Finite Group Databasebeta

← #33056159

Subgroups — #33056159

Order 18688.

620 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619943C211yesmaximal, characteristic
2#22619039C211yesmaximal, characteristic, complemented
3#22608800C211yesmaximal, characteristic, complemented
4#22608793C211yesmaximal, characteristic, complemented
5#22608772C211yesmaximal, characteristic, complemented
6#22608765C211yesmaximal, characteristic, complemented
7#22608753C211yesmaximal, characteristic, complemented
8#22608748C211yesmaximal, characteristic, complemented
9C8×#11924015C211yesmaximal, characteristic, complemented
10C8×#11924016C211yesmaximal, characteristic, complemented
11#22608703C211yesmaximal, characteristic, complemented
12#22608368C211yesmaximal, characteristic, complemented
13#22608344C211yesmaximal, characteristic, complemented
14#22608226C211yesmaximal, characteristic, complemented
15C73×#2993C211yesmaximal, characteristic, complemented
16C4×#11924028C2211yescharacteristic
17#17988925C411yescharacteristic
18#17988908C411yescharacteristic
19#17988891C411yescharacteristic
20#17988884C411yescharacteristic
21#17988806C411yescharacteristic
22#17988799C411yescharacteristic
23#17988747C411yescharacteristic
24#17988730C411yescharacteristic
25C8×Dic146C2211yescharacteristic
26C8×Dic146C2211yescharacteristic
27C4×#11924018C2211yescharacteristic
28C4×#11924015C2211yescharacteristic
29C4×#11924016C2211yescharacteristic
30C4×#11924013C2211yescharacteristic
31C8×D292C2211yescharacteristic
32C8×D292C2211yescharacteristic
33#17988650—21no—
34#17988650—21no—
35#17988640C2211yescharacteristic
36#17988639—21no—
37C2×C4⋊#10596831C2211yescharacteristic
38C4⋊C8×D73—21no—
39C4×#11924012C2211yescharacteristic
40#17988337C2211yescharacteristic
41#17988337C2211yescharacteristic
42#17988337C2211yescharacteristic
43#17988337C2211yescharacteristic
44Q8⋊#10596831C2211yescharacteristic
45Q8⋊#10596831C2211yescharacteristic
46#17988317C2211yescharacteristic
47#17988317C2211yescharacteristic
48D4⋊#10596831C2211yescharacteristic
49D4⋊#10596831C2211yescharacteristic
50#17988314C2211yescharacteristic
51#17988314C2211yescharacteristic
52#17988309C2211yescharacteristic
53#17988309C2211yescharacteristic
54#17988308C2211yescharacteristic
55C8×#10596831C2211yescharacteristic
56#529×C73C2211yescharacteristic
57#446×C73C2211yescharacteristic
58C8×Q8×C73C2211yescharacteristic
59#436×C73—21no—
60#436×C73C2211yescharacteristic
61#435×C73—21no—
62C8×D4×C73C2211yescharacteristic
63#433×C73—21no—
64#431×C73C2211yescharacteristic
65#424×C73—21no—
66#423×C73C2211yescharacteristic
67C2×#11924028C2×C411yescharacteristic
68C2×#11924018C2×C411yescharacteristic
69C2×#11924016C2×C411yescharacteristic
70C2×#11924015C2×C411yescharacteristic
71C2×#11924013C2×C411yescharacteristic
72C2×#11924012—21no—
73C22×#10596831—21no—
74C2×C8×D73—21no—
75C2×C8×D73—21no—
76C4×Dic146C2×C411yescharacteristic
77C4×Dic146C2311yescharacteristic
78C4×D292C2×C411yescharacteristic
79C4×D292C2311yescharacteristic
80C4×C22⋊D73—21no—
81C4×C22⋊D73—21no—
82#14556550C2×C411yescharacteristic
83#14556548—21no—
84C42×D73—21no—
85#14556524C2×C411yescharacteristic
86#14556524C2×C411yescharacteristic
87#14556522C2×C411yescharacteristic
88#14556522C2×C411yescharacteristic
89C4⋊#10596831—21no—
90C4⋊#10596831C2×C411yescharacteristic
91C4⋊#10596831C2×C411yescharacteristic
92C4⋊#10596831C2311yescharacteristic
93C4⋊#10596831C2311yescharacteristic
94#14556520—21no—
95#14556520—21no—
96#14556515C2×C411yescharacteristic
97#14556515C2×C411yescharacteristic
