Finite Group Databasebeta

← #11882303

Subgroups — #11882303

Order 1152.

1194 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596187C211yesmaximal, characteristic, complemented
2#10596051C211yesmaximal, characteristic, complemented
3C32×#460C211yesmaximal, characteristic, complemented
4#10592870C212yesmaximal, complemented
5#10592864C212yesmaximal, complemented
6#10592771C211yesmaximal, characteristic, complemented
7#10592720C211yesmaximal, characteristic, complemented
8#10592541C211yesmaximal, characteristic, complemented
9C3⋊D3×C4⋊C8C211yesmaximal, characteristic, complemented
10#10592474C212yesmaximal, complemented
11#10592462C212yesmaximal, complemented
12#80401—34nomaximal
13C2×#3830—21no—
14C2×C32×SD16C2212yes—
15C32×#127C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17#64156C2211yescharacteristic
18#64155C2211yescharacteristic
19#64147—21no—
20#64147C2212yes—
21#64145—21no—
22D4×C3⋊Dic3—21no—
23D4×C3⋊Dic3C2212yes—
24C2×#3753C2212yes—
25C2×C8×C3⋊D3C2212yes—
26#64107—21no—
27#64104C2211yescharacteristic
28#64103—21no—
29#64099C2211yescharacteristic
30C4×C4⋊(C3⋊D3)—21no—
31C4×C4⋊(C3⋊D3)C2211yescharacteristic
32#64081—21no—
33C42×C3⋊D3C2211yescharacteristic
34#64078C2211yescharacteristic
35C32×C4⋊C8C2211yescharacteristic
36C32×#102C2212yes—
37#63662C2212yes—
38#63659C2212yes—
39#63648C2212yes—
40#63644C2212yes—
41#63641C2212yes—
42#63634C2212yes—
43C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
44#5716—34no—
45#5580—34no—
46C3×#460D314yescomplemented
47#5171—38no—
48#5165—38no—
49#5072—34no—
50#5021—34no—
51#4842—34no—
52D3×C4⋊C8—34no—
53#4775—38no—
54#4763—38no—
55C2×C32×Q8C2311yescharacteristic
56C2×C32×D4—21no—
57C2×C32×D4—21no—
58C2×C32×D4C2312yes—
59C2×#638—22no—
60C22×C3⋊Dic3—22no—
61#3830—44no—
62C2×C4⋊(C3⋊D3)—21no—
63C2×C4⋊(C3⋊D3)C2311yescharacteristic
64C2×C4×C3⋊D3—21no—
65C2×C4×C3⋊D3D411yescharacteristic
66C2×C4×C3⋊D3D411yescharacteristic
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×#634—21no—
69C32×SD16—42no—
70C2×C32×C8C2312yes—
71C32×C4⋊C4—21no—
72C32×C4⋊C4C2311yescharacteristic
73C32×C42—21no—
74C32×C42C2311yescharacteristic
75#3757—22no—
76#3757—22no—
77#3753—42no—
78#3752—21no—
79#3752—21no—
80#3752—21no—
81#3752—21no—
82#3752—21no—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2312yes—
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87#3750—21no—
88#3750—21no—
89C4×C3⋊Dic3D411yescharacteristic
90C4×C3⋊Dic3D411yescharacteristic
91C4×C3⋊Dic3C2311yescharacteristic
92C2×C3⋊(C3⋊C8)C2312yes—
93C8×C3⋊D3—42no—
94#3247—91noSylow
95C2×#237—64no—
96C2×C3×SD16C2×D318yes—
97C3×#127C2×D314yes—
98C3×C4×Q8C2×D314yes—
99#947—34no—
100#946—34no—
101#938—38no—
102#938—64no—
103#936—64no—
104D4×Dic3—38no—
105D4×Dic3—64no—
106C2×#213—38no—
107C2×D3×C8—38no—
108#898—64no—
109#895—34no—
110#894—64no—
111#890—34no—
112C4×D12—34no—
113C4×D12—64no—
114#872—64no—
115C42×D3—34no—
116#869—34no—
117C3×C4⋊C8C2×D314yes—
118C3×#102C2×D318yes—
119#835—38no—
120#832—38no—
121#821—38no—
122#817—38no—
123Dic3⋊C8—38no—
124#807—38no—
125C4⋊(C3⋊C8)—34no—
126C23×C32—22no—
127C22×C3⋊D3—21no—
