Finite Group Databasebeta

← #33189185

Subgroups — #33189185

Order 18688.

674 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22612575C211yesmaximal, characteristic
2#22611432C211yesmaximal, characteristic, complemented
3#22611312C211yesmaximal, characteristic, complemented
4#22611302C211yesmaximal, characteristic
5#22611246C211yesmaximal, characteristic
6#22610788C211yesmaximal, characteristic
7#22610656C211yesmaximal, characteristic, complemented
8#22610627C211yesmaximal, characteristic
9#22610624C211yesmaximal, characteristic, complemented
10#22610562C211yesmaximal, characteristic, complemented
11#22610506C211yesmaximal, characteristic, complemented
12#22610268C211yesmaximal, characteristic
13#22610191C211yesmaximal, characteristic
14#22609788C211yesmaximal, characteristic, complemented
15C73×#2645C211yesmaximal, characteristic, complemented
16C22×#11924015C2211yescharacteristic
17C2×C4×D292C2211yescharacteristic
18C2×#14556522C2211yescharacteristic
19C2×#14556522C2211yescharacteristic
20C2×#14556522C2211yescharacteristic
21C2×C4⋊#10596831C2211yescharacteristic
22C2×C4⋊#10596831C2211yescharacteristic
23C2×#14556515C2211yescharacteristic
24C2×#14556515C2211yescharacteristic
25C2×#14556515C2211yescharacteristic
26C2×#14556511C2211yescharacteristic
27C2×#14556511C2211yescharacteristic
28C2×#14556511C2211yescharacteristic
29C2×#14556502C2211yescharacteristic
30C2×C4×#10596831C2211yescharacteristic
31#17988489C2211yescharacteristic
32#17988489C2211yescharacteristic
33#17988485C2211yescharacteristic
34#17988485C2211yescharacteristic
35#17988476—21no—
36#17988476—21no—
37#17988449—21no—
38#17988446—21no—
39C4×C4⋊Dic73C2211yescharacteristic
40#17988349C2211yescharacteristic
41#17988349C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988342C2211yescharacteristic
47#17988342C2211yescharacteristic
48#401×C73—21no—
49#400×C73—21no—
50#400×C73—21no—
51#400×C73—21no—
52#391×C73C2211yescharacteristic
53#391×C73C2211yescharacteristic
54#391×C73C2211yescharacteristic
55#389×C73C2211yescharacteristic
56#389×C73C2211yescharacteristic
57#389×C73C2211yescharacteristic
58#376×C73C2211yescharacteristic
59C22×D292C2311yescharacteristic
60C22×C4×D73—21no—
61C2×#11924015—22no—
62C2×#11924015—22no—
63C2×#11924015—41no—
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68C4×D292—22no—
69C4×D292—22no—
70C2×C4⋊Dic73C2311yescharacteristic
71C2×C4⋊Dic73C2311yescharacteristic
72C2×C4⋊Dic73C2311yescharacteristic
73C2×#11924007—21no—
74C2×#11924007—21no—
75C2×#11924005—21no—
76C2×#11924005—21no—
77C2×#11924005—21no—
78C2×#11924005—21no—
79C2×#11924005—21no—
80C2×C4×Dic73—21no—
81#14556522—22no—
82#14556522—22no—
83#14556522—41no—
84C4⋊#10596831—22no—
85C4⋊#10596831—22no—
86#14556515—22no—
87#14556515—22no—
88#14556515—41no—
89#14556511—22no—
90#14556511—22no—
91#14556511—41no—
92#14556502—41no—
93C4×#10596831—41no—
94#14556498—21no—
95#14556498—21no—
96#14556498—21no—
97C22×Q8×C73C2311yescharacteristic
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73—21no—
100C2×C4⋊C4×C73—21no—
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C42×C73C2311yescharacteristic
