Finite Group Databasebeta

← C73×#19574 #32928978

Subgroups — C73×#19574 #32928978

Order 18688.

534 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3249C211yesmaximal, characteristic
2C73×#3237C211yesmaximal, characteristic
3C73×#3231C211yesmaximal, characteristic
4C73×#2986C211yesmaximal, characteristic
5C73×#1704C211yesmaximal, characteristic, complemented
6C73×#1700C211yesmaximal, characteristic, complemented
7C73×#1696C211yesmaximal, characteristic, complemented
8C73×#1692C211yesmaximal, characteristic, complemented
9C73×#1684C211yesmaximal, characteristic, complemented
10C73×#1680C211yesmaximal, characteristic, complemented
11C73×#1676C211yesmaximal, characteristic, complemented
12C73×#1672C211yesmaximal, characteristic, complemented
13C73×#1573C211yesmaximal, characteristic
14C73×#1554C211yesmaximal, characteristic
15C73×#1542C211yesmaximal, characteristic
16#533×C73C2211yescharacteristic
17#533×C73C2211yescharacteristic
18#533×C73C2211yescharacteristic
19#501×C73—21no—
20#500×C73C2211yescharacteristic
21#498×C73C2211yescharacteristic
22#491×C73—21no—
23#487×C73C2211yescharacteristic
24#487×C73C2211yescharacteristic
25#485×C73—21no—
26#485×C73—21no—
27#485×C73—21no—
28#485×C73—21no—
29#479×C73—21no—
30#479×C73—21no—
31#477×C73—21no—
32#477×C73C2211yescharacteristic
33#477×C73C2211yescharacteristic
34#477×C73C2211yescharacteristic
35#477×C73C2211yescharacteristic
36#475×C73C2211yescharacteristic
37#475×C73C2211yescharacteristic
38#467×C73—21no—
39#467×C73—21no—
40#462×C73—21no—
41#462×C73C2211yescharacteristic
42#462×C73C2211yescharacteristic
43#446×C73—21no—
44#446×C73C2211yescharacteristic
45#446×C73C2211yescharacteristic
46C8×Q8×C73—21no—
47C8×Q8×C73C2211yescharacteristic
48C8×Q8×C73C2211yescharacteristic
49#433×C73—21no—
50#433×C73—21no—
51#432×C73C2211yescharacteristic
52#431×C73C2211yescharacteristic
53#431×C73C2211yescharacteristic
54C2×C4⋊C8×C73C2211yescharacteristic
55#335×C73C2211yescharacteristic
56#335×C73C2211yescharacteristic
57#334×C73C2211yescharacteristic
58#334×C73C2211yescharacteristic
59#333×C73C2211yescharacteristic
60#333×C73C2211yescharacteristic
61#333×C73C2211yescharacteristic
62#333×C73C2211yescharacteristic
63#332×C73C2211yescharacteristic
64#332×C73C2211yescharacteristic
65#332×C73C2211yescharacteristic
66#332×C73C2211yescharacteristic
67C2×Q16×C73—21no—
68C2×Q16×C73—21no—
69C22×C8×C73—21no—
70C4⋊Q8×C73D411yescharacteristic
71C4⋊Q8×C73D411yescharacteristic
72C4⋊Q8×C73C2311yescharacteristic
73C4⋊Q8×C73C2311yescharacteristic
74C4⋊Q8×C73C2311yescharacteristic
75C4⋊Q8×C73C2311yescharacteristic
76#125×C73—21no—
77#125×C73—21no—
78#125×C73—21no—
79C22⋊Q8×C73—21no—
80C22⋊Q8×C73—21no—
81C22⋊Q8×C73—21no—
82C22⋊Q8×C73—21no—
83C22⋊Q8×C73—21no—
84C22⋊Q8×C73D411yescharacteristic
85C22⋊Q8×C73D411yescharacteristic
86C4×Q8×C73—21no—
87C4×Q8×C73—21no—
88C4×Q8×C73—21no—
89C4×Q8×C73—21no—
90C4×Q8×C73—21no—
91C4×Q8×C73C2311yescharacteristic
92C4×Q8×C73C2311yescharacteristic
93#117×C73—21no—
94#117×C73—21no—
95#117×C73—21no—
96C2×C42×C73C2311yescharacteristic
97#107×C73—21no—
98#107×C73—21no—
99#107×C73—21no—
100#107×C73—21no—
101#107×C73—21no—
102#107×C73—21no—
103#106×C73—21no—
104#106×C73—21no—
105#106×C73—21no—
106#106×C73—21no—
107C4⋊C8×C73—21no—
108C4⋊C8×C73—21no—
109C4⋊C8×C73—21no—
110C4⋊C8×C73—21no—
