Finite Group Databasebeta

← #11861237

Subgroups — #11861237

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 641 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594706C212yesmaximal, complemented
2D3×#904C211yesmaximal, characteristic
3#10592594C211yesmaximal, characteristic, complemented
4C3×#4895C211yesmaximal, characteristic, complemented
5C3×D3×#108C211yesmaximal, characteristic, complemented
6#10591005C212yesmaximal, complemented
7#10590994C212yesmaximal, complemented
8#10590978C212yesmaximal, complemented
9#10590919C211yesmaximal, characteristic, complemented
10#10590917C211yesmaximal, characteristic, complemented
11#10590692C211yesmaximal, characteristic, complemented
12#79890—31nomaximal
13#79249—31nomaximal
14D3×#235C2212yes—
15#64116C2212yescomplemented
16#64113C2211yescharacteristic
17C3×#907C2212yescomplemented
18C3×D3×M16C2212yes—
19C3×#904C2211yescharacteristic
20C2×C3×D3×C8C2211yescharacteristic
21#63855C2211yescharacteristic
22#63829C2212yes—
23C2×#3711C2211yescharacteristic
24#63817C2212yescomplemented
25#63815C2212yescomplemented
26#63808C411yescharacteristic, complemented
27#63807C411yescharacteristic, complemented
28#63806C412yescomplemented
29#63804—22no—
30#63803—22no—
31D3×Dic12C411yescharacteristic, complemented
32D3×D24C411yescharacteristic, complemented
33D3×#204C412yescomplemented
34#63791—22no—
35D3×ΓL(1,𝔽25)—22no—
36C32×#108C2211yescharacteristic, complemented
37#63652C2212yescomplemented
38C8×C3⋊Dic3C2211yescharacteristic, complemented
39C3×#825C2212yescomplemented
40C3×#822C2212yescomplemented
41C3×#819C2211yescharacteristic, complemented
42C3×C8×Dic3C2211yescharacteristic, complemented
43#63570C2212yescomplemented
44#63568C2212yescomplemented
45#63555C2211yescharacteristic, complemented
46#63554C2211yescharacteristic, complemented
47D3×#135—31no—
48#5750—32no—
49#5745—32no—
50C2×#904—31no—
51C3×#443—31no—
52C2×C3×#108—31no—
53#5196—31no—
54#5145—32no—
55#5139—32no—
56#5101—31no—
57#4895—31no—
58#4895—31no—
59#4895—31no—
60#4895—31no—
61#4895—61no—
62#4895D311yescharacteristic, complemented
63#4894—32no—
64#4894—32no—
65D3×#108D311yescharacteristic, complemented
66#4823—32no—
67#4821—32no—
68#4700—31no—
69#4689—31no—
70#3828C2312yes—
71C3×#235C2312yes—
72C2×C3×C4×D3C2311yescharacteristic
73D3×#67—22no—
74#3804—22no—
75D3×D12C2×C412yes—
76C4×D32—22no—
77#3799C2×C412yes—
78#3798—22no—
79#3795C2×C412yes—
80D3×Dic6C2×C412yes—
81C32×M16C2312yes—
82C2×C32×C8C2311yescharacteristic
83C4×C3⋊Dic3C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85#3746C2×C411yescharacteristic
86#3745C2×C411yescharacteristic
87#3744C2×C412yes—
88#3743—22no—
89C8×C3⋊D3—22no—
90C3×C4×Dic3C2311yescharacteristic
91C3×#208C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94C3×Dic12C2×C411yescharacteristic
95C3×D24C2×C411yescharacteristic
96C3×#204C2×C412yes—
97C3×ΓL(1,𝔽25)—22no—
98C3×ΓL(1,𝔽25)—22no—
99C3×D3×C8—22no—
100C3×D3×C8—22no—
101C3×D3×C8C2×C411yescharacteristic
102C3×D3×C8C2×C411yescharacteristic
103C3×D3×C8C2×C411yescharacteristic
104C3×D3×C8C2×C411yescharacteristic
105Dic3⋊Dic3—21no—
106(C2×D3)⋊Dic3—21no—
107#3719C2×C412yes—
108#3717C2×C412yes—
109#3716C2×C412yes—
110#3714C2×C412yes—
111#3712—22no—
112#3711—22no—
113#3711D411yescharacteristic
114#3711D411yescharacteristic
115#3711D411yescharacteristic
116#3711D411yescharacteristic
