Finite Group Databasebeta

← C73×#33917 #32943321

Subgroups — C73×#33917 #32943321

Order 18688.

476 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×#3342C211yesmaximal, characteristic, complemented
2C73×#3339C211yesmaximal, characteristic
3C73×#2255C211yesmaximal, characteristic, complemented
4C73×#2237C211yesmaximal, characteristic, complemented
5C73×#2235C211yesmaximal, characteristic, complemented
6C73×#2234C211yesmaximal, characteristic, complemented
7C73×#2234C211yesmaximal, characteristic, complemented
8C73×#2229C211yesmaximal, characteristic, complemented
9C73×#2226C211yesmaximal, characteristic, complemented
10C73×#2220C211yesmaximal, characteristic, complemented
11C73×#2217C211yesmaximal, characteristic, complemented
12C73×#2175C211yesmaximal, characteristic, complemented
13C73×#2168C211yesmaximal, characteristic, complemented
14C73×#2159C211yesmaximal, characteristic, complemented
15C73×#2158C211yesmaximal, characteristic, complemented
16#556×C73—21no—
17#553×C73—21no—
18C2×SD32×C73C2211yescharacteristic
19C2×M32×C73C2211yescharacteristic
20C22×C16×C73C2211yescharacteristic
21#500×C73C2211yescharacteristic
22#499×C73C2211yescharacteristic
23#485×C73—21no—
24#485×C73—21no—
25#482×C73—21no—
26#481×C73—21no—
27#478×C73—21no—
28#475×C73—21no—
29#467×C73C2211yescharacteristic
30#467×C73C2211yescharacteristic
31#466×C73C2211yescharacteristic
32#466×C73C2211yescharacteristic
33C4×Q16×C73C2211yescharacteristic
34C4×D8×C73C2211yescharacteristic
35C8×D4×C73C2211yescharacteristic
36#427×C73C2211yescharacteristic
37#427×C73C2211yescharacteristic
38#427×C73C2211yescharacteristic
39C2×#107×C73C2211yescharacteristic
40#367×C73C2211yescharacteristic
41#367×C73C2211yescharacteristic
42#367×C73C2211yescharacteristic
43#367×C73C2211yescharacteristic
44#367×C73C2211yescharacteristic
45#366×C73C2211yescharacteristic
46#366×C73C2211yescharacteristic
47#366×C73C2211yescharacteristic
48#366×C73C2211yescharacteristic
49C4⋊C16×C73C2211yescharacteristic
50#358×C73C2211yescharacteristic
51#358×C73C2211yescharacteristic
52#358×C73C2211yescharacteristic
53#357×C73C2211yescharacteristic
54#357×C73C2211yescharacteristic
55#357×C73C2211yescharacteristic
56C22⋊C16×C73C2211yescharacteristic
57C22⋊C16×C73C2211yescharacteristic
58#346×C73C2211yescharacteristic
59C2×Q16×C73C2311yescharacteristic
60C2×D8×C73C2311yescharacteristic
61C22×C8×C73C2311yescharacteristic
62C22×C8×C73C2311yescharacteristic
63C4⋊Q8×C73—21no—
64#126×C73—41no—
65#126×C73—41no—
66#126×C73—41no—
67#125×C73—21no—
68#124×C73—41no—
69#123×C73—41no—
70C22⋊Q8×C73—21no—
71C22⋊Q8×C73—21no—
72#121×C73—21no—
73#121×C73—21no—
74#121×C73—41no—
75C4×Q8×C73—21no—
76C4×Q8×C73—41no—
77C4×D4×C73—21no—
78C4×D4×C73—41no—
79C4×D4×C73D411yescharacteristic
80#117×C73—21no—
81#117×C73—21no—
82#117×C73—21no—
83C2×C4⋊C4×C73—21no—
84SD32×C73—22no—
85M32×C73—22no—
86C2×C16×C73—22no—
87C2×C16×C73C2311yescharacteristic
88C2×C16×C73C2311yescharacteristic
89C2×C16×C73C2311yescharacteristic
90C2×C16×C73C2311yescharacteristic
91#107×C73—21no—
92#107×C73—21no—
