Finite Group Databasebeta

← #33241092

Subgroups — #33241092

Order 18688.

568 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620570C211yesmaximal, characteristic, complemented
2#22612139C211yesmaximal, characteristic, complemented
3#22612122C211yesmaximal, characteristic, complemented
4#22612078C211yesmaximal, characteristic, complemented
5#22612068C211yesmaximal, characteristic, complemented
6#22611986C211yesmaximal, characteristic, complemented
7#22611986C211yesmaximal, characteristic, complemented
8#22611860C211yesmaximal, characteristic, complemented
9#22611843C211yesmaximal, characteristic
10#22611805C211yesmaximal, characteristic, complemented
11#22611795C211yesmaximal, characteristic, complemented
12C4×#14556535C211yesmaximal, characteristic, complemented
13C4×#14556532C211yesmaximal, characteristic, complemented
14#22611738C211yesmaximal, characteristic, complemented
15C73×#2948C211yesmaximal, characteristic, complemented
16#17989208—21no—
17C2×#14556535C2211yescharacteristic
18C2×#14556535C2211yescharacteristic
19C2×#14556532C2211yescharacteristic
20C2×#14556532C2211yescharacteristic
21#17988992C2211yescharacteristic, complemented
22#17988971C2211yescharacteristic, complemented
23#17988947—21no—
24#17988833—21no—
25#17988828C2211yescharacteristic
26#17988823C2211yescharacteristic
27#17988689—21no—
28C4×Dic292C2211yescharacteristic, complemented
29C4×D584C2211yescharacteristic, complemented
30#17988414C2211yescharacteristic, complemented
31#17988414C2211yescharacteristic, complemented
32#17988412C2211yescharacteristic, complemented
33#17988412C2211yescharacteristic, complemented
34C4⋊#11924003C2211yescharacteristic, complemented
35C4⋊#11924003C2211yescharacteristic, complemented
36#17988390C2211yescharacteristic, complemented
37#17988390C2211yescharacteristic, complemented
38#17988388C2211yescharacteristic
39#17988388C2211yescharacteristic
40#17988388C2211yescharacteristic
41#17988388C2211yescharacteristic
42#17988387C2211yescharacteristic, complemented
43#17988387C2211yescharacteristic, complemented
44C22⋊#11924003C2211yescharacteristic
45C22⋊#11924003C2211yescharacteristic
46#17988363C2211yescharacteristic, complemented
47C4×#11924003C2211yescharacteristic, complemented
48C22×D8×C73C2211yescharacteristic
49#518×C73—21no—
50#442×C73—21no—
51#442×C73—21no—
52C4×D8×C73C2211yescharacteristic
53C4×D8×C73C2211yescharacteristic
54C4×D8×C73C2211yescharacteristic
55C4×D8×C73C2211yescharacteristic
56#427×C73C2211yescharacteristic
57#418×C73—21no—
58#405×C73C2211yescharacteristic
59C2×Dic292C2311yescharacteristic
60C2×#11924017—21no—
61C2×D584C2311yescharacteristic
62#14556591—21no—
63#14556586—41no—
64#14556579—21no—
65#14556577—41no—
66#14556573—41no—
67#14556570—21no—
68#14556569—41no—
69#14556565—21no—
70C4×Dic146—21no—
71C4×D292—21no—
72#14556535—22no—
73#14556535—22no—
74#14556532—22no—
75#14556532—22no—
76C2×#11924003C2311yescharacteristic
77C2×#11924003C2311yescharacteristic
78C2×#11924003C2311yescharacteristic
79C2×#11924003C2311yescharacteristic
80#14556525—21no—
81#14556525C2311yescharacteristic
82#14556525C2311yescharacteristic
83#14556516—21no—
84#14556516—21no—
85#14556513—21no—
86#14556513—21no—
87C22×D4×C73—21no—
88C2×D8×C73—22no—
89C2×D8×C73—22no—
90C2×D8×C73—21no—
91C2×D8×C73C2311yescharacteristic
92C2×D8×C73C2311yescharacteristic
93C2×M16×C73D411yescharacteristic
94C22×C8×C73C2311yescharacteristic
95C4×D4×C73—21no—
96C4×D4×C73—21no—
97C4×D4×C73—21no—
98C4×D4×C73—21no—
99C4×D4×C73—41no—
100C4×D4×C73—41no—
101#117×C73—21no—
102#117×C73D411yescharacteristic
103C2×C22⋊C4×C73—41no—
104C2×C22⋊C4×C73—41no—
105#107×C73C2311yescharacteristic
106#107×C73C2311yescharacteristic
107#106×C73—21no—
108#102×C73—21no—
109#102×C73—21no—
110#102×C73—21no—
111#102×C73—21no—
112#97×C73D411yescharacteristic
113#97×C73D411yescharacteristic
114C4×C8×C73C2311yescharacteristic
115C4×C8×C73C2311yescharacteristic
116C2×Dic146—21no—
117C2×Dic146—41no—
118C2×D292—21no—
