Finite Group Databasebeta

← C73×#18848 #32928252

Subgroups — C73×#18848 #32928252

Order 18688.

858 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3507C211yesmaximal, characteristic
2C73×#3255C211yesmaximal, characteristic, complemented
3C73×#3228C211yesmaximal, characteristic
4C73×#3113C211yesmaximal, characteristic, complemented
5C73×#1653C212yesmaximal, complemented
6C73×#1648C212yesmaximal, complemented
7C73×#1640C212yesmaximal, complemented
8C73×#1640C212yesmaximal, complemented
9C73×#1557C211yesmaximal, characteristic
10C73×#1497C211yesmaximal, characteristic, complemented
11C73×#1487C211yesmaximal, characteristic, complemented
12#559×C73C2212yes—
13#557×C73C2212yes—
14#556×C73—21no—
15#556×C73—22no—
16#554×C73—21no—
17#552×C73—22no—
18#539×C73—22no—
19#536×C73—21no—
20#533×C73C2211yescharacteristic
21#533×C73C2211yescharacteristic
22#532×C73C2211yescharacteristic
23#529×C73—22no—
24#520×C73—21no—
25C2×C4×Q8×C73C2211yescharacteristic
26#500×C73C2211yescharacteristic
27#498×C73C2211yescharacteristic
28#486×C73C2211yescharacteristic
29#486×C73C2211yescharacteristic
30#483×C73—21no—
31#482×C73—22no—
32#478×C73—22no—
33#475×C73—21no—
34#475×C73C2212yes—
35#475×C73C2212yes—
36#470×C73—22no—
37#462×C73—21no—
38#462×C73C2212yes—
39#462×C73C2212yes—
40#451×C73—21no—
41#441×C73—22no—
42#432×C73C2211yescharacteristic
43#431×C73C2211yescharacteristic
44#423×C73C2211yescharacteristic
45#332×C73C2212yes—
46#331×C73C2212yes—
47Q8⋊C8×C73C2212yes—
48Q8⋊C8×C73C2212yes—
49Q8⋊C8×C73C2212yes—
50Q8⋊C8×C73C2212yes—
51C2×#41×C73—21no—
52C22×Q8×C73D411yescharacteristic
53C2×Q16×C73—22no—
54C2×Q16×C73—22no—
55C2×M16×C73—21no—
56C4⋊Q8×C73—22no—
57C4⋊Q8×C73D411yescharacteristic
58C4⋊Q8×C73D411yescharacteristic
59C4⋊Q8×C73C2311yescharacteristic
60C4⋊Q8×C73C2311yescharacteristic
61C4⋊Q8×C73C2311yescharacteristic
62#127×C73C2311yescharacteristic
63#126×C73—24no—
64#126×C73—24no—
65#125×C73—22no—
66#125×C73—24no—
67#125×C73—21no—
68#125×C73—21no—
69#124×C73—22no—
70#124×C73—22no—
71#124×C73—21no—
72#123×C73—24no—
73#123×C73—24no—
74C22⋊Q8×C73—22no—
75C22⋊Q8×C73—22no—
76C22⋊Q8×C73—24no—
77C22⋊Q8×C73—21no—
78C22⋊Q8×C73—21no—
79C22⋊Q8×C73—21no—
80C22⋊Q8×C73D412yes—
81#121×C73—21no—
82#121×C73D412yes—
83C4×Q8×C73—22no—
84C4×Q8×C73—22no—
85C4×Q8×C73—21no—
86C4×Q8×C73—21no—
87C4×Q8×C73—21no—
88C4×Q8×C73—21no—
89C4×Q8×C73—21no—
90C4×Q8×C73D412yes—
91C4×Q8×C73C2312yes—
92C4×Q8×C73C2312yes—
93C4×D4×C73—24no—
94C4×D4×C73—22no—
95C4×D4×C73—22no—
96C4×D4×C73—21no—
97C4×D4×C73D412yes—
98#117×C73—22no—
99#117×C73—24no—
100#117×C73—21no—
101#117×C73—21no—
102C2×C4⋊C4×C73—22no—
103C2×C4⋊C4×C73—21no—
104C2×C4⋊C4×C73D411yescharacteristic
105C2×C42×C73—21no—
106C2×C42×C73C2311yescharacteristic
107#107×C73—22no—
108#106×C73—22no—
109#106×C73—22no—
110#106×C73—22no—
111C4⋊C8×C73—21no—
112C4⋊C8×C73—21no—
113C4⋊C8×C73C2312yes—
114C4⋊C8×C73C2312yes—
115#103×C73—22no—
