Finite Group Databasebeta

← #11788006

Subgroups — #11788006

Order 1152.

779 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5745C211yesmaximal, characteristic, complemented
2#10595034C211yesmaximal, characteristic
3#10592825C211yesmaximal, characteristic, complemented
4#10591076C211yesmaximal, characteristic, complemented
5#10591074C211yesmaximal, characteristic, complemented
6C3×#4556C211yesmaximal, characteristic, complemented
7#10589169C211yesmaximal, characteristic, complemented
8#72029—31nomaximal
9#69036—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#907—22no—
18C3×D3×M16—22no—
19C3×#901—22no—
20#63981C412yes—
21#63962C412yes—
22#63916—21no—
23C4×#626—22no—
24#63871—21no—
25#63647—22no—
26#63560—21no—
27#63558—21no—
28#63557—22no—
29C3×#568—31no—
30#5828—31no—
31#5745D311yescharacteristic, complemented
32#5524—31no—
33#5237—31no—
34#5132—31no—
35#5126—31no—
36#5126—31no—
37#5126—31no—
38#5126—31no—
39#5126—61no—
40C3×#344—31no—
41#4556—31no—
42#4556D311yescharacteristic, complemented
43#4533—31no—
44C23×C3⋊D3C2×C411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3C2×C411yescharacteristic
47C2×C4×C3⋊D3—21no—
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—21no—
53C2×C3×#67C2×C412yes—
54C3×#235—21no—
55C3×#235—21no—
56C3×#235—21no—
57C3×#235—21no—
58C2×C3×D12D411yescharacteristic
59C2×C3×C4×D3D412yes—
60C2×C3×Dic6D411yescharacteristic
61C2×#626—22no—
62C32×M16—21no—
63C32×M16—21no—
64C2×C32×C8D412yescomplemented
65#3748—21no—
66#3748—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C3×#217C2×C412yes—
69C3×C4⋊Dic3—21no—
70C3×C4×Dic3—21no—
71C3×#208—21no—
72C3×#208—21no—
73C3×#208—21no—
74C3×#208—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8D412yescomplemented
77C3×ΓL(1,𝔽25)—24no—
78C3×D3×C8—24no—
79Dic3⋊Dic3—22no—
80#3722—22no—
81(C2×D3)⋊Dic3—22no—
82#1891—91noSylow
83C2×C3×#41—31no—
84C2×#235C2×D311yescharacteristic
85C22×C4×D3—31no—
86C22×C4×D3—31no—
87C22×C4×D3—61no—
88C3×#131—62no—
89C3×#131—62no—
90C2×C3×M16—21no—
91C2×C3×M16—31no—
92C2×C3×M16—31no—
93C2×C3×M16—62no—
94C2×C3×M16C2×D311yescharacteristic
95C2×C3×M16C2×D311yescharacteristic
96C3×#117—31no—
97#946—61no—
98#938—61no—
99#937—32no—
100#935—32no—
101C4×#67—62no—
102#926C2×D311yescharacteristic
103C2×#208—31no—
104C2×#208—31no—
105C2×#208—61no—
106C2×#208C2×D311yescharacteristic
107C2×#208C2×D311yescharacteristic
108#907—22no—
109D3×M16—22no—
110#901—22no—
111#897—61no—
112#895—61no—
113#886—32no—
114#882—32no—
115C4×D12—62no—
116#836—61no—
117#833—61no—
118#824—61no—
119#823—61no—
120(C2×D3)⋊C8—62no—
121(C2×D3)⋊C8—64no—
122(C2×D3)⋊C8—62no—
123(C2×D3)⋊C8—62no—
124(C2×D3)⋊C8—62no—
125C23×C32C22×C411yescharacteristic
126C22×C3⋊D3—21no—
127C22×C3⋊D3—21no—
128C22×C3⋊D3—21no—
129C22×C3⋊D3—42no—
130C22×C3×D3C22⋊C412yes—
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—21no—
