Finite Group Databasebeta

← #33057342

Subgroups — #33057342

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#22619962C211yesmaximal, characteristic
2#22619020C211yesmaximal, characteristic, complemented
3#22618997C211yesmaximal, characteristic
4#22608836C211yesmaximal, characteristic, complemented
5#22608818C211yesmaximal, characteristic, complemented
6#22608806C211yesmaximal, characteristic, complemented
7#22608791C211yesmaximal, characteristic, complemented
8#22608771C211yesmaximal, characteristic, complemented
9#22608770C211yesmaximal, characteristic, complemented
10#22608746C211yesmaximal, characteristic, complemented
11#22608728C211yesmaximal, characteristic, complemented
12#22608709C211yesmaximal, characteristic, complemented
13#22608401C211yesmaximal, characteristic
14#22608231C211yesmaximal, characteristic, complemented
15C73×#1479C211yesmaximal, characteristic, complemented
16#17989137C2211yescharacteristic
17#17988905C411yescharacteristic
18#17988905C411yescharacteristic
19#17988872C411yescharacteristic
20#17988872C411yescharacteristic
21#17988787C411yescharacteristic
22#17988787C411yescharacteristic
23#17988726C411yescharacteristic
24#17988726C411yescharacteristic
25#17988718—21no—
26#17988718—21no—
27#17988718C2211yescharacteristic
28#17988718C2211yescharacteristic
29Q8×#10596831C2211yescharacteristic
30Q8×#10596831C2211yescharacteristic
31C4×#11924015C2211yescharacteristic
32C4×#11924015C2211yescharacteristic
33C4×#11924015C2211yescharacteristic
34C4×#11924015C2211yescharacteristic
35#17988666—21no—
36#17988664C2211yescharacteristic
37#17988664C2211yescharacteristic
38C8×D292—21no—
39#17988652C2211yescharacteristic
40#17988652C2211yescharacteristic
41#17988644—21no—
42#17988644C2211yescharacteristic
43#17988640—21no—
44#17988640C2211yescharacteristic
45#17988640C2211yescharacteristic
46#17988552—21no—
47#17988552—21no—
48#17988339C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988337C2211yescharacteristic
52#17988316C2211yescharacteristic
53#17988316C2211yescharacteristic
54#17988316C2211yescharacteristic
55#17988316C2211yescharacteristic
56#17988309C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988308C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60C2×C4×Q8×C73C2211yescharacteristic
61#431×C73C2211yescharacteristic
62#431×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66Q8⋊C8×C73C2211yescharacteristic
67C2×#11924028—21no—
68C2×#11924015C2×C411yescharacteristic
69C2×#11924015C2×C411yescharacteristic
70C2×#11924015C2×C411yescharacteristic
71C2×#11924015C2×C411yescharacteristic
72C2×#11924011—21no—
73C2×#11924011—21no—
74C2×C8×D73—21no—
75C2×C8×D73—21no—
76#14556591C2×C411yescharacteristic
77#14556588C2×C411yescharacteristic
78#14556579—21no—
79#14556565—21no—
80#14556565C2×C411yescharacteristic
81#14556565C2×C411yescharacteristic
82C4×D292—21no—
83C4×D292C2311yescharacteristic
84C4×D292C2311yescharacteristic
85#14556522C2×C411yescharacteristic
86#14556522C2×C411yescharacteristic
87#14556522C2×C411yescharacteristic
88#14556522C2×C411yescharacteristic
89C4⋊#10596831—21no—
90C4⋊#10596831—21no—
91C4⋊#10596831—21no—
92C4⋊#10596831—21no—
93C4⋊#10596831C2×C411yescharacteristic
94C4⋊#10596831C2×C411yescharacteristic
95C4⋊#10596831D411yescharacteristic
96C4⋊#10596831D411yescharacteristic
97C4⋊#10596831C2311yescharacteristic
98C4⋊#10596831C2311yescharacteristic
99#14556515C2×C411yescharacteristic
100#14556515C2×C411yescharacteristic
101#14556515C2×C411yescharacteristic
102#14556515C2×C411yescharacteristic
103#14556511C2×C411yescharacteristic
104#14556511C2×C411yescharacteristic
105#14556511C2×C411yescharacteristic
106#14556511C2×C411yescharacteristic
107C22⋊#10596831—21no—
108C22⋊#10596831C2×C411yescharacteristic
109C22⋊#10596831C2×C411yescharacteristic
110C22⋊#10596831D411yescharacteristic
111C22⋊#10596831D411yescharacteristic
