Finite Group Databasebeta

← #11779550

Subgroups — #11779550

Order 1152.

509 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 509 conjugacy classes of subgroups — too many to draw. Only its 88 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#10593869C211yesmaximal, characteristic
2C3×#4842C211yesmaximal, characteristic, complemented
3#10590300C211yesmaximal, characteristic, complemented
4#10590290C211yesmaximal, characteristic, complemented
5#10589349C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71140—31nomaximal
9#68434—31nomaximal
10C2×#3799—21no—
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63916—21no—
16#63900—21no—
17#63856—21no—
18#63854—22no—
19C32×C4⋊C8C2211yescharacteristic
20C4×C3⋊(C3⋊C8)C2211yescharacteristic
21C3×#821—21no—
22C3×#817—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24#63573—21no—
25#63565—22no—
26#63564—21no—
27#5726—31no—
28#5551—31no—
29C3×#476—31no—
30#5093—31no—
31#5084—31no—
32#5079—31no—
33#4842—31no—
34#4842D311yescharacteristic, complemented
35C3×#332—31no—
36D4⋊(C3⋊C8)—31no—
37#4486D311yescharacteristic, complemented
38#4483—31no—
39#4483—31no—
40#4483—31no—
41#4483—61no—
42C2×C4⋊(C3⋊D3)D411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C3×Dic6—21no—
47C2×C3×Dic6—21no—
48C2×#626—22no—
49C2×#624—22no—
50#3799—42no—
51#3799—42no—
52C2×C32×C8—21no—
53C32×C42C2311yescharacteristic
54#3752—21no—
55C4⋊(C3⋊Dic3)D411yescharacteristic
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#1635—91noSylow
67C2×#239—61no—
68C2×#235—61no—
69C3×C4⋊Q8—31no—
70C3×C4⋊Q8—31no—
71C3×C4×D4—31no—
72#946—61no—
73#938—61no—
74#924—61no—
75#895—61no—
76#894—62no—
77D3×C4⋊C4—61no—
78D3×C4⋊C4—61no—
79#883—62no—
80C4×D12—31no—
81C4×D12—31no—
82C4×D12—61no—
83C4×D12C2×D311yescharacteristic
84#869C2×D311yescharacteristic
85#869C2×D311yescharacteristic
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#821—61no—
95#817—21no—
96#817—61no—
97#810—62no—
98#809—61no—
99#808—61no—
100C4⋊(C3⋊C8)C2×D311yescharacteristic
101C4×C3⋊C8—31no—
102C4×C3⋊C8—31no—
103C4×C3⋊C8—61no—
104C22×C3⋊D3—21no—
105C22×C3×D3—21no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C3⋊Dic3—21no—
110C4⋊(C3⋊D3)—21no—
111C4⋊(C3⋊D3)SD1612yes—
112C4×C3⋊D3—41no—
113C4×C3⋊D3—41no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—41no—
117C3×D12—21no—
118C3×D12—21no—
119C3×C4×D3—41no—
120C3×C4×D3—41no—
121C3×Dic6—41no—
122C3×Dic6—41no—
123C3×Dic6—42no—
124#626—44no—
125#624—44no—
126C32×C8—41no—
127C3⋊(C3⋊C8)—41no—
128C3×C3⋊C8—41no—
129#547—91no—
130#487—91no—
131#476—31no—
132#476—91no—
133#332—31no—
134D4⋊C8—91no—
135D4⋊C8—91no—
136C2×C3×Q8—61no—
137C2×C3×Q8—61no—
138C2×C3×D4—31no—
139C22×C3×C4—61no—
140C2×#67—62no—
141#239—122no—
142#239—122no—
143#235—122no—
144#235—122no—
145C2×D12—31no—
146C2×D12—31no—
147C2×D12—61no—
148C2×D12—62no—
