Finite Group Databasebeta

← #33055815

Subgroups — #33055815

Order 18688.

662 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#22619013C211yesmaximal, characteristic, complemented
2#22618969C211yesmaximal, characteristic
3C4×SD16×D73C211yesmaximal, characteristic
4#22608836C211yesmaximal, characteristic, complemented
5#22608833C211yesmaximal, characteristic, complemented
6#22608831C211yesmaximal, characteristic, complemented
7#22608830C211yesmaximal, characteristic, complemented
8#22608823C211yesmaximal, characteristic, complemented
9#22608822C211yesmaximal, characteristic, complemented
10#22608820C211yesmaximal, characteristic, complemented
11#22608676C211yesmaximal, characteristic, complemented
12#22608324C211yesmaximal, characteristic, complemented
13#22608320C211yesmaximal, characteristic
14#22608213C211yesmaximal, characteristic, complemented
15C73×#1590C211yesmaximal, characteristic, complemented
16C2×SD16×D73C411yescharacteristic
17C4×Q8×D73C2211yescharacteristic
18C4×D4×D73C2211yescharacteristic
19#17988718C2211yescharacteristic, complemented
20#17988717C2211yescharacteristic, complemented
21#17988716—21no—
22#17988715—21no—
23#17988714C2211yescharacteristic, complemented
24#17988678C411yescharacteristic
25C4×#11924017C2211yescharacteristic
26SD16×Dic73C411yescharacteristic
27C4×#11924015C2211yescharacteristic
28#17988674C411yescharacteristic
29C4×#11924016C2211yescharacteristic
30#17988672C411yescharacteristic
31#17988666C2211yescharacteristic
32#17988665C2211yescharacteristic
33#17988664C2211yescharacteristic
34#17988663—21no—
35#17988662—21no—
36#17988643—21no—
37#17988642—21no—
38#17988639C2211yescharacteristic
39#17988639C2211yescharacteristic
40#17988638C2211yescharacteristic
41#17988638C2211yescharacteristic
42#106×D73C411yescharacteristic
43#103×D73C411yescharacteristic
44#102×D73C411yescharacteristic
45#17988550—21no—
46#17988549—21no—
47C4×C8×D73C2211yescharacteristic
48#17988339C2211yescharacteristic, complemented
49#17988339C2211yescharacteristic, complemented
50#17988338C2211yescharacteristic, complemented
51#17988319C2211yescharacteristic, complemented
52Q8⋊#10596831C2211yescharacteristic, complemented
53#17988317C2211yescharacteristic, complemented
54#17988316C2211yescharacteristic
55D4⋊#10596831C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic, complemented
58#17988309C2211yescharacteristic, complemented
59C8×#10596831C2211yescharacteristic, complemented
60#446×C73C2211yescharacteristic, complemented
61C4×SD16×C73C2211yescharacteristic
62#436×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic, complemented
64Q8⋊C8×C73C2211yescharacteristic, complemented
65D4⋊C8×C73C2211yescharacteristic
66C82×C73C2211yescharacteristic, complemented
67C2×Q8×D73C2×C411yescharacteristic
68C2×D4×D73C2×C411yescharacteristic
69C22×C4×D73—21no—
70C2×#11924017C2×C411yescharacteristic
71C2×#11924016C2×C411yescharacteristic
72C2×#11924015C2×C411yescharacteristic
73SD16×D73—24no—
74C2×#11924012—21no—
75C2×#11924011—21no—
76C2×#11924011—21no—
77C2×C8×D73C2×C411yescharacteristic
78C2×C8×D73C2×C411yescharacteristic