119C2×C22⋊D73—41no—
120C2×C4×D73—41no—
121Dic292—21no—
122Dic292—21no—
123#11924017—42no—
124D584—21no—
125D584—21no—
126C4⋊Dic73—21no—
127C4⋊Dic73—21no—
128C4⋊Dic73—41no—
129#11924007—41no—
130#11924007—41no—
131C22⋊Dic73—41no—
132#11924005—41no—
133#11924005—41no—
134#11924005—41no—
135#11924005—41no—
136C4×Dic73—41no—
137#11924003—21no—
138#11924003—21no—
139#11924003—21no—
140#11924003—21no—
141C24×C73—41no—
142C2×D4×C73—24no—
143C2×D4×C73—21no—
144C2×D4×C73—21no—
145C2×D4×C73—42no—
146C2×D4×C73—41no—
147C22×C4×C73—41no—
148C22×C4×C73—41no—
149C22×C4×C73—41no—
150C22×C4×C73—41no—
151C22×C4×C73C2×D411yescharacteristic
152D8×C73—24no—
153D8×C73—21no—
154D8×C73—21no—
155D8×C73#4112yes—
156D8×C73#4112yes—
157M16×C73—41no—
158C2×C8×C73—21no—
159C2×C8×C73—21no—
160C2×C8×C73C2×D411yescharacteristic
161C2×C8×C73C2×D411yescharacteristic
162C2×C8×C73C2×D411yescharacteristic
163C2×C8×C73C2411yescharacteristic
164C4⋊C4×C73—21no—
165C4⋊C4×C73—21no—
166C4⋊C4×C73D811yescharacteristic
167C4⋊C4×C73D811yescharacteristic
168C22⋊C4×C73—41no—
169C22⋊C4×C73—41no—
170C22⋊C4×C73—41no—
171C22⋊C4×C73—41no—
172C22⋊C4×C73—41no—
173C22⋊C4×C73D811yescharacteristic
174C22⋊C4×C73D811yescharacteristic
175C42×C73—41no—
176C42×C73C2×D411yescharacteristic
177C42×C73C2×D411yescharacteristic
178C23×C73—44no—
179C23×C73—41no—
180C23×C73—41no—
181C23×C73—161no—
182C23×C73—161no—
183C23×C73C2×D811yescharacteristic
184C22×D73—41no—
185D4×C73—22no—
186D4×C73—22no—
187D4×C73—44no—
188D4×C73—41no—
189D4×C73—41no—
190C2×C4×C73—21no—
191C2×C4×C73—21no—
192C2×C4×C73—41no—
193C2×C4×C73—41no—
194C2×C4×C73—161no—
195C2×C4×C73—161no—
196C2×C4×C73—161no—
197C2×C4×C73—161no—
198C2×C4×C73C2×D811yescharacteristic
199C2×C4×C73C2×D811yescharacteristic
200C2×C4×C73C2×D811yescharacteristic
201C2×C4×C73C2×D811yescharacteristic
202C2×C4×C73C2×D811yescharacteristic
203C2×C4×C73C22×D411yescharacteristic
204C22⋊D73—161no—
205C2×Dic73—41no—
206C2×Dic73—41no—
207C2×Dic73—41no—
208D292—41no—
209D292—41no—
210C4×D73—161no—
211Dic146—41no—
212Dic146—41no—
213Dic146—161no—
214C8×C73—21no—
215C8×C73—21no—
216C8×C73—21no—
217C8×C73C2×#4111yescharacteristic
218C8×C73C2×#4111yescharacteristic
219C22×C73—21no—
220C22×C73—21no—
221C22×C73—21no—
222C22×C73—42no—
223C22×C73—42no—
224C22×C73—81no—
225C22×C73—81no—
226C22×C73—81no—
227C22×C73—81no—
228C22×C73—164no—
229C22×C73C22×D811yescharacteristic
230C2×D73—81no—
231C2×D73—81no—
232C2×D73—81no—
233C4×C73—21no—
234C4×C73—21no—
235C4×C73—21no—
236C4×C73—21no—
237C4×C73—21no—
238C4×C73—81no—
239C4×C73—81no—
240C4×C73#52511yescharacteristic
241C4×C73#57511yescharacteristic
242Dic73—81no—
243Dic73—81no—
244Dic73—81no—
245#33678—731nomaximal, Sylow
246C2×C73—41no—
247C2×C73—82no—
248C2×C73—82no—
249C2×C73#310011yescharacteristic
250C2×C73#341511yescharacteristic
251C2×C73#341611yescharacteristic
252D73—161no—
253#3175—731no—
254#2948D7311yescharacteristic, complemented
255#2237—731no—
256#2234—731no—
257#2226—731no—
258#2224—731no—
259#2210—731no—
260#2210—731no—
261#2187—731no—
262#2184—731no—
263#2177—731no—
264#2175—731no—
265C4×SD32—731no—
266C4×D16—731no—
267#2164—731no—
268C73#3367811yescharacteristic, complemented, Sylow
269C22×D8C2×D7311yescharacteristic
270#542—1461no—
271#518—21no—
272C2×SD32—731no—
273C2×SD32—731no—
274C2×D16—731no—
275C2×D16—731no—
276#500—731no—
277#495—731no—
278#489—1461no—
279#468—1461no—
280#467—731no—
281#466—731no—
282#442—21no—
283#442—21no—
284#440—1461no—
285C4×Q16—731no—
286C4×D8—731no—
287C4×D8C2×D7311yescharacteristic
288C4×D8C2×D7311yescharacteristic
289C4×D8C2×D7311yescharacteristic
290C4×D8C2×D7311yescharacteristic
291#427C2×D7311yescharacteristic
292#418—21no—
293#405C2×D7311yescharacteristic
294#367—731no—
295#367—731no—
296#366—731no—
297#366—731no—
298C4⋊C16—731no—
299C4⋊C16—731no—
300#358—731no—
301#358—731no—
302#357—731no—
303#357—731no—
304#357—731no—
305#357—731no—
306#357—731no—
307#357—731no—
308C22⋊C16—731no—
309C22⋊C16—731no—
