Finite Group Databasebeta

← #33075059

Subgroups — #33075059

Order 18688.

712 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22621092C211yesmaximal, characteristic, complemented
2#22621090C211yesmaximal, characteristic, complemented
3#22621086C211yesmaximal, characteristic, complemented
4#22620872C211yesmaximal, characteristic
5#22620872C211yesmaximal, characteristic
6#22609583C211yesmaximal, characteristic, complemented
7#22609582C211yesmaximal, characteristic, complemented
8#22609581C211yesmaximal, characteristic, complemented
9#22609552C211yesmaximal, characteristic, complemented
10#22609551C211yesmaximal, characteristic, complemented
11#22609550C211yesmaximal, characteristic, complemented
12#22609542C211yesmaximal, characteristic, complemented
13#22609517C211yesmaximal, characteristic, complemented
14#22608231C211yesmaximal, characteristic, complemented
15C73×#3208C211yesmaximal, characteristic
16#17989144C2211yescharacteristic
17#17989144C2211yescharacteristic
18#17988992C2211yescharacteristic, complemented
19#17988990C2211yescharacteristic, complemented
20#17988990C2211yescharacteristic, complemented
21#17988985C2211yescharacteristic, complemented
22#17988983C2211yescharacteristic, complemented
23#17988983C2211yescharacteristic, complemented
24#17988959C2211yescharacteristic
25#17988959C2211yescharacteristic
26#17988959C2211yescharacteristic
27#17988959C2211yescharacteristic
28#17988939C2211yescharacteristic, complemented
29#17988939C2211yescharacteristic, complemented
30#17988938C2211yescharacteristic, complemented
31#17988938C2211yescharacteristic, complemented
32#17988937C2211yescharacteristic, complemented
33#17988937C2211yescharacteristic, complemented
34#17988933C2211yescharacteristic
35#17988933C2211yescharacteristic
36#17988933C2211yescharacteristic
37#17988933C2211yescharacteristic
38#17988929—22no—
39#17988928—22no—
40#17988925—22no—
41#17988895—22no—
42#17988894—22no—
43#17988891—22no—
44#17988784—22no—
45#17988784—22no—
46#17988738—22no—
47#17988738—22no—
48#17988640C2211yescharacteristic
49#17988640C2211yescharacteristic
50#17988309C2211yescharacteristic, complemented
51#17988309C2211yescharacteristic, complemented
52#17988308C2211yescharacteristic, complemented
53C8×#10596831C2211yescharacteristic, complemented
54#533×C73C2211yescharacteristic
55C2×#127×C73C2211yescharacteristic
56#492×C73C2211yescharacteristic
57#492×C73C2211yescharacteristic
58#486×C73C2211yescharacteristic
59#486×C73C2211yescharacteristic
60#460×C73—22no—
61#450×C73—22no—
62#431×C73C2211yescharacteristic
63C2×#11924016—22no—
64C2×#11924016—22no—
65C2×#11924016—22no—
66C2×#11924016—22no—
67#14556591C2311yescharacteristic
68#14556591C2311yescharacteristic
69#14556591C2311yescharacteristic
70#14556591C2311yescharacteristic
71#14556583—21no—
72#14556583—21no—
73#14556570—21no—
74#14556570—21no—
75#14556570—21no—
76#14556570—21no—
77C4×Dic146—21no—
78C4×Dic146—21no—
79C4×Dic146—21no—
80C4×Dic146—21no—
81#14556550—21no—
82#14556550—21no—
83#14556525—22no—
84#14556524—22no—
85#14556524—22no—
86#14556523—22no—
87#14556522—22no—
88#14556522—22no—
89C4⋊#10596831D412yes—
