Finite Group Databasebeta

← #11895835

Subgroups — #11895835

Order 1152.

1116 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596203C211yesmaximal, characteristic, complemented
2D4×#634C211yesmaximal, characteristic, complemented
3C32×#461C211yesmaximal, characteristic, complemented
4#10592864C212yesmaximal
5#10592863C212yesmaximal, complemented
6#10592778C211yesmaximal, characteristic, complemented
7C4×#3753C211yesmaximal, characteristic
8#10592545C211yesmaximal, characteristic, complemented
9#10592530C211yesmaximal, characteristic, complemented
10#10592493C212yesmaximal, complemented
11#10592492C212yesmaximal, complemented
12#80416—34nomaximal
13C22×#634—21no—
14C2×C32×SD16C2212yes—
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17#64156C2212yes—
18Q8×C3⋊Dic3C2212yes—
19D4×C3⋊Dic3C2212yes—
20C2×#3753C2211yescharacteristic
21#64133—21no—
22#64107—22no—
23#64106—21no—
24#64101—21no—
25#64097C2212yes—
26#64087—22no—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28#64078C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C32×C4⋊C8C2211yescharacteristic
31C32×#103C2212yes—
32#63662C2212yes—
33#63662C2212yes—
34#63659C2211yescharacteristic
35#63648C2212yes—
36#63645C2212yes—
37#63642C2212yes—
38#63641C2212yes—
39#63636C2211yescharacteristic
40#63634C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42#5732—34no—
43D4×Dic6—34no—
44C3×#461D314yescomplemented
45#5165—38no—
46#5164—38no—
47#5079—34no—
48C4×#213—34no—
49#4846—34no—
50#4831—34no—
51#4794—38no—
52#4793—38no—
53C2×C32×Q8C2312yes—
54C2×C32×D4C2311yescharacteristic
55C22×C32×C4—21no—
56C22×C3⋊Dic3—22no—
57C2×C4⋊(C3⋊D3)C2311yescharacteristic
58C2×C4×C3⋊D3—21no—
59C2×#634—21no—
60C2×#634—22no—
61C2×#634—44no—
62C2×#634D411yescharacteristic
63C32×SD16—24no—
64C2×C32×C8C2312yes—
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67C32×C4⋊C4C2311yescharacteristic
68C32×C22⋊C4—21no—
69C32×C42C2311yescharacteristic
70#3757—22no—
71#3753—22no—
72#3752—21no—
73#3752—22no—
74#3752—22no—
75C4⋊(C3⋊Dic3)—21no—
76C4⋊(C3⋊Dic3)—22no—
77C4⋊(C3⋊Dic3)D411yescharacteristic
78C4⋊(C3⋊Dic3)C2312yes—
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80#3750—22no—
81#3750D412yes—
82C4×C3⋊Dic3—22no—
83C4×C3⋊Dic3C2312yes—
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86#3367—91noSylow
87C22×Dic6—64no—
88C2×C3×SD16C2×D318yes—
89C3×C4⋊Q8C2×D314yes—
90C3×C4×D4C2×D314yes—
91#947—38no—
92Q8×Dic3—38no—
93D4×Dic3—38no—
94C2×#213—34no—
95#924—64no—
96#898—68no—
97#897—64no—
98#892—64no—
99#888—38no—
100#878—68no—
101C4×D12—34no—
102#869—34no—
103C4×Dic6—34no—
104C3×C4⋊C8C2×D314yes—
105C3×#103C2×D318yes—
106#835—38no—
107#835—38no—
108#832—34no—
109#821—38no—
110#818—38no—
111#815—38no—
112Dic3⋊C8—38no—
