Finite Group Databasebeta

← #11859535

Subgroups — #11859535

Order 1152.

1123 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596019C211yesmaximal, characteristic
2C2×#63817C212yesmaximal, complemented
3C3×#5011C212yesmaximal, complemented
4#10591157C212yesmaximal, complemented
5#10591153C212yesmaximal, complemented
6#10591149C212yesmaximal, complemented
7#10590340C211yesmaximal, characteristic, complemented
8#10590328C212yesmaximal, complemented
9#10590322C211yesmaximal, characteristic, complemented
10#79480—32nomaximal
11C2×#3828C2212yes—
12C32×C4×D4C2211yescharacteristic
13#64149C411yescharacteristic
14#64147C411yescharacteristic
15C4×#638C2212yes—
16#64104C411yescharacteristic
17#64097C411yescharacteristic
18#64094C412yes—
19#64093C412yes—
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C42×C3⋊D3C2211yescharacteristic
22C2×C3×#208C2212yes—
23C22×C3×C3⋊C8C2212yes—
24C2×#3712C2212yes—
25C2×#3712C2212yes—
26#63817—28no—
27C2×#3710C2211yescharacteristic
28C2×#3710C2212yes—
29C2×#3710C2211yescharacteristic
30C3×#830C2212yes—
31C3×#830C2212yes—
32C3×C4⋊(C3⋊C8)C2212yes—
33C3×#803C2212yes—
34#63572C2211yescharacteristic
35#63572C2211yescharacteristic
36#63557C2212yes—
37#63557C2212yes—
38#63555C2212yes—
39C2×#907—32no—
40C2×#901—32no—
41#5548—32no—
42#5548—61no—
43C3×#435—32no—
44#5127—32no—
45#5111—32no—
46#5011D312yescomplemented
47#4837—32no—
48#4836—32no—
49#4730—32no—
50#4728—32no—
51#4727—32no—
52#4727—32no—
53#4706—32no—
54D3×#97—32no—
55C2×C32×D4C2×C411yescharacteristic
56C22×C32×C4C2312yes—
57C2×#638C2×C412yes—
58C2×#638C2×C412yes—
59C2×#638C2×C412yes—
60#3828—24no—
61#3828—24no—
62C2×C4⋊(C3⋊D3)C2×C412yes—
63C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
64C2×C4×C3⋊D3C2×C411yescharacteristic
65C2×C4×C3⋊D3C2×C411yescharacteristic
66C2×C4×C3⋊D3C2312yes—
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×#634C2×C412yes—
69C32×C4⋊C4C2×C411yescharacteristic
70C32×C22⋊C4C2×C412yes—
71C32×C42C2311yescharacteristic
72#3757C2×C412yes—
73#3752C2×C412yes—
74#3752C2×C412yes—
75C4⋊(C3⋊Dic3)C2×C411yescharacteristic
76#3750C2×C412yes—
77C4×C3⋊Dic3C2×C411yescharacteristic
78C4×C3⋊Dic3C2×C411yescharacteristic
79C4×C3⋊Dic3C2311yescharacteristic
80C3×#208—24no—
81C2×C3×C3⋊C8—24no—
82C2×C3×C3⋊C8C2312yes—
83C2×C3×C3⋊C8C2312yes—
84C2×C3×C3⋊C8C2312yes—
85C2×C3×C3⋊C8C2312yes—
86#3712—24no—
87#3712—24no—
88#3710—22no—
89#3710—24no—
90#3710D414yescomplemented
91#2932—91noSylow
92C2×#235—32no—
93C2×#235—32no—
94C2×#235—62no—
95C2×C3×M16—32no—
96C22×C3×C8—32no—
97C3×C4×D4—21no—
98C3×C4×D4C2×D312yes—
99#940—32no—
100#940—61no—
101#938—32no—
102#938—61no—
103C4×#67—32no—
104C4×#67—32no—
105C4×#67—62no—
106C2×#208C2×D312yes—
107C22×C3⋊C8C2×D312yes—
108#907—68no—
109#901—68no—
110C2×ΓL(1,𝔽25)—32no—
111C2×ΓL(1,𝔽25)—32no—
