Finite Group Databasebeta

← #11858359

Subgroups — #11858359

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#907C211yesmaximal, characteristic
2Dic3×#235C211yesmaximal, characteristic
3C2×#63815C211yesmaximal, characteristic
4#10592818C211yesmaximal, characteristic, complemented
5C3×#5118C211yesmaximal, characteristic, complemented
6#10591119C211yesmaximal, characteristic, complemented
7C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590695C212yesmaximal, complemented
9#10590694C212yesmaximal, complemented
10#10590663C212yesmaximal, complemented
11D3×Dic3⋊C8C212yesmaximal, complemented
12#83783—31nomaximal
13#79049—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16#64135C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#907—24no—
22C2×C3×ΓL(1,𝔽25)C2212yes—
23C2×C3×D3×C8C2212yes—
24Dic3×#67C412yes—
25Dic3×#67C412yes—
26Dic3×D12C411yescharacteristic
27Dic3×D12C411yescharacteristic
28C4×D3×Dic3C2212yes—
29#63855C2212yes—
30Dic3×Dic6C411yescharacteristic
31Dic3×Dic6C411yescharacteristic
32C2×#3711C2212yes—
33#63815—24no—
34C2×D3×C3⋊C8C2212yes—
35#63641C2212yes—
36#63641C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×Dic3⋊C8C2212yes—
39#63572C2212yes—
40#63572C2212yes—
41Dic3⋊(C3⋊C8)C2211yescharacteristic
42Dic3⋊(C3⋊C8)C2211yescharacteristic
43Dic3⋊(C3⋊C8)C2211yescharacteristic
44Dic3⋊(C3⋊C8)C2211yescharacteristic
45C2×C3×#131—31no—
46Dic3×#41—31no—
47C2×#948—31no—
48C2×#907—31no—
49C2×#907D311yescharacteristic
50C4×#235—31no—
51C3×#423—31no—
52#5119—31no—
53#5119—31no—
54#5119—31no—
55#5119—32no—
56#5119—61no—
57#5118—32no—
58#5118D311yescharacteristic, complemented
59#5102—31no—
60#5102—32no—
61C2×Dic3⋊C8—31no—
62C2×Dic3⋊C8—32no—
63C2×C4⋊(C3⋊C8)—31no—
64#4839—32no—
65#4839—32no—
66#4837—32no—
67D3×C4⋊C8—32no—
68C22×C32×C4C2311yescharacteristic
69C2×C3×#67C2×C412yes—
70C22×C3×Dic3C2×C411yescharacteristic
71C22×C3×Dic3C2×C411yescharacteristic
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—
81#3757C2×C412yes—
82C4⋊(C3⋊Dic3)C2×C411yescharacteristic
83C4⋊(C3⋊Dic3)C2×C411yescharacteristic
84C4×C3⋊Dic3C2312yes—
85C2×C3⋊(C3⋊C8)—22no—
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C3×C4×Dic3C2×C411yescharacteristic
89C3×C4×Dic3C2×C411yescharacteristic
90C3×C4×Dic3C2311yescharacteristic
91C3×C4×Dic3C2311yescharacteristic
92C3×#208—22no—
93C2×C3×C3⋊C8—22no—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2312yes—
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—31no—
113C2×C3×M16—32no—
114C2×C3×M16C2×D311yescharacteristic
115C2×C3×M16C2×D311yescharacteristic
116C22×C3×C8—31no—
117C22×C3×C8—32no—
118C2×C3×C42—31no—
119#948—64no—
120Q8×Dic3—31no—
121Q8×Dic3—31no—
122D4×Dic3—32no—
123D4×Dic3—32no—
124D4×Dic3—31no—
125D4×Dic3—31no—
126C4×#67—32no—
127C4×#67—32no—
128#926—31no—
129#926—31no—
130#926—32no—
131#926—61no—
132C2×C4×Dic3—32no—
133C2×C4×Dic3C2×D311yescharacteristic
134C2×#208—32no—
135C2×#208C2×D311yescharacteristic
136C22×C3⋊C8—31no—
137C22×C3⋊C8—31no—
