Finite Group Databasebeta

← #11779501

Subgroups — #11779501

Order 1152.

477 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 477 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C3×#5563C211yesmaximal, characteristic
2C3×#5008C211yesmaximal, characteristic, complemented
3#10590387C211yesmaximal, characteristic, complemented
4#10590266C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
6#10589095C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71928—31nomaximal
9#71145—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C3×#938—21no—
12C3×#930—21no—
13C3×#926—21no—
14C3×#892—21no—
15C3×#885—22no—
16C3×C4×D12C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C2×#3718—22no—
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#832—21no—
23C3×#808—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63574—21no—
26#63562—21no—
27C3×#555—31no—
28#5563D311yescharacteristic
29C3×#476—31no—
30#5092—31no—
31#5092—31no—
32#5084—31no—
33#5008—31no—
34#5008D311yescharacteristic, complemented
35#4546—31no—
36D4⋊(C3⋊C8)—31no—
37D4⋊(C3⋊C8)—31no—
38D4⋊(C3⋊C8)—31no—
39D4⋊(C3⋊C8)—61no—
40#4483—31no—
41#4481—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C2×C3×#67—22no—
45C2×C3×D12D411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×Dic6—21no—
48C2×C3×Dic6D412yes—
49C32×C4⋊C4D411yescharacteristic
50C32×C22⋊C4—21no—
51C32×C42C2311yescharacteristic
52C2×C3⋊(C3⋊C8)—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C3×#217—22no—
55C3×(C2×D3)⋊C4—22no—
56C3×(C2×D3)⋊C4—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×C4×Dic3—22no—
63C2×C3×C3⋊C8—21no—
64#3718—44no—
65#1634—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4⋊Q8—31no—
68C3×#124—62no—
69C3×#121—61no—
70C3×#121—61no—
71C3×C4×D4—21no—
72C3×C4×D4—31no—
73C3×C4×D4C2×D311yescharacteristic
74C3×C4×D4C2×D311yescharacteristic
75C3×#117—61no—
76C3×#117—61no—
77C2×#216—62no—
78C2×#216—62no—
79#938—21no—
80#930—21no—
81#926—21no—
82#892—21no—
83#885—22no—
84C4×D12C2×D311yescharacteristic
85#869C2×D311yescharacteristic
86#869C2×D311yescharacteristic
87C3×#106—61no—
88C3×C4⋊C8—31no—
89C3×#102—61no—
90#832—21no—
91#832—61no—
92#809—61no—
93#808—21no—
94#808—61no—
95#808—61no—
96C4⋊(C3⋊C8)—31no—
97C4⋊(C3⋊C8)—31no—
98C4⋊(C3⋊C8)—61no—
99C4⋊(C3⋊C8)C2×D311yescharacteristic
100C4×C3⋊C8—31no—
101C4×C3⋊C8—31no—
102C4×C3⋊C8—61no—
103C23×C32—21no—
104C22×C3×D3—21no—
105C32×D4—21no—
106C32×D4—21no—
107C2×C32×C4—21no—
108C2×C32×C4—41no—
109C2×C32×C4—41no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C3×#67—82no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—41no—
117C3×D12—21no—
118C3×D12—21no—
119C3×C4×D3—41no—
120C3×C4×D3—41no—
121C3×Dic6—42no—
122C3×Dic6—42no—
123C3⋊(C3⋊C8)—22no—
124C3⋊(C3⋊C8)—41no—
125C3×C3⋊C8—41no—
126#555—31no—
127#494—91no—
128#476—31no—
129#476—91no—
130#333—91no—
131D4⋊C8—91no—
132D4⋊C8—91no—
133C2×C3×Q8—32no—
134C2×C3×Q8—61no—