117#3710—22no—
118D3×C3⋊C8—22no—
119#2957—91noSylow
120D3×#41—32no—
121C2×#235—32no—
122C3×#135—31no—
123C3×#131—32no—
124C2×C3×M16—32no—
125C22×C3×C8—31no—
126#950—32no—
127#948—32no—
128#926—31no—
129C2×#208—31no—
130#919—31no—
131D3×Q16—31no—
132#916—32no—
133D3×SD16—32no—
134#912—31no—
135D3×D8—31no—
136#907—32no—
137#907—32no—
138#907—32no—
139#907—32no—
140#907—62no—
141#907—62no—
142#907C2×D312yescomplemented
143D3×M16—62no—
144D3×M16—62no—
145D3×M16—62no—
146D3×M16C2×D312yes—
147C2×Dic12—31no—
148#904—32no—
149#904—31no—
150#904—31no—
151#904—31no—
152#904—31no—
153#904—32no—
154#904—61no—
155#904C2×D311yescharacteristic
156C2×D24—31no—
157C2×#204—32no—
158#901—32no—
159#901—62no—
160#901—62no—
161#901—62no—
162C2×ΓL(1,𝔽25)—31no—
163C2×ΓL(1,𝔽25)—62no—
164C2×D3×C8C2×D311yescharacteristic
165#872—31no—
166C3×#108—21no—
167C3×#108—32no—
168C3×#108—31no—
169C3×#108C2×D311yescharacteristic, complemented
170C3×#108C2×D311yescharacteristic, complemented
171C3×#104—32no—
172C3×C4×C8—31no—
173#837—32no—
174#825—32no—
175#825—32no—
176#825—32no—
177#825—32no—
178#825—62no—
179#825C2×D312yescomplemented
180#822C2×D312yescomplemented
181#819C2×D311yescharacteristic, complemented
182#815—31no—
183#815—31no—
184#815—31no—
185C8×Dic3—31no—
186C8×Dic3—31no—
187C8×Dic3—61no—
188C8×Dic3C2×D311yescharacteristic, complemented
189#805—32no—
190#803—31no—
191C22×C3×D3#4111yescharacteristic
192C2×D32—22no—
193C2×C32×C4C2411yescharacteristic
194#638—22no—
195C2×C3⋊Dic3—21no—
196C4⋊(C3⋊D3)C22×C412yes—
197C4×C3⋊D3—22no—
198#634C22×C412yes—
199C3×#67—22no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3#4111yescharacteristic
202C3×D12C22×C412yes—
203C3×C4×D3—22no—
204C3×C4×D3C22×C411yescharacteristic
205C3×C4×D3C22×C411yescharacteristic
206C3×C4×D3C2×D411yescharacteristic
207C3×C4×D3C2×D411yescharacteristic
208C3×Dic6C22×C412yes—
209#627—22no—
210#626—22no—
211#626—22no—
212#625—22no—
213#624—22no—
214D3×Dic3—22no—
215D3×Dic3—22no—
216C32×C8—22no—
217C32×C8C22×C411yescharacteristic
218C32×C8C22×C411yescharacteristic
219C3⋊(C3⋊C8)C2×D411yescharacteristic
220C3⋊(C3⋊C8)C2×D411yescharacteristic
221C3×C3⋊C8—22no—
222C3×C3⋊C8C22×C411yescharacteristic
223C3×C3⋊C8C22×C411yescharacteristic
224C3×C3⋊C8C2×D411yescharacteristic
225C3×C3⋊C8C2×D411yescharacteristic
226C2×#135—91no—
227#568—92no—
228#444—92no—
229#444—92no—
230#443—31no—
231#443—91no—
232#443—91no—
233#443—91no—
234C2×#108—31no—
235#421—92no—
236#405—91no—
237C3×#41—32no—
238C22×C3×C4—31no—
239C2×#67—62no—
240#239—32no—
241D3×Q8—32no—
242#237—32no—
243#237—62no—
244D3×D4—32no—
245D3×D4—62no—
246#235—32no—
247#235—32no—
248#235—32no—
249#235—32no—
250#235—62no—
251#235—62no—
252#235—62no—
253#235—62no—
254#235C22×D312yes—
255C2×D12—32no—
256C2×C4×D3—62no—
257C2×C4×D3—62no—
258C2×C4×D3C22×D311yescharacteristic
259C2×Dic6—32no—
260C3×Q16—31no—
261C3×SD16—32no—
262C3×D8—31no—
263C3×M16—22no—
264C3×M16—32no—
265C3×M16—62no—
266C3×M16—62no—
267C3×M16C22×D312yes—
268C3×M16C22×D312yes—
269C2×C3×C8—21no—
270C2×C3×C8—31no—
271C2×C3×C8—31no—
272C2×C3×C8—31no—
273C2×C3×C8—31no—
274C2×C3×C8—31no—
275C2×C3×C8—31no—
276C2×C3×C8—62no—
277C2×C3×C8—62no—
278C2×C3×C8C22×D311yescharacteristic
279C2×C3×C8C22×D311yescharacteristic
280C3×C42—31no—
281#217—61no—
282#216—32no—
283#215—32no—
284#214—32no—
285#213—32no—
286(C2×D3)⋊C4—61no—
287C4⋊Dic3—61no—