113#809—34no—
114#807—34no—
115C4×C3⋊C8—34no—
116C23×C32—21no—
117C22×C3⋊D3—21no—
118C32×Q8—22no—
119C32×Q8—22no—
120C32×D4—21no—
121C32×D4#4112yes—
122C2×C32×C4—22no—
123C2×C32×C4—21no—
124C2×C32×C4—42no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2411yescharacteristic
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—44no—
131C2×C3⋊Dic3C2×D412yes—
132C2×C3⋊Dic3C2×D412yes—
133C4⋊(C3⋊D3)—21no—
134C4⋊(C3⋊D3)—21no—
135C4×C3⋊D3—42no—
136#634—22no—
137#634—44no—
138#634—42no—
139C32×C8—22no—
140C3⋊(C3⋊C8)—21no—
141C3⋊(C3⋊C8)—21no—
142#556—91no—
143D4×Q8—91no—
144#489—92no—
145#487—91no—
146#477—92no—
147#474—91no—
148#463—92no—
149#461C3⋊D311yescharacteristic, complemented
150#446—91no—
151#440—92no—
152C4×D8—91no—
153C2×C3×Q8C22×D318yes—
154C2×C3×D4C22×D314yes—
155C22×C3×C4—24no—
156C22×Dic3—68no—
157C2×D12—34no—
158C2×C4×D3—64no—
159C2×Dic6—34no—
160C2×Dic6—68no—
161C2×Dic6—64no—
162C2×Dic6—1216no—
163C3×SD16—216no—
164C2×C3×C8C22×D318yes—
165C3×C4⋊C4—24no—
166C3×C4⋊C4—24no—
167C3×C4⋊C4C22×D314yes—
168C3×C22⋊C4—24no—
169C3×C42C22×D314yes—
170#217—68no—
171#213—68no—
172(C2×D3)⋊C4—68no—
173(C2×D3)⋊C4—68no—
174(C2×D3)⋊C4—64no—
175C4⋊Dic3—34no—
176C4⋊Dic3—34no—
177C4⋊Dic3—38no—
178C4⋊Dic3—68no—
179C4⋊Dic3—64no—
180Dic3⋊C4—38no—
181Dic3⋊C4—68no—
182C4×Dic3—38no—
183C4×Dic3—68no—
184C2×C3⋊C8—34no—
185C2×C3⋊C8—34no—
186C22×C32—22no—
187C22×C32—41no—
188C22×C32—41no—
189C22×C32C22×D411yescharacteristic
190C2×C3⋊D3—41no—
191C2×C3⋊D3—41no—
192C2×C3⋊D3—41no—
193C32×C4—21no—
194C32×C4—42no—
195C32×C4—41no—
196C32×C4AGL(1,ℤ/8)12yes—
197C32×C4C2×#4111yescharacteristic
198C32×C42−1+411yescharacteristic
199C3⋊Dic3—22no—
200C3⋊Dic3—22no—
201C3⋊Dic3—42no—
202C3⋊Dic3—41no—
203C22×Q8—181no—
204C2×SD16C2×C3⋊D312yes—
205C2×D8—91no—
206C4⋊Q8—92no—
207C4⋊Q8—91no—
208C4⋊Q8C2×C3⋊D311yescharacteristic
209#126—182no—
210#124—92no—
211C22⋊Q8—182no—
212C22⋊Q8—181no—
213C22⋊Q8—181no—
214C4×Q8—91no—
215C4×Q8—92no—
216C4×D4—92no—
217C4×D4—91no—
218C4×D4C2×C3⋊D311yescharacteristic
219#117—181no—
220#107—92no—
221#107—91no—
222C4⋊C8—92no—
223C4⋊C8C2×C3⋊D311yescharacteristic
224#103—92no—
225#103—92no—
226#103C2×C3⋊D312yes—
227#102—91no—
228#102—92no—
229#102—91no—
230#97—92no—
231C4×C8—91no—
232C23×C3—24no—
233C22×D3—64no—
234C3×Q8—28no—
235C3×Q8—28no—
236C3×D4—24no—
237C3×D4#23718yes—
238C2×C3×C4—28no—
239C2×C3×C4—24no—
240C2×C3×C4—48no—
241C2×C3×C4D3×D414yes—
242C2×C3×C4D3×D414yes—
243C2×C3×C4C23×D314yes—
244C2×Dic3—38no—
245C2×Dic3—38no—
246C2×Dic3—64no—
247C2×Dic3—68no—
248C2×Dic3—1216no—
249D12—64no—
250D12—64no—
251C4×D3—128no—
252Dic6—68no—
253Dic6—1216no—
254Dic6—128no—
255C3×C8—28no—
256C3⋊C8—64no—
257C3⋊C8—64no—
258C2×C32—42no—
259C2×C32#54811yescharacteristic
