Finite Group Databasebeta

← C73×#33824 #32943228

Subgroups — C73×#33824 #32943228

Order 18688.

476 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3177C211yesmaximal, characteristic, complemented
2C73×#3175C211yesmaximal, characteristic
3C73×#2229C211yesmaximal, characteristic, complemented
4C73×#2228C211yesmaximal, characteristic, complemented
5C73×#2227C211yesmaximal, characteristic, complemented
6C73×#2225C211yesmaximal, characteristic, complemented
7C73×#2220C211yesmaximal, characteristic
8C73×#2219C211yesmaximal, characteristic, complemented
9C73×#2217C211yesmaximal, characteristic
10C73×#2216C211yesmaximal, characteristic, complemented
11C73×#2211C211yesmaximal, characteristic, complemented
12C73×#2211C211yesmaximal, characteristic, complemented
13C73×#2209C211yesmaximal, characteristic, complemented
14C73×#2208C211yesmaximal, characteristic, complemented
15C73×#2151C211yesmaximal, characteristic, complemented
16#542×C73—21no—
17#541×C73—21no—
18C2×Q32×C73C2211yescharacteristic
19C2×Q32×C73C2211yescharacteristic
20C2×SD32×C73C2211yescharacteristic
21C2×SD32×C73C2211yescharacteristic
22C2×M32×C73C2211yescharacteristic
23C22×C16×C73C2211yescharacteristic
24#500×C73C2211yescharacteristic
25#499×C73C2211yescharacteristic
26#495×C73C2211yescharacteristic
27#494×C73C2211yescharacteristic
28#491×C73—21no—
29#489×C73—21no—
30#470×C73—21no—
31#468×C73—21no—
32#467×C73C2211yescharacteristic
33#467×C73C2211yescharacteristic
34#467×C73C2211yescharacteristic
35#466×C73C2211yescharacteristic
36#441×C73—21no—
37#440×C73—21no—
38C4×Q16×C73C2211yescharacteristic
39C4×Q16×C73C2211yescharacteristic
40C4×Q16×C73C2211yescharacteristic
41C4×D8×C73C2211yescharacteristic
42#405×C73C2211yescharacteristic
43#367×C73C2211yescharacteristic
44#367×C73C2211yescharacteristic
45#366×C73C2211yescharacteristic
46#366×C73C2211yescharacteristic
47C4⋊C16×C73C2211yescharacteristic
48C4⋊C16×C73C2211yescharacteristic
49C4⋊C16×C73C2211yescharacteristic
50C4⋊C16×C73C2211yescharacteristic
51#358×C73C2211yescharacteristic
52#358×C73C2211yescharacteristic
53#358×C73C2211yescharacteristic
54#358×C73C2211yescharacteristic
55#358×C73C2211yescharacteristic
56#358×C73C2211yescharacteristic
57#357×C73C2211yescharacteristic
58#357×C73C2211yescharacteristic
59C2×Q16×C73—21no—
60C2×Q16×C73C2311yescharacteristic
61C2×Q16×C73C2311yescharacteristic
62C2×Q16×C73C2311yescharacteristic
63C2×SD16×C73—21no—
64C2×D8×C73C2311yescharacteristic
65C2×M16×C73D411yescharacteristic
66C22×C8×C73C2311yescharacteristic
67C4⋊Q8×C73—21no—
68C4⋊Q8×C73—21no—
69#126×C73—41no—
70#126×C73—41no—
71#126×C73—41no—
72#125×C73—21no—
73#125×C73—41no—
74#125×C73—41no—
75#124×C73—21no—
76#124×C73—41no—
77#123×C73—41no—
78C22⋊Q8×C73—21no—
79C22⋊Q8×C73—21no—
80C22⋊Q8×C73—21no—
81C22⋊Q8×C73—41no—
82#121×C73—21no—
83C4×Q8×C73—21no—
84C4×Q8×C73—21no—
85C4×Q8×C73—21no—
86C4×D4×C73—21no—
87#117×C73D411yescharacteristic
88Q32×C73—41no—
89Q32×C73—41no—
90SD32×C73—41no—
91SD32×C73—41no—
92M32×C73—41no—
93C2×C16×C73—41no—
94C2×C16×C73C2311yescharacteristic
95C2×C16×C73C2311yescharacteristic