79Q8×Dic73C2×C411yescharacteristic
80C4×Dic146—21no—
81C4×Dic146C2311yescharacteristic
82#14556556—21no—
83#14556556C2×C411yescharacteristic
84C4×D292C2311yescharacteristic
85D4×Dic73C2×C411yescharacteristic
86#14556553C2×C411yescharacteristic
87C4×C22⋊D73—21no—
88#14556551—21no—
89C4⋊C4×D73—21no—
90C4⋊C4×D73C2×C411yescharacteristic
91C4⋊C4×D73C2×C411yescharacteristic
92C22⋊C4×D73—21no—
93C42×D73—21no—
94C42×D73C2311yescharacteristic
95#14556523C2×C411yescharacteristic
96#14556522C2×C411yescharacteristic
97#14556522C2×C411yescharacteristic
98C4⋊#10596831—21no—
99C4⋊#10596831C2311yescharacteristic
100C4⋊#10596831C2311yescharacteristic
101#14556520—21no—
102#14556520—21no—
103#14556520—21no—
104#14556520D411yescharacteristic
105#14556520D411yescharacteristic
106#14556516C2×C411yescharacteristic
107#14556515C2×C411yescharacteristic
108#14556514C2×C411yescharacteristic
109#14556513C2×C411yescharacteristic
110#14556512C2×C411yescharacteristic
111#14556511C2×C411yescharacteristic
112C22⋊#10596831—21no—
113#14556503—21no—
114#14556503—21no—
115#14556503—21no—
116#14556503—21no—
117#14556503—21no—
118#14556503D411yescharacteristic
119#14556503D411yescharacteristic
120#14556502—21no—
121#14556501—21no—
122#14556501—21no—
123C4×#10596831C2311yescharacteristic
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C8×Dic73—21no—
127C8×Dic73—21no—
128C8×Dic73C2×C411yescharacteristic
129C8×Dic73C2×C411yescharacteristic
130C2×SD16×C73C2×C411yescharacteristic
131C2×M16×C73—21no—
132C4×Q8×C73C2311yescharacteristic
133C4×D4×C73C2311yescharacteristic
134#106×C73C2×C411yescharacteristic
135C4⋊C8×C73—21no—
136C4⋊C8×C73C2311yescharacteristic
137C4⋊C8×C73C2311yescharacteristic
138#103×C73C2×C411yescharacteristic
139#102×C73C2×C411yescharacteristic
140C22⋊C8×C73—21no—
141#97×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C4×C8×C73C2311yescharacteristic
145C23×D73—21no—
146C2×Dic146—21no—
147C2×Dic146C22×C411yescharacteristic
148Q8×D73—22no—
149Q8×D73—22no—
150C2×D292C22×C411yescharacteristic
151C2×C22⋊D73—21no—
152D4×D73—22no—
153D4×D73—22no—
154C22×Dic73—21no—
155C2×C4×D73—21no—
156C2×C4×D73—21no—
157C2×C4×D73—21no—
158C2×C4×D73—21no—
159C2×C4×D73—21no—
160C2×C4×D73—81no—
161C2×C4×D73—81no—
162C2×C4×D73C22×C411yescharacteristic
163C2×C4×D73C2×D411yescharacteristic
164C2×C4×D73#4111yescharacteristic
165#11924017—22no—
166#11924016—22no—
167#11924015—22no—
168#11924012—81no—
169#11924011—81no—
170#11924011—81no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831C22×C411yescharacteristic
175C2×#10596831C22×C411yescharacteristic
176C2×#10596831C2×D411yescharacteristic
177C2×#10596831C2×D411yescharacteristic
178C8×D73—22no—
179C8×D73M1614yescomplemented
180C4⋊Dic73—21no—
181C4⋊Dic73C22×C411yescharacteristic
182C4⋊Dic73C22×C411yescharacteristic
183#11924007—21no—
184#11924007—21no—
185#11924007—21no—
186#11924007—21no—
187C22⋊Dic73—21no—
188#11924005—21no—
189#11924005—21no—
190C4×Dic73—21no—
191C4×Dic73—21no—
192C4×Dic73—21no—
193C4×Dic73C22×C411yescharacteristic
194C4×Dic73C2×D411yescharacteristic
