Finite Group Databasebeta

← #33056077

Subgroups — #33056077

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#22619987C211yesmaximal, characteristic
2#22619038C211yesmaximal, characteristic, complemented
3#22619008C211yesmaximal, characteristic, complemented
4#22608811C211yesmaximal, characteristic, complemented
5#22608772C211yesmaximal, characteristic, complemented
6#22608760C211yesmaximal, characteristic, complemented
7#22608752C211yesmaximal, characteristic, complemented
8#22608740C211yesmaximal, characteristic, complemented
9#22608730C211yesmaximal, characteristic, complemented
10D8×#10596831C211yesmaximal, characteristic, complemented
11#22608713C211yesmaximal, characteristic, complemented
12#22608362C211yesmaximal, characteristic, complemented
13#22608328C211yesmaximal, characteristic, complemented
14#22608232C211yesmaximal, characteristic, complemented
15C73×#1586C211yesmaximal, characteristic, complemented
16#17989134C2211yescharacteristic
17C4×#11924027C2211yescharacteristic
18#17988914C411yescharacteristic
19#17988910C411yescharacteristic
20#17988881C411yescharacteristic
21#17988875C411yescharacteristic
22#17988786C411yescharacteristic
23#17988780C411yescharacteristic
24#17988733C411yescharacteristic
25#17988729C411yescharacteristic
26C8×Dic146C2211yescharacteristic
27#17988711C2211yescharacteristic
28C4×#11924017C2211yescharacteristic
29C4×#11924016C2211yescharacteristic
30C4×#11924013C2211yescharacteristic
31#17988666C2211yescharacteristic
32#17988656—21no—
33#17988655—21no—
34D4×#10596831C2211yescharacteristic
35D4×#10596831C2211yescharacteristic
36#17988652C2211yescharacteristic
37C8×C22⋊D73—21no—
38#17988650—21no—
39#17988643C2211yescharacteristic
40#17988638C2211yescharacteristic
41#17988638C2211yescharacteristic
42#17988638C2211yescharacteristic
43#17988637—21no—
44C2×#14556520—21no—
45C4⋊C8×D73C2211yescharacteristic
46#17988555—21no—
47#17988552—21no—
48#17988340C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988319C2211yescharacteristic
52#17988317C2211yescharacteristic
53#17988316C2211yescharacteristic
54D4⋊#10596831C2211yescharacteristic
55D4⋊#10596831C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988308C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60C4×D8×C73C2211yescharacteristic
61#436×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64D4⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924028—21no—
68C2×#11924027C2×C411yescharacteristic
69C2×#11924017C2×C411yescharacteristic
70C2×#11924016C2×C411yescharacteristic
71C2×#11924013C2×C411yescharacteristic
72C2×#11924011—21no—
73C22×#10596831—21no—
74C22×#10596831—21no—
75C2×C8×D73—21no—
76C2×C8×D73—21no—
77#14556590C2×C411yescharacteristic
78#14556587C2×C411yescharacteristic
79#14556577—21no—
80#14556566C2×C411yescharacteristic
81#14556564—21no—
82#14556562C2×C411yescharacteristic
83C4×Dic146C2311yescharacteristic
84#14556556C2×C411yescharacteristic
85C4×D292C2311yescharacteristic
86D4×Dic73C2×C411yescharacteristic
87C4×C22⋊D73—21no—
88C4×C22⋊D73—21no—
89#14556551—21no—
90#14556549C2×C411yescharacteristic
91#14556547—21no—
92C2×C4×Dic73—21no—
93C42×D73C2311yescharacteristic
94#14556524C2×C411yescharacteristic
95#14556523C2×C411yescharacteristic
96#14556522C2×C411yescharacteristic
97C4⋊#10596831C2311yescharacteristic
98C4⋊#10596831C2311yescharacteristic
99#14556520—21no—
100#14556520—21no—
101#14556520—21no—
102#14556520—21no—
103#14556520C2×C411yescharacteristic
