Finite Group Databasebeta

← C73×#25687 #32935091

Subgroups — C73×#25687 #32935091

Order 18688.

1156 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3508C211yesmaximal, characteristic
2C73×#3165C211yesmaximal, characteristic, complemented
3C73×#3079C211yesmaximal, characteristic, complemented
4C73×#2858C211yesmaximal, characteristic, complemented
5C73×#2037C214yesmaximal, complemented
6C73×#1994C211yesmaximal, characteristic, complemented
7C73×#1965C211yesmaximal, characteristic, complemented
8C73×#1856C214yesmaximal, complemented
9C4×#104×C73C211yesmaximal, characteristic, complemented
10#559×C73—21no—
11#559×C73—21no—
12#550×C73—21no—
13#550×C73—21no—
14#546×C73—22no—
15#546×C73—22no—
16#540×C73—22no—
17#535×C73C2212yes—
18#533×C73C2211yescharacteristic
19#532×C73—21no—
20#532×C73—21no—
21C2×C4⋊Q8×C73C2211yescharacteristic
22C2×#127×C73C2211yescharacteristic
23C2×#124×C73—22no—
24#518×C73C2212yes—
25C4×#41×C73C2211yescharacteristic
26#501×C73—22no—
27#500×C73—21no—
28#498×C73—21no—
29#477×C73—21no—
30#476×C73—21no—
31#475×C73—21no—
32#474×C73—21no—
33#428×C73C2214yes—
34#428×C73C2212yes—
35#423×C73C2211yescharacteristic
36C2×#104×C73C2212yes—
37#417×C73C2212yes—
38C2×#100×C73C2214yes—
39C4×M16×C73C2211yescharacteristic
40#390×C73—22no—
41#390×C73C2214yes—
42C43×C73C2211yescharacteristic
43#339×C73C2214yes—
44#339×C73C2212yes—
45C2×#41×C73—22no—
46C2×#41×C73—22no—
47C2×#41×C73C2311yescharacteristic
48C22×Q8×C73—21no—
49C22×D4×C73D412yes—
50C22×D4×C73D412yes—
51C22×D4×C73C2312yes—
52C2×M16×C73C2312yes—
53C2×M16×C73C2312yes—
54C4⋊Q8×C73—21no—
55C4⋊Q8×C73—21no—
56C4⋊Q8×C73—21no—
57C4⋊Q8×C73—21no—
58C4⋊Q8×C73D411yescharacteristic
59C4⋊Q8×C73D411yescharacteristic
60#127×C73—22no—
61#127×C73—21no—
62#127×C73—21no—
63#127×C73—21no—
64#127×C73—21no—
65#125×C73D412yes—
66#124×C73—22no—
67#124×C73—22no—
68#124×C73—22no—
69#124×C73—48no—
70#123×C73—24no—
71#123×C73—24no—
72C22⋊Q8×C73—21no—
73C22⋊Q8×C73—21no—
74#121×C73—22no—
75#121×C73—22no—
76#121×C73—24no—
77#121×C73—24no—
78#121×C73—22no—
79#121×C73—22no—
80#120×C73—24no—
81C4×Q8×C73—21no—
82C4×Q8×C73—21no—
83C4×Q8×C73D411yescharacteristic
84C4×Q8×C73D411yescharacteristic
85C4×D4×C73—22no—
86C4×D4×C73—22no—
87C4×D4×C73—21no—
88C4×D4×C73—21no—
89C4×D4×C73—22no—
90C4×D4×C73—22no—
91C4×D4×C73—22no—
92C4×D4×C73—22no—
93C4×D4×C73D411yescharacteristic
94C4×D4×C73D411yescharacteristic
95#117×C73—21no—
96#117×C73C2311yescharacteristic
97#117×C73C2312yes—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73C2312yes—
100C2×C22⋊C4×C73—24no—
101C2×C22⋊C4×C73—28no—
102C2×C42×C73—21no—
103C2×C42×C73—21no—
104C2×C42×C73—21no—
105C2×C42×C73C2312yes—
106C2×C42×C73C2311yescharacteristic
107#107×C73—22no—
108#107×C73—24no—
109#106×C73—22no—
110#106×C73—24no—
111C4⋊C8×C73—21no—
112C4⋊C8×C73—21no—
113#104×C73—24no—
114#103×C73—22no—
115#102×C73—22no—
116#100×C73—28no—
117#97×C73—21no—
118C4×C8×C73—21no—
119C24×C73C2×D414yes—
120#41×C73—22no—
121#41×C73—22no—
122#41×C73—84no—
123#41×C73—84no—