195C4×Dic73#4111yescharacteristic
196C2×Q8×C73C22×C411yescharacteristic
197C2×D4×C73C22×C411yescharacteristic
198C22×C4×C73—21no—
199SD16×C73—22no—
200M16×C73—81no—
201C2×C8×C73—21no—
202C2×C8×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73C22×C411yescharacteristic
205C2×C8×C73C22×C411yescharacteristic
206C2×C8×C73C2×D411yescharacteristic
207C2×C8×C73C2×D411yescharacteristic
208C4⋊C4×C73—21no—
209C4⋊C4×C73C22×C411yescharacteristic
210C4⋊C4×C73C22×C411yescharacteristic
211C22⋊C4×C73—21no—
212C42×C73—21no—
213C42×C73C2411yescharacteristic
214C23×C73—21no—
215C22×D73—21no—
216C22×D73—42no—
217C22×D73—81no—
218C22×D73—81no—
219C22×D73C4×D411yescharacteristic
220Q8×C73—21no—
221Q8×C73—21no—
222D4×C73—21no—
223D4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—41no—
228C2×C4×C73—41no—
229C2×C4×C73C23×C411yescharacteristic
230C2×C4×C73C22×D411yescharacteristic
231C2×C4×C73C2×#4111yescharacteristic
232C22⋊D73—42no—
233C2×Dic73—21no—
234C2×Dic73—21no—
235C2×Dic73—21no—
236C2×Dic73—81no—
237C2×Dic73C4×D411yescharacteristic
238C2×Dic73C4×D411yescharacteristic
239C2×Dic73C4×D411yescharacteristic
240D292—21no—
241D292—21no—
242C4×D73—21no—
243C4×D73—21no—
244C4×D73—41no—
245C4×D73—42no—
246C4×D73—41no—
247C4×D73—41no—
248C4×D73—81no—
249C4×D73—81no—
250C4×D73—81no—
251C4×D73C2×M1612yes—
252C4×D73#13112yes—
253Dic146—21no—
254Dic146—21no—
255Dic146—42no—
256C8×C73—21no—
257C8×C73—21no—
258C8×C73—21no—
259C8×C73—41no—
260C8×C73—41no—
261C8×C73—41no—
262C8×C73C2×M1612yes—
263#10596831—21no—
264#10596831—21no—
265#10596831—21no—
266#10596831—41no—
267#10596831—41no—
268#10596831—41no—
269#10596831C2×M1612yes—
270C22×C73—41no—
271C22×C73—41no—
272C22×C73—41no—
273C22×C73C2×C4×D411yescharacteristic
274C2×D73—21no—
275C2×D73—21no—
276C2×D73—41no—
277C2×D73—41no—
278C2×D73—41no—
279C2×D73—84no—
280C2×D73#43612yes—
281C4×C73—21no—
282C4×C73—41no—
283C4×C73—41no—
284C4×C73—41no—
285C4×C73C22×M1611yescharacteristic
286C4×C73C2×#13111yescharacteristic
287C4×C73#57711yescharacteristic
288C4×C73#57711yescharacteristic
289Dic73—21no—
290Dic73—21no—
291Dic73—41no—
292Dic73—41no—
293Dic73—41no—
294Dic73#43612yes—
295#17896—731nomaximal, Sylow
296C2×C73—81no—
297C2×C73C2×#43611yescharacteristic
298C2×C73#294911yescharacteristic
299C2×C73#295711yescharacteristic
300D73—22no—
301D73—81no—
302#2983—731no—
303#2975—731no—
304C2×C4×SD16—731no—
305#1592—731no—
306#1592—731no—
307#1592—731no—
308#1592—731no—
309#1590—731no—
310#1590—731no—
311#1590—731no—
312#1590D7311yescharacteristic, complemented
313#1564—731no—
314#1479—731no—
315#1478—731no—
316#1450—731no—
317C73#1789611yescharacteristic, complemented, Sylow
318C22×SD16—731no—
319C2×C4×Q8—731no—
320C2×C4×D4—731no—
321#446—731no—
322#446—731no—
323#446—731no—
324#446—1461no—
325#446—1461no—
326#446C2×D7311yescharacteristic, complemented
327C4×SD16—731no—
328C4×SD16—731no—
329C4×SD16—731no—
330C4×SD16—731no—
331C4×SD16—731no—
332C4×SD16—731no—
333C4×SD16—731no—
334C4×SD16C2×D7311yescharacteristic
335#436—731no—
336#436—731no—
337#436—731no—
338#436—1461no—
339#436—1461no—
340#436C2×D7311yescharacteristic