93#107×C73C2311yescharacteristic
94#107×C73C2311yescharacteristic
95#107×C73C2311yescharacteristic
96#107×C73C2311yescharacteristic
97#107×C73C2311yescharacteristic
98#107×C73C2311yescharacteristic
99#106×C73—21no—
100#106×C73—21no—
101#106×C73—21no—
102#106×C73—21no—
103C4⋊C8×C73D411yescharacteristic
104#103×C73—21no—
105#103×C73—21no—
106#103×C73—21no—
107#102×C73—21no—
108#102×C73—21no—
109#102×C73—21no—
110C22⋊C8×C73D411yescharacteristic
111C22⋊C8×C73D411yescharacteristic
112C4×C8×C73C2311yescharacteristic
113C2×Q8×C73—21no—
114C2×Q8×C73—41no—
115C2×D4×C73—21no—
116C2×D4×C73—41no—
117C2×D4×C73—41no—
118C2×D4×C73D811yescharacteristic
119C22×C4×C73—41no—
120C22×C4×C73—41no—
121C22×C4×C73C2×D411yescharacteristic
122C22×C4×C73C2×D411yescharacteristic
123Q16×C73—21no—
124Q16×C73—21no—
125D8×C73—21no—
126D8×C73—21no—
127C2×C8×C73—21no—
128C2×C8×C73—21no—
129C2×C8×C73—21no—
130C2×C8×C73—21no—
131C2×C8×C73C2×D411yescharacteristic
132C2×C8×C73C2×D411yescharacteristic
133C2×C8×C73C2×D411yescharacteristic
134C2×C8×C73C2411yescharacteristic
135C4⋊C4×C73—21no—
136C4⋊C4×C73—21no—
137C4⋊C4×C73—21no—
138C4⋊C4×C73—21no—
139C4⋊C4×C73—21no—
140C4⋊C4×C73—21no—
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×C73D811yescharacteristic
149C22⋊C4×C73—41no—
150C22⋊C4×C73—41no—
151C22⋊C4×C73—41no—
152C22⋊C4×C73—41no—
153C22⋊C4×C73—41no—
154C22⋊C4×C73—41no—
155C22⋊C4×C73—41no—
156C22⋊C4×C73—41no—
157C22⋊C4×C73D811yescharacteristic
158C22⋊C4×C73D811yescharacteristic
159C42×C73—41no—
160C42×C73—41no—
161C42×C73—41no—
162C42×C73—41no—
163C42×C73C2×D411yescharacteristic
164C16×C73—21no—
165C16×C73—21no—
166C16×C73—21no—
167C16×C73#4112yes—
168C23×C73—41no—
169C23×C73C2×D811yescharacteristic
170C23×C73C2×D811yescharacteristic
171Q8×C73—41no—
172Q8×C73—41no—
173Q8×C73—82no—
174D4×C73—41no—
175D4×C73—41no—
176D4×C73—41no—
177D4×C73—82no—
178D4×C73—161no—
179C2×C4×C73—21no—
180C2×C4×C73—21no—
181C2×C4×C73—21no—
182C2×C4×C73—21no—
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—41no—
190C2×C4×C73—161no—
191C2×C4×C73—161no—
192C2×C4×C73C2×D811yescharacteristic
193C2×C4×C73C2×D811yescharacteristic
194C2×C4×C73C2×D811yescharacteristic
195C2×C4×C73C2×D811yescharacteristic
196C2×C4×C73C22×D411yescharacteristic
197C8×C73—21no—
198C8×C73—21no—
199C8×C73—21no—
200C8×C73C2×#4111yescharacteristic
201C8×C732−1+411yescharacteristic
202C22×C73—21no—
203C22×C73—21no—
204C22×C73—21no—
205C22×C73—21no—
206C22×C73—21no—
207C22×C73—21no—
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—81no—
217C4×C73—81no—
218C4×C73—81no—
219C4×C73—81no—
220C4×C73—81no—
221C4×C73—81no—
222C4×C73—81no—
223C4×C73#54711yescharacteristic
224C4×C73#57811yescharacteristic
225#33917C7311yesmaximal, characteristic, direct product factor, Sylow
226C2×C73—41no—
227C2×C73—41no—
228C2×C73—161no—
229C2×C73#333411yescharacteristic
230C2×C73#341411yescharacteristic
231C2×C73#341611yescharacteristic
232#3342C2×C7311yescharacteristic, complemented
233#3339C2×C7311yescharacteristic
234#2255C2×C7311yescharacteristic, complemented
235#2237C2×C7311yescharacteristic, complemented
