Finite Group Databasebeta

← #11859372

Subgroups — #11859372

Order 1152.

1209 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C8×C3⋊D3C211yesmaximal, characteristic, complemented
2#10595016C211yesmaximal, characteristic
3C2×#63805C211yesmaximal, characteristic, complemented
4C3×#5111C212yesmaximal, complemented
5#10591159C211yesmaximal, characteristic, complemented
6#67⋊(C3⋊C8)C212yesmaximal, complemented
7#10590958C211yesmaximal, characteristic, complemented
8#10590906C212yesmaximal, complemented
9#10590736C212yesmaximal, complemented
10#10590703C211yesmaximal, characteristic, complemented
11#10590701C211yesmaximal, characteristic, complemented
12#79478—32nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C2×#3798C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C8×C3⋊D3—24no—
18C2×C8×C3⋊D3C2211yescharacteristic
19C2×C8×C3⋊D3C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic
21C2×C8×C3⋊D3C2211yescharacteristic
22C3×C4×#67C2212yes—
23C2×C3×ΓL(1,𝔽25)C2212yescomplemented
24#63982C411yescharacteristic
25#63981C412yes—
26#63980C411yescharacteristic
27#63912C411yescharacteristic
28C4×#626C2212yes—
29#63874C2211yescharacteristic
30#63865C411yescharacteristic
31#63853C412yes—
32C2×#3712C2211yescharacteristic
33C2×#3712C2211yescharacteristic
34C2×D3×C3⋊C8C2212yescomplemented
35#63805—24no—
36C3×#830C2212yes—
37C3×(C2×D3)⋊C8C2212yescomplemented
38C3×#815C2212yescomplemented
39C3×Dic3⋊C8C2212yescomplemented
40Dic3⋊(C3⋊C8)C2212yescomplemented
41#63557C2212yes—
42(C2×D3)⋊(C3⋊C8)C2212yescomplemented
43Dic3×C3⋊C8C2212yescomplemented
44C2×#907—32no—
45C22×D3×C8—32no—
46C22×D3×C8—61no—
47#5547—32no—
48C3×#435—32no—
49#5127—32no—
50#5111D312yescomplemented
51D4×C3⋊C8—32no—
52#4839—32no—
53#4834—32no—
54#4727—32no—
55#4726—32no—
56#67⋊C8—32no—
57#67⋊C8—32no—
58#4708—32no—
59#4706—32no—
60C23×C3⋊D3C2×C411yescharacteristic
61C22×C32×C4C2311yescharacteristic
62C22×C3⋊Dic3C2×C411yescharacteristic
63C2×C4×C3⋊D3—22no—
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3C2×C411yescharacteristic
66C2×C4×C3⋊D3C2×C411yescharacteristic
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×C4×C3⋊D3C2311yescharacteristic
69C2×C3×#67C2×C412yes—
70C2×C3×C4×D3C2312yes—
71C2×#627C2×C411yescharacteristic
72C2×#626C2×C412yes—
73C2×#626C2×C412yes—
74C2×#625C2×C411yescharacteristic
75#3798—22no—
76#3798—22no—
77C2×C32×C8—22no—
78C2×C32×C8C2311yescharacteristic
79C2×C32×C8C2311yescharacteristic
80C2×C3⋊(C3⋊C8)—22no—
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C8×C3⋊D3—22no—
84C8×C3⋊D3—22no—