112#14556503—21no—
113#14556503—21no—
114#14556503—21no—
115#14556503—21no—
116#14556502—21no—
117#14556502—21no—
118#14556502—21no—
119C4×#10596831—21no—
120C4×#10596831—21no—
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C4×#10596831C2311yescharacteristic
125C22×Q8×C73C2×C411yescharacteristic
126C4×Q8×C73—21no—
127C4×Q8×C73—21no—
128C4×Q8×C73C2×C411yescharacteristic
129C4×Q8×C73C2×C411yescharacteristic
130C4×Q8×C73C2311yescharacteristic
131C4×Q8×C73C2311yescharacteristic
132C2×C4⋊C4×C73—21no—
133C2×C4⋊C4×C73C2×C411yescharacteristic
134C2×C42×C73—21no—
135C2×C42×C73C2311yescharacteristic
136C4⋊C8×C73—21no—
137C4⋊C8×C73C2311yescharacteristic
138C4⋊C8×C73C2311yescharacteristic
139C22⋊C8×C73—21no—
140C22⋊C8×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924028—81no—
145#11924028—81no—
146C2×Dic146—21no—
147C2×D292—21no—
148C2×D292—21no—
149C2×D292C22×C411yescharacteristic
150C2×D292C22×C411yescharacteristic
151C2×C22⋊D73—21no—
152C2×C22⋊D73—21no—
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155#11924015—22no—
156#11924015—22no—
157#11924015—41no—
158#11924015—41no—
159#11924011—81no—
160#11924011—81no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831C22×C411yescharacteristic
164C2×#10596831C22×C411yescharacteristic
165C2×#10596831C22×C411yescharacteristic
166C2×#10596831C22×C411yescharacteristic
167C2×#10596831C2×D411yescharacteristic
168C2×#10596831C2×D411yescharacteristic
169C2×#10596831C2×D411yescharacteristic
170C2×#10596831C2×D411yescharacteristic
171C8×D73—81no—
172C8×D73—81no—
173C4⋊Dic73—21no—
174C4⋊Dic73C22×C411yescharacteristic
175C4⋊Dic73C22×C411yescharacteristic
176#11924005—21no—
177#11924005—21no—
178#11924005—21no—
179#11924005—21no—
180C2×Q8×C73—21no—
181C2×Q8×C73—22no—
182C2×Q8×C73—41no—
183C2×Q8×C73C22×C411yescharacteristic
184C2×Q8×C73C22×C411yescharacteristic
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—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73C22×C411yescharacteristic
200C4⋊C4×C73C22×C411yescharacteristic
201C42×C73—21no—
202C42×C73—21no—
203C42×C73—21no—
204C42×C73—21no—
205C42×C73C22×C411yescharacteristic
206C42×C73C2×D411yescharacteristic
207C42×C73#4111yescharacteristic
208C42×C73C2411yescharacteristic
209C23×C73C4×D411yescharacteristic
210C22×D73—21no—
211C22×D73—21no—
212Q8×C73—21no—
213Q8×C73—21no—
214Q8×C73—21no—
215Q8×C73—42no—
216Q8×C73#13112yes—
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—21no—
225C2×C4×C73—41no—
226C2×C4×C73—42no—
227C2×C4×C73—42no—
228C2×C4×C73C4×D411yescharacteristic
229C2×C4×C73C4×D411yescharacteristic
230C2×C4×C73C4×D411yescharacteristic
231C2×C4×C73C23×C411yescharacteristic
232C2×C4×C73C22×D411yescharacteristic
233C2×C4×C73C2×#4111yescharacteristic
234C22⋊D73—81no—
235C22⋊D73—81no—
236C2×Dic73—21no—
237C2×Dic73—21no—
238D292—21no—
239D292—21no—
240D292—21no—
241D292—21no—
242D292—42no—
243D292—81no—
244C4×D73—41no—
245C4×D73—41no—
246C4×D73—41no—
247C4×D73—41no—
248Dic146—81no—
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×C73C2×C4×D411yescharacteristic
267C2×D73—41no—
268C2×D73—41no—
269C2×D73—41no—
270C2×D73—41no—
271C2×D73—41no—
272C2×D73—41no—
273C4×C73—21no—
274C4×C73—22no—
275C4×C73—21no—
276C4×C73—21no—
277C4×C73—21no—
278C4×C73—41no—
279C4×C73—41no—
280C4×C73—41no—
281C4×C73C2×#13111yescharacteristic
282C4×C73#56811yescharacteristic
283C4×C73#57711yescharacteristic
284C4×C73#57711yescharacteristic
285Dic73—41no—
286Dic73—41no—
287#18030—731nomaximal, Sylow
288C2×C73—41no—
289C2×C73#293311yescharacteristic
290C2×C73#294911yescharacteristic
291C2×C73#295511yescharacteristic
292D73—81no—
293D73—81no—
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#1496—731no—
307#1479D7311yescharacteristic, complemented
308#1454—731no—
309C73#1803011yescharacteristic, complemented, Sylow
310#532—731no—
311C2×C4×Q8C2×D7311yescharacteristic
