Finite Group Databasebeta

← #33057154

Subgroups — #33057154

Order 18688.

640 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619987C211yesmaximal, characteristic
2#22619054C211yesmaximal, characteristic, complemented
3#22618996C211yesmaximal, characteristic, complemented
4#22608820C211yesmaximal, characteristic, complemented
5#22608819C211yesmaximal, characteristic, complemented
6#22608792C211yesmaximal, characteristic, complemented
7#22608790C211yesmaximal, characteristic, complemented
8#22608785C211yesmaximal, characteristic, complemented
9D8×#10596831C211yesmaximal, characteristic, complemented
10C8×#11924013C211yesmaximal, characteristic, complemented
11#22608718C211yesmaximal, characteristic, complemented
12#22608380C211yesmaximal, characteristic, complemented
13#22608310C211yesmaximal, characteristic, complemented
14#22608216C211yesmaximal, 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
26#17988717C2211yescharacteristic
27#17988714C2211yescharacteristic
28C4×#11924017C2211yescharacteristic
29C4×#11924016C2211yescharacteristic
30C4×#11924013C2211yescharacteristic
31#17988664C2211yescharacteristic
32#17988663—21no—
33#17988658—21no—
34#17988655—21no—
35C8×D292C2211yescharacteristic
36D4×#10596831C2211yescharacteristic
37D4×#10596831C2211yescharacteristic
38#17988650—21no—
39#17988641—21no—
40#17988639C2211yescharacteristic
41#17988638C2211yescharacteristic
42#17988638C2211yescharacteristic
43#17988609C2211yescharacteristic
44C2×#14556520—21no—
45#17988555—21no—
46#17988552—21no—
47C4×C8×D73C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988319C2211yescharacteristic
52#17988317C2211yescharacteristic
53#17988316C2211yescharacteristic
54D4⋊#10596831C2211yescharacteristic
55D4⋊#10596831C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988308C2211yescharacteristic
58C8×#10596831C2211yescharacteristic
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—
73C2×#11924011—21no—
74C22×#10596831—21no—
75C22×#10596831—21no—
76C2×C8×D73—21no—
77C2×C8×D73—21no—
78#14556590C2×C411yescharacteristic
79#14556587C2×C411yescharacteristic
80#14556577—21no—
81#14556566C2×C411yescharacteristic
82#14556564—21no—
83#14556562C2×C411yescharacteristic
84C4×Dic146C2311yescharacteristic
85#14556556C2×C411yescharacteristic
86C4×D292C2311yescharacteristic
87D4×Dic73C2×C411yescharacteristic
88C4×C22⋊D73—21no—
89C4×C22⋊D73—21no—
90#14556551—21no—
91#14556549C2×C411yescharacteristic
92#14556547—21no—
93C2×C4×Dic73—21no—
94C42×D73C2311yescharacteristic
95#14556524C2×C411yescharacteristic
96#14556523C2×C411yescharacteristic
97#14556522C2×C411yescharacteristic
98C4⋊#10596831C2311yescharacteristic
99C4⋊#10596831C2311yescharacteristic
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#14556503C2×C411yescharacteristic
119#14556503C2×C411yescharacteristic
120#14556503D411yescharacteristic
121#14556503D411yescharacteristic
122#14556501—21no—
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—41no—
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—41no—
