Finite Group Databasebeta

← C73×#33937 #32943341

Subgroups — C73×#33937 #32943341

Order 18688.

494 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3396C211yesmaximal, characteristic, complemented
2C73×#3380C211yesmaximal, characteristic, complemented
3C73×#2244C211yesmaximal, characteristic, complemented
4C73×#2243C211yesmaximal, characteristic, complemented
5C73×#2242C211yesmaximal, characteristic, complemented
6C73×#2229C211yesmaximal, characteristic, complemented
7C73×#2228C211yesmaximal, characteristic, complemented
8C73×#2224C211yesmaximal, characteristic, complemented
9C73×#2210C211yesmaximal, characteristic, complemented
10C73×#2210C211yesmaximal, characteristic, complemented
11C73×#2206C211yesmaximal, characteristic
12C73×#2183C211yesmaximal, characteristic, complemented
13C73×#2177C211yesmaximal, characteristic, complemented
14C73×#2175C211yesmaximal, characteristic, complemented
15C4×D16×C73C211yesmaximal, characteristic, complemented
16#559×C73—21no—
17#554×C73—21no—
18C2×SD32×C73C2211yescharacteristic
19C2×D16×C73C2211yescharacteristic
20C2×D16×C73C2211yescharacteristic
21#500×C73C2211yescharacteristic
22#499×C73C2211yescharacteristic
23#499×C73C2211yescharacteristic
24#495×C73C2211yescharacteristic
25#495×C73C2211yescharacteristic
26#493×C73C2211yescharacteristic
27#478×C73—21no—
28#478×C73—21no—
29#476×C73—21no—
30#463×C73—21no—
31#463×C73—21no—
32#460×C73—21no—
33C8×Q8×C73C2211yescharacteristic
34C4×Q16×C73C2211yescharacteristic
35C4×D8×C73C2211yescharacteristic
36C4×D8×C73C2211yescharacteristic
37C4×D8×C73C2211yescharacteristic
38C4×D8×C73C2211yescharacteristic
39C4×D8×C73C2211yescharacteristic
40#367×C73C2211yescharacteristic
41#366×C73C2211yescharacteristic
42#366×C73C2211yescharacteristic
43C4⋊C16×C73C2211yescharacteristic
44C4⋊C16×C73C2211yescharacteristic
45C4⋊C16×C73C2211yescharacteristic
46#358×C73C2211yescharacteristic
47#358×C73C2211yescharacteristic
48#358×C73C2211yescharacteristic
49#357×C73C2211yescharacteristic
50#357×C73C2211yescharacteristic
51#357×C73C2211yescharacteristic
52#357×C73C2211yescharacteristic
53#357×C73C2211yescharacteristic
54#357×C73C2211yescharacteristic
55#357×C73C2211yescharacteristic
56#346×C73C2211yescharacteristic
57#346×C73C2211yescharacteristic
58C4×C16×C73C2211yescharacteristic
59C2×Q16×C73C2311yescharacteristic
60C2×SD16×C73—21no—
61C2×SD16×C73—21no—
62C2×D8×C73—21no—
63C2×D8×C73C2311yescharacteristic
64C2×D8×C73C2311yescharacteristic
65C2×D8×C73C2311yescharacteristic
66C4⋊Q8×C73—21no—
67#127×C73—21no—
68#125×C73—21no—
69#125×C73—21no—
70#124×C73—21no—
71#124×C73—21no—
72#124×C73—41no—
73#123×C73—41no—
74#123×C73—41no—
75C22⋊Q8×C73—41no—
76C22⋊Q8×C73—41no—
77C22⋊Q8×C73—41no—
78C4×Q8×C73—21no—
79C4×Q8×C73D411yescharacteristic
80C4×D4×C73—21no—
81C4×D4×C73—21no—
82C4×D4×C73—21no—
83C4×D4×C73—21no—
84C4×D4×C73—21no—
85C4×D4×C73—41no—
86C2×C4⋊C4×C73—41no—
87SD32×C73—22no—
