Finite Group Databasebeta

← #11895680

Subgroups — #11895680

Order 1152.

744 conjugacy classes of subgroups.

The subgroup lattice has 509 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593951C211yesmaximal, characteristic
2#10593860C211yesmaximal, characteristic, complemented
3#10592550C211yesmaximal, characteristic, complemented
4C3×#4848C211yesmaximal, characteristic
5C3×#4830C211yesmaximal, characteristic, complemented
6#10590863C212yesmaximal, complemented
7#10590859C212yesmaximal, complemented
8#10590772C212yesmaximal, complemented
9Dic3×#204C212yesmaximal, complemented
10C4×#3719C211yesmaximal, characteristic, complemented
11#10590273C211yesmaximal, characteristic
12#80370—31nomaximal
13#79935—31nomaximal
14#64078C2211yescharacteristic
15C4×#634C2211yescharacteristic
16C2×C3×#204C2212yes—
17C3×#874C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63898—21no—
21Dic3×D12C2212yes—
22#63884—22no—
23#63869C2212yes—
24#63866—21no—
25#63863—21no—
26#63860C2212yes—
27#63845—22no—
28#63844—21no—
29Dic3×Dic6C2212yes—
30C2×#3719C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63644C2212yes—
33#63643C2212yes—
34C3×#821C2212yes—
35C3×Dic3⋊C8C2212yes—
36C3×C8×Dic3C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38#63575C2211yescharacteristic
39#63567C2211yescharacteristic
40#63566C2211yescharacteristic
41#63563C2212yes—
42#63563C2212yes—
43#5713—31no—
44#5585—31no—
45#5570—31no—
46#5567—31no—
47C3×#460—31no—
48C3×C8×Q8—31no—
49#5166—32no—
50Dic3×SD16—32no—
51#5070—31no—
52C4×#216—31no—
53#4851—31no—
54#4851—31no—
55#4851—61no—
56#4848D311yescharacteristic
57#4847—32no—
58#4845—32no—
59#4830D311yescharacteristic, complemented
60#4768—32no—
61#4763—32no—
62C4×Dic12—31no—
63#4697—32no—
64#4694—31no—
65C4×#204—32no—
66C2×#634—21no—
67C2×#634C2311yescharacteristic
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12C2312yes—
71C2×C3×Dic6D411yescharacteristic
72C2×C3×Dic6C2311yescharacteristic
73C2×D3×Dic3—22no—
74C2×C32×C8C2312yes—
75C32×C42C2311yescharacteristic
76C4⋊(C3⋊Dic3)—21no—
77C4⋊(C3⋊Dic3)C2312yes—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79#3750—21no—
80C4×C3⋊Dic3—21no—
81C3×C4⋊Dic3D411yescharacteristic
82C3×C4⋊Dic3C2311yescharacteristic
83C3×Dic3⋊C4—21no—
84C3×Dic3⋊C4D412yes—
85C3×C4×Dic3—21no—
86C3×C4×Dic3C2312yes—
87C2×C3×C3⋊C8C2311yescharacteristic
88C2×C3×C3⋊C8C2311yescharacteristic
89C3×#204—24no—
90#3724—22no—
91Dic3⋊Dic3—22no—
92Dic3⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96Dic32—22no—
97#3719—22no—
98#3365—91noSylow
99C2×C3×SD16—32no—
100C3×#127—31no—
101C3×C4×Q8—31no—
102C3×C4×Q8—31no—
103#947—61no—
104Q8×Dic3—32no—
105#944—61no—
106C2×#216—31no—
107#936—32no—
108#936—61no—
109#935—62no—
110D4×Dic3—32no—
111D4×Dic3—61no—
112C2×Dic12—31no—
113C2×#204C2×D312yes—
114#894—62no—
115#893—61no—
116#890—32no—
117#890—62no—
118#889—62no—
119#887—61no—
120#875—32no—
121#874C2×D311yescharacteristic
122C4×D12—32no—
123#870—32no—
124#869—31no—
125#869—31no—
126#869—61no—
127#869—61no—
128C4×Dic6—32no—
129C4×Dic6—31no—
130C4×Dic6—31no—
131C4×Dic6—61no—
132C4×Dic6—61no—
133C4×Dic6C2×D311yescharacteristic
134C4×Dic6C2×D311yescharacteristic
135C3×C4⋊C8—21no—
136C3×C4⋊C8—32no—
137C3×C4⋊C8C2×D311yescharacteristic
138C3×C4⋊C8C2×D311yescharacteristic
139C3×#102—32no—
140C3×C4×C8—32no—
141C3×C4×C8—31no—
142#835—31no—
143#832—32no—
144#832—32no—
145#821—32no—
146#821—32no—
147#821C2×D312yes—
148#818—31no—
149#817—32no—
150#817—32no—
151#817—62no—
152#816—31no—
153#816—32no—
154#816—32no—
155#816—31no—
156#816—62no—
157Dic3⋊C8C2×D312yes—
158C8×Dic3C2×D312yes—
