Finite Group Databasebeta

← #11779645

Subgroups — #11779645

Order 1152.

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

normal subgroups only

This group has 491 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
1#10593904C211yesmaximal, characteristic
2C3×#4842C211yesmaximal, characteristic
3#10590290C211yesmaximal, characteristic, complemented
4#10590284C211yesmaximal, characteristic, complemented
5#10589350C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic
8#71142—31nomaximal
9#68459—31nomaximal
10C2×D3×Dic6—21no—
11C4×#634C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63919—21no—
16#63899—22no—
17#63898—21no—
18#63856—21no—
19C32×C4⋊C8C2211yescharacteristic
20C4×C3⋊(C3⋊C8)C2211yescharacteristic
21C3×#821—21no—
22C3×#817—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24#63575—21no—
25#63567—21no—
26#63565—22no—
27#5727—31no—
28D4×Dic6—31no—
29C3×#476—31no—
30#5093—31no—
31#5091—31no—
32#5079—31no—
33#4850—31no—
34#4842D311yescharacteristic
35C3×#332—31no—
36D4⋊(C3⋊C8)—31no—
37#4486D311yescharacteristic, complemented
38#4484—31no—
39#4484—31no—
40#4484—61no—
41#4483—31no—
42C2×#634D411yescharacteristic
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×Dic6—21no—
46C2×C3×Dic6—21no—
47C2×#627—22no—
48C2×D3×Dic3—22no—
49D3×Dic6—42no—
50D3×Dic6—42no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53C4⋊(C3⋊Dic3)D411yescharacteristic
54#3750—21no—
55C4×C3⋊Dic3—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D412yes—
62C3×C4⋊Dic3D411yescharacteristic
63C2×C3×C3⋊C8—21no—
64#3724—22no—
65(C2×D3)⋊Dic3—22no—
66#1637—91noSylow
67C2×D3×Q8—61no—
68C22×Dic6—61no—
69C3×C4⋊Q8—31no—
70C3×C4⋊Q8—31no—
71C3×C4×D4—31no—
72#946—61no—
73D4×Dic3—61no—
74#924—61no—
75#896—62no—
76#893—61no—
77#888—61no—
78#888—61no—
79#878—62no—
80C4×D12C2×D311yescharacteristic
81#869C2×D311yescharacteristic
82#869C2×D311yescharacteristic
83C4×Dic6—31no—
84C4×Dic6—31no—
85C4×Dic6—61no—
86C3×#106—61no—
87C3×C4⋊C8—21no—
88C3×C4⋊C8—31no—
89C3×C4⋊C8C2×D311yescharacteristic
90C3×C4⋊C8C2×D311yescharacteristic
91C3×#102—61no—
92#835—62no—
93#821—21no—
94#818—61no—
95#817—21no—
96#816—61no—
97#810—61no—
98#810—62no—
99#807—61no—
100C4⋊(C3⋊C8)C2×D311yescharacteristic
101C4×C3⋊C8—31no—
102C4×C3⋊C8—31no—
103C4×C3⋊C8—61no—
104C22×C3×D3—21no—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C3⋊Dic3—21no—
109C2×C3⋊Dic3—21no—
110#634—21no—
111#634SD1612yes—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—41no—
115C3×D12—21no—
116C3×D12Q1612yes—
117C3×C4×D3—41no—
118C3×C4×D3—41no—
119C3×Dic6—41no—
120C3×Dic6—41no—
121C3×Dic6—42no—
122#627—44no—
123D3×Dic3—44no—
124C32×C8—41no—
125C3⋊(C3⋊C8)—41no—
126C3×C3⋊C8—41no—
127D4×Q8—91no—
128#487—91no—
129#477—91no—
130#476—31no—
131#332—31no—
132Q8⋊C8—91no—
133D4⋊C8—91no—
