Finite Group Databasebeta

← #11858357

Subgroups — #11858357

Order 1152.

1031 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#907C211yesmaximal, characteristic
2#10594958C211yesmaximal, characteristic
3C2×#63814C211yesmaximal, characteristic
4#10592817C211yesmaximal, characteristic, complemented
5C3×#5119C211yesmaximal, characteristic, complemented
6C2×#63572C211yesmaximal, characteristic, complemented
7#10591116C211yesmaximal, characteristic, complemented
8#10590695C212yesmaximal, complemented
9#10590694C212yesmaximal, complemented
10#10590663C212yesmaximal, complemented
11D3×Dic3⋊C8C212yesmaximal, complemented
12#83783—31nomaximal
13#79081—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#907—24no—
22C2×C3×ΓL(1,𝔽25)C2212yes—
23C2×C3×D3×C8C2212yes—
24#67⋊Dic3C412yes—
25#67⋊Dic3C412yes—
26#63898C411yescharacteristic
27#63898C411yescharacteristic
28C4×D3×Dic3C2212yes—
29#63855C2212yes—
30#63843C411yescharacteristic
31#63843C411yescharacteristic
32C2×#3711C2212yes—
33#63814—24no—
34C2×D3×C3⋊C8C2212yes—
35#63641C2212yes—
36#63641C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×Dic3⋊C8C2212yes—
39#63572C2211yescharacteristic
40#63572C2211yescharacteristic
41#63572C2211yescharacteristic
42#63572C2211yescharacteristic
43Dic3⋊(C3⋊C8)C2212yes—
44Dic3⋊(C3⋊C8)C2212yes—
45C2×C3×#131—31no—
46Dic3×#41—31no—
47C2×#948—31no—
48C2×#907D311yescharacteristic
49C2×#901—31no—
50#5522—31no—
51C3×#424—31no—
52#5119—32no—
53#5119D311yescharacteristic, complemented
54#5118—31no—
55#5118—31no—
56#5118—32no—
57#5118—61no—
58#5102—31no—
59#5102—32no—
60C2×Dic3⋊C8—31no—
61C2×Dic3⋊C8—31no—
62C2×Dic3⋊C8—32no—
63#4999—31no—
64#4839—32no—
65#4839—32no—
66#4837—32no—
67D3×C4⋊C8—32no—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3C2×C411yescharacteristic
70C22×C3⋊Dic3C2×C411yescharacteristic
71C2×C3×#67C2×C412yes—
72C3×#235D414yes—
73C3×#235Q814yes—
74C2×C3×D12C2×C411yescharacteristic
75C2×C3×C4×D3C2312yes—
76C2×C3×Dic6C2×C411yescharacteristic
77C2×D3×Dic3C2×C412yes—
78C2×D3×Dic3C2×C412yes—
79C32×M16—22no—
80C2×C32×C8C2312yes—
81C4×C3⋊Dic3C2×C411yescharacteristic
82C4×C3⋊Dic3C2×C411yescharacteristic
83C4×C3⋊Dic3C2311yescharacteristic
84C4×C3⋊Dic3C2311yescharacteristic
85#3748—22no—
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×#217C2×C412yes—
88C3×C4⋊Dic3C2×C411yescharacteristic
89C3×C4⋊Dic3C2×C411yescharacteristic
90C3×C4×Dic3C2312yes—
91C2×C3×C3⋊C8—22no—
92C2×C3×C3⋊C8—22no—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97C3×ΓL(1,𝔽25)—24no—
