Finite Group Databasebeta

← #33056897

Subgroups — #33056897

Order 18688.

618 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#22619945C211yesmaximal, characteristic
2#22618939C211yesmaximal, characteristic, complemented
3#22618938C211yesmaximal, characteristic, complemented
4#22608827C211yesmaximal, characteristic, complemented
5#22608819C211yesmaximal, characteristic, complemented
6#22608783C211yesmaximal, characteristic, complemented
7#22608764C211yesmaximal, characteristic, complemented
8#22608764C211yesmaximal, characteristic, complemented
9C8×#11924016C211yesmaximal, characteristic, complemented
10D8×#10596831C211yesmaximal, characteristic, complemented
11#22608710C211yesmaximal, characteristic, complemented
12#22608388C211yesmaximal, characteristic, complemented
13#22608310C211yesmaximal, characteristic, complemented
14#22608210C211yesmaximal, characteristic, complemented
15C73×#1581C211yesmaximal, characteristic, complemented
16#17989119C2211yescharacteristic
17C4×#11924027C2211yescharacteristic
18#17988930C411yescharacteristic
19#17988909C411yescharacteristic
20#17988893C411yescharacteristic
21#17988885C411yescharacteristic
22#17988808C411yescharacteristic
23#17988800C411yescharacteristic
24#17988750C411yescharacteristic
25#17988729C411yescharacteristic
26#17988717C2211yescharacteristic
27#17988714C2211yescharacteristic
28#17988714C2211yescharacteristic
29C8×Dic146C2211yescharacteristic
30C4×Dic292C2211yescharacteristic
31C4×#11924016C2211yescharacteristic
32C4×#11924016C2211yescharacteristic
33#17988663—21no—
34#17988658—21no—
35#17988655—21no—
36#17988655—21no—
37D4×#10596831C2211yescharacteristic
38D4×#10596831C2211yescharacteristic
39#17988645—21no—
40#17988643C2211yescharacteristic
41#17988641—21no—
42#17988639C2211yescharacteristic
43#17988638C2211yescharacteristic
44#17988545—21no—
45C4×#11924011C2211yescharacteristic
46C2×#14556501—21no—
47C4×C8×D73C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988337C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988319C2211yescharacteristic
52#17988319C2211yescharacteristic
53#17988317C2211yescharacteristic
54#17988317C2211yescharacteristic
55D4⋊#10596831C2211yescharacteristic
56D4⋊#10596831C2211yescharacteristic
57#17988309C2211yescharacteristic
58C8×#10596831C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60C4×D8×C73C2211yescharacteristic
61#436×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic
63#335×C73C2211yescharacteristic
64D4⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924027C2×C411yescharacteristic
68C2×Dic292C2×C411yescharacteristic
69C2×#11924016C2×C411yescharacteristic
70C2×#11924016C2×C411yescharacteristic
71C2×#11924011D411yescharacteristic
72C2×#11924011D411yescharacteristic
73C22×#10596831—21no—
74C22×#10596831—21no—
75C2×C8×D73—21no—
76#14556584—21no—
77#14556582C2×C411yescharacteristic
78#14556578C2×C411yescharacteristic
79#14556573—21no—
80#14556571C2×C411yescharacteristic
81#14556562C2×C411yescharacteristic
82C4×Dic146C2311yescharacteristic
83C4×Dic146C2311yescharacteristic
84#14556556C2×C411yescharacteristic
85D4×Dic73C2×C411yescharacteristic
86C4×C22⋊D73—21no—
87C4×C22⋊D73—21no—
88#14556551—21no—
89#14556550—21no—
90#14556549C2×C411yescharacteristic
91#14556547—21no—
92C2×C4×Dic73—21no—
93C42×D73C2311yescharacteristic
94#14556525C2×C411yescharacteristic
95#14556522C2×C411yescharacteristic
96#14556522C2×C411yescharacteristic
97C4⋊#10596831C2311yescharacteristic
