Finite Group Databasebeta

← #33055242

Subgroups — #33055242

Order 18688.

588 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618893C211yesmaximal, characteristic
2#22618596C211yesmaximal, characteristic
3#22618592C211yesmaximal, characteristic
4#22608721C211yesmaximal, characteristic, complemented
5#22608719C211yesmaximal, characteristic, complemented
6#22608714C211yesmaximal, characteristic, complemented
7#22608713C211yesmaximal, characteristic, complemented
8#22608710C211yesmaximal, characteristic, complemented
9#22608708C211yesmaximal, characteristic, complemented
10#22608698C211yesmaximal, characteristic, complemented
11#22608697C211yesmaximal, characteristic, complemented
12#22608693C211yesmaximal, characteristic, complemented
13#22608680C211yesmaximal, characteristic, complemented
14#22608676C211yesmaximal, characteristic, complemented
15C73×#1565C211yesmaximal, characteristic, complemented
16C4×#11924028C2211yescharacteristic
17#17988715C411yescharacteristic
18#17988715C411yescharacteristic
19#17988663C411yescharacteristic
20#17988663C411yescharacteristic
21#17988660C411yescharacteristic
22#17988660C411yescharacteristic
23#17988656C411yescharacteristic
24#17988656C411yescharacteristic
25#17988647—21no—
26#17988647—21no—
27#17988646—21no—
28#17988645—21no—
29#17988644C2211yescharacteristic
30#17988643C2211yescharacteristic
31#17988643C2211yescharacteristic
32#17988643C2211yescharacteristic
33#17988640C2211yescharacteristic
34#17988639C2211yescharacteristic
35#17988639C2211yescharacteristic
36#17988639C2211yescharacteristic
37#17988638C2211yescharacteristic
38#17988638C2211yescharacteristic
39#17988611C2211yescharacteristic
40#17988609C2211yescharacteristic
41C4⋊C8×D73C2211yescharacteristic
42#17988553—21no—
43#17988552—21no—
44#17988542—21no—
45#17988541—21no—
46C4×#11924011C2211yescharacteristic
47C4×C8×D73C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988340C2211yescharacteristic
50#17988339C2211yescharacteristic
51#17988339C2211yescharacteristic
52#17988339C2211yescharacteristic
53#17988339C2211yescharacteristic
54#17988338C2211yescharacteristic
55#17988338C2211yescharacteristic
56#17988337C2211yescharacteristic
57#17988337C2211yescharacteristic
58#17988337C2211yescharacteristic
59#17988337C2211yescharacteristic
60#431×C73C2211yescharacteristic
61C2×C4⋊C8×C73C2211yescharacteristic
62C4×M16×C73C2211yescharacteristic
63#335×C73C2211yescharacteristic
64#335×C73C2211yescharacteristic
65#334×C73C2211yescharacteristic
66#334×C73C2211yescharacteristic
67C2×#11924028D411yescharacteristic
68C2×#11924012—21no—
69C2×#11924011—21no—
70C2×#11924011C2×C411yescharacteristic
71C2×#11924011C2×C411yescharacteristic
72C2×C8×D73—21no—
73C2×C8×D73C2×C411yescharacteristic
74C2×C8×D73C2×C411yescharacteristic
75C4×Dic146C2×C411yescharacteristic
76C4×Dic146Q811yescharacteristic
77C4×D292C2×C411yescharacteristic
78C4×D292Q811yescharacteristic
