Finite Group Databasebeta

← C73×#19504 #32928908

Subgroups — C73×#19504 #32928908

Order 18688.

652 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3235C211yesmaximal, characteristic, complemented
2C73×#3208C211yesmaximal, characteristic, complemented
3C73×#3205C211yesmaximal, characteristic
4C73×#2981C211yesmaximal, characteristic, complemented
5C73×#1697C212yesmaximal, complemented
6C73×#1685C212yesmaximal, complemented
7C73×#1677C212yesmaximal, complemented
8C73×#1665C212yesmaximal, complemented
9C73×#1572C211yesmaximal, characteristic, complemented
10C73×#1555C211yesmaximal, characteristic, complemented
11C73×#1554C211yesmaximal, characteristic, complemented
12#533×C73C2211yescharacteristic
13#532×C73C2211yescharacteristic
14C2×#127×C73C2211yescharacteristic
15#501×C73—21no—
16#493×C73—21no—
17#492×C73C2211yescharacteristic
18#492×C73C2211yescharacteristic
19#490×C73—21no—
20#486×C73—21no—
21#486×C73C2211yescharacteristic
22#486×C73C2211yescharacteristic
23#482×C73—22no—
24#476×C73C2212yescomplemented
25#474×C73C2212yescomplemented
26#460×C73—22no—
27#459×C73C2212yes—
28#459×C73C2212yes—
29#450×C73—22no—
30#447×C73—22no—
31#436×C73C2212yescomplemented
32#435×C73—22no—
33C8×D4×C73C2212yescomplemented
34#432×C73C2211yescharacteristic
35#432×C73C2211yescharacteristic
36#431×C73C2211yescharacteristic
37#431×C73C2211yescharacteristic
38#408×C73—22no—
39#335×C73C2212yescomplemented
40#334×C73C2212yescomplemented
41#333×C73C2212yescomplemented
42#332×C73C2212yescomplemented
43#331×C73C2212yes—
44#331×C73C2212yes—
45C2×#41×C73—21no—
46C22×D4×C73—21no—
47C22×D4×C73—21no—
48C22×D4×C73—21no—
49C2×SD16×C73—22no—
50C2×SD16×C73—22no—
51C2×D8×C73—22no—
52C2×D8×C73—22no—
53C2×M16×C73—22no—
54C22×C8×C73—22no—
55C4⋊Q8×C73D411yescharacteristic
56C4⋊Q8×C73C2311yescharacteristic
57C4⋊Q8×C73C2311yescharacteristic
58#127×C73—21no—
59#127×C73—21no—
60#127×C73—21no—
61#127×C73D411yescharacteristic
62#127×C73C2311yescharacteristic
63#127×C73C2311yescharacteristic
64#125×C73—21no—
65#124×C73—21no—
66C22⋊Q8×C73—21no—
67C22⋊Q8×C73—21no—
68#121×C73—21no—
69#121×C73D412yes—
70C4×Q8×C73—21no—
71C4×Q8×C73—21no—
72C4×D4×C73—21no—
73C4×D4×C73C2312yes—
74#117×C73—21no—
75C2×C42×C73C2311yescharacteristic
76#107×C73—22no—
77#106×C73—22no—
78C4⋊C8×C73D412yes—
79C4⋊C8×C73C2312yes—
80C4⋊C8×C73C2312yes—
81C4⋊C8×C73C2312yes—
82#102×C73—22no—
83#102×C73—22no—
84#102×C73—22no—
85#102×C73—22no—
86#102×C73—22no—
87#102×C73—22no—
88C22⋊C8×C73—21no—
89C22⋊C8×C73—21no—
90C22⋊C8×C73—21no—
91C22⋊C8×C73—22no—
92C22⋊C8×C73—22no—
93C22⋊C8×C73D412yes—
94#97×C73—21no—
95#97×C73—21no—
96C4×C8×C73—21no—
97C4×C8×C73C2311yescharacteristic
98C4×C8×C73C2311yescharacteristic
99C24×C73—41no—