159#810—31no—
160#807—31no—
161C4×C3⋊C8C2×D311yescharacteristic
162C22×C3×D3—22no—
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2411yescharacteristic
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—21no—
169#634—21no—
170#634—21no—
171#634—42no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3C2×D412yes—
175C2×C3×Dic3C2×D412yes—
176C3×D12—22no—
177C3×D12—22no—
178C3×D12—42no—
179C3×D12—81no—
180C3×Dic6—22no—
181C3×Dic6—21no—
182C3×Dic6#4112yes—
183D3×Dic3—82no—
184C32×C8—22no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8—21no—
187#559—91no—
188#557—91no—
189#488—92no—
190#486—91no—
191#478—92no—
192#475—91no—
193#464—92no—
194#460—31no—
195C8×Q8—31no—
196C4×Q16—91no—
197C4×SD16—92no—
198C2×C3×Q8—31no—
199C2×C3×Q8—31no—
200C2×C3×D4—32no—
201C2×C3×D4—61no—
202C2×C3×D4—61no—
203C22×Dic3—62no—
204C2×D12—21no—
205C2×D12—21no—
206C2×D12C22×D312yes—
207C2×C4×D3—62no—
208C2×Dic6—31no—
209C2×Dic6—31no—
210C2×Dic6—61no—
211C2×Dic6—61no—
212C2×Dic6—61no—
213C2×Dic6—121no—
214C2×Dic6D1211yescharacteristic
215C2×Dic6C22×D311yescharacteristic
216C3×SD16—64no—
217C2×C3×C8—22no—
218C2×C3×C8—31no—
219C2×C3×C8—31no—
220C2×C3×C8C22×D312yes—
221C2×C3×C8C22×D312yes—
222C3×C4⋊C4—31no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—61no—
226C3×C42—21no—
227C3×C42—32no—
228C3×C42—61no—
229C3×C42C22×D311yescharacteristic
230C3×C42C22×D311yescharacteristic
231#217—62no—
232#217—62no—
233#217—62no—
234#216—62no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—62no—
237(C2×D3)⋊C4—62no—
238C4⋊Dic3—31no—
239C4⋊Dic3—31no—
240C4⋊Dic3—32no—
241C4⋊Dic3—32no—
242C4⋊Dic3—62no—
243C4⋊Dic3—61no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3—62no—
247C4⋊Dic3—62no—
248C4⋊Dic3—121no—
249C4⋊Dic3D1211yescharacteristic
250C4⋊Dic3C22×D311yescharacteristic
251Dic3⋊C4—21no—
252Dic3⋊C4—62no—
253Dic3⋊C4—62no—
254Dic3⋊C4—62no—
255Dic3⋊C4—61no—
256Dic3⋊C4—61no—
257Dic3⋊C4—62no—
258Dic3⋊C4—121no—
259Dic3⋊C4D1212yes—
260C4×Dic3—21no—
261C4×Dic3—62no—
262C4×Dic3—61no—
263C4×Dic3—61no—
264C4×Dic3—62no—
265C4×Dic3—121no—
266C4×Dic3C22×D312yes—
267C2×C3⋊C8C22×D311yescharacteristic
268C2×C3⋊C8C22×D311yescharacteristic
269Dic12—62no—
270#204—24no—
271C22×C32C22×D411yescharacteristic
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274C2×C3×D3—42no—
275C32×C4—21no—
276C32×C4#13512yes—
277C32×C4C2×#4111yescharacteristic
278C32×C42−1+411yescharacteristic
279C3⋊Dic3—41no—
280C3⋊Dic3—42no—
281C3⋊Dic3—41no—
282C3×Dic3—22no—
283C3×Dic3—22no—
284C3×Dic3—22no—
285C3×Dic3—41no—
286C2×Q16—91no—
287C2×SD16—32no—
288C4⋊Q8—91no—
289C4⋊Q8—181no—
290#127—31no—
291#125—92no—
292#125—182no—
293#124—92no—
294#124—181no—
295#123—182no—
296C4×Q8—31no—
297C4×Q8—31no—
298C4×Q8—92no—
299C4×Q8—91no—
300C4×Q8—181no—
301C4×D4—92no—
302C4×D4—181no—
303#107—91no—
304#106—92no—
305C4⋊C8—32no—
306C4⋊C8D3211yescharacteristic
307#103—91no—
308#103—91no—
309#103—92no—
310#102—32no—
311#102—92no—
312#102—92no—
313C4×C8—32no—
314C4×C8—31no—
315C23×C3—62no—
316C22×D3—22no—
317C3×Q8—32no—
318C3×Q8—62no—
319C3×Q8—61no—
320C3×D4—62no—
321C3×D4—62no—
322C3×D4—122no—
323C3×D4—241no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—32no—
328C2×C3×C4—32no—
329C2×C3×C4—61no—
330C2×C3×C4—61no—
331C2×C3×C4C2×D1211yescharacteristic
332C2×C3×C4C2×D1211yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4C23×D311yescharacteristic
336C2×C3×C4C23×D311yescharacteristic
337C2×Dic3—21no—
338C2×Dic3—21no—
339C2×Dic3—62no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—62no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—121no—
346C2×Dic3—121no—
347C2×Dic3—122no—
