Finite Group Databasebeta

← #33056070

Subgroups — #33056070

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#22619039C211yesmaximal, characteristic, complemented
3#22608807C211yesmaximal, characteristic, complemented
4#22608793C211yesmaximal, characteristic, complemented
5#22608772C211yesmaximal, characteristic, complemented
6#22608758C211yesmaximal, characteristic, complemented
7#22608753C211yesmaximal, characteristic, complemented
8#22608743C211yesmaximal, characteristic, complemented
9C8×#11924016C211yesmaximal, characteristic, complemented
10C8×#11924013C211yesmaximal, characteristic, complemented
11#22608717C211yesmaximal, characteristic, complemented
12#22608363C211yesmaximal, characteristic, complemented
13#22608330C211yesmaximal, characteristic, complemented
14#22608231C211yesmaximal, characteristic, complemented
15C73×#2981C211yesmaximal, characteristic, complemented
16C4×#11924028C2211yescharacteristic
17#17988908C411yescharacteristic
18#17988908C411yescharacteristic
19#17988879C411yescharacteristic
20#17988874C411yescharacteristic
21#17988784C411yescharacteristic
22#17988779C411yescharacteristic
23#17988730C411yescharacteristic
24#17988730C411yescharacteristic
25C8×Dic146C2211yescharacteristic
26C8×Dic146C2211yescharacteristic
27C4×#11924016C2211yescharacteristic
28C4×#11924016C2211yescharacteristic
29C4×#11924013C2211yescharacteristic
30C4×#11924013C2211yescharacteristic
31C8×D292C2211yescharacteristic
32C8×D292C2211yescharacteristic
33#17988650—21no—
34#17988650—21no—
35#17988640C2211yescharacteristic
36#17988640C2211yescharacteristic
37#17988639—21no—
38C2×C4⋊#10596831C2211yescharacteristic
39C4⋊C8×D73—21no—
40#17988339C2211yescharacteristic
41#17988339C2211yescharacteristic
42#17988337C2211yescharacteristic
43#17988337C2211yescharacteristic
44#17988317C2211yescharacteristic
45#17988317C2211yescharacteristic
46D4⋊#10596831C2211yescharacteristic
47D4⋊#10596831C2211yescharacteristic
48D4⋊#10596831C2211yescharacteristic
49D4⋊#10596831C2211yescharacteristic
50#17988314C2211yescharacteristic
51#17988314C2211yescharacteristic
52#17988309C2211yescharacteristic
53#17988309C2211yescharacteristic
54#17988308C2211yescharacteristic
55C8×#10596831C2211yescharacteristic
56#532×C73C2211yescharacteristic
57#436×C73C2211yescharacteristic
58#436×C73C2211yescharacteristic
59#435×C73—21no—
60#435×C73—21no—
61C8×D4×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic
63#432×C73C2211yescharacteristic
64#431×C73C2211yescharacteristic
65#408×C73—21no—
66#408×C73—21no—
67C2×#11924028C2×C411yescharacteristic
68C2×#11924016C2×C411yescharacteristic
69C2×#11924016C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71C2×#11924013C2×C411yescharacteristic
72C22×#10596831—21no—
73C2×C8×D73—21no—
74C2×C8×D73—21no—
75C4×Dic146C2×C411yescharacteristic
76C4×Dic146C2311yescharacteristic
77C4×D292C2×C411yescharacteristic
78C4×D292C2311yescharacteristic
79C4×C22⋊D73—21no—
80C4×C22⋊D73—21no—
81#14556550C2×C411yescharacteristic
82#14556548—21no—
83C42×D73—21no—
84#14556524C2×C411yescharacteristic
85#14556524C2×C411yescharacteristic
86#14556522C2×C411yescharacteristic
87#14556522C2×C411yescharacteristic
88C4⋊#10596831—21no—
89C4⋊#10596831—21no—
90C4⋊#10596831C2×C411yescharacteristic
91C4⋊#10596831C2×C411yescharacteristic
92C4⋊#10596831C2311yescharacteristic
93C4⋊#10596831C2311yescharacteristic
