Finite Group Databasebeta

← #33057387

Subgroups — #33057387

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#22619087C211yesmaximal, characteristic, complemented
3#22619063C211yesmaximal, characteristic, complemented
4#22608830C211yesmaximal, characteristic, complemented
5#22608813C211yesmaximal, characteristic, complemented
6#22608812C211yesmaximal, characteristic, complemented
7#22608806C211yesmaximal, characteristic, complemented
8#22608778C211yesmaximal, characteristic, complemented
9#22608763C211yesmaximal, characteristic, complemented
10#22608746C211yesmaximal, characteristic, complemented
11#22608735C211yesmaximal, characteristic, complemented
12#22608705C211yesmaximal, characteristic, complemented
13#22608397C211yesmaximal, characteristic, complemented
14#22608231C211yesmaximal, characteristic, complemented
15C73×#1477C211yesmaximal, 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#17988665—21no—
34#17988665—21no—
35#17988665C2211yescharacteristic
36#17988665C2211yescharacteristic
37#17988664C2211yescharacteristic
38#17988658—21no—
39#17988652C2211yescharacteristic
40C8×C22⋊D73—21no—
41#17988647—21no—
42#17988640—21no—
43#17988640C2211yescharacteristic
44#17988640C2211yescharacteristic
45#17988612—21no—
46#17988611—21no—
47#17988611C2211yescharacteristic
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#431×C73C2211yescharacteristic
62C2×C4⋊C8×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×#11924012—21no—
72C2×#11924012—21no—
73C2×#11924012—21no—
74C2×#11924011—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
126C22×C8×C73—21no—
127C4×Q8×C73C2×C411yescharacteristic
128C4×Q8×C73C2311yescharacteristic
129C4×D4×C73—21no—
130C4×D4×C73—21no—
131C4×D4×C73C2×C411yescharacteristic
132C4×D4×C73C2311yescharacteristic
133#117×C73—21no—
134#117×C73C2×C411yescharacteristic
135C2×C42×C73—21no—
136C2×C42×C73C2311yescharacteristic
137C4⋊C8×C73—21no—
138C4⋊C8×C73—21no—
139C4⋊C8×C73C2311yescharacteristic
140C4⋊C8×C73C2311yescharacteristic
141C22⋊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#11924012—81no—
153#11924012—81no—
154#11924012—81no—
155#11924011—81no—
156C2×#10596831—21no—
157C2×#10596831—21no—
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—41no—
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
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—81no—
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—41no—
246C8×C73—41no—
247C8×C73—41no—
248C8×C73—41no—
249#10596831—21no—
250#10596831—21no—
251#10596831—21no—
252#10596831—21no—
253#10596831—21no—
254#10596831—21no—
255#10596831—21no—
256#10596831—21no—
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#2991—731no—
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#1477D7311yescharacteristic, complemented
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×Q8—731no—
319C8×Q8—731no—
320C4×Q16—731no—
321C4×SD16—731no—
322C4×SD16—731no—
323C4×D8—731no—
324#436—731no—
325#436—731no—
326#436—731no—
327#436—1461no—
328#436—1461no—
329#435—1461no—
330C8×D4—731no—
331C8×D4—1461no—
332#433—1461no—
333#431—731no—
334#431—731no—
335#431—1461no—
336#431C2×D7311yescharacteristic
337#424—1461no—
338#423—731no—
339#423—1461no—
340C2×C4⋊C8C2×D7311yescharacteristic
341#335—731no—
342#335—731no—
343#335—731no—
344#335—731no—
345Q8⋊C8—731no—
346Q8⋊C8—731no—
347Q8⋊C8C2×D7311yescharacteristic
348Q8⋊C8C2×D7311yescharacteristic
