Finite Group Databasebeta

← #33056059

Subgroups — #33056059

Order 18688.

596 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620011C211yesmaximal, characteristic
2#22619082C211yesmaximal, characteristic
3#22608809C211yesmaximal, characteristic, complemented
4#22608802C211yesmaximal, characteristic, complemented
5#22608781C211yesmaximal, characteristic, complemented
6#22608774C211yesmaximal, characteristic, complemented
7#22608748C211yesmaximal, characteristic, complemented
8#22608741C211yesmaximal, characteristic, complemented
9C8×#11924018C211yesmaximal, characteristic, complemented
10C8×#11924015C211yesmaximal, characteristic, complemented
11#22608719C211yesmaximal, characteristic, complemented
12#22608360C211yesmaximal, characteristic, complemented
13#22608337C211yesmaximal, characteristic
14#22608231C211yesmaximal, characteristic, complemented
15C73×#2982C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17#17988917C411yescharacteristic
18#17988900C411yescharacteristic
19#17988894C411yescharacteristic
20#17988894C411yescharacteristic
21#17988809C411yescharacteristic
22#17988809C411yescharacteristic
23#17988743C411yescharacteristic
24#17988726C411yescharacteristic
25#17988717C2211yescharacteristic
26C8×Dic146C2211yescharacteristic
27C4×#11924018C2211yescharacteristic
28C4×#11924018C2211yescharacteristic
29C4×#11924015C2211yescharacteristic
30C4×#11924015C2211yescharacteristic
31#17988666C2211yescharacteristic
32#17988662—21no—
33#17988661—21no—
34C8×D292C2211yescharacteristic
35#17988647—21no—
36#17988640C2211yescharacteristic
37#17988640C2211yescharacteristic
38#17988612—21no—
39#17988611C2211yescharacteristic
40#17988339C2211yescharacteristic
41#17988339C2211yescharacteristic
42#17988337C2211yescharacteristic
43#17988337C2211yescharacteristic
44Q8⋊#10596831C2211yescharacteristic
45Q8⋊#10596831C2211yescharacteristic
46Q8⋊#10596831C2211yescharacteristic
47Q8⋊#10596831C2211yescharacteristic
48#17988317C2211yescharacteristic
49#17988317C2211yescharacteristic
50#17988314C2211yescharacteristic
51#17988314C2211yescharacteristic
52#17988309C2211yescharacteristic
53#17988309C2211yescharacteristic
54#17988308C2211yescharacteristic
55C8×#10596831C2211yescharacteristic
56C2×C4×Q8×C73C2211yescharacteristic
57C8×Q8×C73—21no—
58C8×Q8×C73—21no—
59C8×Q8×C73C2211yescharacteristic
60C8×Q8×C73C2211yescharacteristic
61C8×Q8×C73C2211yescharacteristic
62C8×Q8×C73C2211yescharacteristic
63#431×C73—21no—
64#431×C73—21no—
65#431×C73C2211yescharacteristic
66#431×C73C2211yescharacteristic
67C2×#11924018C2×C411yescharacteristic
68C2×#11924018C2×C411yescharacteristic
69C2×#11924015C2×C411yescharacteristic
70C2×#11924015C2×C411yescharacteristic
71C2×#11924012—21no—
72C2×#11924011—21no—
73C2×C8×D73—21no—
74#14556585—21no—
75#14556583C2×C411yescharacteristic
76#14556579C2×C411yescharacteristic
77#14556574—21no—
78#14556570C2×C411yescharacteristic
79#14556565C2×C411yescharacteristic
80C4×Dic146C2311yescharacteristic
81C4×D292C2311yescharacteristic
82C4×C22⋊D73—21no—
83#14556548—21no—
84#14556524C2×C411yescharacteristic
85#14556524C2×C411yescharacteristic
86#14556522C2×C411yescharacteristic
87#14556522C2×C411yescharacteristic
88C4⋊#10596831—21no—
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#14556515C2×C411yescharacteristic
99#14556515C2×C411yescharacteristic
100#14556514C2×C411yescharacteristic
101#14556514C2×C411yescharacteristic
102#14556511C2×C411yescharacteristic
