Finite Group Databasebeta

← #11869658

Subgroups — #11869658

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 619 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595005C211yesmaximal, characteristic
2C2×#63841C211yesmaximal, characteristic, complemented
3#10592435C211yesmaximal, characteristic, complemented
4C3×D3×C22⋊C8C211yesmaximal, characteristic, complemented
5C3×#4722C211yesmaximal, characteristic, complemented
6#10591126C211yesmaximal, characteristic, complemented
7#10591125C211yesmaximal, characteristic, complemented
8#10590710C212yesmaximal, complemented
9#10590707C212yesmaximal, complemented
10#10590705C212yesmaximal, complemented
11#10590690C212yesmaximal, complemented
12#81467—31nomaximal
13#78591—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C2×#3799C2211yescharacteristic
16#64139C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C3×#924C2211yescharacteristic
20C2×C3×D3×C8C2212yes—
21#63977—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×Dic32—21no—
24#63952—21no—
25#63909C2211yescharacteristic
26#63904—21no—
27#63856C2211yescharacteristic
28#63850—21no—
29#63841—21no—
30#63841—21no—
31#63841C2211yescharacteristic
32#63841C2212yes—
33#63841C2212yes—
34C32×C22⋊C8C2211yescharacteristic
35#63648C2212yescomplemented
36#63645C2212yescomplemented
37C3×#830C2211yescharacteristic
38C3×(C2×D3)⋊C8C2212yes—
39C3×#818C2212yescomplemented
40C3×#816C2212yescomplemented
41#63573C2212yescomplemented
42#63573C2212yescomplemented
43#63566C2212yescomplemented
44#63564C2212yescomplemented
45#5791—31no—
46C2×#926—31no—
47#5627—31no—
48C2×#892—31no—
49C3×#484—31no—
50C2×C3×C22⋊C8—31no—
51#5113—32no—
52#5106—32no—
53#5043—31no—
54#4968—31no—
55#4885—32no—
56#4880—32no—
57#4814—32no—
58#4804—32no—
59#4737—32no—
60#4736—31no—
61#4736—31no—
62#4736—61no—
63#4735—31no—
64D3×C22⋊C8D311yescharacteristic, complemented
65#4723—32no—
66#4722D311yescharacteristic, complemented
67#4721—31no—
68C23×C3×D3D411yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C2×#638—21no—
71C22×C3⋊Dic3—21no—
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C22×C3×Dic3—21no—
74C22×C3×Dic3D411yescharacteristic
75C2×C3×C4×D3—24no—
76C2×C3×C4×D3D411yescharacteristic
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×C4×D3C2311yescharacteristic
79C2×C3×C4×D3C2311yescharacteristic
80C2×C3×Dic6C2311yescharacteristic
81C2×#626—21no—
82C2×#626—21no—
83C2×#624—21no—
84#3799—24no—
85C2×C32×C8C2312yes—
86#3752—21no—
87C4⋊(C3⋊Dic3)—21no—
88C4⋊(C3⋊Dic3)C2312yes—
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90C3×#217—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4⋊Dic3C2312yes—
94C3×Dic3⋊C4—21no—
95C2×C3×C3⋊C8C2312yes—
96C3×D3×C8—24no—
97#3724—21no—
98#3722—21no—
99(C2×D3)⋊Dic3—22no—
100(C2×D3)⋊Dic3—22no—
101(C2×D3)⋊Dic3—21no—
102(C2×D3)⋊Dic3—21no—
103Dic32—22no—
104Dic32—22no—
105Dic32—21no—
106#3091—91noSylow
107C23×C3×C4—31no—
108C2×#239—31no—
109C2×#235—31no—
110C22×C4×D3C2×D311yescharacteristic
111C22×C3×C8—32no—
112C3×C22⋊Q8—31no—
113C2×C3×C4⋊C4—31no—
114#953—61no—
115C2×#217—61no—
116#946—31no—
117#930—31no—
118#930—31no—
119#930—31no—
120#930—61no—
121#929—61no—
122C4×#67—61no—
123C4×#67—61no—
124C2×(C2×D3)⋊C4—61no—
125#926—32no—
126#926—32no—
127#926—31no—
128#926—61no—
