Finite Group Databasebeta

← #11858358

Subgroups — #11858358

Order 1152.

1101 conjugacy classes of subgroups.

The subgroup lattice has 585 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64116C211yesmaximal, characteristic
2#10594954C211yesmaximal, characteristic
3C2×#63817C211yesmaximal, characteristic
4C3×#5119C211yesmaximal, characteristic, complemented
5C3×#5118C211yesmaximal, characteristic, complemented
6#10591117C211yesmaximal, characteristic, complemented
7C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590702C212yesmaximal, complemented
9#10590701C212yesmaximal, complemented
10#10590666C212yesmaximal, complemented
11#10590658C212yesmaximal, complemented
12#79081—31nomaximal
13#79049—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17#64116—24no—
18C2×#3743C2212yes—
19C2×C8×C3⋊D3C2212yes—
20C3×#926C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24#63952C412yes—
25#63952C412yes—
26#63894C411yescharacteristic
27#63894C411yescharacteristic
28C4×#624C2212yes—
29#63874C2212yes—
30#63844C411yescharacteristic
31#63844C411yescharacteristic
32C2×#3712C2212yes—
33#63817—24no—
34C2×#3710C2212yes—
35C3×Dic3⋊C8C2212yes—
36C3×Dic3⋊C8C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×Dic3⋊C8C2212yes—
39Dic3⋊(C3⋊C8)C2211yescharacteristic
40Dic3⋊(C3⋊C8)C2211yescharacteristic
41Dic3⋊(C3⋊C8)C2211yescharacteristic
42Dic3⋊(C3⋊C8)C2211yescharacteristic
43Dic3⋊(C3⋊C8)C2212yes—
44Dic3⋊(C3⋊C8)C2212yes—
45C2×#907—31no—
46C2×#907—31no—
47C2×#907—31no—
48C2×#907—61no—
49C2×#901—31no—
50#5522—31no—
51C4×#235—31no—
52C3×#424—31no—
53C3×#423—31no—
54#5119—31no—
55#5119D311yescharacteristic, complemented
56#5118D311yescharacteristic, complemented
57C2×Dic3⋊C8—31no—
58#4999—31no—
59C2×C4⋊(C3⋊C8)—31no—
60#4839—32no—
61#4839—32no—
62#4839—32no—
63#4839—32no—
64#4837—32no—
65#4837—32no—
66D3×C4⋊C8—32no—
67D3×C4⋊C8—32no—
68C22×C32×C4C2311yescharacteristic
69C2×#638C2×C412yes—
70#3828D414yes—
71#3828Q814yes—
72C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
73C2×C4×C3⋊D3C2312yes—
74C2×#634C2×C411yescharacteristic
75C22×C3×Dic3C2×C411yescharacteristic
76C22×C3×Dic3C2×C411yescharacteristic
77C2×#624C2×C412yes—
78C2×#624C2×C412yes—
79C32×M16—22no—
80C2×C32×C8C2312yes—
81C2×C3⋊(C3⋊C8)—22no—
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84#3743—24no—
85C8×C3⋊D3—24no—
86C3×#217C2×C412yes—
87C3×C4⋊Dic3C2×C411yescharacteristic
88C3×C4⋊Dic3C2×C411yescharacteristic
89C3×C4×Dic3C2×C411yescharacteristic
90C3×C4×Dic3C2×C411yescharacteristic
91C3×C4×Dic3C2311yescharacteristic
