Finite Group Databasebeta

← #33057393

Subgroups — #33057393

Order 18688.

598 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619949C211yesmaximal, characteristic
2#22619093C211yesmaximal, characteristic, complemented
3#22608833C211yesmaximal, characteristic, complemented
4#22608814C211yesmaximal, characteristic, complemented
5#22608809C211yesmaximal, characteristic, complemented
6#22608807C211yesmaximal, characteristic, complemented
7#22608781C211yesmaximal, characteristic, complemented
8#22608758C211yesmaximal, characteristic, complemented
9#22608741C211yesmaximal, characteristic, complemented
10C8×#11924018C211yesmaximal, characteristic, complemented
11#22608707C211yesmaximal, characteristic, complemented
12#22608394C211yesmaximal, characteristic, complemented
13#22608318C211yesmaximal, characteristic, complemented
14#22608231C211yesmaximal, characteristic, complemented
15C73×#2991C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17#17988928C411yescharacteristic
18#17988911C411yescharacteristic
19#17988894C411yescharacteristic
20#17988887C411yescharacteristic
21#17988809C411yescharacteristic
22#17988802C411yescharacteristic
23#17988749C411yescharacteristic
24#17988732C411yescharacteristic
25#17988717C2211yescharacteristic
26C8×Dic146C2211yescharacteristic
27C4×#11924018C2211yescharacteristic
28C4×#11924015C2211yescharacteristic
29C4×#11924016C2211yescharacteristic
30C4×#11924013C2211yescharacteristic
31#17988666C2211yescharacteristic
32#17988655—21no—
33C8×D292C2211yescharacteristic
34#17988650—21no—
35#17988647—21no—
36#17988640C2211yescharacteristic
37#17988640C2211yescharacteristic
38#17988612—21no—
39C2×C4⋊#10596831C2211yescharacteristic
40#17988339C2211yescharacteristic
41#17988339C2211yescharacteristic
42#17988339C2211yescharacteristic
43#17988339C2211yescharacteristic
44Q8⋊#10596831C2211yescharacteristic
45Q8⋊#10596831C2211yescharacteristic
46#17988317C2211yescharacteristic
47#17988317C2211yescharacteristic
48D4⋊#10596831C2211yescharacteristic
49D4⋊#10596831C2211yescharacteristic
50#17988314C2211yescharacteristic
51#17988314C2211yescharacteristic
52#17988309C2211yescharacteristic
53#17988309C2211yescharacteristic
54#17988308C2211yescharacteristic
55C8×#10596831C2211yescharacteristic
56C4×#41×C73C2211yescharacteristic
57C8×Q8×C73C2211yescharacteristic
58C8×Q8×C73C2211yescharacteristic
59#436×C73—21no—
60#436×C73—21no—
61#436×C73C2211yescharacteristic
62#436×C73C2211yescharacteristic
63#431×C73—21no—
64#431×C73C2211yescharacteristic
65#423×C73—21no—
66#423×C73C2211yescharacteristic
67C2×#11924018C2×C411yescharacteristic
68C2×#11924016C2×C411yescharacteristic
69C2×#11924015C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71C2×#11924011—21no—
72C22×#10596831—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#14556514C2×C411yescharacteristic
99#14556514C2×C411yescharacteristic
100#14556512C2×C411yescharacteristic
101#14556512C2×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—
115C2×#41×C73C2×C411yescharacteristic
116C2×M16×C73—21no—
117C2×M16×C73—21no—
118C2×M16×C73—21no—
119C4×Q8×C73C2×C411yescharacteristic