134C2×C3×Q8—61no—
135C2×C3×Q8—61no—
136C2×C3×D4—31no—
137C22×C3×C4—61no—
138C22×Dic3—62no—
139D3×Q8—122no—
140D3×Q8—122no—
141C2×D12#6711yescharacteristic
142C2×C4×D3—21no—
143C2×C4×D3—62no—
144C2×Dic6—21no—
145C2×Dic6—21no—
146C2×Dic6—31no—
147C2×Dic6—31no—
148C2×Dic6—61no—
149C2×Dic6—62no—
150C2×Dic6—62no—
151C2×Dic6—122no—
152C2×Dic6—122no—
153C2×C3×C8—21no—
154C2×C3×C8—21no—
155C2×C3×C8—41no—
156C2×C3×C8—61no—
157C3×C4⋊C4—32no—
158C3×C4⋊C4—31no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—61no—
161C3×C4⋊C4—61no—
162C3×C22⋊C4—61no—
163C3×C42—21no—
164C3×C42C22×D311yescharacteristic
165C3×C42C22×D311yescharacteristic
166#217—62no—
167(C2×D3)⋊C4—21no—
168(C2×D3)⋊C4—62no—
169C4⋊Dic3—21no—
170C4⋊Dic3—21no—
171C4⋊Dic3—21no—
172C4⋊Dic3—31no—
173C4⋊Dic3—31no—
174C4⋊Dic3—61no—
175C4⋊Dic3D1212yes—
176C4⋊Dic3#6711yescharacteristic
177Dic3⋊C4—62no—
178Dic3⋊C4—62no—
179Dic3⋊C4—61no—
180Dic3⋊C4—61no—
181Dic3⋊C4—121no—
182C4×Dic3—61no—
183C4×Dic3—61no—
184C4×Dic3—121no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—121no—
189C22×C32#12011yescharacteristic
190C2×C3×D3—22no—
191C2×C3×D3—41no—
192C2×C3×D3—41no—
193C32×C4—21no—
194C32×C4C2×SD1611yescharacteristic
195C32×C4C2×Q1611yescharacteristic
196C32×C4AGL(1,ℤ/8)11yescharacteristic
197C32×C4#13711yescharacteristic
198C3⋊Dic3—22no—
199C3⋊Dic3—41no—
200C3×Dic3—42no—
201C3×Dic3—41no—
202C3×Dic3—81no—
203C22×Q8—181no—
204C4⋊Q8—31no—
205C4⋊Q8—31no—
206C4⋊Q8—181no—
207C22⋊Q8—182no—
208C22⋊Q8—181no—
209C4×Q8—91no—
210C4×D4—31no—
211C4×D4—181no—
212#107—181no—
213#106—61no—
214C4⋊C8—31no—
215C4⋊C8D3211yescharacteristic
216#103—182no—
217#103—181no—
218#102—61no—
219C4×C8—91no—
220C23×C3—61no—
221C22×D3—21no—
222C3×Q8—122no—
223C3×Q8—121no—
224C3×Q8—121no—
225C3×D4—32no—
226C3×D4—61no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—61no—
231C2×C3×C4—62no—
232C2×C3×C4—121no—
233C2×C3×C4—121no—
234C2×C3×C4—121no—
235C2×C3×C4C2×D1211yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4D3×D411yescharacteristic
238C2×C3×C4D3×D411yescharacteristic
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4C2×#6711yescharacteristic
241C2×Dic3—22no—
242C2×Dic3—21no—
243C2×Dic3—41no—
244C2×Dic3—61no—
245C2×Dic3—61no—
246C2×Dic3—61no—
247C2×Dic3—61no—
248C2×Dic3—121no—
249C2×Dic3—121no—
250C2×Dic3—124no—
251D12—21no—
252D12#21612yes—
253C4×D3—41no—
254C4×D3—41no—
255C4×D3—124no—
256Dic6—32no—
257Dic6—32no—
258Dic6—41no—
259Dic6—41no—
260Dic6—42no—
261Dic6—62no—
262Dic6—61no—
263Dic6—61no—
264Dic6—121no—
265Dic6—124no—
266Dic6—124no—
267C3×C8—41no—
268C3×C8—41no—
269C3×C8—81no—
270C3×C8—121no—
271C3⋊C8—41no—
272C3⋊C8—121no—
273C3⋊C8—121no—
274C3⋊C8—122no—
275C2×C32#45011yescharacteristic
276C2×C32#45111yescharacteristic
277C2×C32#45411yescharacteristic
278C3×D3—42no—