112C2×ΓL(1,𝔽25)—32no—
113C2×ΓL(1,𝔽25)—32no—
114C2×D3×C8—32no—
115C2×D3×C8—32no—
116C2×D3×C8—32no—
117C2×D3×C8—32no—
118#895—32no—
119#895—61no—
120#888—32no—
121#888—61no—
122#885—32no—
123#885—32no—
124#885—62no—
125#884—32no—
126#884—32no—
127#884—62no—
128C4×D12—32no—
129C4×D12—61no—
130C42×D3—32no—
131C42×D3—61no—
132C3×C4⋊C8—32no—
133C3×C22⋊C8—32no—
134C3×C22⋊C8—32no—
135C3×#97—32no—
136#830C2×D312yes—
137#830C2×D312yes—
138(C2×D3)⋊C8—32no—
139(C2×D3)⋊C8—32no—
140(C2×D3)⋊C8—32no—
141(C2×D3)⋊C8—32no—
142#815—32no—
143#815—32no—
144Dic3⋊C8—32no—
145Dic3⋊C8—32no—
146C4⋊(C3⋊C8)C2×D312yes—
147#803C2×D312yes—
148C23×C32C22×C412yes—
149C22×C3⋊D3C22×C412yes—
150C22×C3⋊D3C22×C411yescharacteristic
151C32×D4—41no—
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C32×C4C22×C411yescharacteristic
155C2×C32×C4C22×C411yescharacteristic
156C2×C32×C4C22×C412yes—
157C2×C32×C4C2411yescharacteristic
158#638—24no—
159#638—24no—
160#638—42no—
161C2×C3⋊Dic3C22×C411yescharacteristic
162C2×C3⋊Dic3C22×C411yescharacteristic
163C2×C3⋊Dic3C22×C412yes—
164C2×C3⋊Dic3C22×C411yescharacteristic
165C4⋊(C3⋊D3)—24no—
166C4⋊(C3⋊D3)—41no—
167C4×C3⋊D3—22no—
168C4×C3⋊D3—22no—
169C4×C3⋊D3—41no—
170C4×C3⋊D3—41no—
171C4×C3⋊D3C2×D412yes—
172C4×C3⋊D3#4112yes—
173#634—24no—
174C3×C3⋊C8—22no—
175C3×C3⋊C8—22no—
176C3×C3⋊C8—22no—
177C3×C3⋊C8C2×D414yes—
178C2×#131—92no—
179#532—91no—
180#435—32no—
181#435—92no—
182#435—92no—
183#435—92no—
184#423—91no—
185#408—92no—
186C2×#97—91no—
187C2×C3×D4—21no—
188C2×C3×D4C4×D312yes—
189C22×C3×C4—22no—
190C22×C3×C4C22×D312yes—
191C22×C3×C4C22×D312yes—
192C2×#67—32no—
193C2×#67—32no—
194C2×#67—32no—
195C2×#67—32no—
196C2×#67—32no—
197C2×#67—32no—
198C2×#67—62no—
199C2×#67—62no—
200C2×#67—62no—
201#235—64no—
202#235—64no—
203#235—64no—
204#235—64no—
205#235—124no—
206#235—124no—
207C2×D12—32no—
208C2×D12—32no—
209C2×D12—32no—
210C2×D12—61no—
211C2×D12—62no—
212C2×C4×D3—32no—
213C2×C4×D3—32no—
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×D3—62no—
221C2×Dic6—32no—
222C2×Dic6—32no—
223C2×Dic6—62no—
224C3×M16—64no—
225C2×C3×C8—32no—
226C2×C3×C8—32no—
227C2×C3×C8—32no—
228C2×C3×C8—32no—
229C2×C3×C8—64no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4C4×D312yes—
232C3×C22⋊C4—22no—
233C3×C22⋊C4C4×D312yes—
234C3×C22⋊C4C4×D312yes—
235C3×C42—21no—
236C3×C42C22×D312yes—
237#217—32no—
238#217—32no—
239#217—62no—
240(C2×D3)⋊C4—32no—
241(C2×D3)⋊C4—32no—
242(C2×D3)⋊C4—32no—
243(C2×D3)⋊C4—32no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246C4⋊Dic3—32no—
247C4⋊Dic3—61no—
248Dic3⋊C4—32no—
249Dic3⋊C4—32no—
250Dic3⋊C4—62no—
251C4×Dic3—32no—
252C4×Dic3—32no—
253C4×Dic3—32no—
254C4×Dic3—61no—
255C4×Dic3—61no—
256C4×Dic3—61no—
257#208—24no—
258C2×C3⋊C8—24no—
259C2×C3⋊C8C22×D312yes—
260C2×C3⋊C8C22×D312yes—