111C4⋊C8×C73—21no—
112C4⋊C8×C73D411yescharacteristic
113C4⋊C8×C73D411yescharacteristic
114C4⋊C8×C73C2311yescharacteristic
115C4⋊C8×C73C2311yescharacteristic
116C4⋊C8×C73C2311yescharacteristic
117C4⋊C8×C73C2311yescharacteristic
118C4⋊C8×C73C2311yescharacteristic
119C4⋊C8×C73C2311yescharacteristic
120#103×C73—21no—
121#103×C73—21no—
122#103×C73—21no—
123#103×C73—21no—
124#103×C73—21no—
125#103×C73—21no—
126#103×C73—21no—
127#103×C73—21no—
128#103×C73—21no—
129#103×C73—21no—
130#103×C73—21no—
131#103×C73—21no—
132C22⋊C8×C73—21no—
133C22⋊C8×C73—21no—
134C22⋊C8×C73D411yescharacteristic
135C22⋊C8×C73D411yescharacteristic
136#97×C73—21no—
137#97×C73—21no—
138#97×C73—21no—
139C4×C8×C73—21no—
140C4×C8×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Q8×C73—21no—
145C2×Q8×C73—21no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×Q8×C73—21no—
149C2×Q8×C73C2×D411yescharacteristic
150C2×Q8×C73C2×D411yescharacteristic
151C22×C4×C73C2×D411yescharacteristic
152C22×C4×C73C2×D411yescharacteristic
153C22×C4×C73#4111yescharacteristic
154Q16×C73—81no—
155Q16×C73—81no—
156C2×C8×C73—21no—
157C2×C8×C73—21no—
158C2×C8×C73—21no—
159C2×C8×C73—21no—
160C2×C8×C73—21no—
161C2×C8×C73—21no—
162C2×C8×C73—81no—
163C2×C8×C73C2×D411yescharacteristic
164C2×C8×C73C2×D411yescharacteristic
165C2×C8×C73C2×D411yescharacteristic
166C2×C8×C73C2×D411yescharacteristic
167C4⋊C4×C73—21no—
168C4⋊C4×C73—21no—
169C4⋊C4×C73—21no—
170C4⋊C4×C73—21no—
171C4⋊C4×C73—21no—
172C4⋊C4×C73—21no—
173C4⋊C4×C73—21no—
174C4⋊C4×C73—21no—
175C4⋊C4×C73—21no—
176C4⋊C4×C73—21no—
177C4⋊C4×C73—21no—
178C4⋊C4×C73—21no—
179C4⋊C4×C73—21no—
180C4⋊C4×C73—21no—
181C4⋊C4×C73—21no—
182C4⋊C4×C73—41no—
183C4⋊C4×C73—41no—
184C4⋊C4×C73—41no—
185C4⋊C4×C73—41no—
186C4⋊C4×C73C2×D411yescharacteristic
187C4⋊C4×C73C2×D411yescharacteristic
188C22⋊C4×C73—21no—
189C22⋊C4×C73—21no—
190C22⋊C4×C73—41no—
191C22⋊C4×C73—41no—
192C42×C73—21no—
193C42×C73—21no—
194C42×C73—41no—
195C42×C73—41no—
196C42×C73C2×D411yescharacteristic
197C42×C73C2×D411yescharacteristic
198C42×C73#4111yescharacteristic
199C42×C73C2411yescharacteristic
200C23×C73#12111yescharacteristic
201Q8×C73—21no—
202Q8×C73—21no—
203Q8×C73—21no—
204Q8×C73—21no—
205Q8×C73—42no—
206Q8×C73—41no—
207Q8×C73—41no—
208Q8×C73—41no—
209Q8×C73—41no—
210Q8×C73—81no—
211Q8×C73—81no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—41no—
221C2×C4×C73—41no—
222C2×C4×C73—41no—
223C2×C4×C73—41no—
224C2×C4×C73—41no—
225C2×C4×C73#12111yescharacteristic
226C2×C4×C73#12111yescharacteristic
227C2×C4×C73#12111yescharacteristic
228C2×C4×C73C22×D411yescharacteristic
229C2×C4×C73C22×D411yescharacteristic
230C2×C4×C73C2×#4111yescharacteristic
231C8×C73—21no—
232C8×C73—21no—
233C8×C73—21no—
234C8×C73—21no—
235C8×C73—41no—
236C8×C73—41no—
237C8×C73—41no—
238C8×C73—41no—
239C8×C73—41no—
240C8×C73—41no—
241C22×C73—21no—
242C22×C73—21no—
243C22×C73—21no—
244C22×C73C2×#12111yescharacteristic
245C4×C73—21no—
246C4×C73—21no—
247C4×C73—21no—
248C4×C73—21no—
249C4×C73—41no—
250C4×C73—41no—
251C4×C73—41no—
252C4×C73—41no—
253C4×C73—81no—
254C4×C73—81no—
255C4×C73—81no—
256C4×C73—81no—
257C4×C73#57711yescharacteristic
258C4×C73#57811yescharacteristic
259C4×C73#57811yescharacteristic
260C4×C73#57811yescharacteristic
261#19574C7311yesmaximal, characteristic, direct product factor, Sylow
