Finite Group Databasebeta

← #33056898

Subgroups — #33056898

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#22619951C211yesmaximal, characteristic
2#22618946C211yesmaximal, characteristic, complemented
3#22618935C211yesmaximal, characteristic, complemented
4#22608829C211yesmaximal, characteristic, complemented
5#22608823C211yesmaximal, characteristic, complemented
6#22608783C211yesmaximal, characteristic, complemented
7#22608769C211yesmaximal, characteristic, complemented
8#22608769C211yesmaximal, characteristic, complemented
9#22608762C211yesmaximal, characteristic, complemented
10C8×#11924017C211yesmaximal, characteristic, complemented
11C8×D584C211yesmaximal, characteristic, complemented
12#22608711C211yesmaximal, characteristic, complemented
13#22608392C211yesmaximal, characteristic, complemented
14#22608314C211yesmaximal, characteristic, complemented
15C8×M16×C73C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17C4×#11924028C2211yescharacteristic
18#17988929C411yescharacteristic
19#17988912C411yescharacteristic
20#17988895C411yescharacteristic
21#17988888C411yescharacteristic
22#17988810C411yescharacteristic
23#17988803C411yescharacteristic
24#17988751C411yescharacteristic
25#17988734C411yescharacteristic
26#17988717C2211yescharacteristic
27#17988717C2211yescharacteristic
28#17988717C2211yescharacteristic
29C8×Dic146C2211yescharacteristic
30C4×Dic292C2211yescharacteristic
31C4×#11924017C2211yescharacteristic
32C4×#11924017C2211yescharacteristic
33C4×D584C2211yescharacteristic
34#17988666C2211yescharacteristic
35#17988663—21no—
36#17988656—21no—
37#17988656—21no—
38#17988656—21no—
39C8×D292C2211yescharacteristic
40C8×D292C2211yescharacteristic
41C8×D292C2211yescharacteristic
42#17988649—21no—
43#17988644C2211yescharacteristic
44#17988642—21no—
45#17988640C2211yescharacteristic
46#17988544—21no—
47#97×D73—21no—
48#17988340C2211yescharacteristic
49#17988340C2211yescharacteristic
50#17988338C2211yescharacteristic
51#17988338C2211yescharacteristic
52#17988319C2211yescharacteristic
53#17988319C2211yescharacteristic
54#17988319C2211yescharacteristic
55#17988319C2211yescharacteristic
56#17988316C2211yescharacteristic
57#17988316C2211yescharacteristic
58#17988316C2211yescharacteristic
59#17988316C2211yescharacteristic
60#431×C73C2211yescharacteristic
61C4×M16×C73C2211yescharacteristic
62C2×C4×C8×C73C2211yescharacteristic
63#322×C73C2211yescharacteristic
64#322×C73C2211yescharacteristic
65C82×C73C2211yescharacteristic
66C82×C73C2211yescharacteristic
67C2×#11924028C2×C411yescharacteristic
68C2×Dic292C2×C411yescharacteristic
69C2×#11924017C2×C411yescharacteristic
70C2×#11924017C2×C411yescharacteristic
71C2×D584C2×C411yescharacteristic
72C2×#11924011—21no—
73C2×C8×D73—21no—
74C2×C8×D73—21no—
75C2×C8×D73—21no—
76#14556585—21no—
77#14556583C2×C411yescharacteristic
78#14556579C2×C411yescharacteristic
79#14556574—21no—
80#14556570C2×C411yescharacteristic
81#14556565C2×C411yescharacteristic
82C4×Dic146C2×C411yescharacteristic
83C4×Dic146C2311yescharacteristic
84C4×Dic146C2311yescharacteristic
85C4×D292C2×C411yescharacteristic
86C4×D292C2311yescharacteristic
87C4×D292C2311yescharacteristic
88C4×C22⋊D73—21no—
89C4×C22⋊D73—21no—
90C4×C22⋊D73—21no—
91#14556550C2×C411yescharacteristic
92#14556548—21no—
93#14556548—21no—
94C42×D73—21no—
95#14556525C2×C411yescharacteristic
96#14556525C2×C411yescharacteristic
97#14556523C2×C411yescharacteristic
98#14556523C2×C411yescharacteristic
