Finite Group Databasebeta

← C73×#33807 #32943211

Subgroups — C73×#33807 #32943211

Order 18688.

466 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3176C211yesmaximal, characteristic
2C73×#3164C211yesmaximal, characteristic, complemented
3C73×#2255C211yesmaximal, characteristic, complemented
4C73×#2253C211yesmaximal, characteristic, complemented
5C73×#2244C211yesmaximal, characteristic, complemented
6C73×#2240C211yesmaximal, characteristic, complemented
7C73×#2234C211yesmaximal, characteristic, complemented
8C73×#2234C211yesmaximal, characteristic, complemented
9C73×#2233C211yesmaximal, characteristic, complemented
10C73×#2232C211yesmaximal, characteristic, complemented
11C73×#2228C211yesmaximal, characteristic, complemented
12C73×#2228C211yesmaximal, characteristic, complemented
13C73×#2226C211yesmaximal, characteristic, complemented
14C73×#2224C211yesmaximal, characteristic, complemented
15C73×#2164C211yesmaximal, characteristic, complemented
16#544×C73—21no—
17#540×C73—21no—
18#501×C73—21no—
19#501×C73—21no—
20#500×C73C2211yescharacteristic
21#500×C73C2211yescharacteristic
22#499×C73C2211yescharacteristic
23#499×C73C2211yescharacteristic
24#499×C73C2211yescharacteristic
25#493×C73C2211yescharacteristic
26#490×C73—21no—
27#469×C73—21no—
28#466×C73C2211yescharacteristic
29#466×C73C2211yescharacteristic
30#442×C73—21no—
31C4×D8×C73C2211yescharacteristic
32C4×D8×C73C2211yescharacteristic
33#428×C73—21no—
34#427×C73C2211yescharacteristic
35C2×#107×C73C2211yescharacteristic
36#405×C73C2211yescharacteristic
37#367×C73C2211yescharacteristic
38#367×C73C2211yescharacteristic
39#367×C73C2211yescharacteristic
40#367×C73C2211yescharacteristic
41#366×C73C2211yescharacteristic
42#366×C73C2211yescharacteristic
43#366×C73C2211yescharacteristic
44#366×C73C2211yescharacteristic
45C4⋊C16×C73C2211yescharacteristic
46C4⋊C16×C73C2211yescharacteristic
47#357×C73C2211yescharacteristic
48#357×C73C2211yescharacteristic
49#357×C73C2211yescharacteristic
50#357×C73C2211yescharacteristic
51#357×C73C2211yescharacteristic
52#357×C73C2211yescharacteristic
53#357×C73C2211yescharacteristic
54#357×C73C2211yescharacteristic
55C22⋊C16×C73C2211yescharacteristic
56C22⋊C16×C73C2211yescharacteristic
57#346×C73C2211yescharacteristic
58C4×C16×C73C2211yescharacteristic
59C2×D8×C73—21no—
60C2×D8×C73C2311yescharacteristic
61C2×D8×C73C2311yescharacteristic
62C2×M16×C73D411yescharacteristic
63C22×C8×C73C2311yescharacteristic
64C4⋊Q8×C73—21no—
65C4⋊Q8×C73—21no—
66C4⋊Q8×C73—41no—
67#127×C73—21no—
68#125×C73—21no—
69#125×C73—21no—
70#125×C73—21no—
71#125×C73—41no—
72#123×C73—41no—
73#123×C73—41no—
74C22⋊Q8×C73—41no—
75C22⋊Q8×C73—41no—
76#121×C73—21no—
77#121×C73—21no—
78#121×C73—41no—
79#121×C73—41no—
80C4×D4×C73—21no—
81C4×D4×C73—21no—
82#117×C73—21no—
83#117×C73D411yescharacteristic
84C2×C4⋊C4×C73—21no—
85C2×C16×C73C2311yescharacteristic
86C2×C16×C73C2311yescharacteristic
87C2×C16×C73C2311yescharacteristic
88C2×C16×C73C2311yescharacteristic
89#107×C73—21no—
90#107×C73—21no—
91#107×C73—21no—
92#107×C73C2311yescharacteristic
93#107×C73C2311yescharacteristic