236#2235C2×C7311yescharacteristic, complemented
237#2234C2×C7311yescharacteristic, complemented
238#2234C2×C7311yescharacteristic, complemented
239#2229C2×C7311yescharacteristic, complemented
240#2226C2×C7311yescharacteristic, complemented
241#2220C2×C7311yescharacteristic, complemented
242#2217C2×C7311yescharacteristic, complemented
243#2175C2×C7311yescharacteristic, complemented
244#2168C2×C7311yescharacteristic, complemented
245#2159C2×C7311yescharacteristic, complemented
246#2158C2×C7311yescharacteristic, complemented
247C73#3391711yescharacteristic, direct product factor, Sylow
248#556—21no—
249#553—21no—
250C2×SD32C22×C7311yescharacteristic
251C2×M32C22×C7311yescharacteristic
252C22×C16C22×C7311yescharacteristic
253#500C22×C7311yescharacteristic
254#499C22×C7311yescharacteristic
255#485—21no—
256#485—21no—
257#482—21no—
258#481—21no—
259#478—21no—
260#475—21no—
261#467C22×C7311yescharacteristic
262#467C22×C7311yescharacteristic
263#466C22×C7311yescharacteristic
264#466C22×C7311yescharacteristic
265C4×Q16C22×C7311yescharacteristic
266C4×D8C22×C7311yescharacteristic
267C8×D4C22×C7311yescharacteristic
268#427C22×C7311yescharacteristic
269#427C22×C7311yescharacteristic
270#427C22×C7311yescharacteristic
271C2×#107C22×C7311yescharacteristic
272#367C22×C7311yescharacteristic
273#367C22×C7311yescharacteristic
274#367C22×C7311yescharacteristic
275#367C22×C7311yescharacteristic
276#367C22×C7311yescharacteristic
277#366C22×C7311yescharacteristic
278#366C22×C7311yescharacteristic
279#366C22×C7311yescharacteristic
280#366C22×C7311yescharacteristic
281C4⋊C16C22×C7311yescharacteristic
282#358C22×C7311yescharacteristic
283#358C22×C7311yescharacteristic
284#358C22×C7311yescharacteristic
285#357C22×C7311yescharacteristic
286#357C22×C7311yescharacteristic
287#357C22×C7311yescharacteristic
288C22⋊C16C22×C7311yescharacteristic
289C22⋊C16C22×C7311yescharacteristic
290#346C22×C7311yescharacteristic
291C2×Q16C23×C7311yescharacteristic
292C2×D8C23×C7311yescharacteristic
293C22×C8C23×C7311yescharacteristic
294C22×C8C23×C7311yescharacteristic
295C4⋊Q8—21no—
296#126—41no—
297#126—41no—
298#126—41no—
299#125—21no—
300#124—41no—
301#123—41no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304#121—21no—
305#121—21no—
306#121—41no—
307C4×Q8—21no—
308C4×Q8—41no—
309C4×D4—21no—
310C4×D4—41no—
311C4×D4D4×C7311yescharacteristic
312#117—21no—
313#117—21no—
314#117—21no—
315C2×C4⋊C4—21no—
316SD32—22no—
317M32—22no—
318C2×C16—22no—
319C2×C16C23×C7311yescharacteristic
320C2×C16C23×C7311yescharacteristic
321C2×C16C23×C7311yescharacteristic
322C2×C16C23×C7311yescharacteristic
323#107—21no—
324#107—21no—
325#107C23×C7311yescharacteristic
326#107C23×C7311yescharacteristic
327#107C23×C7311yescharacteristic
328#107C23×C7311yescharacteristic
329#107C23×C7311yescharacteristic
330#107C23×C7311yescharacteristic
331#106—21no—
332#106—21no—
333#106—21no—
334#106—21no—
335C4⋊C8D4×C7311yescharacteristic
336#103—21no—
337#103—21no—
338#103—21no—
339#102—21no—
340#102—21no—
341#102—21no—
342C22⋊C8D4×C7311yescharacteristic
