Finite Group Databasebeta

← #11868807

Subgroups — #11868807

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#869C211yesmaximal, characteristic, complemented
2C4×#3795C211yesmaximal, characteristic
3#10592550C211yesmaximal, characteristic, complemented
4C3×#4846C211yesmaximal, characteristic, complemented
5C3×#4837C211yesmaximal, characteristic, complemented
6#10590805C212yesmaximal, complemented
7#10590757C212yesmaximal, complemented
8#10590683C212yesmaximal, complemented
9#10590670C212yesmaximal
10#10590307C211yesmaximal, characteristic, complemented
11#10590272C211yesmaximal, characteristic, complemented
12#80966—31nomaximal
13#79060—31nomaximal
14C2×#3795C2211yescharacteristic
15C2×D3×Dic6—21no—
16#64078C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C2×C3×ΓL(1,𝔽25)C2212yes—
19C3×C4×D12C2211yescharacteristic
20C3×C42×D3C2211yescharacteristic
21C3×#869C2211yescharacteristic
22#63918—21no—
23#63918C2212yes—
24C4×#625—21no—
25Dic3×D12C2211yescharacteristic
26D3×C4⋊Dic3—21no—
27D3×C4⋊Dic3C2212yes—
28#63879—21no—
29#63877—21no—
30C4×D3×Dic3—21no—
31#63866—21no—
32#63844C2211yescharacteristic
33#63841C2211yescharacteristic
34C32×C4⋊C8C2211yescharacteristic
35#63644C2212yes—
36#63643C2212yes—
37C3×#821C2212yes—
38C3×#818C2212yes—
39C3×Dic3⋊C8C2212yes—
40C3×C4⋊(C3⋊C8)C2211yescharacteristic
41#63575C2212yes—
42#63573C2212yes—
43#63567C2212yes—
44#63563C2212yes—
45D3×C4⋊Q8—31no—
46C4×#237—31no—
47C4×#235—31no—
48C2×#869—31no—
49C3×#474—31no—
50C3×#423—31no—
51#5133—32no—
52#5121—32no—
53#5094—31no—
54#5007—31no—
55#4881—32no—
56#4875—32no—
57#4851—31no—
58#4851—31no—
59#4851—31no—
60#4851—61no—
61#4850—32no—
62#4846—31no—
63#4846D311yescharacteristic, complemented
64#4842—32no—
65#4837D311yescharacteristic, complemented
66#4771—32no—
67#4761—32no—
68C2×#634—21no—
69C2×#634C2311yescharacteristic
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×C4×D3D411yescharacteristic
73C2×C3×C4×D3D411yescharacteristic
74C2×C3×C4×D3C2311yescharacteristic
75C2×C3×Dic6—21no—
76C2×#627—22no—
77C2×#625—21no—
78C2×D3×Dic3—21no—
79C2×D3×Dic3—22no—
80C2×D3×Dic3—21no—
81#3795—22no—
82#3795Q814yescomplemented
83D3×Dic6—44no—
84C2×C32×C8C2312yes—
85C32×C42C2311yescharacteristic
86C4⋊(C3⋊Dic3)—21no—
87C4⋊(C3⋊Dic3)C2312yes—
88C4⋊(C3⋊Dic3)C2311yescharacteristic
89#3750—21no—
90C4×C3⋊Dic3—21no—
91C3×(C2×D3)⋊C4—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2312yes—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3D411yescharacteristic
97C3×C4×Dic3C2311yescharacteristic
