Finite Group Databasebeta

← #11886547

Subgroups — #11886547

Order 1152.

1075 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63810C212yesmaximal, complemented
2#10593900C212yesmaximal, complemented
3C8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C3×C4×Dic12C211yesmaximal, characteristic, complemented
5C3×#4695C211yesmaximal, characteristic, complemented
6#10590963C214yesmaximal, complemented
7#10590844C212yesmaximal, complemented
8#10590364C212yesmaximal, complemented
9#81790—31nomaximal
10#79734—31nomaximal
11C2×#3796C2214yes—
12C2×C8×C3⋊D3C2212yes—
13C4×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C3×Dic12C2211yescharacteristic
15C2×C3×D24C2212yes—
16C2×C3×D24C2212yes—
17C3×#874C2212yes—
18C3×C4×Dic6C2212yes—
19#63916C2214yes—
20#63911—22no—
21Dic3×D12—22no—
22#63886—24no—
23C2×#3715C2214yes—
24#63810—28no—
25C32×C4×C8C2211yescharacteristic
26#63647C2212yes—
27C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
28C3×#818C2211yescharacteristic
29C3×#816C2212yes—
30#63562C2214yes—
31C2×#919—32no—
32C2×#912—32no—
33#5718—32no—
34#5577—32no—
35C3×#493—31no—
36C3×C4×Q16—31no—
37#5158—34no—
38#5157—32no—
39#5075—32no—
40#5027—32no—
41#4883—32no—
42#4810—34no—
43C4×Dic12D311yescharacteristic, complemented
44#4695D311yescharacteristic, complemented
45C8×D12—31no—
46C8×D12—31no—
47C8×D12—61no—
48C2×C4⋊(C3⋊D3)D411yescharacteristic
49C2×C4×C3⋊D3C2312yes—
50C2×C3×D12—22no—
51C2×C3×D12—22no—
52C2×C3×D12C2314yes—
53C2×C3×Dic6C2312yes—
54C2×#626—24no—
55C2×#626—24no—
56C2×D3×Dic3—24no—
57#3796—28no—
58#3796—44no—
59C2×C32×C8C2311yescharacteristic
60C2×C32×C8C2311yescharacteristic
61C32×C42C2311yescharacteristic
62#3752D412yes—
63C4⋊(C3⋊Dic3)D411yescharacteristic
64C2×C3⋊(C3⋊C8)C2312yes—
65C8×C3⋊D3—24no—
66C3×C4⋊Dic3C2312yes—
67C3×Dic3⋊C4—22no—
68C3×C4×Dic3—22no—
69C3×Dic12D414yescomplemented
70C3×D24—24no—
71C3×D24—42no—
72(C2×D3)⋊Dic3—24no—
73#3715—28no—
74#3287—91noSylow
75C2×#239—34no—
76C2×#237—34no—
77C2×C3×Q16—31no—
78C2×C3×D8—32no—
79C2×C3×D8—32no—
80C3×#127—32no—
81C3×C4×Q8—32no—
82C2×#215—34no—
83#940—62no—
84#939—64no—
85#938—34no—
86D4×Dic3—62no—
87C2×#214—34no—
88#919—68no—
89#912—68no—
90C2×Dic12C2×D311yescharacteristic
91C2×D24C2×D312yes—
92C2×D24C2×D312yes—
93C2×D3×C8—32no—
94C2×D3×C8—32no—
95C2×D3×C8—62no—
96#895—34no—
97#895—64no—
98#874—62no—
99#874C2×D312yes—
100C4×D12—31no—
101C4×D12—31no—
102C4×D12—61no—
103C4×D12—62no—
104C4×Dic6C2×D312yes—
105C3×#107—31no—
106C3×#103—32no—
107C3×C4×C8—21no—
108C3×C4×C8C2×D311yescharacteristic
109C3×C4×C8C2×D311yescharacteristic
110#832—34no—
111(C2×D3)⋊C8—32no—
112(C2×D3)⋊C8—32no—
113(C2×D3)⋊C8—62no—
114#818C2×D311yescharacteristic
115#816C2×D312yes—
116#809—34no—
117C4⋊(C3⋊C8)—31no—
118C4⋊(C3⋊C8)—31no—
119C4⋊(C3⋊C8)—61no—
120C22×C3⋊D3C2×D412yes—
121C22×C3×D3—24no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2411yescharacteristic
125C2×C3⋊Dic3C2×D412yes—
126C4⋊(C3⋊D3)—22no—
127C4×C3⋊D3—22no—
128C4×C3⋊D3—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C3×D12—24no—
132C3×D12—24no—
133C3×D12—44no—
134C3×D12—82no—
135C3×Dic6—22no—
136C3×Dic6C2×D414yes—
137#626—48no—
