Finite Group Databasebeta

← C73×#19740 #32929144

Subgroups — C73×#19740 #32929144

Order 18688.

704 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3230C211yesmaximal, characteristic, complemented
2C73×#3228C211yesmaximal, characteristic, complemented
3C73×#3226C211yesmaximal, characteristic, complemented
4C73×#3210C211yesmaximal, characteristic, complemented
5C73×#3207C211yesmaximal, characteristic
6C73×#3206C211yesmaximal, characteristic, complemented
7C73×#1723C211yesmaximal, characteristic, complemented
8C73×#1722C211yesmaximal, characteristic, complemented
9C73×#1719C211yesmaximal, characteristic, complemented
10C73×#1719C211yesmaximal, characteristic, complemented
11C73×#1717C211yesmaximal, characteristic, complemented
12C73×#1714C211yesmaximal, characteristic, complemented
13C73×#1710C211yesmaximal, characteristic, complemented
14C73×#1706C211yesmaximal, characteristic, complemented
15C73×#1454C211yesmaximal, characteristic, complemented
16#533×C73C2211yescharacteristic
17#532×C73C2211yescharacteristic
18#532×C73C2211yescharacteristic
19C2×C4⋊Q8×C73C2211yescharacteristic
20#500×C73C2211yescharacteristic
21#500×C73C2211yescharacteristic
22#500×C73C2211yescharacteristic
23#500×C73C2211yescharacteristic
24#500×C73C2211yescharacteristic
25#498×C73C2211yescharacteristic
26#494×C73C2211yescharacteristic
27#493×C73C2211yescharacteristic
28#492×C73C2211yescharacteristic
29#492×C73C2211yescharacteristic
30#492×C73C2211yescharacteristic
31#492×C73C2211yescharacteristic
32#487×C73C2211yescharacteristic
33#487×C73C2211yescharacteristic
34#487×C73C2211yescharacteristic
35#487×C73C2211yescharacteristic
36#487×C73C2211yescharacteristic
37#487×C73C2211yescharacteristic
38#486×C73C2211yescharacteristic
39#486×C73C2211yescharacteristic
40#486×C73C2211yescharacteristic
41#486×C73C2211yescharacteristic
42#486×C73C2211yescharacteristic
43#486×C73C2211yescharacteristic
44#484×C73—22no—
45#482×C73—22no—
46#480×C73—22no—
47#478×C73—22no—
48#477×C73—22no—
49#474×C73—22no—
50#464×C73—22no—
51#463×C73—22no—
52#461×C73—22no—
53#452×C73—22no—
54#449×C73—22no—
55#448×C73—22no—
56#431×C73C2211yescharacteristic
57#431×C73C2211yescharacteristic
58#431×C73C2211yescharacteristic
59#322×C73C2211yescharacteristic
60#322×C73C2211yescharacteristic
61#322×C73C2211yescharacteristic
62C82×C73C2211yescharacteristic
63C2×#41×C73—21no—
64C2×#41×C73—21no—
65C22×Q8×C73—21no—
66C2×Q16×C73—22no—
67C2×SD16×C73—22no—
68C2×SD16×C73—22no—
69C2×SD16×C73—22no—
70C2×SD16×C73—22no—
71C2×D8×C73—22no—
72C4⋊Q8×C73—21no—
73C4⋊Q8×C73—21no—
74C4⋊Q8×C73—21no—
75C4⋊Q8×C73C2311yescharacteristic
76C4⋊Q8×C73C2311yescharacteristic
77C4⋊Q8×C73C2311yescharacteristic
78C4⋊Q8×C73C2311yescharacteristic
79C4⋊Q8×C73C2311yescharacteristic
80C4⋊Q8×C73C2311yescharacteristic
81#127×C73C2311yescharacteristic
82#127×C73C2311yescharacteristic
83#125×C73—21no—
84#124×C73—21no—
85#124×C73—21no—
86C22⋊Q8×C73—21no—
87C22⋊Q8×C73—21no—
88#121×C73—21no—
89#121×C73—21no—
90#121×C73—21no—
91#121×C73—21no—
92C4×Q8×C73—21no—
93C4×Q8×C73—21no—
94C4×D4×C73—21no—
95C4×D4×C73—21no—
96C4×D4×C73—21no—
97C4×D4×C73—21no—
98#117×C73—21no—
99C2×C4⋊C4×C73—21no—
100C2×C4⋊C4×C73—21no—
101C2×C42×C73C2311yescharacteristic
102#107×C73—22no—
103#107×C73—22no—
104#107×C73—22no—
105#107×C73—22no—
