Finite Group Databasebeta

← #11779495

Subgroups — #11779495

Order 1152.

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

normal subgroups only

This group has 490 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#10593987C211yesmaximal, characteristic
2#10592783C211yesmaximal, characteristic, complemented
3C3×#5092C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5#10589095C211yesmaximal, characteristic, complemented
6#10589082C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71304—31nomaximal
9#71145—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C3×#216—22no—
13C3×C4×D12C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63916—21no—
16#63909—21no—
17#63907—22no—
18#63849—21no—
19#63841—21no—
20#63636—21no—
21#63635—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×#809—21no—
24C3×#808—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27#5734—31no—
28#5563—31no—
29C3×#494—31no—
30C3×#476—31no—
31#5092D311yescharacteristic, complemented
32#5084—31no—
33#5084—31no—
34#5084—61no—
35#5084D311yescharacteristic, complemented
36#4546—31no—
37D4⋊(C3⋊C8)—31no—
38#4483—31no—
39#4481—31no—
40#4459—31no—
41#4459—31no—
42C2×C32×Q8—21no—
43C2×C4⋊(C3⋊D3)D411yescharacteristic
44C2×C4×C3⋊D3—21no—
45C2×C3×D12D411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×Dic6D412yes—
48C2×#626—22no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4—21no—
51C32×C42C2311yescharacteristic
52#3752—21no—
53C4⋊(C3⋊Dic3)D411yescharacteristic
54C2×C3⋊(C3⋊C8)—21no—
55C3×#216—44no—
56C3×(C2×D3)⋊C4—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62#3722—22no—
63(C2×D3)⋊Dic3—22no—
64Dic32—22no—
65#1634—91noSylow
66C2×C3×Q16—62no—
67C3×C4⋊Q8—21no—
68C3×C4⋊Q8—31no—
69C3×C4⋊Q8C2×D311yescharacteristic
70C3×C4⋊Q8C2×D311yescharacteristic
71C3×C4×D4—31no—
72#947—62no—
73C2×#216—22no—
74#938—61no—
75#930—61no—
76#926—61no—
77#895—61no—
78#895—61no—
79#892—61no—
80#892—61no—
81#892—61no—
82#885—62no—
83C4×D12—31no—
84C4×D12—31no—
85C4×D12—61no—
86C4×D12C2×D311yescharacteristic
87#869C2×D311yescharacteristic
88C3×#106—61no—
89C3×C4⋊C8—31no—
90C3×#102—61no—
91C3×C4×C8—31no—
92#809—21no—
93#809—61no—
94#809—61no—
95#809—62no—
96#808—21no—
97#808—61no—
98#808—61no—
99#808—62no—
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—
106C22×C3×D3—21no—
107C32×Q8—42no—
108C2×C32×C4—41no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3—21no—
113C4⋊(C3⋊D3)—21no—
114C4⋊(C3⋊D3)—21no—
115C4×C3⋊D3—41no—
116C4×C3⋊D3—41no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—22no—
119C3×D12—21no—
120C3×D12—21no—
121C3×C4×D3—41no—
122C3×C4×D3—41no—
123C3×Dic6—42no—
124#626—82no—
125C3⋊(C3⋊C8)—41no—
126C3×C3⋊C8—22no—
127C3×C3⋊C8—41no—
128#555—91no—
129#494—31no—
130#476—31no—
131#476—91no—
132#333—91no—
133D4⋊C8—91no—
134D4⋊C8—91no—
135C2×C3×Q8—21no—
136C2×C3×Q8—21no—
137C2×C3×Q8—32no—
138C2×C3×Q8—41no—