279C2×Q8—61no—
280C2×Q8—61no—
281C2×Q8—91no—
282C2×Q8—182no—
283C2×Q8—362no—
284C2×Q8—362no—
285C2×D4—31no—
286C22×C4—61no—
287C22×C4—182no—
288C2×C8—21no—
289C2×C8—61no—
290C2×C8—181no—
291C4⋊C4—32no—
292C4⋊C4—31no—
293C4⋊C4—61no—
294C4⋊C4—61no—
295C4⋊C4—61no—
296C4⋊C4—91no—
297C4⋊C4—182no—
298C4⋊C4—181no—
299C22⋊C4—61no—
300C22⋊C4—182no—
301C42—181no—
302C42C2×D3211yescharacteristic
303C22×C3—21no—
304C22×C3—62no—
305C22×C3—121no—
306C22×C3—121no—
307C22×C3#88211yescharacteristic
308C22×C3#93711yescharacteristic
309C2×D3—22no—
310C2×D3—41no—
311C2×D3—41no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—41no—
319C3×C4—122no—
320C3×C4—121no—
321C3×C4—241no—
322C3×C4#91111yescharacteristic
323C3×C4D3×SD1611yescharacteristic
324C3×C4D3×SD1611yescharacteristic
325C3×C4#91411yescharacteristic
326C3×C4#91511yescharacteristic
327C3×C4D3×Q1611yescharacteristic
328C3×C4C2×#21611yescharacteristic
329C3×C4#95111yescharacteristic
330Dic3—41no—
331Dic3—42no—
332Dic3—62no—
333Dic3—62no—
334Dic3—81no—
335Dic3—122no—
336Dic3—121no—
337Dic3—121no—
338Dic3—241no—
339C32#163711yescharacteristic, complemented, Sylow
340C23—61no—
341Q8—92no—
342Q8—122no—
343Q8—121no—
344Q8—121no—
345Q8—181no—
346Q8—364no—
347D4—32no—
348D4—61no—
349C2×C4—61no—
350C2×C4—62no—
351C2×C4—121no—
352C2×C4—121no—
353C2×C4—121no—
354C2×C4—181no—
355C2×C4—181no—
356C2×C4—364no—
357C2×C4D3×D1211yescharacteristic
358C2×C4#380211yescharacteristic
359C2×C4D3×#6711yescharacteristic
360C8—41no—
361C8—121no—
362C8—361no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—122no—
367C2×C3#475311yescharacteristic
368C2×C3#477611yescharacteristic
369C2×C3#480911yescharacteristic
370C2×C3#505011yescharacteristic
371C2×C3#516911yescharacteristic
372C2×C3#520111yescharacteristic
373D3—42no—
374C22—62no—
375C22—121no—
376C22—121no—
377C22#6392211yescharacteristic
378C4—21no—
379C4—121no—
380C4—122no—
381C4—182no—
382C4—241no—
383C4—361no—
384C4#6379611yescharacteristic
385C4#6379811yescharacteristic
386C4#6392911yescharacteristic
387C4D3×#21611yescharacteristic
388C3—21no—
389C3#6845911yescharacteristic, complemented
390C3#7114211yescharacteristic, complemented
391C2—122no—
392C2#1059060411yescharacteristic
393C2#1059094311yescharacteristic
394C2#1059102011yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC4⋊C8D32
hypocenterC32#1637
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. #10590290C2semidirect
4. #10590284C2semidirect
5. #10589350C2semidirect
6. C3×#4486C2semidirect
37. #4486D3semidirect
339. C32#1637semidirect
389. C3#68459semidirect
390. C3#71142semidirect

Maximal subgroups

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

subgroupindex
#105939042
C3×#48422
#105902902
#105902842
#105893502
C3×#44862
#105890802
#711423
#684593