85C8×C3⋊D3—22no—
86C8×C3⋊D3D414yescomplemented
87C3×#217C2×C412yes—
88C3×(C2×D3)⋊C4C2×C412yes—
89C3×Dic3⋊C4C2×C412yes—
90C3×C4×Dic3C2312yes—
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2312yes—
93C3×ΓL(1,𝔽25)—24no—
94#3724C2×C411yescharacteristic
95#3724C2×C411yescharacteristic
96Dic3⋊Dic3C2×C412yes—
97#3722C2×C412yes—
98#3722C2×C412yes—
99(C2×D3)⋊Dic3C2×C412yes—
100#3712—22no—
101#3712—22no—
102D3×C3⋊C8—24no—
103#2929—91noSylow
104C2×#235—32no—
105C22×C4×D3—32no—
106C22×C4×D3—61no—
107C2×C3×M16—32no—
108C22×C3×C8—21no—
109C22×C3×C8C2×D312yes—
110C3×C4×D4—32no—
111#939—32no—
112#937—32no—
113C4×#67—32no—
114C4×#67C2×D312yes—
115C22×C3⋊C8—32no—
116C22×C3⋊C8—32no—
117C22×C3⋊C8—61no—
118#907—68no—
119C2×ΓL(1,𝔽25)—32no—
120C2×ΓL(1,𝔽25)—32no—
121C2×ΓL(1,𝔽25)C2×D312yescomplemented
122C2×D3×C8—32no—
123C2×D3×C8—32no—
124C2×D3×C8—32no—
125C2×D3×C8—32no—
126C2×D3×C8—32no—
127C2×D3×C8—61no—
128C2×D3×C8—61no—
129C2×D3×C8—61no—
130C2×D3×C8—61no—
131C2×D3×C8—68no—
132C2×D3×C8—68no—
133#896—32no—
134#894—32no—
135#884—32no—
136#883—32no—
137#882—32no—
138#878—32no—
139C4×D12—32no—
140#872—32no—
141C3×C4⋊C8—32no—
142C3×C22⋊C8—32no—
143C3×C22⋊C8—32no—
144C3×#97—32no—
145#830—32no—
146#830C2×D312yes—
147(C2×D3)⋊C8—32no—
148(C2×D3)⋊C8—32no—
149(C2×D3)⋊C8—32no—
150(C2×D3)⋊C8C2×D312yescomplemented
151#815C2×D312yescomplemented
152Dic3⋊C8—32no—
153Dic3⋊C8C2×D312yescomplemented
154C8×Dic3—32no—
155C4⋊(C3⋊C8)—32no—
156C4×C3⋊C8—32no—
157C23×C32C22×C411yescharacteristic
158C22×C3⋊D3—22no—
159C22×C3⋊D3—22no—
160C22×C3⋊D3—22no—
161C22×C3⋊D3C22×C411yescharacteristic
162C22×C3⋊D3C22×C411yescharacteristic
163C22×C3×D3C22×C412yes—
164C2×C32×C4—21no—
165C2×C32×C4—21no—
166C2×C32×C4C22×C411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3C22×C411yescharacteristic
170C2×C3⋊Dic3C22×C411yescharacteristic
171C4×C3⋊D3—22no—
172C4×C3⋊D3—21no—
173C4×C3⋊D3—21no—
174C4×C3⋊D3—22no—
175C4×C3⋊D3C2×D412yes—
176C4×C3⋊D3#4112yes—
177C3×#67—24no—
178C2×C3×Dic3C22×C412yes—
179C2×C3×Dic3C22×C412yes—
180C2×C3×Dic3C22×C412yes—
181C3×C4×D3—22no—
182C3×C4×D3—22no—
183#627—22no—
184#626—24no—
185#626—24no—
186#625—22no—
187C32×C8—21no—
188C32×C8C2×D412yes—
189C3⋊(C3⋊C8)—21no—
190C3⋊(C3⋊C8)C2×D412yes—
191C3×C3⋊C8—22no—
192C3×C3⋊C8—22no—
193C2×#131—91no—
194C23×C8—91no—
195#525—91no—
196#435—32no—
197#435—92no—
198C8×D4—92no—
199C8×D4—92no—
200#424—91no—
201#408—91no—
202#407—91no—
203#405—91no—
204C23×D3—32no—
205C23×D3—61no—
206C2×C3×D4—32no—
207C22×C3×C4—21no—
208C22×C3×C4—32no—
209C22×C3×C4C22×D312yes—
210C2×#67—32no—
211C2×#67—32no—
