351D4—42no—
352D4—41no—
353D4—82no—
354D4—84no—
355D4—82no—
356D4—82no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—84no—
366C2×C4—82no—
367C2×C4C2×D8×C7311yescharacteristic
368C2×C4C2×D8×C7311yescharacteristic
369C2×C4C2×D8×C7311yescharacteristic
370C2×C4C2×D8×C7311yescharacteristic
371C2×C4C2×D8×C7311yescharacteristic
372C2×C4C22×D4×C7311yescharacteristic
373C8—21no—
374C8—21no—
375C8—21no—
376C8H(5,𝔽2)×C7311yescharacteristic
377C82−1+4×C7311yescharacteristic
378C22—21no—
379C22—21no—
380C22—21no—
381C22—82no—
382C22—81no—
383C22—82no—
384C22—81no—
385C22—82no—
386C22—81no—
387C22C22×D8×C7311yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—81no—
393C4—82no—
394C4—81no—
395C4—81no—
396C4#509×C7312yes—
397C4#537×C7311yescharacteristic
398C4#575×C7311yescharacteristic
399C2—41no—
400C2—162no—
401C2—161no—
402C2C73×#324511yescharacteristic
403C2C2×#509×C7311yescharacteristic
404C2C73×#341411yescharacteristic
subgroupG/H
center, socleC22×C73C22×D8
commutator, Frattini, cosocleC2×C8C24×C73
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×C42×C73 ◁ C2×C4×C8×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3169C2semidirect
2. C73×#3168C2semidirect
3. C73×#2228C2semidirect
4. C73×#2225C2semidirect
5. C73×#2224C2semidirect
6. C73×#2220C2semidirect
7. C73×#2218C2semidirect
8. C73×#2210C2semidirect
9. C73×#2207C2semidirect
10. C73×#2206C2semidirect
11. C73×#2150C2semidirect
196. #33817C73direct (N × H)
203. #3169C2×C73semidirect
204. #3168C2×C73semidirect
205. #2228C2×C73semidirect
206. #2225C2×C73semidirect
207. #2224C2×C73semidirect
208. #2220C2×C73semidirect
209. #2218C2×C73semidirect
210. #2210C2×C73semidirect
211. #2207C2×C73semidirect
212. #2206C2×C73semidirect
213. #2150C2×C73semidirect
214. C73#33817direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#31692
C73×#31682
C73×#22282
C73×#22252
C73×#22242
C73×#22202
C73×#22182
C73×#22102
C73×#22072
C73×#22062
C73×#21502
#3381773