Finite Group Databasebeta

← C73×#18829 #32928233

Subgroups — C73×#18829 #32928233

Order 18688.

872 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3503C211yesmaximal, characteristic
2C73×#3237C211yesmaximal, characteristic, complemented
3C73×#3229C211yesmaximal, characteristic, complemented
4C73×#3116C211yesmaximal, characteristic
5C73×#1653C212yesmaximal, complemented
6C73×#1651C212yesmaximal, complemented
7C73×#1637C212yesmaximal, complemented
8C73×#1636C212yesmaximal, complemented
9C73×#1556C211yesmaximal, characteristic, complemented
10C73×#1497C211yesmaximal, characteristic, complemented
11C73×#1488C211yesmaximal, characteristic
12Q82×C73—21no—
13#557×C73C2212yes—
14#554×C73—21no—
15#554×C73—22no—
16D4×Q8×C73—22no—
17D4×Q8×C73C2212yes—
18#544×C73—22no—
19#544×C73—21no—
20#533×C73—21no—
21#533×C73C2211yescharacteristic
22#533×C73C2211yescharacteristic
23C2×C4⋊Q8×C73—21no—
24C2×C4⋊Q8×C73C2211yescharacteristic
25#520×C73—21no—
26C4×#41×C73C2211yescharacteristic
27#501×C73—21no—
28#498×C73C2212yes—
29#491×C73—21no—
30#487×C73C2212yes—
31#485×C73—22no—
32#485×C73—21no—
33#483×C73—22no—
34#477×C73C2212yes—
35#477×C73C2211yescharacteristic
36#476×C73C2211yescharacteristic
37#475×C73—22no—
38#475×C73C2212yes—
39#462×C73C2211yescharacteristic
40#461×C73C2211yescharacteristic
41#452×C73—21no—
42#441×C73—21no—
43#440×C73—21no—
44#432×C73C2211yescharacteristic
45#432×C73C2211yescharacteristic
46#431×C73C2211yescharacteristic
47#332×C73C2212yes—
48#332×C73C2212yes—
49Q8⋊C8×C73C2212yes—
50Q8⋊C8×C73C2212yes—
51Q8⋊C8×C73C2212yes—
52D4⋊C8×C73C2212yes—
53C2×#41×C73D411yescharacteristic
54C22×Q8×C73—22no—
55C22×Q8×C73—21no—
56C2×Q16×C73—21no—
57C2×SD16×C73—21no—
58C4⋊Q8×C73—22no—
59C4⋊Q8×C73—22no—
60C4⋊Q8×C73—24no—
61C4⋊Q8×C73—22no—
62C4⋊Q8×C73—22no—
63C4⋊Q8×C73—21no—
64C4⋊Q8×C73—21no—
65C4⋊Q8×C73D411yescharacteristic
66C4⋊Q8×C73D412yes—
67C4⋊Q8×C73D411yescharacteristic
68C4⋊Q8×C73C2311yescharacteristic
69C4⋊Q8×C73C2311yescharacteristic
70C4⋊Q8×C73C2312yes—
71#125×C73—22no—
72#125×C73—24no—
73#125×C73—22no—
74#125×C73—21no—
75#125×C73—21no—
76C22⋊Q8×C73—22no—
77C22⋊Q8×C73—24no—
78C22⋊Q8×C73—24no—
79C22⋊Q8×C73—21no—
80C22⋊Q8×C73—22no—
81C22⋊Q8×C73—24no—
82C22⋊Q8×C73—21no—
83C22⋊Q8×C73—21no—
84C22⋊Q8×C73D412yes—
85C4×Q8×C73—22no—
86C4×Q8×C73—22no—
87C4×Q8×C73—22no—
88C4×Q8×C73—21no—
89C4×Q8×C73—21no—
90C4×Q8×C73—21no—
91C4×Q8×C73D411yescharacteristic
92C4×Q8×C73C2311yescharacteristic
93C4×Q8×C73C2312yes—
94C4×D4×C73—24no—
95C4×D4×C73—22no—
96C4×D4×C73—21no—
97C4×D4×C73—21no—
98C4×D4×C73D411yescharacteristic
99C4×D4×C73C2311yescharacteristic
100#117×C73—22no—
101#117×C73—21no—
102#117×C73—21no—
103#117×C73—21no—
104#117×C73D411yescharacteristic
105C2×C4⋊C4×C73—22no—
106C2×C4⋊C4×C73—22no—
107C2×C4⋊C4×C73—21no—
108C2×C4⋊C4×C73D412yes—
109C2×C42×C73—21no—
110C2×C42×C73C2311yescharacteristic
111#107×C73—21no—
112#107×C73—22no—
113#106×C73—21no—
114#106×C73—24no—
115#106×C73—22no—
116C4⋊C8×C73—21no—
117C4⋊C8×C73C2311yescharacteristic
118C4⋊C8×C73C2311yescharacteristic