138C22×C3⋊C8—32no—
139C22×C3⋊C8—61no—
140C22×C3⋊C8C2×D311yescharacteristic
141#907—24no—
142#907—64no—
143C2×ΓL(1,𝔽25)—32no—
144C2×ΓL(1,𝔽25)C2×D312yes—
145C2×D3×C8—32no—
146C2×D3×C8C2×D312yes—
147C4×D12—31no—
148C4×D12—31no—
149#872—32no—
150C42×D3—32no—
151C4×Dic6—31no—
152C4×Dic6—31no—
153C3×C4⋊C8—32no—
154C3×C4⋊C8—32no—
155Dic3⋊C8—32no—
156Dic3⋊C8—32no—
157Dic3⋊C8—32no—
158Dic3⋊C8—32no—
159Dic3⋊C8—31no—
160Dic3⋊C8—31no—
161Dic3⋊C8—31no—
162Dic3⋊C8—31no—
163Dic3⋊C8—32no—
164Dic3⋊C8—32no—
165Dic3⋊C8—32no—
166Dic3⋊C8—32no—
167Dic3⋊C8—62no—
168Dic3⋊C8—62no—
169Dic3⋊C8C2×D312yes—
170Dic3⋊C8C2×D312yes—
171C4⋊(C3⋊C8)—31no—
172C4⋊(C3⋊C8)—31no—
173C4⋊(C3⋊C8)—31no—
174C4⋊(C3⋊C8)—31no—
175C23×C32C22×C411yescharacteristic
176C22×C3×D3C22×C412yes—
177C2×C32×C4C22×C411yescharacteristic
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2×Q812yes—
180C2×C32×C4C2411yescharacteristic
181C2×C3⋊Dic3C22×C412yes—
182C2×C3⋊Dic3C22×C412yes—
183C3×#67C4⋊C418yes—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—41no—
186C2×C3×Dic3C22×C411yescharacteristic
187C2×C3×Dic3C22×C411yescharacteristic
188C2×C3×Dic3C22×C411yescharacteristic
189C2×C3×Dic3C22×C412yes—
190C2×C3×Dic3C22×C411yescharacteristic
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)—21no—
199C3⋊(C3⋊C8)—21no—
200C3×C3⋊C8—22no—
201C3×C3⋊C8—21no—
202C3×C3⋊C8—21no—
203C2×#131—31no—
204C2×#131—91no—
205C4×#41—91no—
206#424—92no—
207#424—92no—
208#424—91no—
209#424—91no—
210#423—31no—
211#423—92no—
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×C4—31no—
222C22×C3×C4—31no—
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C2×#67C4×D312yes—
226C22×Dic3—32no—
227C22×Dic3—32no—
228C22×Dic3C4×D311yescharacteristic
229C22×Dic3C4×D311yescharacteristic
230#235Dic614yes—
231#235#6714yes—
232C2×D12C4×D311yescharacteristic
233C2×C4×D3—32no—
234C2×C4×D3—32no—
235C2×C4×D3C22×D312yes—
236C2×Dic6C4×D311yescharacteristic
237C3×M16—22no—
238C3×M16—22no—
239C3×M16—42no—
240C3×M16—64no—
241C3×M16—62no—
242C2×C3×C8—22no—
243C2×C3×C8—31no—
244C2×C3×C8—31no—
245C2×C3×C8—32no—
246C2×C3×C8—64no—
247C2×C3×C8—62no—
248C2×C3×C8C22×D312yes—
249C2×C3×C8C22×D312yes—
250C3×C42—31no—
251C3×C42—31no—
252C3×C42—31no—
253C3×C42—31no—
254#217—32no—
255#217—32no—
256#217—32no—
257#217—32no—
258#217—62no—
259(C2×D3)⋊C4—32no—
260(C2×D3)⋊C4—32no—
261C4⋊Dic3—31no—
262C4⋊Dic3—31no—
263C4⋊Dic3—31no—
264C4⋊Dic3—31no—
265C4⋊Dic3—32no—
266C4⋊Dic3—32no—
267C4⋊Dic3—61no—
268C4⋊Dic3—61no—
269Dic3⋊C4—32no—
270Dic3⋊C4—32no—
271C4×Dic3—32no—
272C4×Dic3—32no—
273C4×Dic3—32no—
274C4×Dic3—32no—
275C4×Dic3—32no—
276C4×Dic3—32no—
277C4×Dic3—62no—
278C4×Dic3C4×D311yescharacteristic
279C4×Dic3C4×D311yescharacteristic
280C4×Dic3C22×D311yescharacteristic
281C4×Dic3C22×D311yescharacteristic
282#208—22no—
283#208—64no—
284C2×C3⋊C8—22no—
285C2×C3⋊C8—31no—
286C2×C3⋊C8—31no—
287C2×C3⋊C8—31no—
288C2×C3⋊C8—31no—
289C2×C3⋊C8—61no—
290C2×C3⋊C8—61no—
291C2×C3⋊C8—64no—
292C2×C3⋊C8—62no—
293C2×C3⋊C8—62no—
294C2×C3⋊C8—122no—