120C4×Q8×C73C2311yescharacteristic
121C4×D4×C73—21no—
122C4×D4×C73—21no—
123C4×D4×C73C2×C411yescharacteristic
124C4×D4×C73C2311yescharacteristic
125#117×C73—21no—
126#117×C73C2×C411yescharacteristic
127C2×C42×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
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#11924016—41no—
150#11924015—22no—
151#11924013—41no—
152#11924011—81no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—81no—
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—
175#41×C73—22no—
176#41×C73—41no—
177C2×Q8×C73C22×C411yescharacteristic
178C2×D4×C73—21no—
179C2×D4×C73C22×C411yescharacteristic
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73C22×C411yescharacteristic
184C22×C4×C73C2×D411yescharacteristic
185C22×C4×C73#4111yescharacteristic
186M16×C73—81no—
187M16×C73—81no—
188M16×C73—81no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73C2×D411yescharacteristic
192C2×C8×C73C2×D411yescharacteristic
193C2×C8×C73C2×D411yescharacteristic
194C2×C8×C73C2×D411yescharacteristic
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73C22×C411yescharacteristic
198C4⋊C4×C73C22×C411yescharacteristic
199C22⋊C4×C73—21no—
200C22⋊C4×C73—21no—
201C22⋊C4×C73—21no—
202C42×C73—21no—
203C42×C73—21no—
204C42×C73—21no—
205C42×C73C22×C411yescharacteristic
206C42×C73C2×D411yescharacteristic
207C42×C73#4111yescharacteristic
208C42×C73C2411yescharacteristic
209C23×C73—21no—
210C23×C73C4×D411yescharacteristic
211C22×D73—21no—
212Q8×C73—21no—
213Q8×C73#13112yes—
214D4×C73—21no—
215D4×C73—21no—
216D4×C73—42no—
217C2×C4×C73—21no—
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—41no—
225C2×C4×C73—42no—
226C2×C4×C73—42no—
227C2×C4×C73—41no—
228C2×C4×C73—41no—
229C2×C4×C73C4×D411yescharacteristic
230C2×C4×C73C4×D411yescharacteristic
231C2×C4×C73C4×D411yescharacteristic
232C2×C4×C73C23×C411yescharacteristic
233C2×C4×C73C22×D411yescharacteristic
234C2×C4×C73C2×#4111yescharacteristic
235C22⋊D73—42no—
236C2×Dic73—21no—
237C2×Dic73—21no—
238C2×Dic73—21no—
239D292—21no—
240D292—21no—
241C4×D73—41no—
242C4×D73—41no—
243Dic146—21no—
244Dic146—21no—
245C8×C73—21no—
246C8×C73—21no—
247C8×C73—21no—
248C8×C73—21no—
249C8×C73—41no—
250C8×C73—41no—
251#10596831—21no—
252#10596831—21no—
253#10596831—21no—
254#10596831—21no—
255#10596831—41no—
256#10596831—41no—
257#10596831—41no—
258#10596831—41no—
259C22×C73—21no—
260C22×C73—21no—
261C22×C73—21no—
262C22×C73—41no—
263C22×C73—41no—
264C22×C73—41no—
265C22×C73C2×C4×D411yescharacteristic
266C2×D73—41no—
267C2×D73—41no—
268C2×D73—41no—
269C4×C73—21no—
270C4×C73—22no—
271C4×C73—21no—
272C4×C73—21no—
273C4×C73—21no—
274C4×C73—41no—
275C4×C73—41no—
276C4×C73C2×#13111yescharacteristic
277C4×C73#56811yescharacteristic
278C4×C73#57611yescharacteristic
279C4×C73#57811yescharacteristic
280Dic73—41no—
281Dic73—41no—
282Dic73—41no—
283#18033—731nomaximal, Sylow
284C2×C73—41no—
285C2×C73—81no—
286C2×C73#293311yescharacteristic
287C2×C73#295111yescharacteristic
288C2×C73#295511yescharacteristic
289D73—81no—
290#3102—731no—
291#2994—731no—
292#2991D7311yescharacteristic, complemented
293#1592—731no—
294#1589—731no—
