Finite Group Databasebeta

← #11859541

Subgroups — #11859541

Order 1152.

1041 conjugacy classes of subgroups.

The subgroup lattice has 541 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63805C211yesmaximal, characteristic, complemented
2C2×#63803C211yesmaximal, characteristic, complemented
3#10593972C211yesmaximal, characteristic
4C3⋊D3×#97C211yesmaximal, characteristic, complemented
5C3×#4706C212yesmaximal, complemented
6#10590958C211yesmaximal, characteristic, complemented
7#10590958C211yesmaximal, characteristic, complemented
8#10590725C212yesmaximal, complemented
9#10590722C212yesmaximal, complemented
10#10590340C211yesmaximal, characteristic, complemented
11#10590330C212yesmaximal, complemented
12#79480—32nomaximal
13C2×#3798C2211yescharacteristic
14C2×#3798C2211yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17C42×C3⋊D3C2211yescharacteristic
18C2×C3×ΓL(1,𝔽25)C2212yes—
19C2×C3×D3×C8C2212yes—
20C3×C4×D12C2212yes—
21#63919C411yescharacteristic
22#63916C412yes—
23#63915C411yescharacteristic
24#63915C411yescharacteristic
25#63914C411yescharacteristic
26#63912C412yes—
27C4×#625C2212yes—
28C2×#3712C2211yescharacteristic
29C2×#3712C2211yescharacteristic
30C2×#3711C2212yes—
31C2×D3×C3⋊C8C2212yes—
32#63805—24no—
33#63803—24no—
34C32×#97C2211yescharacteristic
35#63642C2211yescharacteristic
36#63642C2211yescharacteristic
37#63630C2211yescharacteristic
38C3×(C2×D3)⋊C8C2212yes—
39C3×(C2×D3)⋊C8C2212yes—
40C3×C4⋊(C3⋊C8)C2212yes—
41#63572C2212yes—
42(C2×D3)⋊(C3⋊C8)C2212yes—
43(C2×D3)⋊(C3⋊C8)C2212yes—
44C2×#907—32no—
45C2×#901—32no—
46#5548—32no—
47C3×#435—32no—
48#5127—32no—
49#5111—32no—
50#5011—32no—
51#4837—32no—
52#4836—32no—
53#4730—32no—
54#4728—32no—
55#4727—32no—
56#4727—32no—
57#4706D312yescomplemented
58D3×#97—32no—
59D3×#97—61no—
60C2×C4×C3⋊D3C2×C411yescharacteristic
61C2×C4×C3⋊D3C2×C411yescharacteristic
62C2×C4×C3⋊D3C2311yescharacteristic
63C2×C3×D12C2×C412yes—
64C2×C3×C4×D3C2312yes—
65C2×C3×C4×D3C2312yes—
66C2×#627C2×C411yescharacteristic
67C2×#627C2×C411yescharacteristic
68C2×#626C2×C412yes—
69C2×#626C2×C412yes—
70C2×#625C2×C411yescharacteristic
71C2×#625C2×C411yescharacteristic
72C2×#625C2×C412yes—
73#3798—22no—
74#3798—22no—
75#3798—22no—
76#3798—22no—
77C2×C32×C8C2311yescharacteristic
78C2×C32×C8C2311yescharacteristic
79C32×C42C2311yescharacteristic
80C4×C3⋊Dic3C2×C411yescharacteristic
81C4×C3⋊Dic3C2×C411yescharacteristic
82C4×C3⋊Dic3C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C8×C3⋊D3—22no—
86C8×C3⋊D3D414yescomplemented
87C3×(C2×D3)⋊C4C2×C412yes—
88C3×(C2×D3)⋊C4C2×C412yes—
89C3×C4⋊Dic3C2×C412yes—
90C2×C3×C3⋊C8C2312yes—
91C2×C3×C3⋊C8C2312yes—
92C3×ΓL(1,𝔽25)—24no—
93C3×D3×C8—24no—
94#3724C2×C412yes—
95(C2×D3)⋊Dic3C2×C412yes—
96(C2×D3)⋊Dic3C2×C412yes—
97#3712—22no—
98#3712—22no—
99#3711—24no—
100D3×C3⋊C8—24no—
101#2932—91noSylow