98C2×C3×C3⋊C8C2312yes—
99C3×ΓL(1,𝔽25)—24no—
100#3724—21no—
101Dic3⋊Dic3—22no—
102Dic3⋊Dic3—22no—
103(C2×D3)⋊Dic3—21no—
104(C2×D3)⋊Dic3—21no—
105Dic32—21no—
106Dic32—21no—
107#3079—91noSylow
108C2×D3×Q8—61no—
109C2×#237—31no—
110C2×#235—31no—
111C22×Dic6—61no—
112C2×C3×M16—32no—
113C3×C4⋊Q8—31no—
114C3×C4×D4—31no—
115C2×C3×C42—31no—
116#944—61no—
117D4×Dic3—31no—
118C4×#67—61no—
119C4×#67—61no—
120C4×#67—61no—
121#926—31no—
122C2×C4⋊Dic3—32no—
123C2×C4⋊Dic3—61no—
124C2×C4×Dic3—61no—
125C2×ΓL(1,𝔽25)C2×D312yes—
126#892—31no—
127D3×C4⋊C4—32no—
128D3×C4⋊C4—61no—
129#888—32no—
130#888—61no—
131#887—31no—
132#67⋊C4—61no—
133#877—61no—
134C4×D12—31no—
135C4×D12C2×D311yescharacteristic
136#872—61no—
137C42×D3—61no—
138C42×D3C2×D311yescharacteristic
139#869—31no—
140#869—31no—
141#869—32no—
142#869—61no—
143#869—61no—
144#869—61no—
145#869C2×D311yescharacteristic
146C4×Dic6—31no—
147C4×Dic6—31no—
148C4×Dic6—31no—
149C4×Dic6—61no—
150C3×#107—32no—
151C3×C4⋊C8—21no—
152C3×C4⋊C8—32no—
153C3×C4⋊C8—31no—
154C3×C4⋊C8C2×D311yescharacteristic
155C3×C4⋊C8C2×D311yescharacteristic
156C3×#102—32no—
157#832—32no—
158#821—32no—
159#821C2×D312yes—
160#818—32no—
161#818C2×D312yes—
162#817—32no—
163#817—32no—
164#817—32no—
165#817—62no—
166#816—32no—
167#816—32no—
168#816—32no—
169#816—62no—
170Dic3⋊C8C2×D312yes—
171#810—32no—
172#808—32no—
173#807—32no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic
175C22×C3×D3—21no—
176C22×C3×D3C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2411yescharacteristic
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—22no—
183#634—21no—
184#634—42no—
185#634C2×Q812yescomplemented
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3C2×D411yescharacteristic
189C2×C3×Dic3C2×D411yescharacteristic
190C2×C3×Dic3C2×D411yescharacteristic
191C3×D12—21no—
192C3×D12C2×Q812yescomplemented
193C3×C4×D3—22no—
194C3×C4×D3—22no—
195C3×C4×D3—42no—
196C3×C4×D3C2×Q812yes—
197C3×C4×D3#4112yes—
198C3×Dic6—42no—
199#627—44no—
200#625—24no—
201D3×Dic3—24no—
202D3×Dic3—44no—
203D3×Dic3—42no—
204C32×C8—22no—
205C3×C3⋊C8—22no—
206C2×C4⋊Q8—91no—
207C4×#41—91no—
208#477—92no—
209#476—92no—
210#475—91no—
211#475—91no—
212#474—31no—
213#474—91no—
214#428—92no—
215#423—31no—
216#417—92no—
217C2×C3×Q8—61no—
218C2×C3×D4—31no—
219C22×C3×C4—31no—
220C22×C3×C4—31no—
221C22×C3×C4—31no—
222C22×C3×C4—61no—
223C2×#67—61no—
224C2×#67—61no—
225C22×Dic3—62no—
226C22×Dic3—61no—
227C22×Dic3—61no—
228D3×Q8—124no—
229#237—34no—
230#237—62no—
231#235—34no—
232#235—62no—
233C2×D12C22×D311yescharacteristic
