Finite Group Databasebeta

← #11788636

Subgroups — #11788636

Order 1152.

713 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63823C211yesmaximal, characteristic
2C2×#63814C211yesmaximal, characteristic, complemented
3C3×#4966C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5C2×#63558C211yesmaximal, characteristic, complemented
6#10589396C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#70303—31nomaximal
9#70218—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3715—21no—
18#63823—22no—
19#63823C414yescomplemented
20C2×#3713—21no—
21C2×#3711—21no—
22#63814—22no—
23#63814—22no—
24C2×D3×C3⋊C8—21no—
25C3×#810—21no—
26C3×#809—21no—
27C3×#809—21no—
28C3×#809—21no—
29#63558—22no—
30C2×#949—31no—
31C2×#948—31no—
32C2×#932—31no—
33C2×#901—31no—
34C3×#417—31no—
35C2×C3×#102—31no—
36C2×#833—31no—
37C2×#823—31no—
38#4966D311yescharacteristic, complemented
39C2×#809D311yescharacteristic, complemented
40#4558—31no—
41#4552—31no—
42#4530—31no—
43#4530—31no—
44#4530—61no—
45C23×C3×D3—21no—
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C2×C3×#67—21no—
49C3×#235—21no—
50C3×#235—21no—
51C3×#235C2×C412yes—
52C3×#235D412yes—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12C2×C412yes—
59C2×C3×D12D411yescharacteristic
60C2×C3×C4×D3—21no—
61C2×C3×Dic6D411yescharacteristic
62C32×C4⋊C4—21no—
63C32×C4⋊C4—21no—
64#3748—21no—
65#3748—21no—
66#3748C2×C412yes—
67#3748D412yes—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C3×#208—21no—
71C3×#208—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8D411yescharacteristic
76C2×C3×C3⋊C8D411yescharacteristic
77#3715—24no—
78#3713—24no—
79#3711—24no—
80D3×C3⋊C8—24no—
81#1907—91noSylow
82C2×C3×#41—31no—
83C22×C3×D4—31no—
84C2×#235C2×D311yescharacteristic
85C22×D12C2×D311yescharacteristic
86C2×C3×M16—31no—
87C22×C3×C8—31no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4C2×D311yescharacteristic
90C2×C3×C4⋊C4C2×D311yescharacteristic
91#949—34no—
92#949—62no—
93#948—62no—
94#948—62no—
95C2×#215—61no—
96C2×#214—61no—
97#932—34no—
98#932—62no—
99C2×#213—61no—
100C2×#213—61no—
101C2×#208—31no—
102C2×#208—31no—
103C2×#208—31no—
104C2×#208—31no—
105C2×#208—61no—
106C2×#208—61no—
107C2×#208—61no—
108C2×#208C2×D311yescharacteristic
109C22×C3⋊C8—61no—
110C22×C3⋊C8C2×D311yescharacteristic
111#901—62no—
112#901—62no—
113C2×ΓL(1,𝔽25)—61no—
114C2×D3×C8—61no—
115C3×#103—61no—
116C3×#102—61no—
117C3×#102—61no—
118C3×#102—61no—
119#833—62no—
120#823—62no—
121#810—21no—
122#809—21no—
123#809—21no—
124#809—21no—
125C23×C32#4111yescharacteristic
126C22×C3×D3—21no—
127C22×C3×D3—22no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—81no—
131C22×C3×D3—81no—
132C2×C32×C4—41no—
133C2×C32×C4—81no—
134C2×C32×C4C22×C411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4#4111yescharacteristic
140C3×#67—22no—
141C3×#67—22no—
142C2×C3×Dic3—21no—
143C3×D12—22no—
144C3×D12—22no—
145C3×D12—21no—
146C3×D12—41no—
147C3×D12—41no—
148C3×D12C22⋊C412yes—
149C3×C4×D3—22no—
150C3×C4×D3—22no—
151C3×Dic6—21no—
152C3×Dic6C22⋊C412yes—
153C3⋊(C3⋊C8)—22no—
154C3⋊(C3⋊C8)—22no—
155C3×C3⋊C8—21no—
156C3×C3⋊C8—21no—
157C3×C3⋊C8—41no—
158C2×AGL(1,ℤ/8)—91no—
159C2×#131—91no—
160#417—31no—
161C2×#102—31no—
162C2×#100—91no—
163#343—91no—
164#341—91no—
165C24×C3—61no—
166C23×D3—21no—
167C3×#41—32no—
168C3×#41—32no—
169C3×#41—61no—
170C3×#41—61no—
171C2×C3×Q8—31no—
172C2×C3×D4—32no—
173C2×C3×D4—31no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C22×C3×C4—22no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—61no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C2×#67—21no—
