Finite Group Databasebeta

← #33056142

Subgroups — #33056142

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#22619949C211yesmaximal, characteristic
2#22619076C211yesmaximal, characteristic, complemented
3#22619042C211yesmaximal, characteristic, complemented
4#22608806C211yesmaximal, characteristic, complemented
5#22608785C211yesmaximal, characteristic, complemented
6#22608778C211yesmaximal, characteristic, complemented
7#22608757C211yesmaximal, characteristic, complemented
8#22608746C211yesmaximal, characteristic, complemented
9#22608740C211yesmaximal, characteristic, complemented
10#22608735C211yesmaximal, characteristic, complemented
11#22608723C211yesmaximal, characteristic, complemented
12#22608707C211yesmaximal, characteristic, complemented
13#22608345C211yesmaximal, characteristic, complemented
14#22608228C211yesmaximal, characteristic, complemented
15C73×#1489C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17#17988928C411yescharacteristic
18#17988911C411yescharacteristic
19#17988894C411yescharacteristic
20#17988887C411yescharacteristic
21#17988809C411yescharacteristic
22#17988802C411yescharacteristic
23#17988749C411yescharacteristic
24#17988732C411yescharacteristic
25#17988714C2211yescharacteristic
26Q8×#10596831C2211yescharacteristic
27Q8×#10596831C2211yescharacteristic
28#17988711C2211yescharacteristic
29C4×#11924018C2211yescharacteristic
30C4×#11924015C2211yescharacteristic
31C4×#11924016C2211yescharacteristic
32C4×#11924013C2211yescharacteristic
33#17988664C2211yescharacteristic
34#17988663—21no—
35#17988656—21no—
36D4×#10596831—21no—
37D4×#10596831—21no—
38D4×#10596831C2211yescharacteristic
39D4×#10596831C2211yescharacteristic
40#17988652C2211yescharacteristic
41#17988647—21no—
42#17988640—21no—
43#17988640C2211yescharacteristic
44#17988640C2211yescharacteristic
45#17988612—21no—
46C2×C4⋊#10596831—21no—
47C2×C4⋊#10596831C2211yescharacteristic
48#17988339C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988339C2211yescharacteristic
51#17988339C2211yescharacteristic
52#17988319C2211yescharacteristic
53#17988319C2211yescharacteristic
54#17988316C2211yescharacteristic
55#17988316C2211yescharacteristic
56#17988309C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988308C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60C4×#41×C73C2211yescharacteristic
61#423×C73C2211yescharacteristic
62C4×M16×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66D4⋊C8×C73C2211yescharacteristic
67C2×#11924018C2×C411yescharacteristic
68C2×#11924016C2×C411yescharacteristic
69C2×#11924015C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71C2×#11924011—21no—
72C22×#10596831—21no—
73C22×#10596831—21no—
74C22×#10596831—21no—
75C2×C8×D73—21no—
76#14556585—21no—
77#14556583C2×C411yescharacteristic
78#14556579C2×C411yescharacteristic
79#14556574—21no—
80#14556570C2×C411yescharacteristic
81#14556565C2×C411yescharacteristic
82C4×Dic146C2311yescharacteristic
83C4×D292C2311yescharacteristic
84C4×C22⋊D73—21no—
85#14556548—21no—
86#14556524C2×C411yescharacteristic
87#14556524C2×C411yescharacteristic
88#14556522C2×C411yescharacteristic
89#14556522C2×C411yescharacteristic
90C4⋊#10596831—21no—
91C4⋊#10596831—21no—
92C4⋊#10596831—21no—
93C4⋊#10596831C2×C411yescharacteristic
94C4⋊#10596831C2×C411yescharacteristic
95C4⋊#10596831D411yescharacteristic
96C4⋊#10596831D411yescharacteristic
97C4⋊#10596831C2311yescharacteristic
