Finite Group Databasebeta

← C73×#33809 #32943213

Subgroups — C73×#33809 #32943213

Order 18688.

454 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3175C211yesmaximal, characteristic
2C73×#3164C211yesmaximal, characteristic, complemented
3C73×#2255C211yesmaximal, characteristic, complemented
4C73×#2252C211yesmaximal, characteristic, complemented
5C73×#2243C211yesmaximal, characteristic, complemented
6C73×#2242C211yesmaximal, characteristic, complemented
7C73×#2237C211yesmaximal, characteristic, complemented
8C73×#2236C211yesmaximal, characteristic, complemented
9C73×#2234C211yesmaximal, characteristic
10C73×#2232C211yesmaximal, characteristic
11C73×#2229C211yesmaximal, characteristic, complemented
12C73×#2228C211yesmaximal, characteristic, complemented
13C73×#2227C211yesmaximal, characteristic, complemented
14C73×#2224C211yesmaximal, characteristic, complemented
15C73×#2164C211yesmaximal, characteristic, complemented
16#544×C73—21no—
17#542×C73—21no—
18#501×C73—21no—
19#501×C73—21no—
20#500×C73C2211yescharacteristic
21#500×C73C2211yescharacteristic
22#500×C73C2211yescharacteristic
23#499×C73C2211yescharacteristic
24#499×C73C2211yescharacteristic
25#495×C73C2211yescharacteristic
26#489×C73—21no—
27#468×C73—21no—
28#467×C73C2211yescharacteristic
29#466×C73C2211yescharacteristic
30#440×C73—21no—
31C4×Q16×C73C2211yescharacteristic
32C4×D8×C73C2211yescharacteristic
33#428×C73—21no—
34#427×C73C2211yescharacteristic
35C2×#107×C73C2211yescharacteristic
36#405×C73C2211yescharacteristic
37#367×C73C2211yescharacteristic
38#367×C73C2211yescharacteristic
39#366×C73C2211yescharacteristic
40#366×C73C2211yescharacteristic
41#366×C73C2211yescharacteristic
42#366×C73C2211yescharacteristic
43#366×C73C2211yescharacteristic
44#366×C73C2211yescharacteristic
45C4⋊C16×C73C2211yescharacteristic
46C4⋊C16×C73C2211yescharacteristic
47#358×C73C2211yescharacteristic
48#358×C73C2211yescharacteristic
49#358×C73C2211yescharacteristic
50#358×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×Q16×C73C2311yescharacteristic
60C2×SD16×C73—21no—
61C2×D8×C73C2311yescharacteristic
62C2×M16×C73D411yescharacteristic
63C22×C8×C73C2311yescharacteristic
64C4⋊Q8×C73—21no—
65C4⋊Q8×C73—21no—
66C4⋊Q8×C73—21no—
67C4⋊Q8×C73—41no—
68#126×C73—41no—
69#125×C73—21no—
70#125×C73—21no—
71#125×C73—41no—
72#124×C73—21no—
73#124×C73—41no—
74#123×C73—41no—
75C22⋊Q8×C73—21no—
76C22⋊Q8×C73—41no—
77C22⋊Q8×C73—41no—
78C22⋊Q8×C73—41no—
79#121×C73—21no—
80C4×Q8×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×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#103×C73—21no—
103#103×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—21no—
111C2×Q8×C73—41no—
112C2×Q8×C73—41no—
113C2×Q8×C73—41no—
114C2×D4×C73—21no—
115C2×D4×C73—41no—
116C22×C4×C73—41no—
117C22×C4×C73—41no—
118C22×C4×C73C2×D411yescharacteristic
119Q16×C73—21no—
120Q16×C73—21no—
121SD16×C73—42no—
122D8×C73—21no—
123D8×C73—21no—
124M16×C73—22no—
125C2×C8×C73—21no—
126C2×C8×C73—21no—
127C2×C8×C73C2×D411yescharacteristic
128C2×C8×C73C2×D411yescharacteristic
129C2×C8×C73C2×D411yescharacteristic
130C2×C8×C73C2411yescharacteristic
131C4⋊C4×C73—21no—
132C4⋊C4×C73—21no—
133C4⋊C4×C73—21no—
134C4⋊C4×C73—21no—
135C4⋊C4×C73—21no—
136C4⋊C4×C73—21no—
137C4⋊C4×C73—41no—
138C4⋊C4×C73—41no—
139C4⋊C4×C73—41no—
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×C73D811yescharacteristic
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×C73D811yescharacteristic
156C22⋊C4×C73D811yescharacteristic
157C42×C73—41no—
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×C73C2×D811yescharacteristic
167Q8×C73—41no—
168Q8×C73—41no—
169Q8×C73—161no—