79C4×C22⋊D73C2×C411yescharacteristic
80C4×C22⋊D73C2×C411yescharacteristic
81C4×C22⋊D73Q811yescharacteristic
82C4×C22⋊D73Q811yescharacteristic
83#14556550D411yescharacteristic
84#14556548D411yescharacteristic
85#14556548D411yescharacteristic
86C42×D73C2311yescharacteristic
87C42×D73C2311yescharacteristic
88C4⋊#10596831—21no—
89C4⋊#10596831C2×C411yescharacteristic
90C4⋊#10596831C2×C411yescharacteristic
91C4⋊#10596831C2311yescharacteristic
92C4⋊#10596831C2311yescharacteristic
93C4⋊#10596831C2311yescharacteristic
94C4⋊#10596831C2311yescharacteristic
95#14556520—21no—
96#14556520—21no—
97#14556520C2×C411yescharacteristic
98#14556520C2×C411yescharacteristic
99#14556520C2×C411yescharacteristic
100#14556520C2×C411yescharacteristic
101C22⋊#10596831—21no—
102C22⋊#10596831C2×C411yescharacteristic
103C22⋊#10596831C2×C411yescharacteristic
104#14556503—21no—
105#14556503—21no—
106#14556503—21no—
107#14556503—21no—
108#14556503—21no—
109#14556503—21no—
110#14556503C2×C411yescharacteristic
111#14556503C2×C411yescharacteristic
112#14556503C2×C411yescharacteristic
113#14556503C2×C411yescharacteristic
114#14556502—21no—
115#14556501—21no—
116#14556501—21no—
117#14556501—21no—
118#14556501C2×C411yescharacteristic
119#14556501C2×C411yescharacteristic
120C4×#10596831C2311yescharacteristic
121C4×#10596831C2311yescharacteristic
122C8×Dic73—21no—
123C8×Dic73—21no—
124C8×Dic73—21no—
125C8×Dic73C2×C411yescharacteristic
126C8×Dic73C2×C411yescharacteristic
127C2×M16×C73C2×C411yescharacteristic
128C2×M16×C73C2×C411yescharacteristic
129C22×C8×C73—21no—
130C2×C42×C73C2311yescharacteristic
131C4⋊C8×C73—21no—
132C4⋊C8×C73C2311yescharacteristic
133C4⋊C8×C73C2311yescharacteristic
134C4⋊C8×C73C2311yescharacteristic
135C4⋊C8×C73C2311yescharacteristic
136C22⋊C8×C73—21no—
137#97×C73C2×C411yescharacteristic
138#97×C73C2×C411yescharacteristic
139C4×C8×C73—21no—
140C4×C8×C73C2311yescharacteristic
141C4×C8×C73C2311yescharacteristic
142#11924028—41no—
143#11924028—41no—
144C2×Dic146C4⋊C411yescharacteristic
145C2×D292C4⋊C411yescharacteristic
146C2×C22⋊D73C4⋊C411yescharacteristic
147C2×C22⋊D73C4⋊C411yescharacteristic
148C2×C4×D73C22×C411yescharacteristic
149C2×C4×D73C22×C411yescharacteristic
150C2×C4×D73C2×D411yescharacteristic
151C2×C4×D73C2×D411yescharacteristic
152C2×C4×D73C2×Q811yescharacteristic
153C2×C4×D73C2×Q811yescharacteristic
154#11924012—42no—
155#11924011—22no—
156#11924011—41no—
157#11924011—42no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C22×C411yescharacteristic
164C2×#10596831C22×C411yescharacteristic
165C2×#10596831C22×C411yescharacteristic
166C8×D73—22no—
167C8×D73—41no—
168C8×D73—42no—
169C4⋊Dic73C4⋊C411yescharacteristic
170C4⋊Dic73C4⋊C411yescharacteristic
171#11924007C4⋊C411yescharacteristic
172#11924007C4⋊C411yescharacteristic
173#11924007C4⋊C411yescharacteristic
174#11924007C4⋊C411yescharacteristic
175C22⋊Dic73C4⋊C411yescharacteristic
176C22⋊Dic73C4⋊C411yescharacteristic