234C2×C4×D3—21no—
235C2×C4×D3—61no—
236C2×C4×D3—61no—
237C2×C4×D3—62no—
238C2×C4×D3D1211yescharacteristic
239C2×C4×D3D1211yescharacteristic
240C2×C4×D3C22×D311yescharacteristic
241C2×Dic6—21no—
242C2×Dic6—31no—
243C2×Dic6—31no—
244C2×Dic6—61no—
245C2×Dic6—62no—
246C2×Dic6—61no—
247C2×Dic6—61no—
248C2×Dic6—62no—
249C2×Dic6—121no—
250C2×Dic6—124no—
251C3×M16—64no—
252C2×C3×C8—22no—
253C2×C3×C8—32no—
254C2×C3×C8C22×D312yes—
255C2×C3×C8C22×D312yes—
256C3×C4⋊C4—31no—
257C3×C4⋊C4—32no—
258C3×C4⋊C4—61no—
259C3×C22⋊C4—61no—
260C3×C42—21no—
261C3×C42—31no—
262C3×C42—31no—
263C3×C42—31no—
264C3×C42C22×D311yescharacteristic
265C3×C42C22×D311yescharacteristic
266#217—61no—
267#217—61no—
268(C2×D3)⋊C4—21no—
269(C2×D3)⋊C4—61no—
270(C2×D3)⋊C4—61no—
271C4⋊Dic3—21no—
272C4⋊Dic3—32no—
273C4⋊Dic3—31no—
274C4⋊Dic3—32no—
275C4⋊Dic3—31no—
276C4⋊Dic3—62no—
277C4⋊Dic3—61no—
278C4⋊Dic3—62no—
279C4⋊Dic3—62no—
280C4⋊Dic3—61no—
281C4⋊Dic3—61no—
282C4⋊Dic3—121no—
283C4⋊Dic3C22×D312yes—
284C4⋊Dic3C22×D311yescharacteristic
285Dic3⋊C4—61no—
286Dic3⋊C4—61no—
287Dic3⋊C4—61no—
288Dic3⋊C4—61no—
289Dic3⋊C4—62no—
290Dic3⋊C4—62no—
291Dic3⋊C4—121no—
292C4×Dic3—61no—
293C4×Dic3—61no—
294C4×Dic3—61no—
295C4×Dic3—61no—
296C4×Dic3—61no—
297C4×Dic3—61no—
298C4×Dic3—121no—
299C4×Dic3D1211yescharacteristic
300C4×Dic3D1211yescharacteristic
301C4×Dic3C22×D311yescharacteristic
302C2×C3⋊C8C22×D312yes—
303ΓL(1,𝔽25)—24no—
304C22×C32C22×D411yescharacteristic
305C2×C3×D3—21no—
306C2×C3×D3—21no—
307C2×C3×D3—22no—
308C2×C3×D3—41no—
309C2×C3×D3—41no—
310C2×C3×D3C22⋊Q812yes—
311C32×C4—21no—
312C32×C4AGL(1,ℤ/8)12yes—
313C32×C4C22×Q811yescharacteristic
314C32×C4C2×#4111yescharacteristic
315C3⋊Dic3—22no—
316C3⋊Dic3—42no—
317C3⋊Dic3—41no—
318C3×Dic3—21no—
319C3×Dic3—42no—
320C3×Dic3—41no—
321C3×Dic3C22⋊Q812yes—
322C3×Dic3#13712yes—
323C2×#41—91no—
324C22×Q8—181no—
325C2×M16—32no—
326C4⋊Q8—31no—
327C4⋊Q8—92no—
328C4⋊Q8—91no—
329C4⋊Q8—181no—
330C4⋊Q8—181no—
331C4×Q8—91no—
332C4×Q8—91no—
333C4×D4—31no—
334C4×D4—91no—
335C4×D4—181no—
336C4×D4—181no—
337#117—91no—
338#117—181no—
339C2×C4⋊C4—92no—
340C2×C4⋊C4—181no—
341C2×C42—31no—
342C2×C42—181no—
343#107—32no—
344#107—92no—
345#106—92no—
346#106—92no—
347C4⋊C8—32no—
348C4⋊C8—31no—
349C4⋊C8D3211yescharacteristic
350#103—92no—
351#103—92no—
352#102—32no—
353#102—92no—
354C23×C3—31no—
355C23×C3—61no—
356C22×D3—21no—
357C22×D3C2×D1211yescharacteristic
358C3×Q8—122no—
359C3×D4—32no—
360C3×D4—61no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—31no—
365C2×C3×C4—31no—