138#626—84no—
139D3×Dic3—48no—
140C32×C8—21no—
141C32×C8C2×D412yes—
142C3⋊(C3⋊C8)—22no—
143C2×#135—92no—
144#550—92no—
145#493—31no—
146#466—92no—
147#460—92no—
148#449—94no—
149C4×Q16—31no—
150C8×D4—91no—
151C2×C3×Q8—32no—
152C2×C3×D4—34no—
153C2×C3×D4—62no—
154C2×C3×D4—62no—
155C2×#67—64no—
156C2×#67—64no—
157C22×Dic3—64no—
158#239—68no—
159#239—124no—
160#237—68no—
161#237—124no—
162C2×D12—22no—
163C2×D12—22no—
164C2×D12—31no—
165C2×D12—31no—
166C2×D12—61no—
167C2×D12—64no—
168C2×D12—64no—
169C2×D12C22×D314yes—
170C2×C4×D3—32no—
171C2×C4×D3—32no—
172C2×C4×D3—62no—
173C2×C4×D3—64no—
174C2×Dic6C22×D312yes—
175C3×Q16—34no—
176C3×D8—64no—
177C3×D8—122no—
178C2×C3×C8—21no—
179C2×C3×C8—21no—
180C2×C3×C8C22×D311yescharacteristic
181C2×C3×C8C22×D311yescharacteristic
182C2×C3×C8C22×D311yescharacteristic
183C2×C3×C8C22×D311yescharacteristic
184C3×C4⋊C4—32no—
185C3×C4⋊C4—62no—
186C3×C42—21no—
187C3×C42—62no—
188C3×C42C22×D311yescharacteristic
189C3×C42C22×D311yescharacteristic
190#217—64no—
191#215—68no—
192#214—68no—
193(C2×D3)⋊C4—32no—
194(C2×D3)⋊C4—32no—
195(C2×D3)⋊C4—62no—
196(C2×D3)⋊C4—64no—
197C4⋊Dic3—31no—
198C4⋊Dic3—31no—
199C4⋊Dic3—61no—
200C4⋊Dic3C22×D312yes—
201Dic3⋊C4—22no—
202C4×Dic3—22no—
203C2×C3⋊C8—32no—
204C2×C3⋊C8—32no—
205C2×C3⋊C8—62no—
206Dic12D1214yescomplemented
207D24—24no—
208D24—42no—
209D3×C8—64no—
210D3×C8—64no—
211D3×C8—124no—
212C22×C32C22×D411yescharacteristic
213C2×C3⋊D3—22no—
214C2×C3⋊D3—22no—
215C2×C3⋊D3—22no—
216C2×C3×D3—44no—
217C2×C3×D3—44no—
218C2×C3×D3—44no—
219C32×C4—21no—
220C32×C4#13512yescomplemented
221C32×C4C22×D411yescharacteristic
222C32×C4H(5,𝔽2)11yescharacteristic
223C3⋊Dic3—22no—
224C3×Dic3—24no—
225C3×Dic3—42no—
226C2×#41—94no—
227#135—188no—
228C2×Q16—31no—
229C2×SD16—94no—
230C2×D8—32no—
231C2×D8—32no—
232C22×C8—92no—
233#127—32no—
234#127—182no—
235#121—94no—
236#121—184no—
237C4×Q8—32no—
238C4×D4—91no—
239C4×D4—182no—
240#107—31no—
241C4⋊C8—91no—
242#103—32no—
243#102—94no—
244C22⋊C8—92no—
245C4×C8D3211yescharacteristic
246C23×C3—64no—
247C22×D3—24no—
248C22×D3—32no—
249C22×D3—32no—
250C22×D3—62no—
251C3×Q8—34no—
252C3×Q8—62no—
253C3×D4—64no—
254C3×D4—64no—
255C3×D4—124no—
256C3×D4—242no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—62no—
261C2×C3×C4—62no—
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4C23×D311yescharacteristic
267C2×C3×C4C23×D311yescharacteristic
268#67—128no—
269#67—244no—
270C2×Dic3—22no—
271C2×Dic3—22no—
272C2×Dic3—32no—
273C2×Dic3—32no—
274C2×Dic3—62no—
275C2×Dic3—128no—
276D12—24no—
277D12—24no—
278D12—44no—
279D12—64no—
280D12—62no—
281D12—62no—
282D12—82no—
283D12—128no—
284D12—244no—
285C4×D3—62no—
286C4×D3—62no—
287C4×D3—62no—
288C4×D3—62no—
289C4×D3—122no—
290C4×D3—122no—
291C4×D3—128no—
292Dic6—22no—
293Dic6C2×D1214yes—
294C3×C8—21no—
295C3×C8—21no—
296C3×C8—22no—
297C3×C8—41no—
298C3×C8C2×D1212yes—
299C3×C8D3×D412yes—
300C3⋊C8—62no—
301C3⋊C8—62no—
302C3⋊C8—122no—
303C2×C32D4211yescharacteristic
304C2×C32C2×#13511yescharacteristic
305C2×C32#57611yescharacteristic
306C3⋊D3—42no—
307C3×D3—84no—
308#41—188no—
309#41—364no—
310C2×Q8—32no—
311C2×D4—34no—
312C2×D4—62no—