94#107×C73C2311yescharacteristic
95#107×C73C2311yescharacteristic
96#107×C73C2311yescharacteristic
97#107×C73C2311yescharacteristic
98#106×C73—21no—
99#106×C73—21no—
100#106×C73—21no—
101#106×C73—21no—
102#102×C73—21no—
103#102×C73—21no—
104#102×C73—21no—
105#102×C73—21no—
106#97×C73D411yescharacteristic
107#97×C73D411yescharacteristic
108C4×C8×C73C2311yescharacteristic
109C4×C8×C73C2311yescharacteristic
110C2×Q8×C73—41no—
111C2×Q8×C73—41no—
112C2×D4×C73—21no—
113C2×D4×C73—21no—
114C2×D4×C73—41no—
115C2×D4×C73—41no—
116C2×D4×C73—41no—
117C2×D4×C73—41no—
118C22×C4×C73—41no—
119C22×C4×C73—41no—
120C22×C4×C73—41no—
121C22×C4×C73C2×D411yescharacteristic
122D8×C73—21no—
123D8×C73—21no—
124D8×C73—21no—
125D8×C73—21no—
126D8×C73—42no—
127M16×C73—22no—
128C2×C8×C73—21no—
129C2×C8×C73—21no—
130C2×C8×C73C2×D411yescharacteristic
131C2×C8×C73C2×D411yescharacteristic
132C2×C8×C73C2×D411yescharacteristic
133C2×C8×C73C2411yescharacteristic
134C4⋊C4×C73—21no—
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×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×C73D811yescharacteristic
150C4⋊C4×C73D811yescharacteristic
151C22⋊C4×C73—41no—
152C22⋊C4×C73—41no—
153C22⋊C4×C73—41no—
154C22⋊C4×C73—41no—
155C22⋊C4×C73—41no—
156C22⋊C4×C73D811yescharacteristic
157C22⋊C4×C73D811yescharacteristic
158C42×C73—41no—
159C42×C73C2×D411yescharacteristic
160C42×C73C2×D411yescharacteristic
161C16×C73—21no—
162C16×C73—21no—
163C16×C73—21no—
164C16×C73—21no—
165C23×C73—41no—
166C23×C73—41no—
167C23×C73C2×D811yescharacteristic
168Q8×C73—161no—
169Q8×C73—161no—
170D4×C73—41no—
171D4×C73—41no—
172D4×C73—41no—
173D4×C73—41no—
174D4×C73—161no—
175D4×C73—161no—
176D4×C73—161no—
177D4×C73—161no—
178C2×C4×C73—21no—
179C2×C4×C73—21no—
180C2×C4×C73—41no—
181C2×C4×C73—41no—
182C2×C4×C73—41no—
183C2×C4×C73—41no—
184C2×C4×C73—41no—
185C2×C4×C73—41no—
186C2×C4×C73—161no—
187C2×C4×C73—161no—
188C2×C4×C73—161no—
189C2×C4×C73C2×D811yescharacteristic
190C2×C4×C73C2×D811yescharacteristic
191C2×C4×C73C2×D811yescharacteristic
192C2×C4×C73C2×D811yescharacteristic
193C2×C4×C73C2×D811yescharacteristic
194C2×C4×C73C22×D411yescharacteristic
195C8×C73—21no—
196C8×C73—21no—
197C8×C73#13712yes—
198C8×C732−1+411yescharacteristic
199C8×C732−1+411yescharacteristic
200C22×C73—21no—
201C22×C73—21no—
202C22×C73—21no—
203C22×C73—81no—
204C22×C73—81no—
205C22×C73—81no—
206C22×C73—81no—
207C22×C73—81no—
208C22×C73—81no—
209C22×C73C22×D811yescharacteristic
210C4×C73—21no—
211C4×C73—21no—
212C4×C73—21no—
213C4×C73—21no—
214C4×C73—21no—
215C4×C73—81no—
216C4×C73—81no—
217C4×C73—81no—
218C4×C73—81no—
219C4×C73—81no—
220C4×C73—81no—
221C4×C73#53611yescharacteristic
222C4×C73C2×#13711yescharacteristic
223#33807C7311yesmaximal, characteristic, direct product factor, Sylow
224C2×C73—41no—
225C2×C73—161no—
226C2×C73—161no—
227C2×C73#322611yescharacteristic
228C2×C73#341511yescharacteristic
229C2×C73#341611yescharacteristic
230#3176C2×C7311yescharacteristic
231#3164C2×C7311yescharacteristic, complemented
232#2255C2×C7311yescharacteristic, complemented
