Finite Group Databasebeta

← C73×#61436 #32970840

Subgroups — C73×#61436 #32970840

Order 18688.

1960 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3483C212yesmaximal, complemented
2C73×#3391C211yesmaximal, characteristic, complemented
3Q8×Q16×C73C211yesmaximal, characteristic, complemented
4C73×#3362C212yesmaximal, complemented
5C73×#3341C213yesmaximal, complemented
6C73×#3305C216yesmaximal, complemented
7C73×#3287C213yesmaximal, complemented
8C73×#3169C213yesmaximal, complemented
9C73×#3106C216yesmaximal, complemented
10C8×#41×C73C211yesmaximal, characteristic, complemented
11C4×#135×C73C213yesmaximal, complemented
12C2×#135×C73C2213yes—
13Q82×C73C2212yes—
14#555×C73—26no—
15#555×C73C2216yes—
16#550×C73—22no—
17#550×C73C2216yes—
18#550×C73C2212yes—
19#532×C73—26no—
20#532×C73C2216yes—
21C4×#41×C73—22no—
22C4×#41×C73C2216yes—
23C4×#41×C73C2211yescharacteristic
24#500×C73C2213yes—
25#493×C73C2213yes—
26#486×C73C2216yes—
27#482×C73C22112yes—
28#477×C73C2216yes—
29#476×C73C2216yes—
30#466×C73C2216yes—
31#466×C73C2216yes—
32#460×C73C2216yes—
33#459×C73C2216yes—
34#449×C73C22112yes—
35C8×Q8×C73C2211yescharacteristic
36C8×Q8×C73C2211yescharacteristic
37C4×Q16×C73C2213yes—
38C4×Q16×C73C2211yescharacteristic
39C4×SD16×C73C2216yes—
40C4×SD16×C73C2216yes—
41C4×D8×C73C2213yes—
42C4×D8×C73C2216yes—
43C4×D8×C73C2213yes—
44C8×D4×C73C2213yes—
45C8×D4×C73C2213yes—
46#431×C73C2213yes—
47#427×C73C2213yes—
48#416×C73C2216yes—
49C2×C4×C8×C73C2213yes—
50C2×#41×C73—22no—
51C2×#41×C73—26no—
52C2×#41×C73D411yescharacteristic
53C2×#41×C73C2316yes—
54#135×C73—212no—
55C2×Q16×C73C2311yescharacteristic
56C2×SD16×C73C2316yes—
57C2×D8×C73C2313yes—
58C2×D8×C73C2316yes—
59C22×C8×C73C2313yes—
60C22×C8×C73C2313yes—
61C4⋊Q8×C73—26no—
62C4⋊Q8×C73C2316yes—
63#127×C73—26no—
64#127×C73C2316yes—
65#124×C73—212no—
66#124×C73—26no—
67#121×C73—26no—
68#121×C73—26no—
69#121×C73—26no—
70#121×C73—212no—
71#121×C73C23112yes—
72C4×Q8×C73—22no—
73C4×Q8×C73D411yescharacteristic
74C4×Q8×C73C2312yes—
75C4×Q8×C73C2316yes—
76C4×Q8×C73C2311yescharacteristic
77C4×D4×C73—26no—
78C4×D4×C73—26no—
79C4×D4×C73—26no—
80C4×D4×C73—26no—
81C4×D4×C73D413yes—
82C4×D4×C73C2316yes—
83C4×D4×C73C2316yes—
84C4×D4×C73C2313yes—
85#117×C73—26no—
86#117×C73—26no—
87#117×C73D413yes—
88#117×C73C2316yes—
89C2×C42×C73—26no—
90C2×C42×C73C2313yes—
91#107×C73C2311yescharacteristic
92#107×C73C2313yes—
93#107×C73C2316yes—
94#106×C73C2316yes—
95C4⋊C8×C73C2313yes—
96C4⋊C8×C73C2313yes—
97#103×C73C2312yes—
98#103×C73C2316yes—
99#102×C73C2316yes—
100#102×C73C2316yes—
101#102×C73C23112yes—
102C22⋊C8×C73C2316yes—
103C4×C8×C73C2311yescharacteristic
104C4×C8×C73C2313yes—