135C2×C3×D4—21no—
136C2×C3×D4—31no—
137C2×C3×D4—62no—
138C2×C3×D4#6711yescharacteristic
139C2×C3×D4#6711yescharacteristic
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—41no—
143C22×C3×C4—61no—
144C2×#67—22no—
145C2×D12#6711yescharacteristic
146C2×C4×D3—21no—
147C2×Dic6—21no—
148C2×Dic6#6712yes—
149C2×C3×C8—61no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—31no—
152C3×C4⋊C4—61no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4#6711yescharacteristic
157C3×C4⋊C4#6711yescharacteristic
158C3×C22⋊C4—21no—
159C3×C22⋊C4—21no—
160C3×C22⋊C4—41no—
161C3×C22⋊C4—62no—
162C3×C22⋊C4—62no—
163C3×C22⋊C4—61no—
164C3×C42—21no—
165C3×C42—62no—
166C3×C42C22×D311yescharacteristic
167C3×C42C22×D311yescharacteristic
168#217—22no—
169#216—124no—
170#216—124no—
171(C2×D3)⋊C4—22no—
172(C2×D3)⋊C4—21no—
173C4⋊Dic3—21no—
174C4⋊Dic3—21no—
175C4⋊Dic3—21no—
176C4⋊Dic3—21no—
177C4⋊Dic3#6711yescharacteristic
178C4×Dic3—22no—
179C2×C3⋊C8—21no—
180C2×C3⋊C8—61no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—61no—
183C2×C3⋊C8—61no—
184C2×C3⋊C8—121no—
185C2×C3⋊C8—121no—
186C22×C32—41no—
187C22×C32—41no—
188C22×C32—41no—
189C22×C32#12011yescharacteristic
190C2×C3×D3—41no—
191C2×C3×D3—41no—
192C2×C3×D3—41no—
193C32×C4—21no—
194C32×C4—41no—
195C32×C4#13511yescharacteristic
196C32×C4#13511yescharacteristic
197C32×C4#13711yescharacteristic
198C32×C4#13711yescharacteristic
199C3×Dic3—41no—
200C3×Dic3—42no—
201C3×Dic3—81no—
202C2×Q16—182no—
203C4⋊Q8—31no—
204C4⋊Q8—31no—
205#124—62no—
206#121—61no—
207#121—61no—
208C4×D4—31no—
209C4×D4D3211yescharacteristic
210#117—61no—
211#117—61no—
212#106—61no—
213#106—181no—
214C4⋊C8—31no—
215C4⋊C8—91no—
216#102—61no—
217#102—181no—
218C4×C8—91no—
219C23×C3—21no—
220C23×C3—21no—
221C23×C3—41no—
222C23×C3—61no—
223C22×D3—21no—
224C3×Q8—122no—
225C3×Q8—122no—
226C3×D4—22no—
227C3×D4—21no—
228C3×D4—21no—
229C3×D4—21no—
230C3×D4—21no—
231C3×D4—41no—
232C3×D4—61no—
233C3×D4—61no—
234C3×D4—242no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—61no—
246C2×C3×C4—62no—
247C2×C3×C4—81no—
248C2×C3×C4—81no—
249C2×C3×C4—121no—
250C2×C3×C4—121no—
251C2×C3×C4—121no—
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4C2×#6711yescharacteristic
255C2×C3×C4C2×#6711yescharacteristic
256C2×C3×C4C2×#6711yescharacteristic
257C2×C3×C4C2×#6711yescharacteristic
258#67—82no—
259C2×Dic3—21no—
260C2×Dic3—22no—
261C2×Dic3—41no—
262D12—21no—
263D12—21no—
264C4×D3—41no—
265C4×D3—41no—
266Dic6—42no—
267Dic6—42no—
268C3×C8—121no—
269C3⋊C8—41no—
270C3⋊C8—62no—
271C3⋊C8—62no—
272C3⋊C8—122no—
273C3⋊C8—121no—
274C3⋊C8—121no—
275C3⋊C8—241no—
276C2×C32—81no—
277C2×C32#45211yescharacteristic
278C2×C32#45211yescharacteristic
279C2×C32#45311yescharacteristic
280C3×D3—81no—
281C2×Q8—32no—
282C2×Q8—61no—
283C2×D4—31no—
284C2×D4—62no—
285C2×D4#62511yescharacteristic
286C22×C4—21no—
287C22×C4—61no—
288Q16—364no—
289C2×C8—61no—
