Finite Group Databasebeta

← #33057354

Subgroups — #33057354

Order 18688.

606 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619958C211yesmaximal, characteristic
2#22619021C211yesmaximal, characteristic, complemented
3#22618998C211yesmaximal, characteristic
4#22608830C211yesmaximal, characteristic, complemented
5#22608824C211yesmaximal, characteristic, complemented
6#22608812C211yesmaximal, characteristic, complemented
7#22608785C211yesmaximal, characteristic, complemented
8#22608777C211yesmaximal, characteristic, complemented
9#22608764C211yesmaximal, characteristic, complemented
10#22608740C211yesmaximal, characteristic, complemented
11#22608734C211yesmaximal, characteristic, complemented
12#22608712C211yesmaximal, characteristic, complemented
13#22608327C211yesmaximal, characteristic, complemented
14#22608231C211yesmaximal, characteristic, complemented
15C73×#1496C211yesmaximal, characteristic
16C2×C4×Dic146C2211yescharacteristic
17#17988903C411yescharacteristic
18#17988903C411yescharacteristic
19#17988869C411yescharacteristic
20#17988869C411yescharacteristic
21#17988784C411yescharacteristic
22#17988784C411yescharacteristic
23#17988725C411yescharacteristic
24#17988725C411yescharacteristic
25#17988715—21no—
26#17988715—21no—
27#17988714C2211yescharacteristic
28#17988714C2211yescharacteristic
29#17988711C2211yescharacteristic
30#17988711C2211yescharacteristic
31C4×#11924016C2211yescharacteristic
32C4×#11924016C2211yescharacteristic
33C4×#11924016C2211yescharacteristic
34C4×#11924016C2211yescharacteristic
35#17988665—21no—
36#17988665C2211yescharacteristic
37#17988665C2211yescharacteristic
38D4×#10596831—21no—
39D4×#10596831C2211yescharacteristic
40D4×#10596831C2211yescharacteristic
41#17988641—21no—
42#17988640C2211yescharacteristic
43#17988640C2211yescharacteristic
44#17988640C2211yescharacteristic
45#17988637—21no—
46#17988554—21no—
47#17988554—21no—
48#17988339C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988337C2211yescharacteristic
52#17988319C2211yescharacteristic
53#17988319C2211yescharacteristic
54#17988319C2211yescharacteristic
55#17988319C2211yescharacteristic
56#17988309C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988308C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60#532×C73C2211yescharacteristic
61#432×C73C2211yescharacteristic
62#431×C73C2211yescharacteristic
63D4⋊C8×C73C2211yescharacteristic
64D4⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66D4⋊C8×C73C2211yescharacteristic
67C22×Dic146C2×C411yescharacteristic
68C2×#11924016C2×C411yescharacteristic
69C2×#11924016C2×C411yescharacteristic
70C2×#11924016C2×C411yescharacteristic
71C2×#11924016C2×C411yescharacteristic
72C2×#11924012—21no—
73C2×#11924012—21no—
74C22×#10596831—21no—
75C22×#10596831—21no—
76C4×Dic146—21no—
77C4×Dic146—21no—
78C4×Dic146C2×C411yescharacteristic
79C4×Dic146C2×C411yescharacteristic
80C4×Dic146C2311yescharacteristic
81C4×Dic146C2311yescharacteristic
82C2×C4⋊Dic73C2×C411yescharacteristic
83C2×#11924007—21no—
84C2×C4×Dic73—21no—
85#14556522C2×C411yescharacteristic
86#14556522C2×C411yescharacteristic
87#14556522C2×C411yescharacteristic
88#14556522C2×C411yescharacteristic
89C4⋊#10596831C2×C411yescharacteristic
90C4⋊#10596831C2×C411yescharacteristic
91C4⋊#10596831D411yescharacteristic
92C4⋊#10596831D411yescharacteristic
93C4⋊#10596831C2311yescharacteristic
94C4⋊#10596831C2311yescharacteristic
95#14556520—21no—
96#14556520—21no—
97#14556520—21no—
98#14556520—21no—
99#14556514C2×C411yescharacteristic
