Finite Group Databasebeta

← #33154626

Subgroups — #33154626

Order 18688.

732 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22613000C211yesmaximal, characteristic
2#22611335C211yesmaximal, characteristic
3#22611302C211yesmaximal, characteristic
4#22611172C211yesmaximal, characteristic
5#22611172C211yesmaximal, characteristic
6#22610606C211yesmaximal, characteristic, complemented
7#22610565C211yesmaximal, characteristic, complemented
8#22610520C211yesmaximal, characteristic, complemented
9#22610513C211yesmaximal, characteristic, complemented
10#22610490C211yesmaximal, characteristic, complemented
11#22610184C211yesmaximal, characteristic, complemented
12#22610177C211yesmaximal, characteristic
13#22609933C211yesmaximal, characteristic, complemented
14C4×#14556511C211yesmaximal, characteristic
15C73×#2506C211yesmaximal, characteristic, complemented
16C2×#14556579C2211yescharacteristic
17C2×C4×Dic146C2211yescharacteristic
18C2×C4×D292C2211yescharacteristic
19C2×#14556524C2211yescharacteristic
20C2×#14556522C2211yescharacteristic
21C2×C4⋊#10596831C2211yescharacteristic
22C2×#14556514C2211yescharacteristic
23C2×#14556514C2211yescharacteristic
24C2×#14556514C2211yescharacteristic
25C2×#14556514C2211yescharacteristic
26C2×#14556511C2211yescharacteristic
27C2×#14556511C2211yescharacteristic
28C2×#14556511C2211yescharacteristic
29C2×#14556511C2211yescharacteristic
30C2×C4×#10596831C2211yescharacteristic
31#17988493C2211yescharacteristic
32#17988489C2211yescharacteristic
33#17988477—21no—
34#17988476—21no—
35#17988458—21no—
36C4×C4⋊Dic73C2211yescharacteristic
37#17988434—21no—
38#17988349C2211yescharacteristic
39#17988349C2211yescharacteristic
40#17988349C2211yescharacteristic
41#17988349C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988342C2211yescharacteristic
45#17988342C2211yescharacteristic
46#17988342C2211yescharacteristic
47#17988342C2211yescharacteristic
48C2×#125×C73—21no—
49#400×C73—21no—
50#398×C73—21no—
51#389×C73C2211yescharacteristic
52#389×C73C2211yescharacteristic
53#389×C73C2211yescharacteristic
54#389×C73C2211yescharacteristic
55#387×C73—21no—
56#384×C73C2211yescharacteristic
57C4×C4⋊C4×C73C2211yescharacteristic
58C4×C4⋊C4×C73C2211yescharacteristic
59C22×Dic146C2311yescharacteristic
60C22×D292C2311yescharacteristic
61C22×C4×D73—21no—
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66#14556579—22no—
67#14556579—22no—
68C4×Dic146—22no—
69C4×Dic146—41no—
70C4×D292—22no—
71C4×D292—41no—
72C2×C4⋊Dic73C2311yescharacteristic
73C2×C4⋊Dic73C2311yescharacteristic
74C2×#11924007—21no—
75C2×#11924005—21no—
76C2×#11924005—21no—
77C2×#11924005—21no—
78C2×#11924005—21no—
79C2×#11924005—21no—
80C2×C4×Dic73—21no—
81C2×C4×Dic73—21no—
82#14556524—22no—
83#14556522—22no—
84C4⋊#10596831—41no—
85#14556514—22no—
86#14556514—22no—
87#14556514—22no—
88#14556514—41no—
89#14556511—22no—
90#14556511—22no—
91#14556511—22no—
92#14556511—41no—
93C4×#10596831—41no—
94#14556498—21no—
95#14556498—21no—
96#14556498—21no—
97#125×C73—44no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73—21no—
100C2×C4⋊C4×C73—21no—
101C2×C4⋊C4×C73—21no—
102C2×C4⋊C4×C73—21no—
103C2×C4⋊C4×C73—21no—
104C2×C4⋊C4×C73D411yescharacteristic
105C2×C4⋊C4×C73D411yescharacteristic
106C2×C4⋊C4×C73C2311yescharacteristic
