Finite Group Databasebeta

← C73×#19514 #32928918

Subgroups — C73×#19514 #32928918

Order 18688.

622 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3226C211yesmaximal, characteristic, complemented
2C73×#3214C211yesmaximal, characteristic
3C73×#3206C211yesmaximal, characteristic, complemented
4C73×#2981C211yesmaximal, characteristic, complemented
5C73×#1701C212yesmaximal, complemented
6C73×#1693C212yesmaximal, complemented
7C73×#1681C212yesmaximal, complemented
8C73×#1673C212yesmaximal, complemented
9C73×#1572C211yesmaximal, characteristic, complemented
10C73×#1556C211yesmaximal, characteristic, complemented
11C73×#1553C211yesmaximal, characteristic, complemented
12#532×C73C2211yescharacteristic
13#532×C73C2211yescharacteristic
14C2×C4⋊Q8×C73C2211yescharacteristic
15#500×C73C2211yescharacteristic
16#500×C73C2211yescharacteristic
17#496×C73—21no—
18#492×C73—21no—
19#489×C73—21no—
20#487×C73—21no—
21#486×C73C2211yescharacteristic
22#486×C73C2211yescharacteristic
23#480×C73—22no—
24#474×C73—22no—
25#461×C73C2212yes—
26#461×C73C2212yes—
27#461×C73C2212yes—
28#459×C73C2212yes—
29#449×C73—22no—
30#448×C73—22no—
31#436×C73C2212yes—
32#435×C73—22no—
33C8×D4×C73C2212yes—
34#432×C73C2211yescharacteristic
35#432×C73C2211yescharacteristic
36#431×C73C2211yescharacteristic
37#431×C73C2211yescharacteristic
38#408×C73—22no—
39#335×C73C2212yes—
40#334×C73C2212yes—
41#332×C73C2212yes—
42#332×C73C2212yes—
43#332×C73C2212yes—
44#331×C73C2212yes—
45C2×#41×C73—21no—
46C2×#41×C73—21no—
47C22×Q8×C73—21no—
48C2×SD16×C73—22no—
49C2×SD16×C73—22no—
50C2×SD16×C73—22no—
51C2×D8×C73—22no—
52C2×M16×C73—22no—
53C22×C8×C73—22no—
54C4⋊Q8×C73—21no—
55C4⋊Q8×C73—21no—
56C4⋊Q8×C73—21no—
57C4⋊Q8×C73D411yescharacteristic
58C4⋊Q8×C73C2311yescharacteristic
59C4⋊Q8×C73C2311yescharacteristic
60C4⋊Q8×C73C2311yescharacteristic
61#127×C73D411yescharacteristic
62#127×C73C2311yescharacteristic
63#124×C73—21no—
64#124×C73—21no—
65#121×C73—21no—
66#121×C73—21no—
67#121×C73—21no—
68#121×C73D412yes—
69C4×D4×C73—21no—
70C4×D4×C73—21no—
71C4×D4×C73—21no—
72C4×D4×C73C2312yes—
73C2×C4⋊C4×C73—21no—
74C2×C4⋊C4×C73—21no—
75C2×C42×C73C2311yescharacteristic
76#107×C73—22no—
77#107×C73—22no—
78C4⋊C8×C73D412yes—
79C4⋊C8×C73C2312yes—
80C4⋊C8×C73C2312yes—
81C4⋊C8×C73C2312yes—
82#103×C73—22no—
83#103×C73—22no—
84#103×C73—22no—
85#102×C73—22no—
86#102×C73—22no—
87#102×C73—22no—
88C22⋊C8×C73—21no—
89C22⋊C8×C73—21no—
90C22⋊C8×C73—21no—
91C22⋊C8×C73—22no—
92C22⋊C8×C73—22no—
93C22⋊C8×C73D412yes—
94#97×C73—21no—
95#97×C73—21no—
96C4×C8×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×Q8×C73—41no—
106C2×Q8×C73—82no—
107C2×D4×C73—22no—
108C2×D4×C73—21no—
109C2×D4×C73—21no—
110C2×D4×C73—21no—
111C2×D4×C73—21no—
112C2×D4×C73—21no—
113C2×D4×C73—41no—
114C2×D4×C73C2×D412yes—
115C22×C4×C73—22no—
116C22×C4×C73—41no—
117C22×C4×C73—41no—
118C22×C4×C73C2×D411yescharacteristic
119C22×C4×C73C2×D411yescharacteristic
120C22×C4×C73#4111yescharacteristic
121SD16×C73—82no—
122SD16×C73—82no—
123SD16×C73—82no—
124D8×C73—82no—
125M16×C73—82no—
126C2×C8×C73—22no—
127C2×C8×C73—22no—
128C2×C8×C73—22no—
129C2×C8×C73—82no—
130C2×C8×C73C2×D412yes—
131C2×C8×C73C2×D412yes—
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—21no—
139C4⋊C4×C73—41no—
140C4⋊C4×C73—41no—
141C4⋊C4×C73C2×D412yes—
142C22⋊C4×C73—22no—
143C22⋊C4×C73—22no—