104#14556520C2×C411yescharacteristic
105#14556520D411yescharacteristic
106#14556520D411yescharacteristic
107#14556516C2×C411yescharacteristic
108#14556514C2×C411yescharacteristic
109#14556513C2×C411yescharacteristic
110#14556512C2×C411yescharacteristic
111#14556512C2×C411yescharacteristic
112#14556511C2×C411yescharacteristic
113C22⋊#10596831—21no—
114C22⋊#10596831—21no—
115#14556503—21no—
116#14556503—21no—
117#14556503—21no—
118#14556503—21no—
119#14556503C2×C411yescharacteristic
120#14556503C2×C411yescharacteristic
121#14556503D411yescharacteristic
122#14556503D411yescharacteristic
123#14556501—21no—
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C4×#10596831C2311yescharacteristic
127C8×Dic73—21no—
128C8×Dic73—21no—
129C2×D8×C73C2×C411yescharacteristic
130C2×M16×C73—21no—
131C22×C8×C73—21no—
132C4×D4×C73C2311yescharacteristic
133C4×D4×C73C2311yescharacteristic
134#107×C73C2×C411yescharacteristic
135C4⋊C8×C73C2311yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137#102×C73C2×C411yescharacteristic
138#102×C73C2×C411yescharacteristic
139C22⋊C8×C73—21no—
140C22⋊C8×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924028—81no—
145#11924028—81no—
146#11924027—22no—
147#11924027—22no—
148C2×Dic146—21no—
149C2×Dic146C22×C411yescharacteristic
150C2×D292—21no—
151C2×D292C22×C411yescharacteristic
152C2×C22⋊D73—21no—
153C2×C22⋊D73—21no—
154C2×C22⋊D73—21no—
155C2×C22⋊D73—21no—
156C22×Dic73—21no—
157C22×Dic73—21no—
158C2×C4×D73—21no—
159C2×C4×D73C22×C411yescharacteristic
160C2×C4×D73C2×D411yescharacteristic
161C2×C4×D73#4111yescharacteristic
162#11924017—22no—
163#11924016—22no—
164#11924013—22no—
165#11924011—81no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—81no—
170C2×#10596831—81no—
171C2×#10596831C22×C411yescharacteristic
172C2×#10596831C22×C411yescharacteristic
173C2×#10596831C2×D411yescharacteristic
174C2×#10596831C2×D411yescharacteristic
175C8×D73—81no—
176C8×D73—81no—
177C4⋊Dic73C22×C411yescharacteristic
178C4⋊Dic73C22×C411yescharacteristic
179#11924007—21no—
180#11924007—21no—
181#11924007—21no—
182C22⋊Dic73—21no—
183C22⋊Dic73—21no—
184#11924005—21no—
185#11924005—21no—
186#11924005—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C4×Dic73C22×C411yescharacteristic
191C4×Dic73C2×D411yescharacteristic
192C4×Dic73#4111yescharacteristic
193C2×D4×C73C22×C411yescharacteristic
194C2×D4×C73C22×C411yescharacteristic
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197D8×C73—22no—
198M16×C73—81no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C2×C8×C73—81no—
203C2×C8×C73C22×C411yescharacteristic
204C2×C8×C73C22×C411yescharacteristic
205C2×C8×C73C2×D411yescharacteristic
206C2×C8×C73C2×D411yescharacteristic
207C4⋊C4×C73C22×C411yescharacteristic
208C4⋊C4×C73C22×C411yescharacteristic
209C22⋊C4×C73—21no—
210C22⋊C4×C73—21no—
211C42×C73C2411yescharacteristic
212C23×C73—21no—
213C23×C73—21no—
214C22×D73—21no—
215C22×D73C4×D411yescharacteristic
216D4×C73—21no—
217D4×C73—21no—
218D4×C73—21no—
219D4×C73#13112yes—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—41no—
223C2×C4×C73—41no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
226C2×C4×C73C23×C411yescharacteristic
227C2×C4×C73C22×D411yescharacteristic
228C2×C4×C73C2×#4111yescharacteristic
229C22⋊D73—24no—
230C22⋊D73—81no—
231C22⋊D73—81no—
232C22⋊D73—81no—
233C2×Dic73—24no—
234C2×Dic73—21no—
235C2×Dic73—21no—
236C2×Dic73—21no—
237C2×Dic73—81no—
238C2×Dic73C4×D411yescharacteristic