341#432—1461no—
342#432—1461no—
343#431—731no—
344#431—731no—
345#431—731no—
346#431—731no—
347C2×#106—731no—
348C2×#103—731no—
349C2×#102—731no—
350#407—1461no—
351#407—1461no—
352C2×C4×C8—731no—
353#335—731no—
354#335—731no—
355#334—731no—
356#334C2×D7311yescharacteristic, complemented
357Q8⋊C8—731no—
358Q8⋊C8—731no—
359Q8⋊C8—731no—
360Q8⋊C8C2×D7311yescharacteristic, complemented
361D4⋊C8—731no—
362D4⋊C8—731no—
363D4⋊C8—731no—
364D4⋊C8C2×D7311yescharacteristic
365#322—731no—
366#322—731no—
367C82—731no—
368C82C2×D7311yescharacteristic, complemented
369C22×Q8—731no—
370C22×D4—731no—
371C23×C4—1461no—
372C2×SD16—731no—
373C2×SD16—731no—
374C2×SD16—731no—
375C2×SD16—1464no—
376C2×SD16C4×D7311yescharacteristic
377C2×M16—21no—
378C2×M16—1461no—
379C2×M16—1461no—
380C2×M16—1461no—
381C22×C8—731no—
382C22×C8—731no—
383C4×Q8—731no—
384C4×Q8—731no—
385C4×Q8—731no—
386C4×Q8—1461no—
387C4×Q8—1461no—
388C4×Q8C22×D7311yescharacteristic
389C4×D4—731no—
390C4×D4—731no—
391C4×D4—731no—
392C4×D4—1461no—
393C4×D4—1461no—
394C4×D4C22×D7311yescharacteristic
395C2×C4⋊C4—731no—
396C2×C4⋊C4—731no—
397C2×C4⋊C4—1461no—
398C2×C22⋊C4—1461no—
399C2×C42—731no—
400C2×C42—1461no—
401#106—731no—
402#106—731no—
403#106—731no—
404#106C4×D7311yescharacteristic
405C4⋊C8—21no—
406C4⋊C8—731no—
407C4⋊C8—731no—
408C4⋊C8—731no—
409C4⋊C8—731no—
410C4⋊C8—1461no—
411C4⋊C8—1461no—
412C4⋊C8—1461no—
413C4⋊C8—1461no—
414C4⋊C8C22×D7311yescharacteristic
415C4⋊C8C22×D7311yescharacteristic
416#103—731no—
417#103—731no—
418#103—731no—
419#103C4×D7311yescharacteristic
420#102—731no—
421#102—731no—
422#102—731no—
423#102C4×D7311yescharacteristic
424C22⋊C8—21no—
425C22⋊C8—731no—
426C22⋊C8—731no—
427C22⋊C8—1461no—
428C22⋊C8—1461no—
429C22⋊C8—1461no—
430C22⋊C8—1461no—
431C22⋊C8—1461no—
432C22⋊C8—1461no—
433#97—21no—
434#97—1461no—
435#97—1461no—
436#97—1461no—
437C4×C8—731no—
438C4×C8—731no—
439C4×C8—731no—
440C4×C8—731no—
441C4×C8—731no—
442C4×C8—1461no—
443C4×C8—1461no—
444C4×C8C22×D7311yescharacteristic
445C4×C8C22×D7311yescharacteristic
446C4×C8C22×D7311yescharacteristic
447C24—1461no—
448C2×Q8—731no—
449C2×Q8—1461no—
450C2×Q8—1462no—
451C2×Q8—1462no—
452C2×Q8C2×C4×D7311yescharacteristic
453C2×D4—731no—
454C2×D4—1462no—
455C2×D4—1462no—
456C2×D4—1461no—
457C2×D4C2×C4×D7311yescharacteristic
458C22×C4—21no—
459C22×C4—5841no—
460C22×C4—5841no—
461C22×C4—731no—
462C22×C4—731no—
463C22×C4—731no—
464C22×C4—1461no—
465C22×C4—1461no—
466C22×C4—1461no—
467C22×C4—1461no—
468C22×C4—1461no—
469C22×C4—1461no—
470SD16—22no—
471SD16—1462no—
472SD16—1462no—
473SD16—1462no—
474M16—81no—
475M16—5841no—
476M16—5841no—
477M16—5841no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—731no—
482C2×C8—734no—
483C2×C8—731no—
484C2×C8—731no—
485C2×C8—731no—
486C2×C8—1462no—
487C2×C8—1461no—
488C2×C8—1461no—
489C2×C8—1461no—
490C2×C8C2×C4×D7311yescharacteristic
491C2×C8C2×C4×D7311yescharacteristic
492C2×C8D4×D7311yescharacteristic
493C2×C8D4×D7311yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—731no—
496C4⋊C4—731no—
497C4⋊C4—1461no—
498C4⋊C4—1461no—
499C4⋊C4—1461no—