290C2×C8—181no—
291C2×C8—181no—
292C4⋊C4—31no—
293C4⋊C4—61no—
294C4⋊C4—61no—
295C4⋊C4—61no—
296C4⋊C4—61no—
297C4⋊C4#62511yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—62no—
300C22⋊C4—62no—
301C22⋊C4—61no—
302C42—62no—
303C42C2×D3211yescharacteristic
304C22×C3—21no—
305C22×C3—42no—
306C22×C3—41no—
307C22×C3—41no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—81no—
313C22×C3—81no—
314C22×C3—121no—
315C22×C3—121no—
316C22×C3—121no—
317C22×C3#93711yescharacteristic
318C22×C3#95311yescharacteristic
319C2×D3—41no—
320C2×D3—41no—
321C2×D3—41no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—41no—
329C3×C4—41no—
330C3×C4—41no—
331C3×C4—81no—
332C3×C4—122no—
333C3×C4—121no—
334C3×C4—241no—
335C3×C4#91511yescharacteristic
336C3×C4#91611yescharacteristic
337C3×C4#94211yescharacteristic
338C3×C4#95011yescharacteristic
339C3×C4#95011yescharacteristic
340C3×C4#95011yescharacteristic
341C3×C4#95111yescharacteristic
342C3×C4#95111yescharacteristic
343Dic3—41no—
344Dic3—42no—
345Dic3—81no—
346C32#163411yescharacteristic, complemented, Sylow
347C23—21no—
348C23—61no—
349Q8—122no—
350Q8—122no—
351D4—21no—
352D4—21no—
353D4—61no—
354D4—61no—
355D4—242no—
356C2×C4—21no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—61no—
360C2×C4—62no—
361C2×C4—121no—
362C2×C4—121no—
363C2×C4—121no—
364C2×C4C2×#62511yescharacteristic
365C2×C4D3×#6711yescharacteristic
366C2×C4D3×#6711yescharacteristic
367C8—121no—
368C8—182no—
369C8—361no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—82no—
374C2×C3—81no—
375C2×C3—81no—
376C2×C3—241no—
377C2×C3#504711yescharacteristic
378C2×C3#517311yescharacteristic
379C2×C3#519811yescharacteristic
380C2×C3#523911yescharacteristic
381C2×C3#523911yescharacteristic
382C2×C3#524111yescharacteristic
383D3—81no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—121no—
388C22—121no—
389C22—121no—
390C22#6397611yescharacteristic
391C4—21no—
392C4—41no—
393C4—122no—
394C4—121no—
395C4—241no—
396C4#6382211yescharacteristic
397C4#6382711yescharacteristic
398C4#6392911yescharacteristic
399C4#6393511yescharacteristic
400C3—21no—
401C3#7114511yescharacteristic, complemented
402C3#7192811yescharacteristic, complemented
403C2—81no—
404C2—241no—
405C2#1059117011yescharacteristic
406C2#1059146111yescharacteristic
407C2#1059166511yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radicalC3×#5563C2
hypercenterC4×D4D32
hypocenterC32#1634
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#5008C2semidirect
3. #10590387C2semidirect
4. #10590266C2semidirect
5. D4⋊(C3⋊(C3⋊C8))C2semidirect
6. #10589095C2semidirect
7. #10589080C2semidirect
34. #5008D3semidirect
346. C32#1634semidirect
401. C3#71145semidirect
402. C3#71928semidirect

Maximal subgroups

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

subgroupindex
C3×#55632
C3×#50082
#105903872
#105902662
D4⋊(C3⋊(C3⋊C8))2
#105890952
#105890802
#719283
#711453