239C2×Dic73C4×D411yescharacteristic
240C2×Dic73C4×D411yescharacteristic
241D292—21no—
242D292—21no—
243D292—81no—
244C4×D73—21no—
245C4×D73—21no—
246C4×D73—21no—
247C4×D73—21no—
248C4×D73—41no—
249C4×D73—41no—
250C4×D73—41no—
251Dic146—21no—
252Dic146—81no—
253Dic146#13112yes—
254C8×C73—21no—
255C8×C73—21no—
256C8×C73—21no—
257C8×C73—21no—
258C8×C73—41no—
259C8×C73—41no—
260C8×C73—41no—
261#10596831—21no—
262#10596831—21no—
263#10596831—21no—
264#10596831—21no—
265#10596831—41no—
266#10596831—41no—
267#10596831—41no—
268C22×C73—22no—
269C22×C73—41no—
270C22×C73—41no—
271C22×C73—41no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73C2×C4×D411yescharacteristic
275C2×D73—21no—
276C2×D73—21no—
277C2×D73—21no—
278C2×D73—41no—
279C2×D73—41no—
280C2×D73—41no—
281C4×C73—21no—
282C4×C73—41no—
283C4×C73—41no—
284C4×C73C2×#13111yescharacteristic
285C4×C73C2×#13111yescharacteristic
286C4×C73#57611yescharacteristic
287C4×C73#57711yescharacteristic
288Dic73—22no—
289Dic73—21no—
290Dic73—21no—
291Dic73—21no—
292Dic73—41no—
293Dic73—41no—
294#17920—731nomaximal, Sylow
295C2×C73—42no—
296C2×C73—81no—
297C2×C73#292911yescharacteristic
298C2×C73#294611yescharacteristic
299C2×C73#295711yescharacteristic
300D73—41no—
301D73—81no—
302#3106—731no—
303#2988—731no—
304#2981—731no—
305#1588—731no—
306#1586D7311yescharacteristic, complemented
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#532—731no—
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×D8C2×D7311yescharacteristic
334#436—731no—
335#436C2×D7311yescharacteristic
336#435—1461no—
337#435—1461no—
338C8×D4—731no—
339C8×D4—731no—
340C8×D4—731no—
341C8×D4—1461no—
342C8×D4—1461no—
343C8×D4C2×D7311yescharacteristic
344#432—731no—
345#431—731no—
346#431—731no—
347#431—731no—
348#431—1461no—
349C2×C4⋊C8—731no—
350C2×C4⋊C8—1461no—
351#408—1461no—
352#408—1461no—
353#335—731no—
354#335—731no—
355#334—731no—
356#334C2×D7311yescharacteristic
357Q8⋊C8—731no—
358Q8⋊C8—731no—
359D4⋊C8—731no—
360D4⋊C8—731no—
361D4⋊C8—731no—
362D4⋊C8—731no—
363D4⋊C8C2×D7311yescharacteristic
364D4⋊C8C2×D7311yescharacteristic
365#322—731no—
366#322—731no—
367#322C2×D7311yescharacteristic
368C82—731no—
369C2×#41—731no—
370C2×#41—1461no—
371C2×SD16—731no—
372C2×SD16—731no—
373C2×D8—731no—
374C2×D8C4×D7311yescharacteristic
375C2×M16—21no—
376C2×M16—1461no—
377C22×C8—21no—
378C22×C8—1461no—
379C22×C8—1461no—
380C22×C8—1461no—
381C22×C8—1461no—
382C4⋊Q8—731no—
383#127—731no—
384#124—1461no—
385#121—731no—
386#121—731no—
387#121—1461no—
388C4×Q8—731no—
389C4×Q8—731no—
390C4×D4—731no—
391C4×D4—731no—
392C4×D4—1461no—
393C4×D4—1461no—
394C4×D4—1461no—
395C4×D4C22×D7311yescharacteristic
396C4×D4C22×D7311yescharacteristic
397#117—731no—
398#117—1461no—
399C2×C42—731no—
400C2×C42—1461no—
401#107—731no—
402#107C4×D7311yescharacteristic
403#106—731no—
404#106—731no—
405C4⋊C8—731no—
406C4⋊C8—731no—
407C4⋊C8—731no—
408C4⋊C8—731no—
409C4⋊C8—731no—
410C4⋊C8—731no—
411C4⋊C8—1461no—
412C4⋊C8—1461no—
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#102C4×D7311yescharacteristic
424#102C4×D7311yescharacteristic
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—731no—
428C22⋊C8—731no—
429C22⋊C8—731no—
430C22⋊C8—731no—
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—1461no—
442C4×C8—1461no—
443C4×C8C22×D7311yescharacteristic
444C4×C8C22×D7311yescharacteristic
445C4×C8C22×D7311yescharacteristic
446#41—5841no—
447#41—5841no—
448#41—1462no—
449#41—1462no—
450C2×Q8—731no—