90C4⋊#10596831D412yes—
91#14556516—22no—
92#14556516—22no—
93#14556515—22no—
94#14556515—22no—
95#14556514—22no—
96#14556514—22no—
97#14556512—22no—
98#14556512—22no—
99#14556512—22no—
100#14556512—22no—
101C22⋊#10596831D412yes—
102C22⋊#10596831D412yes—
103C4×#10596831C2311yescharacteristic
104C4×#10596831C2311yescharacteristic
105C4×#10596831C2311yescharacteristic
106C4×#10596831C2311yescharacteristic
107C22×D4×C73—21no—
108C22×D4×C73—21no—
109C22×D4×C73—21no—
110C2×SD16×C73—22no—
111C2×SD16×C73—22no—
112C4⋊Q8×C73C2311yescharacteristic
113C4⋊Q8×C73C2311yescharacteristic
114#127×C73—21no—
115#127×C73—21no—
116#127×C73—21no—
117#127×C73C2311yescharacteristic
118#127×C73C2311yescharacteristic
119#125×C73—21no—
120C22⋊Q8×C73—21no—
121C22⋊Q8×C73—21no—
122C4×Q8×C73—21no—
123C4×Q8×C73—21no—
124#117×C73—21no—
125C2×C42×C73C2311yescharacteristic
126C4⋊C8×C73D412yes—
127#102×C73—22no—
128#102×C73—22no—
129C22⋊C8×C73D412yes—
130C4×C8×C73C2311yescharacteristic
131C4×C8×C73C2311yescharacteristic
132C2×Dic146—21no—
133C2×Dic146—21no—
134C2×Dic146—21no—
135C2×Dic146—21no—
136#11924016—82no—
137#11924016—82no—
138#11924016—82no—
139#11924016—82no—
140C2×#10596831C2×D412yes—
141C2×#10596831C2×D412yes—
142C2×#10596831C2×D412yes—
143C2×#10596831C2×D412yes—
144C4⋊Dic73—21no—
145C4⋊Dic73—21no—
146C4⋊Dic73—21no—
147C4⋊Dic73—21no—
148C4⋊Dic73—21no—
149C4⋊Dic73—21no—
150C4⋊Dic73—21no—
151C4⋊Dic73—21no—
152#11924007—41no—
153#11924007—41no—
154#11924007—41no—
155#11924007—41no—
156C22⋊Dic73—41no—
157C22⋊Dic73—41no—
158C4×Dic73—41no—
159C4×Dic73—41no—
160C24×C73—41no—
161C2×Q8×C73—21no—
162C2×Q8×C73—21no—
163C2×D4×C73—21no—
164C2×D4×C73—21no—
165C2×D4×C73—21no—
166C2×D4×C73—21no—
167C2×D4×C73—21no—
168C2×D4×C73—21no—
169C2×D4×C73—41no—
170C2×D4×C73—41no—
171C2×D4×C73—41no—
172C2×D4×C73—82no—
173C2×D4×C73—82no—
174C2×D4×C73—82no—
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D411yescharacteristic
178SD16×C73—82no—
179SD16×C73—82no—
180C2×C8×C73C2×D412yes—
181C2×C8×C73C2×D412yes—
182C4⋊C4×C73—21no—
183C4⋊C4×C73—21no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—41no—
187C4⋊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—82no—
197C23×C73—82no—
198C23×C73—82no—
199C23×C73#12711yescharacteristic
200Q8×C73—42no—
201Q8×C73—42no—
202D4×C73—42no—
203D4×C73—42no—
204D4×C73—42no—
205D4×C73—42no—
206D4×C73—42no—
207D4×C73—42no—
208D4×C73—82no—
209D4×C73—82no—
210D4×C73—82no—
211C2×C4×C73—22no—
212C2×C4×C73—22no—
213C2×C4×C73—22no—
214C2×C4×C73—41no—
215C2×C4×C73—41no—
216C2×C4×C73#12711yescharacteristic
217C2×C4×C73#12711yescharacteristic
218C2×C4×C73#12711yescharacteristic
219C2×C4×C73C22×D411yescharacteristic
220C2×C4×C73C22×D411yescharacteristic
221C2×C4×C73C22×D411yescharacteristic
222C2×Dic73—41no—
223C2×Dic73—41no—
224C2×Dic73—41no—
225C2×Dic73—41no—
226Dic146—42no—
227Dic146—42no—
228Dic146—42no—
229Dic146—42no—
230C8×C73—22no—
231C8×C73—22no—
232#10596831—22no—
233#10596831—22no—
234#10596831—22no—
235#10596831—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×C73—164no—
246C22×C73C2×#12711yescharacteristic
247C4×C73—21no—
248C4×C73—21no—
249C4×C73—21no—
250C4×C73—81no—
