Finite Group Databasebeta

← C73×#33943 #32943347

Subgroups — C73×#33943 #32943347

Order 18688.

482 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3393C211yesmaximal, characteristic, complemented
2C73×#3380C211yesmaximal, characteristic, complemented
3C73×#2245C211yesmaximal, characteristic, complemented
4C73×#2243C211yesmaximal, characteristic, complemented
5C73×#2242C211yesmaximal, characteristic, complemented
6C73×#2229C211yesmaximal, characteristic, complemented
7C73×#2228C211yesmaximal, characteristic, complemented
8C73×#2225C211yesmaximal, characteristic, complemented
9C73×#2210C211yesmaximal, characteristic
10C73×#2210C211yesmaximal, characteristic
11C73×#2208C211yesmaximal, characteristic, complemented
12C73×#2183C211yesmaximal, characteristic, complemented
13C73×#2177C211yesmaximal, characteristic
14C73×#2175C211yesmaximal, characteristic, complemented
15C4×SD32×C73C211yesmaximal, characteristic, complemented
16#556×C73—21no—
17#554×C73—21no—
18C2×SD32×C73C2211yescharacteristic
19C2×SD32×C73C2211yescharacteristic
20C2×D16×C73C2211yescharacteristic
21#500×C73C2211yescharacteristic
22#499×C73C2211yescharacteristic
23#499×C73C2211yescharacteristic
24#495×C73C2211yescharacteristic
25#495×C73C2211yescharacteristic
26#494×C73C2211yescharacteristic
27#478×C73—21no—
28#478×C73—21no—
29#476×C73—21no—
30#464×C73—21no—
31#464×C73—21no—
32#461×C73—21no—
33C8×Q8×C73C2211yescharacteristic
34C4×Q16×C73C2211yescharacteristic
35C4×Q16×C73C2211yescharacteristic
36C4×D8×C73C2211yescharacteristic
37C4×D8×C73C2211yescharacteristic
38C4×D8×C73C2211yescharacteristic
39C4×D8×C73C2211yescharacteristic
40#367×C73C2211yescharacteristic
41#367×C73C2211yescharacteristic
42#366×C73C2211yescharacteristic
43C4⋊C16×C73C2211yescharacteristic
44C4⋊C16×C73C2211yescharacteristic
45C4⋊C16×C73C2211yescharacteristic
46#358×C73C2211yescharacteristic
47#358×C73C2211yescharacteristic
48#358×C73C2211yescharacteristic
49#358×C73C2211yescharacteristic
50#358×C73C2211yescharacteristic
51#358×C73C2211yescharacteristic
52#357×C73C2211yescharacteristic
53#357×C73C2211yescharacteristic
54#357×C73C2211yescharacteristic
55#357×C73C2211yescharacteristic
56#346×C73C2211yescharacteristic
57#346×C73C2211yescharacteristic
58C4×C16×C73C2211yescharacteristic
59C2×Q16×C73—21no—
60C2×Q16×C73C2311yescharacteristic
61C2×Q16×C73C2311yescharacteristic
62C2×SD16×C73—21no—
63C2×SD16×C73—21no—
64C2×D8×C73C2311yescharacteristic
65C2×D8×C73C2311yescharacteristic
66C4⋊Q8×C73—21no—
67C4⋊Q8×C73—21no—
68#126×C73—41no—
69#126×C73—41no—
70#125×C73—21no—
71#125×C73—21no—
72#124×C73—21no—
73#124×C73—21no—
74C22⋊Q8×C73—41no—
75C22⋊Q8×C73—41no—
76C22⋊Q8×C73—41no—
77C22⋊Q8×C73—41no—
78C4×Q8×C73—21no—
79C4×Q8×C73—21no—
80C4×Q8×C73D411yescharacteristic
81C4×D4×C73—21no—
82C4×D4×C73—21no—
83C4×D4×C73—21no—
84C4×D4×C73—21no—
85#117×C73—41no—
86C2×C4⋊C4×C73—41no—
87SD32×C73—22no—
88SD32×C73—22no—
89D16×C73—22no—
90C2×C16×C73C2311yescharacteristic
91C2×C16×C73C2311yescharacteristic
92C2×C16×C73C2311yescharacteristic
93C2×C16×C73C2311yescharacteristic
94#107×C73—21no—
95#107×C73C2311yescharacteristic
