Finite Group Databasebeta

← #11895674

Subgroups — #11895674

Order 1152.

755 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593963C211yesmaximal, characteristic
2#10593860C211yesmaximal, characteristic, complemented
3#10592393C211yesmaximal, characteristic
4C3×C4×Dic12C211yesmaximal, characteristic, complemented
5C3×C8×Dic6C211yesmaximal, characteristic, complemented
6#10590872C212yesmaximal, complemented
7#10590801C212yesmaximal, complemented
8#10590792C212yesmaximal, complemented
9#10590774C212yesmaximal, complemented
10#10590367C211yesmaximal, characteristic
11#10590301C211yesmaximal, characteristic, complemented
12#79935—31nomaximal
13#79701—31nomaximal
14#64083C2211yescharacteristic
15#64078C2211yescharacteristic
16C2×C3×Dic12C2211yescharacteristic
17C3×C4×Dic6C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63897—22no—
21#63894—21no—
22#63894C2212yes—
23#63869C2212yes—
24#63866—21no—
25#63864—21no—
26#63864C2212yes—
27#63845—22no—
28#63844—21no—
29Dic3×Dic6C2212yes—
30C2×#3717C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63648C2212yes—
33#63648C2212yes—
34C3×#818C2211yescharacteristic
35C3×#816C2211yescharacteristic
36C3×#816C2211yescharacteristic
37C3×Dic3⋊C8C2212yes—
38C3×C8×Dic3C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63573C2212yes—
41#63566C2212yes—
42#63564C2212yes—
43#5585—31no—
44#5585—31no—
45#5570—31no—
46#5567—31no—
47C3×C8×Q8—31no—
48C3×C4×Q16—31no—
49#5185—32no—
50#5027—31no—
51#5020—31no—
52#4891—32no—
53#4851—31no—
54#4848—31no—
55#4847—32no—
56#4845—32no—
57#4800—32no—
58#4788—32no—
59C4×Dic12D311yescharacteristic, complemented
60#4697—32no—
61#4694—31no—
62#4694—31no—
63#4694—61no—
64C4×#204—32no—
65C8×Dic6D311yescharacteristic, complemented
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)C2312yes—
69C2×#634—21no—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6C2311yescharacteristic
72C2×C3×Dic6C2311yescharacteristic
73C2×#624—22no—
74C2×C32×C8C2311yescharacteristic
75C2×C32×C8C2311yescharacteristic
76C32×C42C2311yescharacteristic
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)C2312yes—
79C3×C4⋊Dic3D411yescharacteristic
80C3×C4⋊Dic3C2311yescharacteristic
81C3×C4⋊Dic3C2311yescharacteristic
82C3×Dic3⋊C4—21no—
83C3×Dic3⋊C4—21no—
84C3×Dic3⋊C4D412yes—
85C3×C4×Dic3—21no—
86C3×C4×Dic3—21no—
87C3×C4×Dic3C2312yes—
88C2×C3×C3⋊C8C2312yes—
89C3×Dic12—22no—
90#3724—22no—
91Dic3⋊Dic3—22no—
92Dic3⋊Dic3—22no—
93#3722—22no—
94#3722—22no—
95#3722—22no—
96Dic32—22no—
97#3717—24no—
98#3365—91noSylow
99C2×C3×Q16—31no—
100C3×C4×Q8—31no—
101C3×C4×Q8—31no—
102C3×C4×Q8—31no—
103#947—32no—
104#947—61no—
105Q8×Dic3—32no—
106#944—61no—
107C2×#215—32no—
108C2×Dic12C2×D311yescharacteristic
109C2×#204—32no—
110#894—62no—
111#894—62no—
112#893—32no—
113#893—61no—
114#890—32no—
115#890—62no—
116#889—62no—
117#887—61no—
118#875—32no—
119#875—61no—
120#874—31no—
121#874—31no—
122#874—61no—
123C4×D12—32no—
124C4×D12—61no—
125#870—32no—
126#869—31no—
127#869—31no—
128#869—61no—
129#869—61no—
130C4×Dic6—32no—
131C4×Dic6—61no—
132C4×Dic6C2×D311yescharacteristic
133C4×Dic6C2×D311yescharacteristic
134C4×Dic6C2×D311yescharacteristic
135C3×#107—31no—
136C3×C4⋊C8—32no—
137C3×C4⋊C8—31no—
138C3×#103—31no—
139C3×#103—31no—
140C3×C4×C8—21no—
141C3×C4×C8—32no—
142C3×C4×C8C2×D311yescharacteristic
143C3×C4×C8C2×D311yescharacteristic
144#835—32no—
145#821—32no—
146#821—32no—
147#821—32no—
148#821—32no—
149#821—32no—
150#821—62no—
151#821—62no—
152#818C2×D311yescharacteristic
153#817—32no—
154#816—32no—
155#816C2×D311yescharacteristic