140C4×C3⋊D3—41no—
141C4×C3⋊D3—41no—
142C4×C3⋊D3—41no—
143C4×C3⋊D3—41no—
144C3×#67—22no—
145C3×#67—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3C22⋊C412yes—
148C3×D12—21no—
149C3×D12—21no—
150C3×C4×D3—22no—
151C3×C4×D3—22no—
152C3×Dic6—21no—
153C3×Dic6—21no—
154#626—44no—
155C32×C8—22no—
156C3⋊(C3⋊C8)—41no—
157C3×C3⋊C8—22no—
158C3×C3⋊C8—41no—
159#568—31no—
160#525—91no—
161#413—91no—
162#407—91no—
163#407—91no—
164#344—31no—
165#344—91no—
166C23×D3—31no—
167C23×D3—31no—
168C23×D3—61no—
169C3×#41—61no—
170C3×#41—61no—
171C3×#41—61no—
172C3×#41—61no—
173C2×C3×Q8—31no—
174C2×C3×D4—32no—
175C2×C3×D4—31no—
176C22×C3×C4—21no—
177C22×C3×C4—32no—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C2×#67—62no—
181C2×#67C4×D312yes—
182C22×Dic3—31no—
183C22×Dic3—31no—
184C22×Dic3—61no—
185#235—21no—
186#235—21no—
187#235—21no—
188#235—21no—
189C2×D12—62no—
190C2×D12D1211yescharacteristic
191C2×C4×D3—62no—
192C2×C4×D3—62no—
193C2×C4×D3—61no—
194C2×C4×D3—61no—
195C2×C4×D3—61no—
196C2×C4×D3—61no—
197C2×C4×D3—61no—
198C2×C4×D3—61no—
199C2×C4×D3—61no—
200C2×C4×D3—61no—
201C2×C4×D3—61no—
202C2×C4×D3—61no—
203C2×C4×D3—61no—
204C2×C4×D3—61no—
205C2×C4×D3—121no—
206C2×C4×D3—121no—
207C2×C4×D3—121no—
208C2×C4×D3—121no—
209C2×C4×D3#6712yes—
210C2×Dic6D1211yescharacteristic
211C3×M16—21no—
212C3×M16—21no—
213C3×M16—21no—
214C3×M16—21no—
215C3×M16—41no—
216C3×M16—41no—
217C3×M16—64no—
218C3×M16—61no—
219C3×M16—61no—
220C3×M16—61no—
221C3×M16—61no—
222C2×C3×C8—22no—
223C2×C3×C8—32no—
224C2×C3×C8—64no—
225C2×C3×C8—61no—
226C2×C3×C8D1212yescomplemented
227C2×C3×C8#6712yescomplemented
228C3×C4⋊C4—61no—
229C3×C22⋊C4—32no—
230C3×C42—61no—
231#217—62no—
232#217C4×D312yes—
233(C2×D3)⋊C4—62no—
234(C2×D3)⋊C4—62no—
235(C2×D3)⋊C4—62no—
236C4⋊Dic3—21no—
237C4⋊Dic3—62no—
238Dic3⋊C4—62no—
239C4×Dic3—21no—
240#208—21no—
241#208—21no—
242#208—21no—
243#208—21no—
244#208—61no—
245#208—61no—
246#208—61no—
247#208—61no—
248#208—121no—
249#208—121no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—62no—
252C2×C3⋊C8—61no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8#6712yescomplemented
255ΓL(1,𝔽25)—24no—
256D3×C8—24no—
257C22×C32—41no—
258C22×C32C2×C22⋊C411yescharacteristic
259C22×C32C4×D411yescharacteristic
260C22×C32C4×D411yescharacteristic
261C2×C3⋊D3—22no—
262C2×C3⋊D3—22no—
263C2×C3⋊D3—22no—
264C2×C3⋊D3—41no—
265C2×C3⋊D3—41no—
266C2×C3⋊D3—41no—
267C2×C3⋊D3—41no—
268C2×C3×D3—22no—
269C2×C3×D3—42no—
270C32×C4#12011yescharacteristic
271C32×C4#12111yescharacteristic
272C32×C4#12111yescharacteristic
273C32×C4#12311yescharacteristic
274C3⋊Dic3—41no—
275C3×Dic3—22no—
276C3×Dic3—42no—
277C2×#41—31no—
278C23×C4—91no—
279#131—62no—
280#131—62no—
281C2×M16—31no—
282C2×M16—31no—
283C2×M16—62no—
284C2×M16—91no—
285C2×M16D3211yescharacteristic
286#123—92no—
287C22⋊Q8—181no—
288#121—181no—
289#120—92no—
290C4×D4—182no—