177#11924005C4⋊C411yescharacteristic
178#11924005C4⋊C411yescharacteristic
179#11924005C4⋊C411yescharacteristic
180#11924005C4⋊C411yescharacteristic
181C4×Dic73C22×C411yescharacteristic
182C4×Dic73C22×C411yescharacteristic
183C4×Dic73C2×D411yescharacteristic
184C4×Dic73C2×D411yescharacteristic
185C4×Dic73C2×Q811yescharacteristic
186C4×Dic73C2×Q811yescharacteristic
187C22×C4×C73C22×C411yescharacteristic
188C22×C4×C73C2×D411yescharacteristic
189C22×C4×C73C2×Q811yescharacteristic
190M16×C73—22no—
191M16×C73—41no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—42no—
197C2×C8×C73C22×C411yescharacteristic
198C2×C8×C73C22×C411yescharacteristic
199C2×C8×C73C22×C411yescharacteristic
200C2×C8×C73C22×C411yescharacteristic
201C42×C73C22×C411yescharacteristic
202C42×C73C2×D411yescharacteristic
203C42×C73C2×Q811yescharacteristic
204C42×C73C2411yescharacteristic
205C23×C73C2×C4⋊C411yescharacteristic
206C22×D73C2×C4⋊C411yescharacteristic
207C22×D73C2×C4⋊C411yescharacteristic
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—41no—
213C2×C4×C73C2×C4⋊C411yescharacteristic
214C2×C4×C73C2×C4⋊C411yescharacteristic
215C2×C4×C73C2×C4⋊C411yescharacteristic
216C2×C4×C73C23×C411yescharacteristic
217C2×C4×C73C22×D411yescharacteristic
218C2×C4×C73C22×Q811yescharacteristic
219C22⋊D73—41no—
220C22⋊D73—41no—
221C2×Dic73C2×C4⋊C411yescharacteristic
222C2×Dic73C2×C4⋊C411yescharacteristic
223C2×Dic73C2×C4⋊C411yescharacteristic
224C2×Dic73C2×C4⋊C411yescharacteristic
225C2×Dic73C2×C4⋊C411yescharacteristic
226C2×Dic73C2×C4⋊C411yescharacteristic
227D292—41no—
228C4×D73—21no—
229C4×D73—21no—
230C4×D73—21no—
231C4×D73—21no—
232C4×D73—21no—
233C4×D73—21no—
234C4×D73—21no—
235C4×D73—21no—
236C4×D73—41no—
237C4×D73—41no—
238Dic146—41no—
239C8×C73—21no—
240C8×C73—21no—
241C8×C73—21no—
242C8×C73—41no—
243C8×C73—41no—
244C8×C73—41no—
245C8×C73—41no—
246C8×C73#13112yes—
247#10596831—21no—
248#10596831—21no—
249#10596831—21no—
250#10596831—21no—
251#10596831—41no—
252#10596831—41no—
253#10596831—41no—
254#10596831—41no—
255C22×C73—21no—
256C22×C73—21no—
257C22×C73—21no—
258C22×C73C22×C4⋊C411yescharacteristic
259C2×D73—21no—
260C2×D73—21no—
261C2×D73—21no—
262C2×D73—21no—
263C2×D73—21no—
264C2×D73—21no—
265C4×C73—21no—
266C4×C73—21no—
267C4×C73—21no—
268C4×C73—21no—
269C4×C73C2×#13111yescharacteristic
270C4×C73#56811yescharacteristic
271C4×C73#57511yescharacteristic
272C4×C73#57511yescharacteristic
273Dic73—21no—
274Dic73—21no—
275Dic73—21no—
276Dic73—21no—
277Dic73—21no—
278Dic73—21no—
279#17831—731nomaximal, Sylow
280C2×C73—41no—
281C2×C73#290611yescharacteristic
282C2×C73#291111yescharacteristic
283C2×C73#291611yescharacteristic
284D73—41no—
285D73—41no—
286#2965—731no—
287#2925—731no—
288#2925—731no—
289#1574—731no—
290#1574—731no—
291#1573—731no—
292#1573—731no—
293#1572—731no—
294#1572—731no—
295#1569—731no—
296#1569—731no—
297#1568—731no—
298#1565—731no—
299#1565D7311yescharacteristic, complemented