103#14556511C2×C411yescharacteristic
104C22⋊#10596831—21no—
105C22⋊#10596831C2×C411yescharacteristic
106C22⋊#10596831C2×C411yescharacteristic
107#14556503—21no—
108#14556503—21no—
109#14556501—21no—
110C4×#10596831C2311yescharacteristic
111C4×#10596831C2311yescharacteristic
112C4×#10596831C2311yescharacteristic
113C4×#10596831C2311yescharacteristic
114C8×Dic73—21no—
115C22×Q8×C73C2×C411yescharacteristic
116C4×Q8×C73—21no—
117C4×Q8×C73—21no—
118C4×Q8×C73C2×C411yescharacteristic
119C4×Q8×C73C2×C411yescharacteristic
120C4×Q8×C73C2311yescharacteristic
121C4×Q8×C73C2311yescharacteristic
122C2×C4⋊C4×C73—21no—
123C2×C4⋊C4×C73C2×C411yescharacteristic
124C2×C42×C73—21no—
125C2×C42×C73C2311yescharacteristic
126C4⋊C8×C73—21no—
127C4⋊C8×C73—21no—
128C4⋊C8×C73—21no—
129C4⋊C8×C73—21no—
130C4⋊C8×C73D411yescharacteristic
131C4⋊C8×C73D411yescharacteristic
132C4⋊C8×C73C2311yescharacteristic
133C4⋊C8×C73C2311yescharacteristic
134C22⋊C8×C73—21no—
135C22⋊C8×C73D411yescharacteristic
136C22⋊C8×C73D411yescharacteristic
137C4×C8×C73—21no—
138C4×C8×C73—21no—
139C4×C8×C73—21no—
140C4×C8×C73—21no—
141C4×C8×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#11924018—22no—
150#11924015—22no—
151#11924015—22no—
152#11924012—81no—
153#11924011—81no—
154C2×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831C22×C411yescharacteristic
159C2×#10596831C22×C411yescharacteristic
160C2×#10596831C22×C411yescharacteristic
161C2×#10596831C22×C411yescharacteristic
162C8×D73—81no—
163C4⋊Dic73C22×C411yescharacteristic
164C4⋊Dic73C22×C411yescharacteristic
165#11924007—21no—
166#11924007—21no—
167#11924007—21no—
168#11924007—21no—
169C22⋊Dic73—21no—
170#11924005—21no—
171#11924005—21no—
172#11924005—21no—
173#11924005—21no—
174C4×Dic73—21no—
175C2×Q8×C73—22no—
176C2×Q8×C73—22no—
177C2×Q8×C73—21no—
178C2×Q8×C73C22×C411yescharacteristic
179C2×Q8×C73C22×C411yescharacteristic
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73C22×C411yescharacteristic
183C22×C4×C73C2×D411yescharacteristic
184C22×C4×C73#4111yescharacteristic
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73C2×D411yescharacteristic
188C2×C8×C73C2×D411yescharacteristic
189C2×C8×C73C2×D411yescharacteristic
190C2×C8×C73C2×D411yescharacteristic
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73C22×C411yescharacteristic
197C4⋊C4×C73C22×C411yescharacteristic
198C42×C73—21no—
199C42×C73—21no—
200C42×C73—21no—
201C42×C73—21no—
202C42×C73C22×C411yescharacteristic
203C42×C73C2×D411yescharacteristic
204C42×C73#4111yescharacteristic
205C42×C73C2411yescharacteristic
206C23×C73C4×D411yescharacteristic
207C22×D73—21no—
208Q8×C73—24no—
209Q8×C73—21no—
210Q8×C73—21no—
211Q8×C73#13112yes—
212Q8×C73#13112yes—
213C2×C4×C73—24no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—41no—
223C2×C4×C73—81no—
224C2×C4×C73C4×D411yescharacteristic
225C2×C4×C73C4×D411yescharacteristic
226C2×C4×C73C4×D411yescharacteristic
227C2×C4×C73C23×C411yescharacteristic
228C2×C4×C73C22×D411yescharacteristic
229C2×C4×C73C2×#4111yescharacteristic
230C22⋊D73—81no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234D292—21no—
235D292—21no—
236C4×D73—41no—
237C4×D73—41no—
238Dic146—21no—
239Dic146—21no—
240C8×C73—21no—
241C8×C73—21no—
242C8×C73—21no—
243C8×C73—21no—
244C8×C73—41no—
245C8×C73—41no—
246#10596831—21no—
247#10596831—21no—
248#10596831—21no—
249#10596831—21no—
250#10596831—41no—
251#10596831—41no—
252#10596831—41no—
253#10596831—41no—
254C22×C73—21no—