100#41×C73—82no—
101C2×Q8×C73—21no—
102C2×Q8×C73—21no—
103C2×Q8×C73—21no—
104C2×D4×C73—22no—
105C2×D4×C73—21no—
106C2×D4×C73—21no—
107C2×D4×C73—21no—
108C2×D4×C73—21no—
109C2×D4×C73—21no—
110C2×D4×C73—21no—
111C2×D4×C73—21no—
112C2×D4×C73—21no—
113C2×D4×C73—41no—
114C2×D4×C73—41no—
115C2×D4×C73—41no—
116C2×D4×C73—82no—
117C2×D4×C73—82no—
118C2×D4×C73—82no—
119C2×D4×C73C2×D412yes—
120C22×C4×C73—22no—
121C22×C4×C73C2×D411yescharacteristic
122C22×C4×C73C2×D411yescharacteristic
123C22×C4×C73#4111yescharacteristic
124SD16×C73—82no—
125SD16×C73—82no—
126D8×C73—82no—
127D8×C73—82no—
128M16×C73—82no—
129C2×C8×C73—22no—
130C2×C8×C73—22no—
131C2×C8×C73—22no—
132C2×C8×C73—82no—
133C2×C8×C73C2×D412yes—
134C2×C8×C73C2×D412yes—
135C4⋊C4×C73—21no—
136C4⋊C4×C73—21no—
137C4⋊C4×C73—21no—
138C4⋊C4×C73—21no—
139C4⋊C4×C73—21no—
140C4⋊C4×C73—41no—
141C4⋊C4×C73—41no—
142C4⋊C4×C73C2×D412yes—
143C22⋊C4×C73—22no—
144C22⋊C4×C73—22no—
145C22⋊C4×C73—41no—
146C42×C73—41no—
147C42×C73C2×D411yescharacteristic
148C42×C73C2×D411yescharacteristic
149C42×C73#4111yescharacteristic
150C42×C73C2411yescharacteristic
151C23×C73—22no—
152C23×C73—41no—
153C23×C73—41no—
154C23×C73—82no—
155C23×C73—82no—
156C23×C73—82no—
157C23×C73#12111yescharacteristic
158Q8×C73—42no—
159Q8×C73—81no—
160Q8×C73—81no—
161D4×C73—22no—
162D4×C73—22no—
163D4×C73—42no—
164D4×C73—42no—
165D4×C73—42no—
166D4×C73—42no—
167D4×C73—81no—
168D4×C73—81no—
169D4×C73—81no—
170D4×C73—81no—
171D4×C73—82no—
172D4×C73—82no—
173D4×C73—82no—
174D4×C73—82no—
175C2×C4×C73—22no—
176C2×C4×C73—22no—
177C2×C4×C73—22no—
178C2×C4×C73—41no—
179C2×C4×C73—42no—
180C2×C4×C73—42no—
181C2×C4×C73—41no—
182C2×C4×C73—41no—
183C2×C4×C73#12111yescharacteristic
184C2×C4×C73#12111yescharacteristic
185C2×C4×C73#12111yescharacteristic
186C2×C4×C73C22×D411yescharacteristic
187C2×C4×C73C22×D411yescharacteristic
188C2×C4×C73C2×#4111yescharacteristic
189C8×C73—22no—
190C8×C73—22no—
191C8×C73—42no—
192C8×C73—42no—
193C8×C73—42no—
194C22×C73—21no—
195C22×C73—21no—
196C22×C73—21no—
197C22×C73—42no—
198C22×C73—42no—
199C22×C73—42no—
200C22×C73—81no—
201C22×C73—81no—
202C22×C73—81no—
203C22×C73—81no—
204C22×C73—81no—
205C22×C73—81no—
206C22×C73—164no—
207C22×C73C2×#12111yescharacteristic
208C4×C73—21no—
209C4×C73—21no—
210C4×C73—21no—
211C4×C73—21no—
212C4×C73—42no—
213C4×C73—81no—
214C4×C73—81no—
215C4×C73#57612yes—
216C4×C73#57712yes—
217#19504C7311yesmaximal, characteristic, direct product factor, Sylow
218C2×C73—41no—
219C2×C73—82no—
220C2×C73—161no—
221C2×C73—161no—
222C2×C73#304111yescharacteristic
223C2×C73#305711yescharacteristic
224C2×C73#306811yescharacteristic
225#3235C2×C7311yescharacteristic, complemented
226#3208C2×C7311yescharacteristic, complemented