119C4⋊C8×C73C2312yes—
120#103×C73—21no—
121#103×C73—22no—
122#103×C73—22no—
123#103×C73—21no—
124#103×C73—21no—
125#103×C73—24no—
126#102×C73—21no—
127C22⋊C8×C73—21no—
128C22⋊C8×C73—21no—
129C22⋊C8×C73—21no—
130#97×C73—21no—
131#97×C73—21no—
132C4×C8×C73C2312yes—
133#41×C73—22no—
134#41×C73—22no—
135C2×Q8×C73—24no—
136C2×Q8×C73—21no—
137C2×Q8×C73—22no—
138C2×Q8×C73—22no—
139C2×Q8×C73—21no—
140C2×Q8×C73—21no—
141C2×Q8×C73—82no—
142C2×Q8×C73—84no—
143C2×Q8×C73C2×D412yes—
144C2×Q8×C73C2×D411yescharacteristic
145C2×D4×C73—21no—
146C2×D4×C73C2×D411yescharacteristic
147C22×C4×C73—21no—
148C22×C4×C73—24no—
149C22×C4×C73—22no—
150C22×C4×C73—21no—
151C22×C4×C73—21no—
152C22×C4×C73C2×D411yescharacteristic
153C22×C4×C73C2×D411yescharacteristic
154C22×C4×C73C2×D411yescharacteristic
155Q16×C73—42no—
156SD16×C73—42no—
157C2×C8×C73—22no—
158C2×C8×C73—21no—
159C2×C8×C73—22no—
160C2×C8×C73—21no—
161C4⋊C4×C73—24no—
162C4⋊C4×C73—24no—
163C4⋊C4×C73—24no—
164C4⋊C4×C73—24no—
165C4⋊C4×C73—21no—
166C4⋊C4×C73—22no—
167C4⋊C4×C73—21no—
168C4⋊C4×C73—22no—
169C4⋊C4×C73—21no—
170C4⋊C4×C73—21no—
171C4⋊C4×C73—22no—
172C4⋊C4×C73—22no—
173C4⋊C4×C73—21no—
174C4⋊C4×C73—22no—
175C4⋊C4×C73—21no—
176C4⋊C4×C73—21no—
177C4⋊C4×C73—21no—
178C4⋊C4×C73—21no—
179C4⋊C4×C73—41no—
180C4⋊C4×C73—41no—
181C4⋊C4×C73C2×D414yes—
182C4⋊C4×C73C2×D411yescharacteristic
183C4⋊C4×C73C2×D411yescharacteristic
184C4⋊C4×C73C2×D412yes—
185C22⋊C4×C73—24no—
186C22⋊C4×C73—22no—
187C22⋊C4×C73—21no—
188C22⋊C4×C73—21no—
189C22⋊C4×C73—21no—
190C22⋊C4×C73—41no—
191C42×C73—24no—
192C42×C73—21no—
193C42×C73—21no—
194C42×C73—21no—
195C42×C73—22no—
196C42×C73—41no—
197C42×C73C2×D411yescharacteristic
198C42×C73C2×D411yescharacteristic
199C42×C73C2×D411yescharacteristic
200C42×C73C2411yescharacteristic
201C23×C73—21no—
202C23×C73#12011yescharacteristic
203Q8×C73—21no—
204Q8×C73—24no—
205Q8×C73—42no—
206Q8×C73—42no—
207Q8×C73—44no—
208Q8×C73—41no—
209Q8×C73—41no—
210Q8×C73—82no—
211Q8×C73—84no—
212Q8×C73#13712yes—
213D4×C73—24no—
214D4×C73—21no—
215D4×C73#13712yes—
216C2×C4×C73—24no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—22no—
221C2×C4×C73—22no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—22no—
225C2×C4×C73—24no—
226C2×C4×C73—41no—
227C2×C4×C73—42no—
228C2×C4×C73—42no—
229C2×C4×C73—41no—
230C2×C4×C73—41no—
231C2×C4×C73—82no—
232C2×C4×C73—84no—
233C2×C4×C73#12011yescharacteristic
234C2×C4×C73#12011yescharacteristic
235C2×C4×C73#12011yescharacteristic
236C2×C4×C73C22×D411yescharacteristic
237C2×C4×C73C22×D411yescharacteristic
238C2×C4×C73C22×D411yescharacteristic
239C8×C73—42no—
240C8×C73—41no—
241C8×C73—41no—
242C8×C73—42no—
243C22×C73—21no—
244C22×C73—22no—
245C22×C73—21no—
246C22×C73—21no—
247C22×C73—41no—
248C22×C73—41no—
249C22×C73C2×#12011yescharacteristic
250C4×C73—21no—
251C4×C73—22no—
252C4×C73—21no—
253C4×C73—21no—
254C4×C73—21no—
255C4×C73—41no—
256C4×C73—42no—
257C4×C73—44no—
258C4×C73—41no—
259C4×C73—42no—
260C4×C73—81no—
261C4×C73—81no—
262C4×C73C2×#13711yescharacteristic
263C4×C73C2×#13711yescharacteristic
264C4×C73#57712yes—
