Finite Group Databasebeta

← #11779506

Subgroups — #11779506

Order 1152.

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

normal subgroups only

This group has 477 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
2C3×#4842C211yesmaximal, characteristic, complemented
3#10590387C211yesmaximal, characteristic, complemented
4#10590300C211yesmaximal, characteristic, complemented
5#10589349C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71145—31nomaximal
9#68493—31nomaximal
10C4×C4⋊(C3⋊D3)C2211yescharacteristic
11C3×C4×D12C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63916—21no—
15#63909—21no—
16#63907—22no—
17#63849—21no—
18#63841—21no—
19C2×#3718—22no—
20C32×C4⋊C8C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#821—21no—
23C3×#817—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63573—21no—
26#63564—21no—
27#5734—31no—
28#5563—31no—
29C3×#476—31no—
30#5092—31no—
31#5092—31no—
32#5084—31no—
33#4842—31no—
34#4842D311yescharacteristic, complemented
35C3×#333—31no—
36D4⋊(C3⋊C8)—31no—
37#4483—31no—
38#4483—31no—
39#4483—31no—
40#4483—61no—
41#4481D311yescharacteristic, complemented
42C2×C4⋊(C3⋊D3)D411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C3×Dic6—21no—
47C2×C3×Dic6D412yes—
48C2×#626—22no—
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51#3752—21no—
52C4⋊(C3⋊Dic3)D411yescharacteristic
53C2×C3⋊(C3⋊C8)—21no—
54C3×(C2×D3)⋊C4—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C2×C3×C3⋊C8—21no—
61#3722—22no—
62(C2×D3)⋊Dic3—22no—
63Dic32—22no—
64#3718—44no—
65#1634—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4⋊Q8—31no—
68C3×C4×D4—31no—
69#947—62no—
70C2×#216—62no—
71C2×#216—62no—
72#938—61no—
73#930—61no—
74#926—61no—
75#895—61no—
76#895—61no—
77#892—61no—
78#892—61no—
79#892—61no—
80#885—62no—
81C4×D12—31no—
82C4×D12—31no—
83C4×D12—61no—
84C4×D12C2×D311yescharacteristic
85#869C2×D311yescharacteristic
86#869C2×D311yescharacteristic
87C3×#106—61no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C4⋊C8C2×D311yescharacteristic
92C3×#102—61no—
93#821—21no—
94#821—61no—
95#817—21no—
96#817—61no—
97#809—61no—
98#808—61no—
99C4⋊(C3⋊C8)C2×D311yescharacteristic
100C4×C3⋊C8—31no—
101C4×C3⋊C8—31no—
102C4×C3⋊C8—61no—
103C22×C3⋊D3—21no—
104C22×C3×D3—21no—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C3⋊Dic3—21no—
109C4⋊(C3⋊D3)—21no—
110C4⋊(C3⋊D3)—21no—
111C4×C3⋊D3—41no—
112C4×C3⋊D3—41no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—41no—
116C3×D12—21no—
117C3×D12—21no—
118C3×C4×D3—41no—
119C3×C4×D3—41no—
120C3×Dic6—42no—
121C3×Dic6—42no—
122#626—82no—
123C32×C8—41no—
124C3⋊(C3⋊C8)—22no—
125C3×C3⋊C8—41no—
126#555—91no—
127#494—91no—
128#476—31no—
129#476—91no—
130#333—31no—
131D4⋊C8—91no—
132D4⋊C8—91no—
133C2×C3×Q8—32no—
134C2×C3×Q8—61no—
135C2×C3×D4—31no—
136C22×C3×C4—61no—
137C2×#67—62no—
138C2×D12—31no—