105C4×C8×C73C2313yes—
106C4×C8×C73C2313yes—
107#41×C73—24no—
108#41×C73—212no—
109#41×C73—46no—
110#41×C73—48no—
111#41×C73—812no—
112C2×Q8×C73—26no—
113C2×Q8×C73C2×D411yescharacteristic
114C2×Q8×C73C2412yes—
115C2×D4×C73—26no—
116C2×D4×C73—212no—
117C2×D4×C73—26no—
118C2×D4×C73—26no—
119C2×D4×C73C2×D413yes—
120C2×D4×C73C2416yes—
121C22×C4×C73—26no—
122C22×C4×C73—26no—
123C22×C4×C73—26no—
124C22×C4×C73C2×D413yes—
125C22×C4×C73C2×D413yes—
126C22×C4×C73C2413yes—
127Q16×C73#4114yescomplemented
128SD16×C73—212no—
129D8×C73—26no—
130D8×C73—46no—
131C2×C8×C73—26no—
132C2×C8×C73—43no—
133C2×C8×C73C2411yescharacteristic
134C2×C8×C73C2413yes—
135C2×C8×C73C2413yes—
136C2×C8×C73C2411yescharacteristic
137C4⋊C4×C73—22no—
138C4⋊C4×C73—26no—
139C4⋊C4×C73—26no—
140C4⋊C4×C73C2×D413yes—
141C4⋊C4×C73C2×D413yes—
142C4⋊C4×C73C2412yes—
143C4⋊C4×C73C2416yes—
144C22⋊C4×C73—26no—
145C22⋊C4×C73—212no—
146C22⋊C4×C73—26no—
147C22⋊C4×C73—26no—
148C22⋊C4×C73C2×D416yes—
149C42×C73—26no—
150C42×C73—26no—
151C42×C73—22no—
152C42×C73C2×D413yes—
153C42×C73C2×D413yes—
154C42×C73C2413yes—
155C42×C73C2411yescharacteristic
156C23×C73—26no—
157C23×C73C22×D413yes—
158Q8×C73—22no—
159Q8×C73—86no—
160Q8×C73#13514yescomplemented
161Q8×C73C2×#4114yes—
162D4×C73—26no—
163D4×C73—26no—
164D4×C73—26no—
165D4×C73—412no—
166D4×C73—412no—
167D4×C73—86no—
168D4×C73—812no—
169C2×C4×C73—22no—
170C2×C4×C73—26no—
171C2×C4×C73—26no—
172C2×C4×C73—23no—
173C2×C4×C73—23no—
174C2×C4×C73—22no—
175C2×C4×C73—26no—
176C2×C4×C73—412no—
177C2×C4×C73—412no—
178C2×C4×C73—412no—
179C2×C4×C73C22×D413yes—
180C2×C4×C73C22×D411yescharacteristic
181C2×C4×C73C22×D413yes—
182C2×C4×C73C22×D413yes—
183C2×C4×C73C22×D411yescharacteristic
184C2×C4×C73C2511yescharacteristic
185C8×C73—23no—
186C8×C73—21no—
187C8×C73—23no—
188C8×C73C2×#4112yes—
189C22×C73—23no—
190C22×C73—23no—
191C22×C73—23no—
192C22×C73—46no—
193C22×C73—46no—
194C22×C73—46no—
195C22×C73C23×D411yescharacteristic
196C4×C73—23no—
197C4×C73—24no—
198C4×C73—21no—
199C4×C73—23no—
200C4×C73—42no—
201C4×C73—46no—
202C4×C73C2×#13516yes—
203C4×C73#57612yes—
204C4×C73C22×#4111yescharacteristic
205C4×C73#58511yescharacteristic
206#61436C7311yesmaximal, characteristic, direct product factor, Sylow
207C2×C73—43no—
208C2×C73—86no—
209C2×C73D4×#4111yescharacteristic
210C2×C73C22×#13511yescharacteristic
211C2×C73C2×#57611yescharacteristic
212#3483C2×C7312yescomplemented
213#3391C2×C7311yescharacteristic, complemented
214Q8×Q16C2×C7311yescharacteristic, complemented
215#3362C2×C7312yescomplemented
216#3341C2×C7313yescomplemented
217#3305C2×C7316yescomplemented
218#3287C2×C7313yescomplemented
219#3169C2×C7313yescomplemented
220#3106C2×C7316yescomplemented