265#18829C7311yesmaximal, characteristic, direct product factor, Sylow
266C2×C73—41no—
267C2×C73—42no—
268C2×C73#300411yescharacteristic
269C2×C73#300911yescharacteristic
270C2×C73#302011yescharacteristic
271#3503C2×C7311yescharacteristic
272#3237C2×C7311yescharacteristic, complemented
273#3229C2×C7311yescharacteristic, complemented
274#3116C2×C7311yescharacteristic
275#1653C2×C7312yescomplemented
276#1651C2×C7312yescomplemented
277#1637C2×C7312yescomplemented
278#1636C2×C7312yescomplemented
279#1556C2×C7311yescharacteristic, complemented
280#1497C2×C7311yescharacteristic, complemented
281#1488C2×C7311yescharacteristic
282C73#1882911yescharacteristic, direct product factor, Sylow
283Q82—21no—
284#557C22×C7312yes—
285#554—21no—
286#554—22no—
287D4×Q8—22no—
288D4×Q8C22×C7312yes—
289#544—22no—
290#544—21no—
291#533—21no—
292#533C22×C7311yescharacteristic
293#533C22×C7311yescharacteristic
294C2×C4⋊Q8—21no—
295C2×C4⋊Q8C22×C7311yescharacteristic
296#520—21no—
297C4×#41C22×C7311yescharacteristic
298#501—21no—
299#498C22×C7312yes—
300#491—21no—
301#487C22×C7312yes—
302#485—22no—
303#485—21no—
304#483—22no—
305#477C22×C7311yescharacteristic
306#477C22×C7312yes—
307#476C22×C7311yescharacteristic
308#475—22no—
309#475C22×C7312yes—
310#462C22×C7311yescharacteristic
311#461C22×C7311yescharacteristic
312#452—21no—
313#441—21no—
314#440—21no—
315#432C22×C7311yescharacteristic
316#432C22×C7311yescharacteristic
317#431C22×C7311yescharacteristic
318#332C22×C7312yes—
319#332C22×C7312yes—
320Q8⋊C8C22×C7312yes—
321Q8⋊C8C22×C7312yes—
322Q8⋊C8C22×C7312yes—
323D4⋊C8C22×C7312yes—
324C2×#41D4×C7311yescharacteristic
325C22×Q8—22no—
326C22×Q8—21no—
327C2×Q16—21no—
328C2×SD16—21no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—24no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—21no—
335C4⋊Q8—21no—
336C4⋊Q8D4×C7311yescharacteristic
337C4⋊Q8D4×C7312yes—
338C4⋊Q8D4×C7311yescharacteristic
339C4⋊Q8C23×C7311yescharacteristic
340C4⋊Q8C23×C7311yescharacteristic
341C4⋊Q8C23×C7312yes—
342#125—22no—
343#125—24no—
344#125—22no—
345#125—21no—
346#125—21no—
347C22⋊Q8—22no—
348C22⋊Q8—24no—
349C22⋊Q8—24no—
350C22⋊Q8—21no—
351C22⋊Q8—22no—
352C22⋊Q8—24no—
353C22⋊Q8—21no—
354C22⋊Q8—21no—
355C22⋊Q8D4×C7312yes—
356C4×Q8—22no—
357C4×Q8—22no—
358C4×Q8—22no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8D4×C7311yescharacteristic
363C4×Q8C23×C7311yescharacteristic
364C4×Q8C23×C7312yes—
365C4×D4—24no—
366C4×D4—22no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4D4×C7311yescharacteristic
370C4×D4C23×C7311yescharacteristic
371#117—22no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117D4×C7311yescharacteristic
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4D4×C7312yes—
380C2×C42—21no—
381C2×C42C23×C7311yescharacteristic
382#107—21no—
383#107—22no—
384#106—21no—
385#106—24no—
386#106—22no—
387C4⋊C8—21no—
388C4⋊C8C23×C7312yes—
389C4⋊C8C23×C7311yescharacteristic
390C4⋊C8C23×C7311yescharacteristic
391#103—21no—
392#103—22no—
393#103—22no—
394#103—21no—
395#103—21no—
396#103—24no—