149C2×D12#6711yescharacteristic
150C2×C4×D3—21no—
151C2×C4×D3—62no—
152C2×C4×D3—62no—
153C2×C4×D3—61no—
154C2×C4×D3—61no—
155C2×C4×D3—121no—
156C2×Dic6—21no—
157C2×Dic6—21no—
158C2×C3×C8—21no—
159C2×C3×C8—21no—
160C2×C3×C8—41no—
161C2×C3×C8—61no—
162C3×C4⋊C4—32no—
163C3×C4⋊C4—31no—
164C3×C4⋊C4—61no—
165C3×C4⋊C4—61no—
166C3×C4⋊C4—61no—
167C3×C22⋊C4—61no—
168C3×C42—21no—
169C3×C42C22×D311yescharacteristic
170C3×C42C22×D311yescharacteristic
171#217—62no—
172(C2×D3)⋊C4—21no—
173(C2×D3)⋊C4—62no—
174(C2×D3)⋊C4—61no—
175(C2×D3)⋊C4—61no—
176(C2×D3)⋊C4—121no—
177C4⋊Dic3—21no—
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180C4⋊Dic3—31no—
181C4⋊Dic3—31no—
182C4⋊Dic3—61no—
183C4⋊Dic3D1212yes—
184C4⋊Dic3#6711yescharacteristic
185Dic3⋊C4—62no—
186Dic3⋊C4—62no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—61no—
189C2×C3⋊C8—61no—
190C2×C3⋊C8—121no—
191C22×C32#12011yescharacteristic
192C2×C3⋊D3—22no—
193C2×C3⋊D3—41no—
194C2×C3⋊D3—41no—
195C2×C3×D3—41no—
196C2×C3×D3—41no—
197C2×C3×D3—41no—
198C32×C4—21no—
199C32×C4C2×SD1611yescharacteristic
200C32×C4#13511yescharacteristic
201C32×C4AGL(1,ℤ/8)11yescharacteristic
202C32×C4#13711yescharacteristic
203C3⋊Dic3—41no—
204C3×Dic3—41no—
205C3×Dic3—42no—
206C3×Dic3—81no—
207C2×#41—181no—
208C4⋊Q8—31no—
209C4⋊Q8—31no—
210#123—182no—
211C22⋊Q8—181no—
212#121—181no—
213C4×D4—31no—
214C4×D4—91no—
215C2×C4⋊C4—181no—
216#106—61no—
217#106—181no—
218C4⋊C8—31no—
219C4⋊C8D3211yescharacteristic
220#103—182no—
221#102—61no—
222#102—181no—
223C4×C8—91no—
224C23×C3—61no—
225C22×D3—21no—
226C22×D3—61no—
227C22×D3—61no—
228C22×D3—121no—
229C3×Q8—122no—
230C3×Q8—121no—
231C3×Q8—121no—
232C3×D4—61no—
233C3×D4—61no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—61no—
238C2×C3×C4—62no—
239C2×C3×C4—121no—
240C2×C3×C4—121no—
241C2×C3×C4—121no—
242C2×C3×C4C2×D1211yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4C2×#6711yescharacteristic
248#67—124no—
249C2×Dic3—22no—
250C2×Dic3—21no—
251C2×Dic3—41no—
252C2×Dic3—61no—
253C2×Dic3—61no—
254C2×Dic3—121no—
255D12—21no—
256D12—21no—
257D12—32no—
258D12—32no—
259D12—62no—
260D12—61no—
261D12—61no—
262D12—121no—
263D12—124no—
264C4×D3—41no—
265C4×D3—41no—
266C4×D3—124no—
267C4×D3—124no—
268C4×D3—121no—
269C4×D3—121no—
270C4×D3—121no—
271C4×D3—121no—
272C4×D3—241no—
273C4×D3—241no—
274Dic6—41no—
275Dic6—41no—
276Dic6—42no—
277C3×C8—41no—
278C3×C8—41no—
279C3×C8—81no—
280C3×C8—121no—
281C3⋊C8—41no—
282C3⋊C8—121no—
283C3⋊C8—121no—
284C3⋊C8—122no—
285C2×C32#45011yescharacteristic
286C2×C32#45211yescharacteristic
287C2×C32#45411yescharacteristic
288C3⋊D3—42no—
289C3×D3—81no—
290#41—362no—
291#41—362no—
292C2×Q8—61no—
293C2×Q8—61no—
294C2×D4—31no—
295C2×D4—91no—
296C2×D4—182no—
297C22×C4—61no—
298C22×C4—182no—
299C22×C4—181no—
300C2×C8—21no—
301C2×C8—61no—
302C2×C8—181no—
303C4⋊C4—32no—
