Finite Group Databasebeta

← #11779504

Subgroups — #11779504

Order 1152.

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

normal subgroups only

This group has 468 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#10593988C211yesmaximal, characteristic
2C3×#4842C211yesmaximal, characteristic, complemented
3#10590386C211yesmaximal, characteristic, complemented
4#10590266C211yesmaximal, characteristic, complemented
5#10589347C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71145—31nomaximal
9#68203—31nomaximal
10#64078C2211yescharacteristic
11C3×C4×D12C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63913—22no—
15#63908—21no—
16#63908—21no—
17#63841—21no—
18#63841—21no—
19C2×#3719—22no—
20C32×C4⋊C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×#821—21no—
23C3×#817—21no—
24C3×C4×C3⋊C8C2211yescharacteristic
25#63574—21no—
26#63562—21no—
27#5563—31no—
28#5563—31no—
29C3×#476—31no—
30#5092—31no—
31#5084—31no—
32#5008—31no—
33#4842D311yescharacteristic, complemented
34#4699—31no—
35C3×D4⋊C8—31no—
36D4⋊(C3⋊C8)—31no—
37#4483D311yescharacteristic, complemented
38#4481—31no—
39#4481—31no—
40#4481—61no—
41#4459—31no—
42C2×#634D412yes—
43C2×C3×D12D411yescharacteristic
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C3×C4×D3—21no—
47C2×C3×Dic6—21no—
48C2×#625—22no—
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C3×(C2×D3)⋊C4—21no—
55C3×(C2×D3)⋊C4—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3D411yescharacteristic
59C3×C4⋊Dic3D411yescharacteristic
60C2×C3×C3⋊C8—21no—
61(C2×D3)⋊Dic3—22no—
62(C2×D3)⋊Dic3—22no—
63Dic32—22no—
64#3719—44no—
65#1634—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4×D4—31no—
68C3×C4×D4—31no—
69C2×#216—62no—
70#938—61no—
71#938—61no—
72#930—61no—
73#930—61no—
74#926—61no—
75#926—61no—
76C2×Dic12—62no—
77#892—61no—
78#892—61no—
79#885—62no—
80#885—62no—
81C4×D12C2×D311yescharacteristic
82C4×D12C2×D311yescharacteristic
83#869—31no—
84#869—31no—
85#869—61no—
86#869C2×D311yescharacteristic
87C3×#106—61no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8C2×D311yescharacteristic
90C3×C4⋊C8C2×D311yescharacteristic
91C3×#102—61no—
92C3×C4×C8—31no—
93#832—61no—
94#821—21no—
95#817—21no—
96#809—61no—
97#808—61no—
98#808—61no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—61no—
102C4×C3⋊C8C2×D311yescharacteristic
103C22×C3×D3—21no—
104C22×C3×D3—21no—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C3⋊Dic3—22no—
109#634—42no—
110C2×C3×Dic3—21no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—41no—
113C3×D12—21no—
114C3×D12—21no—
115C3×D12—21no—
116C3×D12—21no—
117C3×C4×D3—41no—
118C3×C4×D3—41no—
119C3×C4×D3—41no—
120C3×C4×D3—41no—
121C3×Dic6—42no—
122#625—82no—
123C32×C8—41no—
124C3⋊(C3⋊C8)—41no—
125C3×C3⋊C8—22no—
126#555—91no—
127#494—91no—
128#476—31no—
129#476—91no—
130#333—91no—