348C2×Dic3—242no—
349C2×Dic3C2×D1212yes—
350C2×Dic3C2×D1212yes—
351D12—22no—
352D12—22no—
353D12—42no—
354D12—81no—
355C4×D3—242no—
356Dic6—22no—
357Dic6—21no—
358Dic6—62no—
359Dic6—61no—
360Dic6—61no—
361Dic6—61no—
362Dic6—61no—
363Dic6—121no—
364Dic6—122no—
365Dic6—122no—
366Dic6—242no—
367Dic6#23712yes—
368C3×C8—22no—
369C3×C8—22no—
370C3×C8—42no—
371C3×C8—61no—
372C3×C8—61no—
373C3⋊C8—21no—
374C3⋊C8—21no—
375C2×C32#54811yescharacteristic
376C2×C32C2×#13511yescharacteristic
377C2×C32#57711yescharacteristic
378C3×D3—82no—
379C2×Q8—31no—
380C2×Q8—31no—
381C2×Q8—91no—
382C2×Q8—181no—
383C2×D4—32no—
384C2×D4—61no—
385C2×D4—61no—
386C22×C4—182no—
387Q16—182no—
388SD16—64no—
389C2×C8—31no—
390C2×C8—31no—
391C2×C8C2×D3212yes—
392C4⋊C4—31no—
393C4⋊C4—32no—
394C4⋊C4—31no—
395C4⋊C4—61no—
396C4⋊C4—92no—
397C4⋊C4—91no—
398C4⋊C4—182no—
399C4⋊C4—182no—
400C4⋊C4—182no—
401C4⋊C4—181no—
402C4⋊C4—181no—
403C22⋊C4—182no—
404C22⋊C4—182no—
405C22⋊C4—182no—
406C42—32no—
407C42—61no—
408C42—182no—
409C42—181no—
410C42C2×D3211yescharacteristic
411C22×C3—21no—
412C22×C3—122no—
413C22×C3—122no—
414C22×C3—122no—
415C22×C3C22×D1211yescharacteristic
416C22×C3C2×D3×D411yescharacteristic
417C2×D3—42no—
418C2×D3—42no—
419C2×D3—42no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—22no—
425C3×C4—41no—
426C3×C4—62no—
427C3×C4—62no—
428C3×C4—62no—
429C3×C4—121no—
430C3×C4#90412yes—
431C3×C4#91612yes—
432C3×C4C2×#23711yescharacteristic
433C3×C4#100711yescharacteristic
434C3×C4D3×#4111yescharacteristic
435C3×C4#101011yescharacteristic
436Dic3—22no—
437Dic3—22no—
438Dic3—22no—
439Dic3—41no—
440Dic3—122no—
441Dic3—122no—
442Dic3—121no—
443Dic3—122no—
444Dic3—121no—
445Dic3—121no—
446Dic3—121no—
447Dic3—242no—
448Dic3—241no—
449C32#336511yescharacteristic, complemented, Sylow
450C23—62no—
451Q8—32no—
452Q8—61no—
453Q8—62no—
454Q8—181no—
455Q8—181no—
456Q8—362no—
457D4—62no—
458D4—62no—
459D4—122no—
460D4—241no—
461C2×C4—32no—
462C2×C4—32no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—181no—
466C2×C4—181no—
467C2×C4—182no—
468C2×C4—722no—
469C2×C4D3×D1211yescharacteristic
470C2×C4D3×D1211yescharacteristic
471C2×C4C22×D3211yescharacteristic
472C8—22no—
473C8—61no—
474C8—61no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—242no—
479C2×C3#557611yescharacteristic
480C2×C3#559811yescharacteristic
481C2×C3C2×#90411yescharacteristic
482C2×C3#575111yescharacteristic
483C2×C3C2×#91611yescharacteristic
484C2×C3#577511yescharacteristic
485D3—82no—
486C22—122no—
487C22—122no—
488C22—122no—
489C22C2×D3×D1211yescharacteristic
490C4—21no—
491C4—62no—
492C4—62no—
493C4—62no—
494C4—121no—
495C4—361no—
496C4—362no—
497C4—361no—
498C4#6380612yes—
499C4D3×#23711yescharacteristic
500C4#6431511yescharacteristic
501C3—21no—
502C3#7993511yescharacteristic, complemented
503C3#8037011yescharacteristic, complemented
504C2—242no—
505C2#1059438211yescharacteristic
506C2C2×#6380611yescharacteristic
507C2#1059471311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC3×#874C22
hypercenterC4⋊C8D32
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593860C2semidirect
3. #10592550C2semidirect
5. C3×#4830C2semidirect
6. #10590863C2semidirect
7. #10590859C2semidirect
8. #10590772C2semidirect
9. Dic3×#204C2semidirect
10. C4×#3719C2semidirect
59. #4830D3semidirect
449. C32#3365semidirect
502. C3#79935semidirect
503. C3#80370semidirect

Maximal subgroups

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

subgroupindex
#105939512
#105938602
#105925502
C3×#48482
C3×#48302
#105908632
#105908592
#105907722
Dic3×#2042
C4×#37192
#105902732
#803703
#799353