261C2×C3⋊C8C22×D312yes—
262C2×C3⋊C8C22×D312yes—
263ΓL(1,𝔽25)—64no—
264ΓL(1,𝔽25)—64no—
265ΓL(1,𝔽25)—64no—
266ΓL(1,𝔽25)—64no—
267D3×C8—38no—
268D3×C8—64no—
269D3×C8—64no—
270D3×C8—64no—
271C22×C32—22no—
272C22×C32—22no—
273C22×C32—22no—
274C22×C32C23×C411yescharacteristic
275C2×C3⋊D3—21no—
276C2×C3⋊D3—21no—
277C2×C3⋊D3—22no—
278C2×C3⋊D3—22no—
279C2×C3⋊D3—22no—
280C2×C3⋊D3C4×D412yes—
281C32×C4—21no—
282C32×C4—22no—
283C32×C4—21no—
284C32×C4C22×D411yescharacteristic
285C32×C4C2×#4111yescharacteristic
286C3⋊Dic3—21no—
287C3⋊Dic3—22no—
288C3⋊Dic3—21no—
289C3⋊Dic3C4×D412yes—
290C2×#41—92no—
291#131—188no—
292C2×M16—32no—
293C2×M16—92no—
294C2×M16—92no—
295C22×C8—32no—
296C22×C8—91no—
297C22×C8—92no—
298C22×C8—91no—
299C4⋊Q8—91no—
300#127—91no—
301#124—92no—
302#121—91no—
303#121—91no—
304#121—92no—
305C4×D4—92no—
306C4×D4—91no—
307C4×D4D3211yescharacteristic
308C2×C42—91no—
309C4⋊C8—32no—
310C4⋊C8—91no—
311C4⋊C8—91no—
312C22⋊C8—32no—
313C22⋊C8—32no—
314C22⋊C8—92no—
315C22⋊C8—92no—
316#97—32no—
317#97—92no—
318C23×C3—22no—
319C23×C3C2×C4×D312yes—
320C23×C3C2×C4×D312yes—
321C22×D3—32no—
322C22×D3—32no—
323C22×D3—32no—
324C22×D3—61no—
325C22×D3—62no—
326C3×D4—42no—
327C3×D4—42no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—22no—
336C2×C3×C4—42no—
337C2×C3×C4—42no—
338C2×C3×C4C2×C4×D312yes—
339C2×C3×C4C2×C4×D312yes—
340C2×C3×C4C2×C4×D312yes—
341C2×C3×C4C2×C4×D312yes—
342C2×C3×C4C23×D312yes—
343#67—64no—
344#67—64no—
345#67—64no—
346#67—64no—
347#67—124no—
348#67—124no—
349#67—122no—
350#67—122no—
351#67—124no—
352C2×Dic3—32no—
353C2×Dic3—32no—
354C2×Dic3—32no—
355C2×Dic3—32no—
356C2×Dic3—32no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—62no—
361D12—64no—
362D12—64no—
363D12—124no—
364D12—122no—
365D12—122no—
366C4×D3—34no—
367C4×D3—34no—
368C4×D3—62no—
369C4×D3—62no—
370C4×D3—62no—
371C4×D3—62no—
372C4×D3—62no—
373C4×D3—62no—
374C4×D3—122no—
375C4×D3—122no—
376C4×D3—122no—
377C4×D3—122no—
378C4×D3—122no—
379C4×D3—122no—
380Dic6—64no—
381Dic6—64no—
382Dic6—124no—
383C3×C8—34no—
384C3×C8—62no—
385C3×C8—62no—
386C3×C8—62no—
387C3⋊C8—22no—
388C3⋊C8—22no—
389C3⋊C8—22no—
390C3⋊C8D3×D414yes—
391C2×C32—42no—
392C2×C32C2×C4×D411yescharacteristic
393C2×C32#56811yescharacteristic
394C2×C32#56811yescharacteristic
395C3⋊D3—22no—
396C3⋊D3—42no—
397#41—184no—
398#41—184no—
399C2×Q8—92no—
400C2×D4—92no—
401C2×D4—92no—
402C2×D4—92no—
403C2×D4—92no—
404C2×D4—91no—
405C2×D4#62411yescharacteristic
406C22×C4—91no—
407C22×C4—92no—
408C22×C4—91no—
409C22×C4—91no—
410C22×C4C2×D3212yes—
411M16—64no—
412M16—184no—
413M16—184no—
414C2×C8—32no—
415C2×C8—32no—
416C2×C8—32no—
417C2×C8—32no—
418C2×C8—64no—
419C2×C8—94no—
420C2×C8—184no—
421C2×C8—182no—
422C4⋊C4—92no—
423C4⋊C4—91no—
424C4⋊C4#62411yescharacteristic
425C22⋊C4—92no—
426C22⋊C4—92no—