233#2253C2×C7311yescharacteristic, complemented
234#2244C2×C7311yescharacteristic, complemented
235#2240C2×C7311yescharacteristic, complemented
236#2234C2×C7311yescharacteristic, complemented
237#2234C2×C7311yescharacteristic, complemented
238#2233C2×C7311yescharacteristic, complemented
239#2232C2×C7311yescharacteristic, complemented
240#2228C2×C7311yescharacteristic, complemented
241#2228C2×C7311yescharacteristic, complemented
242#2226C2×C7311yescharacteristic, complemented
243#2224C2×C7311yescharacteristic, complemented
244#2164C2×C7311yescharacteristic, complemented
245C73#3380711yescharacteristic, direct product factor, Sylow
246#544—21no—
247#540—21no—
248#501—21no—
249#501—21no—
250#500C22×C7311yescharacteristic
251#500C22×C7311yescharacteristic
252#499C22×C7311yescharacteristic
253#499C22×C7311yescharacteristic
254#499C22×C7311yescharacteristic
255#493C22×C7311yescharacteristic
256#490—21no—
257#469—21no—
258#466C22×C7311yescharacteristic
259#466C22×C7311yescharacteristic
260#442—21no—
261C4×D8C22×C7311yescharacteristic
262C4×D8C22×C7311yescharacteristic
263#428—21no—
264#427C22×C7311yescharacteristic
265C2×#107C22×C7311yescharacteristic
266#405C22×C7311yescharacteristic
267#367C22×C7311yescharacteristic
268#367C22×C7311yescharacteristic
269#367C22×C7311yescharacteristic
270#367C22×C7311yescharacteristic
271#366C22×C7311yescharacteristic
272#366C22×C7311yescharacteristic
273#366C22×C7311yescharacteristic
274#366C22×C7311yescharacteristic
275C4⋊C16C22×C7311yescharacteristic
276C4⋊C16C22×C7311yescharacteristic
277#357C22×C7311yescharacteristic
278#357C22×C7311yescharacteristic
279#357C22×C7311yescharacteristic
280#357C22×C7311yescharacteristic
281#357C22×C7311yescharacteristic
282#357C22×C7311yescharacteristic
283#357C22×C7311yescharacteristic
284#357C22×C7311yescharacteristic
285C22⋊C16C22×C7311yescharacteristic
286C22⋊C16C22×C7311yescharacteristic
287#346C22×C7311yescharacteristic
288C4×C16C22×C7311yescharacteristic
289C2×D8—21no—
290C2×D8C23×C7311yescharacteristic
291C2×D8C23×C7311yescharacteristic
292C2×M16D4×C7311yescharacteristic
293C22×C8C23×C7311yescharacteristic
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8—41no—
297#127—21no—
298#125—21no—
299#125—21no—
300#125—21no—
301#125—41no—
302#123—41no—
303#123—41no—
304C22⋊Q8—41no—
305C22⋊Q8—41no—
306#121—21no—
307#121—21no—
308#121—41no—
309#121—41no—
310C4×D4—21no—
311C4×D4—21no—
312#117—21no—
313#117D4×C7311yescharacteristic
314C2×C4⋊C4—21no—
315C2×C16C23×C7311yescharacteristic
316C2×C16C23×C7311yescharacteristic
317C2×C16C23×C7311yescharacteristic
318C2×C16C23×C7311yescharacteristic
319#107—21no—
320#107—21no—
321#107—21no—
322#107C23×C7311yescharacteristic
323#107C23×C7311yescharacteristic
324#107C23×C7311yescharacteristic
325#107C23×C7311yescharacteristic
326#107C23×C7311yescharacteristic
327#107C23×C7311yescharacteristic
328#106—21no—
329#106—21no—
330#106—21no—
331#106—21no—
332#102—21no—
333#102—21no—
334#102—21no—
335#102—21no—
336#97D4×C7311yescharacteristic
337#97D4×C7311yescharacteristic
338C4×C8C23×C7311yescharacteristic
