Finite Group Databasebeta

← #11865638

Subgroups — #11865638

Order 1152.

1029 conjugacy classes of subgroups.

The subgroup lattice has 409 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63802C212yesmaximal
2#10593909C211yesmaximal, characteristic
3C4×#3797C211yesmaximal, characteristic
4C3⋊D3×C4⋊C8C211yesmaximal, characteristic
5C3×#4849C212yesmaximal, complemented
6#10590798C214yesmaximal, complemented
7#10590672C212yesmaximal
8#10590384C212yesmaximal, complemented
9D3×#462—32nomaximal
10C2×#3797C2212yes—
11C2×#3797C2211yescharacteristic
12C2×C8×C3⋊D3C2212yes—
13C42×C3⋊D3C2211yescharacteristic
14C2×C3×Dic12C2214yes—
15C3×#869C2212yes—
16C3×C4×Dic6C2212yes—
17#63919—21no—
18#63919—21no—
19C4×#627—21no—
20#63900—21no—
21#63900—21no—
22#63900C2211yescharacteristic
23#63883—21no—
24C4×#624—21no—
25#63873C2212yes—
26#63843C2212yes—
27#63838—21no—
28C2×#3718C2214yes—
29#63802—28no—
30C32×C4⋊C8C2211yescharacteristic
31#63641C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#816C2214yes—
34#63565C2214yes—
35C2×D3×Q16—34no—
36D3×C4⋊Q8—32no—
37C4×D3×Q8—32no—
38C3×#462—32no—
39#5182—34no—
40#5090—32no—
41#5031—32no—
42#4849D312yescomplemented
43D3×C4⋊C8—32no—
44D3×C4⋊C8—61no—
45D3×#103—34no—
46#4795—34no—
47C2×C4×C3⋊D3D411yescharacteristic
48C2×C4×C3⋊D3D411yescharacteristic
49C2×C4×C3⋊D3C2311yescharacteristic
50C2×C3×Dic6C2314yes—
51C2×C3×Dic6C2312yes—
52C2×#627—21no—
53C2×#627—22no—
54C2×#624—21no—
55C2×#624—22no—
56C2×#624—21no—
57#3797—22no—
58#3797—24no—
59#3797—24no—
60#3797D414yes—
61C2×C32×C8C2312yes—
62C32×C42C2311yescharacteristic
63C4×C3⋊Dic3D411yescharacteristic
64C4×C3⋊Dic3D411yescharacteristic
65C4×C3⋊Dic3C2311yescharacteristic
66C2×C3⋊(C3⋊C8)C2312yes—
67C8×C3⋊D3—24no—
68C3×C4⋊Dic3—22no—
69C3×C4⋊Dic3—22no—
70C3×C4⋊Dic3C2312yes—
71C3×Dic3⋊C4—22no—
72C3×C4×Dic3—22no—
73C3×Dic12—28no—
74#3724—21no—
75#3724—22no—
76#3724—22no—
77Dic3⋊Dic3—22no—
78Dic32—22no—
79#3718—28no—
80C2×#462—91noSylow
81C2×D3×Q8—32no—
82C2×D3×Q8—34no—
83C2×C3×Q16—34no—
84C3×C4⋊Q8—32no—
85C3×C4×Q8—32no—
86Q8×Dic3—32no—
87#944—34no—
88C2×#216—34no—
89C2×#216—34no—
90D3×Q16—616no—
91C2×Dic12C2×D314yes—
92C2×D3×C8—34no—
93C2×D3×C8—62no—
94D3×C4⋊C4—32no—
95D3×C4⋊C4—62no—
96D3×C4⋊C4—62no—
97D3×C4⋊C4—62no—
98#888—62no—
99#888—62no—
100#887—32no—
101#887—62no—
102C42×D3—32no—
103C42×D3—61no—
104C42×D3—62no—
105#869C2×D312yes—
106C4×Dic6—62no—
107C4×Dic6C2×D312yes—
108C3×C4⋊C8—21no—
109C3×C4⋊C8C2×D312yes—
110C3×#103—34no—
111#835—34no—
112#816C2×D314yes—
113Dic3⋊C8—34no—
114Dic3⋊C8—62no—
115#810—34no—
116C4⋊(C3⋊C8)—32no—
117C4⋊(C3⋊C8)—61no—
118C22×C3⋊D3C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2411yescharacteristic
122C2×C3⋊Dic3C2×D411yescharacteristic
123C2×C3⋊Dic3C2×D411yescharacteristic
124C2×C3⋊Dic3C2×D411yescharacteristic
125C4×C3⋊D3—22no—
126C4×C3⋊D3Q1614yescomplemented