92C3×C4×Dic3C2311yescharacteristic
93C3×C4×Dic3C2312yes—
94C3×#208—22no—
95C2×C3×C3⋊C8—22no—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2312yes—
99#3724C2×C412yes—
100#3724C2×C412yes—
101#3722C2×C412yes—
102#3722C2×C412yes—
103Dic32C2×C412yes—
104Dic32C2×C412yes—
105#3712—24no—
106#3710—24no—
107#2906—91noSylow
108C2×#235—31no—
109C2×#235—31no—
110C2×#235—61no—
111C2×C3×M16—21no—
112C2×C3×M16—31no—
113C2×C3×M16C2×D311yescharacteristic
114C2×C3×M16C2×D311yescharacteristic
115C22×C3×C8—31no—
116C3×#117—31no—
117C2×C3×C42—31no—
118C4×#67—32no—
119C4×#67—32no—
120#926C2×D311yescharacteristic
121C2×C4×Dic3C2×D311yescharacteristic
122C2×#208C2×D311yescharacteristic
123C22×C3⋊C8—31no—
124C22×C3⋊C8—31no—
125C22×C3⋊C8—61no—
126C22×C3⋊C8C2×D311yescharacteristic
127#907—64no—
128#907—64no—
129#907—64no—
130#907—68no—
131#901—64no—
132C2×ΓL(1,𝔽25)—32no—
133C2×ΓL(1,𝔽25)—32no—
134C2×ΓL(1,𝔽25)—32no—
135C2×ΓL(1,𝔽25)—32no—
136C2×ΓL(1,𝔽25)—62no—
137C2×D3×C8—32no—
138C2×D3×C8—32no—
139C2×D3×C8—32no—
140C2×D3×C8—32no—
141C2×D3×C8—62no—
142#893—31no—
143#893—31no—
144#887—31no—
145#887—31no—
146#67⋊C4—32no—
147#67⋊C4—32no—
148C4×D12—31no—
149C4×D12—31no—
150#872—32no—
151#872—32no—
152C42×D3—32no—
153C42×D3—32no—
154C4×Dic6—31no—
155C4×Dic6—31no—
156C3×C4⋊C8—32no—
157C3×C4⋊C8—32no—
158C3×C4⋊C8—32no—
159C3×C4⋊C8—32no—
160Dic3⋊C8—31no—
161Dic3⋊C8—32no—
162Dic3⋊C8—31no—
163Dic3⋊C8—32no—
164Dic3⋊C8—31no—
165Dic3⋊C8—31no—
166Dic3⋊C8C2×D312yes—
167Dic3⋊C8C2×D312yes—
168Dic3⋊C8C2×D312yes—
169Dic3⋊C8C2×D312yes—
170C4⋊(C3⋊C8)—31no—
171C4⋊(C3⋊C8)—31no—
172C4⋊(C3⋊C8)—31no—
173C4⋊(C3⋊C8)—31no—
174C4⋊(C3⋊C8)—32no—
175C4⋊(C3⋊C8)—32no—
176C23×C32C22×C411yescharacteristic
177C22×C3⋊D3C22×C412yes—
178C2×C32×C4C22×C411yescharacteristic
179C2×C32×C4C2×D412yes—
180C2×C32×C4C2×Q812yes—
181C2×C32×C4C2411yescharacteristic
182#638C4⋊C418yes—
183C2×C3⋊Dic3C22×C412yes—
184C4⋊(C3⋊D3)C4⋊C414yes—
185C4×C3⋊D3C2×D414yes—
186C4×C3⋊D3C2×Q814yes—
187#634C4⋊C414yes—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—41no—
190C2×C3×Dic3C22×C411yescharacteristic
191C2×C3×Dic3C22×C412yes—
192C2×C3×Dic3C22×C412yes—
193C2×C3×Dic3C22×C411yescharacteristic
194C2×C3×Dic3C22×C411yescharacteristic
195C2×C3×Dic3C22×C411yescharacteristic
196#624—24no—
197#624—42no—
198C32×C8—22no—
199C3⋊(C3⋊C8)—21no—
200C3⋊(C3⋊C8)—21no—
201C3×C3⋊C8—21no—
202C3×C3⋊C8—22no—
203C3×C3⋊C8—21no—
204C2×#131—91no—
205C2×#131—91no—
206C4×#41—91no—
207#424—31no—
208#424—92no—
209#424—92no—
210#424—91no—
211#423—31no—
212#423—92no—
213C2×C4⋊C8—92no—
214C2×C4⋊C8—91no—
215C22×C3×C4—21no—