88D16×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#102×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—41no—
115C2×Q8×C73D811yescharacteristic
116C2×D4×C73—21no—
117C2×D4×C73—21no—
118C2×D4×C73—21no—
119C2×D4×C73—41no—
120C2×D4×C73—41no—
121C22×C4×C73—41no—
122C22×C4×C73—41no—
123C22×C4×C73—41no—
124C22×C4×C73—41no—
125C22×C4×C73—41no—
126Q16×C73—21no—
127Q16×C73—21no—
128SD16×C73—81no—
129SD16×C73—81no—
130D8×C73—21no—
131D8×C73—21no—
132D8×C73—21no—
133D8×C73—21no—
134D8×C73—21no—
135D8×C73—81no—
136D8×C73#4112yes—
137C2×C8×C73C2×D411yescharacteristic
138C2×C8×C73C2×D411yescharacteristic
139C2×C8×C73C2×D411yescharacteristic
140C2×C8×C73C2411yescharacteristic
141C4⋊C4×C73—21no—
142C4⋊C4×C73—21no—
143C4⋊C4×C73—21no—
144C4⋊C4×C73—21no—
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—
162C22⋊C4×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—
173C23×C73—41no—
174Q8×C73—41no—
175Q8×C73—41no—
176Q8×C73—41no—
177Q8×C73—161no—
178D4×C73—22no—
179D4×C73—41no—
180D4×C73—41no—
181D4×C73—41no—
182D4×C73—41no—
183D4×C73—41no—
184D4×C73—82no—
185D4×C73—161no—
186C2×C4×C73—41no—
187C2×C4×C73—41no—
188C2×C4×C73—41no—
189C2×C4×C73—41no—
190C2×C4×C73—41no—
191C2×C4×C73—82no—
192C2×C4×C73—161no—
193C2×C4×C73—161no—
194C2×C4×C73—161no—
195C2×C4×C73—161no—
196C2×C4×C73C2×D811yescharacteristic
197C2×C4×C73C2×D811yescharacteristic
198C2×C4×C73C2×D811yescharacteristic
199C2×C4×C73C2×D811yescharacteristic
200C2×C4×C73C2×D811yescharacteristic
201C2×C4×C73C2×D811yescharacteristic
202C2×C4×C73C22×D411yescharacteristic
203C8×C73—21no—
204C8×C73—21no—
205C8×C73—21no—
206C8×C73C2×#4111yescharacteristic
207C8×C732−1+411yescharacteristic
208C22×C73—42no—
209C22×C73—81no—
210C22×C73—81no—
211C22×C73—81no—
212C22×C73—81no—
213C22×C73—81no—
214C22×C73—81no—
215C22×C73—81no—
216C22×C73—81no—
217C22×C73C22×D811yescharacteristic
218C4×C73—21no—
219C4×C73—21no—
220C4×C73—21no—
221C4×C73—21no—
222C4×C73—21no—
223C4×C73—21no—
224C4×C73—81no—
225C4×C73—81no—
226C4×C73—81no—
227C4×C73—81no—
228C4×C73—81no—
229C4×C73#54811yescharacteristic
230C4×C73#57711yescharacteristic
231#33937C7311yesmaximal, characteristic, direct product factor, Sylow
232C2×C73—82no—
233C2×C73—161no—
234C2×C73—161no—
235C2×C73#335811yescharacteristic
236C2×C73#341411yescharacteristic
237C2×C73#341511yescharacteristic
238#3396C2×C7311yescharacteristic, complemented
239#3380C2×C7311yescharacteristic, complemented
240#2244C2×C7311yescharacteristic, complemented
241#2243C2×C7311yescharacteristic, complemented
242#2242C2×C7311yescharacteristic, complemented
243#2229C2×C7311yescharacteristic, complemented
244#2228C2×C7311yescharacteristic, complemented
245#2224C2×C7311yescharacteristic, complemented
246#2210C2×C7311yescharacteristic, complemented
247#2210C2×C7311yescharacteristic, complemented
248#2206C2×C7311yescharacteristic
249#2183C2×C7311yescharacteristic, complemented