427C22⋊C4—92no—
428C22⋊C4#62412yes—
429C42—91no—
430C42—91no—
431C42—91no—
432C42C2×D3211yescharacteristic
433C22×C3—22no—
434C22×C3—22no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—22no—
438C22×C3—22no—
439C22×C3—21no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3C22×C4×D312yes—
444C2×D3—34no—
445C2×D3—62no—
446C2×D3—62no—
447C2×D3—62no—
448C2×D3—62no—
449C2×D3—62no—
450C2×D3—62no—
451C2×D3—62no—
452C2×D3—62no—
453C2×D3—62no—
454C2×D3—121no—
455C2×D3—121no—
456C2×D3—122no—
457C2×D3—122no—
458C2×D3—122no—
459C3×C4—22no—
460C3×C4—22no—
461C3×C4—22no—
462C3×C4—22no—
463C3×C4—22no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—42no—
467C3×C4—41no—
468C3×C4C2×D3×D412yes—
469C3×C4D3×#4112yes—
470Dic3—34no—
471Dic3—62no—
472Dic3—62no—
473Dic3—62no—
474Dic3—62no—
475Dic3—62no—
476Dic3—62no—
477Dic3—122no—
478Dic3—121no—
479C32#293211yescharacteristic, complemented, Sylow
480C23—91no—
481C23—92no—
482C23C2×#62412yes—
483Q8—184no—
484D4—41no—
485D4—184no—
486D4—184no—
487D4—184no—
488D4—361no—
489D4—362no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—91no—
493C2×C4—92no—
494C2×C4—92no—
495C2×C4—91no—
496C2×C4—91no—
497C2×C4—92no—
498C2×C4—182no—
499C2×C4—182no—
500C2×C4—361no—
501C2×C4—361no—
502C2×C4C2×#62411yescharacteristic
503C2×C4C2×#62411yescharacteristic
504C2×C4C2×#62412yes—
505C2×C4C22×D3211yescharacteristic
506C8—34no—
507C8—62no—
508C8—62no—
509C8—62no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—42no—
514C2×C3—42no—
515C2×C3—82no—
516C2×C3C4×D3×D412yes—
517C2×C3#574512yes—
518C2×C3#575012yes—
519D3—64no—
520D3—122no—
521D3—122no—
522D3—122no—
523D3—242no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—92no—
528C22—181no—
529C22—181no—
530C22—182no—
531C22—182no—
532C22—182no—
533C22C22×#62411yescharacteristic
534C4—22no—
535C4—21no—
536C4—21no—
537C4—92no—
538C4—182no—
539C4—181no—
540C4—181no—
541C4D32×D411yescharacteristic
542C4#6431211yescharacteristic
543C3—21no—
544C3#7948012yescomplemented
545C2—42no—
546C2—182no—
547C2—362no—
548C2#1059478011yescharacteristic
549C2D4×#62411yescharacteristic
550C2#1059544311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4×D4C22
prime radical#10596019C2
cosocleC2×C32×C4C24
hypercenterC4×D4D32
hypocenterC32#2932
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63817C2semidirect
3. C3×#5011C2semidirect
4. #10591157C2semidirect
5. #10591153C2semidirect
6. #10591149C2semidirect
7. #10590340C2semidirect
8. #10590328C2semidirect
9. #10590322C2semidirect
46. #5011D3semidirect
90. #3710D4semidirect
479. C32#2932semidirect
544. C3#79480semidirect

Maximal subgroups

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

subgroupindex
#105960192
C2×#638172
C3×#50112
#105911572
#105911532
#105911492
#105903402
#105903282
#105903222
#794803