96C2×C16×C73C2311yescharacteristic
97C2×C16×C73C2311yescharacteristic
98#107×C73—21no—
99#107×C73C2311yescharacteristic
100#107×C73C2311yescharacteristic
101#107×C73C2311yescharacteristic
102#107×C73C2311yescharacteristic
103#106×C73—21no—
104#103×C73—21no—
105#103×C73—21no—
106#103×C73—21no—
107#103×C73—21no—
108#103×C73—21no—
109#103×C73—21no—
110#102×C73—21no—
111#102×C73—21no—
112#97×C73D411yescharacteristic
113#97×C73D411yescharacteristic
114C4×C8×C73C2311yescharacteristic
115C4×C8×C73C2311yescharacteristic
116C2×Q8×C73—21no—
117C2×Q8×C73—21no—
118C2×Q8×C73—21no—
119C2×Q8×C73—41no—
120C2×D4×C73—21no—
121C2×D4×C73—41no—
122C22×C4×C73—41no—
123C22×C4×C73C2×D411yescharacteristic
124Q16×C73—21no—
125Q16×C73—21no—
126Q16×C73—21no—
127Q16×C73—21no—
128Q16×C73—21no—
129Q16×C73—21no—
130Q16×C73—42no—
131SD16×C73—42no—
132D8×C73—21no—
133D8×C73—21no—
134M16×C73—41no—
135C2×C8×C73—21no—
136C2×C8×C73—21no—
137C2×C8×C73C2×D411yescharacteristic
138C2×C8×C73C2×D411yescharacteristic
139C2×C8×C73C2×D411yescharacteristic
140C2×C8×C73C2411yescharacteristic
141C4⋊C4×C73—21no—
142C4⋊C4×C73—21no—
143C4⋊C4×C73—21no—
144C4⋊C4×C73—21no—
145C4⋊C4×C73—41no—
146C4⋊C4×C73—41no—
147C4⋊C4×C73—41no—
148C4⋊C4×C73—41no—
149C4⋊C4×C73—41no—
150C4⋊C4×C73—41no—
151C4⋊C4×C73—41no—
152C4⋊C4×C73—41no—
153C4⋊C4×C73—41no—
154C4⋊C4×C73—41no—
155C4⋊C4×C73—41no—
156C4⋊C4×C73D811yescharacteristic
157C4⋊C4×C73D811yescharacteristic
158C22⋊C4×C73—41no—
159C22⋊C4×C73—41no—
160C22⋊C4×C73—41no—
161C22⋊C4×C73—41no—
162C22⋊C4×C73—41no—
163C22⋊C4×C73—41no—
164C22⋊C4×C73—41no—
165C22⋊C4×C73D811yescharacteristic
166C22⋊C4×C73D811yescharacteristic
167C42×C73—41no—
168C42×C73—41no—
169C42×C73—41no—
170C42×C73C2×D411yescharacteristic
171C42×C73C2×D411yescharacteristic
172C16×C73—21no—
173C16×C73—21no—
174C16×C73—21no—
175C16×C73—21no—
176C23×C73—41no—
177C23×C73C2×D811yescharacteristic
178Q8×C73—41no—
179Q8×C73—41no—
180Q8×C73—41no—
181Q8×C73—41no—
182Q8×C73—41no—
183Q8×C73—41no—
184Q8×C73—161no—
185D4×C73—41no—
186D4×C73—41no—
187D4×C73—161no—
188C2×C4×C73—21no—
189C2×C4×C73—21no—
190C2×C4×C73—41no—
191C2×C4×C73—41no—
192C2×C4×C73—41no—
193C2×C4×C73—41no—
194C2×C4×C73—41no—
195C2×C4×C73—41no—
196C2×C4×C73—41no—
197C2×C4×C73—161no—
198C2×C4×C73C2×D811yescharacteristic
199C2×C4×C73C2×D811yescharacteristic
200C2×C4×C73C2×D811yescharacteristic
201C2×C4×C73C2×D811yescharacteristic
202C2×C4×C73C2×D811yescharacteristic
203C2×C4×C73C22×D411yescharacteristic
204C8×C73—21no—
205C8×C73—21no—
206C8×C73—21no—
207C8×C73H(5,𝔽2)11yescharacteristic
208C8×C732−1+411yescharacteristic
209C22×C73—21no—
210C22×C73—21no—
211C22×C73—21no—
212C22×C73—81no—
213C22×C73—81no—
214C22×C73—81no—
215C22×C73C22×D811yescharacteristic
216C4×C73—21no—
217C4×C73—21no—
218C4×C73—21no—
219C4×C73—21no—
220C4×C73—21no—
221C4×C73—81no—
222C4×C73—81no—
223C4×C73—81no—
224C4×C73—81no—
225C4×C73—81no—
226C4×C73—81no—
227C4×C73—81no—
228C4×C73#53711yescharacteristic
229C4×C73#57511yescharacteristic
230#33824C7311yesmaximal, characteristic, direct product factor, Sylow
231C2×C73—41no—
232C2×C73—161no—
233C2×C73#324511yescharacteristic