255C22×C73—21no—
256C22×C73—21no—
257C22×C73C2×C4×D411yescharacteristic
258C2×D73—41no—
259C2×D73—41no—
260C2×D73—41no—
261C4×C73—22no—
262C4×C73—22no—
263C4×C73—21no—
264C4×C73—21no—
265C4×C73—21no—
266C4×C73—21no—
267C4×C73—41no—
268C4×C73—41no—
269C4×C73C2×#13111yescharacteristic
270C4×C73C2×#13111yescharacteristic
271C4×C73#57711yescharacteristic
272C4×C73#57811yescharacteristic
273Dic73—41no—
274Dic73—41no—
275Dic73—41no—
276#17919—731nomaximal, Sylow
277C2×C73—41no—
278C2×C73#292911yescharacteristic
279C2×C73#294711yescharacteristic
280C2×C73#295711yescharacteristic
281D73—81no—
282#3108—731no—
283#2993—731no—
284#2982D7311yescharacteristic, complemented
285#1588—731no—
286#1587—731no—
287#1584—731no—
288#1583—731no—
289#1579—731no—
290SD16⋊C8—731no—
291C8×Q16—731no—
292C8×SD16—731no—
293#1574—731no—
294#1487—731no—
295#1482—731no—
296#1454—731no—
297C73#1791911yescharacteristic, complemented, Sylow
298#529—731no—
299C2×C4×Q8C2×D7311yescharacteristic
300#483—731no—
301#480—731no—
302#479—731no—
303#479—731no—
304#464—731no—
305#464—731no—
306#451—731no—
307#448—731no—
308#446—731no—
309C8×Q8—21no—
310C8×Q8—21no—
311C8×Q8—731no—
312C8×Q8C2×D7311yescharacteristic
313C8×Q8C2×D7311yescharacteristic
314C8×Q8C2×D7311yescharacteristic
315C8×Q8C2×D7311yescharacteristic
316C4×Q16—731no—
317C4×Q16—731no—
318C4×SD16—731no—
319C4×SD16—731no—
320#436—731no—
321#436—1461no—
322#435—1461no—
323C8×D4—731no—
324#433—1461no—
325#431—21no—
326#431—21no—
327#431—731no—
328#431—731no—
329#431C2×D7311yescharacteristic
330#431C2×D7311yescharacteristic
331#424—1461no—
332#423—731no—
333#335—731no—
334#335—731no—
335#334—731no—
336#334—731no—
337Q8⋊C8—731no—
338Q8⋊C8—731no—
339Q8⋊C8—731no—
340Q8⋊C8—731no—
341Q8⋊C8—731no—
342Q8⋊C8—731no—
343D4⋊C8—731no—
344D4⋊C8—731no—
345#322—731no—
346#322—731no—
347#322—731no—
348C82—731no—
349C22×Q8C4×D7311yescharacteristic
350C2×Q16—731no—
351C2×Q16—731no—
352C2×SD16—731no—
353C2×SD16—731no—
354C2×M16—1461no—
355C2×M16—1461no—
356C22×C8—1461no—
357#126—1461no—
358#125—731no—
359#124—731no—
360#123—1461no—
361C22⋊Q8—731no—
362#121—731no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—731no—
366C4×Q8C4×D7311yescharacteristic
367C4×Q8C4×D7311yescharacteristic
368C4×Q8C22×D7311yescharacteristic
369C4×Q8C22×D7311yescharacteristic
370C4×D4—731no—
371C4×D4—1461no—
372#117—1461no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4C4×D7311yescharacteristic
375C2×C42—21no—
376C2×C42C22×D7311yescharacteristic
377#107—731no—
378#107—731no—
379#106—731no—
380#106—731no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—731no—
386C4⋊C8—731no—
387C4⋊C8—731no—
388C4⋊C8—731no—
389C4⋊C8—1461no—
390C4⋊C8—1461no—
391C4⋊C8—1461no—
392C4⋊C8—1461no—
393C4⋊C8C22⋊D7311yescharacteristic
394C4⋊C8C22⋊D7311yescharacteristic
395C4⋊C8C22×D7311yescharacteristic
396C4⋊C8C22×D7311yescharacteristic
397#103—731no—
398#103—731no—
399#103—731no—
400#103—731no—
401#103—731no—
402#103—731no—
403#102—731no—
404#102—731no—
405C22⋊C8—21no—
406C22⋊C8—731no—
407C22⋊C8—731no—
408C22⋊C8—1461no—
409C22⋊C8—1461no—
410C22⋊C8—1461no—
411C22⋊C8C22⋊D7311yescharacteristic
412C22⋊C8C22⋊D7311yescharacteristic
413#97—1461no—
414C4×C8—21no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8—21no—
418C4×C8—21no—
419C4×C8—731no—
420C4×C8—731no—
421C4×C8—731no—
422C4×C8—731no—
423C4×C8—1461no—
424C4×C8C22×D7311yescharacteristic
425C4×C8C22×D7311yescharacteristic
