Finite Group Databasebeta

← #11789954

Subgroups — #11789954

Order 1152.

539 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592812C211yesmaximal, characteristic
2C2×C3×C8×Dic3C211yesmaximal, characteristic, complemented
3#10591119C211yesmaximal, characteristic, complemented
4C2×#63570C211yesmaximal, characteristic
5#10591073C211yesmaximal, characteristic
6C3×#4552C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#69793—31nomaximal
9#68918—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×C3×C4×Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63648C412yescomplemented
18#63643C412yescomplemented
19C3×C8×Dic3—22no—
20#63572—22no—
21#63570—22no—
22#63557—22no—
23C2×C3×C4×C8—31no—
24C2×#825—31no—
25#5129—31no—
26#5119—31no—
27#5113—31no—
28#5113—31no—
29#5113—61no—
30#5110—31no—
31#5102—31no—
32C2×C8×Dic3D311yescharacteristic, complemented
33C2×#805—31no—
34C3×#341—31no—
35#4555—31no—
36#4552D311yescharacteristic, complemented
37#4523—31no—
38C22×C32×C4C2311yescharacteristic
39C2×#638—21no—
40#3828—21no—
41#3828—21no—
42#3828—21no—
43#3828—21no—
44C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
45C2×C4×C3⋊D3—21no—
46C2×#634C2×C411yescharacteristic
47C22×C3×Dic3—21no—
48C2×C32×C8—21no—
49C2×C32×C8—21no—
50C2×C32×C8C2×C412yes—
51#3757—21no—
52C4⋊(C3⋊Dic3)C2×C412yes—
53C4×C3⋊Dic3—21no—
54C3×C4×Dic3—21no—
55C3×C4×Dic3D412yes—
56C3×#208—21no—
57C3×#208—21no—
58C3×#208—21no—
59C3×#208—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8D412yes—
65#1937—91noSylow
66C2×#235—31no—
67C2×#235—31no—
68C2×#235—61no—
69C2×C3×M16—31no—
70C2×C3×M16—31no—
71C22×C3×C8—21no—
72C22×C3×C8—31no—
73C22×C3×C8C2×D311yescharacteristic
74C22×C3×C8C2×D311yescharacteristic
75C2×C3×C42—31no—
76#926—31no—
77#926—31no—
78#926—61no—
79C2×C4×Dic3C2×D311yescharacteristic
80C2×#208C2×D311yescharacteristic
81C2×#208C2×D311yescharacteristic
82C22×C3⋊C8C2×D311yescharacteristic
83C3×C4×C8—62no—
84#825—62no—
85#821—32no—
86#821—32no—
87#821—62no—
88(C2×D3)⋊C8—62no—
89(C2×D3)⋊C8—62no—
90#816—32no—
91#816—32no—
92#816—62no—
93Dic3⋊C8—62no—
94Dic3⋊C8—62no—
95C8×Dic3—22no—
96#805—62no—
97C23×C32#4111yescharacteristic
98C22×C3⋊D3—21no—
99C2×C32×C4C22×C411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C32×C4#4111yescharacteristic
105#638—41no—
106#638—41no—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—21no—
109C4⋊(C3⋊D3)—21no—
110C4⋊(C3⋊D3)—21no—
111C4×C3⋊D3—41no—
112C4×C3⋊D3—41no—
113#634—21no—
114#634—21no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—22no—
117C32×C8—22no—
118C3×C3⋊C8—22no—
119C3×C3⋊C8—41no—
120C3×C3⋊C8—41no—
121#424—91no—
122C2×#104—91no—
123#416—91no—
124#408—91no—
125C2×C4×C8—31no—
126#341—31no—
127#339—91no—
128C22×C3×C4—21no—
129C22×C3×C4—61no—
130C22×C3×C4C22×D311yescharacteristic
131C22×C3×C4C22×D311yescharacteristic
132C2×#67—61no—
133C2×#67—61no—
134C2×#67—121no—
135C22×Dic3—21no—
136#235—62no—
137#235—62no—
138#235—61no—
139#235—61no—
140#235—61no—