124C2×Q8×C73—21no—
125C2×Q8×C73—21no—
126C2×Q8×C73—44no—
127C2×Q8×C73—41no—
128C2×Q8×C73—41no—
129C2×Q8×C73C2×D411yescharacteristic
130C2×D4×C73—21no—
131C2×D4×C73—24no—
132C2×D4×C73—24no—
133C2×D4×C73—22no—
134C2×D4×C73—22no—
135C2×D4×C73—22no—
136C2×D4×C73—22no—
137C2×D4×C73—22no—
138C2×D4×C73—22no—
139C2×D4×C73—24no—
140C2×D4×C73—24no—
141C2×D4×C73—44no—
142C2×D4×C73—44no—
143C2×D4×C73C2×D411yescharacteristic
144C22×C4×C73—22no—
145C22×C4×C73—24no—
146C22×C4×C73—24no—
147C22×C4×C73—21no—
148C22×C4×C73—21no—
149C22×C4×C73—21no—
150C22×C4×C73—22no—
151C22×C4×C73C2×D411yescharacteristic
152C22×C4×C73C2×D411yescharacteristic
153C22×C4×C73C2411yescharacteristic
154M16×C73—22no—
155M16×C73—24no—
156M16×C73#4114yescomplemented
157C2×C8×C73—22no—
158C2×C8×C73—22no—
159C4⋊C4×C73—21no—
160C4⋊C4×C73—21no—
161C4⋊C4×C73—21no—
162C4⋊C4×C73—21no—
163C4⋊C4×C73—22no—
164C4⋊C4×C73—22no—
165C4⋊C4×C73—22no—
166C4⋊C4×C73—22no—
167C4⋊C4×C73—41no—
168C4⋊C4×C73—41no—
169C4⋊C4×C73C2×D411yescharacteristic
170C4⋊C4×C73C2×D412yes—
171C4⋊C4×C73C2×D411yescharacteristic
172C4⋊C4×C73C2×D412yes—
173C22⋊C4×C73—24no—
174C22⋊C4×C73—24no—
175C22⋊C4×C73—24no—
176C22⋊C4×C73—24no—
177C22⋊C4×C73—21no—
178C22⋊C4×C73—22no—
179C22⋊C4×C73—21no—
180C22⋊C4×C73—21no—
181C22⋊C4×C73—416no—
182C42×C73—24no—
183C42×C73—21no—
184C42×C73—21no—
185C42×C73—21no—
186C42×C73—22no—
187C42×C73—22no—
188C42×C73—22no—
189C42×C73—42no—
190C42×C73C2×D411yescharacteristic
191C42×C73C2×D411yescharacteristic
192C42×C73C2×D411yescharacteristic
193C42×C73C2×D411yescharacteristic
194C23×C73—24no—
195C23×C73—21no—
196C23×C73—28no—
197C23×C73—44no—
198C23×C73—44no—
199C23×C73C22×D411yescharacteristic
200Q8×C73—21no—
201Q8×C73—21no—
202Q8×C73—42no—
203Q8×C73—42no—
204Q8×C73—82no—
205Q8×C73—82no—
206D4×C73—21no—
207D4×C73—21no—
208D4×C73—42no—
209D4×C73—42no—
210D4×C73—42no—
211D4×C73—44no—
212D4×C73—44no—
213D4×C73—44no—
214D4×C73—82no—
215D4×C73—82no—
216D4×C73—84no—
217D4×C73—84no—
218C2×C4×C73—22no—
219C2×C4×C73—22no—
220C2×C4×C73—24no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—22no—
225C2×C4×C73—22no—
226C2×C4×C73—42no—
227C2×C4×C73—42no—
228C2×C4×C73—42no—
229C2×C4×C73—42no—
230C2×C4×C73—42no—
231C2×C4×C73—44no—
232C2×C4×C73—42no—
233C2×C4×C73—84no—
234C2×C4×C73—84no—
235C2×C4×C73#12011yescharacteristic
236C2×C4×C73#12011yescharacteristic
237C2×C4×C73#12011yescharacteristic
238C2×C4×C73#12011yescharacteristic
239C2×C4×C73C22×D411yescharacteristic
240C2×C4×C73C22×D411yescharacteristic
241C2×C4×C73C2×#4112yes—
242C2×C4×C732−1+412yes—
243C8×C73—24no—
244C8×C73—42no—
245C22×C73—21no—
246C22×C73—21no—
247C22×C73—41no—
248C22×C73—44no—
249C22×C73—41no—
250C22×C73—44no—
251C22×C73—41no—
252C22×C73—44no—
253C22×C73—88no—
254C22×C73C2×#12011yescharacteristic
255C22×C73#54712yes—
256C4×C73—21no—
257C4×C73—21no—
258C4×C73—44no—
259C4×C73—41no—
260C4×C73—41no—
261C4×C73—42no—
262C4×C73—41no—
263C4×C73—42no—
264C4×C73—82no—
265C4×C73#45312yes—
266C4×C73#45512yes—
267C4×C73#53211yescharacteristic
