Finite Group Databasebeta

← #11788891

Subgroups — #11788891

Order 1152.

773 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5805C211yesmaximal, characteristic
2#10594776C211yesmaximal, characteristic, complemented
3C2×#63660C211yesmaximal, characteristic, complemented
4C2×C3×#833C211yesmaximal, characteristic, complemented
5#10591076C211yesmaximal, characteristic, complemented
6#10589170C211yesmaximal, characteristic, complemented
7#10589169C211yesmaximal, characteristic, complemented
8#71855—31nomaximal
9#70089—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#953C414yes—
15C3×#940—21no—
16C3×#938—22no—
17C3×#936—21no—
18C3×#926C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21#63815—22no—
22#63814—22no—
23D3×#208—22no—
24#63660—22no—
25C3×#833—22no—
26#63560—21no—
27#63558—21no—
28C3×#535—31no—
29#5819—31no—
30#5805D311yescharacteristic
31#5745—31no—
32C2×C3×#100—31no—
33#5237—31no—
34C2×#833—31no—
35C2×#833—31no—
36C2×#833—61no—
37C2×#833D311yescharacteristic, complemented
38#5132—31no—
39#4559—31no—
40#4556—31no—
41#4533—31no—
42#4533—31no—
43C24×C32C2×C412yes—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C22×C32×C4C2311yescharacteristic
51C2×C3×#67—24no—
52C2×C3×#67C2×C412yes—
53C3×#235—21no—
54C3×#235—21no—
55C3×#235—21no—
56C3×#235—21no—
57C2×C3×D12D411yescharacteristic
58C2×C3×C4×D3D412yes—
59C2×C3×Dic6D411yescharacteristic
60#3748—21no—
61#3748—21no—
62#3748—21no—
63#3748D412yescomplemented
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C3×#217—24no—
67C3×#217C2×C412yes—
68C3×C4⋊Dic3—21no—
69C3×C4×Dic3—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208—21no—
73C3×#208D412yescomplemented
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76#3711—24no—
77D3×C3⋊C8—24no—
78#1914—91noSylow
79C2×C3×#41—31no—
80C22×C3×D4—21no—
81C22×C3×D4C2×D311yescharacteristic
82C22×C3×D4C2×D311yescharacteristic
83C2×#235C2×D311yescharacteristic
84C2×C3×M16—31no—
85C2×C3×M16—31no—
86C3×#127—61no—
87C3×#124—61no—
88C3×#121—62no—
89C3×#120—34no—
90C3×#117—31no—
91#953Dic314yes—
92#948—62no—
93#948—62no—
94#940—21no—
95#938—22no—
96#936—21no—
97#926C2×D311yescharacteristic
98C2×#208—31no—
99C2×#208—31no—
100C2×#208—31no—
101C2×#208—31no—
102C2×#208—61no—
103C2×#208—61no—
104C2×#208—62no—
105C2×#208C2×D311yescharacteristic
106C2×#208C2×D311yescharacteristic
107#907—62no—
108D3×M16—62no—
109#901—62no—
110C3×#100—62no—
111#836—61no—
112#833—22no—
113#833—61no—
114#833—62no—
115#833—62no—
116#833—64no—
117#824—61no—
118#823—61no—
119C23×C32—22no—
120C23×C32—22no—
121C23×C32—22no—
122C23×C32—82no—
123C23×C32C22×C411yescharacteristic
124C22×C3×D3C22⋊C412yes—
125C32×D4—41no—
126C32×D4—41no—
127C32×D4—41no—
128C32×D4—41no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C3×#67—22no—
136C3×#67—22no—
137C3×#67—84no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3C22⋊C412yes—
140C3×D12—21no—
141C3×D12—21no—
142C3×C4×D3—22no—
143C3×C4×D3—22no—
144C3×Dic6—21no—
145C3×Dic6—21no—
146C3⋊(C3⋊C8)—22no—
147C3⋊(C3⋊C8)—41no—
148C3×C3⋊C8—22no—
149C3×C3⋊C8—41no—
150#568—91no—
151#535—31no—
152#413—91no—
153C2×#100—31no—
154C2×#100—91no—
155#344—91no—
156#344—91no—
157C24×C3—22no—
158C24×C3C4×D312yes—
159C24×C3C2×Dic312yes—
160C3×#41—61no—
161C3×#41—61no—
162C3×#41—61no—
163C3×#41—61no—
164C2×C3×Q8—31no—
165C2×C3×D4—22no—
166C2×C3×D4—22no—
167C2×C3×D4—21no—
168C2×C3×D4—21no—
169C2×C3×D4—21no—
170C2×C3×D4—21no—