141#235—61no—
142#235—61no—
143#235—61no—
144#235—61no—
145#235—61no—
146#235—121no—
147#235—121no—
148C2×D12—31no—
149C2×D12—31no—
150C2×D12—61no—
151C2×C4×D3—61no—
152C2×C4×D3—61no—
153C2×C4×D3—121no—
154C2×Dic6—31no—
155C2×Dic6—31no—
156C2×Dic6—61no—
157C3×M16—61no—
158C3×M16—61no—
159C3×M16—61no—
160C3×M16—61no—
161C2×C3×C8—21no—
162C2×C3×C8—21no—
163C2×C3×C8—21no—
164C2×C3×C8—21no—
165C2×C3×C8—22no—
166C2×C3×C8—32no—
167C2×C3×C8—41no—
168C2×C3×C8—41no—
169C2×C3×C8—61no—
170C2×C3×C8—61no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C2×C3×C8C4×D312yes—
174C2×C3×C8C4×D312yes—
175C3×C42—32no—
176C3×C42—61no—
177#217—61no—
178#217—61no—
179#217—121no—
180C4⋊Dic3—32no—
181C4⋊Dic3—32no—
182C4⋊Dic3—62no—
183C4×Dic3—21no—
184C4×Dic3—61no—
185C4×Dic3—61no—
186C4×Dic3—121no—
187C4×Dic3#6712yes—
188#208—21no—
189#208—21no—
190#208—21no—
191#208—21no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8D1212yes—
197C22×C32—22no—
198C22×C32C4×D411yescharacteristic
199C22×C32#12311yescharacteristic
200C22×C32#12611yescharacteristic
201C2×C3⋊D3—41no—
202C2×C3⋊D3—42no—
203C32×C4#11711yescharacteristic
204C32×C4C4×D411yescharacteristic
205C32×C4#12111yescharacteristic
206C32×C4#12411yescharacteristic
207C3⋊Dic3—41no—
208C3⋊Dic3—42no—
209C3×Dic3—24no—
210C2×#41—91no—
211C2×M16—31no—
212C2×M16—31no—
213C22×C8—31no—
214C22×C8D3211yescharacteristic
215#117—91no—
216C2×C42—31no—
217C4⋊C8—182no—
218#104—182no—
219#103—92no—
220#102—92no—
221C22⋊C8—182no—
222C4×C8—62no—
223C23×C3—21no—
224C23×C3#23511yescharacteristic
225C23×C3#23911yescharacteristic
226C22×D3—61no—
227C22×D3—61no—
228C22×D3—121no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—64no—
236C2×C3×C4—62no—
237C2×C3×C4C2×C4×D311yescharacteristic
238C2×C3×C4C2×C4×D311yescharacteristic
239C2×C3×C4C2×D1211yescharacteristic
240C2×C3×C4#23511yescharacteristic
241C2×C3×C4#23511yescharacteristic
242C2×C3×C4#23511yescharacteristic
243C2×C3×C4#23511yescharacteristic
244C2×C3×C4#23511yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4#23711yescharacteristic
248C2×C3×C4C2×#6711yescharacteristic
249#67—122no—
250#67—122no—
251#67—121no—
252#67—121no—
253#67—121no—
254#67—121no—
255C2×Dic3—24no—
256C2×Dic3—22no—
257C2×Dic3—62no—
258C2×Dic3—61no—
259C2×Dic3—62no—
260C2×Dic3—61no—
261C2×Dic3—121no—
262C2×Dic3—122no—
263D12—62no—
264D12—61no—
265D12—61no—
266D12—61no—
267D12—61no—
268D12—121no—
269C4×D3—122no—
270C4×D3—122no—
271C4×D3—121no—
272C4×D3—121no—
273C4×D3—121no—
274C4×D3—121no—
275Dic6—62no—
276Dic6—61no—
277Dic6—61no—
278Dic6—61no—
279Dic6—61no—
280Dic6—121no—
281C3×C8—22no—
282C3×C8—22no—
283C3×C8—42no—
284C3×C8—62no—
285C3×C8—121no—
286C3×C8—121no—
287C3⋊C8—22no—
288C3⋊C8—41no—
289C3⋊C8—41no—
290C2×C32—21no—
291C2×C32—21no—
292C2×C32#38811yescharacteristic
293C2×C32#44312yes—
294C3⋊D3—81no—
295#41—181no—
296#41—181no—
297#41—181no—
298#41—181no—
299C2×Q8—91no—
300C2×D4—91no—
301C2×D4—181no—
302C22×C4—61no—
303C22×C4—181no—