107C2×C4⋊C4×C73C2311yescharacteristic
108C2×C4⋊C4×C73C2311yescharacteristic
109C2×C4⋊C4×C73C2311yescharacteristic
110C2×C42×C73—21no—
111C2×C42×C73C2311yescharacteristic
112C2×C42×C73C2311yescharacteristic
113C2×C42×C73C2311yescharacteristic
114#95×C73—21no—
115#95×C73—21no—
116#95×C73—21no—
117#95×C73—21no—
118#95×C73—21no—
119#95×C73D411yescharacteristic
120#95×C73D411yescharacteristic
121C23×D73—21no—
122C2×Dic146—21no—
123C2×Dic146—21no—
124C2×Dic146—21no—
125C2×Dic146—21no—
126C2×Dic146—21no—
127C2×Dic146#4112yes—
128C2×D292—21no—
129C2×D292—21no—
130C2×D292—21no—
131C2×D292—21no—
132C2×D292—21no—
133C2×D292#4112yes—
134C22×Dic73—21no—
135C22×Dic73—21no—
136C22×Dic73—21no—
137C2×C4×D73—42no—
138C2×C4×D73—42no—
139C2×C4×D73—81no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C2×#10596831—21no—
144C2×#10596831—21no—
145C2×#10596831—21no—
146C2×#10596831—21no—
147C2×#10596831—21no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C4⋊Dic73—21no—
153C4⋊Dic73—21no—
154C4⋊Dic73—21no—
155C4⋊Dic73#4112yes—
156#11924007—42no—
157#11924005—24no—
158#11924005—24no—
159#11924005—42no—
160#11924005—42no—
161#11924005—81no—
162C4×Dic73—42no—
163C4×Dic73—81no—
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—22no—
176C4⋊C4×C73—22no—
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—21no—
184C4⋊C4×C73—42no—
185C4⋊C4×C73—42no—
186C4⋊C4×C73—42no—
187C4⋊C4×C73—42no—
188C4⋊C4×C73—42no—
189C4⋊C4×C73—42no—
190C4⋊C4×C73#4112yes—
191C42×C73—21no—
192C42×C73—21no—
193C42×C73—21no—
194C42×C73—21no—
195C42×C73—21no—
196C42×C73—21no—
197C42×C73—42no—
198C23×C73C22×D411yescharacteristic
199C22×D73—22no—
200C22×D73—41no—
201C22×D73—41no—
202C22×D73—41no—
203C22×D73—41no—
204C22×D73—41no—
205C22×D73—41no—
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—22no—
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—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×C73#13512yes—
235C2×C4×C73AGL(1,ℤ/8)12yes—
236C2×C4×C73C2×#4111yescharacteristic
237C2×C4×C73C2×#4111yescharacteristic
238C2×C4×C73C2×#4111yescharacteristic
239C2×C4×C73C2×#4111yescharacteristic
240C2×C4×C73H(5,𝔽2)11yescharacteristic
241C2×C4×C732−1+411yescharacteristic
242C2×Dic73—22no—
243C2×Dic73—22no—
244C2×Dic73—41no—
245C2×Dic73—41no—
246C2×Dic73—41no—
247C2×Dic73—41no—
248C2×Dic73—41no—
249C2×Dic73—41no—
250C2×Dic73—41no—
251D292—22no—
252D292—22no—
253D292—41no—
254D292—41no—
255C4×D73—84no—
256Dic146—22no—
257Dic146—22no—
258Dic146—41no—
259Dic146—41no—
260#10596831—41no—
261#10596831—41no—
262#10596831—41no—
263#10596831—41no—
264C22×C73#52511yescharacteristic
265C22×C73#54611yescharacteristic
266C22×C73#54811yescharacteristic
267C22×C73C2×#13511yescharacteristic
268C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
269C22×C73#57711yescharacteristic
270C22×C73#57811yescharacteristic
271C2×D73—42no—
272C2×D73—42no—
273C2×D73—42no—
274C2×D73—81no—
275C2×D73—81no—
276C2×D73—81no—
277C2×D73—81no—
278C4×C73—22no—
279C4×C73—22no—
280C4×C73—41no—
281C4×C73—42no—
282C4×C73—41no—
283C4×C73—41no—
284C4×C73—41no—
285C4×C73—81no—
286C4×C73—81no—
287C4×C73—81no—
288C4×C73#52911yescharacteristic
289C4×C73#53911yescharacteristic
290C4×C73#55211yescharacteristic
291C4×C73#55311yescharacteristic