139C2×D12—31no—
140C2×D12—61no—
141C2×D12—62no—
142C2×D12#6711yescharacteristic
143C2×C4×D3—21no—
144C2×C4×D3—61no—
145C2×C4×D3—61no—
146C2×C4×D3—121no—
147C2×Dic6—21no—
148C2×Dic6D1212yes—
149C2×C3×C8—21no—
150C2×C3×C8—21no—
151C2×C3×C8—41no—
152C2×C3×C8—61no—
153C3×C4⋊C4—31no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4—61no—
158C3×C22⋊C4—61no—
159C3×C42—21no—
160C3×C42C22×D311yescharacteristic
161C3×C42C22×D311yescharacteristic
162#217—62no—
163#216—124no—
164#216—124no—
165(C2×D3)⋊C4—21no—
166(C2×D3)⋊C4—62no—
167(C2×D3)⋊C4—62no—
168(C2×D3)⋊C4—62no—
169(C2×D3)⋊C4—61no—
170(C2×D3)⋊C4—61no—
171(C2×D3)⋊C4—121no—
172C4⋊Dic3—21no—
173C4⋊Dic3—21no—
174C4⋊Dic3—21no—
175C4⋊Dic3—21no—
176C4⋊Dic3—31no—
177C4⋊Dic3—31no—
178C4⋊Dic3—61no—
179C4⋊Dic3#6711yescharacteristic
180C4×Dic3—62no—
181C4×Dic3—62no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—61no—
184C2×C3⋊C8—61no—
185C2×C3⋊C8—121no—
186C22×C32#12011yescharacteristic
187C2×C3⋊D3—41no—
188C2×C3⋊D3—41no—
189C2×C3⋊D3—41no—
190C2×C3×D3—41no—
191C2×C3×D3—41no—
192C2×C3×D3—41no—
193C32×C4—21no—
194C32×C4#13511yescharacteristic
195C32×C4#13511yescharacteristic
196C32×C4#13711yescharacteristic
197C32×C4#13711yescharacteristic
198C3⋊Dic3—41no—
199C3×Dic3—41no—
200C3×Dic3—42no—
201C3×Dic3—81no—
202C2×Q16—182no—
203C4⋊Q8—31no—
204C4⋊Q8—31no—
205#124—182no—
206#121—181no—
207#121—181no—
208C4×D4—31no—
209C4×D4—91no—
210#117—181no—
211#117—181no—
212#106—61no—
213#106—181no—
214C4⋊C8—31no—
215C4⋊C8D3211yescharacteristic
216#102—61no—
217#102—181no—
218C4×C8—91no—
219C23×C3—61no—
220C22×D3—21no—
221C22×D3—61no—
222C22×D3—61no—
223C22×D3—121no—
224C3×Q8—122no—
225C3×Q8—122no—
226C3×D4—61no—
227C3×D4—61no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—61no—
232C2×C3×C4—62no—
233C2×C3×C4—121no—
234C2×C3×C4—121no—
235C2×C3×C4—121no—
236C2×C3×C4C2×D1211yescharacteristic
237C2×C3×C4D3×D411yescharacteristic
238C2×C3×C4D3×D411yescharacteristic
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4C2×#6711yescharacteristic
242#67—242no—
243C2×Dic3—22no—
244C2×Dic3—21no—
245C2×Dic3—41no—
246C2×Dic3—61no—
247C2×Dic3—61no—
248C2×Dic3—121no—
249D12—21no—
250D12—21no—
251D12—62no—
252D12—61no—
253D12—61no—
254D12—61no—
255D12—61no—
256D12—121no—
257D12—242no—
258C4×D3—41no—
259C4×D3—41no—
260C4×D3—121no—
261C4×D3—121no—
262C4×D3—121no—
263C4×D3—121no—
264C4×D3—241no—
265C4×D3—241no—
266Dic6—42no—
267Dic6—42no—
268C3×C8—41no—
269C3×C8—41no—
270C3×C8—81no—
271C3×C8—121no—
272C3⋊C8—41no—
273C3⋊C8—62no—
274C3⋊C8—62no—
275C3⋊C8—122no—
276C2×C32#45211yescharacteristic
277C2×C32#45211yescharacteristic
278C2×C32#45311yescharacteristic
279C3⋊D3—81no—
280C3×D3—81no—
281C2×Q8—32no—
282C2×Q8—61no—
283C2×D4—31no—
284C2×D4—91no—
285C2×D4—182no—
286C22×C4—61no—
287C22×C4—181no—
288Q16—364no—
289C2×C8—21no—
290C2×C8—61no—
291C2×C8—181no—