127C4×C3⋊D3C2×D412yes—
128C4×C3⋊D3#4112yes—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—24no—
132C3×Dic6—22no—
133C3×Dic6—24no—
134C3×Dic6—24no—
135C3×Dic6C2×D414yes—
136#627—24no—
137#627—44no—
138#624—24no—
139#624—44no—
140#624—42no—
141C32×C8—22no—
142C3⋊(C3⋊C8)—22no—
143C22×Q16—92no—
144C2×C4⋊Q8—91no—
145C2×C4×Q8—91no—
146#462—32no—
147#462—94no—
148#462—92no—
149C2×C4⋊C8—91no—
150C2×#103—92no—
151C2×C3×Q8—32no—
152C2×C3×Q8—34no—
153D3×Q8—38no—
154D3×Q8—64no—
155D3×Q8—68no—
156D3×Q8—68no—
157C2×C4×D3—32no—
158C2×C4×D3—32no—
159C2×C4×D3—32no—
160C2×C4×D3—61no—
161C2×C4×D3—61no—
162C2×C4×D3—61no—
163C2×C4×D3—62no—
164C2×C4×D3—62no—
165C2×C4×D3—64no—
166C2×Dic6—62no—
167C2×Dic6—64no—
168C2×Dic6C22×D314yes—
169C2×Dic6C22×D312yes—
170C3×Q16—68no—
171C2×C3×C8—22no—
172C2×C3×C8C22×D314yes—
173C3×C4⋊C4—32no—
174C3×C4⋊C4—62no—
175C3×C4⋊C4—62no—
176C3×C4⋊C4—62no—
177C3×C42—21no—
178C3×C42—62no—
179C3×C42C22×D312yes—
180#216—68no—
181#216—68no—
182C4⋊Dic3—22no—
183C4⋊Dic3—22no—
184C4⋊Dic3—62no—
185C4⋊Dic3C22×D312yes—
186Dic3⋊C4—22no—
187Dic3⋊C4—62no—
188Dic3⋊C4—62no—
189Dic3⋊C4—64no—
190Dic3⋊C4—64no—
191C4×Dic3—22no—
192C4×Dic3—32no—
193C4×Dic3—32no—
194C4×Dic3—32no—
195C4×Dic3—61no—
196C4×Dic3—61no—
197C4×Dic3—61no—
198C4×Dic3—62no—
199C4×Dic3—62no—
200C2×C3⋊C8—34no—
201C2×C3⋊C8—62no—
202Dic12—28no—
203D3×C8—68no—
204D3×C8—124no—
205C22×C32C22×D411yescharacteristic
206C2×C3⋊D3#12112yes—
207C2×C3⋊D3C2×Q1612yes—
208C2×C3⋊D3#13712yes—
209C32×C4—21no—
210C32×C4C2×Q1612yescomplemented
211C32×C4C22×D411yescharacteristic
212C32×C4C2×#4111yescharacteristic
213C3⋊Dic3—21no—
214C3⋊Dic3#12112yes—
215C3⋊Dic3C2×Q1612yescomplemented
216C3×Dic3—24no—
217C3×Dic3—44no—
218C3×Dic3—42no—
219C22×Q8—91no—
220C22×Q8—92no—
221C2×Q16—34no—
222C2×Q16—94no—
223C2×Q16—188no—
224C22×C8—92no—
225C4⋊Q8—32no—
226C4⋊Q8—92no—
227C4⋊Q8—181no—
228C4⋊Q8—181no—
229C4×Q8—32no—
230C4×Q8—92no—
231C4×Q8—181no—
232C4×Q8—181no—
233C2×C4⋊C4—91no—
234C2×C4⋊C4—181no—
235C2×C4⋊C4—181no—
236C2×C4⋊C4—181no—
237C2×C42—91no—
238C2×C42—181no—
239C4⋊C8—92no—
240C4⋊C8—91no—
241C4⋊C8D3211yescharacteristic
242#103—34no—
243#103—94no—
244C22×D3—32no—
245C22×D3—61no—
246C3×Q8—34no—
247C3×Q8—62no—
248C3×Q8—64no—
249C3×Q8—64no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—62no—
254C2×C3×C4—62no—
255C2×C3×C4—64no—
256C2×C3×C4D3×D412yes—
257C2×C3×C4D3×D412yes—
258C2×C3×C4C23×D312yes—
259C2×Dic3—22no—
260C2×Dic3—22no—
261C2×Dic3—24no—
262C2×Dic3—32no—
263C2×Dic3—32no—
264C2×Dic3—32no—
265C2×Dic3—61no—
266C2×Dic3—61no—
267C2×Dic3—61no—
268C4×D3—38no—
269C4×D3—34no—
270C4×D3—34no—
271C4×D3—64no—
272C4×D3—62no—
273C4×D3—62no—
274C4×D3—68no—
275C4×D3—64no—
276C4×D3—122no—
277C4×D3—124no—
278C4×D3—128no—
279Dic6—22no—
280Dic6—24no—
281Dic6—24no—
282Dic6—68no—
283Dic6—128no—
284Dic6D3×D414yes—