300#1564—731no—
301C73#1783111yescharacteristic, complemented, Sylow
302C4×#41—731no—
303#446—731no—
304#446—731no—
305#436—731no—
306#436—731no—
307#435—731no—
308#435—731no—
309#435—731no—
310#435—731no—
311#433—1461no—
312#433—1461no—
313#433—1461no—
314#433—1461no—
315#432—731no—
316#432—731no—
317#432—731no—
318#432—731no—
319#431—731no—
320#431—731no—
321#431—731no—
322#431—731no—
323#431—731no—
324#431—731no—
325#431C2×D7311yescharacteristic
326#423—731no—
327#423—731no—
328C2×C4⋊C8—731no—
329C2×C4⋊C8C2×D7311yescharacteristic
330#408—1461no—
331#408—1461no—
332#405—1461no—
333#405—1461no—
334C4×M16—731no—
335C4×M16C2×D7311yescharacteristic
336C2×C4×C8—731no—
337#335—731no—
338#335—731no—
339#335—731no—
340#335—731no—
341#335—731no—
342#335—731no—
343#335C2×D7311yescharacteristic
344#335C2×D7311yescharacteristic
345#334—731no—
346#334—731no—
347#334—731no—
348#334—731no—
349#334—731no—
350#334—731no—
351#334C2×D7311yescharacteristic
352#334C2×D7311yescharacteristic
353C2×#41—731no—
354C2×M16—731no—
355C2×M16—731no—
356C2×M16—1461no—
357C2×M16—1461no—
358C2×M16C4×D7311yescharacteristic
359C2×M16C4×D7311yescharacteristic
360C22×C8—21no—
361C22×C8—731no—
362C22×C8—731no—
363C22×C8—1461no—
364C4×Q8—731no—
365C4×Q8—731no—
366C4×D4—731no—
367C4×D4—731no—
368C4×D4—731no—
369C4×D4—731no—
370C4×D4—731no—
371C4×D4—731no—
372#117—731no—
373#117—731no—
374#117—731no—
375C2×C42—731no—
376C2×C42—731no—
377C2×C42C22×D7311yescharacteristic
378C4⋊C8—21no—
379C4⋊C8—731no—
380C4⋊C8—731no—
381C4⋊C8—731no—
382C4⋊C8—731no—
383C4⋊C8—731no—
384C4⋊C8—731no—
385C4⋊C8—731no—
386C4⋊C8—731no—
387C4⋊C8—731no—
388C4⋊C8—731no—
389C4⋊C8—1461no—
390C4⋊C8—1461no—
391C4⋊C8—1461no—
392C4⋊C8C22×D7311yescharacteristic
393C4⋊C8C22×D7311yescharacteristic
394C4⋊C8C22×D7311yescharacteristic
395C4⋊C8C22×D7311yescharacteristic
396C22⋊C8—21no—
397C22⋊C8—731no—
398C22⋊C8—731no—
399C22⋊C8—731no—
400C22⋊C8—731no—
401C22⋊C8—731no—
402C22⋊C8—731no—
403C22⋊C8—1461no—
404C22⋊C8—1461no—
405C22⋊C8—1461no—
406C22⋊C8—1461no—
407C22⋊C8—1461no—
408C22⋊C8—1461no—
409C22⋊C8—1461no—
410#97—731no—
411#97—731no—
412#97—1461no—
413#97—1461no—
414#97—1461no—
415#97—1461no—
416#97C4×D7311yescharacteristic
417#97C4×D7311yescharacteristic
418C4×C8—21no—
419C4×C8—731no—
420C4×C8—731no—
421C4×C8—731no—
422C4×C8—731no—
423C4×C8—1461no—
424C4×C8—1461no—
425C4×C8—1461no—
426C4×C8C22×D7311yescharacteristic
427C4×C8C22×D7311yescharacteristic
428#41—2921no—
429#41—2921no—
430C2×Q8—731no—
431C2×D4—731no—
432C2×D4—731no—
433C2×D4—731no—
434C22×C4—731no—
435C22×C4—731no—
436C22×C4—731no—
437C22×C4—731no—
438C22×C4—731no—
439C22×C4—731no—
440C22×C4C2×C4×D7311yescharacteristic
441C22×C4D4×D7311yescharacteristic
442C22×C4Q8×D7311yescharacteristic
443M16—22no—
444M16—41no—
445M16—2921no—
446M16—2922no—
447M16—2922no—
448M16—1462no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—42no—
454C2×C8—2921no—
455C2×C8—2922no—
456C2×C8—731no—