292C4⋊C4—31no—
293C4⋊C4—61no—
294C4⋊C4—61no—
295C4⋊C4—61no—
296C4⋊C4—61no—
297C4⋊C4—91no—
298C22⋊C4—61no—
299C22⋊C4—182no—
300C22⋊C4—182no—
301C22⋊C4—181no—
302C42—182no—
303C42C2×D3211yescharacteristic
304C22×C3—21no—
305C22×C3—121no—
306C22×C3—121no—
307C22×C3—121no—
308C22×C3#88211yescharacteristic
309C22×C3#93711yescharacteristic
310C2×D3—41no—
311C2×D3—41no—
312C2×D3—41no—
313C2×D3—122no—
314C2×D3—121no—
315C2×D3—121no—
316C2×D3—121no—
317C2×D3—121no—
318C2×D3—121no—
319C2×D3—121no—
320C2×D3—241no—
321C2×D3—241no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—41no—
329C3×C4—122no—
330C3×C4—121no—
331C3×C4—241no—
332C3×C4#91511yescharacteristic
333C3×C4#91611yescharacteristic
334C3×C4#91611yescharacteristic
335C3×C4#91611yescharacteristic
336C3×C4#91811yescharacteristic
337C3×C4#91811yescharacteristic
338C3×C4#94211yescharacteristic
339C3×C4#95011yescharacteristic
340Dic3—41no—
341Dic3—42no—
342Dic3—81no—
343Dic3—121no—
344Dic3—121no—
345Dic3—241no—
346C32#163411yescharacteristic, complemented, Sylow
347C23—61no—
348C23—181no—
349Q8—122no—
350Q8—122no—
351D4—61no—
352D4—61no—
353D4—181no—
354D4—181no—
355D4—722no—
356C2×C4—61no—
357C2×C4—62no—
358C2×C4—121no—
359C2×C4—121no—
360C2×C4—121no—
361C2×C4—181no—
362C2×C4—361no—
363C2×C4—361no—
364C2×C4D3×D1211yescharacteristic
365C2×C4#380211yescharacteristic
366C2×C4D3×#6711yescharacteristic
367C8—41no—
368C8—121no—
369C8—182no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—241no—
374C2×C3#474711yescharacteristic
375C2×C3#480811yescharacteristic
376C2×C3#480811yescharacteristic
377C2×C3#504711yescharacteristic
378C2×C3#517311yescharacteristic
379C2×C3#519811yescharacteristic
380D3—81no—
381D3—242no—
382D3—241no—
383D3—241no—
384C22—121no—
385C22—121no—
386C22—121no—
387C22—361no—
388C22—361no—
389C22—361no—
390C22#6392211yescharacteristic
391C4—21no—
392C4—122no—
393C4—121no—
394C4—241no—
395C4—361no—
396C4#6380911yescharacteristic
397C4#6381111yescharacteristic
398C4#6393511yescharacteristic
399C4#6394811yescharacteristic
400C3—21no—
401C3#6849311yescharacteristic, complemented
402C3#7114511yescharacteristic, complemented
403C2—241no—
404C2—721no—
405C2#1059061611yescharacteristic
406C2#1059096111yescharacteristic
407C2#1059101411yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10593987C2
hypercenterC4⋊C8D32
hypocenterC32#1634
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4842C2semidirect
3. #10590387C2semidirect
4. #10590300C2semidirect
5. #10589349C2semidirect
6. C3×#4481C2semidirect
7. #10589080C2semidirect
34. #4842D3semidirect
41. #4481D3semidirect
346. C32#1634semidirect
401. C3#68493semidirect
402. C3#71145semidirect

Maximal subgroups

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

subgroupindex
#105939872
C3×#48422
#105903872
#105903002
#105893492
C3×#44812
#105890802
#711453
#684933