99C4⋊#10596831C2311yescharacteristic
100C4⋊#10596831C2311yescharacteristic
101C4⋊#10596831C2311yescharacteristic
102C4⋊#10596831C2311yescharacteristic
103#14556520—21no—
104#14556520—21no—
105#14556520—21no—
106#14556520—21no—
107#14556516C2×C411yescharacteristic
108#14556516C2×C411yescharacteristic
109#14556516C2×C411yescharacteristic
110#14556516C2×C411yescharacteristic
111#14556513C2×C411yescharacteristic
112#14556513C2×C411yescharacteristic
113#14556513C2×C411yescharacteristic
114#14556513C2×C411yescharacteristic
115C22⋊#10596831—21no—
116C22⋊#10596831—21no—
117#14556503—21no—
118#14556503—21no—
119#14556503—21no—
120#14556503—21no—
121#14556502—21no—
122#14556501—21no—
123#14556501—21no—
124#14556501—21no—
125C4×#10596831—21no—
126C8×Dic73—21no—
127C2×M16×C73D411yescharacteristic
128C2×M16×C73D411yescharacteristic
129C22×C8×C73—21no—
130C2×C42×C73C2311yescharacteristic
131C4⋊C8×C73C2×C411yescharacteristic
132C4⋊C8×C73C2×C411yescharacteristic
133C22⋊C8×C73C2×C411yescharacteristic
134C22⋊C8×C73C2×C411yescharacteristic
135#97×C73D411yescharacteristic
136#97×C73D411yescharacteristic
137C4×C8×C73—21no—
138C4×C8×C73C2311yescharacteristic
139C4×C8×C73C2311yescharacteristic
140C4×C8×C73C2311yescharacteristic
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924028—22no—
145#11924028—41no—
146C2×Dic146C22×C411yescharacteristic
147C2×Dic146C22×C411yescharacteristic
148C2×D292C22×C411yescharacteristic
149C2×D292C22×C411yescharacteristic
150C2×C22⋊D73—21no—
151C2×C22⋊D73—21no—
152C2×C4×D73—21no—
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—21no—
156Dic292—41no—
157#11924017—22no—
158#11924017—41no—
159D584—22no—
160#11924011—42no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C8×D73—42no—
166C8×D73—42no—
167C8×D73—42no—
168C4⋊Dic73C22×C411yescharacteristic
169C4⋊Dic73C22×C411yescharacteristic
170C4⋊Dic73C22×C411yescharacteristic
171C4⋊Dic73C22×C411yescharacteristic
172#11924007—21no—
173#11924007—21no—
174#11924007—21no—
175#11924007—21no—
176#11924007—21no—
177#11924007—21no—
178C22⋊Dic73—21no—
179C22⋊Dic73—21no—
180#11924005—21no—
181#11924005—21no—
182#11924005—21no—
183#11924005—21no—
184#11924005—21no—
185#11924005—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C22×C4×C73C22×C411yescharacteristic
191C22×C4×C73C2×D411yescharacteristic
192C22×C4×C73#4111yescharacteristic
193M16×C73—22no—
194M16×C73—22no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—42no—
198C2×C8×C73C22×C411yescharacteristic
199C2×C8×C73C22×C411yescharacteristic
200C2×C8×C73C22×C411yescharacteristic
201C2×C8×C73C22×C411yescharacteristic
202C2×C8×C73C2×D411yescharacteristic
203C2×C8×C73C2×D411yescharacteristic
204C2×C8×C73C2×D411yescharacteristic
205C2×C8×C73C2×D411yescharacteristic
206C42×C73C22×C411yescharacteristic
207C42×C73C2×D411yescharacteristic
208C42×C73#4111yescharacteristic
209C42×C73C2411yescharacteristic
210C23×C73C4×D411yescharacteristic
211C22×D73—21no—
212C22×D73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—41no—
218C2×C4×C73C4×D411yescharacteristic
219C2×C4×C73C4×D411yescharacteristic
220C2×C4×C73C4×D411yescharacteristic
221C2×C4×C73C23×C411yescharacteristic
222C2×C4×C73C22×D411yescharacteristic
223C2×C4×C73C2×#4111yescharacteristic
224C22⋊D73—42no—
225C22⋊D73—81no—
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232D292—21no—
233D292—21no—
234D292—21no—
235D292#13112yes—
236C4×D73—42no—
237C4×D73—41no—
238C4×D73—41no—
239C4×D73—41no—