98#14556514C2×C411yescharacteristic
99#14556514C2×C411yescharacteristic
100#14556512C2×C411yescharacteristic
101#14556512C2×C411yescharacteristic
102#14556511C2×C411yescharacteristic
103#14556511C2×C411yescharacteristic
104C22⋊#10596831C2×C411yescharacteristic
105C22⋊#10596831C2×C411yescharacteristic
106#14556503—21no—
107#14556503—21no—
108#14556502—21no—
109C4×#10596831C2311yescharacteristic
110C4×#10596831C2311yescharacteristic
111C4×#10596831C2311yescharacteristic
112C4×#10596831C2311yescharacteristic
113C8×Dic73—21no—
114C8×Dic73—21no—
115C2×M16×C73—21no—
116C2×M16×C73—21no—
117C22×C8×C73—21no—
118#126×C73—21no—
119#125×C73C2×C411yescharacteristic
120#124×C73C2×C411yescharacteristic
121#123×C73—21no—
122C22⋊Q8×C73C2×C411yescharacteristic
123#121×C73C2×C411yescharacteristic
124C4×Q8×C73C2311yescharacteristic
125C4×D4×C73—21no—
126C4×D4×C73C2311yescharacteristic
127#117×C73—21no—
128C2×C42×C73C2311yescharacteristic
129C4⋊C8×C73—21no—
130C4⋊C8×C73—21no—
131C4⋊C8×C73—21no—
132C4⋊C8×C73D411yescharacteristic
133C4⋊C8×C73D411yescharacteristic
134C4⋊C8×C73C2311yescharacteristic
135C4⋊C8×C73C2311yescharacteristic
136C22⋊C8×C73—21no—
137C22⋊C8×C73—21no—
138C22⋊C8×C73D411yescharacteristic
139C22⋊C8×C73D411yescharacteristic
140#97×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924028—22no—
145#11924028—22no—
146C2×Dic146C22×C411yescharacteristic
147C2×D292C22×C411yescharacteristic
148C2×C22⋊D73—21no—
149C2×C4×D73—21no—
150C2×C4×D73—21no—
151C2×C4×D73—21no—
152#11924018—22no—
153#11924016—22no—
154#11924015—22no—
155#11924013—22no—
156#11924012—42no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—81no—
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C22×C411yescharacteristic
164C2×#10596831C22×C411yescharacteristic
165C2×#10596831C22×C411yescharacteristic
166C8×D73—81no—
167C8×D73—81no—
168C4⋊Dic73C22×C411yescharacteristic
169C4⋊Dic73C22×C411yescharacteristic
170#11924007—21no—
171#11924007—21no—
172C22⋊Dic73—21no—
173#11924005—21no—
174#11924005—21no—
175C4×Dic73—21no—
176C4×Dic73—21no—
177C4×Dic73—21no—
178C2×Q8×C73C22×C411yescharacteristic
179C2×D4×C73—21no—
180C2×D4×C73C22×C411yescharacteristic
181C22×C4×C73—21no—
182C22×C4×C73C22×C411yescharacteristic
183C22×C4×C73C2×D411yescharacteristic
184C22×C4×C73#4111yescharacteristic
185M16×C73—81no—
186M16×C73—81no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73—81no—
190C2×C8×C73C2×D411yescharacteristic
191C2×C8×C73C2×D411yescharacteristic
192C2×C8×C73C2×D411yescharacteristic
193C2×C8×C73C2×D411yescharacteristic
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73C22×C411yescharacteristic
199C4⋊C4×C73C22×C411yescharacteristic
200C22⋊C4×C73—21no—
201C22⋊C4×C73—21no—
202C22⋊C4×C73—21no—
203C22⋊C4×C73—21no—
204C22⋊C4×C73—21no—
205C42×C73—21no—
206C42×C73C22×C411yescharacteristic
207C42×C73C2×D411yescharacteristic
208C42×C73#4111yescharacteristic
209C42×C73C2411yescharacteristic
210C23×C73—21no—
211C23×C73C4×D411yescharacteristic
212C22×D73—21no—
213Q8×C73—21no—
214Q8×C73—21no—
215D4×C73—21no—
216D4×C73—21no—
217D4×C73—81no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—41no—
226C2×C4×C73—41no—
227C2×C4×C73—41no—
228C2×C4×C73C4×D411yescharacteristic
229C2×C4×C73C4×D411yescharacteristic
230C2×C4×C73C4×D411yescharacteristic
231C2×C4×C73C23×C411yescharacteristic
232C2×C4×C73C22×D411yescharacteristic
233C2×C4×C73C2×#4111yescharacteristic
234C22⋊D73—24no—
235C2×Dic73—21no—
236C2×Dic73—21no—
237C2×Dic73—21no—
238D292—21no—
239D292#13112yes—
240C4×D73—24no—
241C4×D73—41no—
242C4×D73—41no—
243C4×D73—81no—
244Dic146—21no—