170Q8×C73—161no—
171Q8×C73—161no—
172D4×C73—41no—
173D4×C73—41no—
174D4×C73—161no—
175C2×C4×C73—21no—
176C2×C4×C73—21no—
177C2×C4×C73—41no—
178C2×C4×C73—41no—
179C2×C4×C73—41no—
180C2×C4×C73—41no—
181C2×C4×C73—41no—
182C2×C4×C73—41no—
183C2×C4×C73—41no—
184C2×C4×C73—161no—
185C2×C4×C73—161no—
186C2×C4×C73C2×D811yescharacteristic
187C2×C4×C73C2×D811yescharacteristic
188C2×C4×C73C2×D811yescharacteristic
189C2×C4×C73C2×D811yescharacteristic
190C2×C4×C73C2×D811yescharacteristic
191C2×C4×C73C22×D411yescharacteristic
192C8×C73—21no—
193C8×C73—21no—
194C8×C73#13712yes—
195C8×C732−1+411yescharacteristic
196C8×C732−1+411yescharacteristic
197C22×C73—21no—
198C22×C73—21no—
199C22×C73—21no—
200C22×C73—81no—
201C22×C73—81no—
202C22×C73—81no—
203C22×C73C22×D811yescharacteristic
204C4×C73—21no—
205C4×C73—21no—
206C4×C73—21no—
207C4×C73—21no—
208C4×C73—21no—
209C4×C73—81no—
210C4×C73—81no—
211C4×C73—81no—
212C4×C73—81no—
213C4×C73—81no—
214C4×C73—81no—
215C4×C73—81no—
216C4×C73#53611yescharacteristic
217C4×C73C2×#13711yescharacteristic
218#33809C7311yesmaximal, characteristic, direct product factor, Sylow
219C2×C73—41no—
220C2×C73—161no—
221C2×C73#322611yescharacteristic
222C2×C73#341511yescharacteristic
223C2×C73#341711yescharacteristic
224#3175C2×C7311yescharacteristic
225#3164C2×C7311yescharacteristic, complemented
226#2255C2×C7311yescharacteristic, complemented
227#2252C2×C7311yescharacteristic, complemented
228#2243C2×C7311yescharacteristic, complemented
229#2242C2×C7311yescharacteristic, complemented
230#2237C2×C7311yescharacteristic, complemented
231#2236C2×C7311yescharacteristic, complemented
232#2234C2×C7311yescharacteristic
233#2232C2×C7311yescharacteristic
234#2229C2×C7311yescharacteristic, complemented
235#2228C2×C7311yescharacteristic, complemented
236#2227C2×C7311yescharacteristic, complemented
237#2224C2×C7311yescharacteristic, complemented
238#2164C2×C7311yescharacteristic, complemented
239C73#3380911yescharacteristic, direct product factor, Sylow
240#544—21no—
241#542—21no—
242#501—21no—
243#501—21no—
244#500C22×C7311yescharacteristic
245#500C22×C7311yescharacteristic
246#500C22×C7311yescharacteristic
247#499C22×C7311yescharacteristic
248#499C22×C7311yescharacteristic
249#495C22×C7311yescharacteristic
250#489—21no—
251#468—21no—
252#467C22×C7311yescharacteristic
253#466C22×C7311yescharacteristic
254#440—21no—
255C4×Q16C22×C7311yescharacteristic
256C4×D8C22×C7311yescharacteristic
257#428—21no—
258#427C22×C7311yescharacteristic
259C2×#107C22×C7311yescharacteristic
260#405C22×C7311yescharacteristic
261#367C22×C7311yescharacteristic
262#367C22×C7311yescharacteristic
263#366C22×C7311yescharacteristic
264#366C22×C7311yescharacteristic
265#366C22×C7311yescharacteristic
266#366C22×C7311yescharacteristic
267#366C22×C7311yescharacteristic
268#366C22×C7311yescharacteristic
269C4⋊C16C22×C7311yescharacteristic
270C4⋊C16C22×C7311yescharacteristic
271#358C22×C7311yescharacteristic
272#358C22×C7311yescharacteristic
273#358C22×C7311yescharacteristic
274#358C22×C7311yescharacteristic
275#357C22×C7311yescharacteristic
276#357C22×C7311yescharacteristic
277#357C22×C7311yescharacteristic
278#357C22×C7311yescharacteristic
279C22⋊C16C22×C7311yescharacteristic
280C22⋊C16C22×C7311yescharacteristic
281#346C22×C7311yescharacteristic
282C4×C16C22×C7311yescharacteristic
283C2×Q16C23×C7311yescharacteristic
284C2×SD16—21no—
285C2×D8C23×C7311yescharacteristic
286C2×M16D4×C7311yescharacteristic
287C22×C8C23×C7311yescharacteristic
288C4⋊Q8—21no—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8—41no—
292#126—41no—
293#125—21no—
294#125—21no—
295#125—41no—
