Finite Group Databasebeta

← #33189213

Subgroups — #33189213

Order 18688.

660 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22615891C211yesmaximal, 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#22610558C211yesmaximal, characteristic
11#22610516C211yesmaximal, characteristic, complemented
12#22610286C211yesmaximal, characteristic
13#22610199C211yesmaximal, characteristic, complemented
14#22609788C211yesmaximal, characteristic, complemented
15C73×#2320C211yesmaximal, characteristic, complemented
16C22×#11924015C2211yescharacteristic
17C2×#14556522C2211yescharacteristic
18C2×#14556522C2211yescharacteristic
19C2×#14556522C2211yescharacteristic
20C2×C4⋊#10596831C2211yescharacteristic
21C2×C4⋊#10596831C2211yescharacteristic
22C2×#14556515C2211yescharacteristic
23C2×#14556515C2211yescharacteristic
24C2×#14556515C2211yescharacteristic
25C2×#14556511C2211yescharacteristic
26C2×#14556511C2211yescharacteristic
27C2×#14556511C2211yescharacteristic
28C2×#14556502C2211yescharacteristic
29C2×C4×#10596831C2211yescharacteristic
30#17988516—21no—
31#17988516—21no—
32#17988516—21no—
33#17988511—21no—
34#17988489C2211yescharacteristic
35#17988489C2211yescharacteristic
36#17988489C2211yescharacteristic
37#17988485C2211yescharacteristic
38#17988485C2211yescharacteristic
39#17988485C2211yescharacteristic
40#17988349C2211yescharacteristic
41#17988349C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988342C2211yescharacteristic
47#17988342C2211yescharacteristic
48C2×C4×Q8×C73C2211yescharacteristic
49#391×C73C2211yescharacteristic
50#391×C73C2211yescharacteristic
51#389×C73C2211yescharacteristic
52#389×C73C2211yescharacteristic
53#387×C73—21no—
54#387×C73—21no—
55#383×C73—21no—
56#382×C73—21no—
57C4×C4⋊C4×C73C2211yescharacteristic
58#376×C73C2211yescharacteristic
59C22×D292C2311yescharacteristic
60C2×#11924015—22no—
61C2×#11924015—22no—
62C2×#11924015—41no—
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C2×C4⋊Dic73C2311yescharacteristic
68C2×C4⋊Dic73C2311yescharacteristic
69C2×C4⋊Dic73C2311yescharacteristic
70C2×#11924007—21no—
71C2×#11924007—21no—
72C2×#11924007—21no—
73C2×#11924005—21no—
74C2×#11924005—21no—
75C2×#11924005—21no—
76C2×#11924005—21no—
77C2×#11924005—21no—
78C2×#11924005—21no—
79#14556522—22no—
80#14556522—22no—
81#14556522—41no—
82C4⋊#10596831—22no—
83C4⋊#10596831—22no—
84#14556515—22no—
85#14556515—22no—
86#14556515—41no—
87#14556511—22no—
88#14556511—22no—
89#14556511—41no—
90#14556502—41no—
91C4×#10596831—41no—
92#14556498—21no—
93#14556498—21no—
94#14556498—21no—
95C22×Q8×C73C2311yescharacteristic
96C4×Q8×C73—22no—
97C4×Q8×C73—22no—
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×C73—21no—
105C2×C42×C73—21no—
106C2×C42×C73C2311yescharacteristic
107C2×C42×C73C2311yescharacteristic
108C2×C42×C73C2311yescharacteristic
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—21no—
127C22×Dic73—21no—
128C22×Dic73—21no—
129C22×Dic73—21no—
130#11924015—44no—
131C2×#10596831—21no—
132C2×#10596831—21no—
133C2×#10596831—21no—
134C2×#10596831—21no—
135C2×#10596831—21no—
136C2×#10596831—21no—
137C2×#10596831—21no—
138C2×#10596831—21no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831#4112yes—
142C2×#10596831#4112yes—
143C4⋊Dic73—21no—
144C4⋊Dic73—21no—
145C4⋊Dic73—21no—
146C4⋊Dic73—21no—
147C4⋊Dic73—21no—
148C4⋊Dic73—21no—
149#11924007—81no—
150#11924007—81no—
151#11924007—81no—
152#11924005—81no—
153#11924005—81no—
154#11924005—81no—
155#11924005—81no—
156#11924005—81no—
157#11924005—81no—
158C2×Q8×C73—21no—
159C2×Q8×C73—21no—
160C2×Q8×C73—21no—
161C2×Q8×C73—21no—
162C2×Q8×C73—21no—
163C2×Q8×C73#4112yes—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2411yescharacteristic
175C4⋊C4×C73—24no—
176C4⋊C4×C73—21no—
177C4⋊C4×C73—21no—
178C4⋊C4×C73—21no—
179C4⋊C4×C73—21no—
180C4⋊C4×C73—21no—
181C4⋊C4×C73—81no—
182C4⋊C4×C73—81no—
183C4⋊C4×C73#4112yes—