285C3×C8—24no—
286C3×C8—42no—
287C3⋊C8—64no—
288C3⋊C8—122no—
289C2×C32C2×#12111yescharacteristic
290C2×C32C22×Q1611yescharacteristic
291C2×C32C2×#13711yescharacteristic
292C3⋊D3#46214yescomplemented
293C2×Q8—32no—
294C2×Q8—34no—
295C2×Q8—94no—
296C2×Q8—181no—
297C2×Q8—182no—
298C2×Q8—182no—
299C2×Q8—184no—
300C2×Q8—184no—
301C22×C4—91no—
302C22×C4—91no—
303C22×C4—91no—
304C22×C4—181no—
305C22×C4—181no—
306C22×C4—182no—
307Q16—68no—
308Q16—188no—
309C2×C8—92no—
310C2×C8—184no—
311C2×C8C2×D3212yes—
312C4⋊C4—32no—
313C4⋊C4—62no—
314C4⋊C4—62no—
315C4⋊C4—62no—
316C4⋊C4—181no—
317C4⋊C4—182no—
318C4⋊C4—182no—
319C4⋊C4—182no—
320C42—62no—
321C42—91no—
322C42—91no—
323C42—91no—
324C42—182no—
325C42C2×D3211yescharacteristic
326C22×C3—21no—
327C22×C3C2×D3×D412yes—
328C2×D3—34no—
329C2×D3—34no—
330C2×D3—34no—
331C2×D3—62no—
332C2×D3—62no—
333C2×D3—62no—
334C3×C4—22no—
335C3×C4—21no—
336C3×C4—22no—
337C3×C4—21no—
338C3×C4—41no—
339C3×C4—64no—
340C3×C4—122no—
341C3×C4—124no—
342C3×C4D3×Q1614yescomplemented
343C3×C4C2×D3×D412yes—
344C3×C4D3×#4112yes—
345Dic3—24no—
346Dic3—34no—
347Dic3—34no—
348Dic3—42no—
349Dic3—44no—
350Dic3—62no—
351Dic3—62no—
352Dic3—62no—
353Dic3—121no—
354C32C2×#46211yescharacteristic, complemented, Sylow
355C23—91no—
356Q8—34no—
357Q8—62no—
358Q8—64no—
359Q8—64no—
360Q8—184no—
361Q8—364no—
362C2×C4—62no—
363C2×C4—62no—
364C2×C4—64no—
365C2×C4—91no—
366C2×C4—91no—
367C2×C4—92no—
368C2×C4—94no—
369C2×C4—92no—
370C2×C4—91no—
371C2×C4—182no—
372C2×C4—184no—
373C2×C4—364no—
374C2×C4—362no—
375C2×C4#380211yescharacteristic
376C2×C4#380211yescharacteristic
377C2×C4C22×D3211yescharacteristic
378C8—22no—
379C8—182no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3D3×#12112yes—
384C2×C3C2×D3×Q1612yes—
385C2×C3D3×#13712yes—
386D3—38no—
387D3—64no—
388C22—92no—
389C22—92no—
390C22—92no—
391C22C2×#380211yescharacteristic
392C4—21no—
393C4—64no—
394C4—92no—
395C4—92no—
396C4—124no—
397C4—122no—
398C4—181no—
399C4#6380212yescomplemented
400C4D32×D411yescharacteristic
401C4#6431911yescharacteristic
402C3—21no—
403C3D3×#46212yescomplemented
404C2—94no—
405C2#1059461211yescharacteristic
406C2C2×#6380211yescharacteristic
407C2#1059471711yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4⋊C8D32
hypocenterC32C2×#462
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
5. C3×#4849C2semidirect
6. #10590798C2semidirect
8. #10590384C2semidirect
42. #4849D3semidirect
126. C4×C3⋊D3Q16semidirect
210. C32×C4C2×Q16semidirect
215. C3⋊Dic3C2×Q16semidirect
292. C3⋊D3#462semidirect
342. C3×C4D3×Q16semidirect
354. C32C2×#462semidirect
399. C4#63802semidirect
403. C3D3×#462semidirect

Maximal subgroups

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

subgroupindex
C2×#638022
#105939092
C4×#37972
C3⋊D3×C4⋊C82
C3×#48492
#105907982
#105906722
#105903842
D3×#4623