131D4⋊C8—31no—
132D4⋊C8—91no—
133C2×C3×Q8—61no—
134C2×C3×D4—31no—
135C2×C3×D4—31no—
136C22×C3×C4—61no—
137C22×C3×C4—61no—
138C2×#67—62no—
139C2×#67—62no—
140C2×D12D1211yescharacteristic
141C2×D12#6711yescharacteristic
142C2×C4×D3—21no—
143C2×C4×D3—21no—
144C2×Dic6—21no—
145C2×Dic6—32no—
146C2×Dic6—32no—
147C2×Dic6—62no—
148C2×C3×C8—21no—
149C2×C3×C8—21no—
150C2×C3×C8—41no—
151C2×C3×C8—61no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—31no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C22⋊C4—61no—
157C3×C22⋊C4—61no—
158C3×C42—21no—
159C3×C42C22×D311yescharacteristic
160C3×C42C22×D311yescharacteristic
161#217—62no—
162#217—62no—
163#216—124no—
164(C2×D3)⋊C4—21no—
165(C2×D3)⋊C4—21no—
166(C2×D3)⋊C4—62no—
167(C2×D3)⋊C4—62no—
168C4⋊Dic3—21no—
169C4⋊Dic3—21no—
170C4⋊Dic3—61no—
171C4⋊Dic3—61no—
172C4⋊Dic3—61no—
173C4⋊Dic3—61no—
174C4⋊Dic3—121no—
175C4⋊Dic3—121no—
176C4⋊Dic3D1211yescharacteristic
177C4⋊Dic3#6711yescharacteristic
178C4×Dic3—62no—
179C4×Dic3—62no—
180C2×C3⋊C8—21no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—61no—
183C2×C3⋊C8—121no—
184Dic12—124no—
185C22×C32#12011yescharacteristic
186C2×C3×D3—41no—
187C2×C3×D3—41no—
188C2×C3×D3—41no—
189C2×C3×D3—41no—
190C2×C3×D3—41no—
191C2×C3×D3—41no—
192C32×C4—21no—
193C32×C4#13511yescharacteristic
194C32×C4#13511yescharacteristic
195C32×C4#13711yescharacteristic
196C32×C4#13711yescharacteristic
197C3⋊Dic3—42no—
198C3×Dic3—41no—
199C3×Dic3—41no—
200C3×Dic3—81no—
201C2×Q16—182no—
202C4⋊Q8—31no—
203C4⋊Q8—91no—
204#124—182no—
205#121—181no—
206#121—181no—
207C4×D4—31no—
208C4×D4—31no—
209#117—181no—
210#117—181no—
211#106—61no—
212#106—181no—
213C4⋊C8—91no—
214C4⋊C8D3211yescharacteristic
215#102—61no—
216#102—181no—
217C4×C8—31no—
218C23×C3—61no—
219C23×C3—61no—
220C22×D3—21no—
221C22×D3—21no—
222C3×Q8—122no—
223C3×D4—61no—
224C3×D4—61no—
225C3×D4—61no—
226C3×D4—61no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—61no—
231C2×C3×C4—61no—
232C2×C3×C4—121no—
233C2×C3×C4—121no—
234C2×C3×C4—121no—
235C2×C3×C4—121no—
236C2×C3×C4—121no—
237C2×C3×C4C2×D1211yescharacteristic
238C2×C3×C4D3×D411yescharacteristic
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242C2×C3×C4C2×#6711yescharacteristic
243#67—242no—
244#67—242no—
245C2×Dic3—21no—
246C2×Dic3—21no—
247C2×Dic3—41no—
248C2×Dic3—62no—
249C2×Dic3—62no—
250C2×Dic3—122no—
251D12—21no—
252D12—21no—
253D12—21no—
254D12—21no—
255C4×D3—41no—
256C4×D3—41no—
257C4×D3—41no—
258C4×D3—41no—
259Dic6—42no—
260Dic6—122no—
261Dic6—122no—
262Dic6—242no—
263C3×C8—41no—
264C3×C8—41no—
265C3×C8—62no—
266C3×C8—81no—
267C3⋊C8—22no—
268C3⋊C8—121no—
269C3⋊C8—121no—
270C3⋊C8—241no—
271C2×C32#45211yescharacteristic
272C2×C32#45211yescharacteristic
273C2×C32#45311yescharacteristic
274C3×D3—81no—
275C3×D3—81no—
276C2×Q8—61no—
277C2×Q8—92no—
278C2×D4—31no—
279C2×D4—31no—