304C4⋊C4—31no—
305C4⋊C4—61no—
306C4⋊C4—61no—
307C4⋊C4—61no—
308C4⋊C4—91no—
309C4⋊C4—182no—
310C22⋊C4—61no—
311C22⋊C4—182no—
312C22⋊C4—181no—
313C42C2×D3211yescharacteristic
314C22×C3—21no—
315C22×C3—121no—
316C22×C3—121no—
317C22×C3—121no—
318C22×C3#88211yescharacteristic
319C22×C3#93711yescharacteristic
320C2×D3—41no—
321C2×D3—41no—
322C2×D3—41no—
323C2×D3—62no—
324C2×D3—62no—
325C2×D3—122no—
326C2×D3—121no—
327C2×D3—121no—
328C2×D3—121no—
329C2×D3—121no—
330C2×D3—241no—
331C2×D3—241no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—41no—
339C3×C4—122no—
340C3×C4—121no—
341C3×C4—241no—
342C3×C4#91111yescharacteristic
343C3×C4D3×SD1611yescharacteristic
344C3×C4D3×SD1611yescharacteristic
345C3×C4#91411yescharacteristic
346C3×C4#91611yescharacteristic
347C3×C4#91811yescharacteristic
348C3×C4#94211yescharacteristic
349C3×C4#95011yescharacteristic
350Dic3—41no—
351Dic3—42no—
352Dic3—81no—
353Dic3—121no—
354Dic3—121no—
355Dic3—241no—
356C32#163511yescharacteristic, complemented, Sylow
357C23—61no—
358C23—181no—
359Q8—122no—
360Q8—121no—
361Q8—121no—
362D4—61no—
363D4—61no—
364D4—92no—
365D4—181no—
366D4—364no—
367C2×C4—61no—
368C2×C4—62no—
369C2×C4—121no—
370C2×C4—121no—
371C2×C4—121no—
372C2×C4—181no—
373C2×C4—364no—
374C2×C4—361no—
375C2×C4—361no—
376C2×C4D3×D1211yescharacteristic
377C2×C4#380211yescharacteristic
378C2×C4D3×#6711yescharacteristic
379C8—41no—
380C8—121no—
381C8—361no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—241no—
386C2×C3#475311yescharacteristic
387C2×C3#477611yescharacteristic
388C2×C3#480811yescharacteristic
389C2×C3#504711yescharacteristic
390C2×C3#516911yescharacteristic
391C2×C3#520111yescharacteristic
392D3—81no—
393D3—122no—
394D3—122no—
395D3—242no—
396C22—121no—
397C22—121no—
398C22—121no—
399C22—182no—
400C22—361no—
401C22—361no—
402C22#6392211yescharacteristic
403C4—21no—
404C4—121no—
405C4—122no—
406C4—241no—
407C4—361no—
408C4#6379611yescharacteristic
409C4#6379811yescharacteristic
410C4#6393511yescharacteristic
411C4#6394811yescharacteristic
412C3—21no—
413C3#6843411yescharacteristic, complemented
414C3#7114011yescharacteristic, complemented
415C2—241no—
416C2—362no—
417C2#1059061611yescharacteristic
418C2#1059094311yescharacteristic
419C2#1059102011yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10593869C2
hypercenterC4⋊C8D32
hypocenterC32#1635
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. #10590300C2semidirect
4. #10590290C2semidirect
5. #10589349C2semidirect
6. C3×#4486C2semidirect
7. #10589080C2semidirect
34. #4842D3semidirect
37. #4486D3semidirect
356. C32#1635semidirect
413. C3#68434semidirect
414. C3#71140semidirect

Maximal subgroups

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

subgroupindex
#105938692
C3×#48422
#105903002
#105902902
#105893492
C3×#44862
#105890802
#711403
#684343