Finite Group Databasebeta

← #33056080

Subgroups — #33056080

Order 18688.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619985C211yesmaximal, characteristic
2#22619040C211yesmaximal, characteristic, complemented
3#22619007C211yesmaximal, characteristic, complemented
4#22608812C211yesmaximal, characteristic, complemented
5#22608798C211yesmaximal, characteristic, complemented
6#22608777C211yesmaximal, characteristic, complemented
7#22608763C211yesmaximal, characteristic, complemented
8#22608752C211yesmaximal, characteristic, complemented
9#22608740C211yesmaximal, characteristic, complemented
10#22608734C211yesmaximal, characteristic, complemented
11#22608723C211yesmaximal, characteristic, complemented
12#22608714C211yesmaximal, characteristic, complemented
13#22608366C211yesmaximal, characteristic, complemented
14#22608231C211yesmaximal, characteristic, complemented
15C73×#1480C211yesmaximal, characteristic, complemented
16C4×#11924028C2211yescharacteristic
17#17988908C411yescharacteristic
18#17988908C411yescharacteristic
19#17988879C411yescharacteristic
20#17988874C411yescharacteristic
21#17988784C411yescharacteristic
22#17988779C411yescharacteristic
23#17988730C411yescharacteristic
24#17988730C411yescharacteristic
25#17988711C2211yescharacteristic
26#17988711C2211yescharacteristic
27C4×#11924016C2211yescharacteristic
28C4×#11924016C2211yescharacteristic
29C4×#11924013C2211yescharacteristic
30C4×#11924013C2211yescharacteristic
31#17988665C2211yescharacteristic
32#17988665C2211yescharacteristic
33#17988659—21no—
34#17988659—21no—
35D4×#10596831C2211yescharacteristic
36D4×#10596831C2211yescharacteristic
37#17988652C2211yescharacteristic
38#17988652C2211yescharacteristic
39C8×C22⋊D73—21no—
40C8×C22⋊D73—21no—
41#17988644C2211yescharacteristic
42#17988640C2211yescharacteristic
43#17988640C2211yescharacteristic
44#17988639—21no—
45C4⋊C8×D73—21no—
46#17988554—21no—
47#17988554—21no—
48#17988339C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988337C2211yescharacteristic
52#17988319C2211yescharacteristic
53#17988319C2211yescharacteristic
54#17988316C2211yescharacteristic
55#17988316C2211yescharacteristic
56#17988309C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988308C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60#532×C73C2211yescharacteristic
61#431×C73C2211yescharacteristic
62C2×C4⋊C8×C73C2211yescharacteristic
63D4⋊C8×C73C2211yescharacteristic
64D4⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66D4⋊C8×C73C2211yescharacteristic
67C2×#11924028C2×C411yescharacteristic
68C2×#11924016C2×C411yescharacteristic
69C2×#11924016C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71C2×#11924013C2×C411yescharacteristic
72C2×#11924012—21no—
73C2×#11924012—21no—
74C22×#10596831—21no—
75C22×#10596831—21no—
76C2×C8×D73—21no—
77C2×C8×D73—21no—
78C4×Dic146C2×C411yescharacteristic
79C4×Dic146C2311yescharacteristic
80C4×D292C2×C411yescharacteristic
81C4×D292C2311yescharacteristic
82C4×C22⋊D73—21no—
83C4×C22⋊D73—21no—
84#14556550C2×C411yescharacteristic
85#14556548—21no—
86C42×D73—21no—
87#14556524C2×C411yescharacteristic
88#14556524C2×C411yescharacteristic
89#14556522C2×C411yescharacteristic
90#14556522C2×C411yescharacteristic
91C4⋊#10596831C2×C411yescharacteristic
92C4⋊#10596831C2×C411yescharacteristic
93C4⋊#10596831D411yescharacteristic
94C4⋊#10596831D411yescharacteristic
95C4⋊#10596831C2311yescharacteristic
96C4⋊#10596831C2311yescharacteristic
97#14556520—21no—
98#14556520—21no—
99#14556514C2×C411yescharacteristic
100#14556514C2×C411yescharacteristic
