Finite Group Databasebeta

← #11780244

Subgroups — #11780244

Order 1152.

448 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593863C211yesmaximal, characteristic
2#10592793C211yesmaximal, characteristic, complemented
3C3×#5083C211yesmaximal, characteristic
4C3×#5078C211yesmaximal, characteristic, complemented
5#10589093C211yesmaximal, characteristic, complemented
6#10589085C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic
8#71370—31nomaximal
9#71049—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C4×#634C2211yescharacteristic
12C2×C3×#215—21no—
13C3×C4×D12C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63863—21no—
16#63858—22no—
17#63857—21no—
18#63843—21no—
19#63841—21no—
20#63637—21no—
21#63635—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×#835—21no—
24C3×#807—22no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27#5732—31no—
28#5542—31no—
29C3×#500—31no—
30C3×#461—31no—
31#5094—31no—
32#5094—31no—
33#5094—61no—
34#5083D311yescharacteristic
35#5078D311yescharacteristic, complemented
36#4547—31no—
37D4⋊(C3⋊C8)—31no—
38#4484—31no—
39#4482—31no—
40#4459—31no—
41#4456—31no—
42C2×C32×Q8—21no—
43C2×#634D411yescharacteristic
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C3×Dic6—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49C32×C42C2311yescharacteristic
50C4⋊(C3⋊Dic3)D411yescharacteristic
51#3750—21no—
52C4×C3⋊Dic3—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C3×#215—42no—
55C3×(C2×D3)⋊C4—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3D411yescharacteristic
58C3×C4⋊Dic3D412yes—
59C2×C3×C3⋊C8—21no—
60C2×C3×C3⋊C8—21no—
61Dic3⋊Dic3—22no—
62(C2×D3)⋊Dic3—22no—
63(C2×D3)⋊Dic3—22no—
64Dic32—22no—
65#1650—91noSylow
66C2×C3×SD16—61no—
67C3×C4⋊Q8—21no—
68C3×C4⋊Q8—31no—
69C3×C4⋊Q8C2×D311yescharacteristic
70C3×C4⋊Q8C2×D311yescharacteristic
71C3×C4×D4—31no—
72#947—61no—
73Q8×Dic3—61no—
74C2×#215—21no—
75#936—61no—
76#926—61no—
77#924—61no—
78#898—62no—
79#897—61no—
80#892—61no—
81#887—61no—
82#879—62no—
83C4×D12C2×D311yescharacteristic
84#869C2×D311yescharacteristic
85C4×Dic6—31no—
86C4×Dic6—31no—
87C4×Dic6—61no—
88C3×#107—62no—
89C3×C4⋊C8—31no—
90C3×#103—61no—
91C3×C4×C8—31no—
92#835—21no—
93#810—61no—
94#810—61no—
95#810—62no—
96#808—61no—
97#808—61no—
98#808—62no—
99#807—22no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—61no—
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C4×C3⋊C8C2×D311yescharacteristic
105C22×C3×D3—21no—
106C32×Q8—41no—
107C32×Q8—41no—
108C2×C32×C4—41no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3—21no—
114#634—21no—
115#634—21no—
116C2×C3×Dic3—21no—
117C2×C3×Dic3—22no—
118C3×D12—21no—
119C3×D12—21no—
120C3×C4×D3—41no—
121C3×C4×D3—41no—
122C3×Dic6—41no—
123C3×Dic6—41no—
124C3⋊(C3⋊C8)—41no—
125C3×C3⋊C8—22no—
126C3×C3⋊C8—41no—
127#556—91no—
128#500—31no—
129#475—91no—
130#461—31no—
131#332—91no—
132Q8⋊C8—91no—
133D4⋊C8—91no—
134C2×C3×Q8—21no—
135C2×C3×Q8—21no—
136C2×C3×Q8—41no—
137C2×C3×Q8—61no—
138C2×C3×D4—31no—
139C22×C3×C4—61no—
140C2×D12#6711yescharacteristic
141C2×C4×D3—21no—
142C2×Dic6—21no—
143C2×Dic6—31no—
144C2×Dic6—31no—
145C2×Dic6—61no—
146C3×SD16—122no—
147C2×C3×C8—61no—
148C2×C3×C8—61no—
149C3×C4⋊C4—22no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—21no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—31no—
155C3×C4⋊C4—32no—
156C3×C4⋊C4—41no—
157C3×C4⋊C4—61no—
158C3×C22⋊C4—61no—
159C3×C42—21no—
160C3×C42C22×D311yescharacteristic
161C3×C42C22×D311yescharacteristic
162#217—62no—
163#217—62no—
164#215—42no—
165(C2×D3)⋊C4—21no—
166(C2×D3)⋊C4—62no—
167(C2×D3)⋊C4—62no—
168C4⋊Dic3—21no—
169C4⋊Dic3—31no—
170C4⋊Dic3—31no—
171C4⋊Dic3—61no—
172C4⋊Dic3—62no—
173C4⋊Dic3#6712yes—
174C4⋊Dic3#6711yescharacteristic
175Dic3⋊C4—62no—
176Dic3⋊C4—61no—
177Dic3⋊C4—61no—
178Dic3⋊C4—121no—
179C4×Dic3—62no—
180C4×Dic3—62no—
181C4×Dic3—61no—
182C4×Dic3—61no—
183C4×Dic3—121no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—62no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—61no—
189C22×C32#12011yescharacteristic
190C2×C3×D3—41no—
191C2×C3×D3—41no—
192C2×C3×D3—41no—
193C32×C4—21no—
194C32×C4—81no—
195C32×C4#13511yescharacteristic
196C32×C4#13511yescharacteristic