343C22⋊C8D4×C7311yescharacteristic
344C4×C8C23×C7311yescharacteristic
345C2×Q8—21no—
346C2×Q8—41no—
347C2×D4—21no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4D8×C7311yescharacteristic
351C22×C4—41no—
352C22×C4—41no—
353C22×C4C2×D4×C7311yescharacteristic
354C22×C4C2×D4×C7311yescharacteristic
355Q16—21no—
356Q16—21no—
357D8—21no—
358D8—21no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8C2×D4×C7311yescharacteristic
364C2×C8C2×D4×C7311yescharacteristic
365C2×C8C2×D4×C7311yescharacteristic
366C2×C8C24×C7311yescharacteristic
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4D8×C7311yescharacteristic
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4D8×C7311yescharacteristic
390C22⋊C4D8×C7311yescharacteristic
391C42—41no—
392C42—41no—
393C42—41no—
394C42—41no—
395C42C2×D4×C7311yescharacteristic
396C16—21no—
397C16—21no—
398C16—21no—
399C16#41×C7312yes—
400C23—41no—
401C23C2×D8×C7311yescharacteristic
402C23C2×D8×C7311yescharacteristic
403Q8—41no—
404Q8—41no—
405Q8—82no—
406D4—41no—
407D4—41no—
408D4—41no—
409D4—82no—
410D4—161no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—161no—
423C2×C4—161no—
424C2×C4C2×D8×C7311yescharacteristic
425C2×C4C2×D8×C7311yescharacteristic
426C2×C4C2×D8×C7311yescharacteristic
427C2×C4C2×D8×C7311yescharacteristic
428C2×C4C22×D4×C7311yescharacteristic
429C8—21no—
430C8—21no—
431C8—21no—
432C8C2×#41×C7311yescharacteristic
433C82−1+4×C7311yescharacteristic
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22C22×D8×C7311yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—81no—
449C4—81no—
450C4—81no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4#547×C7311yescharacteristic
456C4#578×C7311yescharacteristic
457C2—41no—
458C2—41no—
459C2—161no—
460C2C73×#333411yescharacteristic
461C2C73×#341411yescharacteristic
462C2C73×#341611yescharacteristic
subgroupG/H
center, socleC22×C73C22×D8
commutator, Frattini, cosocleC2×C8C24×C73
prime radicalC73×#3339C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C4×D4×C73 ◁ C8×D4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3342C2semidirect
3. C73×#2255C2semidirect
4. C73×#2237C2semidirect
5. C73×#2235C2semidirect
6. C73×#2234C2semidirect
7. C73×#2234C2semidirect
8. C73×#2229C2semidirect
9. C73×#2226C2semidirect
10. C73×#2220C2semidirect
11. C73×#2217C2semidirect
12. C73×#2175C2semidirect
13. C73×#2168C2semidirect
14. C73×#2159C2semidirect
15. C73×#2158C2semidirect
225. #33917C73direct (N × H)
232. #3342C2×C73semidirect
234. #2255C2×C73semidirect
235. #2237C2×C73semidirect
236. #2235C2×C73semidirect
237. #2234C2×C73semidirect
238. #2234C2×C73semidirect
239. #2229C2×C73semidirect
240. #2226C2×C73semidirect
241. #2220C2×C73semidirect
242. #2217C2×C73semidirect
243. #2175C2×C73semidirect
244. #2168C2×C73semidirect
245. #2159C2×C73semidirect
246. #2158C2×C73semidirect
247. C73#33917direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#33422
C73×#33392
C73×#22552
C73×#22372
C73×#22352
C73×#22342
C73×#22292
C73×#22262
C73×#22202
C73×#22172
C73×#21752
C73×#21682
C73×#21592
C73×#21582
#3391773