500C4⋊C4—1461no—
501C4⋊C4—1461no—
502C4⋊C4C2×C4×D7311yescharacteristic
503C4⋊C4C2×C4×D7311yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—1461no—
506C22⋊C4—1461no—
507C22⋊C4—1461no—
508C42—21no—
509C42—731no—
510C42—731no—
511C42—731no—
512C42—1461no—
513C42—1461no—
514C42—1461no—
515C42C23×D7311yescharacteristic
516C23—21no—
517C23—2922no—
518C23—5841no—
519C23—5841no—
520C23—731no—
521C23—1461no—
522Q8—21no—
523Q8—21no—
524Q8—2922no—
525Q8—1461no—
526Q8—1461no—
527D4—21no—
528D4—21no—
529D4—2922no—
530D4—1461no—
531D4—1461no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—2921no—
538C2×C4—2922no—
539C2×C4—2921no—
540C2×C4—2921no—
541C2×C4—5841no—
542C2×C4—5841no—
543C2×C4—5841no—
544C2×C4—5841no—
545C2×C4—731no—
546C2×C4—732no—
547C2×C4—732no—
548C2×C4—731no—
549C2×C4—731no—
550C2×C4—1461no—
551C2×C4—1461no—
552C2×C4—1461no—
553C2×C4—1461no—
554C2×C4—1461no—
555C2×C4C22×C4×D7311yescharacteristic
556C2×C4C2×D4×D7311yescharacteristic
557C2×C4#41×D7311yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—2921no—
565C8—2921no—
566C8—2921no—
567C8—732no—
568C8—1461no—
569C8—1461no—
570C8—1461no—
571C8M16×D7312yes—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—2921no—
576C22—2921no—
577C22—2921no—
578C22—5844no—
579C22—732no—
580C22—1461no—
581C22—1461no—
582C22C4×D4×D7311yescharacteristic
583C4—21no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—2921no—
588C4—2921no—
589C4—2921no—
590C4—732no—
591C4—1461no—
592C4—1461no—
593C4C2×M16×D7311yescharacteristic
594C4#131×D7311yescharacteristic
595C4#1798939311yescharacteristic
596C4#1798939411yescharacteristic
597C2—81no—
598C2—5841no—
599C2—1462no—
600C2#436×D7311yescharacteristic
601C2#2261878511yescharacteristic
602C2#2261884311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1590C2
socleC22×C73C2×C4×D4
prime radicalC2×D4×D73C2×C4
cosocleC42×C73C24
hypercenter#1590D73
hypocenterC73#17896
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
1. #22619013C2semidirect
4. #22608836C2semidirect
5. #22608833C2semidirect
6. #22608831C2semidirect
7. #22608830C2semidirect
8. #22608823C2semidirect
9. #22608822C2semidirect
10. #22608820C2semidirect
11. #22608676C2semidirect
12. #22608324C2semidirect
14. #22608213C2semidirect
15. C73×#1590C2semidirect
19. #17988718C22semidirect
20. #17988717C22semidirect
23. #17988714C22semidirect
48. #17988339C22semidirect
49. #17988339C22semidirect
50. #17988338C22semidirect
51. #17988319C22semidirect
52. Q8⋊#10596831C22semidirect
53. #17988317C22semidirect
57. #17988309C22semidirect
58. #17988309C22semidirect
59. C8×#10596831C22semidirect
60. #446×C73C22semidirect
63. #334×C73C22semidirect
64. Q8⋊C8×C73C22semidirect
66. C82×C73C22semidirect
179. C8×D73M16semidirect
312. #1590D73semidirect
317. C73#17896semidirect
326. #446C2×D73semidirect
356. #334C2×D73semidirect
360. Q8⋊C8C2×D73semidirect
368. C82C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226190132
#226189692
C4×SD16×D732
#226088362
#226088332
#226088312
#226088302
#226088232
#226088222
#226088202
#226086762
#226083242
#226083202
#226082132
C73×#15902
#1789673