268C4×C73#53611yescharacteristic
269C4×C73#54812yes—
270#25687C7311yesmaximal, characteristic, direct product factor, Sylow
271C2×C73—22no—
272C2×C73—81no—
273C2×C73—84no—
274C2×C73#243211yescharacteristic
275C2×C73C2×#45311yescharacteristic
276C2×C73C2×#45511yescharacteristic
277#3508C2×C7311yescharacteristic
278#3165C2×C7311yescharacteristic, complemented
279#3079C2×C7311yescharacteristic, complemented
280#2858C2×C7311yescharacteristic, complemented
281#2037C2×C7314yescomplemented
282#1994C2×C7311yescharacteristic, complemented
283#1965C2×C7311yescharacteristic, complemented
284#1856C2×C7314yescomplemented
285C4×#104C2×C7311yescharacteristic, complemented
286C73#2568711yescharacteristic, direct product factor, Sylow
287#559—21no—
288#559—21no—
289#550—21no—
290#550—21no—
291#546—22no—
292#546—22no—
293#540—22no—
294#535C22×C7312yes—
295#533C22×C7311yescharacteristic
296#532—21no—
297#532—21no—
298C2×C4⋊Q8C22×C7311yescharacteristic
299C2×#127C22×C7311yescharacteristic
300C2×#124—22no—
301#518C22×C7312yes—
302C4×#41C22×C7311yescharacteristic
303#501—22no—
304#500—21no—
305#498—21no—
306#477—21no—
307#476—21no—
308#475—21no—
309#474—21no—
310#428C22×C7312yes—
311#428C22×C7314yes—
312#423C22×C7311yescharacteristic
313C2×#104C22×C7312yes—
314#417C22×C7312yes—
315C2×#100C22×C7314yes—
316C4×M16C22×C7311yescharacteristic
317#390—22no—
318#390C22×C7314yes—
319C43C22×C7311yescharacteristic
320#339C22×C7312yes—
321#339C22×C7314yes—
322C2×#41—22no—
323C2×#41—22no—
324C2×#41C23×C7311yescharacteristic
325C22×Q8—21no—
326C22×D4D4×C7312yes—
327C22×D4D4×C7312yes—
328C22×D4C23×C7312yes—
329C2×M16C23×C7312yes—
330C2×M16C23×C7312yes—
331C4⋊Q8—21no—
332C4⋊Q8—21no—
333C4⋊Q8—21no—
334C4⋊Q8—21no—
335C4⋊Q8D4×C7311yescharacteristic
336C4⋊Q8D4×C7311yescharacteristic
337#127—22no—
338#127—21no—
339#127—21no—
340#127—21no—
341#127—21no—
342#125D4×C7312yes—
343#124—22no—
344#124—22no—
345#124—22no—
346#124—48no—
347#123—24no—
348#123—24no—
349C22⋊Q8—21no—
350C22⋊Q8—21no—
351#121—22no—
352#121—22no—
353#121—24no—
354#121—24no—
355#121—22no—
356#121—22no—
357#120—24no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8D4×C7311yescharacteristic
361C4×Q8D4×C7311yescharacteristic
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4D4×C7311yescharacteristic
371C4×D4D4×C7311yescharacteristic
372#117—21no—
373#117C23×C7311yescharacteristic
374#117C23×C7312yes—
375C2×C4⋊C4—21no—
376C2×C4⋊C4C23×C7312yes—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—28no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42C23×C7312yes—
383C2×C42C23×C7311yescharacteristic
384#107—22no—
385#107—24no—
386#106—22no—
387#106—24no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390#104—24no—
391#103—22no—
392#102—22no—
393#100—28no—
394#97—21no—
395C4×C8—21no—
396C24C2×D4×C7314yes—
397#41—22no—
398#41—22no—
399#41—84no—
400#41—84no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—44no—
404C2×Q8—41no—
405C2×Q8—41no—
406C2×Q8C2×D4×C7311yescharacteristic
407C2×D4—21no—