221C8×#41C2×C7311yescharacteristic, complemented
222C4×#135C2×C7313yescomplemented
223C73#6143611yescharacteristic, direct product factor, Sylow
224C2×#135C22×C7313yes—
225Q82C22×C7312yes—
226#555—26no—
227#555C22×C7316yes—
228#550—22no—
229#550C22×C7316yes—
230#550C22×C7312yes—
231#532—26no—
232#532C22×C7316yes—
233C4×#41—22no—
234C4×#41C22×C7316yes—
235C4×#41C22×C7311yescharacteristic
236#500C22×C7313yes—
237#493C22×C7313yes—
238#486C22×C7316yes—
239#482C22×C73112yes—
240#477C22×C7316yes—
241#476C22×C7316yes—
242#466C22×C7316yes—
243#466C22×C7316yes—
244#460C22×C7316yes—
245#459C22×C7316yes—
246#449C22×C73112yes—
247C8×Q8C22×C7311yescharacteristic
248C8×Q8C22×C7311yescharacteristic
249C4×Q16C22×C7313yes—
250C4×Q16C22×C7311yescharacteristic
251C4×SD16C22×C7316yes—
252C4×SD16C22×C7316yes—
253C4×D8C22×C7313yes—
254C4×D8C22×C7316yes—
255C4×D8C22×C7313yes—
256C8×D4C22×C7313yes—
257C8×D4C22×C7313yes—
258#431C22×C7313yes—
259#427C22×C7313yes—
260#416C22×C7316yes—
261C2×C4×C8C22×C7313yes—
262C2×#41—22no—
263C2×#41—26no—
264C2×#41D4×C7311yescharacteristic
265C2×#41C23×C7316yes—
266#135—212no—
267C2×Q16C23×C7311yescharacteristic
268C2×SD16C23×C7316yes—
269C2×D8C23×C7313yes—
270C2×D8C23×C7316yes—
271C22×C8C23×C7313yes—
272C22×C8C23×C7313yes—
273C4⋊Q8—26no—
274C4⋊Q8C23×C7316yes—
275#127—26no—
276#127C23×C7316yes—
277#124—212no—
278#124—26no—
279#121—26no—
280#121—26no—
281#121—26no—
282#121—212no—
283#121C23×C73112yes—
284C4×Q8—22no—
285C4×Q8D4×C7311yescharacteristic
286C4×Q8C23×C7312yes—
287C4×Q8C23×C7316yes—
288C4×Q8C23×C7311yescharacteristic
289C4×D4—26no—
290C4×D4—26no—
291C4×D4—26no—
292C4×D4—26no—
293C4×D4D4×C7313yes—
294C4×D4C23×C7316yes—
295C4×D4C23×C7316yes—
296C4×D4C23×C7313yes—
297#117—26no—
298#117—26no—
299#117D4×C7313yes—
300#117C23×C7316yes—
301C2×C42—26no—
302C2×C42C23×C7313yes—
303#107C23×C7311yescharacteristic
304#107C23×C7313yes—
305#107C23×C7316yes—
306#106C23×C7316yes—
307C4⋊C8C23×C7313yes—
308C4⋊C8C23×C7313yes—
309#103C23×C7312yes—
310#103C23×C7316yes—
311#102C23×C7316yes—
312#102C23×C7316yes—
313#102C23×C73112yes—
314C22⋊C8C23×C7316yes—
315C4×C8C23×C7311yescharacteristic
316C4×C8C23×C7313yes—
317C4×C8C23×C7313yes—
318C4×C8C23×C7313yes—
319#41—24no—
320#41—212no—
321#41—46no—
322#41—48no—
323#41—812no—
324C2×Q8—26no—
325C2×Q8C2×D4×C7311yescharacteristic
326C2×Q8C24×C7312yes—
327C2×D4—26no—
328C2×D4—212no—
329C2×D4—26no—
330C2×D4—26no—
331C2×D4C2×D4×C7313yes—
332C2×D4C24×C7316yes—
333C22×C4—26no—
334C22×C4—26no—
335C22×C4—26no—
336C22×C4C2×D4×C7313yes—
337C22×C4C2×D4×C7313yes—
338C22×C4C24×C7313yes—
339Q16#41×C7314yescomplemented
340SD16—212no—
341D8—26no—
342D8—46no—