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—731no—
337#432—1461no—
338#431—731no—
339#431—731no—
340#431—1461no—
341#431C2×D7311yescharacteristic
342#431C2×D7311yescharacteristic
343#408—1461no—
344#408—1461no—
345#335—731no—
346#335—731no—
347#334—731no—
348#334—731no—
349Q8⋊C8C2×D7311yescharacteristic
350Q8⋊C8C2×D7311yescharacteristic
351Q8⋊C8C2×D7311yescharacteristic
352Q8⋊C8C2×D7311yescharacteristic
353D4⋊C8—731no—
354D4⋊C8—731no—
355D4⋊C8—731no—
356D4⋊C8—731no—
357#322—731no—
358#322—731no—
359#322—731no—
360C82—731no—
361C2×#41—1461no—
362C22×Q8C4×D7311yescharacteristic
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⋊Q8—731no—
372#127—731no—
373#124—1461no—
374#121—731no—
375#121—731no—
376#121—1461no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8C4×D7311yescharacteristic
380C4×Q8C4×D7311yescharacteristic
381C4×Q8C22×D7311yescharacteristic
382C4×Q8C22×D7311yescharacteristic
383C4×D4—731no—
384C4×D4—731no—
385C4×D4—1461no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4C4×D7311yescharacteristic
388C2×C42—21no—
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—1461no—
427#97—1461no—
428#97—1461no—
429C4×C8—21no—
430C4×C8—731no—
431C4×C8—731no—
432C4×C8—731no—
433C4×C8—731no—
434C4×C8—1461no—
435C4×C8—1461no—
436C4×C8C22×D7311yescharacteristic
437C4×C8C22×D7311yescharacteristic
438#41—5841no—
439#41—5841no—
440C2×Q8—21no—
441C2×Q8—22no—
442C2×Q8—41no—
443C2×Q8—1461no—
444C2×Q8C2×C4×D7311yescharacteristic
445C2×Q8C2×C4×D7311yescharacteristic
446C2×D4—731no—
447C2×D4—731no—
448C2×D4—1461no—
449C2×D4—1461no—
450C2×D4—1461no—
451C2×D4—1461no—
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—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—731no—
487C4⋊C4—731no—
488C4⋊C4—1461no—
489C4⋊C4C2×C4×D7311yescharacteristic
490C4⋊C4C2×C4×D7311yescharacteristic
491C22⋊C4—1461no—
492C22⋊C4—1461no—
493C22⋊C4—1461no—
494C22⋊C4—1461no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42C2×C4×D7311yescharacteristic
500C42D4×D7311yescharacteristic
501C42#1192402711yescharacteristic
502C42C23×D7311yescharacteristic
503C23—1461no—
504C23—1461no—
505C23#1455655111yescharacteristic
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—42no—
510Q8—5841no—
511Q8#1455659712yes—
512D4—2922no—
513D4—5841no—
514D4—5841no—
515D4—5841no—
516D4—1461no—
517D4—1461no—
518D4—1461no—
519D4—1461no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—2921no—
532C2×C4—2921no—
533C2×C4—2921no—
534C2×C4—2921no—
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—2921no—
561C22—2921no—
562C22—2921no—
563C22—2921no—
564C22—2921no—
565C22—2921no—
566C22C2×#1455655111yescharacteristic
567C4—21no—
568C4—22no—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—2921no—
576C4—2921no—
577C4C2×#1455659711yescharacteristic
578C4#1798935311yescharacteristic
579C4#1798939611yescharacteristic
580C4#1798939611yescharacteristic
581C2—41no—
582C2—5841no—
583C2—5841no—
584C2#2261865211yescharacteristic
585C2#2261878611yescharacteristic
586C2#2261883011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1479C2
socleC22×C73C2×C4×D4
prime radical#17989137C22
cosocleC42×C73C24
hypercenter#1479D73
hypocenterC73#18030
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
2. #22619020C2semidirect
4. #22608836C2semidirect
5. #22608818C2semidirect
6. #22608806C2semidirect
7. #22608791C2semidirect
8. #22608771C2semidirect
9. #22608770C2semidirect
10. #22608746C2semidirect
11. #22608728C2semidirect
12. #22608709C2semidirect
14. #22608231C2semidirect
15. C73×#1479C2semidirect
307. #1479D73semidirect
309. C73#18030semidirect

Maximal subgroups

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

subgroupindex
#226199622
#226190202
#226189972
#226088362
#226088182
#226088062
#226087912
#226087712
#226087702
#226087462
#226087282
#226087092
#226084012
#226082312
C73×#14792
#1803073