260C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
261C2×C32#57811yescharacteristic
262C3⋊D3—81no—
263C2×Q8—91no—
264C2×Q8—182no—
265C2×Q8—181no—
266C2×Q8—364no—
267C2×Q8C22×C3⋊D312yes—
268C2×D4—91no—
269C2×D4C22×C3⋊D311yescharacteristic
270C22×C4—21no—
271C22×C4—182no—
272C22×C4—181no—
273SD16—24no—
274D8—182no—
275C2×C8—91no—
276C2×C8—91no—
277C2×C8C22×C3⋊D312yes—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—91no—
281C4⋊C4—92no—
282C4⋊C4—92no—
283C4⋊C4—91no—
284C4⋊C4—182no—
285C4⋊C4—182no—
286C4⋊C4—181no—
287C4⋊C4C22×C3⋊D311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—182no—
290C22⋊C4—182no—
291C22⋊C4—182no—
292C22⋊C4—181no—
293C42—92no—
294C42—182no—
295C42C22×C3⋊D311yescharacteristic
296C22×C3—28no—
297C22×C3—44no—
298C22×C3—44no—
299C22×C3C2×D3×D414yes—
300C2×D3—124no—
301C2×D3—124no—
302C2×D3—124no—
303C3×C4—24no—
304C3×C4—44no—
305C3×C4—48no—
306C3×C4#91418yes—
307C3×C4C2×#23714yes—
308C3×C4#101014yes—
309Dic3—68no—
310Dic3—68no—
311Dic3—128no—
312Dic3—124no—
313C32#336711yescharacteristic, complemented, Sylow
314C23—21no—
315C23—181no—
316Q8—22no—
317Q8—22no—
318Q8—182no—
319Q8—364no—
320Q8—362no—
321D4—21no—
322D4—181no—
323D4—181no—
324D4#383012yes—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—92no—
329C2×C4—92no—
330C2×C4—181no—
331C2×C4—182no—
332C2×C4—364no—
333C2×C4—362no—
334C2×C4D4×C3⋊D311yescharacteristic
335C2×C4D4×C3⋊D311yescharacteristic
336C2×C4C23×C3⋊D311yescharacteristic
337C8—22no—
338C8—181no—
339C8—181no—
340C2×C3—48no—
341C2×C3#559814yes—
342C2×C3C2×#91414yes—
343C2×C3#577914yes—
344D3—244no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—361no—
349C22—361no—
350C22—361no—
351C22C2×D4×C3⋊D311yescharacteristic
352C4—21no—
353C4—41no—
354C4—42no—
355C4—182no—
356C4—182no—
357C4—362no—
358C4—361no—
359C4#6412312yes—
360C4C2×#383011yescharacteristic
361C4#6436711yescharacteristic
362C3#8041614yescomplemented
363C2—42no—
364C2—721no—
365C2#1059606911yescharacteristic
366C2C2×#6412311yescharacteristic
367C2#1059625011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#461C2
socleC22×C32C22×D4
prime radicalC2×#3753C22
hypercenter#461C3⋊D3
hypocenterC32#3367
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #10596203C2semidirect
2. D4×#634C2semidirect
3. C32×#461C2semidirect
5. #10592863C2semidirect
6. #10592778C2semidirect
8. #10592545C2semidirect
9. #10592530C2semidirect
10. #10592493C2semidirect
11. #10592492C2semidirect
44. C3×#461D3semidirect
149. #461C3⋊D3semidirect
313. C32#3367semidirect
362. C3#80416semidirect

Maximal subgroups

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

subgroupindex
#105962032
D4×#6342
C32×#4612
#105928642
#105928632
#105927782
C4×#37532
#105925452
#105925302
#105924932
#105924922
#804163