Finite Group Databasebeta

← C73×#19160 #32928564

Subgroups — C73×#19160 #32928564

Order 18688.

642 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3169C211yesmaximal, characteristic, complemented
2C73×#3106C212yesmaximal, complemented
3C73×#2965C211yesmaximal, characteristic, complemented
4C73×#1698C212yesmaximal, complemented
5C73×#1697C212yesmaximal, complemented
6C73×#1696C211yesmaximal, characteristic, complemented
7C73×#1695C211yesmaximal, characteristic, complemented
8C73×#1688C211yesmaximal, characteristic, complemented
9C73×#1687C211yesmaximal, characteristic, complemented
10C73×#1564C211yesmaximal, characteristic, complemented
11C73×#1543C212yesmaximal, complemented
12#532×C73C2212yes—
13C4×#41×C73C2211yescharacteristic
14#500×C73C2211yescharacteristic
15#493×C73C2211yescharacteristic
16#486×C73C2212yes—
17#482×C73—22no—
18#477×C73C2212yes—
19#476×C73C2212yes—
20#466×C73—21no—
21#466×C73—21no—
22#460×C73C2212yes—
23#459×C73C2212yes—
24#449×C73—22no—
25#446×C73C2211yescharacteristic
26#446×C73C2211yescharacteristic
27C4×SD16×C73—22no—
28C4×D8×C73—22no—
29C4×D8×C73—21no—
30C4×D8×C73—21no—
31#436×C73C2211yescharacteristic
32#436×C73C2211yescharacteristic
33#435×C73—21no—
34#435×C73—21no—
35#431×C73—21no—
36#431×C73C2211yescharacteristic
37#431×C73C2212yes—
38C4×M16×C73—21no—
39C2×C4×C8×C73C2211yescharacteristic
40#335×C73C2212yes—
41#334×C73C2211yescharacteristic
42#334×C73C2211yescharacteristic
43#333×C73C2212yes—
44#333×C73C2212yes—
45#331×C73C2212yes—
46#331×C73C2212yes—
47C2×#41×C73—22no—
48C2×#41×C73D411yescharacteristic
49C2×SD16×C73—22no—
50C2×D8×C73—22no—
51C2×D8×C73—21no—
52C2×D8×C73—21no—
53C2×M16×C73—21no—
54C2×M16×C73—21no—
55C22×C8×C73D411yescharacteristic
56C22×C8×C73D411yescharacteristic
57C4⋊Q8×C73C2312yes—
58#127×C73C2312yes—
59#124×C73—22no—
60#121×C73—22no—
61#121×C73—22no—
62C4×Q8×C73D411yescharacteristic
63C4×Q8×C73C2311yescharacteristic
64C4×D4×C73—21no—
65C4×D4×C73—21no—
66C4×D4×C73—22no—
67C4×D4×C73—22no—
68C4×D4×C73D411yescharacteristic
69C4×D4×C73C2311yescharacteristic
70#117×C73—21no—
71#117×C73D411yescharacteristic
72C2×C42×C73—21no—
73C2×C42×C73C2311yescharacteristic
74#107×C73—21no—
75#107×C73—21no—
76#107×C73—22no—
77#106×C73—22no—
78C4⋊C8×C73—21no—
79C4⋊C8×C73—21no—
80C4⋊C8×C73C2311yescharacteristic
81C4⋊C8×C73C2311yescharacteristic
82C4⋊C8×C73C2312yes—
83C4⋊C8×C73C2312yes—
84#103×C73—22no—
85#102×C73—22no—
86#102×C73—22no—
87#102×C73—22no—
88#102×C73—22no—
89#102×C73—22no—
90C22⋊C8×C73—21no—
91C22⋊C8×C73—22no—
92C22⋊C8×C73—21no—
93C22⋊C8×C73—21no—
94#97×C73—21no—
95#97×C73—21no—
96C4×C8×C73—21no—
97C4×C8×C73—22no—
98C4×C8×C73D411yescharacteristic
99C4×C8×C73D411yescharacteristic
100C4×C8×C73C2311yescharacteristic