227#3205C2×C7311yescharacteristic
228#2981C2×C7311yescharacteristic, complemented
229#1697C2×C7312yescomplemented
230#1685C2×C7312yescomplemented
231#1677C2×C7312yescomplemented
232#1665C2×C7312yescomplemented
233#1572C2×C7311yescharacteristic, complemented
234#1555C2×C7311yescharacteristic, complemented
235#1554C2×C7311yescharacteristic, complemented
236C73#1950411yescharacteristic, direct product factor, Sylow
237#533C22×C7311yescharacteristic
238#532C22×C7311yescharacteristic
239C2×#127C22×C7311yescharacteristic
240#501—21no—
241#493—21no—
242#492C22×C7311yescharacteristic
243#492C22×C7311yescharacteristic
244#490—21no—
245#486—21no—
246#486C22×C7311yescharacteristic
247#486C22×C7311yescharacteristic
248#482—22no—
249#476C22×C7312yescomplemented
250#474C22×C7312yescomplemented
251#460—22no—
252#459C22×C7312yes—
253#459C22×C7312yes—
254#450—22no—
255#447—22no—
256#436C22×C7312yescomplemented
257#435—22no—
258C8×D4C22×C7312yescomplemented
259#432C22×C7311yescharacteristic
260#432C22×C7311yescharacteristic
261#431C22×C7311yescharacteristic
262#431C22×C7311yescharacteristic
263#408—22no—
264#335C22×C7312yescomplemented
265#334C22×C7312yescomplemented
266#333C22×C7312yescomplemented
267#332C22×C7312yescomplemented
268#331C22×C7312yes—
269#331C22×C7312yes—
270C2×#41—21no—
271C22×D4—21no—
272C22×D4—21no—
273C22×D4—21no—
274C2×SD16—22no—
275C2×SD16—22no—
276C2×D8—22no—
277C2×D8—22no—
278C2×M16—22no—
279C22×C8—22no—
280C4⋊Q8D4×C7311yescharacteristic
281C4⋊Q8C23×C7311yescharacteristic
282C4⋊Q8C23×C7311yescharacteristic
283#127—21no—
284#127—21no—
285#127—21no—
286#127D4×C7311yescharacteristic
287#127C23×C7311yescharacteristic
288#127C23×C7311yescharacteristic
289#125—21no—
290#124—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293#121—21no—
294#121D4×C7312yes—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×D4—21no—
298C4×D4C23×C7312yes—
299#117—21no—
300C2×C42C23×C7311yescharacteristic
301#107—22no—
302#106—22no—
303C4⋊C8D4×C7312yes—
304C4⋊C8C23×C7312yes—
305C4⋊C8C23×C7312yes—
306C4⋊C8C23×C7312yes—
307#102—22no—
308#102—22no—
309#102—22no—
310#102—22no—
311#102—22no—
312#102—22no—
313C22⋊C8—21no—
314C22⋊C8—21no—
315C22⋊C8—21no—
316C22⋊C8—22no—
317C22⋊C8—22no—
318C22⋊C8D4×C7312yes—
319#97—21no—
320#97—21no—
321C4×C8—21no—
322C4×C8C23×C7311yescharacteristic
323C4×C8C23×C7311yescharacteristic
324C24—41no—
325#41—82no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×D4—22no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—82no—
342C2×D4—82no—
343C2×D4—82no—
344C2×D4C2×D4×C7312yes—
345C22×C4—22no—
346C22×C4C2×D4×C7311yescharacteristic
347C22×C4C2×D4×C7311yescharacteristic
348C22×C4#41×C7311yescharacteristic
349SD16—82no—