295#1588—731no—
296#1588—731no—
297#1584—731no—
298#1581—731no—
299SD16⋊C8—731no—
300C8×Q16—731no—
301#1571—731no—
302#1495—731no—
303#1477—731no—
304#1454—731no—
305C73#1803311yescharacteristic, complemented, Sylow
306#529—731no—
307C4×#41C2×D7311yescharacteristic
308#485—731no—
309#482—731no—
310#479—731no—
311#478—731no—
312#464—731no—
313#463—731no—
314#452—731no—
315#449—731no—
316#446—731no—
317C8×Q8—731no—
318C8×Q8C2×D7311yescharacteristic
319C8×Q8C2×D7311yescharacteristic
320C4×Q16—731no—
321C4×SD16—731no—
322C4×SD16—731no—
323C4×D8—731no—
324#436—21no—
325#436—21no—
326#436—731no—
327#436C2×D7311yescharacteristic
328#436C2×D7311yescharacteristic
329#435—1461no—
330C8×D4—731no—
331C8×D4—1461no—
332#433—1461no—
333#431—21no—
334#431—731no—
335#431—731no—
336#431C2×D7311yescharacteristic
337#424—1461no—
338#423—21no—
339#423C2×D7311yescharacteristic
340C2×C4⋊C8—731no—
341#335—731no—
342#335—731no—
343#335—731no—
344#335—731no—
345Q8⋊C8—731no—
346Q8⋊C8—731no—
347Q8⋊C8—731no—
348Q8⋊C8—731no—
349D4⋊C8—731no—
350D4⋊C8—731no—
351D4⋊C8—731no—
352D4⋊C8—731no—
353#322—731no—
354#322—731no—
355#322—731no—
356C82—731no—
357C2×#41C4×D7311yescharacteristic
358C2×Q16—731no—
359C2×SD16—731no—
360C2×SD16—731no—
361C2×D8—731no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—1461no—
366C22×C8—1461no—
367C22×C8—1461no—
368#126—1461no—
369#125—731no—
370#124—731no—
371#123—1461no—
372C22⋊Q8—731no—
373#121—731no—
374C4×Q8—731no—
375C4×Q8C4×D7311yescharacteristic
376C4×Q8C22×D7311yescharacteristic
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—731no—
380C4×D4—1461no—
381C4×D4C4×D7311yescharacteristic
382C4×D4C22×D7311yescharacteristic
383#117—21no—
384#117—1461no—
385#117C4×D7311yescharacteristic
386C2×C42—21no—
387C2×C42C22×D7311yescharacteristic
388#107—731no—
389#107—731no—
390#106—731no—
391#106—731no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8—731no—
396C4⋊C8—731no—
397C4⋊C8—731no—
398C4⋊C8—731no—
399C4⋊C8—1461no—
400C4⋊C8—1461no—
401C4⋊C8—1461no—
402C4⋊C8—1461no—
403C4⋊C8C22⋊D7311yescharacteristic
404C4⋊C8C22⋊D7311yescharacteristic
405C4⋊C8C22×D7311yescharacteristic
406C4⋊C8C22×D7311yescharacteristic
407#103—731no—
408#103—731no—
409#103—731no—
410#103—731no—
411#102—731no—
412#102—731no—
413#102—731no—
414#102—731no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—731no—
418C22⋊C8—731no—
419C22⋊C8—1461no—
420C22⋊C8—1461no—
421C22⋊C8—1461no—
422C22⋊C8C22⋊D7311yescharacteristic
423C22⋊C8C22⋊D7311yescharacteristic
424#97—1461no—
425C4×C8—21no—
426C4×C8—21no—
427C4×C8—731no—
428C4×C8—731no—
429C4×C8—731no—
430C4×C8—731no—
431C4×C8—1461no—
432C4×C8C22×D7311yescharacteristic
433C4×C8C22×D7311yescharacteristic
434#41—22no—
435#41—41no—
436C2×Q8—731no—
437C2×Q8C2×C4×D7311yescharacteristic
438C2×D4—21no—
439C2×D4—731no—
440C2×D4—1461no—
441C2×D4C2×C4×D7311yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—1461no—
446C22×C4C2×C4×D7311yescharacteristic
447C22×C4C2×C22⋊D7311yescharacteristic
448C22×C4#1192402811yescharacteristic
449Q16—1462no—
450SD16—2921no—
451SD16—1462no—
452D8—2921no—
453M16—81no—
454M16—81no—
455M16—81no—