171C2×C3×D4—21no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—32no—
180C2×C3×D4—31no—
181C2×C3×D4—41no—
182C2×C3×D4—41no—
183C2×C3×D4—41no—
184C2×C3×D4—41no—
185C2×C3×D4—64no—
186C22×C3×C4—21no—
187C22×C3×C4—32no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—24no—
191C2×#67C2×Dic312yes—
192#235—21no—
193#235—21no—
194#235—21no—
195#235—21no—
196C2×D12#6711yescharacteristic
197C2×C4×D3#6712yes—
198C2×Dic6#6711yescharacteristic
199C3×M16—32no—
200C3×M16—61no—
201C3×M16—61no—
202C3×M16—61no—
203C2×C3×C8—61no—
204C2×C3×C8—61no—
205C3×C4⋊C4—61no—
206C3×C22⋊C4—32no—
207C3×C22⋊C4—64no—
208C3×C42—61no—
209#217—24no—
210#217C2×Dic312yes—
211C4⋊Dic3—21no—
212C4×Dic3—21no—
213#208—21no—
214#208—21no—
215#208—21no—
216#208—32no—
217#208—32no—
218#208—62no—
219#208—64no—
220#208—61no—
221#208—61no—
222#208—62no—
223#208—61no—
224#208—61no—
225#208—61no—
226#208—61no—
227#208—121no—
228#208—121no—
229#208#6712yescomplemented
230C2×C3⋊C8—21no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8—64no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8—61no—
235C2×C3⋊C8—61no—
236C2×C3⋊C8—61no—
237C2×C3⋊C8—121no—
238C2×C3⋊C8—121no—
239ΓL(1,𝔽25)—64no—
240D3×C8—64no—
241C22×C32—41no—
242C22×C32—42no—
243C22×C32—44no—
244C22×C32—82no—
245C22×C32—82no—
246C22×C32C2×C22⋊C411yescharacteristic
247C22×C32C4×D411yescharacteristic
248C22×C32C4×D411yescharacteristic
249C2×C3×D3—22no—
250C2×C3×D3—42no—
251C32×C4#12011yescharacteristic
252C32×C4#12111yescharacteristic
253C32×C4#12111yescharacteristic
254C32×C4#12311yescharacteristic
255C3×Dic3—22no—
256C3×Dic3—42no—
257C2×#41—31no—
258C22×D4D3211yescharacteristic
259#131—182no—
260#131—182no—
261C2×M16—31no—
262C2×M16—31no—
263C2×M16—91no—
264C2×M16—91no—
265C2×M16—182no—
266#127—61no—
267#124—61no—
268#121—62no—
269#120—34no—
270#117—31no—
271#101—181no—
272#100—62no—
273#100—181no—
274#100—182no—
275C23×C3—24no—
276C23×C3—22no—
277C23×C3—22no—
278C23×C3—22no—
279C23×C3—22no—
280C23×C3—22no—
281C23×C3—22no—
282C23×C3—21no—
283C23×C3—32no—
284C23×C3—42no—
285C23×C3—42no—
286C23×C3—82no—
287C23×C3—82no—
288C23×C3—84no—
289C23×C3C2×C4×D311yescharacteristic
290C23×C3C22×Dic311yescharacteristic
291C22×D3#21712yes—
292C3×Q8—61no—
293C3×Q8—61no—
294C3×D4—42no—
295C3×D4—42no—
296C3×D4—42no—
297C3×D4—42no—
298C3×D4—41no—
299C3×D4—41no—
300C3×D4—41no—
301C3×D4—41no—
302C3×D4—41no—
303C3×D4—41no—
304C3×D4—41no—
305C3×D4—41no—
306C3×D4—62no—
307C3×D4—62no—
308C3×D4—61no—
309C3×D4—61no—
310C3×D4—244no—
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—32no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4#23511yescharacteristic
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4#23711yescharacteristic
328C2×C3×C4#23711yescharacteristic
329C2×C3×C4#23711yescharacteristic
330C2×C3×C4C2×#6711yescharacteristic
331C2×C3×C4C2×#6711yescharacteristic
332C2×C3×C4C2×#6711yescharacteristic
333#67—22no—
334#67—22no—
335#67—84no—
336C2×Dic3—22no—
337C2×Dic3#21712yes—
338D12—21no—
339D12—21no—
340C4×D3—22no—
341C4×D3—22no—
342Dic6—21no—
343Dic6—21no—
344C3×C8—62no—
345C3×C8—121no—
346C3⋊C8—22no—
347C3⋊C8—41no—
348C3⋊C8—62no—
349C3⋊C8—62no—
350C3⋊C8—122no—
351C3⋊C8—122no—
352C3⋊C8—121no—
353C3⋊C8—121no—
354C2×C32—21no—
355C2×C32—21no—
356C2×C32—21no—
357C2×C32—82no—
358C2×C32#38611yescharacteristic
359C3×D3—42no—
360C24D3×Dic312yes—
361#41—61no—
362#41—61no—
363#41—61no—
364#41—61no—