163#11924016—41no—
164#11924013—22no—
165#11924011—81no—
166#11924011—81no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—81no—
171C2×#10596831—81no—
172C2×#10596831C22×C411yescharacteristic
173C2×#10596831C22×C411yescharacteristic
174C2×#10596831C2×D411yescharacteristic
175C2×#10596831C2×D411yescharacteristic
176C8×D73—24no—
177C8×D73—81no—
178C4⋊Dic73C22×C411yescharacteristic
179C4⋊Dic73C22×C411yescharacteristic
180#11924007—21no—
181#11924007—21no—
182#11924007—21no—
183C22⋊Dic73—21no—
184C22⋊Dic73—21no—
185#11924005—21no—
186#11924005—21no—
187#11924005—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C4×Dic73—21no—
191C4×Dic73C22×C411yescharacteristic
192C4×Dic73C2×D411yescharacteristic
193C4×Dic73#4111yescharacteristic
194C2×D4×C73C22×C411yescharacteristic
195C2×D4×C73C22×C411yescharacteristic
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198D8×C73—22no—
199M16×C73—81no—
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C2×C8×C73—21no—
203C2×C8×C73—81no—
204C2×C8×C73C22×C411yescharacteristic
205C2×C8×C73C22×C411yescharacteristic
206C2×C8×C73C2×D411yescharacteristic
207C2×C8×C73C2×D411yescharacteristic
208C4⋊C4×C73C22×C411yescharacteristic
209C4⋊C4×C73C22×C411yescharacteristic
210C22⋊C4×C73—21no—
211C22⋊C4×C73—21no—
212C42×C73C2411yescharacteristic
213C23×C73—21no—
214C23×C73—21no—
215C22×D73—21no—
216C22×D73C4×D411yescharacteristic
217D4×C73—21no—
218D4×C73—21no—
219D4×C73—21no—
220D4×C73#13112yes—
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×C73C23×C411yescharacteristic
228C2×C4×C73C22×D411yescharacteristic
229C2×C4×C73C2×#4111yescharacteristic
230C22⋊D73—42no—
231C22⋊D73—42no—
232C22⋊D73—81no—
233C22⋊D73—81no—
234C2×Dic73—21no—
235C2×Dic73—21no—
236C2×Dic73—21no—
237C2×Dic73—42no—
238C2×Dic73—42no—
239C2×Dic73C4×D411yescharacteristic
240C2×Dic73C4×D411yescharacteristic
241C2×Dic73C4×D411yescharacteristic
242D292—21no—
243D292—21no—
244D292—81no—
245C4×D73—21no—
246C4×D73—21no—
247C4×D73—21no—
248C4×D73—21no—
249C4×D73—22no—
250C4×D73—41no—
251C4×D73—41no—
252Dic146—21no—
253Dic146—21no—
254Dic146—81no—
255C8×C73—22no—
256C8×C73—21no—
257C8×C73—21no—
258C8×C73—21no—
259C8×C73—21no—
260C8×C73—41no—
261C8×C73—41no—
262#10596831—22no—
263#10596831—21no—
264#10596831—21no—
265#10596831—21no—
266#10596831—21no—
267#10596831—41no—
268#10596831—41no—
269C22×C73—22no—
270C22×C73—41no—
271C22×C73—41no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73C2×C4×D411yescharacteristic
276C2×D73—21no—
277C2×D73—21no—
278C2×D73—21no—
279C2×D73—41no—
280C2×D73—41no—
281C2×D73—41no—
282C4×C73—21no—
283C4×C73—41no—
284C4×C73—41no—
285C4×C73C2×#13111yescharacteristic
286C4×C73#56811yescharacteristic
287C4×C73#57611yescharacteristic
288C4×C73#57711yescharacteristic
289Dic73—21no—
290Dic73—21no—
291Dic73—41no—
292Dic73—41no—
293Dic73—41no—
294Dic73#44312yes—
295#18015—731nomaximal, Sylow
296C2×C73—42no—
297C2×C73—81no—
298C2×C73#293311yescharacteristic
299C2×C73#294611yescharacteristic
300C2×C73C2×#44311yescharacteristic
