Finite Group Databasebeta

← #11868825

Subgroups — #11868825

Order 1152.

891 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63918C211yesmaximal, characteristic, complemented
2Dic3×#235C211yesmaximal, characteristic
3#10592820C211yesmaximal, characteristic, complemented
4C3×#5133C211yesmaximal, characteristic
5C3×#5118C211yesmaximal, characteristic, complemented
6#10591130C211yesmaximal, characteristic, complemented
7#10591088C211yesmaximal, characteristic
8#10590804C212yesmaximal, complemented
9#10590803C212yesmaximal, complemented
10#10590762C212yesmaximal, complemented
11#10590757C212yesmaximal, complemented
12#79060—31nomaximal
13#78870—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C22×#627—21no—
16C2×C32×M16C2211yescharacteristic
17#64135C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22Dic3×#67—21no—
23Dic3×#67—21no—
24C2×Dic3⋊Dic3—21no—
25#63918—21no—
26#63918—21no—
27#63918C2212yes—
28#63918C2212yes—
29Dic3×D12C2211yescharacteristic
30Dic3×D12C2211yescharacteristic
31C4×D3×Dic3—21no—
32#63855—21no—
33Dic3×Dic6C2211yescharacteristic
34Dic3×Dic6C2211yescharacteristic
35#63645C2212yes—
36#63644C2212yes—
37C3×#821C2212yes—
38C3×#816C2212yes—
39C3×Dic3⋊C8C2212yes—
40C3×Dic3⋊C8C2212yes—
41#63575C2212yes—
42#63573C2212yes—
43#63566C2212yes—
44#63563C2212yes—
45Dic3×#41—31no—
46C2×#888—31no—
47C4×#235—31no—
48C2×#869—31no—
49C3×#423—31no—
50C3×#417—31no—
51#5232—31no—
52#5133—31no—
53#5133D311yescharacteristic
54#5121—31no—
55#5121—31no—
56#5121—31no—
57#5121—61no—
58#5118D311yescharacteristic, complemented
59#4964—31no—
60#4851—32no—
61#4850—32no—
62#4846—32no—
63#4842—32no—
64#4793—32no—
65#4791—32no—
66#4761—32no—
67#4759—32no—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3—21no—
70C2×C3×#67—21no—
71C22×C3×Dic3—21no—
72C22×C3×Dic3D411yescharacteristic
73C22×C3×Dic3D411yescharacteristic
74C3×#235—22no—
75C3×#235Q814yescomplemented
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×Dic6C2311yescharacteristic
79C2×#627—22no—
80C2×#627—22no—
81C2×#627—44no—
82C2×D3×Dic3—21no—
83C2×D3×Dic3—21no—
84C32×M16—22no—
85C2×C32×C8C2312yes—
86#3757—21no—
87C4⋊(C3⋊Dic3)—21no—
88C4⋊(C3⋊Dic3)C2312yes—
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91C4×C3⋊Dic3—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2312yes—
94C3×C4×Dic3D411yescharacteristic
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3C2311yescharacteristic
97C3×C4×Dic3C2311yescharacteristic
98C3×#208—22no—
99C2×C3×C3⋊C8C2312yes—
100Dic3⋊Dic3—21no—
101Dic3⋊Dic3—21no—
102Dic3⋊Dic3—22no—
103Dic3⋊Dic3—22no—
104(C2×D3)⋊Dic3—21no—
105(C2×D3)⋊Dic3—21no—
106Dic32—21no—
107Dic32—21no—
108#3079—91noSylow
109C2×C3×#41—31no—
110C2×#235C2×D311yescharacteristic
111C22×Dic6—61no—
112C22×Dic6—61no—
113C2×C3×M16—21no—
114C2×C3×M16—31no—
115C2×C3×M16C2×D311yescharacteristic
116C2×C3×M16C2×D311yescharacteristic
117C2×C3×C4⋊C4—31no—
118C2×C3×C42—31no—
119Q8×Dic3—31no—
120Q8×Dic3—31no—
121D4×Dic3—31no—
122D4×Dic3—31no—
123D4×Dic3—61no—
124D4×Dic3—61no—
125C4×#67—61no—
126C4×#67—61no—
127#926—31no—
128#926—31no—
129#926—61no—
130#926—61no—
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—31no—
133C2×C4⋊Dic3—61no—
134C2×C4⋊Dic3—61no—