105C2×C42×C73C2311yescharacteristic
106C2×C42×C73C2311yescharacteristic
107#95×C73—21no—
108#95×C73—21no—
109#95×C73—21no—
110#95×C73—21no—
111#95×C73—21no—
112#95×C73—21no—
113#95×C73—21no—
114#95×C73—21no—
115#95×C73—21no—
116#95×C73D411yescharacteristic
117#95×C73D411yescharacteristic
118#95×C73D411yescharacteristic
119#95×C73D411yescharacteristic
120C23×D73—21no—
121C2×D292—21no—
122C2×D292—21no—
123C2×D292—21no—
124C2×D292—21no—
125C2×D292—21no—
126C2×D292#4112yes—
127C22×Dic73—21no—
128C22×Dic73—21no—
129C22×Dic73—21no—
130C2×C4×D73—24no—
131C2×C4×D73—81no—
132C2×C4×D73—81no—
133#11924015—44no—
134C2×#10596831—21no—
135C2×#10596831—21no—
136C2×#10596831—21no—
137C2×#10596831—21no—
138C2×#10596831—21no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C2×#10596831—21no—
144C2×#10596831#4112yes—
145C2×#10596831#4112yes—
146C4⋊Dic73—21no—
147C4⋊Dic73—21no—
148C4⋊Dic73—21no—
149C4⋊Dic73—21no—
150C4⋊Dic73—21no—
151C4⋊Dic73#4112yes—
152#11924007—81no—
153#11924007—81no—
154#11924005—24no—
155#11924005—81no—
156#11924005—81no—
157#11924005—81no—
158#11924005—81no—
159C4×Dic73—81no—
160C2×Q8×C73—21no—
161C2×Q8×C73—21no—
162C2×Q8×C73—21no—
163C2×Q8×C73—21no—
164C2×Q8×C73—21no—
165C2×Q8×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2411yescharacteristic
177C4⋊C4×C73—21no—
178C4⋊C4×C73—21no—
179C4⋊C4×C73—21no—
180C4⋊C4×C73—21no—
181C4⋊C4×C73—21no—
182C4⋊C4×C73—21no—
183C4⋊C4×C73—81no—
184C4⋊C4×C73—81no—
185C4⋊C4×C73—81no—
186C42×C73—21no—
187C42×C73—21no—
188C42×C73—21no—
189C42×C73—21no—
190C42×C73—21no—
191C42×C73—21no—
192C23×C73C22×D411yescharacteristic
193C22×D73—22no—
194C22×D73—41no—
195C22×D73—41no—
196C22×D73—41no—
197C22×D73—41no—
198C22×D73—41no—
199C22×D73—41no—
200Q8×C73—41no—
201Q8×C73—41no—
202Q8×C73—41no—
203Q8×C73—41no—
204C2×C4×C73—21no—
205C2×C4×C73—21no—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—41no—
223C2×C4×C73—41no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
226C2×C4×C73—41no—
227C2×C4×C73—41no—
228C2×C4×C73—41no—
229C2×C4×C73—41no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73C2×#4111yescharacteristic
235C2×C4×C73C2×#4111yescharacteristic
236C2×C4×C73C2×#4111yescharacteristic
237C2×C4×C73C2×#4111yescharacteristic
238C2×C4×C73H(5,𝔽2)11yescharacteristic
239C2×C4×C732−1+411yescharacteristic
240C2×Dic73—22no—
241C2×Dic73—41no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73—41no—
245C2×Dic73—41no—
246C2×Dic73—41no—
247C2×Dic73—41no—
248C2×Dic73—41no—
249D292—22no—
250D292—22no—
251D292—41no—
252D292—41no—
253C4×D73—84no—
254#10596831—22no—
255#10596831—22no—
256#10596831—41no—
257#10596831—41no—
258C22×C73#52511yescharacteristic
259C22×C73#53211yescharacteristic
260C22×C73#53711yescharacteristic
261C22×C73#57711yescharacteristic
262C22×C73#57711yescharacteristic
263C22×C73#57711yescharacteristic
264C22×C73#57711yescharacteristic
265C2×D73—42no—
266C2×D73—42no—
267C2×D73—42no—
268C2×D73—81no—
269C2×D73—81no—
270C2×D73—81no—
271C2×D73—81no—
272C4×C73—41no—
273C4×C73—41no—
274C4×C73—41no—
275C4×C73—41no—
276C4×C73—41no—
277C4×C73—41no—
278C4×C73—81no—
279C4×C73—81no—
280C4×C73—81no—
281C4×C73—81no—
282C4×C73#55111yescharacteristic