98C3×D3×C8—24no—
99Dic3⋊Dic3C2×C412yes—
100Dic3⋊Dic3C2×C412yes—
101(C2×D3)⋊Dic3C2×C412yes—
102(C2×D3)⋊Dic3C2×C412yes—
103Dic32C2×C412yes—
104Dic32C2×C412yes—
105#3711—24no—
106D3×C3⋊C8—24no—
107#2906—91noSylow
108C2×C3×#41—31no—
109C2×#235C2×D311yescharacteristic
110C3×#131—64no—
111C2×C3×M16—21no—
112C2×C3×M16—32no—
113C2×C3×M16C2×D311yescharacteristic
114C2×C3×M16C2×D311yescharacteristic
115C22×C3×C8—31no—
116C22×C3×C8—31no—
117C22×C3×C8—32no—
118C3×#117—31no—
119#948—64no—
120Q8×Dic3—31no—
121Q8×Dic3—31no—
122D4×Dic3—32no—
123D4×Dic3—32no—
124D4×Dic3—31no—
125D4×Dic3—31no—
126#926—32no—
127#926C2×D311yescharacteristic
128C2×C4×Dic3—31no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3—61no—
132C2×#208—31no—
133C2×#208—31no—
134C2×#208—32no—
135C2×#208—61no—
136C22×C3⋊C8—32no—
137C22×C3⋊C8C2×D311yescharacteristic
138C22×C3⋊C8C2×D311yescharacteristic
139#907—24no—
140#901—64no—
141C2×ΓL(1,𝔽25)—32no—
142C2×ΓL(1,𝔽25)C2×D312yes—
143C2×D3×C8—32no—
144C2×D3×C8C2×D312yes—
145#893—31no—
146#893—31no—
147#887—31no—
148#887—31no—
149#67⋊C4—32no—
150#67⋊C4—32no—
151#872—32no—
152C42×D3—32no—
153C3×C4⋊C8—32no—
154C3×C4⋊C8—32no—
155Dic3⋊C8—32no—
156Dic3⋊C8—32no—
157Dic3⋊C8—32no—
158Dic3⋊C8—32no—
159Dic3⋊C8—32no—
160Dic3⋊C8—32no—
161Dic3⋊C8—31no—
162Dic3⋊C8—31no—
163Dic3⋊C8—31no—
164Dic3⋊C8—31no—
165Dic3⋊C8—31no—
166Dic3⋊C8—31no—
167Dic3⋊C8—31no—
168Dic3⋊C8—31no—
169Dic3⋊C8—62no—
170Dic3⋊C8—62no—
171Dic3⋊C8C2×D312yes—
172Dic3⋊C8C2×D312yes—
173C4⋊(C3⋊C8)—32no—
174C4⋊(C3⋊C8)—32no—
175C23×C32C22×C411yescharacteristic
176C22×C3×D3C22×C412yes—
177C2×C32×C4C22×C411yescharacteristic
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2×Q812yes—
180C2×C32×C4C2411yescharacteristic
181C2×C3⋊Dic3—22no—
182C2×C3⋊Dic3—41no—
183C2×C3⋊Dic3C22×C411yescharacteristic
184C2×C3⋊Dic3C22×C411yescharacteristic
185C2×C3⋊Dic3C22×C411yescharacteristic
186C2×C3⋊Dic3C22×C411yescharacteristic
187C3×#67C4⋊C418yes—
188C2×C3×Dic3C22×C412yes—
189C2×C3×Dic3C22×C412yes—
190C2×C3×Dic3C22×C412yes—
191C3×D12C4⋊C414yes—
192C3×C4×D3C2×D414yes—
193C3×C4×D3C2×Q814yes—
194C3×Dic6C4⋊C414yes—
195D3×Dic3—24no—
196D3×Dic3—42no—
197C32×C8—22no—
198C3⋊(C3⋊C8)—22no—
199C3×C3⋊C8—21no—
200C3×C3⋊C8—21no—
201C3×C3⋊C8—21no—
202C3×C3⋊C8—21no—
203C2×#131—31no—
204C2×#131—91no—
205C4×#41—91no—
206#424—31no—
207#424—92no—
208#424—92no—
209#424—91no—
210#423—92no—
211#423—91no—
212C2×C4⋊C8—92no—
213C2×C4⋊C8—91no—
214C3×#41—34no—
215C3×#41—34no—
216C2×C3×Q8—31no—
217C2×C3×D4—32no—
218C2×C3×D4—31no—
