Finite Group Databasebeta

← #11779977

Subgroups — #11779977

Order 1152.

448 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 90 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#10593960C211yesmaximal, characteristic
2C3×#4846C211yesmaximal, characteristic
3#10590384C211yesmaximal, characteristic, complemented
4#10590288C211yesmaximal, characteristic, complemented
5#10589347C211yesmaximal, characteristic, complemented
6C3×#4484C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic
8#71113—31nomaximal
9#68270—31nomaximal
10#64078C2211yescharacteristic
11C3×C4×D12C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63896—22no—
15Dic3×D12—21no—
16D3×C4⋊Dic3—21no—
17#63869—21no—
18#63856—21no—
19C2×#3718—21no—
20C32×C4⋊C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×#821—21no—
23C3×#818—21no—
24C3×C4×C3⋊C8C2211yescharacteristic
25#63567—22no—
26#63565—21no—
27#5579—31no—
28#5543—31no—
29C3×#474—31no—
30#5093—31no—
31#5090—31no—
32#5031—31no—
33#4846D311yescharacteristic
34#4681—31no—
35C3×Q8⋊C8—31no—
36D4⋊(C3⋊C8)—31no—
37#4484D311yescharacteristic, complemented
38#4481—31no—
39#4481—31no—
40#4481—61no—
41#4459—31no—
42C2×#634D412yes—
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×Dic6—21no—
46C2×C3×Dic6D411yescharacteristic
47C2×D3×Dic3—22no—
48C2×C32×C8—21no—
49C32×C42C2311yescharacteristic
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C3×(C2×D3)⋊C4—21no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3D411yescharacteristic
57C3×C4⋊Dic3D411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×C4×Dic3—21no—
60C2×C3×C3⋊C8—21no—
61#3724—22no—
62Dic3⋊Dic3—22no—
63(C2×D3)⋊Dic3—22no—
64#3718—42no—
65#1644—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4×Q8—31no—
68C3×C4×D4—31no—
69#946—61no—
70C2×#216—61no—
71C2×#216—61no—
72D4×Dic3—61no—
73C2×C4⋊Dic3—61no—
74#924—61no—
75#896—62no—
76D3×C4⋊C4—61no—
77#890—61no—
78#878—62no—
79C4×D12—61no—
80C4×D12C2×D311yescharacteristic
81#870—61no—
82#869—31no—
83#869—31no—
84#869—61no—
85#869C2×D311yescharacteristic
86C4×Dic6C2×D311yescharacteristic
87C3×#107—61no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8C2×D311yescharacteristic
90C3×C4⋊C8C2×D311yescharacteristic
91C3×#102—61no—
92C3×C4×C8—31no—
93#835—61no—
94#821—21no—
95#818—21no—
96#816—62no—
97#810—62no—
98#810—61no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—61no—
102C4×C3⋊C8C2×D311yescharacteristic
103C22×C3×D3—21no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C3⋊Dic3—22no—
108#634—42no—
109C2×C3×Dic3—21no—
110C2×C3×Dic3—21no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—41no—
113C3×D12—21no—
114C3×D12Q1612yescomplemented
115C3×C4×D3—41no—
116C3×C4×D3—41no—
117C3×Dic6—21no—
118C3×Dic6—21no—
119C3×Dic6—41no—
120C3×Dic6—41no—
121D3×Dic3—82no—