251C4×C73—81no—
252C4×C73#57712yes—
253C4×C73#57712yes—
254C4×C73#57712yes—
255Dic73—81no—
256Dic73—81no—
257Dic73—81no—
258Dic73—81no—
259#19733—731nomaximal, Sylow
260C2×C73—41no—
261C2×C73—161no—
262C2×C73—161no—
263C2×C73#315411yescharacteristic
264C2×C73#315411yescharacteristic
265C2×C73#315411yescharacteristic
266#3231—731no—
267#3231—731no—
268#3231—731no—
269#3208—731no—
270#3208—731no—
271#3208D7311yescharacteristic
272#1719—731no—
273#1719—731no—
274#1719—731no—
275#1714—731no—
276#1714—731no—
277#1714—731no—
278#1711—731no—
279#1705—731no—
280#1454—731no—
281C73#1973311yescharacteristic, complemented, Sylow
282#533—731no—
283#533—731no—
284#533C2×D7311yescharacteristic
285C2×#127C2×D7311yescharacteristic
286#500—731no—
287#500—731no—
288#500—731no—
289#498—731no—
290#498—731no—
291#498—731no—
292#492—731no—
293#492—731no—
294#492—731no—
295#492—731no—
296#492C2×D7311yescharacteristic
297#492C2×D7311yescharacteristic
298#487—731no—
299#487—731no—
300#487—731no—
301#487—731no—
302#487—731no—
303#487—731no—
304#486—731no—
305#486—731no—
306#486—731no—
307#486—731no—
308#486C2×D7311yescharacteristic
309#486C2×D7311yescharacteristic
310#485—1462no—
311#485—1462no—
312#485—1462no—
313#479—1462no—
314#479—1462no—
315#479—1462no—
316#460—22no—
317#460—1462no—
318#460—1462no—
319#450—22no—
320#450—1462no—
321#450—1462no—
322#431—731no—
323#431—731no—
324#431C2×D7311yescharacteristic
325#322—731no—
326#322—731no—
327#322—731no—
328C82—731no—
329C22×D4—21no—
330C22×D4—21no—
331C22×D4—21no—
332C2×SD16—22no—
333C2×SD16—22no—
334C2×SD16—1462no—
335C2×SD16—1462no—
336C2×SD16—1462no—
337C2×SD16—1462no—
338C4⋊Q8—731no—
339C4⋊Q8—731no—
340C4⋊Q8—731no—
341C4⋊Q8—731no—
342C4⋊Q8C22×D7311yescharacteristic
343C4⋊Q8C22×D7311yescharacteristic
344#127—21no—
345#127—21no—
346#127—21no—
347#127C22×D7311yescharacteristic
348#127C22×D7311yescharacteristic
349#125—21no—
350#125—1461no—
351#125—1461no—
352C22⋊Q8—21no—
353C22⋊Q8—21no—
354C22⋊Q8—1461no—
355C22⋊Q8—1461no—
356C22⋊Q8—1461no—
357C22⋊Q8—1461no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—1461no—
361C4×Q8—1461no—
362C4×Q8—1461no—
363C4×Q8—1461no—
364#117—21no—
365#117—1461no—
366#117—1461no—
367C2×C42C22×D7311yescharacteristic
368#107—1462no—
369#107—1462no—
370#107—1462no—
371#106—1462no—
372#106—1462no—
373#106—1462no—
374C4⋊C8—732no—
375C4⋊C8—732no—
376C4⋊C8C22⋊D7312yes—
377#103—1462no—
378#103—1462no—
379#103—1462no—
380#103—1462no—
381#103—1462no—
382#103—1462no—
383#102—22no—
384#102—22no—
385#102—1462no—
386#102—1462no—
387#102—1462no—
388#102—1462no—
389C22⋊C8—732no—
390C22⋊C8—732no—
391C22⋊C8C22⋊D7312yes—
392C4×C8—731no—
393C4×C8—731no—
394C4×C8—731no—
395C4×C8—731no—
396C4×C8C22×D7311yescharacteristic
397C4×C8C22×D7311yescharacteristic
398C24—41no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—1461no—
402C2×Q8—1461no—
403C2×Q8—1461no—
404C2×Q8—1461no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—82no—
415C2×D4—82no—
416C2×D4—82no—
417C22×C4D4×D7311yescharacteristic
418C22×C4D4×D7311yescharacteristic
419C22×C4C2×C22⋊D7311yescharacteristic
420SD16—82no—
421SD16—82no—
422SD16—5842no—
423SD16—5842no—
