Finite Group Databasebeta

← #11779534

Subgroups — #11779534

Order 1152.

517 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 517 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C3×#5726C211yesmaximal, characteristic
2#10592792C211yesmaximal, characteristic, complemented
3#10590268C211yesmaximal, characteristic, complemented
4#10590268C211yesmaximal, characteristic, complemented
5C3×#4547C211yesmaximal, characteristic, complemented
6#10589080C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71911—31nomaximal
9#68434—31nomaximal
10C2×C3×#239—21no—
11C32×C4⋊Q8C2211yescharacteristic
12#64078C2211yescharacteristic
13C3×#946—21no—
14C3×#895—21no—
15C3×#894—22no—
16C3×D3×C4⋊C4—21no—
17C3×C4×D12C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19#63637—22no—
20C4×C3⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23#63573—21no—
24#63573—21no—
25#63563—21no—
26#63563—21no—
27C3×#547—31no—
28#5726D311yescharacteristic
29#5093—31no—
30#5093—31no—
31#5093—61no—
32#5008—31no—
33#5008—31no—
34#4842—31no—
35#4842—31no—
36C3×#332—31no—
37#4547D311yescharacteristic, complemented
38D4⋊(C3⋊C8)—31no—
39D4⋊(C3⋊C8)—31no—
40#4483—31no—
41#4483—31no—
42C2×C32×Q8—21no—
43C2×#634—21no—
44C3×#239—42no—
45C3×#239—42no—
46C2×C3×D12—22no—
47C2×C3×D12D411yescharacteristic
48C2×C3×D12D411yescharacteristic
49C2×C3×C4×D3—22no—
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4D412yes—
54C32×C42C2311yescharacteristic
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×(C2×D3)⋊C4—22no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—22no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66#1635—91noSylow
67C2×C3×#41—61no—
68C2×#239—21no—
69C3×C4⋊Q8—21no—
70C3×C4⋊Q8C2×D311yescharacteristic
71C3×C4⋊Q8C2×D311yescharacteristic
72C3×#123—62no—
73C3×C22⋊Q8—61no—
74C3×#121—61no—
75C3×C4×D4—31no—
76C3×C4×D4—31no—
77C2×C3×C4⋊C4—61no—
78#946—21no—
79#895—21no—
80#894—22no—
81D3×C4⋊C4—21no—
82C4×D12C2×D311yescharacteristic
83C4×D12C2×D311yescharacteristic
84#869—31no—
85#869—31no—
86#869—61no—
87C3×C4⋊C8—31no—
88C3×C4⋊C8—31no—
89#832—61no—
90#832—61no—
91#821—61no—
92#821—61no—
93#817—61no—
94#817—61no—
95#810—64no—
96#810—62no—
97#810—62no—
98#808—61no—
99#808—61no—
100C4⋊(C3⋊C8)C2×D311yescharacteristic
101C4⋊(C3⋊C8)C2×D311yescharacteristic
102C4×C3⋊C8—31no—
103C4×C3⋊C8—31no—
104C4×C3⋊C8—61no—
105C22×C3×D3—21no—
106C22×C3×D3—21no—
107C32×Q8—41no—
108C32×Q8—41no—
109C2×C32×C4—22no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C3⋊Dic3—41no—
114#634—42no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—21no—
117C3×D12—21no—
118C3×D12—21no—
119C3×D12—21no—
120C3×D12—44no—
121C3×D12SD1612yes—
122C3×C4×D3—44no—
123C3×C4×D3—41no—
124C3×C4×D3—41no—
125C3×C4×D3—41no—
126C3×C4×D3—41no—
127C3⋊(C3⋊C8)—41no—
128C3×C3⋊C8—41no—
129C3×C3⋊C8—41no—
130#547—31no—
131#487—91no—
132#476—91no—
133#476—91no—
134#332—31no—
135D4⋊C8—91no—
136D4⋊C8—91no—
137C3×#41—122no—
138C3×#41—122no—
139C2×C3×Q8—21no—
140C2×C3×Q8—21no—
141C2×C3×Q8—41no—
142C2×C3×D4—31no—
143C2×C3×D4—31no—
144C2×C3×D4—62no—
145C22×C3×C4—62no—
146C22×C3×C4—61no—
147C22×C3×C4—61no—
148#239—42no—
149#239—42no—
150C2×D12—22no—
151C2×D12#6711yescharacteristic
152C2×D12#6711yescharacteristic
153C2×C4×D3—22no—
154C2×C4×D3—21no—
155C2×C4×D3—21no—
156C2×Dic6—62no—
157C2×Dic6—61no—
158C2×Dic6—61no—
159C2×C3×C8—61no—
160C2×C3×C8—61no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—22no—
164C3×C4⋊C4—31no—
165C3×C4⋊C4—31no—