366C2×C3×C4—32no—
367C2×C3×C4—32no—
368C2×C3×C4—31no—
369C2×C3×C4—62no—
370C2×C3×C4—62no—
371C2×C3×C4—61no—
372C2×C3×C4—62no—
373C2×C3×C4—122no—
374C2×C3×C4C2×D1211yescharacteristic
375C2×C3×C4C2×D1211yescharacteristic
376C2×C3×C4D3×D411yescharacteristic
377C2×C3×C4D3×D411yescharacteristic
378C2×C3×C4C23×D311yescharacteristic
379C2×C3×C4C23×D311yescharacteristic
380#67—64no—
381#67—64no—
382C2×Dic3—21no—
383C2×Dic3—22no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386C2×Dic3—64no—
387C2×Dic3—61no—
388C2×Dic3—62no—
389C2×Dic3—61no—
390C2×Dic3—62no—
391C2×Dic3—121no—
392C2×Dic3—121no—
393C2×Dic3—122no—
394C2×Dic3—124no—
395C2×Dic3—122no—
396C2×Dic3C2×D1211yescharacteristic
397C2×Dic3C2×D1211yescharacteristic
398C2×Dic3C2×D1211yescharacteristic
399D12—21no—
400D12D3×Q812yescomplemented
401C4×D3—22no—
402C4×D3—22no—
403C4×D3—42no—
404C4×D3—64no—
405C4×D3—122no—
406C4×D3—124no—
407C4×D3#23712yes—
408C4×D3D3×Q812yes—
409Dic6—32no—
410Dic6—32no—
411Dic6—42no—
412Dic6—62no—
413Dic6—61no—
414Dic6—61no—
415Dic6—121no—
416Dic6—124no—
417Dic6—124no—
418Dic6—122no—
419Dic6—122no—
420Dic6—242no—
421C3×C8—22no—
422C3×C8—22no—
423C3×C8—42no—
424C3×C8—62no—
425C3⋊C8—22no—
426C2×C32C2×C22⋊Q811yescharacteristic
427C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
428C2×C32C2×#13711yescharacteristic
429C3×D3—22no—
430C3×D3—42no—
431#41—94no—
432#41—182no—
433C2×Q8—61no—
434C2×Q8—91no—
435C2×Q8—182no—
436C2×Q8—181no—
437C2×Q8—364no—
438C2×D4—31no—
439C2×D4—181no—
440C22×C4—31no—
441C22×C4—31no—
442C22×C4—31no—
443C22×C4—61no—
444C22×C4—181no—
445C22×C4—181no—
446C22×C4—182no—
447M16—64no—
448C2×C8—32no—
449C2×C8C2×D3212yes—
450C4⋊C4—32no—
451C4⋊C4—31no—
452C4⋊C4—61no—
453C4⋊C4—92no—
454C4⋊C4—91no—
455C4⋊C4—182no—
456C4⋊C4—182no—
457C4⋊C4—181no—
458C4⋊C4—181no—
459C4⋊C4—181no—
460C22⋊C4—61no—
461C22⋊C4—181no—
462C22⋊C4—181no—
463C42—31no—
464C42—31no—
465C42—31no—
466C42—181no—
467C42—181no—
468C42—181no—
469C42C2×D3211yescharacteristic
470C22×C3—21no—
471C22×C3—32no—
472C22×C3—61no—
473C22×C3—61no—
474C22×C3—62no—
475C22×C3—121no—
476C22×C3—121no—
477C22×C3C22×D1211yescharacteristic
478C22×C3C2×D3×D411yescharacteristic
479C2×D3—21no—
480C2×D3—21no—
481C2×D3—22no—
482C2×D3—41no—
483C2×D3—41no—
484C2×D3#89712yes—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—22no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—32no—
491C3×C4—32no—
492C3×C4—41no—
493C3×C4—61no—
494C3×C4—122no—
495C3×C4—121no—
496C3×C4#90812yes—
497C3×C4#91112yes—
498C3×C4C2×#23711yescharacteristic