102C2×#235—32no—
103C2×#235—32no—
104C2×C3×M16—32no—
105C22×C3×C8—32no—
106C3×C4×D4—32no—
107#940—32no—
108#938—32no—
109C4×#67—32no—
110C4×#67—32no—
111C2×#208—32no—
112C22×C3⋊C8—32no—
113#907—68no—
114#901—68no—
115C2×ΓL(1,𝔽25)—32no—
116C2×ΓL(1,𝔽25)—32no—
117C2×ΓL(1,𝔽25)—32no—
118C2×ΓL(1,𝔽25)C2×D312yes—
119C2×D3×C8—32no—
120C2×D3×C8—32no—
121C2×D3×C8—32no—
122C2×D3×C8—61no—
123C2×D3×C8—61no—
124C2×D3×C8C2×D312yes—
125#895—32no—
126#888—32no—
127#885—32no—
128#885—32no—
129#884—32no—
130#884—32no—
131C4×D12C2×D312yes—
132C42×D3—32no—
133C42×D3—61no—
134C3×C4⋊C8—32no—
135C3×C22⋊C8—32no—
136C3×C22⋊C8—32no—
137C3×#97—21no—
138C3×#97C2×D312yes—
139#830—32no—
140#830—32no—
141(C2×D3)⋊C8—32no—
142(C2×D3)⋊C8—32no—
143(C2×D3)⋊C8C2×D312yes—
144(C2×D3)⋊C8C2×D312yes—
145#815—32no—
146#815—32no—
147#815—61no—
148#815—61no—
149Dic3⋊C8—32no—
150Dic3⋊C8—32no—
151C4⋊(C3⋊C8)C2×D312yes—
152#803—32no—
153#803—61no—
154C22×C3⋊D3C22×C411yescharacteristic
155C22×C3×D3C22×C412yes—
156C22×C3×D3C22×C412yes—
157C2×C32×C4C22×C411yescharacteristic
158C2×C32×C4C22×C411yescharacteristic
159C2×C32×C4C2411yescharacteristic
160C2×C3⋊Dic3C22×C411yescharacteristic
161C2×C3⋊Dic3C22×C411yescharacteristic
162C2×C3⋊Dic3C22×C411yescharacteristic
163C4×C3⋊D3—41no—
164C4×C3⋊D3—41no—
165C4×C3⋊D3C2×D412yes—
166C4×C3⋊D3#4112yes—
167C2×C3×Dic3C22×C412yes—
168C2×C3×Dic3C22×C412yes—
169C3×D12—42no—
170C3×C4×D3—22no—
171C3×C4×D3—22no—
172C3×C4×D3—22no—
173C3×C4×D3—22no—
174#627—22no—
175#627—22no—
176#626—24no—
177#626—24no—
178#625—22no—
179#625—22no—
180#625—42no—
181C32×C8—21no—
182C32×C8C2×D412yes—
183C3⋊(C3⋊C8)—21no—
184C3⋊(C3⋊C8)C2×D412yes—
185C3×C3⋊C8—22no—
186C3×C3⋊C8—22no—
187C2×#131—91no—
188C2×#131—91no—
189#532—91no—
190#435—32no—
191#435—92no—
192#435—92no—
193#435—92no—
194#423—91no—
195#408—91no—
196#408—91no—
197C2×#97—91no—
198C2×C3×D4—32no—
199C22×C3×C4—32no—
200C22×C3×C4—32no—
201C2×#67—32no—
202C2×#67—32no—
203C2×#67—32no—
204C2×#67—32no—
205C2×#67—32no—
206C2×#67—32no—
207#235—64no—
208#235—64no—
209#235—64no—
210#235—64no—
211C2×D12—32no—
212C2×D12—32no—
213C2×D12C4×D312yes—
214C2×C4×D3—32no—
215C2×C4×D3—32no—
216C2×C4×D3—32no—
217C2×C4×D3—61no—
218C2×C4×D3—61no—
219C2×C4×D3—61no—
220C2×C4×D3C22×D312yes—
221C2×C4×D3C22×D312yes—
222C2×Dic6—32no—
223C2×Dic6—32no—
224C3×M16—64no—
225C2×C3×C8—21no—
226C2×C3×C8—21no—
227C2×C3×C8—32no—
228C2×C3×C8—32no—
229C2×C3×C8—64no—
230C2×C3×C8C22×D312yes—
231C2×C3×C8C22×D312yes—
232C3×C4⋊C4—32no—
233C3×C22⋊C4—32no—
234C3×C22⋊C4—32no—
235C3×C42—21no—
236C3×C42C22×D312yes—
237#217—32no—
238#217—32no—
239(C2×D3)⋊C4—32no—
240(C2×D3)⋊C4—32no—
241(C2×D3)⋊C4C4×D312yes—
242(C2×D3)⋊C4C4×D312yes—
243C4⋊Dic3C4×D312yes—
244Dic3⋊C4—32no—
245Dic3⋊C4—32no—
246C4×Dic3—32no—
247C4×Dic3—32no—
248C4×Dic3—32no—
249C4×Dic3—61no—
250C4×Dic3—61no—
251C4×Dic3—61no—
252#208—64no—