288Dic3⋊C4—61no—
289C4×Dic3—31no—
290C4×Dic3—31no—
291C4×Dic3—61no—
292C4×Dic3C22×D311yescharacteristic
293#208—31no—
294#208—31no—
295#208—31no—
296#208—31no—
297#208—62no—
298#208C22×D312yes—
299C2×C3⋊C8—31no—
300C2×C3⋊C8—31no—
301C2×C3⋊C8—61no—
302C2×C3⋊C8—62no—
303C2×C3⋊C8C22×D311yescharacteristic
304C2×C3⋊C8C22×D311yescharacteristic
305Dic12—32no—
306Dic12—31no—
307Dic12—31no—
308Dic12—61no—
309Dic12C4×D311yescharacteristic
310D24—32no—
311D24—31no—
312D24—31no—
313D24—61no—
314D24C4×D311yescharacteristic
315#204—32no—
316#204—32no—
317#204—32no—
318#204—32no—
319#204—62no—
320#204C4×D312yes—
321ΓL(1,𝔽25)—22no—
322ΓL(1,𝔽25)—22no—
323ΓL(1,𝔽25)—31no—
324ΓL(1,𝔽25)—31no—
325ΓL(1,𝔽25)—31no—
326ΓL(1,𝔽25)—31no—
327ΓL(1,𝔽25)—62no—
328ΓL(1,𝔽25)—62no—
329ΓL(1,𝔽25)—62no—
330ΓL(1,𝔽25)—62no—
331ΓL(1,𝔽25)—62no—
332ΓL(1,𝔽25)—122no—
333D3×C8—22no—
334D3×C8—22no—
335D3×C8—62no—
336D3×C8—62no—
337D3×C8—62no—
338D3×C8—62no—
339D3×C8—62no—
340D3×C8—122no—
341D3×C8C4×D311yescharacteristic
342D3×C8C4×D311yescharacteristic
343D3×C8C4×D311yescharacteristic
344D3×C8C4×D311yescharacteristic
345C22×C32C2×#4111yescharacteristic
346C2×C3⋊D3—22no—
347C2×C3×D3—22no—
348C2×C3×D3—41no—
349C2×C3×D3C4×D411yescharacteristic
350C2×C3×D3C4×D411yescharacteristic
351D32—82no—
352C32×C4C23×C411yescharacteristic
353C32×C4C22×D411yescharacteristic
354C3⋊Dic3—22no—
355C3⋊Dic3—41no—
356C3×Dic3—22no—
357C3×Dic3—41no—
358C3×Dic3C4×D411yescharacteristic
359C3×Dic3C4×D411yescharacteristic
360C2×#41—92no—
361#135—31no—
362#135—91no—
363#135—92no—
364#135—91no—
365#135—92no—
366#135—91no—
367C2×Q16—91no—
368C2×SD16—92no—
369C2×D8—91no—
370#131—32no—
371#131—92no—
372#131—92no—
373#131—92no—
374#131—182no—
375#131—182no—
376C2×M16—32no—
377C2×M16—91no—
378C2×M16—182no—
379C2×M16—182no—
380C22×C8—31no—
381#117—91no—
382#108—32no—
383#108—31no—
384#108D3211yescharacteristic, complemented
385#104—32no—
386#104—92no—
387#104—92no—
388#104—92no—
389#97—91no—
390#97—91no—
391C4×C8—31no—
392C4×C8—91no—
393C23×C3—31no—
394C22×D3—62no—
395C22×D3—62no—
396C22×D3#23911yescharacteristic
397C3×Q8—32no—
398C3×D4—32no—
399C3×D4—62no—
400C2×C3×C4—21no—
401C2×C3×C4—31no—
402C2×C3×C4—31no—
403C2×C3×C4—31no—
404C2×C3×C4—31no—
405C2×C3×C4—31no—
406C2×C3×C4—62no—
407C2×C3×C4—61no—
408C2×C3×C4C23×D311yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410#67—22no—
411#67—62no—
412#67—62no—
413#67—62no—
414#67—62no—
415#67—62no—
416#67—62no—
417#67—122no—
418C2×Dic3—21no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—61no—
422C2×Dic3—61no—
423C2×Dic3—121no—
424C2×Dic3#23911yescharacteristic
425D12—32no—
426D12—32no—
427D12—62no—
428D12—62no—
429D12—62no—
430D12C2×C4×D312yes—
431C4×D3—22no—
432C4×D3—62no—
433C4×D3—62no—
434C4×D3—62no—
435C4×D3—62no—
436C4×D3—62no—
437C4×D3—62no—
438C4×D3—122no—
439C4×D3C2×C4×D311yescharacteristic
440C4×D3C2×C4×D311yescharacteristic
441C4×D3D3×D411yescharacteristic
442C4×D3D3×D411yescharacteristic
443Dic6—32no—
444Dic6—32no—
445Dic6—62no—
446Dic6—62no—
447Dic6—62no—
448Dic6C2×C4×D312yes—
449C3×C8—22no—
450C3×C8—22no—
451C3×C8—21no—
452C3×C8—21no—
453C3×C8—31no—
454C3×C8—31no—
455C3×C8—31no—
456C3×C8—31no—
457C3×C8—42no—
458C3×C8—62no—
459C3×C8C2×C4×D311yescharacteristic
460C3×C8C2×C4×D311yescharacteristic
461C3×C8C2×C4×D311yescharacteristic
462C3×C8C2×C4×D311yescharacteristic
463C3⋊C8—22no—
