Finite Group Databasebeta

← C73×#19511 #32928915

Subgroups — C73×#19511 #32928915

Order 18688.

614 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3254C211yesmaximal, characteristic, complemented
2C73×#3245C211yesmaximal, characteristic
3C73×#3210C211yesmaximal, characteristic, complemented
4C73×#2981C211yesmaximal, characteristic, complemented
5C73×#1699C212yesmaximal, complemented
6C73×#1685C212yesmaximal, complemented
7C73×#1681C212yesmaximal, complemented
8C73×#1669C212yesmaximal, complemented
9C73×#1571C211yesmaximal, characteristic, complemented
10C73×#1557C211yesmaximal, characteristic, complemented
11C73×#1552C211yesmaximal, characteristic, complemented
12#533×C73C2211yescharacteristic
13#532×C73C2211yescharacteristic
14#532×C73C2211yescharacteristic
15#494×C73C2211yescharacteristic
16#492×C73C2211yescharacteristic
17#487×C73C2211yescharacteristic
18#486×C73C2211yescharacteristic
19#477×C73—21no—
20#474×C73—21no—
21#474×C73C2212yes—
22#474×C73C2212yes—
23#468×C73—22no—
24#466×C73—22no—
25#464×C73—22no—
26#461×C73C2212yes—
27#460×C73—21no—
28#459×C73—21no—
29#459×C73C2212yes—
30#452×C73—22no—
31#436×C73C2212yes—
32#435×C73—22no—
33C8×D4×C73C2212yes—
34#432×C73C2211yescharacteristic
35#431×C73C2211yescharacteristic
36#423×C73C2211yescharacteristic
37C2×C4⋊C8×C73C2211yescharacteristic
38#408×C73—22no—
39#335×C73C2212yes—
40#335×C73C2212yes—
41#332×C73C2212yes—
42#332×C73C2212yes—
43#332×C73C2212yes—
44#331×C73C2212yes—
45C2×#41×C73—21no—
46C2×#41×C73—21no—
47C2×Q16×C73—22no—
48C2×SD16×C73—22no—
49C2×SD16×C73—22no—
50C2×D8×C73—22no—
51C2×M16×C73—21no—
52C2×M16×C73—22no—
53C22×C8×C73—21no—
54C22×C8×C73—22no—
55C4⋊Q8×C73D411yescharacteristic
56C4⋊Q8×C73C2311yescharacteristic
57C4⋊Q8×C73C2311yescharacteristic
58C4⋊Q8×C73C2311yescharacteristic
59#127×C73D411yescharacteristic
60#127×C73C2311yescharacteristic
61#125×C73—21no—
62#124×C73—21no—
63#124×C73—21no—
64C22⋊Q8×C73—21no—
65C22⋊Q8×C73—21no—
66#121×C73—21no—
67#121×C73—21no—
68#121×C73—21no—
69#121×C73D412yes—
70C4×Q8×C73—21no—
71C4×Q8×C73—21no—
72C4×D4×C73—21no—
73C4×D4×C73—21no—
74C4×D4×C73—21no—
75C4×D4×C73C2312yes—
76#117×C73—21no—
77C2×C42×C73C2311yescharacteristic
78#107×C73—22no—
79#107×C73—22no—
80C4⋊C8×C73—21no—
81C4⋊C8×C73—21no—
82C4⋊C8×C73D412yes—
83C4⋊C8×C73C2312yes—
84C4⋊C8×C73C2312yes—
85C4⋊C8×C73C2312yes—
86#103×C73—22no—
87#103×C73—22no—
88#102×C73—22no—
89#102×C73—22no—
90#102×C73—22no—
91#102×C73—22no—
92C22⋊C8×C73—21no—
93C22⋊C8×C73—22no—
94C22⋊C8×C73—22no—
95C22⋊C8×C73D412yes—
96#97×C73—21no—
97C4×C8×C73C2311yescharacteristic
98C4×C8×C73C2311yescharacteristic
99#41×C73—82no—
100#41×C73—82no—
101C2×Q8×C73—21no—
102C2×Q8×C73—21no—
103C2×Q8×C73—21no—
104C2×Q8×C73—21no—
105C2×D4×C73—22no—
106C2×D4×C73—21no—
107C2×D4×C73—21no—
108C2×D4×C73—21no—
109C2×D4×C73—21no—
110C2×D4×C73—21no—
111C2×D4×C73—41no—
112C2×D4×C73C2×D412yes—
113C22×C4×C73—22no—
114C22×C4×C73—41no—
115C22×C4×C73C2×D411yescharacteristic
116C22×C4×C73C2×D411yescharacteristic
117C22×C4×C73#4111yescharacteristic
118Q16×C73—82no—
119SD16×C73—82no—
120SD16×C73—82no—
121D8×C73—82no—
122M16×C73—82no—
123M16×C73—81no—
124C2×C8×C73—22no—
125C2×C8×C73—22no—
126C2×C8×C73—22no—
127C2×C8×C73—82no—
128C2×C8×C73—81no—
129C2×C8×C73C2×D412yes—
130C2×C8×C73C2×D412yes—
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—21no—
138C4⋊C4×C73—41no—
139C4⋊C4×C73—41no—
140C4⋊C4×C73C2×D412yes—
141C22⋊C4×C73—22no—
142C22⋊C4×C73—22no—