253C2×C3⋊C8—32no—
254C2×C3⋊C8—32no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—64no—
258C2×C3⋊C8C22×D312yes—
259C2×C3⋊C8C22×D312yes—
260ΓL(1,𝔽25)—24no—
261ΓL(1,𝔽25)—64no—
262ΓL(1,𝔽25)—64no—
263ΓL(1,𝔽25)—64no—
264D3×C8—24no—
265D3×C8—38no—
266D3×C8—64no—
267D3×C8—64no—
268D3×C8—64no—
269D3×C8—64no—
270C22×C32C23×C411yescharacteristic
271C2×C3⋊D3—21no—
272C2×C3⋊D3—21no—
273C2×C3⋊D3C4×D412yes—
274C2×C3×D3—22no—
275C2×C3×D3—22no—
276C2×C3×D3—22no—
277C2×C3×D3—22no—
278C2×C3×D3—22no—
279C2×C3×D3—22no—
280C32×C4—21no—
281C32×C4—21no—
282C32×C4C22×D411yescharacteristic
283C32×C4C2×#4111yescharacteristic
284C3⋊Dic3—21no—
285C3⋊Dic3—21no—
286C3⋊Dic3C4×D412yes—
287C3×Dic3—22no—
288C3×Dic3—22no—
289C2×#41—91no—
290C2×#41—91no—
291#131—184no—
292#131—184no—
293C2×M16—32no—
294C2×M16—91no—
295C2×M16—91no—
296C2×M16—92no—
297C22×C8—32no—
298C22×C8—92no—
299C22×C8—91no—
300C22×C8—91no—
301C4⋊Q8—91no—
302#127—91no—
303#124—91no—
304#124—91no—
305#121—92no—
306#121—92no—
307C4×D4—32no—
308C4×D4—92no—
309C2×C42—91no—
310C4⋊C8—32no—
311C4⋊C8—92no—
312C22⋊C8—32no—
313C22⋊C8—32no—
314C22⋊C8—92no—
315C22⋊C8—92no—
316#97—91no—
317#97—91no—
318#97—91no—
319#97D3211yescharacteristic
320C23×C3—32no—
321C23×C3—32no—
322C22×D3—32no—
323C22×D3—61no—
324C22×D3C2×C4×D312yes—
325C22×D3C2×C4×D312yes—
326C3×D4—122no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—32no—
331C2×C3×C4—32no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4C2×C4×D312yes—
337C2×C3×C4C2×C4×D312yes—
338C2×C3×C4C23×D312yes—
339#67—64no—
340#67—64no—
341#67—64no—
342#67—64no—
343#67—122no—
344#67—122no—
345C2×Dic3—32no—
346C2×Dic3—32no—
347C2×Dic3—32no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3C2×C4×D312yes—
352C2×Dic3C2×C4×D312yes—
353D12—42no—
354D12—64no—
355D12—64no—
356C4×D3—22no—
357C4×D3—22no—
358C4×D3—22no—
359C4×D3—22no—
360C4×D3—34no—
361C4×D3—34no—
362C4×D3—62no—
363C4×D3—62no—
364C4×D3—122no—
365C4×D3—122no—
366C4×D3—122no—
367C4×D3—122no—
368Dic6—64no—
369Dic6—64no—
370C3×C8—22no—
371C3×C8—22no—
372C3×C8—22no—
373C3×C8—62no—
374C3×C8—62no—
375C3×C8D3×D414yes—
376C3⋊C8—22no—
377C3⋊C8—22no—
378C3⋊C8—34no—
379C3⋊C8—62no—
380C3⋊C8—62no—
381C3⋊C8—62no—
382C2×C32C2×C4×D411yescharacteristic
383C2×C32#56811yescharacteristic
384C2×C32#56811yescharacteristic
385C3⋊D3—22no—
386C3×D3—42no—
387C3×D3—42no—
388#41—182no—
389#41—182no—
390#41—182no—
391#41—182no—
392C2×Q8—91no—
393C2×Q8—91no—
394C2×D4—32no—
395C2×D4—92no—
396C2×D4—92no—
397C2×D4—91no—
398C2×D4—91no—
399C2×D4—92no—
400C22×C4—32no—
401C22×C4—32no—
402C22×C4—91no—
403C22×C4—91no—
404C22×C4—91no—
405M16—64no—
406M16—182no—
407M16—182no—
408M16—184no—
409C2×C8—32no—
410C2×C8—32no—
411C2×C8—64no—
412C2×C8—91no—
413C2×C8—94no—
414C2×C8—91no—
415C2×C8—182no—
416C2×C8—184no—
417C2×C8C2×D3211yescharacteristic
418C2×C8C2×D3211yescharacteristic