216C22×C3×C4—31no—
217C22×C3×C4—31no—
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C2×#67—32no—
221C2×#67—32no—
222C2×#67—62no—
223C22×Dic3C4×D311yescharacteristic
224C22×Dic3C4×D311yescharacteristic
225#235—34no—
226#235—34no—
227#235—34no—
228#235—34no—
229#235—64no—
230#235—64no—
231C2×D12—31no—
232C2×D12—31no—
233C2×D12—61no—
234C2×C4×D3—32no—
235C2×C4×D3—32no—
236C2×C4×D3—32no—
237C2×C4×D3—32no—
238C2×C4×D3—32no—
239C2×C4×D3—32no—
240C2×C4×D3—62no—
241C2×Dic6—31no—
242C2×Dic6—31no—
243C2×Dic6—61no—
244C3×M16—24no—
245C3×M16—22no—
246C3×M16—22no—
247C3×M16—62no—
248C2×C3×C8—22no—
249C2×C3×C8—31no—
250C2×C3×C8—32no—
251C2×C3×C8—31no—
252C2×C3×C8—62no—
253C2×C3×C8C22×D312yes—
254C2×C3×C8C22×D312yes—
255C3×C4⋊C4—31no—
256C3×C4⋊C4—31no—
257C3×C22⋊C4—32no—
258C3×C42—31no—
259C3×C42—31no—
260C3×C42—31no—
261C3×C42—32no—
262C3×C42—31no—
263#217C4×D312yes—
264(C2×D3)⋊C4—32no—
265(C2×D3)⋊C4—32no—
266(C2×D3)⋊C4—32no—
267(C2×D3)⋊C4—32no—
268C4⋊Dic3C4×D311yescharacteristic
269C4⋊Dic3C4×D311yescharacteristic
270Dic3⋊C4—32no—
271Dic3⋊C4—32no—
272Dic3⋊C4—32no—
273Dic3⋊C4—32no—
274C4×Dic3—32no—
275C4×Dic3—32no—
276C4×Dic3—32no—
277C4×Dic3—32no—
278C4×Dic3C4×D311yescharacteristic
279C4×Dic3C4×D311yescharacteristic
280C4×Dic3C22×D311yescharacteristic
281C4×Dic3C22×D312yes—
282C4×Dic3C22×D311yescharacteristic
283#208—22no—
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⋊C8C22×D311yescharacteristic
295C2×C3⋊C8C22×D312yes—
296C2×C3⋊C8C22×D311yescharacteristic
297ΓL(1,𝔽25)—64no—
298ΓL(1,𝔽25)—64no—
299ΓL(1,𝔽25)—64no—
300ΓL(1,𝔽25)—64no—
301ΓL(1,𝔽25)—68no—
302D3×C8—64no—
303D3×C8—64no—
304D3×C8—64no—
305D3×C8—64no—
306D3×C8—68no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32C2×C4⋊C412yes—
310C22×C32C23×C411yescharacteristic
311C2×C3⋊D3—22no—
312C2×C3⋊D3—22no—
313C2×C3⋊D3C2×C4⋊C414yes—
314C32×C4C2×C4⋊C412yes—
315C32×C4C22×D411yescharacteristic
316C32×C4C22×Q811yescharacteristic
317C3⋊Dic3C2×C4⋊C414yes—
318C3×Dic3—22no—
319C3×Dic3—21no—
320C3×Dic3—21no—
321C3×Dic3—22no—
322C3×Dic3—21no—
323C3×Dic3#13112yescomplemented
324C2×#41—91no—
325#131—184no—
326#131—184no—
327C2×M16—31no—
328C2×M16—92no—
329C2×M16—92no—
330C2×M16D3211yescharacteristic
331C22×C8—31no—
332C22×C8—92no—
333C22×C8—91no—
334C22×C8—92no—
335C4×Q8—91no—
336C4×Q8—91no—
337C4×D4—91no—
338C4×D4—91no—
339C4×D4—92no—
340C4×D4—92no—
341#117—31no—
342#117—92no—
343C2×C42—31no—
344C2×C42—92no—
345C4⋊C8—32no—
346C4⋊C8—32no—
347C4⋊C8—32no—
348C4⋊C8—32no—
349C4⋊C8—91no—
350C4⋊C8—91no—
351C4⋊C8—91no—
352C4⋊C8—91no—
353C4⋊C8—92no—