135C2×C4⋊Dic3C2×D311yescharacteristic
136C2×Dic3⋊C4—61no—
137C2×C4×Dic3—61no—
138C2×C4×Dic3C2×D311yescharacteristic
139C2×#208C2×D311yescharacteristic
140#888—32no—
141#888—32no—
142#888—61no—
143#888—61no—
144C4×D12—31no—
145C4×D12—31no—
146#872—61no—
147C42×D3—61no—
148#869—32no—
149#869—32no—
150#869—61no—
151#869—61no—
152C4×Dic6—31no—
153C4×Dic6—31no—
154C3×C4⋊C8—32no—
155C3×C4⋊C8—32no—
156C3×#103—32no—
157C3×#102—32no—
158#835—32no—
159#832—32no—
160#821—32no—
161#821C2×D312yes—
162#818—32no—
163#818—32no—
164#818—32no—
165#818—62no—
166#817—32no—
167#817—32no—
168#817—32no—
169#817—62no—
170#816—32no—
171#816C2×D312yes—
172Dic3⋊C8C2×D312yes—
173Dic3⋊C8C2×D312yes—
174#808—32no—
175#807—32no—
176C23×C32C2×D411yescharacteristic
177C22×C3×D3—21no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×Q812yes—
180C2×C32×C4#4112yes—
181C2×C32×C4C2411yescharacteristic
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—42no—
186C3×#67—24no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—42no—
192C2×C3×Dic3C2×D411yescharacteristic
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C3×D12—21no—
197C3×D12C2×Q812yescomplemented
198C3×C4×D3—24no—
199C3×Dic6—21no—
200C3×Dic6C2×Q812yescomplemented
201#627—44no—
202#627—44no—
203D3×Dic3—42no—
204D3×Dic3—42no—
205C32×C8—22no—
206C3×C3⋊C8—22no—
207C2×C4⋊Q8—91no—
208C4×#41—91no—
209#477—92no—
210#476—92no—
211#475—92no—
212#474—92no—
213#428—91no—
214#428—91no—
215#423—31no—
216#417—31no—
217#417—91no—
218C3×#41—34no—
219C3×#41—62no—
220C2×C3×Q8—31no—
221C2×C3×D4—31no—
222C2×C3×D4—61no—
223C22×C3×C4—21no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—61no—
227C22×C3×C4—61no—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C2×#67—21no—
231C22×Dic3—21no—
232C22×Dic3—61no—
233C22×Dic3—61no—
234C22×Dic3—61no—
235C22×Dic3—61no—
236C22×Dic3—121no—
237C22×Dic3D1211yescharacteristic
238C22×Dic3D1211yescharacteristic
239#235—22no—
240#235Dic614yescomplemented
241C2×D12C22×D311yescharacteristic
242C2×C4×D3—21no—
243C2×C4×D3—61no—
244C2×C4×D3—61no—
245C2×Dic6—62no—
246C2×Dic6—62no—
247C2×Dic6—62no—
248C2×Dic6—62no—
249C2×Dic6—124no—
250C2×Dic6—124no—
251C2×Dic6C22×D311yescharacteristic
252C3×M16—24no—
253C3×M16—22no—
254C3×M16—22no—
255C3×M16—62no—
256C2×C3×C8—22no—
257C2×C3×C8—32no—
258C2×C3×C8C22×D312yes—
259C2×C3×C8C22×D312yes—
260C3×C4⋊C4—32no—
261C3×C4⋊C4—61no—
262C3×C42—31no—
263C3×C42—31no—
264C3×C42—31no—
265C3×C42—31no—
266#217—61no—
267#217—61no—
268#217—61no—
269#217—61no—
270#217—121no—
271(C2×D3)⋊C4—61no—
272(C2×D3)⋊C4—61no—
273C4⋊Dic3—21no—
274C4⋊Dic3—31no—
275C4⋊Dic3—31no—
276C4⋊Dic3—32no—
277C4⋊Dic3—31no—
278C4⋊Dic3—32no—
279C4⋊Dic3—31no—
280C4⋊Dic3—61no—
281C4⋊Dic3—62no—
282C4⋊Dic3—61no—
283C4⋊Dic3—62no—
284C4⋊Dic3—62no—
285C4⋊Dic3—61no—
286C4⋊Dic3—61no—
287C4⋊Dic3—61no—
288C4⋊Dic3—61no—
289C4⋊Dic3—121no—
290C4⋊Dic3C22×D312yes—
291Dic3⋊C4—61no—
292Dic3⋊C4—61no—
293Dic3⋊C4—62no—
294Dic3⋊C4—62no—
295C4×Dic3—61no—
296C4×Dic3—61no—
297C4×Dic3—61no—
298C4×Dic3—61no—
299C4×Dic3—61no—
300C4×Dic3—61no—
301C4×Dic3—121no—
302C4×Dic3D1211yescharacteristic
303C4×Dic3D1211yescharacteristic
304C4×Dic3C22×D311yescharacteristic
305C4×Dic3C22×D311yescharacteristic