98C4⋊#10596831C2311yescharacteristic
99#14556520—21no—
100#14556520—21no—
101#14556515C2×C411yescharacteristic
102#14556515C2×C411yescharacteristic
103#14556514C2×C411yescharacteristic
104#14556514C2×C411yescharacteristic
105#14556512C2×C411yescharacteristic
106#14556512C2×C411yescharacteristic
107#14556511C2×C411yescharacteristic
108#14556511C2×C411yescharacteristic
109C22⋊#10596831—21no—
110C22⋊#10596831—21no—
111C22⋊#10596831C2×C411yescharacteristic
112C22⋊#10596831C2×C411yescharacteristic
113C22⋊#10596831D411yescharacteristic
114C22⋊#10596831D411yescharacteristic
115#14556503—21no—
116#14556503—21no—
117#14556501—21no—
118C4×#10596831—21no—
119C4×#10596831—21no—
120C4×#10596831C2311yescharacteristic
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C8×Dic73—21no—
125C2×#41×C73C2×C411yescharacteristic
126C2×M16×C73—21no—
127C2×M16×C73—21no—
128C4×Q8×C73C2×C411yescharacteristic
129C4×Q8×C73C2311yescharacteristic
130C4×D4×C73—21no—
131C4×D4×C73—21no—
132C4×D4×C73C2×C411yescharacteristic
133C4×D4×C73C2311yescharacteristic
134#117×C73—21no—
135#117×C73C2×C411yescharacteristic
136C2×C42×C73—21no—
137C2×C42×C73C2311yescharacteristic
138C4⋊C8×C73—21no—
139C4⋊C8×C73C2311yescharacteristic
140C4⋊C8×C73C2311yescharacteristic
141#97×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146C22×C411yescharacteristic
145C2×D292C22×C411yescharacteristic
146C2×C22⋊D73—21no—
147C2×C4×D73—21no—
148#11924018—22no—
149#11924016—22no—
150#11924015—22no—
151#11924013—22no—
152#11924011—81no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831—81no—
156C2×#10596831—81no—
157C2×#10596831—81no—
158C2×#10596831C22×C411yescharacteristic
159C2×#10596831C22×C411yescharacteristic
160C2×#10596831C22×C411yescharacteristic
161C2×#10596831C22×C411yescharacteristic
162C2×#10596831C2×D411yescharacteristic
163C2×#10596831C2×D411yescharacteristic
164C2×#10596831C2×D411yescharacteristic
165C2×#10596831C2×D411yescharacteristic
166C8×D73—81no—
167C4⋊Dic73C22×C411yescharacteristic
168C4⋊Dic73C22×C411yescharacteristic
169#11924007—21no—
170#11924007—21no—
171#11924007—21no—
172#11924007—21no—
173C22⋊Dic73—21no—
174#11924005—21no—
175#11924005—21no—
176#11924005—21no—
177#11924005—21no—
178C4×Dic73—21no—
179#41×C73—22no—
180#41×C73—22no—
181C2×Q8×C73C22×C411yescharacteristic
182C2×D4×C73—21no—
183C2×D4×C73C22×C411yescharacteristic
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73C22×C411yescharacteristic
188C22×C4×C73C2×D411yescharacteristic
189C22×C4×C73#4111yescharacteristic
190M16×C73—42no—
191M16×C73—81no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×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—
203C42×C73—21no—
204C42×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#13112yes—
215D4×C73—24no—
216D4×C73—21no—
217D4×C73#13112yes—
218C2×C4×C73—24no—
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—21no—
226C2×C4×C73—41no—
227C2×C4×C73—41no—
228C2×C4×C73—41no—
229C2×C4×C73—81no—
230C2×C4×C73C4×D411yescharacteristic
231C2×C4×C73C4×D411yescharacteristic
232C2×C4×C73C4×D411yescharacteristic
233C2×C4×C73C23×C411yescharacteristic
234C2×C4×C73C22×D411yescharacteristic
235C2×C4×C73C2×#4111yescharacteristic
236C22⋊D73—81no—
237C2×Dic73—21no—
238C2×Dic73—21no—
239C2×Dic73—21no—
240D292—21no—
241D292—21no—
242C4×D73—41no—
243C4×D73—41no—
244Dic146—21no—
245Dic146—21no—
246C8×C73—22no—
247C8×C73—41no—
248C8×C73—41no—