240C4×D73—41no—
241C4×D73—81no—
242Dic146—21no—
243Dic146—21no—
244Dic146—21no—
245Dic146—21no—
246C8×C73—22no—
247C8×C73—21no—
248C8×C73—21no—
249C8×C73—21no—
250C8×C73—21no—
251C8×C73—21no—
252C8×C73—21no—
253C8×C73—41no—
254C8×C73#13512yes—
255C8×C73#13512yes—
256#10596831—41no—
257#10596831—41no—
258#10596831—41no—
259#10596831—41no—
260C22×C73—21no—
261C22×C73—21no—
262C22×C73—21no—
263C22×C73C2×C4×D411yescharacteristic
264C2×D73—22no—
265C2×D73—41no—
266C2×D73—41no—
267C2×D73—41no—
268C2×D73—41no—
269C2×D73—41no—
270C4×C73—21no—
271C4×C73—21no—
272C4×C73—21no—
273C4×C73—21no—
274C4×C73C2×#13111yescharacteristic
275C4×C73#56811yescharacteristic
276C4×C73C2×#13511yescharacteristic
277C4×C73C2×#13511yescharacteristic
278Dic73—41no—
279Dic73—41no—
280Dic73—41no—
281Dic73—41no—
282Dic73—41no—
283Dic73—41no—
284#17996—731nomaximal, Sylow
285C2×C73—41no—
286C2×C73#293311yescharacteristic
287C2×C73C4×#13511yescharacteristic
288C2×C73#295611yescharacteristic
289D73—42no—
290D73—81no—
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#1581—731no—
300C8×SD16—731no—
301C8×D8—731no—
302#1572—731no—
303#1494—731no—
304#1476—731no—
305C8×M16D7311yescharacteristic, complemented
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×D8—731no—
325#436—731no—
326#436—1461no—
327#435—1461no—
328#435—1461no—
329#435—1461no—
330C8×D4—731no—
331C8×D4—731no—
332C8×D4—731no—
333#433—1461no—
334#432—731no—
335#432—1461no—
336#431—731no—
337#431C2×D7311yescharacteristic
338#405—1461no—
339C4×M16C2×D7311yescharacteristic
340C2×#97—1461no—
341C2×C4×C8C2×D7311yescharacteristic
342#335—731no—
343#335—731no—
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⋊C8—731no—
353D4⋊C8—731no—
354#322C2×D7311yescharacteristic
355#322C2×D7311yescharacteristic
356C82C2×D7311yescharacteristic
357C82C2×D7311yescharacteristic
358C2×#41—731no—
359C2×Q16—731no—
360C2×SD16—731no—
361C2×SD16—731no—
362C2×D8—731no—
363C2×M16—1461no—
364C2×M16D29211yescharacteristic
365C2×M16D29211yescharacteristic
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—731no—
381C4×D4—731no—
382C4×D4—1461no—
383C4×D4—1461no—
384C4×D4—1461no—
385#117—731no—
386#117—1461no—
387#117—1461no—
388C2×C42—1461no—
389C2×C42C22×D7311yescharacteristic
390#107—731no—
391#107—731no—
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⋊C8C4×D7311yescharacteristic
403C4⋊C8C4×D7311yescharacteristic
404#103—731no—
405#103—731no—
406#103—731no—
407#103—731no—
408#102—731no—
409#102—731no—
410#102—731no—
411#102—731no—
412C22⋊C8—1461no—
413C22⋊C8—1461no—
414C22⋊C8—1461no—
415C22⋊C8—1461no—
416C22⋊C8—1461no—
417C22⋊C8—1461no—
418C22⋊C8C4×D7311yescharacteristic
419C22⋊C8C4×D7311yescharacteristic
420#97—1461no—
421#97—1461no—
422#97—1461no—
423#97—1461no—
424#97D29211yescharacteristic
425#97D29211yescharacteristic
426C4×C8—21no—
427C4×C8—1461no—
428C4×C8—1461no—
429C4×C8C22×D7311yescharacteristic
430C4×C8C22×D7311yescharacteristic
431C4×C8C22×D7311yescharacteristic
432C4×C8C22×D7311yescharacteristic
433C4×C8C22×D7311yescharacteristic
434C4×C8C22×D7311yescharacteristic
435#41—2921no—
436#41—1462no—
437C2×Q8—731no—
438C2×Q8—731no—
439C2×D4—731no—
440C2×D4—731no—
441C2×D4—1461no—
442C2×D4—1461no—
443C22×C4—1461no—
444C22×C4—1461no—
445C22×C4—1461no—
446C22×C4—1461no—
447C22×C4C2×C4×D7311yescharacteristic
448C22×C4C2×D29211yescharacteristic
449C22×C4#1192402811yescharacteristic
450Q16—2921no—
451SD16—2921no—
452SD16—1462no—
453D8—1462no—
454M16—22no—
455M16—22no—