304C22×C4C2×D3211yescharacteristic
305M16—61no—
306M16—61no—
307M16—61no—
308M16—61no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—32no—
312C2×C8—61no—
313C2×C8—61no—
314C2×C8—61no—
315C2×C8—61no—
316C2×C8#62412yes—
317C4⋊C4—92no—
318C22⋊C4—181no—
319C42—32no—
320C42—61no—
321C42—181no—
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—42no—
328C22×C3C4×D1211yescharacteristic
329C22×C3#87611yescharacteristic
330C22×C3#89311yescharacteristic
331C22×C3#89411yescharacteristic
332C22×C3#89811yescharacteristic
333C22×C3#92911yescharacteristic
334C2×D3—122no—
335C2×D3—122no—
336C2×D3—121no—
337C2×D3—121no—
338C2×D3—122no—
339C2×D3—242no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—64no—
345C3×C4#87211yescharacteristic
346C3×C4#87211yescharacteristic
347C3×C4#87511yescharacteristic
348C3×C4#67⋊C411yescharacteristic
349C3×C4#88411yescharacteristic
350C3×C4#88511yescharacteristic
351C3×C4C4×#6711yescharacteristic
352C3×C4#93011yescharacteristic
353Dic3—24no—
354Dic3—122no—
355Dic3—122no—
356Dic3—121no—
357Dic3—121no—
358Dic3—122no—
359Dic3—242no—
360C32#193711yescharacteristic, complemented, Sylow
361C23—181no—
362C23#379911yescharacteristic
363Q8—181no—
364Q8—181no—
365D4—181no—
366D4—181no—
367D4—361no—
368D4—361no—
369C2×C4—64no—
370C2×C4—62no—
371C2×C4—182no—
372C2×C4—181no—
373C2×C4—361no—
374C2×C4—361no—
375C2×C4#379811yescharacteristic
376C2×C4#379811yescharacteristic
377C2×C4D3×D1211yescharacteristic
378C2×C4#380411yescharacteristic
379C2×C4C2×#62411yescharacteristic
380C2×C4D3×#6711yescharacteristic
381C8—22no—
382C8—62no—
383C8—121no—
384C8—121no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—22no—
390C2×C3—21no—
391C2×C3—41no—
392C2×C3—41no—
393C2×C3#466911yescharacteristic
394C2×C3#470012yes—
395C2×C3#489512yes—
396C2×C3#494011yescharacteristic
397D3—242no—
398D3—241no—
399D3—241no—
400C22—22no—
401C22—362no—
402C22—361no—
403C22#6385011yescharacteristic
404C22#6386811yescharacteristic
405C22#6389411yescharacteristic
406C4—64no—
407C4—362no—
408C4—361no—
409C4#6385211yescharacteristic
410C4#6387411yescharacteristic
411C4#6390611yescharacteristic
412C4#6395211yescharacteristic
413C3—21no—
414C3#6891811yescharacteristic, complemented
415C3#6979311yescharacteristic, complemented
416C2—21no—
417C2—21no—
418C2—721no—
419C2#1059091712yes—
420C2#1059120211yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32C4×D4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1937
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×C8×Dic3C2semidirect
3. #10591119C2semidirect
6. C3×#4552C2semidirect
7. #10589162C2semidirect
17. #63648C4semidirect
18. #63643C4semidirect
32. C2×C8×Dic3D3semidirect
36. #4552D3semidirect
360. C32#1937semidirect
414. C3#68918semidirect
415. C3#69793semidirect

Maximal subgroups

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

subgroupindex
#105928122
C2×C3×C8×Dic32
#105911192
C2×#635702
#105910732
C3×#45522
#105891622
#697933
#689183