116#103×C73—22no—
117#103×C73—22no—
118#103×C73—22no—
119#102×C73—22no—
120#102×C73—22no—
121C22⋊C8×C73—21no—
122C22⋊C8×C73—21no—
123#97×C73—21no—
124C4×C8×C73C2311yescharacteristic
125C4×C8×C73C2311yescharacteristic
126#41×C73—44no—
127C2×Q8×C73—21no—
128C2×Q8×C73—21no—
129C2×Q8×C73—21no—
130C2×Q8×C73—21no—
131C2×Q8×C73—21no—
132C2×Q8×C73—42no—
133C2×Q8×C73C2×D412yes—
134C2×Q8×C73C2×D412yes—
135C2×D4×C73—22no—
136C2×D4×C73—21no—
137C2×D4×C73—21no—
138C2×D4×C73C2×D412yes—
139C22×C4×C73—21no—
140C22×C4×C73—24no—
141C22×C4×C73—21no—
142C22×C4×C73—22no—
143C22×C4×C73C2×D411yescharacteristic
144C22×C4×C73C2×D411yescharacteristic
145C22×C4×C73C2×D411yescharacteristic
146Q16×C73—44no—
147Q16×C73—82no—
148M16×C73—81no—
149C2×C8×C73—21no—
150C2×C8×C73—21no—
151C2×C8×C73—22no—
152C2×C8×C73—22no—
153C4⋊C4×C73—24no—
154C4⋊C4×C73—24no—
155C4⋊C4×C73—24no—
156C4⋊C4×C73—21no—
157C4⋊C4×C73—21no—
158C4⋊C4×C73—22no—
159C4⋊C4×C73—21no—
160C4⋊C4×C73—22no—
161C4⋊C4×C73—21no—
162C4⋊C4×C73—22no—
163C4⋊C4×C73—21no—
164C4⋊C4×C73—22no—
165C4⋊C4×C73—21no—
166C4⋊C4×C73—21no—
167C4⋊C4×C73—21no—
168C4⋊C4×C73—21no—
169C4⋊C4×C73—41no—
170C4⋊C4×C73—41no—
171C4⋊C4×C73C2×D412yes—
172C4⋊C4×C73C2×D412yes—
173C4⋊C4×C73C2×D412yes—
174C22⋊C4×C73—24no—
175C22⋊C4×C73—24no—
176C22⋊C4×C73—24no—
177C22⋊C4×C73—22no—
178C22⋊C4×C73—22no—
179C22⋊C4×C73—22no—
180C22⋊C4×C73—41no—
181C42×C73—24no—
182C42×C73—22no—
183C42×C73—22no—
184C42×C73—22no—
185C42×C73—41no—
186C42×C73C2×D411yescharacteristic
187C42×C73C2×D411yescharacteristic
188C42×C73C2×D411yescharacteristic
189C42×C73C2411yescharacteristic
190C23×C73—22no—
191C23×C73#12011yescharacteristic
192Q8×C73—22no—
193Q8×C73—22no—
194Q8×C73—22no—
195Q8×C73—22no—
196Q8×C73—42no—
197Q8×C73—42no—
198Q8×C73—42no—
199Q8×C73—41no—
200Q8×C73—41no—
201Q8×C73—81no—
202D4×C73—42no—
203D4×C73—44no—
204D4×C73—42no—
205D4×C73—41no—
206D4×C73—41no—
207C2×C4×C73—22no—
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—22no—
211C2×C4×C73—22no—
212C2×C4×C73—22no—
213C2×C4×C73—22no—
214C2×C4×C73—22no—
215C2×C4×C73—41no—
216C2×C4×C73—44no—
217C2×C4×C73—42no—
218C2×C4×C73—41no—
219C2×C4×C73—41no—
220C2×C4×C73—81no—
221C2×C4×C73—84no—
222C2×C4×C73#12011yescharacteristic
223C2×C4×C73#12011yescharacteristic
224C2×C4×C73#12011yescharacteristic
225C2×C4×C73C22×D411yescharacteristic
226C2×C4×C73C22×D411yescharacteristic
227C2×C4×C73C22×D411yescharacteristic
228C8×C73—41no—
229C8×C73—41no—
230C8×C73—42no—
231C8×C73—42no—
232C22×C73—21no—
233C22×C73—21no—
234C22×C73—21no—
235C22×C73—42no—
236C22×C73—42no—
237C22×C73—42no—
238C22×C73C2×#12011yescharacteristic
239C4×C73—21no—
240C4×C73—21no—
241C4×C73—21no—
242C4×C73—21no—
243C4×C73—42no—
244C4×C73—42no—
245C4×C73—42no—
246C4×C73—42no—
247C4×C73—42no—
248C4×C73—81no—
249C4×C73—81no—
250C4×C73#57512yes—
251C4×C73#57711yescharacteristic
252C4×C73#57811yescharacteristic