397#102—21no—
398C22⋊C8—21no—
399C22⋊C8—21no—
400C22⋊C8—21no—
401#97—21no—
402#97—21no—
403C4×C8C23×C7312yes—
404#41—22no—
405#41—22no—
406C2×Q8—24no—
407C2×Q8—21no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—82no—
413C2×Q8—84no—
414C2×Q8C2×D4×C7312yes—
415C2×Q8C2×D4×C7311yescharacteristic
416C2×D4—21no—
417C2×D4C2×D4×C7311yescharacteristic
418C22×C4—21no—
419C22×C4—24no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4C2×D4×C7311yescharacteristic
424C22×C4C2×D4×C7311yescharacteristic
425C22×C4C2×D4×C7311yescharacteristic
426Q16—42no—
427SD16—42no—
428C2×C8—22no—
429C2×C8—21no—
430C2×C8—22no—
431C2×C8—21no—
432C4⋊C4—24no—
433C4⋊C4—24no—
434C4⋊C4—24no—
435C4⋊C4—24no—
436C4⋊C4—21no—
437C4⋊C4—22no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4C2×D4×C7314yes—
453C4⋊C4C2×D4×C7311yescharacteristic
454C4⋊C4C2×D4×C7311yescharacteristic
455C4⋊C4C2×D4×C7312yes—
456C22⋊C4—24no—
457C22⋊C4—22no—
458C22⋊C4—21no—
459C22⋊C4—21no—
460C22⋊C4—21no—
461C22⋊C4—41no—
462C42—24no—
463C42—21no—
464C42—21no—
465C42—21no—
466C42—22no—
467C42—41no—
468C42C2×D4×C7311yescharacteristic
469C42C2×D4×C7311yescharacteristic
470C42C2×D4×C7311yescharacteristic
471C42C24×C7311yescharacteristic
472C23—21no—
473C23#120×C7311yescharacteristic
474Q8—21no—
475Q8—24no—
476Q8—42no—
477Q8—42no—
478Q8—44no—
479Q8—41no—
480Q8—41no—
481Q8—82no—
482Q8—84no—
483Q8#137×C7312yes—
484D4—24no—
485D4—21no—
486D4#137×C7312yes—
487C2×C4—24no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—82no—
503C2×C4—84no—
504C2×C4#120×C7311yescharacteristic
505C2×C4#120×C7311yescharacteristic
506C2×C4#120×C7311yescharacteristic
507C2×C4C22×D4×C7311yescharacteristic
508C2×C4C22×D4×C7311yescharacteristic
509C2×C4C22×D4×C7311yescharacteristic
510C8—42no—
511C8—41no—
512C8—41no—
513C8—42no—
514C22—21no—
515C22—22no—
516C22—21no—
517C22—21no—
518C22—41no—
519C22—41no—
520C22C2×#120×C7311yescharacteristic
521C4—21no—
522C4—22no—
523C4—21no—
524C4—21no—
525C4—21no—
526C4—41no—
527C4—42no—
528C4—44no—
529C4—41no—
530C4—42no—
531C4—81no—
532C4—81no—
533C4C2×#137×C7311yescharacteristic
534C4C2×#137×C7311yescharacteristic
535C4#577×C7312yes—
536C2—41no—
537C2—42no—
538C2C73×#300411yescharacteristic
539C2C73×#300911yescharacteristic
540C2C73×#302011yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC42C24×C73
prime radicalC2×#41×C73D4
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
2. C73×#3237C2semidirect
3. C73×#3229C2semidirect
5. C73×#1653C2semidirect
6. C73×#1651C2semidirect
7. C73×#1637C2semidirect
8. C73×#1636C2semidirect
9. C73×#1556C2semidirect
10. C73×#1497C2semidirect
265. #18829C73direct (N × H)
272. #3237C2×C73semidirect
273. #3229C2×C73semidirect
275. #1653C2×C73semidirect
276. #1651C2×C73semidirect
277. #1637C2×C73semidirect
278. #1636C2×C73semidirect
279. #1556C2×C73semidirect
280. #1497C2×C73semidirect
282. C73#18829direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#35032
C73×#32372
C73×#32292
C73×#31162
C73×#16532
C73×#16512
C73×#16372
C73×#16362
C73×#15562
C73×#14972
C73×#14882
#1882973