156#816C2×D311yescharacteristic
157Dic3⋊C8C2×D312yes—
158C8×Dic3C2×D312yes—
159#809—32no—
160#808—32no—
161C4⋊(C3⋊C8)C2×D311yescharacteristic
162C22×C3⋊D3—22no—
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2411yescharacteristic
166C2×C3⋊Dic3—22no—
167C4⋊(C3⋊D3)—22no—
168C4⋊(C3⋊D3)—22no—
169C4⋊(C3⋊D3)—42no—
170C4⋊(C3⋊D3)—81no—
171#634—42no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3C2×D412yes—
177C2×C3×Dic3C2×D412yes—
178C3×Dic6—22no—
179C3×Dic6—21no—
180C3×Dic6—21no—
181C3×Dic6—21no—
182C3×Dic6#4112yes—
183#624—82no—
184C32×C8—21no—
185C32×C8—21no—
186C3×C3⋊C8—22no—
187#559—91no—
188#557—91no—
189#488—92no—
190#486—91no—
191#478—92no—
192#475—91no—
193#464—92no—
194#460—91no—
195C8×Q8—31no—
196C4×Q16—31no—
197C4×SD16—92no—
198C2×C3×Q8—31no—
199C2×C3×Q8—31no—
200C2×C3×Q8—31no—
201C2×D12—32no—
202C2×D12—32no—
203C2×D12—62no—
204C2×D12—61no—
205C2×D12—61no—
206C2×D12—61no—
207C2×D12—61no—
208C2×D12—121no—
209C2×D12—121no—
210C2×C4×D3—62no—
211C2×C4×D3—62no—
212C2×Dic6—61no—
213C2×Dic6—61no—
214C2×Dic6—121no—
215C2×Dic6D1211yescharacteristic
216C2×Dic6C22×D311yescharacteristic
217C2×Dic6C22×D311yescharacteristic
218C3×Q16—62no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—32no—
222C2×C3×C8C22×D311yescharacteristic
223C2×C3×C8C22×D311yescharacteristic
224C2×C3×C8C22×D311yescharacteristic
225C2×C3×C8C22×D311yescharacteristic
226C3×C4⋊C4—31no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—61no—
232C3×C42—21no—
233C3×C42—32no—
234C3×C42—61no—
235C3×C42—61no—
236C3×C42C22×D311yescharacteristic
237C3×C42C22×D311yescharacteristic
238#215—64no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245C4⋊Dic3—32no—
246C4⋊Dic3—32no—
247C4⋊Dic3—62no—
248C4⋊Dic3—61no—
249C4⋊Dic3—61no—
250C4⋊Dic3—62no—
251C4⋊Dic3—62no—
252C4⋊Dic3—121no—
253C4⋊Dic3D1211yescharacteristic
254C4⋊Dic3C22×D311yescharacteristic
255C4⋊Dic3C22×D311yescharacteristic
256Dic3⋊C4—21no—
257Dic3⋊C4—21no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262Dic3⋊C4D1212yes—
263C4×Dic3—21no—
264C4×Dic3—21no—
265C4×Dic3—62no—
266C4×Dic3—62no—
267C4×Dic3C22×D312yes—
268C2×C3⋊C8C22×D312yes—
269Dic12—22no—
270#204—64no—
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—42no—
280C3×Dic3—22no—
281C3×Dic3—22no—
282C3×Dic3—22no—
283C3×Dic3—41no—
284C3×Dic3—41no—
285C3×Dic3—41no—
286C2×Q16—31no—
287C2×SD16—92no—
288C4⋊Q8—91no—
289C4⋊Q8—181no—
290#127—91no—
291#125—92no—
292#125—182no—
293#124—92no—
294#124—181no—
295#123—182no—
296C4×Q8—31no—
297C4×Q8—31no—
298C4×Q8—31no—
299C4×Q8—92no—
300C4×Q8—181no—
301C4×D4—92no—
302C4×D4—181no—
303#107—31no—
304#106—92no—
305C4⋊C8—32no—
306C4⋊C8—31no—
307#103—31no—
308#103—31no—
309#103—92no—
310#102—92no—
311#102—92no—
312#102—92no—
313C4×C8—32no—
314C4×C8D3211yescharacteristic
315C22×D3—62no—
316C22×D3—62no—
317C22×D3—122no—
318C3×Q8—32no—
319C3×Q8—62no—
320C3×Q8—61no—
321C3×Q8—61no—
322C3×Q8—61no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—32no—
327C2×C3×C4—32no—
328C2×C3×C4—61no—
329C2×C3×C4—61no—
330C2×C3×C4—61no—
331C2×C3×C4—61no—
332C2×C3×C4C2×D1211yescharacteristic
333C2×C3×C4C2×D1211yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4C23×D311yescharacteristic
337C2×C3×C4C23×D311yescharacteristic
338C2×Dic3—21no—
339C2×Dic3—21no—
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—62no—
343C2×Dic3—62no—
344C2×Dic3—122no—
345C2×Dic3C2×D1212yes—
346C2×Dic3C2×D1212yes—
347D12—62no—
348D12—62no—
349D12—62no—
350D12—62no—
351D12—122no—
352D12—122no—
353D12—122no—
354D12—122no—
355D12—242no—
356D12—241no—