249C8×C73—41no—
250#10596831—21no—
251#10596831—21no—
252#10596831—21no—
253#10596831—21no—
254#10596831—21no—
255#10596831—21no—
256#10596831—21no—
257#10596831—21no—
258#10596831—41no—
259#10596831—41no—
260C22×C73—21no—
261C22×C73—22no—
262C22×C73—21no—
263C22×C73—21no—
264C22×C73—41no—
265C22×C73—41no—
266C22×C73C2×C4×D411yescharacteristic
267C2×D73—41no—
268C2×D73—41no—
269C2×D73—41no—
270C4×C73—21no—
271C4×C73—22no—
272C4×C73—21no—
273C4×C73—21no—
274C4×C73—21no—
275C4×C73—41no—
276C4×C73—41no—
277C4×C73C2×#13111yescharacteristic
278C4×C73C2×#13111yescharacteristic
279C4×C73#57611yescharacteristic
280C4×C73#57811yescharacteristic
281Dic73—41no—
282Dic73—41no—
283Dic73—41no—
284#17926—731nomaximal, Sylow
285C2×C73—41no—
286C2×C73—42no—
287C2×C73#292911yescharacteristic
288C2×C73#295111yescharacteristic
289C2×C73#295611yescharacteristic
290D73—81no—
291#3102—731no—
292#2993—731no—
293#2988—731no—
294#1588—731no—
295#1585—731no—
296#1584—731no—
297#1581—731no—
298SD16⋊C8—731no—
299SD16⋊C8—731no—
300C8×Q16—731no—
301C8×D8—731no—
302#1571—731no—
303#1489D7311yescharacteristic, complemented
304#1483—731no—
305#1453—731no—
306C73#1792611yescharacteristic, complemented, Sylow
307#529—731no—
308C4×#41C2×D7311yescharacteristic
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#446—731no—
318C8×Q8—731no—
319C8×Q8—731no—
320C8×Q8—731no—
321C4×Q16—731no—
322C4×SD16—731no—
323C4×SD16—731no—
324C4×D8—731no—
325#436—731no—
326#436—1461no—
327#435—1461no—
328C8×D4—731no—
329C8×D4—731no—
330C8×D4—731no—
331C8×D4—1461no—
332C8×D4—1461no—
333#433—1461no—
334#431—731no—
335#431—731no—
336#431—1461no—
337#424—1461no—
338#423C2×D7311yescharacteristic
339C2×C4⋊C8—731no—
340C2×C4⋊C8—1461no—
341C4×M16C2×D7311yescharacteristic
342#335—731no—
343#335—731no—
344#335—731no—
345#335—731no—
346Q8⋊C8—731no—
347Q8⋊C8—731no—
348Q8⋊C8C2×D7311yescharacteristic
349Q8⋊C8C2×D7311yescharacteristic
350D4⋊C8—731no—
351D4⋊C8—731no—
352D4⋊C8C2×D7311yescharacteristic
353D4⋊C8C2×D7311yescharacteristic
354#322—731no—
355#322—731no—
356#322—731no—
357C82—731no—
358C2×#41C4×D7311yescharacteristic
359C2×Q16—731no—
360C2×SD16—731no—
361C2×SD16—731no—
362C2×D8—731no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—1461no—
366C22×C8—1461no—
367C22×C8—1461no—
368C22×C8—1461no—
369C22×C8—1461no—
370#126—1461no—
371#125—731no—
372#124—731no—
373#123—1461no—
374C22⋊Q8—731no—
375#121—731no—
376C4×Q8—731no—
377C4×Q8C4×D7311yescharacteristic
378C4×Q8C22×D7311yescharacteristic
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—731no—
382C4×D4—1461no—
383C4×D4C4×D7311yescharacteristic
384C4×D4C22×D7311yescharacteristic
385#117—21no—
386#117—1461no—
387#117C4×D7311yescharacteristic
388C2×C42—21no—
389C2×C42C22×D7311yescharacteristic
390#107—731no—
391#107—731no—
392#106—731no—
393#106—731no—
394C4⋊C8—21no—
395C4⋊C8—731no—
396C4⋊C8—731no—
397C4⋊C8—731no—
398C4⋊C8—731no—
399C4⋊C8—731no—
400C4⋊C8—731no—
401C4⋊C8—1461no—
402C4⋊C8—1461no—
403C4⋊C8—1461no—
404C4⋊C8—1461no—
405C4⋊C8—1461no—
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—731no—
417C22⋊C8—731no—
418C22⋊C8—731no—
419C22⋊C8—731no—
420C22⋊C8—1461no—
421C22⋊C8—1461no—
422C22⋊C8—1461no—
423C22⋊C8—1461no—
424#97—21no—
425#97—1461no—
426C4×C8—731no—
427C4×C8—731no—
428C4×C8—731no—
429C4×C8—731no—
430C4×C8—1461no—
431C4×C8—1461no—
432C4×C8—1461no—
433C4×C8C22×D7311yescharacteristic