106#107×C73—22no—
107#106×C73—22no—
108C4⋊C8×C73D412yes—
109C4⋊C8×C73D412yes—
110C4⋊C8×C73D412yes—
111#103×C73—22no—
112#103×C73—22no—
113#103×C73—22no—
114#103×C73—22no—
115#103×C73—22no—
116#103×C73—22no—
117#102×C73—22no—
118#102×C73—22no—
119#102×C73—22no—
120#102×C73—22no—
121#102×C73—22no—
122#102×C73—22no—
123C22⋊C8×C73D412yes—
124C22⋊C8×C73D412yes—
125C22⋊C8×C73D412yes—
126C4×C8×C73C2311yescharacteristic
127C4×C8×C73C2311yescharacteristic
128C4×C8×C73C2311yescharacteristic
129C4×C8×C73C2311yescharacteristic
130C4×C8×C73C2311yescharacteristic
131C4×C8×C73C2311yescharacteristic
132#41×C73—82no—
133#41×C73—82no—
134C2×Q8×C73—21no—
135C2×Q8×C73—21no—
136C2×Q8×C73—21no—
137C2×Q8×C73—21no—
138C2×Q8×C73—21no—
139C2×Q8×C73—21no—
140C2×Q8×C73—41no—
141C2×Q8×C73—82no—
142C2×D4×C73—21no—
143C2×D4×C73—21no—
144C2×D4×C73—21no—
145C2×D4×C73—21no—
146C2×D4×C73—21no—
147C2×D4×C73—21no—
148C2×D4×C73—41no—
149C2×D4×C73—41no—
150C22×C4×C73—41no—
151C22×C4×C73—41no—
152C22×C4×C73—41no—
153C22×C4×C73C2×D411yescharacteristic
154C22×C4×C73C2×D411yescharacteristic
155C22×C4×C73C2×D411yescharacteristic
156Q16×C73—82no—
157SD16×C73—82no—
158SD16×C73—82no—
159SD16×C73—82no—
160SD16×C73—82no—
161D8×C73—82no—
162C2×C8×C73C2×D412yes—
163C2×C8×C73C2×D412yes—
164C2×C8×C73C2×D412yes—
165C2×C8×C73C2×D412yes—
166C2×C8×C73C2×D412yes—
167C2×C8×C73C2×D412yes—
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—41no—
181C4⋊C4×C73—41no—
182C4⋊C4×C73—41no—
183C4⋊C4×C73—41no—
184C22⋊C4×C73—41no—
185C22⋊C4×C73—41no—
186C22⋊C4×C73—41no—
187C22⋊C4×C73—41no—
188C22⋊C4×C73—41no—
189C42×C73—41no—
190C42×C73C2×D411yescharacteristic
191C42×C73C2×D411yescharacteristic
192C42×C73C2×D411yescharacteristic
193C42×C73C2411yescharacteristic
194C23×C73—41no—
195C23×C73—41no—
196C23×C73#12711yescharacteristic
197Q8×C73—42no—
198Q8×C73—42no—
199Q8×C73—42no—
200Q8×C73—42no—
201Q8×C73—42no—
202Q8×C73—42no—
203Q8×C73—82no—
204D4×C73—42no—
205D4×C73—42no—
206D4×C73—42no—
207D4×C73—42no—
208D4×C73—42no—
209D4×C73—42no—
210D4×C73—82no—
211D4×C73—82no—
212C2×C4×C73—22no—
213C2×C4×C73—22no—
214C2×C4×C73—22no—
215C2×C4×C73—41no—
216C2×C4×C73—41no—
217C2×C4×C73—41no—
218C2×C4×C73—41no—
219C2×C4×C73—41no—
220C2×C4×C73—41no—
221C2×C4×C73—82no—
222C2×C4×C73—82no—
223C2×C4×C73—82no—
224C2×C4×C73#12711yescharacteristic
225C2×C4×C73#12711yescharacteristic
226C2×C4×C73#12711yescharacteristic
227C2×C4×C73C22×D411yescharacteristic
228C2×C4×C73C22×D411yescharacteristic
229C2×C4×C73C22×D411yescharacteristic
230C8×C73—22no—
231C8×C73—22no—
232C8×C73—22no—
233C8×C73—22no—
234C8×C73—22no—
235C8×C73—22no—
236C22×C73—21no—
237C22×C73—21no—
238C22×C73—21no—
239C22×C73—81no—
240C22×C73—81no—
241C22×C73—81no—
242C22×C73—81no—
243C22×C73—81no—
244C22×C73—81no—
245C22×C73C2×#12711yescharacteristic
246C4×C73—21no—
247C4×C73—21no—
248C4×C73—21no—
249C4×C73—81no—
250C4×C73—81no—
251C4×C73—81no—
252C4×C73—81no—
253C4×C73—81no—
254C4×C73—81no—
255C4×C73#57612yes—
256C4×C73#57712yes—
257C4×C73#57812yes—
258#19740C7311yesmaximal, characteristic, direct product factor, Sylow
259C2×C73—41no—
260C2×C73—161no—
261C2×C73—161no—
262C2×C73#315411yescharacteristic
263C2×C73#315511yescharacteristic
264C2×C73#315611yescharacteristic
265#3230C2×C7311yescharacteristic, complemented