245Dic146#13112yes—
246C8×C73—21no—
247C8×C73—21no—
248C8×C73—21no—
249C8×C73—21no—
250C8×C73—41no—
251C8×C73—41no—
252#10596831—22no—
253#10596831—21no—
254#10596831—21no—
255#10596831—21no—
256#10596831—21no—
257#10596831—41no—
258#10596831—41no—
259#10596831—41no—
260C22×C73—21no—
261C22×C73—21no—
262C22×C73—21no—
263C22×C73—41no—
264C22×C73—41no—
265C22×C73—41no—
266C22×C73C2×C4×D411yescharacteristic
267C2×D73—22no—
268C2×D73—41no—
269C2×D73—41no—
270C4×C73—21no—
271C4×C73—21no—
272C4×C73—21no—
273C4×C73—21no—
274C4×C73—41no—
275C4×C73—41no—
276C4×C73—41no—
277C4×C73C2×#13111yescharacteristic
278C4×C73C2×#13111yescharacteristic
279C4×C73#57711yescharacteristic
280C4×C73#57711yescharacteristic
281Dic73—22no—
282Dic73—41no—
283Dic73—41no—
284#17927—731nomaximal, Sylow
285C2×C73—41no—
286C2×C73—81no—
287C2×C73#292911yescharacteristic
288C2×C73#295211yescharacteristic
289C2×C73#295611yescharacteristic
290D73—42no—
291#3102—731no—
292#2993D7311yescharacteristic, complemented
293#2988—731no—
294#1587—731no—
295#1586—731no—
296#1583—731no—
297#1582—731no—
298#1580—731no—
299#1579—731no—
300C8×SD16—731no—
301C8×SD16—731no—
302#1570—731no—
303#1489—731no—
304#1483—731no—
305#1453—731no—
306C73#1792711yescharacteristic, complemented, Sylow
307#529C2×D7311yescharacteristic
308C4×#41—731no—
309#485—731no—
310#482—731no—
311#479—731no—
312#478—731no—
313#464—731no—
314#463—731no—
315#452—731no—
316#449—731no—
317#446C2×D7311yescharacteristic
318C8×Q8—731no—
319C8×Q8—731no—
320C8×Q8C2×D7311yescharacteristic
321C4×Q16—731no—
322C4×SD16—731no—
323C4×SD16—731no—
324C4×D8—731no—
325#436—21no—
326#436C2×D7311yescharacteristic
327#435—21no—
328C8×D4—731no—
329C8×D4—731no—
330C8×D4—1461no—
331C8×D4—1461no—
332C8×D4C2×D7311yescharacteristic
333#433—21no—
334#431—731no—
335#431—1461no—
336#431C2×D7311yescharacteristic
337#424—21no—
338#423C2×D7311yescharacteristic
339C2×C4⋊C8—731no—
340C2×C4⋊C8—1461no—
341C4×M16—731no—
342#334—731no—
343#334—731no—
344#334—731no—
345#334—731no—
346Q8⋊C8—731no—
347Q8⋊C8—731no—
348Q8⋊C8—731no—
349Q8⋊C8—731no—
350D4⋊C8—731no—
351D4⋊C8—731no—
352D4⋊C8—731no—
353D4⋊C8—731no—
354#322—731no—
355#322—731no—
356#322—731no—
357C82—731no—
358C2×#41—731no—
359C2×Q16—731no—
360C2×SD16—731no—
361C2×SD16—731no—
362C2×D8—731no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—1461no—
366C22×C8—21no—
367C22×C8—1461no—
368C22×C8—1461no—
369C22×C8—1461no—
370#126—21no—
371#125C4×D7311yescharacteristic
372#124C4×D7311yescharacteristic
373#123—21no—
374C22⋊Q8C4×D7311yescharacteristic
375#121C4×D7311yescharacteristic
376C4×Q8—731no—
377C4×Q8—731no—
378C4×Q8C22×D7311yescharacteristic
379C4×D4—21no—
380C4×D4—731no—
381C4×D4—731no—
382C4×D4—1461no—
383C4×D4—1461no—
384C4×D4C22×D7311yescharacteristic
385#117—21no—
386#117—731no—
387#117—1461no—
388C2×C42—1461no—
389C2×C42C22×D7311yescharacteristic
390#107—731no—
391#107—731no—
392#106—731no—
393#106—731no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—731no—
398C4⋊C8—731no—
399C4⋊C8—731no—
400C4⋊C8—731no—
401C4⋊C8—1461no—
402C4⋊C8—1461no—
403C4⋊C8—1461no—
404C4⋊C8C22⋊D7311yescharacteristic
405C4⋊C8C22⋊D7311yescharacteristic
406C4⋊C8C22×D7311yescharacteristic
407C4⋊C8C22×D7311yescharacteristic
408#103—731no—
409#103—731no—
410#103—731no—
411#103—731no—
412#102—731no—
413#102—731no—
414#102—731no—
415#102—731no—
416C22⋊C8—21no—
417C22⋊C8—21no—
418C22⋊C8—731no—
419C22⋊C8—731no—
420C22⋊C8—1461no—
421C22⋊C8—1461no—
422C22⋊C8C22⋊D7311yescharacteristic
423C22⋊C8C22⋊D7311yescharacteristic
424#97—21no—
425#97—1461no—
426C4×C8—21no—
427C4×C8—731no—