306#208—22no—
307C2×C3⋊C8C22×D312yes—
308C22×C32—21no—
309C22×C32—21no—
310C22×C32C22⋊Q812yes—
311C22×C32C22×D411yescharacteristic
312C2×C3×D3—22no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C32×C4C22⋊Q812yes—
316C32×C4C22×Q811yescharacteristic
317C32×C4C2×#4111yescharacteristic
318C3⋊Dic3—41no—
319C3⋊Dic3—42no—
320C3⋊Dic3—41no—
321C3×Dic3—22no—
322C3×Dic3—21no—
323C3×Dic3—21no—
324C3×Dic3—42no—
325C3×Dic3AGL(1,ℤ/8)12yes—
326C3×Dic3#13712yes—
327C2×#41—31no—
328C22×Q8—181no—
329C2×M16—31no—
330C2×M16D3211yescharacteristic
331C4⋊Q8—92no—
332C4⋊Q8—92no—
333C4⋊Q8—181no—
334C4⋊Q8—181no—
335C4×Q8—91no—
336C4×Q8—91no—
337C4×D4—91no—
338C4×D4—91no—
339C4×D4—181no—
340C4×D4—181no—
341#117—91no—
342#117—181no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4—91no—
345C2×C4⋊C4—181no—
346C2×C42—31no—
347C2×C42—181no—
348#107—92no—
349#107—92no—
350#106—92no—
351#106—92no—
352C4⋊C8—32no—
353C4⋊C8—32no—
354#103—32no—
355#103—92no—
356#102—32no—
357#102—92no—
358C23×C3—21no—
359C23×C3—61no—
360C23×C3C2×D1211yescharacteristic
361C23×C3D3×D411yescharacteristic
362C22×D3—21no—
363C3×Q8—32no—
364C3×Q8—61no—
365C3×D4—32no—
366C3×D4—64no—
367C3×D4—61no—
368C2×C3×C4—21no—
369C2×C3×C4—22no—
370C2×C3×C4—21no—
371C2×C3×C4—22no—
372C2×C3×C4—31no—
373C2×C3×C4—31no—
374C2×C3×C4—31no—
375C2×C3×C4—31no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—61no—
379C2×C3×C4—64no—
380C2×C3×C4—62no—
381C2×C3×C4—122no—
382C2×C3×C4C2×Dic612yes—
383C2×C3×C4C2×D1211yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4#23712yes—
386C2×C3×C4#23712yes—
387C2×C3×C4D3×Q812yes—
388C2×C3×C4C23×D311yescharacteristic
389C2×C3×C4C23×D311yescharacteristic
390#67—24no—
391C2×Dic3—21no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—42no—
396C2×Dic3—61no—
397C2×Dic3—61no—
398C2×Dic3—62no—
399C2×Dic3—61no—
400C2×Dic3—61no—
401C2×Dic3—62no—
402C2×Dic3—121no—
403C2×Dic3—121no—
404C2×Dic3—122no—
405C2×Dic3—122no—
406C2×Dic3—122no—
407C2×Dic3—122no—
408C2×Dic3—122no—
409C2×Dic3—242no—
410C2×Dic3C2×D1211yescharacteristic
411C2×Dic3C2×D1211yescharacteristic
412C2×Dic3C2×D1211yescharacteristic
413C2×Dic3C2×D1211yescharacteristic
414D12—21no—
415D12C2×Dic612yescomplemented
416C4×D3—24no—
417C4×D3—122no—
418C4×D3—122no—
419Dic6—21no—
420Dic6—124no—
421Dic6—124no—
422Dic6—124no—
423Dic6—124no—
424Dic6C2×Dic612yescomplemented
425C3×C8—24no—
426C3×C8—22no—
427C3×C8—22no—
428C3×C8—62no—
429C3⋊C8—22no—
430C2×C32—22no—
431C2×C32C2×C22⋊Q811yescharacteristic
432C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
433C2×C32C2×#13711yescharacteristic
434C3×D3—42no—
435#41—34no—
436#41—62no—
437C2×Q8—31no—
438C2×Q8—182no—
439C2×Q8—182no—
440C2×Q8—364no—
441C2×D4—31no—
442C2×D4—61no—
443C22×C4—31no—
444C22×C4—31no—
445C22×C4—61no—
446C22×C4—61no—
447C22×C4—181no—
448C22×C4—181no—
449C22×C4—181no—
450C22×C4C2×D3211yescharacteristic
451M16—22no—
452M16—62no—
453C2×C8—32no—
454C2×C8C2×D3212yes—
455C4⋊C4—32no—
456C4⋊C4—61no—
457C4⋊C4—92no—
458C4⋊C4—91no—
459C4⋊C4—91no—
460C4⋊C4—182no—
461C4⋊C4—182no—
462C4⋊C4—181no—
463C4⋊C4—181no—
464C4⋊C4—181no—
465C22⋊C4—181no—
466C22⋊C4—181no—
467C22⋊C4—181no—
468C42—31no—
469C42—31no—
470C42—31no—
471C42—31no—