339C4×C8C23×C7311yescharacteristic
340C2×Q8—41no—
341C2×Q8—41no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4C2×D4×C7311yescharacteristic
352D8—21no—
353D8—21no—
354D8—21no—
355D8—21no—
356D8—42no—
357M16—22no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8C2×D4×C7311yescharacteristic
361C2×C8C2×D4×C7311yescharacteristic
362C2×C8C2×D4×C7311yescharacteristic
363C2×C8C24×C7311yescharacteristic
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4D8×C7311yescharacteristic
380C4⋊C4D8×C7311yescharacteristic
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4D8×C7311yescharacteristic
387C22⋊C4D8×C7311yescharacteristic
388C42—41no—
389C42C2×D4×C7311yescharacteristic
390C42C2×D4×C7311yescharacteristic
391C16—21no—
392C16—21no—
393C16—21no—
394C16—21no—
395C23—41no—
396C23—41no—
397C23C2×D8×C7311yescharacteristic
398Q8—161no—
399Q8—161no—
400D4—41no—
401D4—41no—
402D4—41no—
403D4—41no—
404D4—161no—
405D4—161no—
406D4—161no—
407D4—161no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—161no—
417C2×C4—161no—
418C2×C4—161no—
419C2×C4C2×D8×C7311yescharacteristic
420C2×C4C2×D8×C7311yescharacteristic
421C2×C4C2×D8×C7311yescharacteristic
422C2×C4C2×D8×C7311yescharacteristic
423C2×C4C2×D8×C7311yescharacteristic
424C2×C4C22×D4×C7311yescharacteristic
425C8—21no—
426C8—21no—
427C8#137×C7312yes—
428C82−1+4×C7311yescharacteristic
429C82−1+4×C7311yescharacteristic
430C22—21no—
431C22—21no—
432C22—21no—
433C22—81no—
434C22—81no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22—81no—
439C22C22×D8×C7311yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—81no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—81no—
450C4—81no—
451C4#536×C7311yescharacteristic
452C4C2×#137×C7311yescharacteristic
453C2—41no—
454C2—161no—
455C2—161no—
456C2C73×#322611yescharacteristic
457C2C73×#341511yescharacteristic
458C2C73×#341611yescharacteristic
subgroupG/H
center, socleC22×C73C22×D8
commutator, Frattini, cosocleC2×C8C24×C73
prime radicalC73×#3176C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ #117×C73 ◁ #405×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#3164C2semidirect
3. C73×#2255C2semidirect
4. C73×#2253C2semidirect
5. C73×#2244C2semidirect
6. C73×#2240C2semidirect
7. C73×#2234C2semidirect
8. C73×#2234C2semidirect
9. C73×#2233C2semidirect
10. C73×#2232C2semidirect
11. C73×#2228C2semidirect
12. C73×#2228C2semidirect
13. C73×#2226C2semidirect
14. C73×#2224C2semidirect
15. C73×#2164C2semidirect
223. #33807C73direct (N × H)
231. #3164C2×C73semidirect
232. #2255C2×C73semidirect
233. #2253C2×C73semidirect
234. #2244C2×C73semidirect
235. #2240C2×C73semidirect
236. #2234C2×C73semidirect
237. #2234C2×C73semidirect
238. #2233C2×C73semidirect
239. #2232C2×C73semidirect
240. #2228C2×C73semidirect
241. #2228C2×C73semidirect
242. #2226C2×C73semidirect
243. #2224C2×C73semidirect
244. #2164C2×C73semidirect
245. C73#33807direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#31762
C73×#31642
C73×#22552
C73×#22532
C73×#22442
C73×#22402
C73×#22342
C73×#22332
C73×#22322
C73×#22282
C73×#22262
C73×#22242
C73×#21642
#3380773