188#235—21no—
189#235—21no—
190#235C4×D312yes—
191#235D1212yes—
192C2×D12—21no—
193C2×D12—21no—
194C2×D12—21no—
195C2×D12—21no—
196C2×D12—21no—
197C2×D12C4×D312yes—
198C2×D12#6711yescharacteristic
199C2×C4×D3—21no—
200C2×Dic6#6711yescharacteristic
201C3×M16—61no—
202C3×M16—61no—
203C2×C3×C8—31no—
204C2×C3×C8—31no—
205C2×C3×C8—61no—
206C2×C3×C8—61no—
207C2×C3×C8—61no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—41no—
213C3×C4⋊C4—41no—
214#215—64no—
215#214—64no—
216#213—64no—
217#213—64no—
218#208—21no—
219#208—21no—
220#208—32no—
221#208—32no—
222#208—32no—
223#208—32no—
224#208—62no—
225#208—62no—
226#208—64no—
227#208—61no—
228#208—61no—
229#208—61no—
230#208—61no—
231#208—121no—
232#208—121no—
233C2×C3⋊C8—21no—
234C2×C3⋊C8—21no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8—64no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—61no—
240C2×C3⋊C8—61no—
241C2×C3⋊C8—121no—
242C2×C3⋊C8—121no—
243C2×C3⋊C8#6711yescharacteristic
244C2×C3⋊C8#6711yescharacteristic
245ΓL(1,𝔽25)—64no—
246D3×C8—64no—
247C22×C32—21no—
248C22×C32—21no—
249C22×C32C4×D411yescharacteristic
250C22×C32#12111yescharacteristic
251C22×C32#12311yescharacteristic
252C2×C3×D3—22no—
253C2×C3×D3—41no—
254C2×C3×D3—41no—
255C2×C3×D3—42no—
256C2×C3×D3—82no—
257C2×C3×D3—81no—
258C2×C3×D3—81no—
259C2×C3×D3—82no—
260C32×C4—81no—
261C32×C4C2×C22⋊C411yescharacteristic
262C32×C4C4×D411yescharacteristic
263C32×C4#12011yescharacteristic
264C32×C4#12111yescharacteristic
265C3×Dic3—22no—
266C2×#41—31no—
267C22×D4—31no—
268AGL(1,ℤ/8)—94no—
269AGL(1,ℤ/8)—182no—
270C2×SD16—181no—
271C2×D8—181no—
272#131—182no—
273#131—182no—
274C2×M16—31no—
275C2×M16—91no—
276C2×M16—91no—
277C2×M16—181no—
278C22×C8—31no—
279C22×C8—181no—
280C2×C4⋊C4D3211yescharacteristic
281#103—61no—
282#102—61no—
283#102—61no—
284#102—61no—
285#100—182no—
286C23×C3—21no—
287C23×C3—61no—
288C23×C3—62no—
289C23×C3—121no—
290C23×C3—121no—
291C23×C3—241no—
292C23×C3—241no—
293C23×C3#23711yescharacteristic
294C23×C3#23711yescharacteristic
295C22×D3—21no—
296C22×D3—22no—
297C22×D3—41no—
298C22×D3—41no—
299C22×D3—81no—
300C22×D3—81no—
301C3×Q8—32no—
302C3×Q8—61no—
303C3×D4—32no—
304C3×D4—62no—
305C3×D4—62no—
306C3×D4—62no—
307C3×D4—61no—
308C3×D4—62no—
309C3×D4—121no—
310C3×D4—121no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—42no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—61no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—81no—
324C2×C3×C4—81no—
325C2×C3×C4—82no—
326C2×C3×C4C2×C4×D311yescharacteristic
327C2×C3×C4C2×C4×D311yescharacteristic
328C2×C3×C4C2×D1211yescharacteristic
329C2×C3×C4#23511yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4#23711yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337C2×C3×C4C2×#6711yescharacteristic
338#67—22no—
339#67—22no—
340C2×Dic3—21no—
341D12—22no—
342D12—22no—
343D12—21no—
344D12—41no—
345D12—41no—
346D12(C2×D3)⋊C412yes—
347C4×D3—22no—
348C4×D3—22no—
349Dic6—21no—
350Dic6(C2×D3)⋊C412yes—
351C3×C8—61no—
352C3×C8—61no—
353C3×C8—121no—
354C3⋊C8—21no—
355C3⋊C8—21no—
356C3⋊C8—41no—
357C3⋊C8—62no—
358C3⋊C8—62no—
359C3⋊C8—62no—
360C3⋊C8—62no—
361C3⋊C8—122no—
362C3⋊C8—122no—
363C2×C32—21no—
364C2×C32—21no—
365C2×C32#38611yescharacteristic
366C2×C32#47111yescharacteristic
367C2×C32#47211yescharacteristic
368C3×D3—42no—
369C3×D3—82no—
370C24—61no—
371#41—32no—
372#41—32no—
373#41—61no—
374#41—61no—
375C2×Q8—31no—
376C2×D4—32no—
377C2×D4—31no—
378C2×D4—61no—
379C2×D4—61no—
380C2×D4—61no—
381C2×D4—61no—
382C2×D4—61no—
383C2×D4—61no—