291#117—31no—
292#101—181no—
293#100—181no—
294C22⋊C8—182no—
295C22⋊C8—182no—
296C23×C3—21no—
297C23×C3—32no—
298C23×C3C2×C4×D311yescharacteristic
299C23×C3C2×C4×D311yescharacteristic
300C22×D3—62no—
301C22×D3—61no—
302C22×D3—61no—
303C22×D3—61no—
304C22×D3—61no—
305C22×D3—61no—
306C22×D3—61no—
307C22×D3—121no—
308C22×D3—121no—
309C22×D3—122no—
310C22×D3—122no—
311C22×D3—124no—
312C22×D3(C2×D3)⋊C412yes—
313C3×Q8—61no—
314C3×Q8—61no—
315C3×D4—62no—
316C3×D4—62no—
317C3×D4—61no—
318C3×D4—61no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—32no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4C2×D1211yescharacteristic
330C2×C3×C4C2×D1211yescharacteristic
331C2×C3×C4#23511yescharacteristic
332C2×C3×C4#23511yescharacteristic
333C2×C3×C4#23511yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4#23911yescharacteristic
338C2×C3×C4C2×#6711yescharacteristic
339C2×C3×C4C2×#6711yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341#67—22no—
342#67—22no—
343#67—124no—
344C2×Dic3—22no—
345C2×Dic3—62no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—121no—
353C2×Dic3—121no—
354C2×Dic3(C2×D3)⋊C412yes—
355D12—21no—
356D12—21no—
357D12—124no—
358C4×D3—22no—
359C4×D3—22no—
360C4×D3—122no—
361C4×D3—122no—
362C4×D3—122no—
363C4×D3—122no—
364C4×D3—121no—
365C4×D3—121no—
366C4×D3—121no—
367C4×D3—121no—
368C4×D3—121no—
369C4×D3—121no—
370C4×D3—121no—
371C4×D3—121no—
372Dic6—21no—
373Dic6—21no—
374C3×C8—22no—
375C3×C8—22no—
376C3×C8—42no—
377C3×C8—62no—
378C3×C8—121no—
379C3⋊C8—22no—
380C3⋊C8—41no—
381C3⋊C8—122no—
382C3⋊C8—121no—
383C3⋊C8—121no—
384C2×C32—21no—
385C2×C32—21no—
386C2×C32—21no—
387C2×C32#38611yescharacteristic
388C3⋊D3—42no—
389C3×D3—42no—
390C24—91no—
391#41—61no—
392#41—61no—
393#41—61no—
394#41—61no—
395C2×Q8—31no—
396C2×D4—32no—
397C2×D4—31no—
398C2×D4—182no—
399C22×C4—32no—
400C22×C4—91no—
401C22×C4—181no—
402C22×C4—181no—
403C22×C4—181no—
404C22×C4—181no—
405C22×C4—181no—
406C22×C4—181no—
407C22×C4C2×D3211yescharacteristic
408M16—21no—
409M16—21no—
410M16—64no—
411M16—61no—
412M16—61no—
413M16—61no—
414M16—61no—
415M16—181no—
416M16—181no—
417C2×C8—32no—
418C2×C8—64no—
419C2×C8—61no—
420C2×C8—181no—
421C2×C8#62612yescomplemented
422C4⋊C4—61no—
423C4⋊C4—182no—
424C22⋊C4—32no—
425C22⋊C4—182no—
426C22⋊C4—182no—
427C42—61no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3—42no—
434C22×C3—62no—
435C22×C3—122no—
436C22×C3C4×D1211yescharacteristic
437C22×C3D3×C22⋊C411yescharacteristic
438C22×C3#89311yescharacteristic
439C22×C3C2×(C2×D3)⋊C411yescharacteristic
440C22×C3C4×#6711yescharacteristic
441C22×C3C4×#6711yescharacteristic
442C2×D3—22no—
443C2×D3—42no—
444C2×D3—62no—
445C2×D3—62no—
446C2×D3—64no—
447C2×D3—62no—
448C2×D3—62no—
449C2×D3—62no—
450C2×D3—62no—
451C2×D3—122no—
452C2×D3—122no—
453C2×D3—122no—
454C2×D3—122no—
455C2×D3—121no—
456C2×D3—121no—
457C2×D3—121no—