408C2×D4—24no—
409C2×D4—24no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4C2×D4×C7311yescharacteristic
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4C2×D4×C7311yescharacteristic
429C22×C4C2×D4×C7311yescharacteristic
430C22×C4C24×C7311yescharacteristic
431M16—22no—
432M16—24no—
433M16#41×C7314yescomplemented
434C2×C8—22no—
435C2×C8—22no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—41no—
445C4⋊C4—41no—
446C4⋊C4C2×D4×C7311yescharacteristic
447C4⋊C4C2×D4×C7312yes—
448C4⋊C4C2×D4×C7311yescharacteristic
449C4⋊C4C2×D4×C7312yes—
450C22⋊C4—24no—
451C22⋊C4—24no—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—21no—
455C22⋊C4—22no—
456C22⋊C4—21no—
457C22⋊C4—21no—
458C22⋊C4—416no—
459C42—24no—
460C42—21no—
461C42—21no—
462C42—21no—
463C42—22no—
464C42—22no—
465C42—22no—
466C42—42no—
467C42C2×D4×C7311yescharacteristic
468C42C2×D4×C7311yescharacteristic
469C42C2×D4×C7311yescharacteristic
470C42C2×D4×C7311yescharacteristic
471C23—24no—
472C23—21no—
473C23—28no—
474C23—44no—
475C23—44no—
476C23C22×D4×C7311yescharacteristic
477Q8—21no—
478Q8—21no—
479Q8—42no—
480Q8—42no—
481Q8—82no—
482Q8—82no—
483D4—21no—
484D4—21no—
485D4—42no—
486D4—44no—
487D4—44no—
488D4—42no—
489D4—42no—
490D4—44no—
491D4—82no—
492D4—82no—
493D4—84no—
494D4—84no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—44no—
509C2×C4—42no—
510C2×C4—84no—
511C2×C4—84no—
512C2×C4#120×C7311yescharacteristic
513C2×C4#120×C7311yescharacteristic
514C2×C4#120×C7311yescharacteristic
515C2×C4#120×C7311yescharacteristic
516C2×C4C22×D4×C7311yescharacteristic
517C2×C4C22×D4×C7311yescharacteristic
518C2×C4C2×#41×C7312yes—
519C2×C42−1+4×C7312yes—
520C8—24no—
521C8—42no—
522C22—21no—
523C22—21no—
524C22—41no—
525C22—44no—
526C22—41no—
527C22—44no—
528C22—41no—
529C22—44no—
530C22—88no—
531C22C2×#120×C7311yescharacteristic
532C22#547×C7312yes—
533C4—21no—
534C4—21no—
535C4—44no—
536C4—41no—
537C4—42no—
538C4—41no—
539C4—42no—
540C4—41no—
541C4—82no—
542C4#453×C7312yes—
543C4#455×C7312yes—
544C4#532×C7311yescharacteristic
545C4#536×C7311yescharacteristic
546C4#548×C7312yes—
547C2—22no—
548C2—84no—
549C2—81no—
550C2C73×#243211yescharacteristic
551C2C2×#453×C7311yescharacteristic
552C2C2×#455×C7311yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#3508C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C73×#3165C2semidirect
3. C73×#3079C2semidirect
4. C73×#2858C2semidirect
5. C73×#2037C2semidirect
6. C73×#1994C2semidirect
7. C73×#1965C2semidirect
8. C73×#1856C2semidirect
9. C4×#104×C73C2semidirect
156. M16×C73#41semidirect
270. #25687C73direct (N × H)
278. #3165C2×C73semidirect
279. #3079C2×C73semidirect
280. #2858C2×C73semidirect
281. #2037C2×C73semidirect
282. #1994C2×C73semidirect
283. #1965C2×C73semidirect
284. #1856C2×C73semidirect
285. C4×#104C2×C73semidirect
286. C73#25687direct (N × H)
433. M16#41×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#35082
C73×#31652
C73×#30792
C73×#28582
C73×#20372
C73×#19942
C73×#19652
C73×#18562
C4×#104×C732
#2568773