283C4×C73#55211yescharacteristic
284C4×C73#55311yescharacteristic
285C4×C73#55611yescharacteristic
286Dic73—42no—
287Dic73—81no—
288Dic73—81no—
289#29440—731nomaximal, Sylow
290C2×C73#260111yescharacteristic
291C2×C73#312311yescharacteristic
292C2×C73#312511yescharacteristic
293C2×C73#317311yescharacteristic
294C2×C73#317411yescharacteristic
295C2×C73#326011yescharacteristic
296C2×C73#326311yescharacteristic
297D73—82no—
298#2645D7311yescharacteristic, complemented
299#2319—731no—
300#2088—731no—
301#2066—731no—
302#2065—731no—
303#2055—731no—
304#1968—731no—
305#1941—731no—
306#1936—731no—
307#1935—731no—
308#1927—731no—
309#1919—731no—
310#1877—731no—
311#1864—731no—
312#1768—731no—
313C73#2944011yescharacteristic, complemented, Sylow
314C22×SD16—731no—
315C2×C4×D4—731no—
316C2×#106—731no—
317C2×#106—731no—
318C2×#106—731no—
319C2×C4⋊C8—731no—
320C2×C4⋊C8—731no—
321C2×#103—731no—
322C2×#103—731no—
323C2×#103—731no—
324C2×#102—731no—
325C2×#102—731no—
326C2×#102—731no—
327C2×#97—731no—
328C2×C4×C8—731no—
329#401—21no—
330#400—21no—
331#400—21no—
332#400—21no—
333#391C2×D7311yescharacteristic
334#391C2×D7311yescharacteristic
335#391C2×D7311yescharacteristic
336#390—731no—
337#390—731no—
338#389—731no—
339#389—731no—
340#389C2×D7311yescharacteristic
341#389C2×D7311yescharacteristic
342#389C2×D7311yescharacteristic
343#388—1461no—
344#388—1461no—
345#381—1461no—
346#380—1461no—
347C4×C4⋊C4—731no—
348#376C2×D7311yescharacteristic
349#340—731no—
350#340—731no—
351#340—731no—
352#340—731no—
353#340—731no—
354#340—731no—
355#336—731no—
356#336—731no—
357C22×Q8C22×D7311yescharacteristic
358C22×D4—731no—
359C23×C4—1461no—
360C2×SD16—2921no—
361C2×SD16—1462no—
362C2×SD16—1462no—
363C22×C8—731no—
364C22×C8—731no—
365C22×C8—731no—
366C22×C8—731no—
367C4×D4—1462no—
368C4×D4—1462no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—731no—
373C2×C4⋊C4—731no—
374C2×C4⋊C4—731no—
375C2×C4⋊C4—1461no—
376C2×C4⋊C4—1461no—
377C2×C4⋊C4C22×D7311yescharacteristic
378C2×C4⋊C4C22×D7311yescharacteristic
379C2×C4⋊C4C22×D7311yescharacteristic
380C2×C22⋊C4—1461no—
381C2×C22⋊C4—1461no—
382C2×C22⋊C4—1461no—
383C2×C22⋊C4—1461no—
384C2×C22⋊C4—1461no—
385C2×C42—1461no—
386C2×C42C22×D7311yescharacteristic
387C2×C42C22×D7311yescharacteristic
388C2×C42C22×D7311yescharacteristic
389#106—2921no—
390#106—1462no—
391#106—1462no—
392C4⋊C8—1462no—
393C4⋊C8—1462no—
394#103—2921no—
395#103—1462no—
396#103—1462no—
397#102—2921no—
398#102—1462no—
399#102—1462no—
400#97—2921no—
401C4×C8—2921no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—1461no—
412#95—1461no—
413#95—1461no—
414#95C22⋊D7311yescharacteristic
415#95C22⋊D7311yescharacteristic
416#95C22⋊D7311yescharacteristic
417#95C22⋊D7311yescharacteristic
418C24—1461no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×D4—732no—
426C2×D4—1461no—
427C2×D4—1461no—
428C2×D4—1461no—
429C2×D4—1461no—
430C2×D4—1461no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—5841no—
436C22×C4—5841no—
437C22×C4—1464no—
438C22×C4—1461no—
439C22×C4—1461no—
440C22×C4—1461no—
441C22×C4C2×C22⋊D7311yescharacteristic
442C22×C4C2×C22⋊D7311yescharacteristic