101C4×C8×C73C2311yescharacteristic
102#41×C73—42no—
103#41×C73—84no—
104C2×Q8×C73—22no—
105C2×Q8×C73C2×D411yescharacteristic
106C2×D4×C73—21no—
107C2×D4×C73—22no—
108C2×D4×C73—22no—
109C2×D4×C73—22no—
110C2×D4×C73—42no—
111C2×D4×C73C2×D411yescharacteristic
112C22×C4×C73—21no—
113C22×C4×C73—21no—
114C22×C4×C73—21no—
115C22×C4×C73—42no—
116C22×C4×C73C2×D411yescharacteristic
117C22×C4×C73C2×D411yescharacteristic
118C22×C4×C73#4111yescharacteristic
119SD16×C73—44no—
120D8×C73—42no—
121D8×C73—44no—
122D8×C73—42no—
123M16×C73—42no—
124M16×C73—42no—
125C2×C8×C73—22no—
126C2×C8×C73—21no—
127C2×C8×C73—21no—
128C2×C8×C73—22no—
129C2×C8×C73—22no—
130C2×C8×C73—41no—
131C2×C8×C73C2×D411yescharacteristic
132C2×C8×C73C2×D411yescharacteristic
133C2×C8×C73C2×D411yescharacteristic
134C2×C8×C73C2×D411yescharacteristic
135C4⋊C4×C73—21no—
136C4⋊C4×C73—21no—
137C4⋊C4×C73—22no—
138C4⋊C4×C73—22no—
139C4⋊C4×C73C2×D411yescharacteristic
140C4⋊C4×C73C2×D411yescharacteristic
141C22⋊C4×C73—21no—
142C22⋊C4×C73—21no—
143C22⋊C4×C73—21no—
144C22⋊C4×C73—42no—
145C22⋊C4×C73—42no—
146C42×C73—21no—
147C42×C73—21no—
148C42×C73—21no—
149C42×C73C2×D411yescharacteristic
150C42×C73C2×D411yescharacteristic
151C42×C73#4111yescharacteristic
152C42×C73C2411yescharacteristic
153C23×C73—21no—
154C23×C73—42no—
155C23×C73#12111yescharacteristic
156Q8×C73—22no—
157Q8×C73—82no—
158D4×C73—22no—
159D4×C73—42no—
160D4×C73—42no—
161D4×C73—42no—
162D4×C73—42no—
163D4×C73—42no—
164D4×C73—82no—
165D4×C73—84no—
166C2×C4×C73—21no—
167C2×C4×C73—21no—
168C2×C4×C73—22no—
169C2×C4×C73—22no—
170C2×C4×C73—21no—
171C2×C4×C73—21no—
172C2×C4×C73—21no—
173C2×C4×C73—42no—
174C2×C4×C73—41no—
175C2×C4×C73—41no—
176C2×C4×C73—42no—
177C2×C4×C73—42no—
178C2×C4×C73—84no—
179C2×C4×C73#12111yescharacteristic
180C2×C4×C73#12111yescharacteristic
181C2×C4×C73#12111yescharacteristic
182C2×C4×C73C22×D411yescharacteristic
183C2×C4×C73C22×D411yescharacteristic
184C2×C4×C73C2×#4111yescharacteristic
185C8×C73—21no—
186C8×C73—21no—
187C8×C73—21no—
188C8×C73—41no—
189C8×C73—41no—
190C8×C73—42no—
191C8×C73—42no—
192C8×C73#13512yes—
193C22×C73—21no—
194C22×C73—21no—
195C22×C73—21no—
196C22×C73—41no—
197C22×C73—41no—
198C22×C73—41no—
199C22×C73—82no—
200C22×C73—82no—
201C22×C73—82no—
202C22×C73C2×#12111yescharacteristic
203C4×C73—21no—
204C4×C73—21no—
205C4×C73—21no—
206C4×C73—41no—
207C4×C73—41no—
208C4×C73—41no—
209C4×C73—82no—
210C4×C73#47212yes—
211C4×C73C2×#13511yescharacteristic
212C4×C73#57511yescharacteristic
213C4×C73#57512yes—
214#19160C7311yesmaximal, characteristic, direct product factor, Sylow
215C2×C73—41no—
216C2×C73—81no—
217C2×C73—162no—
218C2×C73#303511yescharacteristic
219C2×C73#305411yescharacteristic
220C2×C73C2×#47211yescharacteristic
221#3169C2×C7311yescharacteristic, complemented