94#14556520—21no—
95#14556520—21no—
96#14556514C2×C411yescharacteristic
97#14556514C2×C411yescharacteristic
98#14556512C2×C411yescharacteristic
99#14556512C2×C411yescharacteristic
100#14556512C2×C411yescharacteristic
101#14556512C2×C411yescharacteristic
102#14556511C2×C411yescharacteristic
103#14556511C2×C411yescharacteristic
104C22⋊#10596831—21no—
105C22⋊#10596831C2×C411yescharacteristic
106C22⋊#10596831C2×C411yescharacteristic
107#14556503—21no—
108#14556503—21no—
109C4×#10596831C2311yescharacteristic
110C4×#10596831C2311yescharacteristic
111C4×#10596831C2311yescharacteristic
112C4×#10596831C2311yescharacteristic
113C8×Dic73—21no—
114C8×Dic73—21no—
115C2×#41×C73—21no—
116C2×M16×C73—21no—
117C2×M16×C73—21no—
118C22×C8×C73—21no—
119C22×C8×C73—21no—
120C4⋊Q8×C73C2×C411yescharacteristic
121#127×C73C2×C411yescharacteristic
122#124×C73—21no—
123#121×C73—21no—
124#121×C73C2×C411yescharacteristic
125#121×C73C2×C411yescharacteristic
126C4×D4×C73—21no—
127C4×D4×C73C2311yescharacteristic
128C4×D4×C73C2311yescharacteristic
129C2×C42×C73C2311yescharacteristic
130C4⋊C8×C73D411yescharacteristic
131C4⋊C8×C73D411yescharacteristic
132C4⋊C8×C73C2311yescharacteristic
133C4⋊C8×C73C2311yescharacteristic
134C22⋊C8×C73—21no—
135C22⋊C8×C73—21no—
136C22⋊C8×C73—21no—
137C22⋊C8×C73—21no—
138C22⋊C8×C73—21no—
139C22⋊C8×C73D411yescharacteristic
140C22⋊C8×C73D411yescharacteristic
141#97×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—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—81no—
161C2×#10596831C22×C411yescharacteristic
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C22×C411yescharacteristic
164C2×#10596831C22×C411yescharacteristic
165C8×D73—81no—
166C8×D73—81no—
167C4⋊Dic73C22×C411yescharacteristic
168C4⋊Dic73C22×C411yescharacteristic
169#11924007—21no—
170#11924007—21no—
171C22⋊Dic73—21no—
172#11924005—21no—
173#11924005—21no—
174C4×Dic73—21no—
175C4×Dic73—21no—
176C4×Dic73—21no—
177#41×C73—81no—
178#41×C73—81no—
179C2×Q8×C73—21no—
180C2×D4×C73—21no—
181C2×D4×C73—21no—
182C2×D4×C73—21no—
183C2×D4×C73—21no—
184C2×D4×C73C22×C411yescharacteristic
185C2×D4×C73C22×C411yescharacteristic
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73C22×C411yescharacteristic
189C22×C4×C73C2×D411yescharacteristic
190C22×C4×C73#4111yescharacteristic
191M16×C73—81no—
192M16×C73—81no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—81no—
196C2×C8×C73—81no—
197C2×C8×C73C2×D411yescharacteristic
198C2×C8×C73C2×D411yescharacteristic
199C2×C8×C73C2×D411yescharacteristic
200C2×C8×C73C2×D411yescharacteristic
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—21no—
255C8×C73—21no—
256C8×C73—21no—
257C8×C73—21no—
258C8×C73—41no—
259C8×C73—41no—
260#10596831—21no—
261#10596831—21no—
262#10596831—21no—
263#10596831—21no—
264#10596831—41no—
265#10596831—41no—
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#2981D7311yescharacteristic, complemented
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#1480—731no—
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#436C2×D7311yescharacteristic
335#436C2×D7311yescharacteristic
336#435—21no—
337#435—21no—
338C8×D4—731no—
339C8×D4—731no—
340C8×D4—1461no—
341C8×D4—1461no—
342C8×D4C2×D7311yescharacteristic
343C8×D4C2×D7311yescharacteristic
344#432C2×D7311yescharacteristic
345#431—731no—
346#431—731no—
347#431—1461no—
348#431C2×D7311yescharacteristic