96#107×C73C2311yescharacteristic
97#107×C73C2311yescharacteristic
98#107×C73C2311yescharacteristic
99#106×C73—21no—
100#106×C73—21no—
101C4⋊C8×C73D411yescharacteristic
102C4⋊C8×C73D411yescharacteristic
103C4⋊C8×C73D411yescharacteristic
104#103×C73—21no—
105#103×C73—21no—
106#102×C73—21no—
107#102×C73—21no—
108#102×C73—21no—
109#102×C73—21no—
110C4×C8×C73C2311yescharacteristic
111C4×C8×C73C2311yescharacteristic
112C4×C8×C73C2311yescharacteristic
113C2×Q8×C73—21no—
114C2×Q8×C73—21no—
115C2×Q8×C73—41no—
116C2×Q8×C73D811yescharacteristic
117C2×D4×C73—21no—
118C2×D4×C73—21no—
119C22×C4×C73—41no—
120C22×C4×C73—41no—
121C22×C4×C73—41no—
122C22×C4×C73—41no—
123Q16×C73—21no—
124Q16×C73—21no—
125Q16×C73—21no—
126Q16×C73—21no—
127Q16×C73—81no—
128SD16×C73—81no—
129SD16×C73—81no—
130D8×C73—21no—
131D8×C73—21no—
132D8×C73—21no—
133D8×C73#4112yes—
134C2×C8×C73C2×D411yescharacteristic
135C2×C8×C73C2×D411yescharacteristic
136C2×C8×C73C2×D411yescharacteristic
137C2×C8×C73C2411yescharacteristic
138C4⋊C4×C73—21no—
139C4⋊C4×C73—21no—
140C4⋊C4×C73—21no—
141C4⋊C4×C73—21no—
142C4⋊C4×C73—41no—
143C4⋊C4×C73—41no—
144C4⋊C4×C73—41no—
145C4⋊C4×C73—41no—
146C4⋊C4×C73—41no—
147C4⋊C4×C73—41no—
148C4⋊C4×C73—41no—
149C4⋊C4×C73—41no—
150C4⋊C4×C73—41no—
151C4⋊C4×C73D811yescharacteristic
152C4⋊C4×C73D811yescharacteristic
153C4⋊C4×C73D811yescharacteristic
154C22⋊C4×C73—41no—
155C22⋊C4×C73—41no—
156C22⋊C4×C73—41no—
157C22⋊C4×C73—41no—
158C22⋊C4×C73—41no—
159C22⋊C4×C73—41no—
160C22⋊C4×C73—41no—
161C22⋊C4×C73—41no—
162C42×C73—41no—
163C42×C73—41no—
164C42×C73C2×D411yescharacteristic
165C42×C73C2×D411yescharacteristic
166C42×C73C2×D411yescharacteristic
167C16×C73—21no—
168C16×C73—21no—
169C16×C73—21no—
170C16×C73—21no—
171C23×C73—41no—
172C23×C73—41no—
173Q8×C73—41no—
174Q8×C73—41no—
175Q8×C73—41no—
176Q8×C73—41no—
177Q8×C73—41no—
178Q8×C73—161no—
179D4×C73—22no—
180D4×C73—41no—
181D4×C73—41no—
182D4×C73—41no—
183C2×C4×C73—41no—
184C2×C4×C73—41no—
185C2×C4×C73—41no—
186C2×C4×C73—41no—
187C2×C4×C73—41no—
188C2×C4×C73—41no—
189C2×C4×C73—82no—
190C2×C4×C73—82no—
191C2×C4×C73—161no—
192C2×C4×C73—161no—
193C2×C4×C73C2×D811yescharacteristic
194C2×C4×C73C2×D811yescharacteristic
195C2×C4×C73C2×D811yescharacteristic
196C2×C4×C73C2×D811yescharacteristic
197C2×C4×C73C2×D811yescharacteristic
198C2×C4×C73C2×D811yescharacteristic
199C2×C4×C73C22×D411yescharacteristic
200C8×C73—21no—
201C8×C73—21no—
202C8×C73—21no—
203C8×C73C2×#4111yescharacteristic
204C8×C732−1+411yescharacteristic
205C22×C73—42no—
206C22×C73—81no—
207C22×C73—81no—
208C22×C73—81no—
209C22×C73—81no—
210C22×C73—81no—
211C22×C73C22×D811yescharacteristic
212C4×C73—21no—
213C4×C73—21no—
214C4×C73—21no—
215C4×C73—21no—
216C4×C73—21no—
217C4×C73—21no—
218C4×C73—81no—
219C4×C73—81no—
220C4×C73—81no—
221C4×C73—81no—
222C4×C73—81no—
223C4×C73—81no—
224C4×C73#54811yescharacteristic
225C4×C73#57711yescharacteristic
226#33943C7311yesmaximal, characteristic, direct product factor, Sylow
227C2×C73—82no—
228C2×C73—161no—
229C2×C73#335811yescharacteristic
230C2×C73#341411yescharacteristic
231C2×C73#341611yescharacteristic