443C22×C4C2×C22⋊D7311yescharacteristic
444C22×C4C2×C22⋊D7311yescharacteristic
445C22×C4C2×C22⋊D7311yescharacteristic
446C22×C4C2×C22⋊D7311yescharacteristic
447C22×C4C23×D7311yescharacteristic
448SD16—2924no—
449C2×C8—732no—
450C2×C8—732no—
451C2×C8—1461no—
452C2×C8—1461no—
453C2×C8—1461no—
454C2×C8—1461no—
455C2×C8—1461no—
456C2×C8—1461no—
457C2×C8—1461no—
458C2×C8—1461no—
459C2×C8—1461no—
460C2×C8—1461no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—81no—
468C4⋊C4—81no—
469C4⋊C4—81no—
470C4⋊C4—5841no—
471C4⋊C4—5841no—
472C4⋊C4—732no—
473C4⋊C4—1461no—
474C4⋊C4—1461no—
475C4⋊C4—1461no—
476C4⋊C4—1461no—
477C4⋊C4—1461no—
478C22⋊C4—5841no—
479C22⋊C4—5841no—
480C22⋊C4—5841no—
481C22⋊C4—5841no—
482C22⋊C4—1464no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—5841no—
490C23—2921no—
491C23—2921no—
492C23—2921no—
493C23—2921no—
494C23—2921no—
495C23—2921no—
496C23—1462no—
497C23C22×C22⋊D7311yescharacteristic
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502D4—2921no—
503D4—2921no—
504D4—1462no—
505D4—1462no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—2921no—
537C2×C4—2921no—
538C2×C4—2921no—
539C2×C4—2921no—
540C2×C4—2921no—
541C2×C4—2921no—
542C2×C4—2921no—
543C2×C4—2921no—
544C2×C4—5844no—
545C2×C4—1462no—
546C2×C4#41×D7311yescharacteristic
547C2×C4#41×D7311yescharacteristic
548C2×C4#41×D7311yescharacteristic
549C2×C4#41×D7311yescharacteristic
550C2×C4#1455663711yescharacteristic
551C2×C4#1455663811yescharacteristic
552C8—2921no—
553C8—2921no—
554C8—1462no—
555C8—1462no—
556C22—2922no—
557C22—2922no—
558C22—2922no—
559C22—5841no—
560C22—5841no—
561C22—5841no—
562C22—5841no—
563C22#1798909411yescharacteristic
564C22#1798913311yescharacteristic
565C22#1798916511yescharacteristic
566C22#1798939511yescharacteristic
567C22#1798939511yescharacteristic
568C22#1798939511yescharacteristic
569C22#1798939811yescharacteristic
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—2922no—
581C4—5841no—
582C4—5841no—
583C4#1798926211yescharacteristic
584C4#1798927311yescharacteristic
585C4#1798928811yescharacteristic
586C4#1798930411yescharacteristic
587C2—5842no—
588C2#2261553011yescharacteristic
589C2#2262017811yescharacteristic
590C2#2262020211yescharacteristic
591C2#2262054211yescharacteristic
592C2#2262056011yescharacteristic
593C2#2262137211yescharacteristic
594C2#2262139611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2645C2
socleC23×C73C22×D4
prime radicalC22×D292C23
hypercenter#2645D73
hypocenterC73#29440
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ #376 ◁ #2645

Complements

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

NH ≅ G/Ntype
2. #22611432C2semidirect
3. #22611312C2semidirect
7. #22610656C2semidirect
9. #22610624C2semidirect
10. #22610562C2semidirect
11. #22610506C2semidirect
14. #22609788C2semidirect
15. C73×#2645C2semidirect
298. #2645D73semidirect
313. C73#29440semidirect

Maximal subgroups

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

subgroupindex
#226125752
#226114322
#226113122
#226113022
#226112462
#226107882
#226106562
#226106272
#226106242
#226105622
#226105062
#226102682
#226101912
#226097882
C73×#26452
#2944073