234C2×C73#341611yescharacteristic
235C2×C73#341711yescharacteristic
236#3177C2×C7311yescharacteristic, complemented
237#3175C2×C7311yescharacteristic
238#2229C2×C7311yescharacteristic, complemented
239#2228C2×C7311yescharacteristic, complemented
240#2227C2×C7311yescharacteristic, complemented
241#2225C2×C7311yescharacteristic, complemented
242#2220C2×C7311yescharacteristic
243#2219C2×C7311yescharacteristic, complemented
244#2217C2×C7311yescharacteristic
245#2216C2×C7311yescharacteristic, complemented
246#2211C2×C7311yescharacteristic, complemented
247#2211C2×C7311yescharacteristic, complemented
248#2209C2×C7311yescharacteristic, complemented
249#2208C2×C7311yescharacteristic, complemented
250#2151C2×C7311yescharacteristic, complemented
251C73#3382411yescharacteristic, direct product factor, Sylow
252#542—21no—
253#541—21no—
254C2×Q32C22×C7311yescharacteristic
255C2×Q32C22×C7311yescharacteristic
256C2×SD32C22×C7311yescharacteristic
257C2×SD32C22×C7311yescharacteristic
258C2×M32C22×C7311yescharacteristic
259C22×C16C22×C7311yescharacteristic
260#500C22×C7311yescharacteristic
261#499C22×C7311yescharacteristic
262#495C22×C7311yescharacteristic
263#494C22×C7311yescharacteristic
264#491—21no—
265#489—21no—
266#470—21no—
267#468—21no—
268#467C22×C7311yescharacteristic
269#467C22×C7311yescharacteristic
270#467C22×C7311yescharacteristic
271#466C22×C7311yescharacteristic
272#441—21no—
273#440—21no—
274C4×Q16C22×C7311yescharacteristic
275C4×Q16C22×C7311yescharacteristic
276C4×Q16C22×C7311yescharacteristic
277C4×D8C22×C7311yescharacteristic
278#405C22×C7311yescharacteristic
279#367C22×C7311yescharacteristic
280#367C22×C7311yescharacteristic
281#366C22×C7311yescharacteristic
282#366C22×C7311yescharacteristic
283C4⋊C16C22×C7311yescharacteristic
284C4⋊C16C22×C7311yescharacteristic
285C4⋊C16C22×C7311yescharacteristic
286C4⋊C16C22×C7311yescharacteristic
287#358C22×C7311yescharacteristic
288#358C22×C7311yescharacteristic
289#358C22×C7311yescharacteristic
290#358C22×C7311yescharacteristic
291#358C22×C7311yescharacteristic
292#358C22×C7311yescharacteristic
293#357C22×C7311yescharacteristic
294#357C22×C7311yescharacteristic
295C2×Q16—21no—
296C2×Q16C23×C7311yescharacteristic
297C2×Q16C23×C7311yescharacteristic
298C2×Q16C23×C7311yescharacteristic
299C2×SD16—21no—
300C2×D8C23×C7311yescharacteristic
301C2×M16D4×C7311yescharacteristic
302C22×C8C23×C7311yescharacteristic
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305#126—41no—
306#126—41no—
307#126—41no—
308#125—21no—
309#125—41no—
310#125—41no—
311#124—21no—
312#124—41no—
313#123—41no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—41no—
318#121—21no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×D4—21no—
323#117D4×C7311yescharacteristic
324Q32—41no—
325Q32—41no—
326SD32—41no—
327SD32—41no—
328M32—41no—
329C2×C16—41no—
330C2×C16C23×C7311yescharacteristic
331C2×C16C23×C7311yescharacteristic
332C2×C16C23×C7311yescharacteristic
333C2×C16C23×C7311yescharacteristic
334#107—21no—
335#107C23×C7311yescharacteristic
336#107C23×C7311yescharacteristic
337#107C23×C7311yescharacteristic