464C3⋊C8—31no—
465C3⋊C8—31no—
466C3⋊C8—31no—
467C3⋊C8—31no—
468C3⋊C8—61no—
469C3⋊C8—61no—
470C3⋊C8C2×C4×D311yescharacteristic
471C3⋊C8C2×C4×D311yescharacteristic
472C3⋊C8D3×D411yescharacteristic
473C3⋊C8D3×D411yescharacteristic
474C2×C32—21no—
475C2×C32C2×C4×D411yescharacteristic
476C3⋊D3—42no—
477C3×D3—21no—
478C3×D3—21no—
479C3×D3—42no—
480#41—32no—
481#41—92no—
482#41—92no—
483#41—92no—
484#41—182no—
485#41—182no—
486C2×Q8—92no—
487C2×D4—92no—
488C2×D4—182no—
489C22×C4—31no—
490C22×C4—182no—
491Q16—31no—
492Q16—92no—
493Q16—91no—
494SD16—32no—
495SD16—92no—
496SD16—92no—
497SD16—92no—
498D8—31no—
499D8—92no—
500D8—91no—
501M16—32no—
502M16—62no—
503M16—62no—
504M16—91no—
505M16—91no—
506M16—91no—
507M16—91no—
508M16—182no—
509M16—182no—
510M16—182no—
511M16C2×D3212yes—
512C2×C8—31no—
513C2×C8—31no—
514C2×C8—31no—
515C2×C8—31no—
516C2×C8—31no—
517C2×C8—31no—
518C2×C8—62no—
519C2×C8—62no—
520C2×C8—91no—
521C2×C8—182no—
522C2×C8—182no—
523C2×C8—182no—
524C2×C8C2×D3211yescharacteristic
525C4⋊C4—181no—
526C22⋊C4—181no—
527C42—31no—
528C42—91no—
529C22×C3—21no—
530C22×C3—31no—
531C22×C3—31no—
532C22×C3—62no—
533C22×C3—121no—
534C22×C3C2×#23911yescharacteristic
535C22×C3D3×#4111yescharacteristic
536C2×D3—22no—
537C2×D3—41no—
538C2×D3—62no—
539C2×D3—62no—
540C2×D3—122no—
541C2×D3—242no—
542C2×D3—242no—
543C2×D3#89311yescharacteristic
544C2×D3#89311yescharacteristic
545C3×C4—21no—
546C3×C4—21no—
547C3×C4—31no—
548C3×C4—31no—
549C3×C4—62no—
550C3×C4—121no—
551C3×C4C22×C4×D311yescharacteristic
552C3×C4C22×C4×D311yescharacteristic
553C3×C4C2×D3×D411yescharacteristic
554C3×C4C2×D3×D411yescharacteristic
555Dic3—22no—
556Dic3—41no—
557Dic3—62no—
558Dic3—62no—
559Dic3—122no—
560Dic3—121no—
561Dic3—121no—
562Dic3—122no—
563Dic3#89311yescharacteristic
564Dic3#89311yescharacteristic
565C32#295711yescharacteristic, complemented, Sylow
566C23—31no—
567C23—182no—
568Q8—32no—
569Q8—92no—
570Q8—182no—
571D4—32no—
572D4—62no—
573D4—92no—
574D4—182no—
575D4—182no—
576D4—182no—
577D4—182no—
578C2×C4—31no—
579C2×C4—31no—
580C2×C4—31no—
581C2×C4—31no—
582C2×C4—31no—
583C2×C4—62no—
584C2×C4—61no—
585C2×C4—182no—
586C2×C4—182no—
587C2×C4—182no—
588C2×C4—182no—
589C2×C4—181no—
590C2×C4C22×D3211yescharacteristic
591C8—22no—
592C8—31no—
593C8—31no—
594C8—31no—
595C8—31no—
596C8—62no—
597C8—91no—
598C8—91no—
599C8C4×D3211yescharacteristic
600C8C4×D3211yescharacteristic
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—41no—
605C2×C3—61no—
606C2×C3—61no—
607C2×C3—122no—
608C2×C3C2×#89311yescharacteristic
609C2×C3C4×D3×D411yescharacteristic
610D3—21no—
611D3—21no—
612D3—42no—
613D3—122no—
614D3—122no—
615D3—242no—
616C22—31no—
617C22—31no—
618C22—62no—
619C22—121no—
620C22—182no—
621C22—722no—
622C22D3×#23911yescharacteristic
623C4—31no—
624C4—31no—
625C4—62no—
626C4—121no—
627C4—182no—
628C4—361no—
629C4C2×C4×D3211yescharacteristic
630C4D32×D411yescharacteristic
631C3—21no—
632C3#7924911yescharacteristic, complemented
633C3#7989011yescharacteristic, complemented
634C2—21no—
635C2—61no—
636C2—61no—
637C2—122no—
638C2—362no—
639C2D3×#89311yescharacteristic
subgroupG/H
centerC4D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#108C22
socleC2×C32C2×C4×D4
prime radicalD3×#904C2
cosocleC2×C32×C4C24
hypercenter#108D32
hypocenterC32#2957
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