101#14556512C2×C411yescharacteristic
102#14556512C2×C411yescharacteristic
103#14556512C2×C411yescharacteristic
104#14556512C2×C411yescharacteristic
105#14556511C2×C411yescharacteristic
106#14556511C2×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#14556503—21no—
117#14556503—21no—
118#14556502—21no—
119C4×#10596831C2311yescharacteristic
120C4×#10596831C2311yescharacteristic
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C8×Dic73—21no—
124C8×Dic73—21no—
125C2×#41×C73—21no—
126C22×C8×C73—21no—
127C4⋊Q8×C73C2×C411yescharacteristic
128#127×C73C2×C411yescharacteristic
129#124×C73—21no—
130#121×C73—21no—
131#121×C73C2×C411yescharacteristic
132#121×C73C2×C411yescharacteristic
133C4×D4×C73—21no—
134C4×D4×C73C2311yescharacteristic
135C4×D4×C73C2311yescharacteristic
136C2×C42×C73C2311yescharacteristic
137C4⋊C8×C73—21no—
138C4⋊C8×C73—21no—
139C4⋊C8×C73C2311yescharacteristic
140C4⋊C8×C73C2311yescharacteristic
141C22⋊C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924028—22no—
145#11924028—22no—
146C2×Dic146C22×C411yescharacteristic
147C2×D292C22×C411yescharacteristic
148C2×C22⋊D73—21no—
149C2×C4×D73—21no—
150C2×C4×D73—21no—
151C2×C4×D73—21no—
152#11924016—22no—
153#11924016—22no—
154#11924013—22no—
155#11924013—22no—
156#11924012—81no—
157#11924012—81no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—81no—
161C2×#10596831—81no—
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C22×C411yescharacteristic
164C2×#10596831C22×C411yescharacteristic
165C2×#10596831C22×C411yescharacteristic
166C2×#10596831C2×D411yescharacteristic
167C2×#10596831C2×D411yescharacteristic
168C2×#10596831C2×D411yescharacteristic
169C2×#10596831C2×D411yescharacteristic
170C8×D73—81no—
171C8×D73—81no—
172C4⋊Dic73C22×C411yescharacteristic
173C4⋊Dic73C22×C411yescharacteristic
174#11924007—21no—
175#11924007—21no—
176C22⋊Dic73—21no—
177#11924005—21no—
178#11924005—21no—
179C4×Dic73—21no—
180C4×Dic73—21no—
181C4×Dic73—21no—
182#41×C73—81no—
183#41×C73—81no—
184C2×Q8×C73—21no—
185C2×D4×C73—21no—
186C2×D4×C73—21no—
187C2×D4×C73—21no—
188C2×D4×C73—21no—
189C2×D4×C73C22×C411yescharacteristic
190C2×D4×C73C22×C411yescharacteristic
191C22×C4×C73—21no—
192C22×C4×C73—21no—
193C22×C4×C73C22×C411yescharacteristic
194C22×C4×C73C2×D411yescharacteristic
195C22×C4×C73#4111yescharacteristic
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—81no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73C22×C411yescharacteristic
203C4⋊C4×C73C22×C411yescharacteristic
204C22⋊C4×C73—21no—
205C22⋊C4×C73—21no—
206C22⋊C4×C73—21no—
207C22⋊C4×C73—21no—
208C42×C73C22×C411yescharacteristic
209C42×C73C2×D411yescharacteristic
210C42×C73#4111yescharacteristic
211C42×C73C2411yescharacteristic
212C23×C73—21no—
213C23×C73—21no—
214C23×C73C4×D411yescharacteristic
215C22×D73—21no—
216Q8×C73—81no—
217D4×C73—21no—
218D4×C73—21no—
219D4×C73—21no—
220D4×C73—21no—
221D4×C73—81no—
222D4×C73—81no—
223D4×C73—81no—
224D4×C73—81no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73C4×D411yescharacteristic
237C2×C4×C73C4×D411yescharacteristic
238C2×C4×C73C4×D411yescharacteristic
239C2×C4×C73C23×C411yescharacteristic
240C2×C4×C73C22×D411yescharacteristic
241C2×C4×C73C2×#4111yescharacteristic
242C22⋊D73—24no—
243C2×Dic73—21no—
244C2×Dic73—21no—
245C2×Dic73—21no—
246D292—21no—
247D292#13112yes—
248C4×D73—24no—
249C4×D73—41no—
250C4×D73—41no—
251C4×D73—81no—
252Dic146—21no—
253Dic146#13112yes—
254C8×C73—41no—
255C8×C73—41no—
256C8×C73—41no—
257C8×C73—41no—
258#10596831—21no—
259#10596831—21no—
260#10596831—21no—
261#10596831—21no—