253#18848C7311yesmaximal, characteristic, direct product factor, Sylow
254C2×C73—41no—
255C2×C73—82no—
256C2×C73#300511yescharacteristic
257C2×C73#301311yescharacteristic
258C2×C73#302211yescharacteristic
259#3507C2×C7311yescharacteristic
260#3255C2×C7311yescharacteristic, complemented
261#3228C2×C7311yescharacteristic
262#3113C2×C7311yescharacteristic, complemented
263#1653C2×C7312yescomplemented
264#1648C2×C7312yescomplemented
265#1640C2×C7312yescomplemented
266#1640C2×C7312yescomplemented
267#1557C2×C7311yescharacteristic
268#1497C2×C7311yescharacteristic, complemented
269#1487C2×C7311yescharacteristic, complemented
270C73#1884811yescharacteristic, direct product factor, Sylow
271#559C22×C7312yes—
272#557C22×C7312yes—
273#556—21no—
274#556—22no—
275#554—21no—
276#552—22no—
277#539—22no—
278#536—21no—
279#533C22×C7311yescharacteristic
280#533C22×C7311yescharacteristic
281#532C22×C7311yescharacteristic
282#529—22no—
283#520—21no—
284C2×C4×Q8C22×C7311yescharacteristic
285#500C22×C7311yescharacteristic
286#498C22×C7311yescharacteristic
287#486C22×C7311yescharacteristic
288#486C22×C7311yescharacteristic
289#483—21no—
290#482—22no—
291#478—22no—
292#475—21no—
293#475C22×C7312yes—
294#475C22×C7312yes—
295#470—22no—
296#462—21no—
297#462C22×C7312yes—
298#462C22×C7312yes—
299#451—21no—
300#441—22no—
301#432C22×C7311yescharacteristic
302#431C22×C7311yescharacteristic
303#423C22×C7311yescharacteristic
304#332C22×C7312yes—
305#331C22×C7312yes—
306Q8⋊C8C22×C7312yes—
307Q8⋊C8C22×C7312yes—
308Q8⋊C8C22×C7312yes—
309Q8⋊C8C22×C7312yes—
310C2×#41—21no—
311C22×Q8D4×C7311yescharacteristic
312C2×Q16—22no—
313C2×Q16—22no—
314C2×M16—21no—
315C4⋊Q8—22no—
316C4⋊Q8D4×C7311yescharacteristic
317C4⋊Q8D4×C7311yescharacteristic
318C4⋊Q8C23×C7311yescharacteristic
319C4⋊Q8C23×C7311yescharacteristic
320C4⋊Q8C23×C7311yescharacteristic
321#127C23×C7311yescharacteristic
322#126—24no—
323#126—24no—
324#125—22no—
325#125—24no—
326#125—21no—
327#125—21no—
328#124—22no—
329#124—22no—
330#124—21no—
331#123—24no—
332#123—24no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—24no—
336C22⋊Q8—21no—
337C22⋊Q8—21no—
338C22⋊Q8—21no—
339C22⋊Q8D4×C7312yes—
340#121—21no—
341#121D4×C7312yes—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8—21no—
348C4×Q8—21no—
349C4×Q8D4×C7312yes—
350C4×Q8C23×C7312yes—
351C4×Q8C23×C7312yes—
352C4×D4—24no—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—21no—
356C4×D4D4×C7312yes—
357#117—22no—
358#117—24no—
359#117—21no—
360#117—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4D4×C7311yescharacteristic
364C2×C42—21no—
365C2×C42C23×C7311yescharacteristic
366#107—22no—
367#106—22no—
368#106—22no—
369#106—22no—
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8C23×C7312yes—
373C4⋊C8C23×C7312yes—
374#103—22no—
375#103—22no—
376#103—22no—
377#103—22no—
378#102—22no—
379#102—22no—
380C22⋊C8—21no—
381C22⋊C8—21no—
382#97—21no—
383C4×C8C23×C7311yescharacteristic