219C22×C3×C4—21no—
220C22×C3×C4—32no—
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C2×#67C4×D312yes—
224C22×Dic3—31no—
225C22×Dic3—31no—
226C22×Dic3—31no—
227C22×Dic3—31no—
228C22×Dic3—32no—
229C22×Dic3—32no—
230C22×Dic3—61no—
231C22×Dic3—61no—
232#235Dic614yes—
233#235#6714yes—
234C2×D12C4×D311yescharacteristic
235C2×C4×D3—32no—
236C2×C4×D3—32no—
237C2×C4×D3C22×D312yes—
238C2×Dic6C4×D311yescharacteristic
239C3×M16—22no—
240C3×M16—22no—
241C3×M16—42no—
242C3×M16—64no—
243C2×C3×C8—22no—
244C2×C3×C8—31no—
245C2×C3×C8—31no—
246C2×C3×C8—31no—
247C2×C3×C8—31no—
248C2×C3×C8—64no—
249C2×C3×C8—62no—
250C2×C3×C8—62no—
251C2×C3×C8C22×D312yes—
252C2×C3×C8C22×D312yes—
253C3×C4⋊C4—31no—
254C3×C4⋊C4—31no—
255C3×C22⋊C4—32no—
256C3×C42—32no—
257#217—32no—
258#217—32no—
259#217C4×D312yes—
260(C2×D3)⋊C4—32no—
261(C2×D3)⋊C4—32no—
262C4⋊Dic3—32no—
263C4⋊Dic3—32no—
264C4⋊Dic3C4×D311yescharacteristic
265C4⋊Dic3C4×D311yescharacteristic
266Dic3⋊C4—32no—
267Dic3⋊C4—32no—
268C4×Dic3—31no—
269C4×Dic3—31no—
270C4×Dic3—31no—
271C4×Dic3—31no—
272C4×Dic3—31no—
273C4×Dic3—31no—
274C4×Dic3—31no—
275C4×Dic3—31no—
276C4×Dic3—32no—
277C4×Dic3—32no—
278C4×Dic3—32no—
279C4×Dic3—32no—
280C4×Dic3—61no—
281C4×Dic3—61no—
282C4×Dic3—61no—
283C4×Dic3—61no—
284C4×Dic3C22×D312yes—
285#208—64no—
286#208—62no—
287#208—62no—
288#208—122no—
289C2×C3⋊C8—22no—
290C2×C3⋊C8—22no—
291C2×C3⋊C8—32no—
292C2×C3⋊C8—32no—
293C2×C3⋊C8—62no—
294C2×C3⋊C8—64no—
295C2×C3⋊C8C22×D311yescharacteristic
296C2×C3⋊C8C22×D311yescharacteristic
297C2×C3⋊C8C22×D311yescharacteristic
298C2×C3⋊C8C22×D311yescharacteristic
299ΓL(1,𝔽25)—24no—
300ΓL(1,𝔽25)—64no—
301D3×C8—24no—
302D3×C8—64no—
303C22×C32—21no—
304C22×C32—21no—
305C22×C32C2×C4⋊C412yes—
306C22×C32C23×C411yescharacteristic
307C2×C3×D3—22no—
308C2×C3×D3—22no—
309C2×C3×D3C2×C4⋊C414yes—
310C32×C4C2×C4⋊C412yes—
311C32×C4C22×D411yescharacteristic
312C32×C4C22×Q811yescharacteristic
313C3⋊Dic3—21no—
314C3⋊Dic3—21no—
315C3⋊Dic3—21no—
316C3⋊Dic3#13112yescomplemented
317C3×Dic3—22no—
318C3×Dic3—22no—
319C3×Dic3C2×C4⋊C414yes—
320C2×#41—31no—
321#131—64no—
322#131—184no—
323C2×M16—32no—
324C2×M16—92no—
325C2×M16—91no—
326C2×M16D3211yescharacteristic
327C22×C8—31no—
328C22×C8—31no—
329C22×C8—32no—
330C22×C8—92no—
331C4×Q8—91no—
332C4×Q8—91no—
333C4×D4—92no—
334C4×D4—92no—
335C4×D4—91no—
336C4×D4—91no—
337#117—31no—
338#117—92no—
339C2×C42—92no—
340C2×C42—91no—
341C4⋊C8—32no—
342C4⋊C8—32no—
343C4⋊C8—92no—
344C4⋊C8—92no—
345C4⋊C8—91no—
346C4⋊C8—91no—
347C4⋊C8—91no—
348C4⋊C8—91no—