144C22⋊C4×C73—41no—
145C22⋊C4×C73—41no—
146C42×C73C2×D411yescharacteristic
147C42×C73C2×D411yescharacteristic
148C42×C73#4111yescharacteristic
149C42×C73C2411yescharacteristic
150C23×C73—22no—
151C23×C73—41no—
152C23×C73#12111yescharacteristic
153Q8×C73—42no—
154Q8×C73—42no—
155Q8×C73—42no—
156Q8×C73—81no—
157Q8×C73—82no—
158D4×C73—22no—
159D4×C73—22no—
160D4×C73—42no—
161D4×C73—42no—
162D4×C73—81no—
163D4×C73—81no—
164D4×C73—81no—
165D4×C73—82no—
166D4×C73—82no—
167C2×C4×C73—22no—
168C2×C4×C73—22no—
169C2×C4×C73—22no—
170C2×C4×C73—41no—
171C2×C4×C73—42no—
172C2×C4×C73—42no—
173C2×C4×C73—41no—
174C2×C4×C73—41no—
175C2×C4×C73—41no—
176C2×C4×C73—82no—
177C2×C4×C73—82no—
178C2×C4×C73#12111yescharacteristic
179C2×C4×C73#12111yescharacteristic
180C2×C4×C73#12111yescharacteristic
181C2×C4×C73C22×D411yescharacteristic
182C2×C4×C73C22×D411yescharacteristic
183C2×C4×C73C2×#4111yescharacteristic
184C8×C73—22no—
185C8×C73—22no—
186C8×C73—42no—
187C8×C73—42no—
188C8×C73—42no—
189C22×C73—21no—
190C22×C73—21no—
191C22×C73—21no—
192C22×C73—42no—
193C22×C73—42no—
194C22×C73—42no—
195C22×C73—81no—
196C22×C73—81no—
197C22×C73—81no—
198C22×C73C2×#12111yescharacteristic
199C4×C73—21no—
200C4×C73—21no—
201C4×C73—21no—
202C4×C73—21no—
203C4×C73—42no—
204C4×C73—81no—
205C4×C73—81no—
206C4×C73—81no—
207C4×C73#57612yes—
208C4×C73#57712yes—
209#19514C7311yesmaximal, characteristic, direct product factor, Sylow
210C2×C73—41no—
211C2×C73—82no—
212C2×C73—161no—
213C2×C73#304211yescharacteristic
214C2×C73#305811yescharacteristic
215C2×C73#306911yescharacteristic
216#3226C2×C7311yescharacteristic, complemented
217#3214C2×C7311yescharacteristic
218#3206C2×C7311yescharacteristic, complemented
219#2981C2×C7311yescharacteristic, complemented
220#1701C2×C7312yescomplemented
221#1693C2×C7312yescomplemented
222#1681C2×C7312yescomplemented
223#1673C2×C7312yescomplemented
224#1572C2×C7311yescharacteristic, complemented
225#1556C2×C7311yescharacteristic, complemented
226#1553C2×C7311yescharacteristic, complemented
227C73#1951411yescharacteristic, direct product factor, Sylow
228#532C22×C7311yescharacteristic
229#532C22×C7311yescharacteristic
230C2×C4⋊Q8C22×C7311yescharacteristic
231#500C22×C7311yescharacteristic
232#500C22×C7311yescharacteristic
233#496—21no—
234#492—21no—
235#489—21no—
236#487—21no—
237#486C22×C7311yescharacteristic
238#486C22×C7311yescharacteristic
239#480—22no—
240#474—22no—
241#461C22×C7312yes—
242#461C22×C7312yes—
243#461C22×C7312yes—
244#459C22×C7312yes—
245#449—22no—
246#448—22no—
247#436C22×C7312yes—
248#435—22no—
249C8×D4C22×C7312yes—
250#432C22×C7311yescharacteristic
251#432C22×C7311yescharacteristic
252#431C22×C7311yescharacteristic
253#431C22×C7311yescharacteristic
254#408—22no—
255#335C22×C7312yes—
256#334C22×C7312yes—
257#332C22×C7312yes—
258#332C22×C7312yes—
259#332C22×C7312yes—
260#331C22×C7312yes—
261C2×#41—21no—
262C2×#41—21no—
263C22×Q8—21no—
264C2×SD16—22no—
265C2×SD16—22no—
266C2×SD16—22no—
267C2×D8—22no—
268C2×M16—22no—
269C22×C8—22no—
270C4⋊Q8—21no—
271C4⋊Q8—21no—
272C4⋊Q8—21no—
273C4⋊Q8D4×C7311yescharacteristic
274C4⋊Q8C23×C7311yescharacteristic
275C4⋊Q8C23×C7311yescharacteristic
276C4⋊Q8C23×C7311yescharacteristic
277#127D4×C7311yescharacteristic
278#127C23×C7311yescharacteristic
279#124—21no—
280#124—21no—
281#121—21no—