349D4⋊C8—731no—
350D4⋊C8—731no—
351D4⋊C8C2×D7311yescharacteristic
352D4⋊C8C2×D7311yescharacteristic
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—1461no—
363C2×M16—1461no—
364C2×M16—1461no—
365C2×M16—1461no—
366C22×C8—21no—
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—731no—
395C4⋊C8—731no—
396C4⋊C8—731no—
397C4⋊C8—731no—
398C4⋊C8—731no—
399C4⋊C8—731no—
400C4⋊C8—1461no—
401C4⋊C8—1461no—
402C4⋊C8—1461no—
403C4⋊C8—1461no—
404C4⋊C8—1461no—
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—731no—
417C22⋊C8—731no—
418C22⋊C8—731no—
419C22⋊C8—731no—
420C22⋊C8—1461no—
421C22⋊C8—1461no—
422C22⋊C8—1461no—
423C22⋊C8—1461no—
424#97—1461no—
425C4×C8—731no—
426C4×C8—731no—
427C4×C8—731no—
428C4×C8—731no—
429C4×C8—1461no—
430C4×C8—1461no—
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×C4D4×D7311yescharacteristic
448C22×C4#1192402711yescharacteristic
449Q16—1462no—
450SD16—2921no—
451SD16—1462no—
452D8—2921no—
453M16—5841no—
454M16—5841no—
455M16—5841no—
456M16—5841no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—81no—
462C2×C8—5841no—
463C2×C8—731no—
464C2×C8—731no—
465C2×C8—731no—
466C2×C8—731no—
467C2×C8—731no—
468C2×C8—731no—
469C2×C8—731no—
470C2×C8—731no—
471C2×C8—1461no—
472C2×C8—1461no—
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
496C42D4×D7311yescharacteristic
497C42#1192402711yescharacteristic
498C42C23×D7311yescharacteristic
499C23—21no—
500C23—1461no—
501C23#1455655111yescharacteristic
502Q8—21no—
503Q8—1461no—
504Q8—1461no—
505Q8#1455659712yes—
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×C4#1455655111yescharacteristic
530C2×C4#1455655111yescharacteristic
531C2×C4#1455655111yescharacteristic
532C2×C4C22×C4×D7311yescharacteristic
533C2×C4C2×D4×D7311yescharacteristic
534C2×C4C2×#1192402711yescharacteristic
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—2921no—
540C8—2921no—
541C8—1461no—
542C8—1461no—
543C8—1461no—
544C8—1461no—
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×#1455655111yescharacteristic
559C4—21no—
560C4—22no—
561C4—21no—
562C4—21no—
563C4—21no—
564C4—41no—
565C4—41no—
566C4—2921no—
567C4—2921no—
568C4—2921no—
569C4C2×#1455659711yescharacteristic
570C4#1798935311yescharacteristic
571C4#1798939111yescharacteristic
572C4#1798940311yescharacteristic
573C2—41no—
574C2—81no—
575C2—5841no—
576C2#2261865211yescharacteristic
577C2#2261880211yescharacteristic
578C2#2261883011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1477C2
socleC22×C73C2×C4×D4
prime radical#17988732C4
cosocleC42×C73C24
hypercenter#1477D73
hypocenterC73#18033
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1477

Complements

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

NH ≅ G/Ntype
2. #22619087C2semidirect
3. #22619063C2semidirect
4. #22608830C2semidirect
5. #22608813C2semidirect
6. #22608812C2semidirect
7. #22608806C2semidirect
8. #22608778C2semidirect
9. #22608763C2semidirect
10. #22608746C2semidirect
11. #22608735C2semidirect
12. #22608705C2semidirect
13. #22608397C2semidirect
14. #22608231C2semidirect
15. C73×#1477C2semidirect
303. #1477D73semidirect
305. C73#18033semidirect

Maximal subgroups

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

subgroupindex
#226199492
#226190872
#226190632
#226088302
#226088132
#226088122
#226088062
#226087782
#226087632
#226087462
#226087352
#226087052
#226083972
#226082312
C73×#14772
#1803373