262C2×C73—41no—
263C2×C73#304411yescharacteristic
264C2×C73#306311yescharacteristic
265C2×C73#306711yescharacteristic
266#3249C2×C7311yescharacteristic
267#3237C2×C7311yescharacteristic
268#3231C2×C7311yescharacteristic
269#2986C2×C7311yescharacteristic
270#1704C2×C7311yescharacteristic, complemented
271#1700C2×C7311yescharacteristic, complemented
272#1696C2×C7311yescharacteristic, complemented
273#1692C2×C7311yescharacteristic, complemented
274#1684C2×C7311yescharacteristic, complemented
275#1680C2×C7311yescharacteristic, complemented
276#1676C2×C7311yescharacteristic, complemented
277#1672C2×C7311yescharacteristic, complemented
278#1573C2×C7311yescharacteristic
279#1554C2×C7311yescharacteristic
280#1542C2×C7311yescharacteristic
281C73#1957411yescharacteristic, direct product factor, Sylow
282#533C22×C7311yescharacteristic
283#533C22×C7311yescharacteristic
284#533C22×C7311yescharacteristic
285#501—21no—
286#500C22×C7311yescharacteristic
287#498C22×C7311yescharacteristic
288#491—21no—
289#487C22×C7311yescharacteristic
290#487C22×C7311yescharacteristic
291#485—21no—
292#485—21no—
293#485—21no—
294#485—21no—
295#479—21no—
296#479—21no—
297#477—21no—
298#477C22×C7311yescharacteristic
299#477C22×C7311yescharacteristic
300#477C22×C7311yescharacteristic
301#477C22×C7311yescharacteristic
302#475C22×C7311yescharacteristic
303#475C22×C7311yescharacteristic
304#467—21no—
305#467—21no—
306#462—21no—
307#462C22×C7311yescharacteristic
308#462C22×C7311yescharacteristic
309#446—21no—
310#446C22×C7311yescharacteristic
311#446C22×C7311yescharacteristic
312C8×Q8—21no—
313C8×Q8C22×C7311yescharacteristic
314C8×Q8C22×C7311yescharacteristic
315#433—21no—
316#433—21no—
317#432C22×C7311yescharacteristic
318#431C22×C7311yescharacteristic
319#431C22×C7311yescharacteristic
320C2×C4⋊C8C22×C7311yescharacteristic
321#335C22×C7311yescharacteristic
322#335C22×C7311yescharacteristic
323#334C22×C7311yescharacteristic
324#334C22×C7311yescharacteristic
325#333C22×C7311yescharacteristic
326#333C22×C7311yescharacteristic
327#333C22×C7311yescharacteristic
328#333C22×C7311yescharacteristic
329#332C22×C7311yescharacteristic
330#332C22×C7311yescharacteristic
331#332C22×C7311yescharacteristic
332#332C22×C7311yescharacteristic
333C2×Q16—21no—
334C2×Q16—21no—
335C22×C8—21no—
336C4⋊Q8D4×C7311yescharacteristic
337C4⋊Q8D4×C7311yescharacteristic
338C4⋊Q8C23×C7311yescharacteristic
339C4⋊Q8C23×C7311yescharacteristic
340C4⋊Q8C23×C7311yescharacteristic
341C4⋊Q8C23×C7311yescharacteristic
342#125—21no—
343#125—21no—
344#125—21no—
345C22⋊Q8—21no—
346C22⋊Q8—21no—
347C22⋊Q8—21no—
348C22⋊Q8—21no—
349C22⋊Q8—21no—
350C22⋊Q8D4×C7311yescharacteristic
351C22⋊Q8D4×C7311yescharacteristic
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8—21no—
356C4×Q8—21no—
357C4×Q8C23×C7311yescharacteristic
358C4×Q8C23×C7311yescharacteristic
359#117—21no—
360#117—21no—
361#117—21no—
362C2×C42C23×C7311yescharacteristic
363#107—21no—
364#107—21no—
365#107—21no—
366#107—21no—
367#107—21no—
368#107—21no—
369#106—21no—
370#106—21no—
371#106—21no—
372#106—21no—
373C4⋊C8—21no—
374C4⋊C8—21no—
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—21no—
378C4⋊C8D4×C7311yescharacteristic
379C4⋊C8D4×C7311yescharacteristic
380C4⋊C8C23×C7311yescharacteristic
381C4⋊C8C23×C7311yescharacteristic