143C22⋊C4×C73—41no—
144C22⋊C4×C73—41no—
145C22⋊C4×C73—41no—
146C42×C73—41no—
147C42×C73C2×D411yescharacteristic
148C42×C73C2×D411yescharacteristic
149C42×C73#4111yescharacteristic
150C42×C73C2411yescharacteristic
151C23×C73—22no—
152C23×C73—41no—
153C23×C73#12111yescharacteristic
154Q8×C73—41no—
155Q8×C73—42no—
156Q8×C73—42no—
157Q8×C73—41no—
158Q8×C73—81no—
159D4×C73—22no—
160D4×C73—22no—
161D4×C73—41no—
162D4×C73—42no—
163D4×C73—41no—
164D4×C73—81no—
165D4×C73—81no—
166D4×C73—81no—
167D4×C73—82no—
168D4×C73—82no—
169C2×C4×C73—21no—
170C2×C4×C73—22no—
171C2×C4×C73—21no—
172C2×C4×C73—22no—
173C2×C4×C73—41no—
174C2×C4×C73—42no—
175C2×C4×C73—42no—
176C2×C4×C73—41no—
177C2×C4×C73—41no—
178C2×C4×C73—41no—
179C2×C4×C73—82no—
180C2×C4×C73#12111yescharacteristic
181C2×C4×C73#12111yescharacteristic
182C2×C4×C73#12111yescharacteristic
183C2×C4×C73C22×D411yescharacteristic
184C2×C4×C73C22×D411yescharacteristic
185C2×C4×C73C2×#4111yescharacteristic
186C8×C73—22no—
187C8×C73—22no—
188C8×C73—42no—
189C8×C73—42no—
190C8×C73—42no—
191C22×C73—21no—
192C22×C73—21no—
193C22×C73—21no—
194C22×C73—42no—
195C22×C73—42no—
196C22×C73—42no—
197C22×C73—81no—
198C22×C73—81no—
199C22×C73—81no—
200C22×C73C2×#12111yescharacteristic
201C4×C73—21no—
202C4×C73—21no—
203C4×C73—21no—
204C4×C73—21no—
205C4×C73—42no—
206C4×C73—81no—
207C4×C73—81no—
208C4×C73—81no—
209C4×C73#57612yes—
210C4×C73#57611yescharacteristic
211C4×C73#57811yescharacteristic
212#19511C7311yesmaximal, characteristic, direct product factor, Sylow
213C2×C73—41no—
214C2×C73—82no—
215C2×C73—161no—
216C2×C73#304111yescharacteristic
217C2×C73#306111yescharacteristic
218C2×C73#306911yescharacteristic
219#3254C2×C7311yescharacteristic, complemented
220#3245C2×C7311yescharacteristic
221#3210C2×C7311yescharacteristic, complemented
222#2981C2×C7311yescharacteristic, complemented
223#1699C2×C7312yescomplemented
224#1685C2×C7312yescomplemented
225#1681C2×C7312yescomplemented
226#1669C2×C7312yescomplemented
227#1571C2×C7311yescharacteristic, complemented
228#1557C2×C7311yescharacteristic, complemented
229#1552C2×C7311yescharacteristic, complemented
230C73#1951111yescharacteristic, direct product factor, Sylow
231#533C22×C7311yescharacteristic
232#532C22×C7311yescharacteristic
233#532C22×C7311yescharacteristic
234#494C22×C7311yescharacteristic
235#492C22×C7311yescharacteristic
236#487C22×C7311yescharacteristic
237#486C22×C7311yescharacteristic
238#477—21no—
239#474—21no—
240#474C22×C7312yes—
241#474C22×C7312yes—
242#468—22no—
243#466—22no—
244#464—22no—
245#461C22×C7312yes—
246#460—21no—
247#459—21no—
248#459C22×C7312yes—
249#452—22no—
250#436C22×C7312yes—
251#435—22no—
252C8×D4C22×C7312yes—
253#432C22×C7311yescharacteristic
254#431C22×C7311yescharacteristic
255#423C22×C7311yescharacteristic
256C2×C4⋊C8C22×C7311yescharacteristic
257#408—22no—
258#335C22×C7312yes—
259#335C22×C7312yes—
260#332C22×C7312yes—
261#332C22×C7312yes—
262#332C22×C7312yes—
263#331C22×C7312yes—
264C2×#41—21no—
265C2×#41—21no—
266C2×Q16—22no—
267C2×SD16—22no—
268C2×SD16—22no—
269C2×D8—22no—
270C2×M16—21no—
271C2×M16—22no—
272C22×C8—21no—
273C22×C8—22no—
274C4⋊Q8D4×C7311yescharacteristic
275C4⋊Q8C23×C7311yescharacteristic
276C4⋊Q8C23×C7311yescharacteristic
277C4⋊Q8C23×C7311yescharacteristic
278#127D4×C7311yescharacteristic
279#127C23×C7311yescharacteristic
280#125—21no—
281#124—21no—
282#124—21no—
283C22⋊Q8—21no—
284C22⋊Q8—21no—
285#121—21no—