262#10596831—21no—
263#10596831—21no—
264#10596831—21no—
265#10596831—21no—
266#10596831—41no—
267#10596831—41no—
268C22×C73—21no—
269C22×C73—21no—
270C22×C73—21no—
271C22×C73—41no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73—41no—
277C22×C73C2×C4×D411yescharacteristic
278C2×D73—22no—
279C2×D73—41no—
280C2×D73—41no—
281C4×C73—21no—
282C4×C73—21no—
283C4×C73—21no—
284C4×C73—21no—
285C4×C73—41no—
286C4×C73—41no—
287C4×C73C2×#13111yescharacteristic
288C4×C73C2×#13111yescharacteristic
289C4×C73#57611yescharacteristic
290C4×C73#57711yescharacteristic
291Dic73—22no—
292Dic73—41no—
293Dic73—41no—
294#17920—731nomaximal, Sylow
295C2×C73—41no—
296C2×C73—81no—
297C2×C73—81no—
298C2×C73#292911yescharacteristic
299C2×C73#294611yescharacteristic
300C2×C73#295711yescharacteristic
301D73—42no—
302#3106—731no—
303#2988—731no—
304#2981—731no—
305#1588—731no—
306#1586—731no—
307#1583—731no—
308#1581—731no—
309#1580—731no—
310SD16⋊C8—731no—
311C8×SD16—731no—
312C8×D8—731no—
313#1573—731no—
314#1488—731no—
315#1480D7311yescharacteristic, complemented
316#1454—731no—
317C73#1792011yescharacteristic, complemented, Sylow
318#532C2×D7311yescharacteristic
319C4×#41—731no—
320#482—731no—
321#482—731no—
322#477—731no—
323#476—731no—
324#460—731no—
325#459—731no—
326#449—731no—
327#449—731no—
328C8×Q8—731no—
329C8×Q8—731no—
330C4×SD16—731no—
331C4×SD16—731no—
332C4×D8—731no—
333C4×D8—731no—
334#436—731no—
335#436—731no—
336#435—1461no—
337#435—1461no—
338C8×D4—731no—
339C8×D4—731no—
340C8×D4—731no—
341C8×D4—731no—
342C8×D4—1461no—
343C8×D4—1461no—
344#432—731no—
345#431—731no—
346#431—731no—
347#431—1461no—
348#431C2×D7311yescharacteristic
349C2×C4⋊C8—1461no—
350C2×C4⋊C8C2×D7311yescharacteristic
351#408—1461no—
352#408—1461no—
353#335—731no—
354#335—731no—
355#334—731no—
356#334—731no—
357Q8⋊C8—731no—
358Q8⋊C8—731no—
359D4⋊C8—731no—
360D4⋊C8—731no—
361D4⋊C8C2×D7311yescharacteristic
362D4⋊C8C2×D7311yescharacteristic
363D4⋊C8C2×D7311yescharacteristic
364D4⋊C8C2×D7311yescharacteristic
365#322—731no—
366#322—731no—
367#322—731no—
368C82—731no—
369C2×#41—21no—
370C2×#41—731no—
371C2×SD16—731no—
372C2×SD16—731no—
373C2×D8—731no—
374C2×D8—731no—
375C2×M16—1461no—
376C2×M16—1461no—
377C22×C8—21no—
378C22×C8—1461no—
379C22×C8—1461no—
380C22×C8—1461no—
381C22×C8—1461no—
382C4⋊Q8C4×D7311yescharacteristic
383#127C4×D7311yescharacteristic
384#124—21no—
385#121—21no—
386#121C4×D7311yescharacteristic
387#121C4×D7311yescharacteristic
388C4×Q8—731no—
389C4×Q8—731no—
390C4×D4—21no—
391C4×D4—731no—
392C4×D4—731no—
393C4×D4—1461no—
394C4×D4—1461no—
395C4×D4C22×D7311yescharacteristic
396C4×D4C22×D7311yescharacteristic
397#117—731no—
398#117—1461no—
399C2×C42—1461no—
400C2×C42C22×D7311yescharacteristic
401#107—731no—
402#107—731no—
403#106—731no—
404#106—731no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8—731no—
408C4⋊C8—731no—
409C4⋊C8—731no—
410C4⋊C8—731no—
411C4⋊C8—731no—
412C4⋊C8—731no—
413C4⋊C8—1461no—
414C4⋊C8—1461no—
415C4⋊C8C22×D7311yescharacteristic
416C4⋊C8C22×D7311yescharacteristic
417#103—731no—
418#103—731no—
419#102—731no—
420#102—731no—
421#102—731no—
422#102—731no—
423#102—731no—
424#102—731no—
425C22⋊C8—21no—
426C22⋊C8—731no—
427C22⋊C8—731no—
428C22⋊C8—731no—
429C22⋊C8—731no—
430C22⋊C8—1461no—
431C22⋊C8—1461no—
432C22⋊C8—1461no—
433C22⋊C8—1461no—
434C22⋊C8—1461no—
435C22⋊C8—1461no—
436C22⋊C8—1461no—
437#97—1461no—
438C4×C8—731no—
439C4×C8—731no—
440C4×C8—731no—
441C4×C8—731no—
442C4×C8—1461no—
443C4×C8—1461no—
444C4×C8C22×D7311yescharacteristic
445C4×C8C22×D7311yescharacteristic