212C2×#67—32no—
213C2×#67C4×D312yes—
214C22×Dic3—32no—
215C22×Dic3—61no—
216#235—64no—
217#235—64no—
218C2×D12—32no—
219C2×D12—32no—
220C2×C4×D3—32no—
221C2×C4×D3—32no—
222C2×C4×D3—32no—
223C2×C4×D3—32no—
224C2×C4×D3—61no—
225C2×C4×D3—61no—
226C2×C4×D3—61no—
227C2×C4×D3—61no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×C4×D3—64no—
231C2×C4×D3—64no—
232C2×C4×D3C22×D312yes—
233C2×Dic6—32no—
234C3×M16—64no—
235C2×C3×C8—24no—
236C2×C3×C8—24no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—32no—
240C2×C3×C8—32no—
241C2×C3×C8C22×D312yes—
242C2×C3×C8C22×D312yes—
243C3×C4⋊C4—32no—
244C3×C22⋊C4—32no—
245C3×C22⋊C4—32no—
246C3×C42—32no—
247#217—32no—
248#217C4×D312yes—
249(C2×D3)⋊C4—32no—
250(C2×D3)⋊C4—32no—
251(C2×D3)⋊C4—32no—
252(C2×D3)⋊C4—32no—
253(C2×D3)⋊C4—32no—
254(C2×D3)⋊C4C4×D312yes—
255C4⋊Dic3—32no—
256Dic3⋊C4—32no—
257Dic3⋊C4—32no—
258Dic3⋊C4—32no—
259Dic3⋊C4C4×D312yes—
260C4×Dic3C22×D312yes—
261C2×C3⋊C8—32no—
262C2×C3⋊C8—32no—
263C2×C3⋊C8—61no—
264C2×C3⋊C8—61no—
265C2×C3⋊C8—64no—
266C2×C3⋊C8—64no—
267C2×C3⋊C8—64no—
268C2×C3⋊C8C22×D312yes—
269C2×C3⋊C8C22×D312yes—
270ΓL(1,𝔽25)—24no—
271ΓL(1,𝔽25)—64no—
272ΓL(1,𝔽25)—64no—
273D3×C8—38no—
274D3×C8—64no—
275D3×C8—64no—
276D3×C8—64no—
277D3×C8—64no—
278D3×C8—64no—
279D3×C8—64no—
280D3×C8—64no—
281D3×C8—64no—
282C22×C32—21no—
283C22×C32—21no—
284C22×C32#13112yescomplemented
285C22×C32C23×C411yescharacteristic
286C2×C3⋊D3—28no—
287C2×C3⋊D3—21no—
288C2×C3⋊D3—21no—
289C2×C3⋊D3—21no—
290C2×C3⋊D3—21no—
291C2×C3⋊D3C4×D412yes—
292C2×C3⋊D3#13112yescomplemented
293C2×C3×D3—22no—
294C2×C3×D3—22no—
295C2×C3×D3—22no—
296C32×C4—21no—
297C32×C4C22×D411yescharacteristic
298C32×C4C2×#4111yescharacteristic
299C3⋊Dic3—21no—
300C3⋊Dic3C4×D412yes—
301C3×Dic3—22no—
302C3×Dic3—22no—
303C3×Dic3—22no—
304C2×#41—91no—
305C23×C4—91no—
306#131—184no—
307C2×M16—32no—
308C2×M16—91no—
309C2×M16—91no—
310C22×C8—92no—
311C22×C8—91no—
312C22×C8—91no—
313C22×C8—91no—
314C22×C8—91no—
315C22×C8—91no—
316C22×C8—184no—
317C22×C8D3211yescharacteristic
318#123—92no—
319C22⋊Q8—91no—
320C22⋊Q8—91no—
321#121—91no—
322#121—91no—
323#120—92no—
324C4×D4—32no—
325C4×D4—92no—
326#117—91no—
327C4⋊C8—32no—
328C4⋊C8—92no—
329C22⋊C8—32no—
330C22⋊C8—32no—
331C22⋊C8—92no—
332C22⋊C8—92no—
333#97—32no—
334C4×C8—92no—
335C23×C3—21no—
336C23×C3—32no—
337C23×C3C2×C4×D312yes—
338C22×D3—32no—
339C22×D3—32no—
340C22×D3—61no—
341C22×D3—61no—
342C22×D3—64no—
343C22×D3—64no—
344C22×D3—64no—
345C22×D3—64no—
346C22×D3—64no—
347C22×D3—64no—
348C22×D3C2×C4×D312yes—