232#3393C2×C7311yescharacteristic, complemented
233#3380C2×C7311yescharacteristic, complemented
234#2245C2×C7311yescharacteristic, complemented
235#2243C2×C7311yescharacteristic, complemented
236#2242C2×C7311yescharacteristic, complemented
237#2229C2×C7311yescharacteristic, complemented
238#2228C2×C7311yescharacteristic, complemented
239#2225C2×C7311yescharacteristic, complemented
240#2210C2×C7311yescharacteristic
241#2210C2×C7311yescharacteristic
242#2208C2×C7311yescharacteristic, complemented
243#2183C2×C7311yescharacteristic, complemented
244#2177C2×C7311yescharacteristic
245#2175C2×C7311yescharacteristic, complemented
246C4×SD32C2×C7311yescharacteristic, complemented
247C73#3394311yescharacteristic, direct product factor, Sylow
248#556—21no—
249#554—21no—
250C2×SD32C22×C7311yescharacteristic
251C2×SD32C22×C7311yescharacteristic
252C2×D16C22×C7311yescharacteristic
253#500C22×C7311yescharacteristic
254#499C22×C7311yescharacteristic
255#499C22×C7311yescharacteristic
256#495C22×C7311yescharacteristic
257#495C22×C7311yescharacteristic
258#494C22×C7311yescharacteristic
259#478—21no—
260#478—21no—
261#476—21no—
262#464—21no—
263#464—21no—
264#461—21no—
265C8×Q8C22×C7311yescharacteristic
266C4×Q16C22×C7311yescharacteristic
267C4×Q16C22×C7311yescharacteristic
268C4×D8C22×C7311yescharacteristic
269C4×D8C22×C7311yescharacteristic
270C4×D8C22×C7311yescharacteristic
271C4×D8C22×C7311yescharacteristic
272#367C22×C7311yescharacteristic
273#367C22×C7311yescharacteristic
274#366C22×C7311yescharacteristic
275C4⋊C16C22×C7311yescharacteristic
276C4⋊C16C22×C7311yescharacteristic
277C4⋊C16C22×C7311yescharacteristic
278#358C22×C7311yescharacteristic
279#358C22×C7311yescharacteristic
280#358C22×C7311yescharacteristic
281#358C22×C7311yescharacteristic
282#358C22×C7311yescharacteristic
283#358C22×C7311yescharacteristic
284#357C22×C7311yescharacteristic
285#357C22×C7311yescharacteristic
286#357C22×C7311yescharacteristic
287#357C22×C7311yescharacteristic
288#346C22×C7311yescharacteristic
289#346C22×C7311yescharacteristic
290C4×C16C22×C7311yescharacteristic
291C2×Q16—21no—
292C2×Q16C23×C7311yescharacteristic
293C2×Q16C23×C7311yescharacteristic
294C2×SD16—21no—
295C2×SD16—21no—
296C2×D8C23×C7311yescharacteristic
297C2×D8C23×C7311yescharacteristic
298C4⋊Q8—21no—
299C4⋊Q8—21no—
300#126—41no—
301#126—41no—
302#125—21no—
303#125—21no—
304#124—21no—
305#124—21no—
306C22⋊Q8—41no—
307C22⋊Q8—41no—
308C22⋊Q8—41no—
309C22⋊Q8—41no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×Q8D4×C7311yescharacteristic
313C4×D4—21no—
314C4×D4—21no—
315C4×D4—21no—
316C4×D4—21no—
317#117—41no—
318C2×C4⋊C4—41no—
319SD32—22no—
320SD32—22no—
321D16—22no—
322C2×C16C23×C7311yescharacteristic
323C2×C16C23×C7311yescharacteristic
324C2×C16C23×C7311yescharacteristic
325C2×C16C23×C7311yescharacteristic
326#107—21no—
327#107C23×C7311yescharacteristic
328#107C23×C7311yescharacteristic
329#107C23×C7311yescharacteristic
330#107C23×C7311yescharacteristic
331#106—21no—
332#106—21no—
333C4⋊C8D4×C7311yescharacteristic
334C4⋊C8D4×C7311yescharacteristic
335C4⋊C8D4×C7311yescharacteristic
336#103—21no—
337#103—21no—