446#41—81no—
447#41—81no—
448#41—1462no—
449#41—1462no—
450C2×Q8—21no—
451C2×Q8—731no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—731no—
457C2×D4—1461no—
458C2×D4C2×C4×D7311yescharacteristic
459C2×D4C2×C4×D7311yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—1461no—
463C22×C4—1461no—
464C22×C4—1461no—
465C22×C4C2×C4×D7311yescharacteristic
466C22×C4D4×D7311yescharacteristic
467C22×C4#1192402711yescharacteristic
468SD16—1462no—
469SD16—1462no—
470D8—1462no—
471D8—1462no—
472M16—5841no—
473M16—5841no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—81no—
479C2×C8—5841no—
480C2×C8—5841no—
481C2×C8—5841no—
482C2×C8—5841no—
483C2×C8—731no—
484C2×C8—731no—
485C2×C8—731no—
486C2×C8—731no—
487C2×C8—731no—
488C2×C8—731no—
489C2×C8—731no—
490C2×C8—731no—
491C2×C8—1461no—
492C2×C8—1461no—
493C4⋊C4—21no—
494C4⋊C4—731no—
495C4⋊C4—731no—
496C4⋊C4—1461no—
497C4⋊C4—1461no—
498C4⋊C4C2×C4×D7311yescharacteristic
499C4⋊C4C2×C4×D7311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—1461no—
505C22⋊C4—1461no—
506C22⋊C4—1461no—
507C42—1461no—
508C42—1461no—
509C42—1461no—
510C42C2×C4×D7311yescharacteristic
511C42D4×D7311yescharacteristic
512C42#1192402711yescharacteristic
513C42C23×D7311yescharacteristic
514C23—21no—
515C23—21no—
516C23—1461no—
517C23#1455655111yescharacteristic
518Q8—81no—
519Q8—732no—
520Q8—1461no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—81no—
526D4—81no—
527D4—81no—
528D4—81no—
529D4—732no—
530D4—1464no—
531D4—1461no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—2921no—
544C2×C4—2921no—
545C2×C4—5841no—
546C2×C4—1464no—
547C2×C4—1461no—
548C2×C4—1461no—
549C2×C4—1461no—
550C2×C4#1455655111yescharacteristic
551C2×C4#1455655111yescharacteristic
552C2×C4#1455655111yescharacteristic
553C2×C4C22×C4×D7311yescharacteristic
554C2×C4C2×D4×D7311yescharacteristic
555C2×C4C2×#1192402711yescharacteristic
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—2921no—
561C8—2921no—
562C8—1461no—
563C8—1461no—
564C8—1461no—
565C8—1461no—
566C8—1461no—
567C8—1461no—
568C8—1461no—
569C8—1461no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—2921no—
580C22—2921no—
581C22—1462no—
582C22C2×#1455655111yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—41no—
588C4—41no—
589C4—2921no—
590C4—2921no—
591C4—1462no—
592C4#131×D7311yescharacteristic
593C4#131×D7311yescharacteristic
594C4#1798938811yescharacteristic
595C4#1798939311yescharacteristic
596C2—41no—
597C2—81no—
598C2—81no—
599C2—2922no—
600C2#2261862811yescharacteristic
601C2#2261875711yescharacteristic
602C2#2261884411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1480C2
socleC22×C73C2×C4×D4
prime radical#22619985C2
cosocleC42×C73C24
hypercenter#1480D73
hypocenterC73#17920
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1480

Complements

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

NH ≅ G/Ntype
2. #22619040C2semidirect
3. #22619007C2semidirect
4. #22608812C2semidirect
5. #22608798C2semidirect
6. #22608777C2semidirect
7. #22608763C2semidirect
8. #22608752C2semidirect
9. #22608740C2semidirect
10. #22608734C2semidirect
11. #22608723C2semidirect
12. #22608714C2semidirect
13. #22608366C2semidirect
14. #22608231C2semidirect
15. C73×#1480C2semidirect
315. #1480D73semidirect
317. C73#17920semidirect

Maximal subgroups

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

subgroupindex
#226199852
#226190402
#226190072
#226088122
#226087982
#226087772
#226087632
#226087522
#226087402
#226087342
#226087232
#226087142
#226083662
#226082312
C73×#14802
#1792073