354C4⋊C8—92no—
355C23×C3—21no—
356C23×C3C2×C4×D311yescharacteristic
357C23×C3C2×C4×D311yescharacteristic
358C22×D3—32no—
359C22×D3—32no—
360C22×D3—62no—
361C2×C3×C4—21no—
362C2×C3×C4—22no—
363C2×C3×C4—21no—
364C2×C3×C4—22no—
365C2×C3×C4—31no—
366C2×C3×C4—31no—
367C2×C3×C4—32no—
368C2×C3×C4—32no—
369C2×C3×C4—31no—
370C2×C3×C4—31no—
371C2×C3×C4—62no—
372C2×C3×C4—121no—
373C2×C3×C4C2×C4×D311yescharacteristic
374C2×C3×C4C2×C4×D311yescharacteristic
375C2×C3×C4D3×D412yes—
376C2×C3×C4D3×D412yes—
377C2×C3×C4D3×Q812yes—
378C2×C3×C4D3×Q812yes—
379C2×C3×C4C23×D311yescharacteristic
380C2×C3×C4C23×D311yescharacteristic
381#67—38no—
382#67—38no—
383#67—68no—
384C2×Dic3—22no—
385C2×Dic3—32no—
386C2×Dic3—32no—
387C2×Dic3—41no—
388C2×Dic3—62no—
389C2×Dic3C2×C4×D311yescharacteristic
390C2×Dic3C2×C4×D312yes—
391C2×Dic3C2×C4×D312yes—
392C2×Dic3C2×C4×D311yescharacteristic
393C2×Dic3C2×C4×D311yescharacteristic
394C2×Dic3C2×C4×D311yescharacteristic
395D12—34no—
396D12—34no—
397D12—64no—
398C4×D3—34no—
399C4×D3—34no—
400C4×D3—34no—
401C4×D3—34no—
402C4×D3—64no—
403C4×D3—64no—
404C4×D3—64no—
405C4×D3—64no—
406C4×D3—122no—
407C4×D3—122no—
408Dic6—34no—
409Dic6—34no—
410Dic6—64no—
411C3×C8—24no—
412C3×C8—22no—
413C3×C8—22no—
414C3×C8—61no—
415C3×C8—62no—
416C3×C8—61no—
417C3⋊C8—21no—
418C3⋊C8—22no—
419C3⋊C8—21no—
420C3⋊C8—62no—
421C3⋊C8—62no—
422C3⋊C8—61no—
423C3⋊C8—61no—
424C3⋊C8—61no—
425C3⋊C8—61no—
426C2×C32—22no—
427C2×C32C22×C4⋊C411yescharacteristic
428C2×C32C2×#13111yescharacteristic
429C2×C32#56811yescharacteristic
430C3⋊D3—24no—
431#41—94no—
432#41—94no—
433C2×Q8—91no—
434C2×D4—92no—
435C2×D4—91no—
436C22×C4—31no—
437C22×C4—31no—
438C22×C4—92no—
439C22×C4—92no—
440C22×C4—92no—
441C22×C4C2×D3211yescharacteristic
442M16—22no—
443M16—62no—
444M16—184no—
445M16—184no—
446C2×C8—31no—
447C2×C8—31no—
448C2×C8—32no—
449C2×C8—62no—
450C2×C8—91no—
451C2×C8—91no—
452C2×C8—184no—
453C2×C8—184no—
454C2×C8—182no—
455C2×C8C2×D3212yes—
456C4⋊C4—31no—
457C4⋊C4—31no—
458C4⋊C4—92no—
459C4⋊C4—92no—
460C22⋊C4—32no—
461C22⋊C4—92no—
462C22⋊C4—92no—
463C42—31no—
464C42—31no—
465C42—32no—
466C42—31no—
467C42—31no—
468C42—92no—
469C42—92no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—22no—
476C22×C3—41no—
477C22×C3—41no—
478C22×C3D3×C4⋊C412yes—
479C22×C3D3×C4⋊C412yes—
480C22×C3C22×C4×D311yescharacteristic
481C22×C3C22×C4×D311yescharacteristic
482C2×D3—34no—
483C2×D3—34no—
484C2×D3—64no—
485C2×D3—62no—
486C2×D3—62no—
487C2×D3—62no—
488C2×D3—62no—
489C2×D3—122no—
490C2×D3—122no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—22no—