350SD16—82no—
351D8—82no—
352D8—82no—
353M16—82no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—82no—
358C2×C8C2×D4×C7312yes—
359C2×C8C2×D4×C7312yes—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4C2×D4×C7312yes—
368C22⋊C4—22no—
369C22⋊C4—22no—
370C22⋊C4—41no—
371C42—41no—
372C42C2×D4×C7311yescharacteristic
373C42C2×D4×C7311yescharacteristic
374C42#41×C7311yescharacteristic
375C42C24×C7311yescharacteristic
376C23—22no—
377C23—41no—
378C23—41no—
379C23—82no—
380C23—82no—
381C23—82no—
382C23#121×C7311yescharacteristic
383Q8—42no—
384Q8—81no—
385Q8—81no—
386D4—22no—
387D4—22no—
388D4—42no—
389D4—42no—
390D4—42no—
391D4—42no—
392D4—81no—
393D4—81no—
394D4—81no—
395D4—81no—
396D4—82no—
397D4—82no—
398D4—82no—
399D4—82no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4#121×C7311yescharacteristic
409C2×C4#121×C7311yescharacteristic
410C2×C4#121×C7311yescharacteristic
411C2×C4C22×D4×C7311yescharacteristic
412C2×C4C22×D4×C7311yescharacteristic
413C2×C4C2×#41×C7311yescharacteristic
414C8—22no—
415C8—22no—
416C8—42no—
417C8—42no—
418C8—42no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22—164no—
432C22C2×#121×C7311yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—42no—
438C4—81no—
439C4—81no—
440C4#576×C7312yes—
441C4#577×C7312yes—
442C2—41no—
443C2—82no—
444C2—161no—
445C2—161no—
446C2C73×#304111yescharacteristic
447C2C73×#305711yescharacteristic
448C2C73×#306811yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3205C2
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
1. C73×#3235C2semidirect
2. C73×#3208C2semidirect
4. C73×#2981C2semidirect
5. C73×#1697C2semidirect
6. C73×#1685C2semidirect
7. C73×#1677C2semidirect
8. C73×#1665C2semidirect
9. C73×#1572C2semidirect
10. C73×#1555C2semidirect
11. C73×#1554C2semidirect
24. #476×C73C22semidirect
25. #474×C73C22semidirect
31. #436×C73C22semidirect
33. C8×D4×C73C22semidirect
39. #335×C73C22semidirect
40. #334×C73C22semidirect
41. #333×C73C22semidirect
42. #332×C73C22semidirect
217. #19504C73direct (N × H)
225. #3235C2×C73semidirect
226. #3208C2×C73semidirect
228. #2981C2×C73semidirect
229. #1697C2×C73semidirect
230. #1685C2×C73semidirect
231. #1677C2×C73semidirect
232. #1665C2×C73semidirect
233. #1572C2×C73semidirect
234. #1555C2×C73semidirect
235. #1554C2×C73semidirect
236. C73#19504direct (N × H)
249. #476C22×C73semidirect
250. #474C22×C73semidirect
256. #436C22×C73semidirect
258. C8×D4C22×C73semidirect
264. #335C22×C73semidirect
265. #334C22×C73semidirect
266. #333C22×C73semidirect
267. #332C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#32352
C73×#32082
C73×#32052
C73×#29812
C73×#16972
C73×#16852
C73×#16772
C73×#16652
C73×#15722
C73×#15552
C73×#15542
#1950473