458C2×D3—121no—
459C2×D3—121no—
460C2×D3—121no—
461C2×D3—122no—
462C2×D3—122no—
463C2×D3—121no—
464C2×D3—121no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—62no—
470C3×C4—122no—
471C3×C4#88211yescharacteristic
472C3×C4#88411yescharacteristic
473C3×C4#89411yescharacteristic
474C3×C4#89511yescharacteristic
475C3×C4#92911yescharacteristic
476C3×C4#93011yescharacteristic
477C3×C4#93011yescharacteristic
478C3×C4#95311yescharacteristic
479Dic3—22no—
480Dic3—42no—
481Dic3—122no—
482Dic3—121no—
483Dic3—121no—
484C32#189111yescharacteristic, complemented, Sylow
485C23—32no—
486C23—181no—
487C23—181no—
488C23—181no—
489C23—362no—
490C23C4×D3211yescharacteristic
491Q8—61no—
492Q8—61no—
493D4—62no—
494D4—62no—
495D4—61no—
496D4—61no—
497D4—364no—
498C2×C4—32no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—181no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—361no—
506C2×C4—361no—
507C2×C4—361no—
508C2×C4—361no—
509C2×C4#379811yescharacteristic
510C2×C4#379911yescharacteristic
511C2×C4D3×D1211yescharacteristic
512C2×C4C2×#62611yescharacteristic
513C2×C4D3×#6711yescharacteristic
514C2×C4D3×#6711yescharacteristic
515C8—22no—
516C8—62no—
517C8—121no—
518C8—361no—
519C2×C3—22no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—41no—
528C2×C3—41no—
529C2×C3—122no—
530C2×C3#466511yescharacteristic
531C2×C3#521311yescharacteristic
532D3—42no—
533D3—124no—
534D3—122no—
535D3—122no—
536C22—41no—
537C22—62no—
538C22—122no—
539C22—182no—
540C22—182no—
541C22—182no—
542C22—361no—
543C22—361no—
544C22—361no—
545C22—361no—
546C22C4×#62611yescharacteristic
547C22#6390411yescharacteristic
548C22D3×(C2×D3)⋊C411yescharacteristic
549C4—62no—
550C4—122no—
551C4—361no—
552C4#6385011yescharacteristic
553C4#6390611yescharacteristic
554C4#6390911yescharacteristic
555C4#6397711yescharacteristic
556C3—21no—
557C3#6903611yescharacteristic, complemented
558C3#7202911yescharacteristic, complemented
559C2—21no—
560C2—21no—
561C2—21no—
562C2—122no—
563C2—362no—
564C2#1059138211yescharacteristic
subgroupG/H
centerC4#63977
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#386
prime radical#10595034C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1891
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C3×#5745C2semidirect
3. #10592825C2semidirect
4. #10591076C2semidirect
5. #10591074C2semidirect
6. C3×#4556C2semidirect
7. #10589169C2semidirect
31. #5745D3semidirect
42. #4556D3semidirect
64. C2×C32×C8D4semidirect
76. C2×C3×C3⋊C8D4semidirect
226. C2×C3×C8D12semidirect
227. C2×C3×C8#67semidirect
254. C2×C3⋊C8#67semidirect
421. C2×C8#626semidirect
484. C32#1891semidirect
557. C3#69036semidirect
558. C3#72029semidirect

Maximal subgroups

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

subgroupindex
C3×#57452
#105950342
#105928252
#105910762
#105910742
C3×#45562
#105891692
#720293
#690363