266#3228C2×C7311yescharacteristic, complemented
267#3226C2×C7311yescharacteristic, complemented
268#3210C2×C7311yescharacteristic, complemented
269#3207C2×C7311yescharacteristic
270#3206C2×C7311yescharacteristic, complemented
271#1723C2×C7311yescharacteristic, complemented
272#1722C2×C7311yescharacteristic, complemented
273#1719C2×C7311yescharacteristic, complemented
274#1719C2×C7311yescharacteristic, complemented
275#1717C2×C7311yescharacteristic, complemented
276#1714C2×C7311yescharacteristic, complemented
277#1710C2×C7311yescharacteristic, complemented
278#1706C2×C7311yescharacteristic, complemented
279#1454C2×C7311yescharacteristic, complemented
280C73#1974011yescharacteristic, direct product factor, Sylow
281#533C22×C7311yescharacteristic
282#532C22×C7311yescharacteristic
283#532C22×C7311yescharacteristic
284C2×C4⋊Q8C22×C7311yescharacteristic
285#500C22×C7311yescharacteristic
286#500C22×C7311yescharacteristic
287#500C22×C7311yescharacteristic
288#500C22×C7311yescharacteristic
289#500C22×C7311yescharacteristic
290#498C22×C7311yescharacteristic
291#494C22×C7311yescharacteristic
292#493C22×C7311yescharacteristic
293#492C22×C7311yescharacteristic
294#492C22×C7311yescharacteristic
295#492C22×C7311yescharacteristic
296#492C22×C7311yescharacteristic
297#487C22×C7311yescharacteristic
298#487C22×C7311yescharacteristic
299#487C22×C7311yescharacteristic
300#487C22×C7311yescharacteristic
301#487C22×C7311yescharacteristic
302#487C22×C7311yescharacteristic
303#486C22×C7311yescharacteristic
304#486C22×C7311yescharacteristic
305#486C22×C7311yescharacteristic
306#486C22×C7311yescharacteristic
307#486C22×C7311yescharacteristic
308#486C22×C7311yescharacteristic
309#484—22no—
310#482—22no—
311#480—22no—
312#478—22no—
313#477—22no—
314#474—22no—
315#464—22no—
316#463—22no—
317#461—22no—
318#452—22no—
319#449—22no—
320#448—22no—
321#431C22×C7311yescharacteristic
322#431C22×C7311yescharacteristic
323#431C22×C7311yescharacteristic
324#322C22×C7311yescharacteristic
325#322C22×C7311yescharacteristic
326#322C22×C7311yescharacteristic
327C82C22×C7311yescharacteristic
328C2×#41—21no—
329C2×#41—21no—
330C22×Q8—21no—
331C2×Q16—22no—
332C2×SD16—22no—
333C2×SD16—22no—
334C2×SD16—22no—
335C2×SD16—22no—
336C2×D8—22no—
337C4⋊Q8—21no—
338C4⋊Q8—21no—
339C4⋊Q8—21no—
340C4⋊Q8C23×C7311yescharacteristic
341C4⋊Q8C23×C7311yescharacteristic
342C4⋊Q8C23×C7311yescharacteristic
343C4⋊Q8C23×C7311yescharacteristic
344C4⋊Q8C23×C7311yescharacteristic
345C4⋊Q8C23×C7311yescharacteristic
346#127C23×C7311yescharacteristic
347#127C23×C7311yescharacteristic
348#125—21no—
349#124—21no—
350#124—21no—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353#121—21no—
354#121—21no—
355#121—21no—
356#121—21no—
357C4×Q8—21no—
358C4×Q8—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—21no—
363#117—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C42C23×C7311yescharacteristic
367#107—22no—
368#107—22no—
369#107—22no—
370#107—22no—
371#107—22no—
372#106—22no—
373C4⋊C8D4×C7312yes—
374C4⋊C8D4×C7312yes—
375C4⋊C8D4×C7312yes—
376#103—22no—
377#103—22no—
378#103—22no—
379#103—22no—
380#103—22no—
381#103—22no—
382#102—22no—
383#102—22no—
384#102—22no—
385#102—22no—
386#102—22no—
387#102—22no—
388C22⋊C8D4×C7312yes—
389C22⋊C8D4×C7312yes—
390C22⋊C8D4×C7312yes—