365C2×Q8—31no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—32no—
373C2×D4—31no—
374C2×D4—64no—
375C22×C4—32no—
376C22×C4C2×D3211yescharacteristic
377M16—32no—
378M16—61no—
379M16—61no—
380M16—61no—
381M16—92no—
382M16—184no—
383M16—181no—
384M16—181no—
385M16—181no—
386C2×C8—61no—
387C2×C8—61no—
388C2×C8—184no—
389C2×C8—181no—
390C2×C8—181no—
391C4⋊C4—61no—
392C22⋊C4—32no—
393C22⋊C4—64no—
394C42—61no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—42no—
401C22×C3—44no—
402C22×C3—44no—
403C22×C3—44no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—62no—
407C22×C3—84no—
408C22×C3—82no—
409C22×C3—82no—
410C22×C3—82no—
411C22×C3—82no—
412C22×C3—84no—
413C22×C3—84no—
414C22×C3—122no—
415C22×C3D3×C22⋊C411yescharacteristic
416C22×C3#67⋊C411yescharacteristic
417C22×C3C4×#6711yescharacteristic
418C22×C3D4×Dic311yescharacteristic
419C22×C3D4×Dic311yescharacteristic
420C22×C3C2×#21711yescharacteristic
421C2×D3—22no—
422C2×D3—42no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—62no—
428C3×C4—122no—
429C3×C4#88311yescharacteristic
430C3×C4#88411yescharacteristic
431C3×C4#93511yescharacteristic
432C3×C4#93711yescharacteristic
433C3×C4#93711yescharacteristic
434C3×C4#93811yescharacteristic
435C3×C4#93911yescharacteristic
436C3×C4#93911yescharacteristic
437Dic3—22no—
438Dic3—42no—
439C32#191411yescharacteristic, complemented, Sylow
440C23—22no—
441C23—22no—
442C23—22no—
443C23—32no—
444C23—82no—
445C23C2×D3×Dic311yescharacteristic
446Q8—61no—
447Q8—61no—
448D4—41no—
449D4—41no—
450D4—41no—
451D4—41no—
452D4—62no—
453D4—62no—
454D4—61no—
455D4—61no—
456D4—244no—
457C2×C4—32no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4#380411yescharacteristic
462C2×C4#380511yescharacteristic
463C2×C4D3×#6711yescharacteristic
464C2×C4D3×#6711yescharacteristic
465C2×C4D3×#6711yescharacteristic
466C2×C4#381111yescharacteristic
467C8—62no—
468C8—121no—
469C8—182no—
470C8—361no—
471C2×C3—22no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—41no—
480C2×C3—41no—
481C2×C3—84no—
482C2×C3—82no—
483C2×C3—82no—
484C2×C3—122no—
485C2×C3#495611yescharacteristic
486C2×C3#522011yescharacteristic
487D3—42no—
488C22—41no—
489C22—44no—
490C22—42no—
491C22—62no—
492C22—82no—
493C22—82no—
494C22—122no—
495C22D3×#21711yescharacteristic
496C22Dic3×#6711yescharacteristic
497C22#67⋊Dic311yescharacteristic
498C4—62no—
499C4—122no—
500C4#6396911yescharacteristic
501C4#6397011yescharacteristic
502C4#6397111yescharacteristic
503C4#6398311yescharacteristic
504C3—21no—
505C3#7008911yescharacteristic, complemented
506C3#7185511yescharacteristic, complemented
507C2—21no—
508C2—21no—
509C2—21no—
510C2—82no—
511C2—122no—
512C2#1059172111yescharacteristic
subgroupG/H
centerC2#10591721
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC2×C32#386
prime radicalC3×#5805C2
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1914
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10594776C2semidirect
3. C2×#63660C2semidirect
4. C2×C3×#833C2semidirect
5. #10591076C2semidirect
6. #10589170C2semidirect
7. #10589169C2semidirect
37. C2×#833D3semidirect
63. #3748D4semidirect
73. C3×#208D4semidirect
229. #208#67semidirect
439. C32#1914semidirect
505. C3#70089semidirect
506. C3#71855semidirect

Maximal subgroups

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

subgroupindex
C3×#58052
#105947762
C2×#636602
C2×C3×#8332
#105910762
#105891702
#105891692
#718553
#700893