349C4⋊C8—92no—
350C4⋊C8—92no—
351C23×C3—21no—
352C23×C3—32no—
353C23×C3C2×C4×D311yescharacteristic
354C23×C3C2×C4×D311yescharacteristic
355C22×D3C2×C4×D312yes—
356C3×Q8—34no—
357C3×D4—38no—
358C3×D4—34no—
359C2×C3×C4—21no—
360C2×C3×C4—22no—
361C2×C3×C4—21no—
362C2×C3×C4—22no—
363C2×C3×C4—32no—
364C2×C3×C4—34no—
365C2×C3×C4—34no—
366C2×C3×C4—32no—
367C2×C3×C4—32no—
368C2×C3×C4C2×Dic612yes—
369C2×C3×C4C2×C4×D311yescharacteristic
370C2×C3×C4C2×C4×D311yescharacteristic
371C2×C3×C4D3×D412yes—
372C2×C3×C4D3×Q812yes—
373C2×C3×C4C2×#6712yes—
374C2×C3×C4C23×D311yescharacteristic
375C2×C3×C4C23×D311yescharacteristic
376#67Dic3⋊C418yes—
377C2×Dic3—31no—
378C2×Dic3—31no—
379C2×Dic3—31no—
380C2×Dic3—31no—
381C2×Dic3—31no—
382C2×Dic3—31no—
383C2×Dic3—31no—
384C2×Dic3—31no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—61no—
389C2×Dic3—64no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—122no—
393C2×Dic3—122no—
394C2×Dic3—121no—
395C2×Dic3—121no—
396C2×Dic3—122no—
397C2×Dic3C2×C4×D312yes—
398C2×Dic3C2×C4×D312yes—
399C2×Dic3C2×C4×D312yes—
400D12Dic3⋊C414yes—
401C4×D3—64no—
402C4×D3—122no—
403C4×D3C2×Dic614yes—
404C4×D3C2×#6714yes—
405Dic6Dic3⋊C414yes—
406C3×C8—22no—
407C3×C8—22no—
408C3×C8—42no—
409C3×C8—61no—
410C3×C8—61no—
411C3×C8—61no—
412C3×C8—61no—
413C3⋊C8—21no—
414C3⋊C8—21no—
415C3⋊C8—21no—
416C3⋊C8—21no—
417C3⋊C8—62no—
418C3⋊C8—62no—
419C3⋊C8—122no—
420C2×C32—22no—
421C2×C32C22×C4⋊C411yescharacteristic
422C2×C32C2×#13111yescharacteristic
423C2×C32#56811yescharacteristic
424C3×D3—24no—
425#41—34no—
426#41—34no—
427C2×Q8—31no—
428C2×D4—32no—
429C2×D4—31no—
430C22×C4—32no—
431C22×C4—92no—
432C22×C4—92no—
433C22×C4—91no—
434C22×C4—91no—
435C22×C4C2×D3211yescharacteristic
436M16—22no—
437M16—64no—
438M16—184no—
439M16—182no—
440C2×C8—31no—
441C2×C8—31no—
442C2×C8—31no—
443C2×C8—31no—
444C2×C8—64no—
445C2×C8—62no—
446C2×C8—62no—
447C2×C8—92no—
448C2×C8—184no—
449C2×C8C2×D3212yes—
450C4⋊C4—31no—
451C4⋊C4—31no—
452C4⋊C4—92no—
453C4⋊C4—92no—
454C22⋊C4—32no—
455C22⋊C4—92no—
456C22⋊C4—92no—
457C42—32no—
458C42—92no—
459C42—92no—
460C42—91no—
461C42—91no—
462C42—91no—
463C42—91no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—22no—
470C22×C3—34no—
471C22×C3—41no—
472C22×C3—41no—
473C22×C3—62no—
474C22×C3—62no—
475C22×C3D3×C4⋊C412yes—
476C22×C3C2×Dic3⋊C412yes—
477C22×C3C22×C4×D311yescharacteristic
478C22×C3C22×C4×D311yescharacteristic
479C2×D3—22no—
480C2×D3—22no—
481C2×D3C2×Dic3⋊C414yes—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—22no—