310#346—731no—
311C4×C16—731no—
312C22×D4—21no—
313C2×Q16—731no—
314C2×SD16—1461no—
315C2×D8—22no—
316C2×D8—22no—
317C2×D8—21no—
318C2×D8—731no—
319C2×D8C22×D7311yescharacteristic
320C2×D8C22×D7311yescharacteristic
321C2×M16C22⋊D7311yescharacteristic
322C22×C8C22×D7311yescharacteristic
323C4⋊Q8—1461no—
324#126—2921no—
325#124—2921no—
326#124—1461no—
327#123—2921no—
328C22⋊Q8—2921no—
329C22⋊Q8—1461no—
330#121—1461no—
331C4×Q8—1461no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—41no—
337C4×D4—41no—
338C4×D4—1461no—
339#117—21no—
340#117C22⋊D7311yescharacteristic
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343SD32—1462no—
344SD32—1462no—
345D16—1462no—
346D16—1462no—
347C2×C16—731no—
348C2×C16—731no—
349C2×C16—731no—
350C2×C16—731no—
351#107—731no—
352#107—731no—
353#107—1461no—
354#107C22×D7311yescharacteristic
355#107C22×D7311yescharacteristic
356#106—21no—
357#103—1461no—
358#103—1461no—
359#102—21no—
360#102—21no—
361#102—21no—
362#102—21no—
363#102—1461no—
364#102—1461no—
365#97C22⋊D7311yescharacteristic
366#97C22⋊D7311yescharacteristic
367C4×C8C22×D7311yescharacteristic
368C4×C8C22×D7311yescharacteristic
369C24—41no—
370C2×Q8—2921no—
371C2×Q8—1461no—
372C2×D4—24no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—42no—
376C2×D4—41no—
377C2×D4—2921no—
378C2×D4—1461no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—2921no—
384C22×C4C2×C22⋊D7311yescharacteristic
385Q16—1461no—
386Q16—1461no—
387SD16—2922no—
388D8—24no—
389D8—21no—
390D8—21no—
391D8—1461no—
392D8—1461no—
393D8#1192402812yes—
394D8#1192402812yes—
395M16—41no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8C2×C22⋊D7311yescharacteristic
399C2×C8C2×C22⋊D7311yescharacteristic
400C2×C8C2×C22⋊D7311yescharacteristic
401C2×C8C23×D7311yescharacteristic
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—2921no—
405C4⋊C4—2921no—
406C4⋊C4—2921no—
407C4⋊C4—1461no—
408C4⋊C4—1461no—
409C4⋊C4#1192401311yescharacteristic
410C4⋊C4#1192401311yescharacteristic
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—2921no—
417C22⋊C4—2921no—
418C22⋊C4—2921no—
419C22⋊C4—2921no—
420C22⋊C4—2921no—
421C22⋊C4#1192401311yescharacteristic
422C22⋊C4#1192401311yescharacteristic
423C42—41no—
424C42—2921no—
425C42C2×C22⋊D7311yescharacteristic
426C42C2×C22⋊D7311yescharacteristic
427C16—1461no—
428C16—1461no—
429C16—1461no—
430C16—1461no—
431C23—44no—
432C23—41no—
433C23—41no—
434C23—161no—
435C23—161no—
436C23—2921no—
437C23C2×#1192401311yescharacteristic
438Q8—2921no—
439Q8—2921no—
440Q8—11681no—
441D4—22no—
442D4—22no—
443D4—44no—
444D4—41no—
445D4—41no—
446D4—2921no—
447D4—2921no—
448D4—11681no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—161no—
454C2×C4—161no—
455C2×C4—161no—
456C2×C4—161no—
457C2×C4—2921no—
458C2×C4—2921no—
459C2×C4—2921no—
460C2×C4—11681no—
461C2×C4C2×#1192401311yescharacteristic
462C2×C4C2×#1192401311yescharacteristic
463C2×C4C2×#1192401311yescharacteristic
464C2×C4C2×#1192401311yescharacteristic
465C2×C4C2×#1192401311yescharacteristic
466C2×C4C22×C22⋊D7311yescharacteristic
467C8—21no—
468C8—21no—
469C8—21no—
470C8C2×#1192402811yescharacteristic
471C8C2×#1192402811yescharacteristic
472C22—21no—
473C22—21no—
474C22—21no—
475C22—42no—
476C22—42no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22—164no—
482C22—5841no—
483C22—5841no—
484C22—5841no—
485C22C22×#1192401311yescharacteristic
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—81no—
492C4—81no—
493C4—5841no—
494C4—5841no—
495C4—5841no—
496C4#1798909811yescharacteristic
497C4#1798938511yescharacteristic
498C2—41no—
499C2—82no—
500C2—82no—
501C2—11681no—
502C2#2261993111yescharacteristic
503C2#2262307011yescharacteristic
504C2#2262307811yescharacteristic
subgroupG/H
centerC22C22×#11924013
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
FittingC73×#2948C2
socleC22×C73C22×D8
prime radical#22611843C2
hypercenter#2948D73
hypocenterC73#33678
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2948