122C32×C8—41no—
123C3⋊(C3⋊C8)—41no—
124C3×C3⋊C8—41no—
125#554—91no—
126#487—91no—
127#474—31no—
128#462—91no—
129#333—91no—
130Q8⋊C8—31no—
131D4⋊C8—91no—
132C2×C3×Q8—31no—
133C2×C3×Q8—61no—
134C2×C3×D4—31no—
135C22×C3×C4—61no—
136C22×Dic3—62no—
137C2×D12#6711yescharacteristic
138C2×C4×D3—21no—
139C2×C4×D3—62no—
140C2×Dic6—21no—
141C2×Dic6—32no—
142C2×Dic6—32no—
143C2×Dic6—62no—
144C2×Dic6D1211yescharacteristic
145C2×C3×C8—21no—
146C2×C3×C8—21no—
147C2×C3×C8—41no—
148C2×C3×C8—61no—
149C3×C4⋊C4—31no—
150C3×C4⋊C4—31no—
151C3×C4⋊C4—61no—
152C3×C4⋊C4—61no—
153C3×C4⋊C4—61no—
154C3×C22⋊C4—61no—
155C3×C42—21no—
156C3×C42—61no—
157C3×C42C22×D311yescharacteristic
158C3×C42C22×D311yescharacteristic
159#217—62no—
160#216—122no—
161#216—122no—
162(C2×D3)⋊C4—21no—
163(C2×D3)⋊C4—62no—
164C4⋊Dic3—21no—
165C4⋊Dic3—21no—
166C4⋊Dic3—62no—
167C4⋊Dic3—61no—
168C4⋊Dic3—61no—
169C4⋊Dic3—61no—
170C4⋊Dic3—61no—
171C4⋊Dic3—121no—
172C4⋊Dic3—121no—
173C4⋊Dic3D1211yescharacteristic
174C4⋊Dic3#6711yescharacteristic
175Dic3⋊C4—21no—
176Dic3⋊C4—62no—
177Dic3⋊C4—62no—
178Dic3⋊C4—62no—
179C4×Dic3—21no—
180C2×C3⋊C8—21no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—61no—
183C2×C3⋊C8—121no—
184C22×C32#12011yescharacteristic
185C2×C3×D3—22no—
186C2×C3×D3—41no—
187C2×C3×D3—41no—
188C32×C4—21no—
189C32×C4C2×Q1611yescharacteristic
190C32×C4#13511yescharacteristic
191C32×C4AGL(1,ℤ/8)11yescharacteristic
192C32×C4#13711yescharacteristic
193C3⋊Dic3—42no—
194C3×Dic3—41no—
195C3×Dic3—41no—
196C3×Dic3—41no—
197C3×Dic3—81no—
198C2×Q16—181no—
199C4⋊Q8—31no—
200C4⋊Q8—91no—
201#125—181no—
202C22⋊Q8—182no—
203C22⋊Q8—181no—
204C4×Q8—31no—
205C4×D4—31no—
206C4×D4—181no—
207C2×C4⋊C4—181no—
208#107—61no—
209C4⋊C8—91no—
210C4⋊C8D3211yescharacteristic
211#103—181no—
212#103—182no—
213#102—61no—
214C4×C8—31no—
215C23×C3—61no—
216C22×D3—21no—
217C3×Q8—61no—
218C3×Q8—61no—
219C3×Q8—121no—
220C3×Q8—121no—
221C3×D4—32no—
222C3×D4—61no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—61no—
227C2×C3×C4—61no—
228C2×C3×C4—61no—
229C2×C3×C4—121no—
230C2×C3×C4—121no—
231C2×C3×C4—121no—
232C2×C3×C4C2×D1211yescharacteristic
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4C2×#6711yescharacteristic
238C2×Dic3—21no—
239C2×Dic3—21no—
240C2×Dic3—21no—
241C2×Dic3—41no—
242C2×Dic3—62no—
243C2×Dic3—62no—
244C2×Dic3—122no—
245C2×Dic3—242no—
246D12—21no—
247D12#21612yescomplemented
248C4×D3—41no—
249C4×D3—41no—
250C4×D3—242no—
251Dic6—21no—
252Dic6—21no—
253Dic6—41no—
254Dic6—41no—
255Dic6—122no—
256Dic6—122no—
257Dic6—242no—
258C3×C8—41no—
259C3×C8—41no—
260C3×C8—81no—
261C3×C8—121no—
262C3⋊C8—41no—
263C3⋊C8—121no—
264C3⋊C8—121no—
265C3⋊C8—241no—
266C2×C32#44911yescharacteristic
267C2×C32#45111yescharacteristic
268C2×C32#45511yescharacteristic
269C3×D3—42no—