382C4⋊C8C23×C7311yescharacteristic
383C4⋊C8C23×C7311yescharacteristic
384C4⋊C8C23×C7311yescharacteristic
385C4⋊C8C23×C7311yescharacteristic
386#103—21no—
387#103—21no—
388#103—21no—
389#103—21no—
390#103—21no—
391#103—21no—
392#103—21no—
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398C22⋊C8—21no—
399C22⋊C8—21no—
400C22⋊C8D4×C7311yescharacteristic
401C22⋊C8D4×C7311yescharacteristic
402#97—21no—
403#97—21no—
404#97—21no—
405C4×C8—21no—
406C4×C8—21no—
407C4×C8—21no—
408C4×C8C23×C7311yescharacteristic
409C4×C8C23×C7311yescharacteristic
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8C2×D4×C7311yescharacteristic
416C2×Q8C2×D4×C7311yescharacteristic
417C22×C4C2×D4×C7311yescharacteristic
418C22×C4C2×D4×C7311yescharacteristic
419C22×C4#41×C7311yescharacteristic
420Q16—81no—
421Q16—81no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—81no—
429C2×C8C2×D4×C7311yescharacteristic
430C2×C8C2×D4×C7311yescharacteristic
431C2×C8C2×D4×C7311yescharacteristic
432C2×C8C2×D4×C7311yescharacteristic
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—41no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4C2×D4×C7311yescharacteristic
453C4⋊C4C2×D4×C7311yescharacteristic
454C22⋊C4—21no—
455C22⋊C4—21no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C42—21no—
459C42—21no—
460C42—41no—
461C42—41no—
462C42C2×D4×C7311yescharacteristic
463C42C2×D4×C7311yescharacteristic
464C42#41×C7311yescharacteristic
465C42C24×C7311yescharacteristic
466C23#121×C7311yescharacteristic
467Q8—21no—
468Q8—21no—
469Q8—21no—
470Q8—21no—
471Q8—42no—
472Q8—41no—
473Q8—41no—
474Q8—41no—
475Q8—41no—
476Q8—81no—
477Q8—81no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4#121×C7311yescharacteristic
492C2×C4#121×C7311yescharacteristic
493C2×C4#121×C7311yescharacteristic
494C2×C4C22×D4×C7311yescharacteristic
495C2×C4C22×D4×C7311yescharacteristic
496C2×C4C2×#41×C7311yescharacteristic
497C8—21no—
498C8—21no—
499C8—21no—
500C8—21no—
501C8—41no—
502C8—41no—
503C8—41no—
504C8—41no—
505C8—41no—
506C8—41no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22C2×#121×C7311yescharacteristic
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—41no—
516C4—41no—
517C4—41no—
518C4—41no—
519C4—81no—
520C4—81no—
521C4—81no—
522C4—81no—
523C4#577×C7311yescharacteristic
524C4#578×C7311yescharacteristic
525C4#578×C7311yescharacteristic
526C4#578×C7311yescharacteristic
527C2—41no—
528C2C73×#304411yescharacteristic
529C2C73×#306311yescharacteristic
530C2C73×#306711yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC42C24×C73
prime radicalC23×C73#121
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
5. C73×#1704C2semidirect
6. C73×#1700C2semidirect
7. C73×#1696C2semidirect
8. C73×#1692C2semidirect
9. C73×#1684C2semidirect
10. C73×#1680C2semidirect
11. C73×#1676C2semidirect
12. C73×#1672C2semidirect
261. #19574C73direct (N × H)
270. #1704C2×C73semidirect
271. #1700C2×C73semidirect
272. #1696C2×C73semidirect
273. #1692C2×C73semidirect
274. #1684C2×C73semidirect
275. #1680C2×C73semidirect
276. #1676C2×C73semidirect
277. #1672C2×C73semidirect
281. C73#19574direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#32492
C73×#32372
C73×#32312
C73×#29862
C73×#17042
C73×#17002
C73×#16962
C73×#16922
C73×#16842
C73×#16802
C73×#16762
C73×#16722
C73×#15732
C73×#15542
C73×#15422
#1957473