451C2×Q8—1461no—
452C2×D4—731no—
453C2×D4—1461no—
454C2×D4—1461no—
455C2×D4—1461no—
456C2×D4—1461no—
457C2×D4—1461no—
458C2×D4C2×C4×D7311yescharacteristic
459C2×D4C2×C4×D7311yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—731no—
463C22×C4—731no—
464C22×C4—731no—
465C22×C4—1461no—
466C22×C4—1461no—
467C22×C4—1461no—
468SD16—1462no—
469SD16—1462no—
470D8—22no—
471D8—1462no—
472M16—81no—
473M16—5841no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—81no—
478C2×C8—5841no—
479C2×C8—5841no—
480C2×C8—5841no—
481C2×C8—5841no—
482C2×C8—731no—
483C2×C8—731no—
484C2×C8—731no—
485C2×C8—731no—
486C2×C8—1461no—
487C2×C8—1461no—
488C2×C8—1461no—
489C2×C8C2×C4×D7311yescharacteristic
490C2×C8C2×C4×D7311yescharacteristic
491C2×C8D4×D7311yescharacteristic
492C2×C8D4×D7311yescharacteristic
493C4⋊C4—731no—
494C4⋊C4—731no—
495C4⋊C4—1461no—
496C4⋊C4—1461no—
497C4⋊C4—1461no—
498C4⋊C4C2×C4×D7311yescharacteristic
499C4⋊C4C2×C4×D7311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—1461no—
503C22⋊C4—1461no—
504C22⋊C4—1461no—
505C22⋊C4—1461no—
506C22⋊C4—1461no—
507C42—731no—
508C42—731no—
509C42—731no—
510C42—1461no—
511C42—1461no—
512C42—1461no—
513C42C23×D7311yescharacteristic
514C23—21no—
515C23—21no—
516C23—731no—
517C23—1461no—
518Q8—5841no—
519Q8—732no—
520Q8—1461no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—5841no—
525D4—5841no—
526D4—5841no—
527D4—5841no—
528D4—1464no—
529D4—1461no—
530D4—1461no—
531D4#1455659912yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—2921no—
539C2×C4—2921no—
540C2×C4—2921no—
541C2×C4—5841no—
542C2×C4—731no—
543C2×C4—731no—
544C2×C4—731no—
545C2×C4—1461no—
546C2×C4—1461no—
547C2×C4—1464no—
548C2×C4—1461no—
549C2×C4—1461no—
550C2×C4—1461no—
551C2×C4—1461no—
552C2×C4—1461no—
553C2×C4C22×C4×D7311yescharacteristic
554C2×C4C2×D4×D7311yescharacteristic
555C2×C4#41×D7311yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—2921no—
564C8—2921no—
565C8—2921no—
566C8—1461no—
567C8—1461no—
568C8—1461no—
569C8—1461no—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—2921no—
577C22—2921no—
578C22—2921no—
579C22—1461no—
580C22—1461no—
581C22—1461no—
582C22C4×D4×D7311yescharacteristic
583C4—21no—
584C4—41no—
585C4—41no—
586C4—2921no—
587C4—2921no—
588C4—1461no—
589C4—1461no—
590C4—1461no—
591C4—1462no—
592C4#131×D7311yescharacteristic
593C4C2×#1455659911yescharacteristic
594C4#1798939111yescharacteristic
595C4#1798939711yescharacteristic
596C2—42no—
597C2—81no—
598C2—2921no—
599C2—5841no—
600C2#2261862211yescharacteristic
601C2#2261876011yescharacteristic
602C2#2261884311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1586C2
socleC22×C73C2×C4×D4
prime radical#22619987C2
cosocleC42×C73C24
hypercenter#1586D73
hypocenterC73#17920
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
2. #22619038C2semidirect
3. #22619008C2semidirect
4. #22608811C2semidirect
5. #22608772C2semidirect
6. #22608760C2semidirect
7. #22608752C2semidirect
8. #22608740C2semidirect
9. #22608730C2semidirect
10. D8×#10596831C2semidirect
11. #22608713C2semidirect
12. #22608362C2semidirect
13. #22608328C2semidirect
14. #22608232C2semidirect
15. C73×#1586C2semidirect
306. #1586D73semidirect
317. C73#17920semidirect

Maximal subgroups

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

subgroupindex
#226199872
#226190382
#226190082
#226088112
#226087722
#226087602
#226087522
#226087402
#226087302
D8×#105968312
#226087132
#226083622
#226083282
#226082322
C73×#15862
#1792073