222#3106C2×C7312yescomplemented
223#2965C2×C7311yescharacteristic, complemented
224#1698C2×C7312yescomplemented
225#1697C2×C7312yescomplemented
226#1696C2×C7311yescharacteristic, complemented
227#1695C2×C7311yescharacteristic, complemented
228#1688C2×C7311yescharacteristic, complemented
229#1687C2×C7311yescharacteristic, complemented
230#1564C2×C7311yescharacteristic, complemented
231#1543C2×C7312yescomplemented
232C73#1916011yescharacteristic, direct product factor, Sylow
233#532C22×C7312yes—
234C4×#41C22×C7311yescharacteristic
235#500C22×C7311yescharacteristic
236#493C22×C7311yescharacteristic
237#486C22×C7312yes—
238#482—22no—
239#477C22×C7312yes—
240#476C22×C7312yes—
241#466—21no—
242#466—21no—
243#460C22×C7312yes—
244#459C22×C7312yes—
245#449—22no—
246#446C22×C7311yescharacteristic
247#446C22×C7311yescharacteristic
248C4×SD16—22no—
249C4×D8—22no—
250C4×D8—21no—
251C4×D8—21no—
252#436C22×C7311yescharacteristic
253#436C22×C7311yescharacteristic
254#435—21no—
255#435—21no—
256#431—21no—
257#431C22×C7311yescharacteristic
258#431C22×C7312yes—
259C4×M16—21no—
260C2×C4×C8C22×C7311yescharacteristic
261#335C22×C7312yes—
262#334C22×C7311yescharacteristic
263#334C22×C7311yescharacteristic
264#333C22×C7312yes—
265#333C22×C7312yes—
266#331C22×C7312yes—
267#331C22×C7312yes—
268C2×#41—22no—
269C2×#41D4×C7311yescharacteristic
270C2×SD16—22no—
271C2×D8—22no—
272C2×D8—21no—
273C2×D8—21no—
274C2×M16—21no—
275C2×M16—21no—
276C22×C8D4×C7311yescharacteristic
277C22×C8D4×C7311yescharacteristic
278C4⋊Q8C23×C7312yes—
279#127C23×C7312yes—
280#124—22no—
281#121—22no—
282#121—22no—
283C4×Q8D4×C7311yescharacteristic
284C4×Q8C23×C7311yescharacteristic
285C4×D4—21no—
286C4×D4—21no—
287C4×D4—22no—
288C4×D4—22no—
289C4×D4D4×C7311yescharacteristic
290C4×D4C23×C7311yescharacteristic
291#117—21no—
292#117D4×C7311yescharacteristic
293C2×C42—21no—
294C2×C42C23×C7311yescharacteristic
295#107—21no—
296#107—21no—
297#107—22no—
298#106—22no—
299C4⋊C8—21no—
300C4⋊C8—21no—
301C4⋊C8C23×C7311yescharacteristic
302C4⋊C8C23×C7311yescharacteristic
303C4⋊C8C23×C7312yes—
304C4⋊C8C23×C7312yes—
305#103—22no—
306#102—22no—
307#102—22no—
308#102—22no—
309#102—22no—
310#102—22no—
311C22⋊C8—21no—
312C22⋊C8—22no—
313C22⋊C8—21no—
314C22⋊C8—21no—
315#97—21no—
316#97—21no—
317C4×C8—21no—
318C4×C8—22no—
319C4×C8D4×C7311yescharacteristic
320C4×C8D4×C7311yescharacteristic
321C4×C8C23×C7311yescharacteristic
322C4×C8C23×C7311yescharacteristic
323#41—42no—
324#41—84no—
325C2×Q8—22no—
326C2×Q8C2×D4×C7311yescharacteristic
327C2×D4—21no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—42no—
332C2×D4C2×D4×C7311yescharacteristic
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—42no—
337C22×C4C2×D4×C7311yescharacteristic