292Dic73—42no—
293Dic73—42no—
294Dic73—81no—
295#26761—731nomaximal, Sylow
296C2×C73#246011yescharacteristic
297C2×C73#310611yescharacteristic
298C2×C73#312011yescharacteristic
299C2×C73#330011yescharacteristic
300C2×C73#330611yescharacteristic
301C2×C73#336511yescharacteristic
302C2×C73#336711yescharacteristic
303D73—82no—
304#2506D7311yescharacteristic, complemented
305#2367—731no—
306#2071—731no—
307#2065—731no—
308#2042—731no—
309#2042—731no—
310#1933—731no—
311#1927—731no—
312#1921—731no—
313#1920—731no—
314#1916—731no—
315#1863—731no—
316#1862—731no—
317#1803—731no—
318C4×#102—731no—
319C73#2676111yescharacteristic, complemented, Sylow
320C2×#125—21no—
321C2×#124—731no—
322C2×C4×Q8—731no—
323C2×C4×D4—731no—
324C2×#107—731no—
325C2×#106—731no—
326C2×C4⋊C8—731no—
327C2×#103—731no—
328C2×#103—731no—
329C2×#103—731no—
330C2×#103—731no—
331C2×#102—731no—
332C2×#102—731no—
333C2×#102—731no—
334C2×#102—731no—
335C2×C4×C8—731no—
336#400—21no—
337#398—21no—
338#391—731no—
339#390—731no—
340#389C2×D7311yescharacteristic
341#389C2×D7311yescharacteristic
342#389C2×D7311yescharacteristic
343#389C2×D7311yescharacteristic
344#388—1461no—
345#388—1461no—
346#387—21no—
347#385—1461no—
348#384C2×D7311yescharacteristic
349C4×C4⋊C4—731no—
350C4×C4⋊C4C2×D7311yescharacteristic
351C4×C4⋊C4C2×D7311yescharacteristic
352C4×C22⋊C4—1461no—
353#340—731no—
354#340—731no—
355#340—731no—
356#340—731no—
357#340—731no—
358#340—731no—
359#336—731no—
360#336—731no—
361#336—731no—
362#336—731no—
363C22×Q8—731no—
364C22×D4—731no—
365C23×C4—1461no—
366C22×C8—731no—
367C22×C8—731no—
368C22×C8—731no—
369C22×C8—731no—
370#125—44no—
371#124—1462no—
372#124—1462no—
373C4×Q8—2921no—
374C4×Q8—1462no—
375C4×D4—2921no—
376C4×D4—1462no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—731no—
384C2×C4⋊C4—731no—
385C2×C4⋊C4—1461no—
386C2×C4⋊C4C22⋊D7311yescharacteristic
387C2×C4⋊C4C22⋊D7311yescharacteristic
388C2×C4⋊C4C22×D7311yescharacteristic
389C2×C4⋊C4C22×D7311yescharacteristic
390C2×C4⋊C4C22×D7311yescharacteristic
391C2×C4⋊C4C22×D7311yescharacteristic
392C2×C22⋊C4—1461no—
393C2×C22⋊C4—1461no—
394C2×C22⋊C4—1461no—
395C2×C22⋊C4—1461no—
396C2×C22⋊C4—1461no—
397C2×C42—21no—
398C2×C42—1461no—
399C2×C42—1461no—
400C2×C42C22×D7311yescharacteristic
401C2×C42C22×D7311yescharacteristic
402C2×C42C22×D7311yescharacteristic
403#107—1462no—
404#106—1462no—
405C4⋊C8—2921no—
406#103—2921no—
407#103—1462no—
408#103—1462no—
409#103—1462no—
410#102—2921no—
411#102—1462no—
412#102—1462no—
413#102—1462no—
414C4×C8—2921no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—1461no—
421#95—1461no—
422#95—1461no—
423#95C22⋊D7311yescharacteristic
424#95C22⋊D7311yescharacteristic
425C24—1461no—
426C2×Q8—732no—
427C2×Q8—1461no—
428C2×Q8—1461no—
429C2×Q8—1461no—
430C2×Q8—1461no—
431C2×Q8—1461no—
432C2×D4—732no—
433C2×D4—1461no—
434C2×D4—1461no—
435C2×D4—1461no—
436C2×D4—1461no—
437C2×D4—1461no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—2922no—
443C22×C4—2922no—
444C22×C4—5841no—
445C22×C4—1461no—
446C22×C4—1461no—
447C22×C4—1461no—
448C22×C4C2×C22⋊D7311yescharacteristic
449C22×C4C2×C22⋊D7311yescharacteristic
450C22×C4C2×C22⋊D7311yescharacteristic
451C22×C4C2×C22⋊D7311yescharacteristic
452C22×C4C2×C22⋊D7311yescharacteristic