391C4×C8C23×C7311yescharacteristic
392C4×C8C23×C7311yescharacteristic
393C4×C8C23×C7311yescharacteristic
394C4×C8C23×C7311yescharacteristic
395C4×C8C23×C7311yescharacteristic
396C4×C8C23×C7311yescharacteristic
397#41—82no—
398#41—82no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—41no—
406C2×Q8—82no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—41no—
414C2×D4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4C2×D4×C7311yescharacteristic
419C22×C4C2×D4×C7311yescharacteristic
420C22×C4C2×D4×C7311yescharacteristic
421Q16—82no—
422SD16—82no—
423SD16—82no—
424SD16—82no—
425SD16—82no—
426D8—82no—
427C2×C8C2×D4×C7312yes—
428C2×C8C2×D4×C7312yes—
429C2×C8C2×D4×C7312yes—
430C2×C8C2×D4×C7312yes—
431C2×C8C2×D4×C7312yes—
432C2×C8C2×D4×C7312yes—
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—41no—
446C4⋊C4—41no—
447C4⋊C4—41no—
448C4⋊C4—41no—
449C22⋊C4—41no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C22⋊C4—41no—
454C42—41no—
455C42C2×D4×C7311yescharacteristic
456C42C2×D4×C7311yescharacteristic
457C42C2×D4×C7311yescharacteristic
458C42C24×C7311yescharacteristic
459C23—41no—
460C23—41no—
461C23#127×C7311yescharacteristic
462Q8—42no—
463Q8—42no—
464Q8—42no—
465Q8—42no—
466Q8—42no—
467Q8—42no—
468Q8—82no—
469D4—42no—
470D4—42no—
471D4—42no—
472D4—42no—
473D4—42no—
474D4—42no—
475D4—82no—
476D4—82no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—82no—
487C2×C4—82no—
488C2×C4—82no—
489C2×C4#127×C7311yescharacteristic
490C2×C4#127×C7311yescharacteristic
491C2×C4#127×C7311yescharacteristic
492C2×C4C22×D4×C7311yescharacteristic
493C2×C4C22×D4×C7311yescharacteristic
494C2×C4C22×D4×C7311yescharacteristic
495C8—22no—
496C8—22no—
497C8—22no—
498C8—22no—
499C8—22no—
500C8—22no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22C2×#127×C7311yescharacteristic
511C4—21no—
512C4—21no—
513C4—21no—
514C4—81no—
515C4—81no—
516C4—81no—
517C4—81no—
518C4—81no—
519C4—81no—
520C4#576×C7312yes—
521C4#577×C7312yes—
522C4#578×C7312yes—
523C2—41no—
524C2—161no—
525C2—161no—
526C2C73×#315411yescharacteristic
527C2C73×#315511yescharacteristic
528C2C73×#315611yescharacteristic
subgroupG/H
center, socleC22×C73C2×#127
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3207C2
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×#3230C2semidirect
2. C73×#3228C2semidirect
3. C73×#3226C2semidirect
4. C73×#3210C2semidirect
6. C73×#3206C2semidirect
7. C73×#1723C2semidirect
8. C73×#1722C2semidirect
9. C73×#1719C2semidirect
10. C73×#1719C2semidirect
11. C73×#1717C2semidirect
12. C73×#1714C2semidirect
13. C73×#1710C2semidirect
14. C73×#1706C2semidirect
15. C73×#1454C2semidirect
258. #19740C73direct (N × H)
265. #3230C2×C73semidirect
266. #3228C2×C73semidirect
267. #3226C2×C73semidirect
268. #3210C2×C73semidirect
270. #3206C2×C73semidirect
271. #1723C2×C73semidirect
272. #1722C2×C73semidirect
273. #1719C2×C73semidirect
274. #1719C2×C73semidirect
275. #1717C2×C73semidirect
276. #1714C2×C73semidirect
277. #1710C2×C73semidirect
278. #1706C2×C73semidirect
279. #1454C2×C73semidirect
280. C73#19740direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#32302
C73×#32282
C73×#32262
C73×#32102
C73×#32072
C73×#32062
C73×#17232
C73×#17222
C73×#17192
C73×#17172
C73×#17142
C73×#17102
C73×#17062
C73×#14542
#1974073