349C2×C4⋊C8—731no—
350C2×C4⋊C8—1461no—
351#408—21no—
352#408—21no—
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⋊C8—731no—
362D4⋊C8—731no—
363D4⋊C8—731no—
364D4⋊C8—731no—
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—21no—
376C2×M16—21no—
377C22×C8—21no—
378C22×C8—21no—
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—731no—
406C4⋊C8—731no—
407C4⋊C8—731no—
408C4⋊C8—731no—
409C4⋊C8—1461no—
410C4⋊C8—1461no—
411C4⋊C8—1461no—
412C4⋊C8—1461no—
413C4⋊C8C22⋊D7311yescharacteristic
414C4⋊C8C22⋊D7311yescharacteristic
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—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—731no—
431C22⋊C8—731no—
432C22⋊C8—1461no—
433C22⋊C8—1461no—
434C22⋊C8—1461no—
435C22⋊C8C22⋊D7311yescharacteristic
436C22⋊C8C22⋊D7311yescharacteristic
437#97—21no—
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×C4C2×C22⋊D7311yescharacteristic
467C22×C4#1192402811yescharacteristic
468SD16—1462no—
469SD16—1462no—
470D8—1462no—
471D8—1462no—
472M16—81no—
473M16—81no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—81no—
477C2×C8—81no—
478C2×C8—5841no—
479C2×C8—5841no—
480C2×C8—5841no—
481C2×C8—731no—
482C2×C8—731no—
483C2×C8—731no—
484C2×C8—731no—
485C2×C8—1461no—
486C2×C8—1461no—
487C2×C8—1461no—
488C2×C8—1461no—
489C2×C8C2×C22⋊D7311yescharacteristic
490C2×C8C2×C22⋊D7311yescharacteristic
491C2×C8C2×C22⋊D7311yescharacteristic
492C2×C8C2×C22⋊D7311yescharacteristic
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
511C42C2×C22⋊D7311yescharacteristic
512C42#1192402811yescharacteristic
513C42C23×D7311yescharacteristic
514C23—21no—
515C23—21no—
516C23—1461no—
517C23C4×C22⋊D7311yescharacteristic
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×C4C4×C22⋊D7311yescharacteristic
551C2×C4C4×C22⋊D7311yescharacteristic
552C2×C4C4×C22⋊D7311yescharacteristic
553C2×C4C22×C4×D7311yescharacteristic
554C2×C4C22×C22⋊D7311yescharacteristic
555C2×C4C2×#1192402811yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—2921no—
563C8—2921no—
564C8—2921no—
565C8—2921no—
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×C4×C22⋊D7311yescharacteristic
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#1798939011yescharacteristic
595C4#1798939811yescharacteristic
596C2—41no—
597C2—81no—
598C2—81no—
599C2—2922no—
600C2#2261862311yescharacteristic
601C2#2261876311yescharacteristic
602C2#2261884611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2981C2
socleC22×C73C2×C4×D4
prime radical#22619985C2
cosocleC42×C73C24
hypercenter#2981D73
hypocenterC73#17920
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2981

Complements

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

NH ≅ G/Ntype
2. #22619039C2semidirect
3. #22608807C2semidirect
4. #22608793C2semidirect
5. #22608772C2semidirect
6. #22608758C2semidirect
7. #22608753C2semidirect
8. #22608743C2semidirect
9. C8×#11924016C2semidirect
10. C8×#11924013C2semidirect
11. #22608717C2semidirect
12. #22608363C2semidirect
13. #22608330C2semidirect
14. #22608231C2semidirect
15. C73×#2981C2semidirect
304. #2981D73semidirect
317. C73#17920semidirect

Maximal subgroups

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

subgroupindex
#226199852
#226190392
#226088072
#226087932
#226087722
#226087582
#226087532
#226087432
C8×#119240162
C8×#119240132
#226087172
#226083632
#226083302
#226082312
C73×#29812
#1792073