419C4⋊C4—32no—
420C4⋊C4—92no—
421C22⋊C4—32no—
422C22⋊C4—32no—
423C22⋊C4—92no—
424C22⋊C4—92no—
425C42—91no—
426C42—91no—
427C42—91no—
428C42C2×D3211yescharacteristic
429C22×C3—21no—
430C22×C3—62no—
431C22×C3—62no—
432C22×C3—62no—
433C22×C3—62no—
434C22×C3—62no—
435C22×C3—62no—
436C22×C3C22×C4×D312yes—
437C2×D3—22no—
438C2×D3—22no—
439C2×D3—22no—
440C2×D3—22no—
441C2×D3—22no—
442C2×D3—22no—
443C2×D3—34no—
444C2×D3—62no—
445C2×D3—62no—
446C2×D3—62no—
447C2×D3—62no—
448C2×D3—62no—
449C3×C4—22no—
450C3×C4—22no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—41no—
454C3×C4—41no—
455C3×C4—62no—
456C3×C4—62no—
457C3×C4C2×D3×D412yes—
458C3×C4D3×#4112yes—
459Dic3—22no—
460Dic3—22no—
461Dic3—34no—
462Dic3—62no—
463Dic3—62no—
464Dic3—62no—
465Dic3—121no—
466Dic3—121no—
467C32#293211yescharacteristic, complemented, Sylow
468C23—32no—
469C23—32no—
470C23—91no—
471Q8—182no—
472Q8—182no—
473D4—122no—
474D4—184no—
475D4—184no—
476D4—182no—
477D4—182no—
478D4—362no—
479C2×C4—32no—
480C2×C4—32no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—91no—
486C2×C4—92no—
487C2×C4—92no—
488C2×C4—91no—
489C2×C4—91no—
490C2×C4—361no—
491C2×C4—361no—
492C2×C4C4×D3211yescharacteristic
493C2×C4C4×D3211yescharacteristic
494C2×C4C22×D3211yescharacteristic
495C8—21no—
496C8—62no—
497C8—62no—
498C8—92no—
499C8—181no—
500C8#380212yes—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—122no—
505C2×C3—122no—
506C2×C3C4×D3×D412yes—
507C2×C3#574512yes—
508C2×C3#575012yes—
509D3—42no—
510D3—42no—
511D3—64no—
512D3—64no—
513C22—62no—
514C22—62no—
515C22—62no—
516C22—62no—
517C22—62no—
518C22—62no—
519C22—92no—
520C22—181no—
521C22—181no—
522C22C2×C4×D3211yescharacteristic
523C4—21no—
524C4—21no—
525C4—62no—
526C4—62no—
527C4—92no—
528C4—181no—
529C4—181no—
530C4C2×#380211yescharacteristic
531C4#6430611yescharacteristic
532C3—21no—
533C3#7948012yescomplemented
534C2—122no—
535C2—122no—
536C2—182no—
537C2C4×#380211yescharacteristic
538C2#1059470811yescharacteristic
539C2#1059472211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×#97C22
prime radical#10593972C2
cosocleC2×C32×C4C24
hypercenter#97D32
hypocenterC32#2932
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #97

Complements

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

NH ≅ G/Ntype
1. C2×#63805C2semidirect
2. C2×#63803C2semidirect
4. C3⋊D3×#97C2semidirect
5. C3×#4706C2semidirect
6. #10590958C2semidirect
7. #10590958C2semidirect
8. #10590725C2semidirect
9. #10590722C2semidirect
10. #10590340C2semidirect
11. #10590330C2semidirect
57. #4706D3semidirect
86. C8×C3⋊D3D4semidirect
467. C32#2932semidirect
533. C3#79480semidirect

Maximal subgroups

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

subgroupindex
C2×#638052
C2×#638032
#105939722
C3⋊D3×#972
C3×#47062
#105909582
#105907252
#105907222
#105903402
#105903302
#794803