457C2×C8—731no—
458C2×C8—731no—
459C2×C8—731no—
460C2×C8—1461no—
461C2×C8—1461no—
462C2×C8—1461no—
463C2×C8—1461no—
464C2×C8—1462no—
465C2×C8C2×C4×D7311yescharacteristic
466C2×C8C2×C4×D7311yescharacteristic
467C2×C8C2×C4×D7311yescharacteristic
468C2×C8C2×C4×D7311yescharacteristic
469C4⋊C4—731no—
470C4⋊C4—731no—
471C4⋊C4—731no—
472C4⋊C4—731no—
473C4⋊C4—731no—
474C4⋊C4—731no—
475C22⋊C4—731no—
476C22⋊C4—731no—
477C22⋊C4—731no—
478C22⋊C4—731no—
479C22⋊C4—731no—
480C22⋊C4—731no—
481C42—731no—
482C42—731no—
483C42—731no—
484C42—731no—
485C42—731no—
486C42—731no—
487C42C2×C4×D7311yescharacteristic
488C42D4×D7311yescharacteristic
489C42Q8×D7311yescharacteristic
490C42C23×D7311yescharacteristic
491C23—731no—
492C23—731no—
493C23C4⋊C4×D7311yescharacteristic
494Q8—2921no—
495D4—2921no—
496D4—2921no—
497D4—2921no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—2921no—
504C2×C4—2921no—
505C2×C4—731no—
506C2×C4—731no—
507C2×C4—731no—
508C2×C4—731no—
509C2×C4—731no—
510C2×C4—731no—
511C2×C4—1461no—
512C2×C4—1461no—
513C2×C4—1461no—
514C2×C4—1461no—
515C2×C4—1461no—
516C2×C4—1461no—
517C2×C4—1461no—
518C2×C4—1461no—
519C2×C4C4⋊C4×D7311yescharacteristic
520C2×C4C4⋊C4×D7311yescharacteristic
521C2×C4C4⋊C4×D7311yescharacteristic
522C2×C4C22×C4×D7311yescharacteristic
523C2×C4C2×D4×D7311yescharacteristic
524C2×C4C2×Q8×D7311yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—2921no—
533C8—2921no—
534C8—2921no—
535C8—2921no—
536C8—1461no—
537C8—1461no—
538C8—1461no—
539C8—1461no—
540C8#1455659712yes—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—1461no—
545C22—1461no—
546C22—1461no—
547C22—1461no—
548C22—1461no—
549C22—1461no—
550C22C2×C4⋊C4×D7311yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—1461no—
556C4—1461no—
557C4—1461no—
558C4—1461no—
559C4—1461no—
560C4—1461no—
561C4C2×#1455659711yescharacteristic
562C4#1798935311yescharacteristic
563C4#1798938311yescharacteristic
564C4#1798938611yescharacteristic
565C2—41no—
566C2—2921no—
567C2—2921no—
568C2#2261849611yescharacteristic
569C2#2261851811yescharacteristic
570C2#2261854111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1565C2
socleC22×C73C22×C4⋊C4
prime radicalC2×#11924028D4
cosocleC42×C73C24
hypercenter#1565D73
hypocenterC73#17831
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
4. #22608721C2semidirect
5. #22608719C2semidirect
6. #22608714C2semidirect
7. #22608713C2semidirect
8. #22608710C2semidirect
9. #22608708C2semidirect
10. #22608698C2semidirect
11. #22608697C2semidirect
12. #22608693C2semidirect
13. #22608680C2semidirect
14. #22608676C2semidirect
15. C73×#1565C2semidirect
299. #1565D73semidirect
301. C73#17831semidirect

Maximal subgroups

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

subgroupindex
#226188932
#226185962
#226185922
#226087212
#226087192
#226087142
#226087132
#226087102
#226087082
#226086982
#226086972
#226086932
#226086802
#226086762
C73×#15652
#1783173