98C4⋊#10596831C2311yescharacteristic
99#14556520—21no—
100#14556520—21no—
101#14556520—21no—
102#14556520—21no—
103#14556520C2×C411yescharacteristic
104#14556520C2×C411yescharacteristic
105#14556516C2×C411yescharacteristic
106#14556516C2×C411yescharacteristic
107#14556514C2×C411yescharacteristic
108#14556514C2×C411yescharacteristic
109#14556512C2×C411yescharacteristic
110#14556512C2×C411yescharacteristic
111C22⋊#10596831—21no—
112C22⋊#10596831—21no—
113#14556503—21no—
114#14556503—21no—
115#14556503C2×C411yescharacteristic
116#14556503C2×C411yescharacteristic
117#14556501—21no—
118#14556501—21no—
119#14556501—21no—
120#14556501—21no—
121#14556501D411yescharacteristic
122#14556501D411yescharacteristic
123C4×#10596831C2311yescharacteristic
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C8×Dic73—21no—
127C8×Dic73—21no—
128C8×Dic73—21no—
129C2×D8×C73C2×C411yescharacteristic
130C2×M16×C73—21no—
131C22×C8×C73—21no—
132C4×D4×C73C2311yescharacteristic
133C4×D4×C73C2311yescharacteristic
134#107×C73C2×C411yescharacteristic
135C4⋊C8×C73C2311yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137#102×C73C2×C411yescharacteristic
138#102×C73C2×C411yescharacteristic
139C22⋊C8×C73—21no—
140C22⋊C8×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924027—22no—
145#11924027—41no—
146C2×Dic146C22×C411yescharacteristic
147C2×Dic146C22×C411yescharacteristic
148C2×C22⋊D73—21no—
149C2×C22⋊D73—21no—
150C22×Dic73—21no—
151C22×Dic73—21no—
152C2×C4×D73C22×C411yescharacteristic
153C2×C4×D73C2×D411yescharacteristic
154C2×C4×D73#4111yescharacteristic
155Dic292—41no—
156#11924016—22no—
157#11924016—41no—
158#11924011—22no—
159#11924011—22no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—42no—
164C2×#10596831—42no—
165C2×#10596831C22×C411yescharacteristic
166C2×#10596831C22×C411yescharacteristic
167C2×#10596831C2×D411yescharacteristic
168C2×#10596831C2×D411yescharacteristic
169C8×D73—42no—
170C4⋊Dic73—21no—
171C4⋊Dic73—21no—
172C4⋊Dic73C22×C411yescharacteristic
173C4⋊Dic73C22×C411yescharacteristic
174#11924007—21no—
175#11924007—21no—
176#11924007—21no—
177#11924007—21no—
178C22⋊Dic73—21no—
179C22⋊Dic73—21no—
180C22⋊Dic73—21no—
181C22⋊Dic73—21no—
182#11924005—21no—
183#11924005—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73C22×C411yescharacteristic
189C4×Dic73C2×D411yescharacteristic
190C4×Dic73#4111yescharacteristic
191C2×D4×C73C22×C411yescharacteristic
192C2×D4×C73C22×C411yescharacteristic
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195D8×C73—22no—
196M16×C73—42no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—42no—
201C2×C8×C73C22×C411yescharacteristic
202C2×C8×C73C22×C411yescharacteristic
203C2×C8×C73C2×D411yescharacteristic
204C2×C8×C73C2×D411yescharacteristic
205C4⋊C4×C73C22×C411yescharacteristic
206C4⋊C4×C73C22×C411yescharacteristic
207C22⋊C4×C73—21no—
208C22⋊C4×C73—21no—
209C42×C73C2411yescharacteristic
210C23×C73—21no—
211C23×C73—21no—
212C22×D73C4×D411yescharacteristic
213D4×C73—21no—
214D4×C73—21no—
215D4×C73—21no—
216D4×C73#13112yes—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—41no—
220C2×C4×C73—41no—
221C2×C4×C73—41no—
222C2×C4×C73—41no—
223C2×C4×C73C23×C411yescharacteristic
224C2×C4×C73C22×D411yescharacteristic
225C2×C4×C73C2×#4111yescharacteristic
226C22⋊D73—42no—
227C22⋊D73—81no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—42no—
233C2×Dic73—81no—
234C2×Dic73C4×D411yescharacteristic
235C2×Dic73C4×D411yescharacteristic
236C2×Dic73C4×D411yescharacteristic