424SD16—5842no—
425SD16—5842no—
426C2×C8—732no—
427C2×C8—732no—
428C2×C8—732no—
429C2×C8—732no—
430C2×C8C2×C22⋊D7312yes—
431C2×C8C2×C22⋊D7312yes—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—41no—
437C4⋊C4—41no—
438C4⋊C4—2921no—
439C4⋊C4—2921no—
440C4⋊C4—2921no—
441C4⋊C4—2921no—
442C4⋊C4—1461no—
443C4⋊C4—1461no—
444C4⋊C4—1461no—
445C4⋊C4—1461no—
446C4⋊C4—1461no—
447C4⋊C4—1461no—
448C4⋊C4—1461no—
449C4⋊C4—1461no—
450C22⋊C4—41no—
451C22⋊C4—2921no—
452C22⋊C4—2921no—
453C42—41no—
454C42—2921no—
455C42—2921no—
456C42D4×D7311yescharacteristic
457C42D4×D7311yescharacteristic
458C42C2×C22⋊D7311yescharacteristic
459C42C23×D7311yescharacteristic
460C23—41no—
461C23—41no—
462C23—82no—
463C23—82no—
464C23—82no—
465C23#1455658711yescharacteristic
466Q8—42no—
467Q8—42no—
468Q8—2922no—
469Q8—2922no—
470Q8—2922no—
471Q8—2922no—
472D4—42no—
473D4—42no—
474D4—42no—
475D4—42no—
476D4—42no—
477D4—42no—
478D4—82no—
479D4—82no—
480D4—82no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—2921no—
487C2×C4—2921no—
488C2×C4—2921no—
489C2×C4—2921no—
490C2×C4#1455658711yescharacteristic
491C2×C4#1455658711yescharacteristic
492C2×C4#1455658711yescharacteristic
493C2×C4C2×D4×D7311yescharacteristic
494C2×C4C2×D4×D7311yescharacteristic
495C2×C4C22×C22⋊D7311yescharacteristic
496C8—22no—
497C8—22no—
498C8—1462no—
499C8—1462no—
500C8—1462no—
501C8—1462no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—164no—
512C22C2×#1455658711yescharacteristic
513C4—21no—
514C4—21no—
515C4—21no—
516C4—81no—
517C4—81no—
518C4—5841no—
519C4—5841no—
520C4—5841no—
521C4—5841no—
522C4#1798939312yes—
523C4#1798939712yes—
524C4#1798939812yes—
525C2—41no—
526C2—161no—
527C2—161no—
528C2#2262040111yescharacteristic
529C2#2262040311yescharacteristic
530C2#2262040511yescharacteristic
subgroupG/H
centerC22C2×#14556587
commutator, cosocleC42×C73C24
FrattiniC42C23×D73
FittingC73×#3208C2
socleC22×C73C2×#127
prime radicalC2×#127×C73C22
hypercenter#3208D73
hypocenterC73#19733
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3208

Complements

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

NH ≅ G/Ntype
1. #22621092C2semidirect
2. #22621090C2semidirect
3. #22621086C2semidirect
6. #22609583C2semidirect
7. #22609582C2semidirect
8. #22609581C2semidirect
9. #22609552C2semidirect
10. #22609551C2semidirect
11. #22609550C2semidirect
12. #22609542C2semidirect
13. #22609517C2semidirect
14. #22608231C2semidirect
18. #17988992C22semidirect
19. #17988990C22semidirect
20. #17988990C22semidirect
21. #17988985C22semidirect
22. #17988983C22semidirect
23. #17988983C22semidirect
28. #17988939C22semidirect
29. #17988939C22semidirect
30. #17988938C22semidirect
31. #17988938C22semidirect
32. #17988937C22semidirect
33. #17988937C22semidirect
50. #17988309C22semidirect
51. #17988309C22semidirect
52. #17988308C22semidirect
53. C8×#10596831C22semidirect
281. C73#19733semidirect

Maximal subgroups

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

subgroupindex
#226210922
#226210902
#226210862
#226208722
#226095832
#226095822
#226095812
#226095522
#226095512
#226095502
#226095422
#226095172
#226082312
C73×#32082
#1973373