456M16—2922no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—42no—
460C2×C8—2922no—
461C2×C8—2922no—
462C2×C8—2922no—
463C2×C8—1461no—
464C2×C8—1461no—
465C2×C8—1461no—
466C2×C8—1461no—
467C2×C8C2×C4×D7311yescharacteristic
468C2×C8C2×C4×D7311yescharacteristic
469C2×C8C2×C4×D7311yescharacteristic
470C2×C8C2×C4×D7311yescharacteristic
471C2×C8C2×D29211yescharacteristic
472C2×C8C2×D29211yescharacteristic
473C2×C8C2×D29211yescharacteristic
474C2×C8C2×D29211yescharacteristic
475C4⋊C4—731no—
476C4⋊C4—731no—
477C4⋊C4—731no—
478C4⋊C4—731no—
479C4⋊C4—1461no—
480C4⋊C4—1461no—
481C4⋊C4—1461no—
482C4⋊C4—1461no—
483C4⋊C4—1461no—
484C4⋊C4—1461no—
485C22⋊C4—1461no—
486C22⋊C4—1461no—
487C22⋊C4—1461no—
488C22⋊C4—1461no—
489C22⋊C4—1461no—
490C22⋊C4—1461no—
491C22⋊C4—1461no—
492C22⋊C4—1461no—
493C42—1461no—
494C42—1461no—
495C42—1461no—
496C42—1461no—
497C42C2×C4×D7311yescharacteristic
498C42C2×D29211yescharacteristic
499C42#1192402811yescharacteristic
500C42C23×D7311yescharacteristic
501C23—1461no—
502C23—1461no—
503C23C4×D29211yescharacteristic
504Q8—1461no—
505Q8—1461no—
506Q8—1461no—
507Q8—1461no—
508D4—2922no—
509D4—5841no—
510D4—732no—
511D4—1461no—
512D4—1461no—
513D4—1461no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—2922no—
520C2×C4—2921no—
521C2×C4—2921no—
522C2×C4—2921no—
523C2×C4—2921no—
524C2×C4—5841no—
525C2×C4—1461no—
526C2×C4—1461no—
527C2×C4—1461no—
528C2×C4—1461no—
529C2×C4—1461no—
530C2×C4—1461no—
531C2×C4C4×D29211yescharacteristic
532C2×C4C4×D29211yescharacteristic
533C2×C4C4×D29211yescharacteristic
534C2×C4C22×C4×D7311yescharacteristic
535C2×C4C22×D29211yescharacteristic
536C2×C4C2×#1192402811yescharacteristic
537C8—22no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—21no—
543C8—21no—
544C8—41no—
545C8—2921no—
546C8—2921no—
547C8—2921no—
548C8—2921no—
549C8#1455661312yes—
550C8#1455661312yes—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—2921no—
555C22—2921no—
556C22—2921no—
557C22—2921no—
558C22—2921no—
559C22—1462no—
560C22C2×C4×D29211yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—2921no—
566C4—2921no—
567C4—2921no—
568C4—2921no—
569C4—2921no—
570C4—2921no—
571C4#131×D7311yescharacteristic
572C4#1798935211yescharacteristic
573C4C2×#1455661311yescharacteristic
574C4C2×#1455661311yescharacteristic
575C2—41no—
576C2—2922no—
577C2—5841no—
578C2#2261865911yescharacteristic
579C2C4×#1455661311yescharacteristic
580C2#2261884211yescharacteristic
subgroupG/H
centerC2×C4C22×D292
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC8×M16×C73C2
socleC22×C73C2×C4×D4
prime radical#17988734C4
cosocleC42×C73C24
hypercenterC8×M16D73
hypocenterC73#17996
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ C8×M16

Complements

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

NH ≅ G/Ntype
2. #22618946C2semidirect
3. #22618935C2semidirect
4. #22608829C2semidirect
5. #22608823C2semidirect
6. #22608783C2semidirect
7. #22608769C2semidirect
8. #22608769C2semidirect
9. #22608762C2semidirect
10. C8×#11924017C2semidirect
11. C8×D584C2semidirect
12. #22608711C2semidirect
13. #22608392C2semidirect
14. #22608314C2semidirect
15. C8×M16×C73C2semidirect
305. C8×M16D73semidirect
306. C73#17996semidirect

Maximal subgroups

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

subgroupindex
#226199512
#226189462
#226189352
#226088292
#226088232
#226087832
#226087692
#226087622
C8×#119240172
C8×D5842
#226087112
#226083922
#226083142
C8×M16×C732
#1799673