485C3×C4—34no—
486C3×C4—62no—
487C3×C4—62no—
488C3×C4D3×C4⋊C412yes—
489C3×C4C2×Dic3⋊C412yes—
490C3×C4C22×Dic611yescharacteristic
491C3×C4C2×D3×D411yescharacteristic
492C3×C4C2×D3×Q811yescharacteristic
493C3×C4C22×#6711yescharacteristic
494Dic3—22no—
495Dic3—22no—
496Dic3—32no—
497Dic3—32no—
498Dic3—62no—
499Dic3—62no—
500Dic3—61no—
501Dic3—61no—
502Dic3—61no—
503Dic3—61no—
504Dic3—61no—
505Dic3—61no—
506Dic3—121no—
507Dic3—121no—
508Dic3C2×Dic3⋊C414yes—
509C32#290611yescharacteristic, complemented, Sylow
510C23—32no—
511C23C4×D3211yescharacteristic
512Q8—34no—
513D4—38no—
514D4—34no—
515C2×C4—32no—
516C2×C4—34no—
517C2×C4—34no—
518C2×C4—32no—
519C2×C4—32no—
520C2×C4—91no—
521C2×C4—91no—
522C2×C4—91no—
523C2×C4—91no—
524C2×C4—184no—
525C2×C4—182no—
526C2×C4—362no—
527C2×C4—361no—
528C2×C4D3×Dic612yes—
529C2×C4C4×D3211yescharacteristic
530C2×C4D3×#6712yes—
531C2×C4C22×D3211yescharacteristic
532C8—22no—
533C8—61no—
534C8—61no—
535C8—61no—
536C8—61no—
537C8—182no—
538C2×C3—22no—
539C2×C3—22no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—42no—
544C2×C3—64no—
545C2×C3C2×D3×C4⋊C411yescharacteristic
546C2×C3D3×#13111yescharacteristic
547C2×C3D3×#13111yescharacteristic
548C2×C3#575011yescharacteristic
549C2×C3#575011yescharacteristic
550C2×C3C22×Dic3⋊C411yescharacteristic
551D3—24no—
552C22—21no—
553C22—21no—
554C22—34no—
555C22—62no—
556C22—62no—
557C22D3×Dic3⋊C412yes—
558C22C2×C4×D3211yescharacteristic
559C4—34no—
560C4—62no—
561C4—62no—
562C4—92no—
563C4—181no—
564C4—181no—
565C4—181no—
566C4D3×Dic3⋊C412yes—
567C4C2×D3×Dic611yescharacteristic
568C4C2×D3×#6711yescharacteristic
569C3—21no—
570C3#7908111yescharacteristic, complemented
571C3#8378311yescharacteristic, complemented
572C2—22no—
573C2—64no—
574C2#1059470711yescharacteristic
575C2#1059470811yescharacteristic
576C2C2×D3×Dic3⋊C411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×M16C22
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2906
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #10592817C2semidirect
5. C3×#5119C2semidirect
6. C2×#63572C2semidirect
7. #10591116C2semidirect
8. #10590695C2semidirect
9. #10590694C2semidirect
10. #10590663C2semidirect
11. D3×Dic3⋊C8C2semidirect
53. #5119D3semidirect
316. C3⋊Dic3#131semidirect
509. C32#2906semidirect
570. C3#79081semidirect
571. C3#83783semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9072
#105949582
C2×#638142
#105928172
C3×#51192
C2×#635722
#105911162
#105906952
#105906942
#105906632
D3×Dic3⋊C82
#837833
#790813