197C32×C4AGL(1,ℤ/8)11yescharacteristic
198C32×C4#13711yescharacteristic
199C3⋊Dic3—41no—
200C3⋊Dic3—41no—
201C3×Dic3—42no—
202C3×Dic3—41no—
203C2×SD16—61no—
204C4⋊Q8—31no—
205C4⋊Q8D3211yescharacteristic
206#126—182no—
207#124—181no—
208C22⋊Q8—181no—
209C4×Q8—91no—
210C4×Q8—181no—
211C4×D4—31no—
212#117—181no—
213#107—62no—
214#106—181no—
215C4⋊C8—31no—
216C4⋊C8—91no—
217#103—61no—
218#103—181no—
219C4×C8—31no—
220C23×C3—61no—
221C22×D3—21no—
222C3×Q8—41no—
223C3×Q8—41no—
224C3×Q8—41no—
225C3×Q8—41no—
226C3×Q8—81no—
227C3×Q8—81no—
228C3×Q8—121no—
229C3×Q8—121no—
230C3×D4—61no—
231C3×D4—61no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—42no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4—61no—
239C2×C3×C4—62no—
240C2×C3×C4—121no—
241C2×C3×C4—121no—
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4C2×#6711yescharacteristic
247C2×C3×C4C2×#6711yescharacteristic
248C2×Dic3—21no—
249C2×Dic3—22no—
250C2×Dic3—61no—
251C2×Dic3—61no—
252C2×Dic3—61no—
253C2×Dic3—61no—
254C2×Dic3—121no—
255C2×Dic3—121no—
256D12—21no—
257D12—21no—
258C4×D3—41no—
259C4×D3—41no—
260Dic6—41no—
261Dic6—41no—
262Dic6—62no—
263Dic6—61no—
264Dic6—61no—
265Dic6—61no—
266Dic6—61no—
267Dic6—121no—
268C3×C8—62no—
269C3×C8—121no—
270C3⋊C8—22no—
271C3⋊C8—41no—
272C3⋊C8—122no—
273C3⋊C8—121no—
274C3⋊C8—121no—
275C2×C32#44911yescharacteristic
276C2×C32#45211yescharacteristic
277C2×C32#45611yescharacteristic
278C3×D3—81no—
279C2×Q8—21no—
280C2×Q8—61no—
281C2×Q8—91no—
282C2×D4—31no—
283C22×C4—61no—
284SD16—122no—
285C2×C8—61no—
286C2×C8—61no—
287C2×C8—181no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—31no—
291C4⋊C4—32no—
292C4⋊C4—61no—
293C4⋊C4—91no—
294C4⋊C4—182no—
295C4⋊C4—181no—
296C22⋊C4—61no—
297C22⋊C4—182no—
298C22⋊C4—182no—
299C42—182no—
300C42—181no—
301C42C2×D3211yescharacteristic
302C22×C3—21no—
303C22×C3—121no—
304C22×C3—121no—
305C22×C3—121no—
306C22×C3#93711yescharacteristic
307C22×C3#93711yescharacteristic
308C2×D3—41no—
309C2×D3—41no—
310C2×D3—41no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—41no—
318C3×C4—82no—
319C3×C4—81no—
320C3×C4—81no—
321C3×C4—121no—
322C3×C4—122no—
323C3×C4#91111yescharacteristic
324C3×C4#91211yescharacteristic
325C3×C4#91511yescharacteristic
326C3×C4#91611yescharacteristic
327C3×C4#91811yescharacteristic
328C3×C4#91911yescharacteristic
329C3×C4#93211yescharacteristic
330C3×C4#95011yescharacteristic
331Dic3—42no—
332Dic3—41no—
333Dic3—122no—
334Dic3—121no—
335Dic3—121no—
336Dic3—121no—
337Dic3—121no—
338Dic3—241no—
339C32#165011yescharacteristic, complemented, Sylow
340C23—61no—
341Q8—41no—
342Q8—41no—
343Q8—121no—
344Q8—121no—
345Q8—181no—
346Q8—181no—
347D4—61no—
348D4—61no—
349C2×C4—41no—
350C2×C4—61no—
351C2×C4—62no—
352C2×C4—121no—
353C2×C4—121no—
354C2×C4—181no—
355C2×C4—181no—
356C2×C4D3×#6711yescharacteristic
357C2×C4D3×#6711yescharacteristic
358C2×C4#381111yescharacteristic
359C8—62no—
360C8—121no—
361C8—361no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—241no—
366C2×C3#503711yescharacteristic
367C2×C3#509511yescharacteristic
368C2×C3#515811yescharacteristic
369C2×C3#517311yescharacteristic
370C2×C3#518711yescharacteristic
371C2×C3#520511yescharacteristic
372D3—81no—
373C22—121no—
374C22—121no—
375C22—121no—
376C22#6398311yescharacteristic
377C4—21no—
378C4—81no—
379C4—122no—
380C4—121no—
381C4—361no—
382C4—361no—
383C4#6393211yescharacteristic
384C4#6393311yescharacteristic
385C4#6395011yescharacteristic
386C4#6395111yescharacteristic
387C3—21no—
388C3#7104911yescharacteristic, complemented
389C3#7137011yescharacteristic, complemented
390C2—241no—
391C2#1059151911yescharacteristic
392C2#1059165611yescharacteristic
393C2#1059166111yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC4⋊Q8D32
hypocenterC32#1650
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10592793C2semidirect
4. C3×#5078C2semidirect
5. #10589093C2semidirect
6. #10589085C2semidirect
35. #5078D3semidirect
339. C32#1650semidirect
388. C3#71049semidirect
389. C3#71370semidirect

Maximal subgroups

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

subgroupindex
#105938632
#105927932
C3×#50832
C3×#50782
#105890932
#105890852
#105890812
#713703
#710493