100#14556514C2×C411yescharacteristic
101#14556514C2×C411yescharacteristic
102#14556514C2×C411yescharacteristic
103#14556512C2×C411yescharacteristic
104#14556512C2×C411yescharacteristic
105#14556512C2×C411yescharacteristic
106#14556512C2×C411yescharacteristic
107C22⋊#10596831—21no—
108C22⋊#10596831—21no—
109C22⋊#10596831—21no—
110C22⋊#10596831—21no—
111C22⋊#10596831—21no—
112C22⋊#10596831C2×C411yescharacteristic
113C22⋊#10596831C2×C411yescharacteristic
114C22⋊#10596831D411yescharacteristic
115C22⋊#10596831D411yescharacteristic
116#14556501—21no—
117#14556501—21no—
118C4×#10596831—21no—
119C4×#10596831C2311yescharacteristic
120C4×#10596831C2311yescharacteristic
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C8×Dic73—21no—
124C8×Dic73—21no—
125C2×#41×C73—21no—
126C4⋊Q8×C73C2×C411yescharacteristic
127#127×C73C2×C411yescharacteristic
128#124×C73—21no—
129#121×C73—21no—
130#121×C73C2×C411yescharacteristic
131#121×C73C2×C411yescharacteristic
132C4×D4×C73—21no—
133C4×D4×C73C2311yescharacteristic
134C4×D4×C73C2311yescharacteristic
135C2×C42×C73C2311yescharacteristic
136C4⋊C8×C73—21no—
137C4⋊C8×C73C2311yescharacteristic
138C4⋊C8×C73C2311yescharacteristic
139C22⋊C8×C73—21no—
140C22⋊C8×C73—21no—
141#97×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146—22no—
145C2×Dic146—21no—
146C2×Dic146—41no—
147C2×Dic146C22×C411yescharacteristic
148C2×Dic146C22×C411yescharacteristic
149C22×Dic73—21no—
150C22×Dic73—21no—
151#11924016—22no—
152#11924016—22no—
153#11924016—41no—
154#11924016—41no—
155#11924012—81no—
156#11924012—81no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—81no—
160C2×#10596831—81no—
161C2×#10596831C22×C411yescharacteristic
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C22×C411yescharacteristic
164C2×#10596831C22×C411yescharacteristic
165C2×#10596831C2×D411yescharacteristic
166C2×#10596831C2×D411yescharacteristic
167C2×#10596831C2×D411yescharacteristic
168C2×#10596831C2×D411yescharacteristic
169C4⋊Dic73—21no—
170C4⋊Dic73C22×C411yescharacteristic
171C4⋊Dic73C22×C411yescharacteristic
172#11924007—21no—
173#11924007—21no—
174#11924007—21no—
175#11924007—21no—
176C4×Dic73—21no—
177C4×Dic73—21no—
178C4×Dic73—21no—
179C4×Dic73—21no—
180#41×C73—81no—
181#41×C73—81no—
182C2×Q8×C73—21no—
183C2×D4×C73—21no—
184C2×D4×C73—21no—
185C2×D4×C73—21no—
186C2×D4×C73—21no—
187C2×D4×C73C22×C411yescharacteristic
188C2×D4×C73C22×C411yescharacteristic
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73C22×C411yescharacteristic
192C22×C4×C73C2×D411yescharacteristic
193C22×C4×C73#4111yescharacteristic
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73C22×C411yescharacteristic
200C4⋊C4×C73C22×C411yescharacteristic
201C22⋊C4×C73—21no—
202C22⋊C4×C73—21no—
203C22⋊C4×C73—21no—
204C22⋊C4×C73—21no—
205C42×C73C22×C411yescharacteristic
206C42×C73C2×D411yescharacteristic
207C42×C73#4111yescharacteristic
208C42×C73C2411yescharacteristic
209C23×C73—21no—
210C23×C73—21no—
211C23×C73C4×D411yescharacteristic
212Q8×C73—81no—
213D4×C73—21no—
214D4×C73—21no—
215D4×C73—21no—
216D4×C73—21no—
217D4×C73—42no—
218D4×C73—81no—
219D4×C73—81no—
220D4×C73—81no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—41no—
228C2×C4×C73—41no—
229C2×C4×C73—41no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73C4×D411yescharacteristic
233C2×C4×C73C4×D411yescharacteristic
234C2×C4×C73C4×D411yescharacteristic
235C2×C4×C73C23×C411yescharacteristic
236C2×C4×C73C22×D411yescharacteristic
237C2×C4×C73C2×#4111yescharacteristic