295C2×C3⋊C8C22×D311yescharacteristic
296C2×C3⋊C8C22×D311yescharacteristic
297C2×C3⋊C8C22×D312yes—
298ΓL(1,𝔽25)—24no—
299ΓL(1,𝔽25)—64no—
300D3×C8—24no—
301D3×C8—64no—
302C22×C32—21no—
303C22×C32—21no—
304C22×C32C2×C4⋊C412yes—
305C22×C32C23×C411yescharacteristic
306C2×C3×D3—22no—
307C2×C3×D3—22no—
308C2×C3×D3C2×C4⋊C414yes—
309C32×C4C2×C4⋊C412yes—
310C32×C4C22×D411yescharacteristic
311C32×C4C22×Q811yescharacteristic
312C3⋊Dic3—22no—
313C3⋊Dic3—22no—
314C3×Dic3—21no—
315C3×Dic3—21no—
316C3×Dic3—21no—
317C3×Dic3C2×C4⋊C414yes—
318C3×Dic3#13112yescomplemented
319C2×#41—31no—
320#131—64no—
321#131—184no—
322C2×M16—31no—
323C2×M16—32no—
324C2×M16—92no—
325C2×M16D3211yescharacteristic
326C22×C8—31no—
327C22×C8—32no—
328C22×C8—92no—
329C22×C8—91no—
330C4×Q8—91no—
331C4×Q8—91no—
332C4×D4—91no—
333C4×D4—91no—
334C4×D4—92no—
335C4×D4—92no—
336#117—92no—
337#117—91no—
338C2×C42—31no—
339C2×C42—92no—
340C4⋊C8—32no—
341C4⋊C8—32no—
342C4⋊C8—91no—
343C4⋊C8—91no—
344C4⋊C8—91no—
345C4⋊C8—91no—
346C4⋊C8—92no—
347C4⋊C8—92no—
348C4⋊C8—92no—
349C4⋊C8—92no—
350C23×C3—21no—
351C23×C3—32no—
352C23×C3C2×C4×D311yescharacteristic
353C23×C3C2×C4×D311yescharacteristic
354C22×D3C2×C4×D312yes—
355C3×Q8—34no—
356C3×D4—38no—
357C3×D4—34no—
358C2×C3×C4—21no—
359C2×C3×C4—22no—
360C2×C3×C4—21no—
361C2×C3×C4—22no—
362C2×C3×C4—32no—
363C2×C3×C4—31no—
364C2×C3×C4—34no—
365C2×C3×C4—34no—
366C2×C3×C4—31no—
367C2×C3×C4—31no—
368C2×C3×C4—31no—
369C2×C3×C4—62no—
370C2×C3×C4—121no—
371C2×C3×C4C2×Dic612yes—
372C2×C3×C4C2×C4×D311yescharacteristic
373C2×C3×C4C2×C4×D311yescharacteristic
374C2×C3×C4D3×D412yes—
375C2×C3×C4D3×Q812yes—
376C2×C3×C4C2×#6712yes—
377C2×C3×C4C23×D311yescharacteristic
378C2×C3×C4C23×D311yescharacteristic
379#67Dic3⋊C418yes—
380C2×Dic3—22no—
381C2×Dic3—32no—
382C2×Dic3—32no—
383C2×Dic3—32no—
384C2×Dic3—32no—
385C2×Dic3—41no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—64no—
389C2×Dic3—122no—
390C2×Dic3C2×C4×D311yescharacteristic
391C2×Dic3C2×C4×D311yescharacteristic
392C2×Dic3C2×C4×D311yescharacteristic
393C2×Dic3C2×C4×D311yescharacteristic
394C2×Dic3C2×C4×D312yes—
395D12Dic3⋊C414yes—
396C4×D3—64no—
397C4×D3—122no—
398C4×D3C2×Dic614yes—
399C4×D3C2×#6714yes—
400Dic6Dic3⋊C414yes—
401C3×C8—22no—
402C3×C8—22no—
403C3×C8—42no—
404C3×C8—61no—
405C3×C8—61no—
406C3×C8—62no—
407C3⋊C8—22no—
408C3⋊C8—21no—
409C3⋊C8—21no—
410C3⋊C8—61no—
411C3⋊C8—61no—
412C3⋊C8—61no—
413C3⋊C8—61no—
414C3⋊C8—121no—
415C3⋊C8—121no—
416C2×C32—22no—
417C2×C32C22×C4⋊C411yescharacteristic
418C2×C32C2×#13111yescharacteristic
419C2×C32#56811yescharacteristic
420C3×D3—24no—
421#41—34no—
422#41—34no—
423C2×Q8—31no—
424C2×D4—32no—
425C2×D4—31no—
426C22×C4—32no—
427C22×C4—31no—
428C22×C4—31no—
429C22×C4—92no—
430C22×C4—92no—
431C22×C4C2×D3211yescharacteristic
432M16—22no—
433M16—64no—
434M16—62no—
435M16—184no—
436C2×C8—32no—
437C2×C8—31no—
438C2×C8—31no—
439C2×C8—64no—
440C2×C8—62no—
441C2×C8—91no—
442C2×C8—91no—
443C2×C8—184no—
444C2×C8—182no—