494C3×C4—32no—
495C3×C4—62no—
496C3×C4—62no—
497C3×C4—61no—
498C3×C4—61no—
499C3×C4—61no—
500C3×C4D3×C4⋊C412yes—
501C3×C4D3×C4⋊C412yes—
502C3×C4C2×D3×D411yescharacteristic
503C3×C4C2×D3×D411yescharacteristic
504C3×C4C2×D3×Q811yescharacteristic
505C3×C4C2×D3×Q811yescharacteristic
506Dic3—21no—
507Dic3—21no—
508Dic3—21no—
509Dic3—22no—
510Dic3—22no—
511Dic3—34no—
512Dic3—34no—
513Dic3—64no—
514Dic3#90712yescomplemented
515C32#290611yescharacteristic, complemented, Sylow
516C23—92no—
517C23C4×D3211yescharacteristic
518Q8—94no—
519D4—98no—
520D4—94no—
521C2×C4—31no—
522C2×C4—31no—
523C2×C4—31no—
524C2×C4—31no—
525C2×C4—32no—
526C2×C4—32no—
527C2×C4—62no—
528C2×C4—92no—
529C2×C4—94no—
530C2×C4—94no—
531C2×C4—121no—
532C2×C4—184no—
533C2×C4—362no—
534C2×C4#379712yes—
535C2×C4C4×D3211yescharacteristic
536C2×C4#381112yes—
537C2×C4C22×D3211yescharacteristic
538C8—22no—
539C8—61no—
540C8—61no—
541C8—62no—
542C8—181no—
543C8—181no—
544C2×C3—22no—
545C2×C3—22no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—42no—
550C2×C3C2×D3×C4⋊C411yescharacteristic
551C2×C3C2×D3×C4⋊C411yescharacteristic
552C2×C3C2×#90711yescharacteristic
553C2×C3#574511yescharacteristic
554C2×C3D3×#13111yescharacteristic
555C2×C3#575011yescharacteristic
556D3—64no—
557D3—64no—
558D3—124no—
559C22—21no—
560C22—21no—
561C22—94no—
562C22—182no—
563C22—182no—
564C22#6388312yes—
565C22C2×C4×D3211yescharacteristic
566C4—32no—
567C4—61no—
568C4—62no—
569C4—61no—
570C4—61no—
571C4—62no—
572C4—94no—
573C4#6388312yes—
574C4C2×#379711yescharacteristic
575C4C2×#381111yescharacteristic
576C3—21no—
577C3#7904911yescharacteristic, complemented
578C3#7908111yescharacteristic, complemented
579C2—22no—
580C2—184no—
581C2D3×#90711yescharacteristic
582C2#1059470611yescharacteristic
583C2C2×#6388311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×M16C22
prime radicalC2×#3828C22
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. C3×#5119C2semidirect
5. C3×#5118C2semidirect
6. #10591117C2semidirect
7. C2×Dic3⋊(C3⋊C8)C2semidirect
8. #10590702C2semidirect
9. #10590701C2semidirect
10. #10590666C2semidirect
11. #10590658C2semidirect
55. #5119D3semidirect
56. #5118D3semidirect
323. C3×Dic3#131semidirect
514. Dic3#907semidirect
515. C32#2906semidirect
577. C3#79049semidirect
578. C3#79081semidirect

Maximal subgroups

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

subgroupindex
C2×#641162
#105949542
C2×#638172
C3×#51192
C3×#51182
#105911172
C2×Dic3⋊(C3⋊C8)2
#105907022
#105907012
#105906662
#105906582
#790813
#790493