286#121—21no—
287#121—21no—
288#121D4×C7312yes—
289C4×Q8—21no—
290C4×Q8—21no—
291C4×D4—21no—
292C4×D4—21no—
293C4×D4—21no—
294C4×D4C23×C7312yes—
295#117—21no—
296C2×C42C23×C7311yescharacteristic
297#107—22no—
298#107—22no—
299C4⋊C8—21no—
300C4⋊C8—21no—
301C4⋊C8D4×C7312yes—
302C4⋊C8C23×C7312yes—
303C4⋊C8C23×C7312yes—
304C4⋊C8C23×C7312yes—
305#103—22no—
306#103—22no—
307#102—22no—
308#102—22no—
309#102—22no—
310#102—22no—
311C22⋊C8—21no—
312C22⋊C8—22no—
313C22⋊C8—22no—
314C22⋊C8D4×C7312yes—
315#97—21no—
316C4×C8C23×C7311yescharacteristic
317C4×C8C23×C7311yescharacteristic
318#41—82no—
319#41—82no—
320C2×Q8—21no—
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8—21no—
324C2×D4—22no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—41no—
331C2×D4C2×D4×C7312yes—
332C22×C4—22no—
333C22×C4—41no—
334C22×C4C2×D4×C7311yescharacteristic
335C22×C4C2×D4×C7311yescharacteristic
336C22×C4#41×C7311yescharacteristic
337Q16—82no—
338SD16—82no—
339SD16—82no—
340D8—82no—
341M16—82no—
342M16—81no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8—22no—
346C2×C8—82no—
347C2×C8—81no—
348C2×C8C2×D4×C7312yes—
349C2×C8C2×D4×C7312yes—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4C2×D4×C7312yes—
360C22⋊C4—22no—
361C22⋊C4—22no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C42—41no—
366C42C2×D4×C7311yescharacteristic
367C42C2×D4×C7311yescharacteristic
368C42#41×C7311yescharacteristic
369C42C24×C7311yescharacteristic
370C23—22no—
371C23—41no—
372C23#121×C7311yescharacteristic
373Q8—41no—
374Q8—42no—
375Q8—42no—
376Q8—41no—
377Q8—81no—
378D4—22no—
379D4—22no—
380D4—41no—
381D4—42no—
382D4—41no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—82no—
387D4—82no—
388C2×C4—21no—
389C2×C4—22no—
390C2×C4—21no—
391C2×C4—22no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—82no—
399C2×C4#121×C7311yescharacteristic
400C2×C4#121×C7311yescharacteristic
401C2×C4#121×C7311yescharacteristic
402C2×C4C22×D4×C7311yescharacteristic
403C2×C4C22×D4×C7311yescharacteristic
404C2×C4C2×#41×C7311yescharacteristic
405C8—22no—
406C8—22no—
407C8—42no—
408C8—42no—
409C8—42no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—42no—
414C22—42no—
415C22—42no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22C2×#121×C7311yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—21no—
424C4—42no—
425C4—81no—
426C4—81no—
427C4—81no—
428C4#576×C7312yes—
429C4#576×C7311yescharacteristic
430C4#578×C7311yescharacteristic
431C2—41no—
432C2—82no—
433C2—161no—
434C2C73×#304111yescharacteristic
435C2C73×#306111yescharacteristic
436C2C73×#306911yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3245C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3254C2semidirect
3. C73×#3210C2semidirect
4. C73×#2981C2semidirect
5. C73×#1699C2semidirect
6. C73×#1685C2semidirect
7. C73×#1681C2semidirect
8. C73×#1669C2semidirect
9. C73×#1571C2semidirect
10. C73×#1557C2semidirect
11. C73×#1552C2semidirect
212. #19511C73direct (N × H)
219. #3254C2×C73semidirect
221. #3210C2×C73semidirect
222. #2981C2×C73semidirect
223. #1699C2×C73semidirect
224. #1685C2×C73semidirect
225. #1681C2×C73semidirect
226. #1669C2×C73semidirect
227. #1571C2×C73semidirect
228. #1557C2×C73semidirect
229. #1552C2×C73semidirect
230. C73#19511direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#32542
C73×#32452
C73×#32102
C73×#29812
C73×#16992
C73×#16852
C73×#16812
C73×#16692
C73×#15712
C73×#15572
C73×#15522
#1951173