349C3×D4—64no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—32no—
357C2×C3×C4—32no—
358C2×C3×C4—32no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4C2×C4×D312yes—
362C2×C3×C4C23×D312yes—
363#67—24no—
364#67—64no—
365#67—64no—
366#67—64no—
367C2×Dic3—32no—
368C2×Dic3—32no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—64no—
372C2×Dic3—64no—
373C2×Dic3C2×C4×D312yes—
374C2×Dic3C2×C4×D312yes—
375C2×Dic3C2×C4×D312yes—
376D12—64no—
377D12—64no—
378C4×D3—22no—
379C4×D3—22no—
380C4×D3—34no—
381C4×D3—34no—
382C4×D3—62no—
383C4×D3—62no—
384C4×D3—64no—
385C4×D3—64no—
386C4×D3—62no—
387C4×D3—64no—
388C4×D3—64no—
389C4×D3—62no—
390C4×D3—62no—
391C4×D3—62no—
392Dic6—64no—
393C3×C8—22no—
394C3×C8—22no—
395C3×C8—22no—
396C3×C8—62no—
397C3×C8—62no—
398C3×C8D3×D414yes—
399C3⋊C8—22no—
400C3⋊C8—22no—
401C3⋊C8—34no—
402C3⋊C8—62no—
403C3⋊C8—62no—
404C3⋊C8—62no—
405C2×C32—22no—
406C2×C32C2×C4×D411yescharacteristic
407C2×C32C2×#13111yescharacteristic
408C2×C32C2×#13111yescharacteristic
409C3⋊D3—22no—
410C3⋊D3—22no—
411C3×D3—42no—
412C24—91no—
413#41—182no—
414#41—182no—
415C2×Q8—91no—
416C2×D4—32no—
417C2×D4—92no—
418C2×D4—92no—
419C2×D4—91no—
420C22×C4—32no—
421C22×C4—91no—
422C22×C4—91no—
423C22×C4—91no—
424C22×C4—91no—
425C22×C4—91no—
426C22×C4—182no—
427C22×C4—182no—
428C22×C4C2×D3211yescharacteristic
429M16—64no—
430M16—182no—
431M16—182no—
432C2×C8—22no—
433C2×C8—32no—
434C2×C8—32no—
435C2×C8—91no—
436C2×C8—94no—
437C2×C8—91no—
438C2×C8—182no—
439C2×C8—182no—
440C2×C8—184no—
441C2×C8—182no—
442C2×C8—182no—
443C2×C8C2×D3211yescharacteristic
444C2×C8C2×D3211yescharacteristic
445C4⋊C4—32no—
446C4⋊C4—91no—
447C4⋊C4—91no—
448C4⋊C4—92no—
449C22⋊C4—32no—
450C22⋊C4—32no—
451C22⋊C4—92no—
452C22⋊C4—92no—
453C22⋊C4—92no—
454C42—32no—
455C22×C3—22no—
456C22×C3—22no—
457C22×C3—22no—
458C22×C3—22no—
459C22×C3—21no—
460C22×C3—22no—
461C22×C3—62no—
462C22×C3—62no—
463C22×C3—62no—
464C22×C3#90714yescomplemented
465C22×C3C22×C4×D312yes—
466C2×D3—22no—
467C2×D3—22no—
468C2×D3—22no—
469C2×D3—34no—
470C2×D3—34no—
471C2×D3—62no—
472C2×D3—62no—
473C2×D3—62no—
474C2×D3—616no—
475C2×D3—616no—
476C2×D3—62no—
477C2×D3—62no—
478C2×D3—62no—
479C2×D3—62no—
480C2×D3—62no—
481C2×D3—62no—
482C2×D3—62no—
483C3×C4—22no—
484C3×C4—22no—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—62no—
488C3×C4—62no—
489C3×C4—62no—
490C3×C4C2×D3×D412yes—
491C3×C4D3×#4112yes—
492Dic3—22no—
493Dic3—22no—
494Dic3—22no—
495Dic3—34no—
496Dic3—62no—
497Dic3—62no—
498Dic3—62no—
499C32#292911yescharacteristic, complemented, Sylow
500C23—32no—
501C23—91no—
502C23—91no—