384C22×C4—21no—
385C22×C4—61no—
386C22×C4C2×D3211yescharacteristic
387SD16—184no—
388D8—184no—
389M16—61no—
390M16—61no—
391M16—92no—
392M16—92no—
393M16—184no—
394M16—181no—
395M16—181no—
396C2×C8—31no—
397C2×C8—31no—
398C2×C8—61no—
399C2×C8—61no—
400C2×C8—61no—
401C2×C8—184no—
402C2×C8—181no—
403C2×C8—181no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—41no—
414C22×C3—41no—
415C22×C3—62no—
416C22×C3—121no—
417C22×C3—121no—
418C22×C3—122no—
419C22×C3—242no—
420C22×C3—242no—
421C22×C3—241no—
422C22×C3—241no—
423C22×C3#67⋊C411yescharacteristic
424C22×C3#67⋊C411yescharacteristic
425C22×C3#88311yescharacteristic
426C22×C3#88611yescharacteristic
427C22×C3#93811yescharacteristic
428C22×C3#93911yescharacteristic
429C2×D3—22no—
430C2×D3—41no—
431C2×D3—41no—
432C2×D3—42no—
433C2×D3—82no—
434C2×D3—81no—
435C2×D3—81no—
436C2×D3—82no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—62no—
442C3×C4—82no—
443C3×C4—81no—
444C3×C4—81no—
445C3×C4D3×C22⋊C411yescharacteristic
446C3×C4#67⋊C411yescharacteristic
447C3×C4#88211yescharacteristic
448C3×C4#88411yescharacteristic
449C3×C4C2×(C2×D3)⋊C411yescharacteristic
450C3×C4C4×#6711yescharacteristic
451C3×C4#93711yescharacteristic
452C3×C4#93911yescharacteristic
453Dic3—22no—
454C32#190711yescharacteristic, complemented, Sylow
455C23—61no—
456C23—62no—
457C23—121no—
458C23—121no—
459C23—241no—
460C23—241no—
461C23#380511yescharacteristic
462Q8—32no—
463Q8—61no—
464D4—32no—
465D4—62no—
466D4—62no—
467D4—62no—
468D4—61no—
469D4—62no—
470D4—121no—
471D4—121no—
472C2×C4—41no—
473C2×C4—61no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4—81no—
477C2×C4#379511yescharacteristic
478C2×C4C4×D3211yescharacteristic
479C2×C4D3×D1211yescharacteristic
480C2×C4#380211yescharacteristic
481C2×C4D3×#6711yescharacteristic
482C2×C4D3×#6711yescharacteristic
483C8—61no—
484C8—61no—
485C8—121no—
486C8—182no—
487C8—182no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—41no—
496C2×C3—41no—
497C2×C3—122no—
498C2×C3—242no—
499C2×C3#495611yescharacteristic
500C2×C3#495811yescharacteristic
501C2×C3#516011yescharacteristic
502C2×C3#517711yescharacteristic
503C2×C3#519911yescharacteristic
504C2×C3#520311yescharacteristic
505D3—42no—
506D3—82no—
507C22—21no—
508C22—21no—
509C22—62no—
510C22—121no—
511C22—121no—
512C22—122no—
513C22—242no—
514C22—242no—
515C22—241no—
516C22—241no—
517C22#6389111yescharacteristic
518C22#6390211yescharacteristic
519C22#6397011yescharacteristic
520C4—62no—
521C4—81no—
522C4#6387911yescharacteristic
523C4#6388511yescharacteristic
524C4D3×(C2×D3)⋊C411yescharacteristic
525C4#6392211yescharacteristic
526C3—21no—
527C3#7021811yescharacteristic, complemented
528C3#7030311yescharacteristic, complemented
529C2—21no—
530C2—21no—
531C2—122no—
532C2—242no—
533C2#1059136311yescharacteristic
534C2#1059150511yescharacteristic
535C2#1059164211yescharacteristic
subgroupG/H
centerC22#63970
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#121
prime radicalC2×#63823C2
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1907
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63814C2semidirect
3. C3×#4966C2semidirect
4. C2×C3×#809C2semidirect
5. C2×#63558C2semidirect
6. #10589396C2semidirect
7. #10589166C2semidirect
19. #63823C4semidirect
38. #4966D3semidirect
39. C2×#809D3semidirect
454. C32#1907semidirect
527. C3#70218semidirect
528. C3#70303semidirect

Maximal subgroups

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

subgroupindex
C2×#638232
C2×#638142
C3×#49662
C2×C3×#8092
C2×#635582
#105893962
#105891662
#703033
#702183