237C4×D73—21no—
238C4×D73—21no—
239C4×D73—21no—
240C4×D73—21no—
241C4×D73—41no—
242Dic146—21no—
243Dic146—21no—
244Dic146—21no—
245Dic146—21no—
246C8×C73—21no—
247C8×C73—21no—
248C8×C73—21no—
249C8×C73—41no—
250C8×C73—41no—
251C8×C73—41no—
252C8×C73#13512yes—
253#10596831—22no—
254#10596831—21no—
255#10596831—21no—
256#10596831—21no—
257#10596831—41no—
258#10596831—41no—
259#10596831#13512yes—
260C22×C73—22no—
261C22×C73—41no—
262C22×C73—41no—
263C22×C73—41no—
264C22×C73—41no—
265C22×C73—41no—
266C22×C73C2×C4×D411yescharacteristic
267C2×D73—21no—
268C2×D73—21no—
269C2×D73—21no—
270C4×C73—21no—
271C4×C73—41no—
272C4×C73—41no—
273C4×C73C2×#13111yescharacteristic
274C4×C73#56811yescharacteristic
275C4×C73C2×#13511yescharacteristic
276C4×C73C2×#13511yescharacteristic
277Dic73—21no—
278Dic73—21no—
279Dic73—21no—
280Dic73—41no—
281Dic73—41no—
282Dic73—41no—
283Dic73—41no—
284#17996—731nomaximal, Sylow
285C2×C73—42no—
286C2×C73—81no—
287C2×C73#293311yescharacteristic
288C2×C73C4×#13511yescharacteristic
289C2×C73#295611yescharacteristic
290D73—41no—
291#3102—731no—
292#2970—731no—
293#2969—731no—
294#1591—731no—
295#1590—731no—
296#1584—731no—
297#1582—731no—
298#1582—731no—
299#1581D7311yescharacteristic, complemented
300C8×SD16—731no—
301C8×D8—731no—
302#1572—731no—
303#1494—731no—
304#1476—731no—
305C8×M16—731no—
306C73#1799611yescharacteristic, complemented, Sylow
307#529—731no—
308C4×#41—731no—
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—
318#446—731no—
319#446—731no—
320C8×Q8—731no—
321C4×Q16—731no—
322C4×SD16—731no—
323C4×SD16—731no—
324C4×D8C2×D7311yescharacteristic
325#436—1461no—
326#436C2×D7311yescharacteristic
327#435—1461no—
328#435—1461no—
329#435—1461no—
330C8×D4—731no—
331C8×D4—731no—
332C8×D4C2×D7311yescharacteristic
333#433—1461no—
334#432—731no—
335#432—1461no—
336#431—731no—
337#431—731no—
338#405—1461no—
339C4×M16—731no—
340C2×#97—1461no—
341C2×C4×C8—731no—
342#335—731no—
343#335C2×D7311yescharacteristic
344#334—731no—
345#334—731no—
346Q8⋊C8—731no—
347Q8⋊C8—731no—
348Q8⋊C8—731no—
349Q8⋊C8—731no—
350D4⋊C8—731no—
351D4⋊C8—731no—
352D4⋊C8C2×D7311yescharacteristic
353D4⋊C8C2×D7311yescharacteristic
354#322—731no—
355#322C2×D7311yescharacteristic
356C82—731no—
357C82—731no—
358C2×#41—731no—
359C2×Q16—731no—
360C2×SD16—731no—
361C2×SD16—731no—
362C2×D8C4×D7311yescharacteristic
363C2×M16—21no—
364C2×M16—731no—
365C2×M16—731no—
366C22×C8—21no—
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×Q8—731no—
378C4×Q8—731no—
379C4×D4—731no—
380C4×D4—1461no—
381C4×D4—1461no—
382C4×D4—1461no—
383C4×D4C22×D7311yescharacteristic
384C4×D4C22×D7311yescharacteristic
385#117—731no—
386#117—1461no—
387#117—1461no—
388C2×C42—731no—
389C2×C42—1461no—
390#107—731no—
391#107C4×D7311yescharacteristic
392#106—731no—
393#106—731no—
394C4⋊C8—731no—
395C4⋊C8—731no—
396C4⋊C8—731no—
397C4⋊C8—731no—
398C4⋊C8—1461no—
399C4⋊C8—1461no—
400C4⋊C8—1461no—
401C4⋊C8—1461no—
402C4⋊C8C22×D7311yescharacteristic
403C4⋊C8C22×D7311yescharacteristic
404#103—731no—
405#103—731no—
406#103—731no—
407#103—731no—
408#102—731no—
409#102—731no—
410#102C4×D7311yescharacteristic
411#102C4×D7311yescharacteristic
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—731no—
415C22⋊C8—731no—
416C22⋊C8—1461no—
417C22⋊C8—1461no—
418C22⋊C8—1461no—
419C22⋊C8—1461no—
420#97—731no—
421#97—731no—
422#97—1461no—
423#97—1461no—
424#97—1461no—
425#97—1461no—
426C4×C8—731no—
427C4×C8—731no—
428C4×C8—731no—
429C4×C8—1461no—
430C4×C8—1461no—