128C22×C3⋊D3C2×D411yescharacteristic
129C32×Q8—21no—
130C32×Q8—21no—
131C32×D4—22no—
132C32×D4—22no—
133C32×D4—42no—
134C32×D4—42no—
135C2×C32×C4—21no—
136C2×C32×C4—21no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2411yescharacteristic
140#638—44no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—44no—
144C2×C3⋊Dic3C2×D411yescharacteristic
145C2×C3⋊Dic3C2×D411yescharacteristic
146C2×C3⋊Dic3C2×D411yescharacteristic
147C4⋊(C3⋊D3)—21no—
148C4⋊(C3⋊D3)—21no—
149C4⋊(C3⋊D3)—42no—
150C4×C3⋊D3—22no—
151C4×C3⋊D3—22no—
152C4×C3⋊D3—21no—
153C4×C3⋊D3—21no—
154C4×C3⋊D3—42no—
155#634—42no—
156C32×C8—22no—
157C3⋊(C3⋊C8)—22no—
158#532—91no—
159#529—91no—
160#478—92no—
161#477—91no—
162#476—91no—
163#466—92no—
164#465—92no—
165#463—92no—
166#460C3⋊D311yescharacteristic, complemented
167#459—91no—
168C2×C4⋊C8—91no—
169C2×C3×Q8C22×D314yes—
170C2×C3×D4—24no—
171C2×C3×D4—24no—
172C2×C3×D4C22×D318yes—
173C2×#67—68no—
174C22×Dic3—68no—
175#237—1216no—
176C2×D12—34no—
177C2×D12—64no—
178C2×C4×D3—34no—
179C2×C4×D3—34no—
180C2×C4×D3—34no—
181C2×C4×D3—64no—
182C2×Dic6—64no—
183C3×SD16—48no—
184C2×C3×C8C22×D318yes—
185C3×C4⋊C4—24no—
186C3×C4⋊C4C22×D314yes—
187C3×C42—24no—
188C3×C42C22×D314yes—
189#217—68no—
190#217—68no—
191#213—128no—
192(C2×D3)⋊C4—64no—
193(C2×D3)⋊C4—64no—
194(C2×D3)⋊C4—64no—
195(C2×D3)⋊C4—64no—
196(C2×D3)⋊C4—64no—
197C4⋊Dic3—38no—
198C4⋊Dic3—34no—
199C4⋊Dic3—64no—
200C4⋊Dic3—64no—
201Dic3⋊C4—64no—
202Dic3⋊C4—64no—
203C4×Dic3—34no—
204C4×Dic3—34no—
205C4×Dic3—34no—
206C2×C3⋊C8—38no—
207D3×C8—128no—
208C22×C32—42no—
209C22×C32—42no—
210C22×C32—42no—
211C22×C32C22×D411yescharacteristic
212C2×C3⋊D3—21no—
213C2×C3⋊D3—21no—
214C2×C3⋊D3—41no—
215C2×C3⋊D3—41no—
216C2×C3⋊D3—41no—
217C2×C3⋊D3AGL(1,ℤ/8)12yes—
218C32×C4—21no—
219C32×C4—41no—
220C32×C4—41no—
221C32×C4#13512yes—
222C32×C4H(5,𝔽2)11yescharacteristic
223C32×C42−1+411yescharacteristic
224C3⋊Dic3—21no—
225C3⋊Dic3—21no—
226C3⋊Dic3—21no—
227C3⋊Dic3—41no—
228C3⋊Dic3—42no—
229C2×#41—181no—
230C2×SD16C2×C3⋊D312yes—
231C2×D8—92no—
232C22×C8—92no—
233C4⋊Q8—91no—
234#127C2×C3⋊D311yescharacteristic
235#126—181no—
236#125—91no—
237#124—91no—
238#124—181no—
239#123—181no—
240C22⋊Q8—91no—
241#121—92no—
242#121—91no—
243#121—181no—
244C4×Q8C2×C3⋊D311yescharacteristic
245C4×D4—92no—
246C4×D4—91no—
247C4×D4—181no—
248C4×D4—181no—
249#117—181no—
250C2×C42—91no—
251#107—92no—
252#106—92no—
253C4⋊C8—92no—
254C4⋊C8—91no—
255C4⋊C8C2×C3⋊D311yescharacteristic
256#103—92no—
257#102—92no—
258#102—92no—
259#102C2×C3⋊D312yes—
260C23×C3—28no—
261C22×D3—34no—
262C22×D3—64no—
263C3×Q8—24no—
264C3×Q8—24no—
265C3×D4—28no—
266C3×D4—28no—
267C3×D4—48no—
268C3×D4—48no—
269C2×C3×C4—24no—
270C2×C3×C4—24no—
271C2×C3×C4D3×D414yes—
272C2×C3×C4D3×D414yes—
273C2×C3×C4C23×D314yes—
274#67—1216no—
275C2×Dic3—34no—
276C2×Dic3—34no—
277C2×Dic3—34no—
278C2×Dic3—64no—
279C2×Dic3—68no—
280C2×Dic3—1216no—
281D12—64no—
282D12—64no—
283D12—128no—
284C4×D3—68no—
285C4×D3—68no—
286C4×D3—64no—
287C4×D3—64no—
288C4×D3—128no—
289Dic6—128no—
290C3×C8—28no—
291C3⋊C8—68no—
292C2×C32—82no—
293C2×C32#53711yescharacteristic
294C2×C32C2×#13511yescharacteristic