139C2×C3×D4—31no—
140C22×C3×C4—61no—
141C2×#67—62no—
142C2×D12—31no—
143C2×D12—31no—
144C2×D12—61no—
145C2×D12—62no—
146C2×D12#6711yescharacteristic
147C2×C4×D3—21no—
148C2×C4×D3—61no—
149C2×C4×D3—61no—
150C2×C4×D3—121no—
151C2×Dic6#6712yes—
152C3×Q16—124no—
153C2×C3×C8—61no—
154C2×C3×C8—61no—
155C3×C4⋊C4—22no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4—31no—
161C3×C4⋊C4—41no—
162C3×C4⋊C4—61no—
163C3×C4⋊C4—61no—
164C3×C22⋊C4—61no—
165C3×C42—21no—
166C3×C42C22×D311yescharacteristic
167C3×C42C22×D311yescharacteristic
168#217—62no—
169#216—44no—
170(C2×D3)⋊C4—21no—
171(C2×D3)⋊C4—62no—
172(C2×D3)⋊C4—62no—
173(C2×D3)⋊C4—62no—
174(C2×D3)⋊C4—61no—
175(C2×D3)⋊C4—61no—
176(C2×D3)⋊C4—121no—
177C4⋊Dic3—21no—
178C4⋊Dic3—21no—
179C4⋊Dic3—31no—
180C4⋊Dic3—31no—
181C4⋊Dic3—61no—
182C4⋊Dic3#6711yescharacteristic
183C4×Dic3—62no—
184C4×Dic3—62no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—62no—
188C2×C3⋊C8—61no—
189C2×C3⋊C8—61no—
190C22×C32#12011yescharacteristic
191C2×C3⋊D3—41no—
192C2×C3⋊D3—41no—
193C2×C3⋊D3—41no—
194C2×C3×D3—41no—
195C2×C3×D3—41no—
196C2×C3×D3—41no—
197C32×C4—21no—
198C32×C4—81no—
199C32×C4#13511yescharacteristic
200C32×C4#13511yescharacteristic
201C32×C4#13711yescharacteristic
202C32×C4#13711yescharacteristic
203C3⋊Dic3—41no—
204C3×Dic3—41no—
205C3×Dic3—42no—
206C2×Q16—62no—
207C4⋊Q8—31no—
208C4⋊Q8D3211yescharacteristic
209#124—182no—
210#121—181no—
211#121—181no—
212C4×D4—31no—
213C4×D4—91no—
214#117—181no—
215#117—181no—
216#106—61no—
217#106—181no—
218C4⋊C8—31no—
219C4⋊C8—91no—
220#102—61no—
221#102—181no—
222C4×C8—31no—
223C23×C3—61no—
224C22×D3—21no—
225C22×D3—61no—
226C22×D3—61no—
227C22×D3—121no—
228C3×Q8—42no—
229C3×Q8—42no—
230C3×Q8—82no—
231C3×Q8—122no—
232C3×D4—61no—
233C3×D4—61no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—42no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—61no—
241C2×C3×C4—62no—
242C2×C3×C4—121no—
243C2×C3×C4—121no—
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4C2×#6711yescharacteristic
249C2×C3×C4C2×#6711yescharacteristic
250#67—242no—
251C2×Dic3—21no—
252C2×Dic3—22no—
253C2×Dic3—61no—
254C2×Dic3—61no—
255C2×Dic3—121no—
256D12—21no—
257D12—21no—
258D12—62no—
259D12—61no—
260D12—61no—
261D12—61no—
262D12—61no—
263D12—121no—
264D12—242no—
265C4×D3—41no—
266C4×D3—41no—
267C4×D3—121no—
268C4×D3—121no—
269C4×D3—121no—
270C4×D3—121no—
271C4×D3—241no—
272C4×D3—241no—
273Dic6—42no—
274C3×C8—62no—
275C3×C8—121no—
276C3⋊C8—22no—
277C3⋊C8—41no—
278C3⋊C8—122no—
279C3⋊C8—121no—
280C3⋊C8—121no—
281C2×C32#45211yescharacteristic
282C2×C32#45211yescharacteristic
283C2×C32#45311yescharacteristic
284C3⋊D3—81no—
285C3×D3—81no—
286C2×Q8—21no—
287C2×Q8—32no—
288C2×D4—31no—
289C2×D4—91no—
290C2×D4—182no—
291C22×C4—61no—
292C22×C4—181no—
293Q16—124no—
294C2×C8—61no—
295C2×C8—61no—
296C2×C8—181no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—31no—