472C42—181no—
473C42—181no—
474C42—181no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—22no—
481C22×C3—41no—
482C22×C3—41no—
483C22×C3—62no—
484C22×C3—121no—
485C22×C3—121no—
486C22×C3#87812yes—
487C22×C3#89712yes—
488C22×C3C22×D1211yescharacteristic
489C22×C3C2×D3×D411yescharacteristic
490C2×D3—22no—
491C2×D3—41no—
492C2×D3—41no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—22no—
496C3×C4—32no—
497C3×C4—32no—
498C3×C4—62no—
499C3×C4—61no—
500C3×C4—61no—
501C3×C4—122no—
502C3×C4#87812yes—
503C3×C4#89712yes—
504C3×C4C22×Dic611yescharacteristic
505C3×C4C2×#23711yescharacteristic
506C3×C4C2×#23711yescharacteristic
507C3×C4C2×D3×Q811yescharacteristic
508Dic3—22no—
509Dic3—21no—
510Dic3—21no—
511Dic3—42no—
512Dic3—122no—
513Dic3—121no—
514Dic3—121no—
515Dic3—122no—
516Dic3—121no—
517Dic3—121no—
518Dic3—242no—
519Dic3—241no—
520Dic3—241no—
521Dic3#90812yes—
522Dic3#90912yes—
523C32#307911yescharacteristic, complemented, Sylow
524C23—61no—
525C23D3×D1211yescharacteristic
526Q8—32no—
527Q8—61no—
528Q8—364no—
529Q8—364no—
530D4—32no—
531D4—64no—
532D4—61no—
533C2×C4—31no—
534C2×C4—31no—
535C2×C4—31no—
536C2×C4—31no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—61no—
540C2×C4—64no—
541C2×C4—62no—
542C2×C4—122no—
543C2×C4—181no—
544C2×C4—181no—
545C2×C4—182no—
546C2×C4—362no—
547C2×C4—362no—
548C2×C4—362no—
549C2×C4D3×Dic612yes—
550C2×C4D3×D1211yescharacteristic
551C2×C4#380512yes—
552C2×C4C22×D3211yescharacteristic
553C8—22no—
554C8—62no—
555C2×C3—22no—
556C2×C3—22no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—42no—
561C2×C3—122no—
562C2×C3C2×#87811yescharacteristic
563C2×C3C2×#89711yescharacteristic
564C2×C3C2×#90811yescharacteristic
565C2×C3C2×#90911yescharacteristic
566C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
567C2×C3D3×#13711yescharacteristic
568D3—42no—
569C22—21no—
570C22—21no—
571C22—62no—
572C22—121no—
573C22—121no—
574C22#6389312yes—
575C22C2×D3×D1211yescharacteristic
576C4—32no—
577C4—32no—
578C4—62no—
579C4—61no—
580C4—61no—
581C4—122no—
582C4—362no—
583C4—361no—
584C4—361no—
585C4#6389312yes—
586C4C2×D3×Dic611yescharacteristic
587C4C2×#380511yescharacteristic
588C3—21no—
589C3#7887011yescharacteristic, complemented
590C3#7906011yescharacteristic, complemented
591C2—22no—
592C2—122no—
593C2D3×#90811yescharacteristic
594C2D3×#90911yescharacteristic
595C2C2×#6389311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
hypercenterC2×M16D32
hypocenterC32#3079
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#63918C2semidirect
3. #10592820C2semidirect
5. C3×#5118C2semidirect
6. #10591130C2semidirect
8. #10590804C2semidirect
9. #10590803C2semidirect
10. #10590762C2semidirect
11. #10590757C2semidirect
58. #5118D3semidirect
75. C3×#235Q8semidirect
197. C3×D12C2×Q8semidirect
200. C3×Dic6C2×Q8semidirect
240. #235Dic6semidirect
415. D12C2×Dic6semidirect
424. Dic6C2×Dic6semidirect
523. C32#3079semidirect
589. C3#78870semidirect
590. C3#79060semidirect

Maximal subgroups

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

subgroupindex
C2×#639182
Dic3×#2352
#105928202
C3×#51332
C3×#51182
#105911302
#105910882
#105908042
#105908032
#105907622
#105907572
#790603
#788703