270C2×Q8—31no—
271C2×Q8—61no—
272C2×Q8—92no—
273C2×D4—31no—
274C22×C4—61no—
275C22×C4—182no—
276Q16—362no—
277C2×C8—21no—
278C2×C8—61no—
279C2×C8—181no—
280C4⋊C4—31no—
281C4⋊C4—31no—
282C4⋊C4—61no—
283C4⋊C4—61no—
284C4⋊C4—61no—
285C4⋊C4—182no—
286C4⋊C4—182no—
287C4⋊C4—181no—
288C4⋊C4—181no—
289C22⋊C4—61no—
290C22⋊C4—182no—
291C42—61no—
292C42C2×D3211yescharacteristic
293C22×C3—21no—
294C22×C3—62no—
295C22×C3—121no—
296C22×C3—121no—
297C22×C3#88211yescharacteristic
298C22×C3#93711yescharacteristic
299C2×D3—22no—
300C2×D3—41no—
301C2×D3—41no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—41no—
309C3×C4—121no—
310C3×C4—121no—
311C3×C4—121no—
312C3×C4—241no—
313C3×C4#90411yescharacteristic
314C3×C4#90811yescharacteristic
315C3×C4#91111yescharacteristic
316C3×C4#91211yescharacteristic
317C3×C4#91511yescharacteristic
318C3×C4D3×Q1611yescharacteristic
319C3×C4C2×#21611yescharacteristic
320C3×C4#95111yescharacteristic
321Dic3—41no—
322Dic3—41no—
323Dic3—41no—
324Dic3—81no—
325Dic3—122no—
326Dic3—122no—
327Dic3—242no—
328C32#164411yescharacteristic, complemented, Sylow
329C23—61no—
330Q8—61no—
331Q8—61no—
332Q8—121no—
333Q8—121no—
334Q8—362no—
335D4—32no—
336D4—61no—
337C2×C4—61no—
338C2×C4—61no—
339C2×C4—61no—
340C2×C4—121no—
341C2×C4—121no—
342C2×C4—121no—
343C2×C4—182no—
344C2×C4—722no—
345C2×C4D3×D1211yescharacteristic
346C2×C4#380211yescharacteristic
347C2×C4D3×#6711yescharacteristic
348C8—41no—
349C8—121no—
350C8—361no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—122no—
355C2×C3#473411yescharacteristic
356C2×C3#480911yescharacteristic
357C2×C3#482511yescharacteristic
358C2×C3#505011yescharacteristic
359C2×C3#515811yescharacteristic
360C2×C3#520211yescharacteristic
361D3—42no—
362C22—62no—
363C22—121no—
364C22—121no—
365C22#6392211yescharacteristic
366C4—21no—
367C4—121no—
368C4—121no—
369C4—121no—
370C4—241no—
371C4—362no—
372C4#6379511yescharacteristic
373C4#6380711yescharacteristic
374C4#6392911yescharacteristic
375C4D3×#21611yescharacteristic
376C3—21no—
377C3#6827011yescharacteristic, complemented
378C3#7111311yescharacteristic, complemented
379C2—122no—
380C2#1059060411yescharacteristic
381C2#1059096211yescharacteristic
382C2#1059101111yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC4⋊C8D32
hypocenterC32#1644
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
3. #10590384C2semidirect
4. #10590288C2semidirect
5. #10589347C2semidirect
6. C3×#4484C2semidirect
37. #4484D3semidirect
114. C3×D12Q16semidirect
247. D12#216semidirect
328. C32#1644semidirect
377. C3#68270semidirect
378. C3#71113semidirect

Maximal subgroups

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

subgroupindex
#105939602
C3×#48462
#105903842
#105902882
#105893472
C3×#44842
#105890812
#711133
#682703