453C22×C4C2×C22⋊D7311yescharacteristic
454C22×C4C23×D7311yescharacteristic
455C2×C8—1461no—
456C2×C8—1461no—
457C2×C8—1461no—
458C2×C8—1461no—
459C2×C8—1461no—
460C2×C8—1461no—
461C2×C8—1461no—
462C2×C8—1461no—
463C2×C8—1461no—
464C2×C8—1461no—
465C2×C8—1461no—
466C2×C8—1461no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—42no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—2922no—
483C4⋊C4—732no—
484C4⋊C4—1461no—
485C4⋊C4—1461no—
486C4⋊C4—1461no—
487C4⋊C4#1192402912yes—
488C22⋊C4—2922no—
489C22⋊C4—2922no—
490C22⋊C4—5841no—
491C22⋊C4—1464no—
492C22⋊C4—1464no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—42no—
500C42—2922no—
501C42—5841no—
502C23—2921no—
503C23—2921no—
504C23—2921no—
505C23—2921no—
506C23—2921no—
507C23—2921no—
508C23—1462no—
509C23C22×C22⋊D7311yescharacteristic
510Q8—2921no—
511Q8—2921no—
512Q8—1462no—
513Q8—1462no—
514D4—2921no—
515D4—2921no—
516D4—1462no—
517D4—1462no—
518C2×C4—21no—
519C2×C4—21no—
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—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—2921no—
547C2×C4—2921no—
548C2×C4—2921no—
549C2×C4—2921no—
550C2×C4—2921no—
551C2×C4—2921no—
552C2×C4—2921no—
553C2×C4—5844no—
554C2×C4—1462no—
555C2×C4—1462no—
556C2×C4#1455661112yes—
557C2×C4#1455661712yes—
558C2×C4#41×D7311yescharacteristic
559C2×C4#41×D7311yescharacteristic
560C2×C4#41×D7311yescharacteristic
561C2×C4C2×#1192402911yescharacteristic
562C2×C4#1455663711yescharacteristic
563C2×C4#1455663911yescharacteristic
564C8—2921no—
565C8—2921no—
566C8—2921no—
567C8—2921no—
568C22—2922no—
569C22—2922no—
570C22—2922no—
571C22—5841no—
572C22—5841no—
573C22—5841no—
574C22—5841no—
575C22#1798909411yescharacteristic
576C22#1798922511yescharacteristic
577C22#1798924811yescharacteristic
578C22C2×#1455661111yescharacteristic
579C22C2×#1455661711yescharacteristic
580C22#1798939511yescharacteristic
581C22#1798940211yescharacteristic
582C4—22no—
583C4—22no—
584C4—41no—
585C4—41no—
586C4—42no—
587C4—41no—
588C4—41no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4—2922no—
593C4—2922no—
594C4—5841no—
595C4#1798912211yescharacteristic
596C4#1798918511yescharacteristic
597C4#1798926911yescharacteristic
598C4#1798929011yescharacteristic
599C2—5842no—
600C2#2261387911yescharacteristic
601C2#2261998511yescharacteristic
602C2#2262013911yescharacteristic
603C2#2262181211yescharacteristic
604C2#2262188611yescharacteristic
605C2#2262262711yescharacteristic
606C2#2262264911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2506C2
socleC23×C73C22×D4
prime radicalC22×D292C23
hypercenter#2506D73
hypocenterC73#26761
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2506

Complements

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

NH ≅ G/Ntype
6. #22610606C2semidirect
7. #22610565C2semidirect
8. #22610520C2semidirect
9. #22610513C2semidirect
10. #22610490C2semidirect
11. #22610184C2semidirect
13. #22609933C2semidirect
15. C73×#2506C2semidirect
304. #2506D73semidirect
319. C73#26761semidirect

Maximal subgroups

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

subgroupindex
#226130002
#226113352
#226113022
#226111722
#226106062
#226105652
#226105202
#226105132
#226104902
#226101842
#226101772
#226099332
C4×#145565112
C73×#25062
#2676173