129#926—61no—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—61no—
133C2×C4⋊Dic3C2×D311yescharacteristic
134#924—31no—
135#924C2×D311yescharacteristic
136C2×C4×Dic3—61no—
137C2×C4×Dic3—61no—
138C2×D3×C8C2×D312yes—
139#895—31no—
140#894—61no—
141#893—61no—
142#892—31no—
143#892—32no—
144#892—32no—
145#892—61no—
146#892—61no—
147#882—61no—
148#67⋊C4—61no—
149C3×#107—32no—
150C3×#103—32no—
151C3×C22⋊C8—21no—
152C3×C22⋊C8—31no—
153C3×C22⋊C8—32no—
154C3×C22⋊C8C2×D311yescharacteristic
155C3×C22⋊C8C2×D311yescharacteristic
156#835—32no—
157#830C2×D311yescharacteristic
158#821—32no—
159#821—32no—
160#821—32no—
161#821—62no—
162(C2×D3)⋊C8C2×D312yes—
163#818—32no—
164#818—32no—
165#818—62no—
166#818C2×D312yescomplemented
167#817—32no—
168#817—32no—
169#816—32no—
170#816C2×D312yescomplemented
171#809—32no—
172#808—32no—
173#808—32no—
174C23×C32C2×D411yescharacteristic
175C22×C3⋊D3—21no—
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3—41no—
179C22×C3×D3C2×D411yescharacteristic
180C22×C3×D3C2×D411yescharacteristic
181C2×C32×C4—22no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184#638—42no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—42no—
188C4⋊(C3⋊D3)—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—42no—
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C3×C4×D3—22no—
197C3×C4×D3—22no—
198C3×C4×D3—22no—
199C3×C4×D3#4114yes—
200C3×Dic6—22no—
201#626—42no—
202#626—42no—
203#624—42no—
204C32×C8—22no—
205C3×C3⋊C8—22no—
206#525—91no—
207C2×#117—91no—
208#485—92no—
209#484—31no—
210#483—91no—
211#482—92no—
212#481—91no—
213#480—91no—
214#427—92no—
215#416—92no—
216C2×C22⋊C8—31no—
217C24×C3—31no—
218C23×D3D1211yescharacteristic
219C2×C3×Q8—31no—
220C22×C3×C4—21no—
221C22×C3×C4—31no—
222C22×C3×C4—31no—
223C22×C3×C4—31no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—64no—
227C22×C3×C4—61no—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C2×#67—61no—
231C2×#67—61no—
232C2×#67—61no—
233C2×#67—61no—
234C2×#67—121no—
235C22×Dic3—21no—
236C22×Dic3—61no—
237C22×Dic3—61no—
238C22×Dic3—121no—
239C22×Dic3D1211yescharacteristic
240#239—64no—
241#235—64no—
242C2×D12—31no—
243C2×D12—31no—
244C2×D12—61no—
245C2×D12—61no—
246C2×D12—61no—
247C2×C4×D3—24no—
248C2×C4×D3—61no—
249C2×C4×D3—61no—
250C2×C4×D3D1211yescharacteristic
251C2×C4×D3D1211yescharacteristic
252C2×C4×D3C22×D311yescharacteristic
253C2×C4×D3C22×D311yescharacteristic
254C2×Dic6C22×D311yescharacteristic
255C2×C3×C8—22no—
256C2×C3×C8—32no—
257C2×C3×C8—64no—
258C2×C3×C8C22×D312yes—
259C2×C3×C8C22×D312yes—
260C3×C4⋊C4—31no—
261C3×C4⋊C4—32no—
262C3×C4⋊C4—61no—
263C3×C4⋊C4—61no—
264C3×C22⋊C4—61no—
265#217—21no—
266#217—61no—
267#217—62no—
268#217—62no—
269#217—61no—
270(C2×D3)⋊C4—61no—
271(C2×D3)⋊C4—61no—
272(C2×D3)⋊C4—61no—
273(C2×D3)⋊C4—62no—
274(C2×D3)⋊C4—62no—
275(C2×D3)⋊C4—61no—
276(C2×D3)⋊C4—61no—
277(C2×D3)⋊C4—61no—
278(C2×D3)⋊C4—121no—
279C4⋊Dic3—21no—
280C4⋊Dic3—31no—
281C4⋊Dic3—32no—
282C4⋊Dic3—32no—
283C4⋊Dic3—31no—
284C4⋊Dic3—61no—
285C4⋊Dic3—62no—
286C4⋊Dic3—61no—
287C4⋊Dic3—61no—
288C4⋊Dic3—121no—
289C4⋊Dic3C22×D312yes—
290C4⋊Dic3C22×D311yescharacteristic
291Dic3⋊C4—21no—
292Dic3⋊C4—61no—
293Dic3⋊C4—61no—
294C4×Dic3—62no—
295C4×Dic3—62no—
296C4×Dic3—61no—
297C4×Dic3—61no—
298C4×Dic3—62no—
299C4×Dic3—62no—
300C2×C3⋊C8C22×D312yes—