338C22×C4C2×D4×C7311yescharacteristic
339C22×C4#41×C7311yescharacteristic
340SD16—44no—
341D8—42no—
342D8—44no—
343D8—42no—
344M16—42no—
345M16—42no—
346C2×C8—22no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—41no—
352C2×C8C2×D4×C7311yescharacteristic
353C2×C8C2×D4×C7311yescharacteristic
354C2×C8C2×D4×C7311yescharacteristic
355C2×C8C2×D4×C7311yescharacteristic
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4C2×D4×C7311yescharacteristic
361C4⋊C4C2×D4×C7311yescharacteristic
362C22⋊C4—21no—
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—42no—
366C22⋊C4—42no—
367C42—21no—
368C42—21no—
369C42—21no—
370C42C2×D4×C7311yescharacteristic
371C42C2×D4×C7311yescharacteristic
372C42#41×C7311yescharacteristic
373C42C24×C7311yescharacteristic
374C23—21no—
375C23—42no—
376C23#121×C7311yescharacteristic
377Q8—22no—
378Q8—82no—
379D4—22no—
380D4—42no—
381D4—42no—
382D4—42no—
383D4—42no—
384D4—42no—
385D4—82no—
386D4—84no—
387C2×C4—22no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—84no—
400C2×C4#121×C7311yescharacteristic
401C2×C4#121×C7311yescharacteristic
402C2×C4#121×C7311yescharacteristic
403C2×C4C22×D4×C7311yescharacteristic
404C2×C4C22×D4×C7311yescharacteristic
405C2×C4C2×#41×C7311yescharacteristic
406C8—21no—
407C8—21no—
408C8—21no—
409C8—41no—
410C8—41no—
411C8—42no—
412C8—42no—
413C8#135×C7312yes—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—82no—
421C22—82no—
422C22—82no—
423C22C2×#121×C7311yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—41no—
428C4—41no—
429C4—41no—
430C4—82no—
431C4#472×C7312yes—
432C4C2×#135×C7311yescharacteristic
433C4#575×C7311yescharacteristic
434C4#575×C7312yes—
435C2—41no—
436C2—81no—
437C2—162no—
438C2C73×#303511yescharacteristic
439C2C73×#305411yescharacteristic
440C2C2×#472×C7311yescharacteristic
subgroupG/H
centerC2×C4×C73#121
commutator, Frattini, cosocleC42C24×C73
socleC22×C73C2×#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3169C2semidirect
2. C73×#3106C2semidirect
3. C73×#2965C2semidirect
4. C73×#1698C2semidirect
5. C73×#1697C2semidirect
6. C73×#1696C2semidirect
7. C73×#1695C2semidirect
8. C73×#1688C2semidirect
9. C73×#1687C2semidirect
10. C73×#1564C2semidirect
11. C73×#1543C2semidirect
214. #19160C73direct (N × H)
221. #3169C2×C73semidirect
222. #3106C2×C73semidirect
223. #2965C2×C73semidirect
224. #1698C2×C73semidirect
225. #1697C2×C73semidirect
226. #1696C2×C73semidirect
227. #1695C2×C73semidirect
228. #1688C2×C73semidirect
229. #1687C2×C73semidirect
230. #1564C2×C73semidirect
231. #1543C2×C73semidirect
232. C73#19160direct (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×#31062
C73×#29652
C73×#16982
C73×#16972
C73×#16962
C73×#16952
C73×#16882
C73×#16872
C73×#15642
C73×#15432
#1916073