338#102—21no—
339#102—21no—
340#102—21no—
341#102—21no—
342C4×C8C23×C7311yescharacteristic
343C4×C8C23×C7311yescharacteristic
344C4×C8C23×C7311yescharacteristic
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—41no—
348C2×Q8D8×C7311yescharacteristic
349C2×D4—21no—
350C2×D4—21no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355Q16—21no—
356Q16—21no—
357Q16—21no—
358Q16—21no—
359Q16—81no—
360SD16—81no—
361SD16—81no—
362D8—21no—
363D8—21no—
364D8—21no—
365D8#41×C7312yes—
366C2×C8C2×D4×C7311yescharacteristic
367C2×C8C2×D4×C7311yescharacteristic
368C2×C8C2×D4×C7311yescharacteristic
369C2×C8C24×C7311yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4D8×C7311yescharacteristic
384C4⋊C4D8×C7311yescharacteristic
385C4⋊C4D8×C7311yescharacteristic
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C42—41no—
395C42—41no—
396C42C2×D4×C7311yescharacteristic
397C42C2×D4×C7311yescharacteristic
398C42C2×D4×C7311yescharacteristic
399C16—21no—
400C16—21no—
401C16—21no—
402C16—21no—
403C23—41no—
404C23—41no—
405Q8—41no—
406Q8—41no—
407Q8—41no—
408Q8—41no—
409Q8—41no—
410Q8—161no—
411D4—22no—
412D4—41no—
413D4—41no—
414D4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—161no—
424C2×C4—161no—
425C2×C4C2×D8×C7311yescharacteristic
426C2×C4C2×D8×C7311yescharacteristic
427C2×C4C2×D8×C7311yescharacteristic
428C2×C4C2×D8×C7311yescharacteristic
429C2×C4C2×D8×C7311yescharacteristic
430C2×C4C2×D8×C7311yescharacteristic
431C2×C4C22×D4×C7311yescharacteristic
432C8—21no—
433C8—21no—
434C8—21no—
435C8C2×#41×C7311yescharacteristic
436C82−1+4×C7311yescharacteristic
437C22—42no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22C22×D8×C7311yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—81no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4—81no—
456C4#548×C7311yescharacteristic
457C4#577×C7311yescharacteristic
458C2—82no—
459C2—161no—
460C2C73×#335811yescharacteristic
461C2C73×#341411yescharacteristic
462C2C73×#341611yescharacteristic
subgroupG/H
center, socleC22×C73C22×D8
commutator, Frattini, cosocleC2×C8C24×C73
prime radicalC2×D16×C73C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C4×Q8×C73 ◁ C8×Q8×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3393C2semidirect
2. C73×#3380C2semidirect
3. C73×#2245C2semidirect
4. C73×#2243C2semidirect
5. C73×#2242C2semidirect
6. C73×#2229C2semidirect
7. C73×#2228C2semidirect
8. C73×#2225C2semidirect
11. C73×#2208C2semidirect
12. C73×#2183C2semidirect
14. C73×#2175C2semidirect
15. C4×SD32×C73C2semidirect
226. #33943C73direct (N × H)
232. #3393C2×C73semidirect
233. #3380C2×C73semidirect
234. #2245C2×C73semidirect
235. #2243C2×C73semidirect
236. #2242C2×C73semidirect
237. #2229C2×C73semidirect
238. #2228C2×C73semidirect
239. #2225C2×C73semidirect
242. #2208C2×C73semidirect
243. #2183C2×C73semidirect
245. #2175C2×C73semidirect
246. C4×SD32C2×C73semidirect
247. C73#33943direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#33932
C73×#33802
C73×#22452
C73×#22432
C73×#22422
C73×#22292
C73×#22282
C73×#22252
C73×#22102
C73×#22082
C73×#21832
C73×#21772
C73×#21752
C4×SD32×C732
#3394373