Complements

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

NH ≅ G/Ntype
1. #10594706C2semidirect
3. #10592594C2semidirect
4. C3×#4895C2semidirect
5. C3×D3×#108C2semidirect
6. #10591005C2semidirect
7. #10590994C2semidirect
8. #10590978C2semidirect
9. #10590919C2semidirect
10. #10590917C2semidirect
11. #10590692C2semidirect
15. #64116C22semidirect
17. C3×#907C22semidirect
24. #63817C22semidirect
25. #63815C22semidirect
26. #63808C4semidirect
27. #63807C4semidirect
28. #63806C4semidirect
31. D3×Dic12C4semidirect
32. D3×D24C4semidirect
33. D3×#204C4semidirect
36. C32×#108C22semidirect
37. #63652C22semidirect
38. C8×C3⋊Dic3C22semidirect
39. C3×#825C22semidirect
40. C3×#822C22semidirect
41. C3×#819C22semidirect
42. C3×C8×Dic3C22semidirect
43. #63570C22semidirect
44. #63568C22semidirect
45. #63555C22semidirect
46. #63554C22semidirect
62. #4895D3semidirect
65. D3×#108D3semidirect
142. #907C2×D3semidirect
169. C3×#108C2×D3semidirect
170. C3×#108C2×D3semidirect
179. #825C2×D3semidirect
180. #822C2×D3semidirect
181. #819C2×D3semidirect
188. C8×Dic3C2×D3semidirect
384. #108D32semidirect
565. C32#2957semidirect
632. C3#79249semidirect
633. C3#79890semidirect

Maximal subgroups

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

subgroupindex
#105947062
D3×#9042
#105925942
C3×#48952
C3×D3×#1082
#105910052
#105909942
#105909782
#105909192
#105909172
#105906922
#798903
#792493