296#124—21no—
297#124—41no—
298#123—41no—
299C22⋊Q8—21no—
300C22⋊Q8—41no—
301C22⋊Q8—41no—
302C22⋊Q8—41no—
303#121—21no—
304C4×Q8—21no—
305C4×D4—21no—
306#117—21no—
307#117D4×C7311yescharacteristic
308C2×C4⋊C4—21no—
309C2×C16C23×C7311yescharacteristic
310C2×C16C23×C7311yescharacteristic
311C2×C16C23×C7311yescharacteristic
312C2×C16C23×C7311yescharacteristic
313#107—21no—
314#107—21no—
315#107—21no—
316#107—21no—
317#107C23×C7311yescharacteristic
318#107C23×C7311yescharacteristic
319#107C23×C7311yescharacteristic
320#107C23×C7311yescharacteristic
321#107C23×C7311yescharacteristic
322#107C23×C7311yescharacteristic
323#106—21no—
324#106—21no—
325#106—21no—
326#103—21no—
327#103—21no—
328#102—21no—
329#102—21no—
330#97D4×C7311yescharacteristic
331#97D4×C7311yescharacteristic
332C4×C8C23×C7311yescharacteristic
333C4×C8C23×C7311yescharacteristic
334C2×Q8—21no—
335C2×Q8—41no—
336C2×Q8—41no—
337C2×Q8—41no—
338C2×D4—21no—
339C2×D4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4C2×D4×C7311yescharacteristic
343Q16—21no—
344Q16—21no—
345SD16—42no—
346D8—21no—
347D8—21no—
348M16—22no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8C2×D4×C7311yescharacteristic
352C2×C8C2×D4×C7311yescharacteristic
353C2×C8C2×D4×C7311yescharacteristic
354C2×C8C24×C7311yescharacteristic
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4D8×C7311yescharacteristic
372C4⋊C4D8×C7311yescharacteristic
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4D8×C7311yescharacteristic
380C22⋊C4D8×C7311yescharacteristic
381C42—41no—
382C42—41no—
383C42C2×D4×C7311yescharacteristic
384C42C2×D4×C7311yescharacteristic
385C16—21no—
386C16—21no—
387C16—21no—
388C16—21no—
389C23—41no—
390C23C2×D8×C7311yescharacteristic
391Q8—41no—
392Q8—41no—
393Q8—161no—
394Q8—161no—
395Q8—161no—
396D4—41no—
397D4—41no—
398D4—161no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—161no—
409C2×C4—161no—
410C2×C4C2×D8×C7311yescharacteristic
411C2×C4C2×D8×C7311yescharacteristic
412C2×C4C2×D8×C7311yescharacteristic
413C2×C4C2×D8×C7311yescharacteristic
414C2×C4C2×D8×C7311yescharacteristic
415C2×C4C22×D4×C7311yescharacteristic
416C8—21no—
417C8—21no—
418C8#137×C7312yes—
419C82−1+4×C7311yescharacteristic
420C82−1+4×C7311yescharacteristic
421C22—21no—
422C22—21no—
423C22—21no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22C22×D8×C7311yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4—81no—
438C4—81no—
439C4—81no—
440C4#536×C7311yescharacteristic
441C4C2×#137×C7311yescharacteristic
442C2—41no—
443C2—161no—
444C2C73×#322611yescharacteristic
445C2C73×#341511yescharacteristic
446C2C73×#341711yescharacteristic
subgroupG/H
center, socleC22×C73C22×D8
commutator, Frattini, cosocleC2×C8C24×C73
prime radical#466×C73C22
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×#2252C2semidirect
5. C73×#2243C2semidirect
6. C73×#2242C2semidirect
7. C73×#2237C2semidirect
8. C73×#2236C2semidirect
11. C73×#2229C2semidirect
12. C73×#2228C2semidirect
13. C73×#2227C2semidirect
14. C73×#2224C2semidirect
15. C73×#2164C2semidirect
218. #33809C73direct (N × H)
225. #3164C2×C73semidirect
226. #2255C2×C73semidirect
227. #2252C2×C73semidirect
228. #2243C2×C73semidirect
229. #2242C2×C73semidirect
230. #2237C2×C73semidirect
231. #2236C2×C73semidirect
234. #2229C2×C73semidirect
235. #2228C2×C73semidirect
236. #2227C2×C73semidirect
237. #2224C2×C73semidirect
238. #2164C2×C73semidirect
239. C73#33809direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#31752
C73×#31642
C73×#22552
C73×#22522
C73×#22432
C73×#22422
C73×#22372
C73×#22362
C73×#22342
C73×#22322
C73×#22292
C73×#22282
C73×#22272
C73×#22242
C73×#21642
#3380973