456M16—5841no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—5841no—
460C2×C8—5841no—
461C2×C8—731no—
462C2×C8—731no—
463C2×C8—731no—
464C2×C8—731no—
465C2×C8—1461no—
466C2×C8—1461no—
467C2×C8—1461no—
468C2×C8—1461no—
469C2×C8C2×C22⋊D7311yescharacteristic
470C2×C8C2×C22⋊D7311yescharacteristic
471C2×C8C2×C22⋊D7311yescharacteristic
472C2×C8C2×C22⋊D7311yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—731no—
476C4⋊C4—731no—
477C4⋊C4—1461no—
478C4⋊C4—1461no—
479C4⋊C4—1461no—
480C4⋊C4—1461no—
481C4⋊C4C2×C4×D7311yescharacteristic
482C4⋊C4C2×C4×D7311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—1461no—
487C22⋊C4—1461no—
488C22⋊C4—1461no—
489C22⋊C4—1461no—
490C22⋊C4—1461no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—1461no—
495C42C2×C4×D7311yescharacteristic
496C42C2×C22⋊D7311yescharacteristic
497C42#1192402811yescharacteristic
498C42C23×D7311yescharacteristic
499C23—21no—
500C23—1461no—
501C23C4×C22⋊D7311yescharacteristic
502Q8—21no—
503Q8—1461no—
504Q8—1461no—
505Q8#1455659912yes—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—2922no—
510D4—1461no—
511D4—1461no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—2921no—
525C2×C4—2921no—
526C2×C4—1461no—
527C2×C4—1461no—
528C2×C4—1461no—
529C2×C4C4×C22⋊D7311yescharacteristic
530C2×C4C4×C22⋊D7311yescharacteristic
531C2×C4C4×C22⋊D7311yescharacteristic
532C2×C4C22×C4×D7311yescharacteristic
533C2×C4C22×C22⋊D7311yescharacteristic
534C2×C4C2×#1192402811yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—2921no—
542C8—2921no—
543C8—2921no—
544C8—2921no—
545C8—1461no—
546C8—1461no—
547C8—1461no—
548C8—1461no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—2921no—
556C22—2921no—
557C22—2921no—
558C22C2×C4×C22⋊D7311yescharacteristic
559C4—21no—
560C4—22no—
561C4—21no—
562C4—21no—
563C4—21no—
564C4—41no—
565C4—41no—
566C4—2921no—
567C4—2921no—
568C4—2921no—
569C4C2×#1455659911yescharacteristic
570C4#1798935311yescharacteristic
571C4#1798939011yescharacteristic
572C4#1798940211yescharacteristic
573C2—41no—
574C2—81no—
575C2—5841no—
576C2#2261865611yescharacteristic
577C2#2261880411yescharacteristic
578C2#2261883211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2991C2
socleC22×C73C2×C4×D4
prime radical#17988732C4
cosocleC42×C73C24
hypercenter#2991D73
hypocenterC73#18033
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2991

Complements

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

NH ≅ G/Ntype
2. #22619093C2semidirect
3. #22608833C2semidirect
4. #22608814C2semidirect
5. #22608809C2semidirect
6. #22608807C2semidirect
7. #22608781C2semidirect
8. #22608758C2semidirect
9. #22608741C2semidirect
10. C8×#11924018C2semidirect
11. #22608707C2semidirect
12. #22608394C2semidirect
13. #22608318C2semidirect
14. #22608231C2semidirect
15. C73×#2991C2semidirect
292. #2991D73semidirect
305. C73#18033semidirect

Maximal subgroups

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

subgroupindex
#226199492
#226190932
#226088332
#226088142
#226088092
#226088072
#226087812
#226087582
#226087412
C8×#119240182
#226087072
#226083942
#226083182
#226082312
C73×#29912
#1803373