384C4×C8C23×C7311yescharacteristic
385#41—44no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—42no—
392C2×Q8C2×D4×C7312yes—
393C2×Q8C2×D4×C7312yes—
394C2×D4—22no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4C2×D4×C7312yes—
398C22×C4—21no—
399C22×C4—24no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4C2×D4×C7311yescharacteristic
403C22×C4C2×D4×C7311yescharacteristic
404C22×C4C2×D4×C7311yescharacteristic
405Q16—44no—
406Q16—82no—
407M16—81no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—22no—
411C2×C8—22no—
412C4⋊C4—24no—
413C4⋊C4—24no—
414C4⋊C4—24no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—22no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4C2×D4×C7312yes—
431C4⋊C4C2×D4×C7312yes—
432C4⋊C4C2×D4×C7312yes—
433C22⋊C4—24no—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—41no—
440C42—24no—
441C42—22no—
442C42—22no—
443C42—22no—
444C42—41no—
445C42C2×D4×C7311yescharacteristic
446C42C2×D4×C7311yescharacteristic
447C42C2×D4×C7311yescharacteristic
448C42C24×C7311yescharacteristic
449C23—22no—
450C23#120×C7311yescharacteristic
451Q8—22no—
452Q8—22no—
453Q8—22no—
454Q8—22no—
455Q8—42no—
456Q8—42no—
457Q8—42no—
458Q8—41no—
459Q8—41no—
460Q8—81no—
461D4—42no—
462D4—44no—
463D4—42no—
464D4—41no—
465D4—41no—
466C2×C4—22no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—41no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—81no—
480C2×C4—84no—
481C2×C4#120×C7311yescharacteristic
482C2×C4#120×C7311yescharacteristic
483C2×C4#120×C7311yescharacteristic
484C2×C4C22×D4×C7311yescharacteristic
485C2×C4C22×D4×C7311yescharacteristic
486C2×C4C22×D4×C7311yescharacteristic
487C8—41no—
488C8—41no—
489C8—42no—
490C8—42no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22C2×#120×C7311yescharacteristic
498C4—21no—
499C4—21no—
500C4—21no—
501C4—21no—
502C4—42no—
503C4—42no—
504C4—42no—
505C4—42no—
506C4—42no—
507C4—81no—
508C4—81no—
509C4#575×C7312yes—
510C4#577×C7311yescharacteristic
511C4#578×C7311yescharacteristic
512C2—41no—
513C2—82no—
514C2C73×#300511yescharacteristic
515C2C73×#301311yescharacteristic
516C2C73×#302211yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC42C24×C73
prime radical#532×C73C22
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×#3255C2semidirect
4. C73×#3113C2semidirect
5. C73×#1653C2semidirect
6. C73×#1648C2semidirect
7. C73×#1640C2semidirect
8. C73×#1640C2semidirect
10. C73×#1497C2semidirect
11. C73×#1487C2semidirect
253. #18848C73direct (N × H)
260. #3255C2×C73semidirect
262. #3113C2×C73semidirect
263. #1653C2×C73semidirect
264. #1648C2×C73semidirect
265. #1640C2×C73semidirect
266. #1640C2×C73semidirect
268. #1497C2×C73semidirect
269. #1487C2×C73semidirect
270. C73#18848direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#35072
C73×#32552
C73×#32282
C73×#31132
C73×#16532
C73×#16482
C73×#16402
C73×#15572
C73×#14972
C73×#14872
#1884873