280C2×D4—182no—
281C22×C4—61no—
282C22×C4—61no—
283Q16—364no—
284C2×C8—21no—
285C2×C8—61no—
286C2×C8—181no—
287C4⋊C4—31no—
288C4⋊C4—31no—
289C4⋊C4—61no—
290C4⋊C4—61no—
291C4⋊C4—181no—
292C4⋊C4—181no—
293C22⋊C4—61no—
294C22⋊C4—61no—
295C22⋊C4—182no—
296C22⋊C4—182no—
297C42—182no—
298C42C2×D3211yescharacteristic
299C22×C3—21no—
300C22×C3—121no—
301C22×C3—121no—
302C22×C3—121no—
303C22×C3—121no—
304C22×C3—121no—
305C22×C3—121no—
306C22×C3#88211yescharacteristic
307C22×C3#93711yescharacteristic
308C2×D3—41no—
309C2×D3—41no—
310C2×D3—41no—
311C2×D3—41no—
312C2×D3—41no—
313C2×D3—41no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—41no—
321C3×C4—121no—
322C3×C4—121no—
323C3×C4—241no—
324C3×C4#90411yescharacteristic
325C3×C4#90911yescharacteristic
326C3×C4#91211yescharacteristic
327C3×C4#91511yescharacteristic
328C3×C4#91511yescharacteristic
329C3×C4#91611yescharacteristic
330C3×C4#94211yescharacteristic
331C3×C4#95011yescharacteristic
332Dic3—41no—
333Dic3—41no—
334Dic3—81no—
335Dic3—122no—
336Dic3—122no—
337Dic3—242no—
338C32#163411yescharacteristic, complemented, Sylow
339C23—61no—
340C23—61no—
341Q8—122no—
342Q8—362no—
343D4—61no—
344D4—61no—
345D4—61no—
346D4—61no—
347D4—722no—
348C2×C4—61no—
349C2×C4—61no—
350C2×C4—121no—
351C2×C4—121no—
352C2×C4—121no—
353C2×C4—121no—
354C2×C4—121no—
355C2×C4—182no—
356C2×C4D3×D1211yescharacteristic
357C2×C4#380211yescharacteristic
358C2×C4D3×#6711yescharacteristic
359C8—41no—
360C8—62no—
361C8—361no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—241no—
366C2×C3—241no—
367C2×C3#473311yescharacteristic
368C2×C3#478311yescharacteristic
369C2×C3#482211yescharacteristic
370C2×C3#504711yescharacteristic
371C2×C3#517311yescharacteristic
372C2×C3#519811yescharacteristic
373D3—81no—
374D3—81no—
375C22—121no—
376C22—121no—
377C22—121no—
378C22—121no—
379C22—121no—
380C22—121no—
381C22#6392211yescharacteristic
382C4—21no—
383C4—121no—
384C4—121no—
385C4—241no—
386C4—362no—
387C4#6380011yescharacteristic
388C4#6380611yescharacteristic
389C4#6393311yescharacteristic
390C4#6394611yescharacteristic
391C3—21no—
392C3#6820311yescharacteristic, complemented
393C3#7114511yescharacteristic, complemented
394C2—241no—
395C2—241no—
396C2#1059061411yescharacteristic
397C2#1059096011yescharacteristic
398C2#1059101311yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10593988C2
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. #10590386C2semidirect
4. #10590266C2semidirect
5. #10589347C2semidirect
6. C3×#4483C2semidirect
7. #10589081C2semidirect
33. #4842D3semidirect
37. #4483D3semidirect
338. C32#1634semidirect
392. C3#68203semidirect
393. C3#71145semidirect

Maximal subgroups

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

subgroupindex
#105939882
C3×#48422
#105903862
#105902662
#105893472
C3×#44832
#105890812
#711453
#682033