Complements

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

NH ≅ G/Ntype
1. #22620570C2semidirect
2. #22612139C2semidirect
3. #22612122C2semidirect
4. #22612078C2semidirect
5. #22612068C2semidirect
6. #22611986C2semidirect
7. #22611986C2semidirect
8. #22611860C2semidirect
10. #22611805C2semidirect
11. #22611795C2semidirect
12. C4×#14556535C2semidirect
13. C4×#14556532C2semidirect
14. #22611738C2semidirect
15. C73×#2948C2semidirect
21. #17988992C22semidirect
22. #17988971C22semidirect
28. C4×Dic292C22semidirect
29. C4×D584C22semidirect
30. #17988414C22semidirect
31. #17988414C22semidirect
32. #17988412C22semidirect
33. #17988412C22semidirect
34. C4⋊#11924003C22semidirect
35. C4⋊#11924003C22semidirect
36. #17988390C22semidirect
37. #17988390C22semidirect
42. #17988387C22semidirect
43. #17988387C22semidirect
46. #17988363C22semidirect
47. C4×#11924003C22semidirect
254. #2948D73semidirect
268. C73#33678semidirect

Maximal subgroups

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

subgroupindex
#226205702
#226121392
#226121222
#226120782
#226120682
#226119862
#226118602
#226118432
#226118052
#226117952
C4×#145565352
C4×#145565322
#226117382
C73×#29482
#3367873