301D73—41no—
302D73—81no—
303#3106—731no—
304#2990—731no—
305#2979—731no—
306#1590—731no—
307#1590—731no—
308#1586—731no—
309#1586D7311yescharacteristic, complemented
310#1585—731no—
311#1585—731no—
312C8×D8—731no—
313C8×D8—731no—
314#1574—731no—
315#1492—731no—
316#1476—731no—
317#1450—731no—
318C73#1801511yescharacteristic, complemented, Sylow
319#532—731no—
320C4×#41—731no—
321#482—731no—
322#482—731no—
323#477—731no—
324#476—731no—
325#460—731no—
326#459—731no—
327#449—731no—
328#449—731no—
329#446—731no—
330#446—731no—
331C4×SD16—731no—
332C4×SD16—731no—
333C4×D8—731no—
334C4×D8C2×D7311yescharacteristic
335#436—731no—
336#436—1461no—
337#436C2×D7311yescharacteristic
338#435—1461no—
339#435—1461no—
340C8×D4—731no—
341C8×D4—731no—
342C8×D4—731no—
343C8×D4—1461no—
344C8×D4C2×D7311yescharacteristic
345#432—1461no—
346#431—731no—
347#431—731no—
348#431—731no—
349#423—731no—
350C2×C4⋊C8—1461no—
351#408—1461no—
352#408—1461no—
353C2×C4×C8—731no—
354#335—731no—
355#335—731no—
356#334—731no—
357#334C2×D7311yescharacteristic
358Q8⋊C8—731no—
359Q8⋊C8—731no—
360D4⋊C8—731no—
361D4⋊C8—731no—
362D4⋊C8—731no—
363D4⋊C8—731no—
364D4⋊C8C2×D7311yescharacteristic
365D4⋊C8C2×D7311yescharacteristic
366#322—731no—
367#322C2×D7311yescharacteristic
368C82—731no—
369C82—731no—
370C2×#41—731no—
371C2×#41—1461no—
372C2×SD16—731no—
373C2×SD16—731no—
374C2×D8—731no—
375C2×D8C4×D7311yescharacteristic
376C2×M16—21no—
377C2×M16—1461no—
378C2×M16—1461no—
379C22×C8—21no—
380C22×C8—1461no—
381C22×C8—1461no—
382C22×C8—1461no—
383C22×C8—1461no—
384C4⋊Q8—731no—
385#127—731no—
386#124—1461no—
387#121—731no—
388#121—731no—
389#121—1461no—
390C4×Q8—731no—
391C4×Q8—731no—
392C4×D4—731no—
393C4×D4—731no—
394C4×D4—1461no—
395C4×D4—1461no—
396C4×D4—1461no—
397C4×D4C22×D7311yescharacteristic
398C4×D4C22×D7311yescharacteristic
399#117—731no—
400#117—1461no—
401C2×C42—731no—
402C2×C42—1461no—
403#107—731no—
404#107C4×D7311yescharacteristic
405#106—731no—
406#106—731no—
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⋊C8—1461no—
416C4⋊C8C22×D7311yescharacteristic
417C4⋊C8C22×D7311yescharacteristic
418#103—731no—
419#103—731no—
420#102—731no—
421#102—731no—
422#102—731no—
423#102—731no—
424#102C4×D7311yescharacteristic
425#102C4×D7311yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—731no—
429C22⋊C8—731no—
430C22⋊C8—731no—
431C22⋊C8—731no—
432C22⋊C8—1461no—
433C22⋊C8—1461no—
434C22⋊C8—1461no—
435C22⋊C8—1461no—
436C22⋊C8—1461no—
437#97—1461no—
438#97—1461no—
439C4×C8—731no—
440C4×C8—731no—
441C4×C8—731no—
442C4×C8—1461no—
443C4×C8—1461no—
444C4×C8C22×D7311yescharacteristic
445C4×C8C22×D7311yescharacteristic
446C4×C8C22×D7311yescharacteristic
447#41—2921no—
448#41—5841no—
449#41—5841no—
450#41—1462no—
451C2×Q8—731no—
452C2×Q8—1461no—
453C2×D4—731no—
454C2×D4—1461no—
455C2×D4—1461no—
456C2×D4—1461no—
457C2×D4—1461no—
458C2×D4—1461no—
459C2×D4C2×C4×D7311yescharacteristic
460C2×D4C2×C4×D7311yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—731no—
464C22×C4—731no—
465C22×C4—731no—