428C4×C8—731no—
429C4×C8—731no—
430C4×C8—731no—
431C4×C8—1461no—
432C4×C8—1461no—
433C4×C8C22×D7311yescharacteristic
434C4×C8C22×D7311yescharacteristic
435#41—1462no—
436#41—1462no—
437C2×Q8—731no—
438C2×Q8C2×C4×D7311yescharacteristic
439C2×D4—21no—
440C2×D4—731no—
441C2×D4—1461no—
442C2×D4C2×C4×D7311yescharacteristic
443C22×C4—21no—
444C22×C4—1461no—
445C22×C4—1461no—
446C22×C4—1461no—
447C22×C4C2×C4×D7311yescharacteristic
448C22×C4C2×C22⋊D7311yescharacteristic
449C22×C4#1192402811yescharacteristic
450Q16—1462no—
451SD16—1462no—
452SD16—1462no—
453D8—1462no—
454M16—81no—
455M16—81no—
456M16—2922no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—81no—
460C2×C8—5841no—
461C2×C8—5841no—
462C2×C8—5841no—
463C2×C8—731no—
464C2×C8—731no—
465C2×C8—731no—
466C2×C8—731no—
467C2×C8—1461no—
468C2×C8—1461no—
469C2×C8—1461no—
470C2×C8—1461no—
471C2×C8C2×C22⋊D7311yescharacteristic
472C2×C8C2×C22⋊D7311yescharacteristic
473C2×C8C2×C22⋊D7311yescharacteristic
474C2×C8C2×C22⋊D7311yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—731no—
480C4⋊C4—731no—
481C4⋊C4—1461no—
482C4⋊C4—1461no—
483C4⋊C4C2×C4×D7311yescharacteristic
484C4⋊C4C2×C4×D7311yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—1461no—
491C22⋊C4—1461no—
492C22⋊C4—1461no—
493C42—21no—
494C42—1461no—
495C42—1461no—
496C42—1461no—
497C42C2×C4×D7311yescharacteristic
498C42C2×C22⋊D7311yescharacteristic
499C42#1192402811yescharacteristic
500C42C23×D7311yescharacteristic
501C23—21no—
502C23—1461no—
503C23C4×C22⋊D7311yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—732no—
507Q8—1461no—
508D4—21no—
509D4—21no—
510D4—81no—
511D4—732no—
512D4—1464no—
513D4—1461no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—2921no—
525C2×C4—2921no—
526C2×C4—5841no—
527C2×C4—1464no—
528C2×C4—1461no—
529C2×C4—1461no—
530C2×C4—1461no—
531C2×C4C4×C22⋊D7311yescharacteristic
532C2×C4C4×C22⋊D7311yescharacteristic
533C2×C4C4×C22⋊D7311yescharacteristic
534C2×C4C22×C4×D7311yescharacteristic
535C2×C4C22×C22⋊D7311yescharacteristic
536C2×C4C2×#1192402811yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—2921no—
544C8—2921no—
545C8—2921no—
546C8—1462no—
547C8—1461no—
548C8—1461no—
549C8—1461no—
550C8—1461no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—2921no—
558C22—2921no—
559C22—1462no—
560C22C2×C4×C22⋊D7311yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—2921no—
569C4—2921no—
570C4—1462no—
571C4#131×D7311yescharacteristic
572C4#131×D7311yescharacteristic
573C4#1798939511yescharacteristic
574C4#1798939811yescharacteristic
575C2—41no—
576C2—81no—
577C2—2922no—
578C2#2261862311yescharacteristic
579C2#2261881211yescharacteristic
580C2#2261883811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2993C2
socleC22×C73C2×C4×D4
prime radical#17988730C4
cosocleC42×C73C24
hypercenter#2993D73
hypocenterC73#17927
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #22619039C2semidirect
3. #22608800C2semidirect
4. #22608793C2semidirect
5. #22608772C2semidirect
6. #22608765C2semidirect
7. #22608753C2semidirect
8. #22608748C2semidirect
9. C8×#11924015C2semidirect
10. C8×#11924016C2semidirect
11. #22608703C2semidirect
12. #22608368C2semidirect
13. #22608344C2semidirect
14. #22608226C2semidirect
15. C73×#2993C2semidirect
292. #2993D73semidirect
306. C73#17927semidirect

Maximal subgroups

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

subgroupindex
#226199432
#226190392
#226088002
#226087932
#226087722
#226087652
#226087532
#226087482
C8×#119240152
C8×#119240162
#226087032
#226083682
#226083442
#226082262
C73×#29932
#1792773