301D3×C8—24no—
302C22×C32—21no—
303C22×C32—21no—
304C22×C32#13512yes—
305C22×C32C22×D411yescharacteristic
306C2×C3⋊D3—41no—
307C2×C3⋊D3—41no—
308C2×C3⋊D3—41no—
309C2×C3×D3—21no—
310C2×C3×D3—21no—
311C2×C3×D3—21no—
312C2×C3×D3—21no—
313C2×C3×D3—21no—
314C2×C3×D3—44no—
315C2×C3×D3#12312yes—
316C32×C4—21no—
317C32×C4C2×#4112yes—
318C3⋊Dic3—42no—
319C3⋊Dic3—41no—
320C3×Dic3—21no—
321C3×Dic3—41no—
322C3×Dic3—41no—
323C3×Dic3—42no—
324C3×Dic3#12312yes—
325C2×#41—91no—
326C23×C4—31no—
327C22×C8—32no—
328#123—181no—
329C22⋊Q8—31no—
330C22⋊Q8—91no—
331#121—91no—
332#121—91no—
333#120—181no—
334C4×D4—181no—
335C4×D4—181no—
336#117—92no—
337#117—92no—
338#117—91no—
339#117—181no—
340#117—181no—
341C2×C4⋊C4—31no—
342C2×C4⋊C4—91no—
343C2×C22⋊C4—181no—
344C2×C42—181no—
345#107—32no—
346#107—92no—
347#106—92no—
348#106—92no—
349#103—32no—
350#103—92no—
351#102—92no—
352#102—92no—
353C22⋊C8—31no—
354C22⋊C8—32no—
355C22⋊C8D3211yescharacteristic
356C23×C3—21no—
357C23×C3—31no—
358C23×C3—31no—
359C23×C3—62no—
360C23×C3—62no—
361C23×C3—121no—
362C23×C3C2×D1211yescharacteristic
363C23×C3D3×D411yescharacteristic
364C22×D3—22no—
365C22×D3—22no—
366C22×D3—41no—
367C22×D3—61no—
368C22×D3—61no—
369C22×D3—121no—
370C22×D3C2×D1211yescharacteristic
371C22×D3C2×D1211yescharacteristic
372C3×Q8—62no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—31no—
378C2×C3×C4—34no—
379C2×C3×C4—31no—
380C2×C3×C4—42no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—61no—
387C2×C3×C4—61no—
388C2×C3×C4—122no—
389C2×C3×C4C2×D1211yescharacteristic
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4C23×D311yescharacteristic
392C2×C3×C4C23×D311yescharacteristic
393#67—122no—
394#67—122no—
395#67—122no—
396#67—122no—
397#67—242no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—21no—
401C2×Dic3—21no—
402C2×Dic3—42no—
403C2×Dic3—62no—
404C2×Dic3—61no—
405C2×Dic3—62no—
406C2×Dic3—61no—
407C2×Dic3—122no—
408C2×Dic3—121no—
409C2×Dic3—122no—
410C2×Dic3—122no—
411C2×Dic3—242no—
412C2×Dic3C2×D1211yescharacteristic
413C2×Dic3C2×D1211yescharacteristic
414D12—62no—
415D12—62no—
416D12—122no—
417D12—122no—
418D12—122no—
419C4×D3—22no—
420C4×D3—22no—
421C4×D3—22no—
422C4×D3—122no—
423C4×D3—122no—
424C4×D3#23714yes—
425Dic6—22no—
426C3×C8—22no—
427C3×C8—22no—
428C3×C8—42no—
429C3×C8—62no—
430C3⋊C8—22no—
431C2×C32—22no—
432C2×C32C2×#12311yescharacteristic
433C2×C32C2×#13511yescharacteristic
434C2×C32#57511yescharacteristic
435C3⋊D3—81no—
436C3×D3—22no—
437C3×D3—41no—
438C24—31no—
439#41—184no—
440C2×Q8—31no—
441C2×D4—91no—
442C2×D4—181no—
443C2×D4—181no—
444C2×D4—181no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—31no—
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—64no—
451C22×C4—61no—
452C22×C4—181no—
453C22×C4—181no—
454C22×C4C2×D3211yescharacteristic
455C2×C8—32no—
456C2×C8—64no—
457C2×C8C2×D3212yes—
458C4⋊C4—32no—
459C4⋊C4—31no—
460C4⋊C4—61no—
461C4⋊C4—61no—
462C4⋊C4—92no—
463C4⋊C4—91no—
464C4⋊C4—181no—
465C4⋊C4—181no—
466C22⋊C4—61no—
467C22⋊C4—181no—
468C22⋊C4—182no—
469C22⋊C4—182no—
470C22⋊C4—181no—
471C22⋊C4—181no—
472C22⋊C4—181no—
473C42—182no—
474C42—182no—
475C42—181no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—22no—
482C22×C3—32no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3—61no—
486C22×C3—61no—