434C4×C8C22×D7311yescharacteristic
435#41—22no—
436#41—22no—
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—21no—
445C22×C4—21no—
446C22×C4—1461no—
447C22×C4C2×C4×D7311yescharacteristic
448C22×C4D4×D7311yescharacteristic
449C22×C4#1192402711yescharacteristic
450Q16—1462no—
451SD16—1462no—
452SD16—1462no—
453D8—1462no—
454M16—42no—
455M16—81no—
456M16—5841no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—5841no—
462C2×C8—5841no—
463C2×C8—5841no—
464C2×C8—5841no—
465C2×C8—731no—
466C2×C8—731no—
467C2×C8—731no—
468C2×C8—731no—
469C2×C8—731no—
470C2×C8—731no—
471C2×C8—731no—
472C2×C8—731no—
473C2×C8—1461no—
474C2×C8—1461no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—731no—
478C4⋊C4—731no—
479C4⋊C4—1461no—
480C4⋊C4—1461no—
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—1461no—
489C22⋊C4—1461no—
490C22⋊C4—1461no—
491C22⋊C4—1461no—
492C22⋊C4—1461no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—1461no—
497C42C2×C4×D7311yescharacteristic
498C42D4×D7311yescharacteristic
499C42#1192402711yescharacteristic
500C42C23×D7311yescharacteristic
501C23—21no—
502C23—1461no—
503C23#1455655111yescharacteristic
504Q8—21no—
505Q8—1461no—
506Q8—1461no—
507Q8#1455659912yes—
508D4—24no—
509D4—21no—
510D4—5841no—
511D4—1461no—
512D4—1461no—
513D4#1455659912yes—
514C2×C4—24no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—81no—
526C2×C4—2921no—
527C2×C4—2921no—
528C2×C4—1461no—
529C2×C4—1461no—
530C2×C4—1461no—
531C2×C4#1455655111yescharacteristic
532C2×C4#1455655111yescharacteristic
533C2×C4#1455655111yescharacteristic
534C2×C4C22×C4×D7311yescharacteristic
535C2×C4C2×D4×D7311yescharacteristic
536C2×C4C2×#1192402711yescharacteristic
537C8—22no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—2921no—
542C8—2921no—
543C8—1461no—
544C8—1461no—
545C8—1461no—
546C8—1461no—
547C8—1461no—
548C8—1461no—
549C8—1461no—
550C8—1461no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—22no—
555C22—41no—
556C22—41no—
557C22—2921no—
558C22—2921no—
559C22—2921no—
560C22C2×#1455655111yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—22no—
566C4—41no—
567C4—41no—
568C4—2921no—
569C4—2921no—
570C4—2921no—
571C4C2×#1455659911yescharacteristic
572C4C2×#1455659911yescharacteristic
573C4#1798939111yescharacteristic
574C4#1798940311yescharacteristic
575C2—41no—
576C2—42no—
577C2—5841no—
578C2#2261862111yescharacteristic
579C2#2261880211yescharacteristic
580C2#2261883711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1489C2
socleC22×C73C2×C4×D4
prime radical#17988732C4
cosocleC42×C73C24
hypercenter#1489D73
hypocenterC73#17926
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1489

Complements

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

NH ≅ G/Ntype
2. #22619076C2semidirect
3. #22619042C2semidirect
4. #22608806C2semidirect
5. #22608785C2semidirect
6. #22608778C2semidirect
7. #22608757C2semidirect
8. #22608746C2semidirect
9. #22608740C2semidirect
10. #22608735C2semidirect
11. #22608723C2semidirect
12. #22608707C2semidirect
13. #22608345C2semidirect
14. #22608228C2semidirect
15. C73×#1489C2semidirect
303. #1489D73semidirect
306. C73#17926semidirect

Maximal subgroups

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

subgroupindex
#226199492
#226190762
#226190422
#226088062
#226087852
#226087782
#226087572
#226087462
#226087402
#226087352
#226087232
#226087072
#226083452
#226082282
C73×#14892
#1792673