445C2×C8C2×D3212yes—
446C4⋊C4—92no—
447C4⋊C4—92no—
448C4⋊C4—91no—
449C4⋊C4—91no—
450C22⋊C4—92no—
451C22⋊C4—92no—
452C22⋊C4—92no—
453C42—31no—
454C42—31no—
455C42—31no—
456C42—31no—
457C42—92no—
458C42—92no—
459C42—92no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—22no—
466C22×C3—34no—
467C22×C3—41no—
468C22×C3—41no—
469C22×C3—62no—
470C22×C3—62no—
471C22×C3D3×C4⋊C412yes—
472C22×C3C2×Dic3⋊C412yes—
473C22×C3C22×C4×D311yescharacteristic
474C22×C3C22×C4×D311yescharacteristic
475C2×D3—22no—
476C2×D3—22no—
477C2×D3C2×Dic3⋊C414yes—
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—22no—
481C3×C4—32no—
482C3×C4—34no—
483C3×C4—61no—
484C3×C4—61no—
485C3×C4—61no—
486C3×C4D3×C4⋊C412yes—
487C3×C4C2×Dic3⋊C412yes—
488C3×C4C22×Dic611yescharacteristic
489C3×C4C2×D3×D411yescharacteristic
490C3×C4C2×D3×Q811yescharacteristic
491C3×C4C22×#6711yescharacteristic
492Dic3—21no—
493Dic3—21no—
494Dic3—21no—
495Dic3—62no—
496Dic3—62no—
497Dic3—62no—
498Dic3—62no—
499Dic3—122no—
500Dic3—122no—
501Dic3#90712yescomplemented
502Dic3C2×Dic3⋊C414yes—
503C32#290611yescharacteristic, complemented, Sylow
504C23—32no—
505C23C4×D3211yescharacteristic
506Q8—34no—
507D4—38no—
508D4—34no—
509C2×C4—31no—
510C2×C4—32no—
511C2×C4—34no—
512C2×C4—34no—
513C2×C4—31no—
514C2×C4—31no—
515C2×C4—31no—
516C2×C4—62no—
517C2×C4—92no—
518C2×C4—92no—
519C2×C4—121no—
520C2×C4—184no—
521C2×C4—362no—
522C2×C4D3×Dic612yes—
523C2×C4C4×D3211yescharacteristic
524C2×C4D3×#6712yes—
525C2×C4C22×D3211yescharacteristic
526C8—22no—
527C8—61no—
528C8—61no—
529C8—62no—
530C8—181no—
531C8—181no—
532C2×C3—22no—
533C2×C3—22no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—42no—
538C2×C3—64no—
539C2×C3C2×D3×C4⋊C411yescharacteristic
540C2×C3C2×#90711yescharacteristic
541C2×C3#574511yescharacteristic
542C2×C3D3×#13111yescharacteristic
543C2×C3#575011yescharacteristic
544C2×C3C22×Dic3⋊C411yescharacteristic
545D3—24no—
546C22—21no—
547C22—21no—
548C22—34no—
549C22—62no—
550C22—62no—
551C22D3×Dic3⋊C412yes—
552C22C2×C4×D3211yescharacteristic
553C4—34no—
554C4—32no—
555C4—61no—
556C4—61no—
557C4—61no—
558C4—182no—
559C4—182no—
560C4D3×Dic3⋊C412yes—
561C4C2×D3×Dic611yescharacteristic
562C4C2×D3×#6711yescharacteristic
563C3—21no—
564C3#7904911yescharacteristic, complemented
565C3#8378311yescharacteristic, complemented
566C2—22no—
567C2—64no—
568C2D3×#90711yescharacteristic
569C2#1059470611yescharacteristic
570C2C2×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. #10592818C2semidirect
5. C3×#5118C2semidirect
6. #10591119C2semidirect
7. C2×Dic3⋊(C3⋊C8)C2semidirect
8. #10590695C2semidirect
9. #10590694C2semidirect
10. #10590663C2semidirect
11. D3×Dic3⋊C8C2semidirect
58. #5118D3semidirect
318. C3×Dic3#131semidirect
501. Dic3#907semidirect
503. C32#2906semidirect
564. C3#79049semidirect
565. 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
Dic3×#2352
C2×#638152
#105928182
C3×#51182
#105911192
C2×Dic3⋊(C3⋊C8)2
#105906952
#105906942
#105906632
D3×Dic3⋊C82
#837833
#790493