282#121—21no—
283#121—21no—
284#121D4×C7312yes—
285C4×D4—21no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4C23×C7312yes—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C42C23×C7311yescharacteristic
292#107—22no—
293#107—22no—
294C4⋊C8D4×C7312yes—
295C4⋊C8C23×C7312yes—
296C4⋊C8C23×C7312yes—
297C4⋊C8C23×C7312yes—
298#103—22no—
299#103—22no—
300#103—22no—
301#102—22no—
302#102—22no—
303#102—22no—
304C22⋊C8—21no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307C22⋊C8—22no—
308C22⋊C8—22no—
309C22⋊C8D4×C7312yes—
310#97—21no—
311#97—21no—
312C4×C8—21no—
313C4×C8C23×C7311yescharacteristic
314C4×C8C23×C7311yescharacteristic
315#41—82no—
316#41—82no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—41no—
322C2×Q8—82no—
323C2×D4—22no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—41no—
330C2×D4C2×D4×C7312yes—
331C22×C4—22no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4C2×D4×C7311yescharacteristic
335C22×C4C2×D4×C7311yescharacteristic
336C22×C4#41×C7311yescharacteristic
337SD16—82no—
338SD16—82no—
339SD16—82no—
340D8—82no—
341M16—82no—
342C2×C8—22no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8—82no—
346C2×C8C2×D4×C7312yes—
347C2×C8C2×D4×C7312yes—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4C2×D4×C7312yes—
358C22⋊C4—22no—
359C22⋊C4—22no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C42C2×D4×C7311yescharacteristic
363C42C2×D4×C7311yescharacteristic
364C42#41×C7311yescharacteristic
365C42C24×C7311yescharacteristic
366C23—22no—
367C23—41no—
368C23#121×C7311yescharacteristic
369Q8—42no—
370Q8—42no—
371Q8—42no—
372Q8—81no—
373Q8—82no—
374D4—22no—
375D4—22no—
376D4—42no—
377D4—42no—
378D4—81no—
379D4—81no—
380D4—81no—
381D4—82no—
382D4—82no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4#121×C7311yescharacteristic
395C2×C4#121×C7311yescharacteristic
396C2×C4#121×C7311yescharacteristic
397C2×C4C22×D4×C7311yescharacteristic
398C2×C4C22×D4×C7311yescharacteristic
399C2×C4C2×#41×C7311yescharacteristic
400C8—22no—
401C8—22no—
402C8—42no—
403C8—42no—
404C8—42no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—42no—
409C22—42no—
410C22—42no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22C2×#121×C7311yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—42no—
420C4—81no—
421C4—81no—
422C4—81no—
423C4#576×C7312yes—
424C4#577×C7312yes—
425C2—41no—
426C2—82no—
427C2—161no—
428C2C73×#304211yescharacteristic
429C2C73×#305811yescharacteristic
430C2C73×#306911yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3214C2
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×#3226C2semidirect
3. C73×#3206C2semidirect
4. C73×#2981C2semidirect
5. C73×#1701C2semidirect
6. C73×#1693C2semidirect
7. C73×#1681C2semidirect
8. C73×#1673C2semidirect
9. C73×#1572C2semidirect
10. C73×#1556C2semidirect
11. C73×#1553C2semidirect
209. #19514C73direct (N × H)
216. #3226C2×C73semidirect
218. #3206C2×C73semidirect
219. #2981C2×C73semidirect
220. #1701C2×C73semidirect
221. #1693C2×C73semidirect
222. #1681C2×C73semidirect
223. #1673C2×C73semidirect
224. #1572C2×C73semidirect
225. #1556C2×C73semidirect
226. #1553C2×C73semidirect
227. C73#19514direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#32262
C73×#32142
C73×#32062
C73×#29812
C73×#17012
C73×#16932
C73×#16812
C73×#16732
C73×#15722
C73×#15562
C73×#15532
#1951473