343C2×C8—26no—
344C2×C8—43no—
345C2×C8C24×C7311yescharacteristic
346C2×C8C24×C7313yes—
347C2×C8C24×C7313yes—
348C2×C8C24×C7311yescharacteristic
349C4⋊C4—22no—
350C4⋊C4—26no—
351C4⋊C4—26no—
352C4⋊C4C2×D4×C7313yes—
353C4⋊C4C2×D4×C7313yes—
354C4⋊C4C24×C7312yes—
355C4⋊C4C24×C7316yes—
356C22⋊C4—26no—
357C22⋊C4—212no—
358C22⋊C4—26no—
359C22⋊C4—26no—
360C22⋊C4C2×D4×C7316yes—
361C42—22no—
362C42—26no—
363C42—26no—
364C42C2×D4×C7313yes—
365C42C2×D4×C7313yes—
366C42C24×C7311yescharacteristic
367C42C24×C7313yes—
368C23—26no—
369C23C22×D4×C7313yes—
370Q8—22no—
371Q8—86no—
372Q8#135×C7314yescomplemented
373Q8C2×#41×C7314yes—
374D4—26no—
375D4—26no—
376D4—26no—
377D4—412no—
378D4—412no—
379D4—86no—
380D4—812no—
381C2×C4—22no—
382C2×C4—26no—
383C2×C4—26no—
384C2×C4—23no—
385C2×C4—23no—
386C2×C4—22no—
387C2×C4—26no—
388C2×C4—412no—
389C2×C4—412no—
390C2×C4—412no—
391C2×C4C22×D4×C7313yes—
392C2×C4C22×D4×C7311yescharacteristic
393C2×C4C22×D4×C7313yes—
394C2×C4C22×D4×C7313yes—
395C2×C4C22×D4×C7311yescharacteristic
396C2×C4C25×C7311yescharacteristic
397C8—23no—
398C8—21no—
399C8—23no—
400C8C2×#41×C7312yes—
401C22—23no—
402C22—23no—
403C22—23no—
404C22—46no—
405C22—46no—
406C22—46no—
407C22C23×D4×C7311yescharacteristic
408C4—23no—
409C4—24no—
410C4—21no—
411C4—23no—
412C4—42no—
413C4—46no—
414C4C2×#135×C7316yes—
415C4#576×C7312yes—
416C4C22×#41×C7311yescharacteristic
417C4#585×C7311yescharacteristic
418C2—43no—
419C2—86no—
420C2D4×#41×C7311yescharacteristic
421C2C22×#135×C7311yescharacteristic
422C2C2×#576×C7311yescharacteristic
subgroupG/H
centerC2×C4×C73C22×D4
commutator, Frattini, cosocleC2×C4C25×C73
socleC22×C73C23×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C73 ◁ C4×#41×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3483C2semidirect
2. C73×#3391C2semidirect
3. Q8×Q16×C73C2semidirect
4. C73×#3362C2semidirect
5. C73×#3341C2semidirect
6. C73×#3305C2semidirect
7. C73×#3287C2semidirect
8. C73×#3169C2semidirect
9. C73×#3106C2semidirect
10. C8×#41×C73C2semidirect
11. C4×#135×C73C2semidirect
127. Q16×C73#41semidirect
160. Q8×C73#135semidirect
206. #61436C73direct (N × H)
212. #3483C2×C73semidirect
213. #3391C2×C73semidirect
214. Q8×Q16C2×C73semidirect
215. #3362C2×C73semidirect
216. #3341C2×C73semidirect
217. #3305C2×C73semidirect
218. #3287C2×C73semidirect
219. #3169C2×C73semidirect
220. #3106C2×C73semidirect
221. C8×#41C2×C73semidirect
222. C4×#135C2×C73semidirect
223. C73#61436direct (N × H)
339. Q16#41×C73semidirect
372. Q8#135×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#34832
C73×#33912
Q8×Q16×C732
C73×#33622
C73×#33412
C73×#33052
C73×#32872
C73×#31692
C73×#31062
C8×#41×C732
C4×#135×C732
#6143673