338#107C23×C7311yescharacteristic
339#106—21no—
340#103—21no—
341#103—21no—
342#103—21no—
343#103—21no—
344#103—21no—
345#103—21no—
346#102—21no—
347#102—21no—
348#97D4×C7311yescharacteristic
349#97D4×C7311yescharacteristic
350C4×C8C23×C7311yescharacteristic
351C4×C8C23×C7311yescharacteristic
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—41no—
356C2×D4—21no—
357C2×D4—41no—
358C22×C4—41no—
359C22×C4C2×D4×C7311yescharacteristic
360Q16—21no—
361Q16—21no—
362Q16—21no—
363Q16—21no—
364Q16—21no—
365Q16—21no—
366Q16—42no—
367SD16—42no—
368D8—21no—
369D8—21no—
370M16—41no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8C2×D4×C7311yescharacteristic
374C2×C8C2×D4×C7311yescharacteristic
375C2×C8C2×D4×C7311yescharacteristic
376C2×C8C24×C7311yescharacteristic
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4D8×C7311yescharacteristic
393C4⋊C4D8×C7311yescharacteristic
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4D8×C7311yescharacteristic
402C22⋊C4D8×C7311yescharacteristic
403C42—41no—
404C42—41no—
405C42—41no—
406C42C2×D4×C7311yescharacteristic
407C42C2×D4×C7311yescharacteristic
408C16—21no—
409C16—21no—
410C16—21no—
411C16—21no—
412C23—41no—
413C23C2×D8×C7311yescharacteristic
414Q8—41no—
415Q8—41no—
416Q8—41no—
417Q8—41no—
418Q8—41no—
419Q8—41no—
420Q8—161no—
421D4—41no—
422D4—41no—
423D4—161no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—161no—
434C2×C4C2×D8×C7311yescharacteristic
435C2×C4C2×D8×C7311yescharacteristic
436C2×C4C2×D8×C7311yescharacteristic
437C2×C4C2×D8×C7311yescharacteristic
438C2×C4C2×D8×C7311yescharacteristic
439C2×C4C22×D4×C7311yescharacteristic
440C8—21no—
441C8—21no—
442C8—21no—
443C8H(5,𝔽2)×C7311yescharacteristic
444C82−1+4×C7311yescharacteristic
445C22—21no—
446C22—21no—
447C22—21no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22C22×D8×C7311yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—81no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4—81no—
462C4—81no—
463C4—81no—
464C4#537×C7311yescharacteristic
465C4#575×C7311yescharacteristic
466C2—41no—
467C2—161no—
468C2C73×#324511yescharacteristic
469C2C73×#341611yescharacteristic
470C2C73×#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
1. C73×#3177C2semidirect
3. C73×#2229C2semidirect
4. C73×#2228C2semidirect
5. C73×#2227C2semidirect
6. C73×#2225C2semidirect
8. C73×#2219C2semidirect
10. C73×#2216C2semidirect
11. C73×#2211C2semidirect
12. C73×#2211C2semidirect
13. C73×#2209C2semidirect
14. C73×#2208C2semidirect
15. C73×#2151C2semidirect
230. #33824C73direct (N × H)
236. #3177C2×C73semidirect
238. #2229C2×C73semidirect
239. #2228C2×C73semidirect
240. #2227C2×C73semidirect
241. #2225C2×C73semidirect
243. #2219C2×C73semidirect
245. #2216C2×C73semidirect
246. #2211C2×C73semidirect
247. #2211C2×C73semidirect
248. #2209C2×C73semidirect
249. #2208C2×C73semidirect
250. #2151C2×C73semidirect
251. C73#33824direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#31772
C73×#31752
C73×#22292
C73×#22282
C73×#22272
C73×#22252
C73×#22202
C73×#22192
C73×#22172
C73×#22162
C73×#22112
C73×#22092
C73×#22082
C73×#21512
#3382473