238C2×Dic73—21no—
239C2×Dic73—21no—
240C2×Dic73—21no—
241C2×Dic73—21no—
242C2×Dic73—42no—
243C2×Dic73—42no—
244Dic146—21no—
245Dic146—21no—
246Dic146—21no—
247Dic146—42no—
248Dic146#13112yes—
249C8×C73—41no—
250C8×C73—41no—
251C8×C73—41no—
252C8×C73—41no—
253#10596831—21no—
254#10596831—21no—
255#10596831—21no—
256#10596831—21no—
257#10596831—21no—
258#10596831—21no—
259#10596831—21no—
260#10596831—21no—
261#10596831—41no—
262#10596831—41no—
263C22×C73—21no—
264C22×C73—21no—
265C22×C73—21no—
266C22×C73—41no—
267C22×C73—41no—
268C22×C73—41no—
269C22×C73—41no—
270C22×C73—41no—
271C22×C73—41no—
272C22×C73C2×C4×D411yescharacteristic
273C4×C73—21no—
274C4×C73—21no—
275C4×C73—21no—
276C4×C73—21no—
277C4×C73—41no—
278C4×C73—41no—
279C4×C73C2×#13111yescharacteristic
280C4×C73#56811yescharacteristic
281C4×C73#57711yescharacteristic
282C4×C73#57711yescharacteristic
283Dic73—22no—
284Dic73—41no—
285Dic73—41no—
286Dic73—41no—
287#18030—731nomaximal, Sylow
288C2×C73—41no—
289C2×C73—81no—
290C2×C73—81no—
291C2×C73#293311yescharacteristic
292C2×C73#294911yescharacteristic
293C2×C73#295511yescharacteristic
294#3103—731no—
295#2984—731no—
296#2979—731no—
297#1592—731no—
298#1590—731no—
299#1588—731no—
300#1585—731no—
301#1583—731no—
302#1582—731no—
303SD16⋊C8—731no—
304C8×SD16—731no—
305#1572—731no—
306#1496D7311yescharacteristic
307#1479—731no—
308#1454—731no—
309C73#1803011yescharacteristic, complemented, Sylow
310#532C2×D7311yescharacteristic
311C2×C4×Q8—731no—
312#481—731no—
313#481—731no—
314#475—731no—
315#475—731no—
316#460—731no—
317#460—731no—
318#448—731no—
319#448—731no—
320#446—731no—
321#446—731no—
322#446—1461no—
323#446—1461no—
324C8×Q8—731no—
325C8×Q8—731no—
326C4×SD16—731no—
327C4×SD16—731no—
328C4×SD16—731no—
329C4×SD16—731no—
330#436—731no—
331#436—731no—
332#436—1461no—
333C8×D4—731no—
334C8×D4—731no—
335C8×D4—1461no—
336#432—1461no—
337#432C2×D7311yescharacteristic
338#431—731no—
339#431—731no—
340#431—731no—
341#431—1461no—
342#431C2×D7311yescharacteristic
343#408—1461no—
344#408—1461no—
345#335—731no—
346#335—731no—
347#334—731no—
348#334—731no—
349Q8⋊C8—731no—
350Q8⋊C8—731no—
351Q8⋊C8—731no—
352Q8⋊C8—731no—
353D4⋊C8C2×D7311yescharacteristic
354D4⋊C8C2×D7311yescharacteristic
355D4⋊C8C2×D7311yescharacteristic
356D4⋊C8C2×D7311yescharacteristic
357#322—731no—
358#322—731no—
359#322—731no—
360C82—731no—
361C2×#41—21no—
362C22×Q8—731no—
363C2×SD16—731no—
364C2×SD16—731no—
365C2×SD16—731no—
366C2×SD16—731no—
367C2×M16—1461no—
368C2×M16—1461no—
369C22×C8—1461no—
370C22×C8—1461no—
371C4⋊Q8C4×D7311yescharacteristic
372#127C4×D7311yescharacteristic
373#124—21no—
374#121—21no—
375#121C4×D7311yescharacteristic
376#121C4×D7311yescharacteristic
377C4×Q8—731no—
378C4×Q8—731no—
379C4×Q8—731no—
380C4×Q8—731no—
381C4×Q8—1461no—
382C4×Q8—1461no—
383C4×D4—21no—
384C4×D4C22×D7311yescharacteristic
385C4×D4C22×D7311yescharacteristic
386C2×C4⋊C4—731no—
387C2×C4⋊C4—1461no—
388C2×C42—1461no—
389C2×C42C22×D7311yescharacteristic
390#106—731no—
391#106—731no—
392#106—731no—
393#106—731no—
394C4⋊C8—21no—
395C4⋊C8—731no—
396C4⋊C8—731no—
397C4⋊C8—731no—
398C4⋊C8—731no—
399C4⋊C8—731no—
400C4⋊C8—731no—
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—21no—
417C22⋊C8—731no—
418C22⋊C8—731no—
419C22⋊C8—731no—
420C22⋊C8—731no—
421C22⋊C8—1461no—
422C22⋊C8—1461no—
423C22⋊C8—1461no—
424C22⋊C8—1461no—
425C22⋊C8—1461no—
426#97—21no—
427#97—1461no—
428#97—1461no—
429C4×C8—731no—
430C4×C8—731no—
431C4×C8—731no—
432C4×C8—731no—
433C4×C8—1461no—