250#2177C2×C7311yescharacteristic, complemented
251#2175C2×C7311yescharacteristic, complemented
252C4×D16C2×C7311yescharacteristic, complemented
253C73#3393711yescharacteristic, direct product factor, Sylow
254#559—21no—
255#554—21no—
256C2×SD32C22×C7311yescharacteristic
257C2×D16C22×C7311yescharacteristic
258C2×D16C22×C7311yescharacteristic
259#500C22×C7311yescharacteristic
260#499C22×C7311yescharacteristic
261#499C22×C7311yescharacteristic
262#495C22×C7311yescharacteristic
263#495C22×C7311yescharacteristic
264#493C22×C7311yescharacteristic
265#478—21no—
266#478—21no—
267#476—21no—
268#463—21no—
269#463—21no—
270#460—21no—
271C8×Q8C22×C7311yescharacteristic
272C4×Q16C22×C7311yescharacteristic
273C4×D8C22×C7311yescharacteristic
274C4×D8C22×C7311yescharacteristic
275C4×D8C22×C7311yescharacteristic
276C4×D8C22×C7311yescharacteristic
277C4×D8C22×C7311yescharacteristic
278#367C22×C7311yescharacteristic
279#366C22×C7311yescharacteristic
280#366C22×C7311yescharacteristic
281C4⋊C16C22×C7311yescharacteristic
282C4⋊C16C22×C7311yescharacteristic
283C4⋊C16C22×C7311yescharacteristic
284#358C22×C7311yescharacteristic
285#358C22×C7311yescharacteristic
286#358C22×C7311yescharacteristic
287#357C22×C7311yescharacteristic
288#357C22×C7311yescharacteristic
289#357C22×C7311yescharacteristic
290#357C22×C7311yescharacteristic
291#357C22×C7311yescharacteristic
292#357C22×C7311yescharacteristic
293#357C22×C7311yescharacteristic
294#346C22×C7311yescharacteristic
295#346C22×C7311yescharacteristic
296C4×C16C22×C7311yescharacteristic
297C2×Q16C23×C7311yescharacteristic
298C2×SD16—21no—
299C2×SD16—21no—
300C2×D8—21no—
301C2×D8C23×C7311yescharacteristic
302C2×D8C23×C7311yescharacteristic
303C2×D8C23×C7311yescharacteristic
304C4⋊Q8—21no—
305#127—21no—
306#125—21no—
307#125—21no—
308#124—21no—
309#124—21no—
310#124—41no—
311#123—41no—
312#123—41no—
313C22⋊Q8—41no—
314C22⋊Q8—41no—
315C22⋊Q8—41no—
316C4×Q8—21no—
317C4×Q8D4×C7311yescharacteristic
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4—41no—
324C2×C4⋊C4—41no—
325SD32—22no—
326D16—22no—
327D16—22no—
328C2×C16C23×C7311yescharacteristic
329C2×C16C23×C7311yescharacteristic
330C2×C16C23×C7311yescharacteristic
331C2×C16C23×C7311yescharacteristic
332#107—21no—
333#107C23×C7311yescharacteristic
334#107C23×C7311yescharacteristic
335#107C23×C7311yescharacteristic
336#107C23×C7311yescharacteristic
337#106—21no—
338#106—21no—
339C4⋊C8D4×C7311yescharacteristic
340C4⋊C8D4×C7311yescharacteristic
341C4⋊C8D4×C7311yescharacteristic
342#103—21no—
343#102—21no—
344#102—21no—
345#102—21no—
346#102—21no—
347#102—21no—
348C4×C8C23×C7311yescharacteristic
349C4×C8C23×C7311yescharacteristic
350C4×C8C23×C7311yescharacteristic
351C2×Q8—21no—
352C2×Q8—41no—
353C2×Q8D8×C7311yescharacteristic
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—41no—
358C2×D4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364Q16—21no—