487C22×C3—61no—
488C22×C3—61no—
489C22×C3—61no—
490C22×C3—124no—
491C22×C3#90412yes—
492C22×C3#91912yes—
493C22×C3C22×D1211yescharacteristic
494C22×C3C2×D3×D411yescharacteristic
495C2×D3—21no—
496C2×D3—21no—
497C2×D3—21no—
498C2×D3—21no—
499C2×D3—21no—
500C2×D3—44no—
501C2×D3—121no—
502C2×D3—121no—
503C2×D3—121no—
504C2×D3—121no—
505C2×D3—121no—
506C2×D3—121no—
507C2×D3—241no—
508C2×D3—241no—
509C2×D3—241no—
510C2×D3#88612yes—
511C3×C4—21no—
512C3×C4—21no—
513C3×C4—22no—
514C3×C4—32no—
515C3×C4—41no—
516C3×C4—61no—
517C3×C4—121no—
518C3×C4—121no—
519C3×C4—122no—
520C3×C4C2×#23712yes—
521C3×C4D3×#4112yes—
522Dic3—21no—
523Dic3—41no—
524Dic3—42no—
525Dic3—41no—
526Dic3—122no—
527Dic3—121no—
528Dic3—122no—
529Dic3—121no—
530Dic3—242no—
531Dic3—241no—
532Dic3#88612yes—
533C32#309111yescharacteristic, complemented, Sylow
534C23—31no—
535C23—31no—
536C23—62no—
537C23—62no—
538C23—121no—
539C23—181no—
540C23D3×D1211yescharacteristic
541Q8—62no—
542D4—182no—
543D4—362no—
544D4—362no—
545D4—362no—
546C2×C4—22no—
547C2×C4—31no—
548C2×C4—34no—
549C2×C4—31no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—61no—
556C2×C4—61no—
557C2×C4—122no—
558C2×C4—182no—
559C2×C4—181no—
560C2×C4—362no—
561C2×C4—362no—
562C2×C4D3×D1211yescharacteristic
563C2×C4C22×D3211yescharacteristic
564C8—22no—
565C8—62no—
566C2×C3—22no—
567C2×C3—22no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—42no—
572C2×C3—62no—
573C2×C3—121no—
574C2×C3C2×#88611yescharacteristic
575C2×C3D3×#12311yescharacteristic
576C2×C3C2×#90411yescharacteristic
577C2×C3#574811yescharacteristic
578C2×C3C2×#91911yescharacteristic
579C2×C3#577311yescharacteristic
580D3—22no—
581D3—41no—
582D3—241no—
583D3—241no—
584D3—481no—
585C22—21no—
586C22—21no—
587C22—32no—
588C22—61no—
589C22—61no—
590C22—61no—
591C22—61no—
592C22—61no—
593C22—124no—
594C22—361no—
595C22—361no—
596C22—361no—
597C22#6380812yes—
598C22C2×D3×D1211yescharacteristic
599C4—21no—
600C4—32no—
601C4—61no—
602C4—122no—
603C4—121no—
604C4—121no—
605C4—362no—
606C4—361no—
607C4D3×#23712yes—
608C3—21no—
609C3#7859111yescharacteristic, complemented
610C3#8146711yescharacteristic, complemented
611C2—22no—
612C2—62no—
613C2—121no—
614C2—721no—
615C2D3×#88611yescharacteristic
616C2C2×#6380811yescharacteristic
617C2#1059471211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10595005C2
hypercenterC22⋊C8D32
hypocenterC32#3091
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#63841C2semidirect
3. #10592435C2semidirect
4. C3×D3×C22⋊C8C2semidirect
5. C3×#4722C2semidirect
6. #10591126C2semidirect
7. #10591125C2semidirect
8. #10590710C2semidirect
9. #10590707C2semidirect
10. #10590705C2semidirect
11. #10590690C2semidirect
35. #63648C22semidirect
36. #63645C22semidirect
39. C3×#818C22semidirect
40. C3×#816C22semidirect
41. #63573C22semidirect
42. #63573C22semidirect
43. #63566C22semidirect
44. #63564C22semidirect
64. D3×C22⋊C8D3semidirect
66. #4722D3semidirect
166. #818C2×D3semidirect
170. #816C2×D3semidirect
533. C32#3091semidirect
609. C3#78591semidirect
610. C3#81467semidirect

Maximal subgroups

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

subgroupindex
#105950052
C2×#638412
#105924352
C3×D3×C22⋊C82
C3×#47222
#105911262
#105911252
#105907102
#105907072
#105907052
#105906902
#814673
#785913