499C3×C4C2×D3×Q811yescharacteristic
500C3×C4C2×D3×Q811yescharacteristic
501C3×C4D3×#4111yescharacteristic
502Dic3—21no—
503Dic3—42no—
504Dic3—41no—
505Dic3—62no—
506Dic3—62no—
507Dic3—122no—
508Dic3—122no—
509Dic3—121no—
510Dic3—122no—
511Dic3—121no—
512Dic3—242no—
513Dic3—241no—
514Dic3#89712yes—
515Dic3#90912yes—
516C32#307911yescharacteristic, complemented, Sylow
517C23—31no—
518C23—61no—
519Q8—92no—
520Q8—122no—
521Q8—181no—
522Q8—364no—
523Q8—362no—
524D4—32no—
525D4—61no—
526D4—184no—
527C2×C4—31no—
528C2×C4—31no—
529C2×C4—32no—
530C2×C4—32no—
531C2×C4—31no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—61no—
535C2×C4—62no—
536C2×C4—122no—
537C2×C4—184no—
538C2×C4—181no—
539C2×C4—181no—
540C2×C4—182no—
541C2×C4—362no—
542C2×C4—364no—
543C2×C4D3×D1211yescharacteristic
544C2×C4D3×D1211yescharacteristic
545C2×C4C22×D3211yescharacteristic
546C8—22no—
547C8—62no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—62no—
552C2×C3—122no—
553C2×C3C2×#89711yescharacteristic
554C2×C3D3×C22⋊Q811yescharacteristic
555C2×C3C2×#90811yescharacteristic
556C2×C3C2×#90911yescharacteristic
557C2×C3C2×#91111yescharacteristic
558C2×C3D3×#13711yescharacteristic
559D3—22no—
560D3—42no—
561C22—32no—
562C22—61no—
563C22—61no—
564C22—62no—
565C22—121no—
566C22—121no—
567C22C2×D3×D1211yescharacteristic
568C4—21no—
569C4—32no—
570C4—32no—
571C4—61no—
572C4—121no—
573C4—122no—
574C4—182no—
575C4—362no—
576C4—361no—
577C4#6379512yes—
578C4D3×#23711yescharacteristic
579C4D32×Q811yescharacteristic
580C3—21no—
581C3#7906011yescharacteristic, complemented
582C3#8096611yescharacteristic, complemented
583C2—62no—
584C2—122no—
585C2D3×#89711yescharacteristic
586C2C2×#6379511yescharacteristic
587C2D3×#90911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#3795C22
hypercenterC4⋊C8D32
hypocenterC32#3079
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. D3×#869C2semidirect
3. #10592550C2semidirect
4. C3×#4846C2semidirect
5. C3×#4837C2semidirect
6. #10590805C2semidirect
7. #10590757C2semidirect
8. #10590683C2semidirect
10. #10590307C2semidirect
11. #10590272C2semidirect
63. #4846D3semidirect
65. #4837D3semidirect
82. #3795Q8semidirect
185. #634C2×Q8semidirect
192. C3×D12C2×Q8semidirect
400. D12D3×Q8semidirect
516. C32#3079semidirect
581. C3#79060semidirect
582. C3#80966semidirect

Maximal subgroups

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

subgroupindex
D3×#8692
C4×#37952
#105925502
C3×#48462
C3×#48372
#105908052
#105907572
#105906832
#105906702
#105903072
#105902722
#809663
#790603