503C23—182no—
504C23—182no—
505C23—182no—
506C23C4×D3211yescharacteristic
507Q8—182no—
508D4—64no—
509D4—184no—
510D4—184no—
511D4—182no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—32no—
515C2×C4—32no—
516C2×C4—32no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—91no—
520C2×C4—92no—
521C2×C4—92no—
522C2×C4—91no—
523C2×C4—182no—
524C2×C4—182no—
525C2×C4—182no—
526C2×C4—181no—
527C2×C4—181no—
528C2×C4C4×D3211yescharacteristic
529C2×C4C22×D3211yescharacteristic
530C8—21no—
531C8—62no—
532C8—62no—
533C8—92no—
534C8—181no—
535C8#381112yes—
536C2×C3—24no—
537C2×C3—24no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—122no—
542C2×C3C4×D3×D412yes—
543C2×C3C2×#90712yes—
544C2×C3D3×#13112yes—
545D3—42no—
546D3—64no—
547D3—64no—
548D3—64no—
549D3—64no—
550C22—21no—
551C22—21no—
552C22—62no—
553C22—62no—
554C22—62no—
555C22—92no—
556C22—92no—
557C22—188no—
558C22—181no—
559C22—181no—
560C22—181no—
561C22—181no—
562C22#6380512yescomplemented
563C22C2×C4×D3211yescharacteristic
564C4—21no—
565C4—62no—
566C4—62no—
567C4—62no—
568C4—92no—
569C4—181no—
570C4#6430611yescharacteristic
571C4C2×#381111yescharacteristic
572C3—21no—
573C3#7947812yescomplemented
574C2—22no—
575C2—122no—
576C2—182no—
577C2—182no—
578C2#1059466911yescharacteristic
579C2C2×#6380511yescharacteristic
580C2C4×#381111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC22×C32×C8C22
prime radical#10595016C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2929
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C8×C3⋊D3C2semidirect
3. C2×#63805C2semidirect
4. C3×#5111C2semidirect
5. #10591159C2semidirect
6. #67⋊(C3⋊C8)C2semidirect
7. #10590958C2semidirect
8. #10590906C2semidirect
9. #10590736C2semidirect
10. #10590703C2semidirect
11. #10590701C2semidirect
23. C2×C3×ΓL(1,𝔽25)C22semidirect
34. C2×D3×C3⋊C8C22semidirect
37. C3×(C2×D3)⋊C8C22semidirect
38. C3×#815C22semidirect
39. C3×Dic3⋊C8C22semidirect
40. Dic3⋊(C3⋊C8)C22semidirect
42. (C2×D3)⋊(C3⋊C8)C22semidirect
43. Dic3×C3⋊C8C22semidirect
50. #5111D3semidirect
86. C8×C3⋊D3D4semidirect
121. C2×ΓL(1,𝔽25)C2×D3semidirect
150. (C2×D3)⋊C8C2×D3semidirect
151. #815C2×D3semidirect
153. Dic3⋊C8C2×D3semidirect
284. C22×C32#131semidirect
292. C2×C3⋊D3#131semidirect
464. C22×C3#907semidirect
499. C32#2929semidirect
562. C22#63805semidirect
573. C3#79478semidirect

Maximal subgroups

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

subgroupindex
C22×C8×C3⋊D32
#105950162
C2×#638052
C3×#51112
#105911592
#67⋊(C3⋊C8)2
#105909582
#105909062
#105907362
#105907032
#105907012
#794783