300C4⋊C4—61no—
301C4⋊C4—61no—
302C4⋊C4—91no—
303C22⋊C4—61no—
304C22⋊C4—182no—
305C22⋊C4—182no—
306C22⋊C4—181no—
307C42—182no—
308C42C2×D3211yescharacteristic
309C22×C3—21no—
310C22×C3—121no—
311C22×C3—121no—
312C22×C3—121no—
313C22×C3#93711yescharacteristic
314C22×C3#93711yescharacteristic
315C2×D3—41no—
316C2×D3—41no—
317C2×D3—41no—
318C2×D3—122no—
319C2×D3—121no—
320C2×D3—121no—
321C2×D3—121no—
322C2×D3—121no—
323C2×D3—121no—
324C2×D3—121no—
325C2×D3—241no—
326C2×D3—241no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—41no—
334C3×C4—82no—
335C3×C4—81no—
336C3×C4—81no—
337C3×C4—121no—
338C3×C4—122no—
339C3×C4#91511yescharacteristic
340C3×C4#91611yescharacteristic
341C3×C4#91811yescharacteristic
342C3×C4#91811yescharacteristic
343C3×C4#91911yescharacteristic
344C3×C4#91911yescharacteristic
345C3×C4#94211yescharacteristic
346C3×C4#95011yescharacteristic
347Dic3—41no—
348Dic3—42no—
349Dic3—121no—
350Dic3—121no—
351Dic3—241no—
352C32#163411yescharacteristic, complemented, Sylow
353C23—61no—
354C23—181no—
355Q8—42no—
356Q8—122no—
357D4—61no—
358D4—61no—
359D4—181no—
360D4—181no—
361D4—722no—
362C2×C4—41no—
363C2×C4—61no—
364C2×C4—62no—
365C2×C4—121no—
366C2×C4—121no—
367C2×C4—181no—
368C2×C4—361no—
369C2×C4—361no—
370C2×C4D3×#6711yescharacteristic
371C2×C4D3×#6711yescharacteristic
372C2×C4#381111yescharacteristic
373C8—62no—
374C8—121no—
375C8—361no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—241no—
380C2×C3#504711yescharacteristic
381C2×C3#507711yescharacteristic
382C2×C3#517311yescharacteristic
383C2×C3#518711yescharacteristic
384C2×C3#518711yescharacteristic
385C2×C3#519811yescharacteristic
386D3—81no—
387D3—242no—
388D3—241no—
389D3—241no—
390C22—121no—
391C22—121no—
392C22—121no—
393C22—361no—
394C22—361no—
395C22—361no—
396C22#6398311yescharacteristic
397C4—21no—
398C4—81no—
399C4—122no—
400C4—121no—
401C4—361no—
402C4#6394811yescharacteristic
403C4#6394911yescharacteristic
404C4#6395011yescharacteristic
405C4#6395111yescharacteristic
406C3—21no—
407C3#7114511yescharacteristic, complemented
408C3#7130411yescharacteristic, complemented
409C2—241no—
410C2—721no—
411C2#1059152311yescharacteristic
412C2#1059165611yescharacteristic
413C2#1059165711yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radical#10593987C2
hypercenterC4⋊Q8D32
hypocenterC32#1634
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. #10592783C2semidirect
3. C3×#5092C2semidirect
4. C3×#5084C2semidirect
5. #10589095C2semidirect
6. #10589082C2semidirect
7. #10589081C2semidirect
31. #5092D3semidirect
35. #5084D3semidirect
352. C32#1634semidirect
407. C3#71145semidirect
408. C3#71304semidirect

Maximal subgroups

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

subgroupindex
#105939872
#105927832
C3×#50922
C3×#50842
#105890952
#105890822
#105890812
#713043
#711453