434C4×C8—1461no—
435C4×C8—1461no—
436C4×C8C22×D7311yescharacteristic
437C4×C8C22×D7311yescharacteristic
438#41—81no—
439#41—81no—
440C2×Q8—21no—
441C2×Q8—2921no—
442C2×Q8—731no—
443C2×Q8—731no—
444C2×Q8—1462no—
445C2×Q8—1461no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4C2×C4×D7311yescharacteristic
451C2×D4C2×C4×D7311yescharacteristic
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—1461no—
455C22×C4—1461no—
456C22×C4C2×C4×D7311yescharacteristic
457C22×C4D4×D7311yescharacteristic
458C22×C4#1192402711yescharacteristic
459SD16—2921no—
460SD16—2921no—
461SD16—1462no—
462SD16—1462no—
463M16—5841no—
464M16—5841no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—5841no—
470C2×C8—5841no—
471C2×C8—731no—
472C2×C8—731no—
473C2×C8—731no—
474C2×C8—731no—
475C2×C8—731no—
476C2×C8—731no—
477C2×C8—731no—
478C2×C8—731no—
479C2×C8—1461no—
480C2×C8—1461no—
481C4⋊C4—21no—
482C4⋊C4—731no—
483C4⋊C4—731no—
484C4⋊C4—1461no—
485C4⋊C4—1461no—
486C4⋊C4—1461no—
487C4⋊C4—1461no—
488C4⋊C4—1461no—
489C4⋊C4C2×C4×D7311yescharacteristic
490C4⋊C4C2×C4×D7311yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C42—1461no—
496C42—1461no—
497C42—1461no—
498C42—1461no—
499C42C2×C4×D7311yescharacteristic
500C42D4×D7311yescharacteristic
501C42#1192402711yescharacteristic
502C42C23×D7311yescharacteristic
503C23—21no—
504C23—21no—
505C23#1455655111yescharacteristic
506Q8—81no—
507Q8—2922no—
508Q8—732no—
509Q8—1461no—
510Q8—1461no—
511Q8—1461no—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—42no—
517D4—81no—
518D4—81no—
519D4—81no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—2922no—
532C2×C4—2922no—
533C2×C4—1461no—
534C2×C4—1461no—
535C2×C4—1461no—
536C2×C4—1461no—
537C2×C4#1455655111yescharacteristic
538C2×C4#1455655111yescharacteristic
539C2×C4#1455655111yescharacteristic
540C2×C4C22×C4×D7311yescharacteristic
541C2×C4C2×D4×D7311yescharacteristic
542C2×C4C2×#1192402711yescharacteristic
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—2921no—
548C8—2921no—
549C8—1461no—
550C8—1461no—
551C8—1461no—
552C8—1461no—
553C8—1461no—
554C8—1461no—
555C8—1461no—
556C8—1461no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22C2×#1455655111yescharacteristic
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—41no—
572C4—41no—
573C4—2921no—
574C4—2921no—
575C4—2921no—
576C4—1462no—
577C4#131×D7311yescharacteristic
578C4#1798935211yescharacteristic
579C4#1798939711yescharacteristic
580C4#1798939711yescharacteristic
581C2—41no—
582C2—81no—
583C2—81no—
584C2#2261866111yescharacteristic
585C2#2261879311yescharacteristic
586C2#2261883011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1496C2
socleC22×C73C2×C4×D4
prime radical#532×C73C22
cosocleC42×C73C24
hypercenter#1496D73
hypocenterC73#18030
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1496

Complements

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

NH ≅ G/Ntype
2. #22619021C2semidirect
4. #22608830C2semidirect
5. #22608824C2semidirect
6. #22608812C2semidirect
7. #22608785C2semidirect
8. #22608777C2semidirect
9. #22608764C2semidirect
10. #22608740C2semidirect
11. #22608734C2semidirect
12. #22608712C2semidirect
13. #22608327C2semidirect
14. #22608231C2semidirect
309. C73#18030semidirect

Maximal subgroups

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

subgroupindex
#226199582
#226190212
#226189982
#226088302
#226088242
#226088122
#226087852
#226087772
#226087642
#226087402
#226087342
#226087122
#226083272
#226082312
C73×#14962
#1803073