365Q16—21no—
366SD16—81no—
367SD16—81no—
368D8—21no—
369D8—21no—
370D8—21no—
371D8—21no—
372D8—21no—
373D8—81no—
374D8#41×C7312yes—
375C2×C8C2×D4×C7311yescharacteristic
376C2×C8C2×D4×C7311yescharacteristic
377C2×C8C2×D4×C7311yescharacteristic
378C2×C8C24×C7311yescharacteristic
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4D8×C7311yescharacteristic
390C4⋊C4D8×C7311yescharacteristic
391C4⋊C4D8×C7311yescharacteristic
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C42—41no—
402C42C2×D4×C7311yescharacteristic
403C42C2×D4×C7311yescharacteristic
404C42C2×D4×C7311yescharacteristic
405C16—21no—
406C16—21no—
407C16—21no—
408C16—21no—
409C23—41no—
410C23—41no—
411C23—41no—
412Q8—41no—
413Q8—41no—
414Q8—41no—
415Q8—161no—
416D4—22no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—41no—
421D4—41no—
422D4—82no—
423D4—161no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—82no—
430C2×C4—161no—
431C2×C4—161no—
432C2×C4—161no—
433C2×C4—161no—
434C2×C4C2×D8×C7311yescharacteristic
435C2×C4C2×D8×C7311yescharacteristic
436C2×C4C2×D8×C7311yescharacteristic
437C2×C4C2×D8×C7311yescharacteristic
438C2×C4C2×D8×C7311yescharacteristic
439C2×C4C2×D8×C7311yescharacteristic
440C2×C4C22×D4×C7311yescharacteristic
441C8—21no—
442C8—21no—
443C8—21no—
444C8C2×#41×C7311yescharacteristic
445C82−1+4×C7311yescharacteristic
446C22—42no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22C22×D8×C7311yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—21no—
462C4—81no—
463C4—81no—
464C4—81no—
465C4—81no—
466C4—81no—
467C4#548×C7311yescharacteristic
468C4#577×C7311yescharacteristic
469C2—82no—
470C2—161no—
471C2—161no—
472C2C73×#335811yescharacteristic
473C2C73×#341411yescharacteristic
474C2C73×#341511yescharacteristic
subgroupG/H
center, socleC22×C73C22×D8
commutator, Frattini, cosocleC2×C8C24×C73
prime radicalC73×#2206C2
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×#3396C2semidirect
2. C73×#3380C2semidirect
3. C73×#2244C2semidirect
4. C73×#2243C2semidirect
5. C73×#2242C2semidirect
6. C73×#2229C2semidirect
7. C73×#2228C2semidirect
8. C73×#2224C2semidirect
9. C73×#2210C2semidirect
10. C73×#2210C2semidirect
12. C73×#2183C2semidirect
13. C73×#2177C2semidirect
14. C73×#2175C2semidirect
15. C4×D16×C73C2semidirect
231. #33937C73direct (N × H)
238. #3396C2×C73semidirect
239. #3380C2×C73semidirect
240. #2244C2×C73semidirect
241. #2243C2×C73semidirect
242. #2242C2×C73semidirect
243. #2229C2×C73semidirect
244. #2228C2×C73semidirect
245. #2224C2×C73semidirect
246. #2210C2×C73semidirect
247. #2210C2×C73semidirect
249. #2183C2×C73semidirect
250. #2177C2×C73semidirect
251. #2175C2×C73semidirect
252. C4×D16C2×C73semidirect
253. C73#33937direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#33962
C73×#33802
C73×#22442
C73×#22432
C73×#22422
C73×#22292
C73×#22282
C73×#22242
C73×#22102
C73×#22062
C73×#21832
C73×#21772
C73×#21752
C4×D16×C732
#3393773