357D12—241no—
358D12—242no—
359C4×D3—242no—
360C4×D3—242no—
361Dic6—22no—
362Dic6—21no—
363Dic6—21no—
364Dic6—21no—
365Dic6—122no—
366Dic6—122no—
367Dic6—242no—
368Dic6#23512yes—
369C3×C8—21no—
370C3×C8—21no—
371C3×C8—21no—
372C3×C8—21no—
373C3×C8—41no—
374C3×C8—41no—
375C3×C8—62no—
376C3⋊C8—22no—
377C2×C32#54811yescharacteristic
378C2×C32C2×#13511yescharacteristic
379C2×C32#57711yescharacteristic
380C3⋊D3—82no—
381C2×Q8—31no—
382C2×Q8—31no—
383C2×Q8—31no—
384C2×Q8—181no—
385C2×D4—92no—
386C2×D4—181no—
387C2×D4—181no—
388C22×C4—182no—
389Q16—62no—
390SD16—184no—
391C2×C8—32no—
392C2×C8C2×D3211yescharacteristic
393C2×C8C2×D3211yescharacteristic
394C4⋊C4—31no—
395C4⋊C4—32no—
396C4⋊C4—31no—
397C4⋊C4—31no—
398C4⋊C4—61no—
399C4⋊C4—61no—
400C4⋊C4—92no—
401C4⋊C4—182no—
402C4⋊C4—182no—
403C4⋊C4—182no—
404C4⋊C4—181no—
405C22⋊C4—182no—
406C22⋊C4—182no—
407C22⋊C4—182no—
408C42—32no—
409C42—61no—
410C42—61no—
411C42—182no—
412C42C2×D3211yescharacteristic
413C22×C3—21no—
414C22×C3C22×D1211yescharacteristic
415C22×C3C2×D3×D411yescharacteristic
416C2×D3—122no—
417C2×D3—122no—
418C2×D3—122no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—122no—
422C2×D3—242no—
423C2×D3—242no—
424C2×D3—242no—
425C3×C4—22no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—22no—
431C3×C4—62no—
432C3×C4—62no—
433C3×C4—62no—
434C3×C4—121no—
435C3×C4—121no—
436C3×C4—121no—
437C3×C4#90412yes—
438C3×C4#91912yes—
439C3×C4C2×#23511yescharacteristic
440C3×C4#100711yescharacteristic
441C3×C4D3×#4111yescharacteristic
442C3×C4#101011yescharacteristic
443Dic3—22no—
444Dic3—22no—
445Dic3—22no—
446Dic3—41no—
447Dic3—41no—
448Dic3—41no—
449Dic3—122no—
450Dic3—122no—
451Dic3—242no—
452C32#336511yescharacteristic, complemented, Sylow
453C23—182no—
454Q8—32no—
455Q8—61no—
456Q8—62no—
457Q8—61no—
458Q8—61no—
459Q8—362no—
460D4—182no—
461D4—182no—
462D4—362no—
463D4—721no—
464C2×C4—32no—
465C2×C4—32no—
466C2×C4—61no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—182no—
471C2×C4—722no—
472C2×C4D3×D1211yescharacteristic
473C2×C4D3×D1211yescharacteristic
474C2×C4C22×D3211yescharacteristic
475C8—21no—
476C8—21no—
477C8—62no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3#555211yescharacteristic
482C2×C3#557611yescharacteristic
483C2×C3C2×#90411yescharacteristic
484C2×C3#575111yescharacteristic
485C2×C3C2×#91911yescharacteristic
486C2×C3#577011yescharacteristic
487D3—242no—
488D3—242no—
489D3—482no—
490C22—362no—
491C22—362no—
492C22—362no—
493C22C2×D3×D1211yescharacteristic
494C4—21no—
495C4—62no—
496C4—62no—
497C4—62no—
498C4—121no—
499C4—121no—
500C4—121no—
501C4—362no—
502C4#6380812yes—
503C4#6429711yescharacteristic
504C4D3×#23511yescharacteristic
505C3—21no—
506C3#7970111yescharacteristic, complemented
507C3#7993511yescharacteristic, complemented
508C2—722no—
509C2#1059389911yescharacteristic
510C2#1059467911yescharacteristic
511C2C2×#6380811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#64083C22
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
4. C3×C4×Dic12C2semidirect
5. C3×C8×Dic6C2semidirect
6. #10590872C2semidirect
7. #10590801C2semidirect
8. #10590792C2semidirect
9. #10590774C2semidirect
11. #10590301C2semidirect
59. C4×Dic12D3semidirect
65. C8×Dic6D3semidirect
452. C32#3365semidirect
506. C3#79701semidirect
507. C3#79935semidirect

Maximal subgroups

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

subgroupindex
#105939632
#105938602
#105923932
C3×C4×Dic122
C3×C8×Dic62
#105908722
#105908012
#105907922
#105907742
#105903672
#105903012
#799353
#797013