313C2×D4—62no—
314C2×D4—91no—
315C2×D4—184no—
316C2×D4—184no—
317C22×C4—92no—
318C22×C4—184no—
319Q16—34no—
320SD16—188no—
321D8—64no—
322D8—122no—
323C2×C8—92no—
324C2×C8—184no—
325C2×C8C2×D3211yescharacteristic
326C2×C8C2×D3211yescharacteristic
327C4⋊C4—32no—
328C4⋊C4—62no—
329C4⋊C4—91no—
330C22⋊C4—92no—
331C22⋊C4—184no—
332C42—62no—
333C42C2×D3211yescharacteristic
334C22×C3—21no—
335C22×C3—124no—
336C22×C3—124no—
337C22×C3—124no—
338C22×C3C2×D3×D411yescharacteristic
339C22×C3C2×D3×D411yescharacteristic
340C2×D3—44no—
341C2×D3—44no—
342C2×D3—44no—
343C2×D3—64no—
344C2×D3—62no—
345C2×D3—62no—
346C2×D3—62no—
347C2×D3—62no—
348C2×D3—62no—
349C2×D3—62no—
350C2×D3—122no—
351C2×D3—122no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—22no—
357C3×C4—41no—
358C3×C4—64no—
359C3×C4—122no—
360C3×C4#91212yescomplemented
361C3×C4#91912yescomplemented
362C3×C4C22×D1211yescharacteristic
363C3×C4C2×D3×D411yescharacteristic
364C3×C4#100411yescharacteristic
365C3×C4#100911yescharacteristic
366Dic3—24no—
367Dic3—42no—
368Dic3—62no—
369Dic3—62no—
370Dic3—122no—
371C32#328711yescharacteristic, complemented, Sylow
372C23—64no—
373C23—92no—
374Q8—34no—
375Q8—62no—
376D4—64no—
377D4—64no—
378D4—124no—
379D4—182no—
380D4—242no—
381D4—368no—
382D4—724no—
383C2×C4—62no—
384C2×C4—62no—
385C2×C4—92no—
386C2×C4—182no—
387C2×C4—182no—
388C2×C4—368no—
389C2×C4#380211yescharacteristic
390C2×C4#380211yescharacteristic
391C2×C4C22×D3211yescharacteristic
392C8—21no—
393C8—182no—
394C8D3×D1212yes—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—244no—
399C2×C3D4×D1211yescharacteristic
400C2×C3#571711yescharacteristic
401C2×C3C2×#91211yescharacteristic
402C2×C3#575711yescharacteristic
403C2×C3C2×#91911yescharacteristic
404C2×C3#576911yescharacteristic
405D3—84no—
406D3—124no—
407D3—122no—
408D3—122no—
409C22—124no—
410C22—124no—
411C22—124no—
412C22—182no—
413C22—182no—
414C22—182no—
415C22C2×#380211yescharacteristic
416C4—21no—
417C4—64no—
418C4—122no—
419C4—182no—
420C4#6381012yescomplemented
421C4C2×D3×D1211yescharacteristic
422C4#6430711yescharacteristic
423C3—21no—
424C3#7973411yescharacteristic, complemented
425C3#8179011yescharacteristic, complemented
426C2—244no—
427C2—362no—
428C2#1059400411yescharacteristic
429C2#1059468711yescharacteristic
430C2C2×#6381011yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
hypercenterC4×C8D32
hypocenterC32#3287
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
1. C2×#63810C2semidirect
2. #10593900C2semidirect
3. C8×C4⋊(C3⋊D3)C2semidirect
4. C3×C4×Dic12C2semidirect
5. C3×#4695C2semidirect
6. #10590963C2semidirect
7. #10590844C2semidirect
8. #10590364C2semidirect
43. C4×Dic12D3semidirect
44. #4695D3semidirect
69. C3×Dic12D4semidirect
206. Dic12D12semidirect
220. C32×C4#135semidirect
360. C3×C4#912semidirect
361. C3×C4#919semidirect
371. C32#3287semidirect
420. C4#63810semidirect
424. C3#79734semidirect
425. C3#81790semidirect

Maximal subgroups

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

subgroupindex
C2×#638102
#105939002
C8×C4⋊(C3⋊D3)2
C3×C4×Dic122
C3×#46952
#105909632
#105908442
#105903642
#817903
#797343