184C42×C73—24no—
185C42×C73—21no—
186C42×C73—21no—
187C42×C73—21no—
188C42×C73—21no—
189C42×C73—21no—
190C42×C73—21no—
191C42×C73—81no—
192C23×C73C22×D411yescharacteristic
193C22×D73—41no—
194C22×D73—41no—
195C22×D73—41no—
196C22×D73—41no—
197C22×D73—41no—
198C22×D73—41no—
199C22×D73—41no—
200Q8×C73—22no—
201Q8×C73—22no—
202Q8×C73—41no—
203Q8×C73—41no—
204C2×C4×C73—21no—
205C2×C4×C73—21no—
206C2×C4×C73—22no—
207C2×C4×C73—22no—
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—21no—
223C2×C4×C73—21no—
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—41no—
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—41no—
250D292—41no—
251D292—41no—
252D292—41no—
253#10596831—22no—
254#10596831—22no—
255#10596831—41no—
256#10596831—41no—
257C22×C73#52511yescharacteristic
258C22×C73#53211yescharacteristic
259C22×C73#53711yescharacteristic
260C22×C73#57711yescharacteristic
261C22×C73#57711yescharacteristic
262C22×C73#57711yescharacteristic
263C22×C73#57711yescharacteristic
264C2×D73—81no—
265C2×D73—81no—
266C2×D73—81no—
267C2×D73—81no—
268C2×D73—81no—
269C2×D73—81no—
270C2×D73—81no—
271C4×C73—42no—
272C4×C73—41no—
273C4×C73—42no—
274C4×C73—41no—
275C4×C73—41no—
276C4×C73—41no—
277C4×C73—41no—
278C4×C73—41no—
279C4×C73—81no—
280C4×C73—81no—
281C4×C73#55111yescharacteristic
282C4×C73#55211yescharacteristic
283C4×C73#55311yescharacteristic
284C4×C73#55611yescharacteristic
285Dic73—81no—
286Dic73—81no—
287Dic73—81no—
288#29442—731nomaximal, Sylow
289C2×C73#260111yescharacteristic
290C2×C73#312511yescharacteristic
291C2×C73#312611yescharacteristic
292C2×C73#317311yescharacteristic
293C2×C73#317411yescharacteristic
294C2×C73#326011yescharacteristic
295C2×C73#326311yescharacteristic
296D73—161no—
297#2644—731no—
298#2320D7311yescharacteristic, complemented
299#2088—731no—
300#2066—731no—
301#2065—731no—
302#2055—731no—
303#1968—731no—
304#1941—731no—
305#1936—731no—
306#1935—731no—
307#1926—731no—
308#1920—731no—
309#1880—731no—
310#1865—731no—
311#1768—731no—
312C73#2944211yescharacteristic, complemented, Sylow
313C22×SD16—731no—
314C2×C4×Q8C2×D7311yescharacteristic
315C2×#106—731no—
316C2×#106—731no—
317C2×#106—731no—
318C2×C4⋊C8—731no—
319C2×C4⋊C8—731no—
320C2×#103—731no—
321C2×#103—731no—
322C2×#103—731no—
323C2×#102—731no—
324C2×#102—731no—
325C2×#102—731no—
326C2×#97—731no—
327C2×C4×C8—731no—
328#397—1461no—
329#397—1461no—
330#397—1461no—
331#396—1461no—
332#391C2×D7311yescharacteristic
333#391C2×D7311yescharacteristic
334#390—731no—
335#390—731no—
336#390—731no—
337#389—731no—
338#389—731no—
339#389—731no—
340#389C2×D7311yescharacteristic
341#389C2×D7311yescharacteristic
342#387—21no—
343#387—21no—
344#383—21no—
345#382—21no—
346C4×C4⋊C4C2×D7311yescharacteristic
347#376C2×D7311yescharacteristic
348#340—731no—
349#340—731no—
350#340—731no—
351#340—731no—
352#340—731no—
353#340—731no—
354#336—731no—
355#336—731no—
356C22×Q8C22×D7311yescharacteristic
357C22×D4—731no—
358C2×SD16—2921no—
359C2×SD16—1462no—
360C2×SD16—1462no—
361C22×C8—731no—
362C22×C8—731no—
363C22×C8—731no—
364C22×C8—731no—
365C4×Q8—22no—
366C4×Q8—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—731no—
371C2×C4⋊C4—731no—
372C2×C4⋊C4—731no—
373C2×C4⋊C4—1461no—
374C2×C4⋊C4—1461no—
375C2×C4⋊C4—1461no—
376C2×C4⋊C4C22×D7311yescharacteristic
377C2×C4⋊C4C22×D7311yescharacteristic
378C2×C4⋊C4C22×D7311yescharacteristic
379C2×C22⋊C4—1461no—
380C2×C22⋊C4—1461no—
381C2×C22⋊C4—1461no—
382C2×C22⋊C4—1461no—
383C2×C22⋊C4—1461no—
384C2×C22⋊C4—1461no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42C22×D7311yescharacteristic
388C2×C42C22×D7311yescharacteristic
389C2×C42C22×D7311yescharacteristic
390#106—2921no—
391#106—1462no—
392#106—1462no—
393C4⋊C8—1462no—
394C4⋊C8—1462no—
395#103—2921no—
396#103—1462no—
397#103—1462no—
398#102—2921no—
399#102—1462no—
400#102—1462no—
401#97—2921no—