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—21no—
429C2×Q8—731no—
430C2×Q8C2×C4×D7311yescharacteristic
431C2×Q8C2×C4×D7311yescharacteristic
432C2×D4—731no—
433C2×D4—1461no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—1461no—
437C22×C4C2×C4×D7311yescharacteristic
438C22×C4C2×C22⋊D7311yescharacteristic
439C22×C4#1192402811yescharacteristic
440Q16—1462no—
441Q16—1462no—
442SD16—1462no—
443SD16—1462no—
444M16—5841no—
445M16—5841no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—5841no—
449C2×C8—731no—
450C2×C8—731no—
451C2×C8—731no—
452C2×C8—731no—
453C2×C8—1461no—
454C2×C8—1461no—
455C2×C8—1461no—
456C2×C8—1461no—
457C2×C8C2×C22⋊D7311yescharacteristic
458C2×C8C2×C22⋊D7311yescharacteristic
459C2×C8C2×C22⋊D7311yescharacteristic
460C2×C8C2×C22⋊D7311yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—731no—
467C4⋊C4—731no—
468C4⋊C4—1461no—
469C4⋊C4—1461no—
470C4⋊C4—1461no—
471C4⋊C4—1461no—
472C4⋊C4C2×C4×D7311yescharacteristic
473C4⋊C4C2×C4×D7311yescharacteristic
474C22⋊C4—1461no—
475C22⋊C4—1461no—
476C22⋊C4—1461no—
477C22⋊C4—1461no—
478C22⋊C4—1461no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—1461no—
484C42C2×C4×D7311yescharacteristic
485C42C2×C22⋊D7311yescharacteristic
486C42#1192402811yescharacteristic
487C42C23×D7311yescharacteristic
488C23—1461no—
489C23C4×C22⋊D7311yescharacteristic
490Q8—24no—
491Q8—21no—
492Q8—21no—
493Q8—1461no—
494Q8—1461no—
495Q8#1455659712yes—
496Q8#1455659712yes—
497D4—5841no—
498D4—1461no—
499D4—1461no—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—81no—
511C2×C4—2921no—
512C2×C4—2921no—
513C2×C4—1461no—
514C2×C4—1461no—
515C2×C4—1461no—
516C2×C4C4×C22⋊D7311yescharacteristic
517C2×C4C4×C22⋊D7311yescharacteristic
518C2×C4C4×C22⋊D7311yescharacteristic
519C2×C4C22×C4×D7311yescharacteristic
520C2×C4C22×C22⋊D7311yescharacteristic
521C2×C4C2×#1192402811yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—2921no—
529C8—2921no—
530C8—2921no—
531C8—2921no—
532C8—1461no—
533C8—1461no—
534C8—1461no—
535C8—1461no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—2921no—
540C22—2921no—
541C22—2921no—
542C22C2×C4×C22⋊D7311yescharacteristic
543C4—22no—
544C4—22no—
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—2921no—
552C4—2921no—
553C4—2921no—
554C4C2×#1455659711yescharacteristic
555C4C2×#1455659711yescharacteristic
556C4#1798939511yescharacteristic
557C4#1798940211yescharacteristic
558C2—41no—
559C2—5841no—
560C2#2261862511yescharacteristic
561C2#2261877411yescharacteristic
562C2#2261884611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2982C2
socleC22×C73C2×C4×D4
prime radical#14556565C2×C4
cosocleC42×C73C24
hypercenter#2982D73
hypocenterC73#17919
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2982

Complements

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

NH ≅ G/Ntype
3. #22608809C2semidirect
4. #22608802C2semidirect
5. #22608781C2semidirect
6. #22608774C2semidirect
7. #22608748C2semidirect
8. #22608741C2semidirect
9. C8×#11924018C2semidirect
10. C8×#11924015C2semidirect
11. #22608719C2semidirect
12. #22608360C2semidirect
14. #22608231C2semidirect
15. C73×#2982C2semidirect
284. #2982D73semidirect
297. C73#17919semidirect

Maximal subgroups

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

subgroupindex
#226200112
#226190822
#226088092
#226088022
#226087812
#226087742
#226087482
#226087412
C8×#119240182
C8×#119240152
#226087192
#226083602
#226083372
#226082312
C73×#29822
#1791973