466C22×C4—1461no—
467C22×C4—1461no—
468C22×C4—1461no—
469SD16—2921no—
470SD16—2921no—
471D8—22no—
472D8—1462no—
473M16—81no—
474M16—5841no—
475M16—5841no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—81no—
480C2×C8—5841no—
481C2×C8—5841no—
482C2×C8—5841no—
483C2×C8—731no—
484C2×C8—731no—
485C2×C8—731no—
486C2×C8—731no—
487C2×C8—1464no—
488C2×C8—1461no—
489C2×C8—1461no—
490C2×C8—1461no—
491C2×C8C2×C4×D7311yescharacteristic
492C2×C8C2×C4×D7311yescharacteristic
493C2×C8D4×D7311yescharacteristic
494C2×C8D4×D7311yescharacteristic
495C4⋊C4—731no—
496C4⋊C4—731no—
497C4⋊C4—1461no—
498C4⋊C4—1461no—
499C4⋊C4—1461no—
500C4⋊C4C2×C4×D7311yescharacteristic
501C4⋊C4C2×C4×D7311yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—1461no—
505C22⋊C4—1461no—
506C22⋊C4—1461no—
507C22⋊C4—1461no—
508C22⋊C4—1461no—
509C42—731no—
510C42—731no—
511C42—731no—
512C42—1461no—
513C42—1461no—
514C42—1461no—
515C42C23×D7311yescharacteristic
516C23—21no—
517C23—21no—
518C23—731no—
519C23—1461no—
520Q8—5841no—
521Q8—1461no—
522Q8—1461no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—2922no—
527D4—2922no—
528D4—5841no—
529D4—5841no—
530D4—5841no—
531D4—1461no—
532D4—1461no—
533D4#1455659912yes—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—2922no—
541C2×C4—2922no—
542C2×C4—2921no—
543C2×C4—2921no—
544C2×C4—731no—
545C2×C4—731no—
546C2×C4—731no—
547C2×C4—1462no—
548C2×C4—1461no—
549C2×C4—1461no—
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—22no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—2921no—
566C8—2921no—
567C8—1462no—
568C8—1461no—
569C8—1461no—
570C8—1461no—
571C8—1461no—
572C22—22no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—2921no—
579C22—2921no—
580C22—2921no—
581C22—1461no—
582C22—1461no—
583C22—1461no—
584C22C4×D4×D7311yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—2921no—
589C4—2921no—
590C4—2921no—
591C4—732no—
592C4—1461no—
593C4—1461no—
594C4C2×#1455659911yescharacteristic
595C4#1798935211yescharacteristic
596C4#1798939111yescharacteristic
597C4#1798939711yescharacteristic
598C2—42no—
599C2—81no—
600C2—2921no—
601C2—5841no—
602C2#2261865711yescharacteristic
603C2#2261876011yescharacteristic
604C2#443×D7311yescharacteristic
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#18015
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. #22619054C2semidirect
3. #22618996C2semidirect
4. #22608820C2semidirect
5. #22608819C2semidirect
6. #22608792C2semidirect
7. #22608790C2semidirect
8. #22608785C2semidirect
9. D8×#10596831C2semidirect
10. C8×#11924013C2semidirect
11. #22608718C2semidirect
12. #22608380C2semidirect
13. #22608310C2semidirect
14. #22608216C2semidirect
15. C73×#1586C2semidirect
309. #1586D73semidirect
318. C73#18015semidirect

Maximal subgroups

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

subgroupindex
#226199872
#226190542
#226189962
#226088202
#226088192
#226087922
#226087902
#226087852
D8×#105968312
C8×#119240132
#226087182
#226083802
#226083102
#226082162
C73×#15862
#1801573