402C4×C8—2921no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—1461no—
411#95—1461no—
412#95—1461no—
413#95C22⋊D7311yescharacteristic
414#95C22⋊D7311yescharacteristic
415#95C22⋊D7311yescharacteristic
416#95C22⋊D7311yescharacteristic
417C24—1461no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8#1192402812yes—
424C2×D4—1461no—
425C2×D4—1461no—
426C2×D4—1461no—
427C2×D4—1461no—
428C2×D4—1461no—
429C2×D4—1461no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—1461no—
435C22×C4—1461no—
436C22×C4—1461no—
437C22×C4C2×C22⋊D7311yescharacteristic
438C22×C4C2×C22⋊D7311yescharacteristic
439C22×C4C2×C22⋊D7311yescharacteristic
440C22×C4C2×C22⋊D7311yescharacteristic
441C22×C4C2×C22⋊D7311yescharacteristic
442C22×C4C2×C22⋊D7311yescharacteristic
443C22×C4C23×D7311yescharacteristic
444SD16—2924no—
445C2×C8—732no—
446C2×C8—732no—
447C2×C8—1461no—
448C2×C8—1461no—
449C2×C8—1461no—
450C2×C8—1461no—
451C2×C8—1461no—
452C2×C8—1461no—
453C2×C8—1461no—
454C2×C8—1461no—
455C2×C8—1461no—
456C2×C8—1461no—
457C4⋊C4—24no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—81no—
464C4⋊C4—81no—
465C4⋊C4—5841no—
466C4⋊C4—5841no—
467C4⋊C4—5841no—
468C4⋊C4—1461no—
469C4⋊C4—1461no—
470C4⋊C4—1461no—
471C4⋊C4—1461no—
472C4⋊C4—1461no—
473C4⋊C4—1461no—
474C4⋊C4#1192402812yes—
475C22⋊C4—5841no—
476C22⋊C4—5841no—
477C22⋊C4—5841no—
478C22⋊C4—5841no—
479C22⋊C4—5841no—
480C22⋊C4—5841no—
481C42—24no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—81no—
489C23—2921no—
490C23—2921no—
491C23—2921no—
492C23—2921no—
493C23—2921no—
494C23—2921no—
495C23—2921no—
496C23C22×C22⋊D7311yescharacteristic
497Q8—22no—
498Q8—22no—
499Q8—41no—
500Q8—41no—
501D4—2921no—
502D4—2921no—
503D4—2921no—
504D4—2921no—
505C2×C4—21no—
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—22no—
524C2×C4—22no—
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—2921no—
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#41×D7311yescharacteristic
545C2×C4#41×D7311yescharacteristic
546C2×C4C2×#1192402811yescharacteristic
547C2×C4C2×#1192402811yescharacteristic
548C2×C4#1455663711yescharacteristic
549C2×C4#1455663811yescharacteristic
550C8—2921no—
551C8—2921no—
552C8—1462no—
553C8—1462no—
554C22—5841no—
555C22—5841no—
556C22—5841no—
557C22—5841no—
558C22—5841no—
559C22—5841no—
560C22—5841no—
561C22#1798909811yescharacteristic
562C22#1798913311yescharacteristic
563C22#1798916511yescharacteristic
564C22#1798939511yescharacteristic
565C22#1798939511yescharacteristic
566C22#1798939511yescharacteristic
567C22#1798939811yescharacteristic
568C4—41no—
569C4—42no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—42no—
576C4—81no—
577C4—81no—
578C4—5841no—
579C4—5841no—
580C4—5841no—
581C4#1798926111yescharacteristic
582C4#1798927011yescharacteristic
583C4#1798928111yescharacteristic
584C4#1798930511yescharacteristic
585C2—11681no—
586C2#2261552811yescharacteristic
587C2#2262020811yescharacteristic
588C2#2262022211yescharacteristic
589C2#2262054211yescharacteristic
590C2#2262056011yescharacteristic
591C2#2262137211yescharacteristic
592C2#2262139611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2320C2
socleC23×C73C22×D4
prime radicalC22×D292C23
hypercenter#2320D73
hypocenterC73#29442
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ #376 ◁ #2320

Complements

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

NH ≅ G/Ntype
2. #22611432C2semidirect
3. #22611312C2semidirect
7. #22610656C2semidirect
9. #22610624C2semidirect
11. #22610516C2semidirect
13. #22610199C2semidirect
14. #22609788C2semidirect
15. C73×#2320C2semidirect
298. #2320D73semidirect
312. C73#29442semidirect

Maximal subgroups

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

subgroupindex
#226158912
#226114322
#226113122
#226113022
#226112462
#226107882
#226106562
#226106272
#226106242
#226105582
#226105162
#226102862
#226101992
#226097882
C73×#23202
#2944273