431C4×C8—1461no—
432C4×C8C22×D7311yescharacteristic
433C4×C8C22×D7311yescharacteristic
434C4×C8C22×D7311yescharacteristic
435#41—2921no—
436#41—1462no—
437C2×Q8—731no—
438C2×Q8—731no—
439C2×D4—1461no—
440C2×D4—1461no—
441C2×D4C2×C4×D7311yescharacteristic
442C2×D4C2×C4×D7311yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—731no—
446C22×C4—731no—
447C22×C4—731no—
448C22×C4—1461no—
449C22×C4—1461no—
450Q16—2921no—
451SD16—2921no—
452SD16—1462no—
453D8—22no—
454M16—42no—
455M16—1462no—
456M16—1462no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—42no—
461C2×C8—2922no—
462C2×C8—2922no—
463C2×C8—2922no—
464C2×C8—731no—
465C2×C8—731no—
466C2×C8—731no—
467C2×C8—731no—
468C2×C8—1461no—
469C2×C8—1461no—
470C2×C8—1461no—
471C2×C8C2×C4×D7311yescharacteristic
472C2×C8C2×C4×D7311yescharacteristic
473C2×C8D4×D7311yescharacteristic
474C2×C8D4×D7311yescharacteristic
475C4⋊C4—731no—
476C4⋊C4—731no—
477C4⋊C4—1461no—
478C4⋊C4—1461no—
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—1461no—
488C22⋊C4—1461no—
489C22⋊C4—1461no—
490C22⋊C4—1461no—
491C22⋊C4—1461no—
492C22⋊C4—1461no—
493C42—731no—
494C42—731no—
495C42—731no—
496C42—1461no—
497C42—1461no—
498C42—1461no—
499C42—1461no—
500C42C23×D7311yescharacteristic
501C23—21no—
502C23—21no—
503C23—731no—
504Q8—1461no—
505Q8—1461no—
506Q8—1461no—
507Q8—1461no—
508D4—21no—
509D4—21no—
510D4—21no—
511D4—2922no—
512D4—5841no—
513D4#1455659912yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—2921no—
521C2×C4—2922no—
522C2×C4—5841no—
523C2×C4—731no—
524C2×C4—731no—
525C2×C4—731no—
526C2×C4—1461no—
527C2×C4—1461no—
528C2×C4—1461no—
529C2×C4—1461no—
530C2×C4—1461no—
531C2×C4—1461no—
532C2×C4—1461no—
533C2×C4—1461no—
534C2×C4C22×C4×D7311yescharacteristic
535C2×C4C2×D4×D7311yescharacteristic
536C2×C4#41×D7311yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—2921no—
544C8—2921no—
545C8—732no—
546C8—1462no—
547C8—1461no—
548C8—1461no—
549C8—1461no—
550C8#1455661012yes—
551C22—22no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—1461no—
558C22—1461no—
559C22—1461no—
560C22C4×D4×D7311yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—2921no—
565C4—2921no—
566C4—2921no—
567C4—2921no—
568C4—1461no—
569C4—1461no—
570C4—1461no—
571C4C2×#1455659911yescharacteristic
572C4#1798935211yescharacteristic
573C4#135×D7311yescharacteristic
574C4C2×#1455661011yescharacteristic
575C2—42no—
576C2—81no—
577C2—2921no—
578C2#2261865711yescharacteristic
579C2C4×#1455661011yescharacteristic
580C2#2261883911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1581C2
socleC22×C73C2×C4×D4
prime radical#17988729C4
cosocleC42×C73C24
hypercenter#1581D73
hypocenterC73#17996
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1581

Complements

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

NH ≅ G/Ntype
2. #22618939C2semidirect
3. #22618938C2semidirect
4. #22608827C2semidirect
5. #22608819C2semidirect
6. #22608783C2semidirect
7. #22608764C2semidirect
8. #22608764C2semidirect
9. C8×#11924016C2semidirect
10. D8×#10596831C2semidirect
11. #22608710C2semidirect
12. #22608388C2semidirect
13. #22608310C2semidirect
14. #22608210C2semidirect
15. C73×#1581C2semidirect
299. #1581D73semidirect
306. C73#17996semidirect

Maximal subgroups

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

subgroupindex
#226199452
#226189392
#226189382
#226088272
#226088192
#226087832
#226087642
C8×#119240162
D8×#105968312
#226087102
#226083882
#226083102
#226082102
C73×#15812
#1799673