295C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
296C3⋊D3—22no—
297C3⋊D3—81no—
298#41—364no—
299C2×Q8—181no—
300C2×Q8C22×C3⋊D311yescharacteristic
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—91no—
304C2×D4—181no—
305C2×D4—182no—
306C2×D4C22×C3⋊D312yes—
307C22×C4—91no—
308C22×C4—91no—
309C22×C4—91no—
310C22×C4—182no—
311C22×C4—181no—
312SD16—42no—
313D8—362no—
314C2×C8—92no—
315C2×C8—362no—
316C2×C8C22×C3⋊D312yes—
317C4⋊C4—21no—
318C4⋊C4—91no—
319C4⋊C4—92no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4—181no—
323C4⋊C4—181no—
324C4⋊C4C22×C3⋊D311yescharacteristic
325C22⋊C4—181no—
326C22⋊C4—181no—
327C22⋊C4—181no—
328C22⋊C4—181no—
329C22⋊C4—182no—
330C22⋊C4—182no—
331C22⋊C4—181no—
332C42—21no—
333C42—91no—
334C42—91no—
335C42—91no—
336C42C22×C3⋊D311yescharacteristic
337C22×C3—48no—
338C22×C3—48no—
339C22×C3—48no—
340C22×C3C2×D3×D414yes—
341C2×D3—38no—
342C2×D3—64no—
343C2×D3—64no—
344C2×D3—124no—
345C2×D3—124no—
346C2×D3—124no—
347C3×C4—24no—
348C3×C4—44no—
349C3×C4—44no—
350C3×C4#91618yes—
351C3×C4#100414yes—
352C3×C4#101014yes—
353Dic3—64no—
354Dic3—64no—
355Dic3—64no—
356Dic3—124no—
357Dic3—128no—
358C32#324711yescharacteristic, complemented, Sylow
359C23—22no—
360C23—91no—
361C23—181no—
362Q8—21no—
363Q8—21no—
364Q8—362no—
365D4—22no—
366D4—22no—
367D4—42no—
368D4—42no—
369D4—181no—
370D4—181no—
371D4—362no—
372D4—364no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—91no—
376C2×C4—91no—
377C2×C4—91no—
378C2×C4—182no—
379C2×C4—181no—
380C2×C4—181no—
381C2×C4—182no—
382C2×C4—181no—
383C2×C4—182no—
384C2×C4—364no—
385C2×C4—362no—
386C2×C4D4×C3⋊D311yescharacteristic
387C2×C4D4×C3⋊D311yescharacteristic
388C2×C4C23×C3⋊D311yescharacteristic
389C8—22no—
390C8—182no—
391C2×C3—88no—
392C2×C3#560814yes—
393C2×C3C2×#91614yes—
394C2×C3D3×AGL(1,ℤ/8)14yes—
395D3—68no—
396D3—244no—
397C22—42no—
398C22—42no—
399C22—42no—
400C22—92no—
401C22—181no—
402C22—181no—
403C22—361no—
404C22—361no—
405C22—361no—
406C22C2×D4×C3⋊D311yescharacteristic
407C4—21no—
408C4—41no—
409C4—41no—
410C4—181no—
411C4—181no—
412C4—181no—
413C4—361no—
414C4—362no—
415C4#6412512yes—
416C4#6436111yescharacteristic
417C4#6436711yescharacteristic
418C3#8040114yescomplemented
419C2—82no—
420C2—182no—
421C2—721no—
422C2#1059607911yescharacteristic
423C2C2×#6412511yescharacteristic
424C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#460C2
socleC22×C32C22×D4
hypercenter#460C3⋊D3
hypocenterC32#3247
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #10596187C2semidirect
2. #10596051C2semidirect
3. C32×#460C2semidirect
4. #10592870C2semidirect
5. #10592864C2semidirect
6. #10592771C2semidirect
7. #10592720C2semidirect
8. #10592541C2semidirect
9. C3⋊D3×C4⋊C8C2semidirect
10. #10592474C2semidirect
11. #10592462C2semidirect
46. C3×#460D3semidirect
166. #460C3⋊D3semidirect
358. C32#3247semidirect
418. C3#80401semidirect

Maximal subgroups

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

subgroupindex
#105961872
#105960512
C32×#4602
#105928702
#105928642
#105927712
#105927202
#105925412
C3⋊D3×C4⋊C82
#105924742
#105924622
#804013