166C3×C4⋊C4—41no—
167C3×C4⋊C4—62no—
168C3×C4⋊C4D1212yes—
169C3×C4⋊C4#6712yes—
170C3×C22⋊C4—62no—
171C3×C22⋊C4—61no—
172C3×C22⋊C4—61no—
173C3×C42—21no—
174C3×C42C22×D311yescharacteristic
175C3×C42C22×D311yescharacteristic
176(C2×D3)⋊C4—22no—
177(C2×D3)⋊C4—21no—
178(C2×D3)⋊C4—21no—
179C4⋊Dic3—61no—
180C4⋊Dic3—61no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3—121no—
184C4⋊Dic3—121no—
185C4⋊Dic3#6711yescharacteristic
186C4⋊Dic3#6711yescharacteristic
187Dic3⋊C4—22no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—62no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C22×C32#12011yescharacteristic
194C2×C3×D3—22no—
195C2×C3×D3—41no—
196C2×C3×D3—41no—
197C2×C3×D3—41no—
198C2×C3×D3—41no—
199C2×C3×D3—41no—
200C32×C4—21no—
201C32×C4—42no—
202C32×C4C2×SD1611yescharacteristic
203C32×C4#13511yescharacteristic
204C32×C4AGL(1,ℤ/8)11yescharacteristic
205C32×C4#13711yescharacteristic
206C3⋊Dic3—81no—
207C3×Dic3—41no—
208C3×Dic3—41no—
209C2×#41—61no—
210C4⋊Q8—91no—
211C4⋊Q8D3211yescharacteristic
212#123—62no—
213C22⋊Q8—61no—
214#121—61no—
215C4×D4—31no—
216C4×D4—31no—
217C2×C4⋊C4—61no—
218#106—181no—
219#106—181no—
220C4⋊C8—31no—
221C4⋊C8—31no—
222#103—182no—
223#102—181no—
224#102—181no—
225C4×C8—91no—
226C23×C3—61no—
227C23×C3—61no—
228C22×D3—21no—
229C22×D3—21no—
230C3×Q8—41no—
231C3×Q8—41no—
232C3×Q8—41no—
233C3×Q8—41no—
234C3×Q8—81no—
235C3×Q8—81no—
236C3×D4—32no—
237C3×D4—61no—
238C3×D4—61no—
239C3×D4—61no—
240C3×D4—124no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—42no—
247C2×C3×C4—61no—
248C2×C3×C4—61no—
249C2×C3×C4—124no—
250C2×C3×C4—121no—
251C2×C3×C4—121no—
252C2×C3×C4—121no—
253C2×C3×C4—121no—
254C2×C3×C4C2×D1211yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×C3×C4C2×#6711yescharacteristic
258C2×C3×C4C2×#6711yescharacteristic
259C2×C3×C4C2×#6711yescharacteristic
260C2×Dic3—21no—
261C2×Dic3—21no—
262C2×Dic3—122no—
263C2×Dic3—121no—
264C2×Dic3—121no—
265D12—21no—
266D12—21no—
267D12—21no—
268D12—44no—
269D12#21412yes—
270C4×D3—44no—
271C4×D3—41no—
272C4×D3—41no—
273C4×D3—41no—
274C4×D3—41no—
275Dic6—124no—
276Dic6—122no—
277Dic6—122no—
278C3×C8—121no—
279C3×C8—121no—
280C3⋊C8—41no—
281C3⋊C8—41no—
282C3⋊C8—122no—
283C3⋊C8—121no—
284C3⋊C8—121no—
285C2×C32#45011yescharacteristic
286C2×C32#45211yescharacteristic
287C2×C32#45411yescharacteristic
288C3×D3—42no—
289C3×D3—81no—
290#41—122no—
291#41—122no—
292C2×Q8—21no—
293C2×Q8—181no—
294C2×D4—31no—
295C2×D4—31no—
296C2×D4—62no—
297C22×C4—62no—
298C22×C4—61no—
299C22×C4—61no—
300C2×C8—61no—
301C2×C8—61no—
302C2×C8—181no—
303C4⋊C4—21no—
304C4⋊C4—31no—
305C4⋊C4—31no—
306C4⋊C4—62no—
307C4⋊C4—181no—
308C4⋊C4—181no—
309C4⋊C4#62612yes—
310C22⋊C4—62no—
311C22⋊C4—61no—
312C22⋊C4—61no—
313C42C2×D3211yescharacteristic
314C22×C3—21no—
315C22×C3—62no—
316C22×C3—121no—
317C22×C3—121no—
318C22×C3—121no—
319C22×C3—121no—
320C22×C3—121no—
321C22×C3#88211yescharacteristic
322C22×C3#95311yescharacteristic
323C2×D3—22no—
324C2×D3—41no—
325C2×D3—41no—
326C2×D3—41no—
327C2×D3—41no—
328C2×D3—41no—
329C3×C4—22no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—42no—
337C3×C4—42no—
338C3×C4—82no—
339C3×C4—121no—
340C3×C4—121no—
341C3×C4#91111yescharacteristic
342C3×C4D3×SD1611yescharacteristic
343C3×C4#91611yescharacteristic
344C3×C4#91811yescharacteristic
345C3×C4#93211yescharacteristic
346C3×C4C2×#21411yescharacteristic
347C3×C4#95011yescharacteristic
348C3×C4#95111yescharacteristic
349Dic3—41no—
350Dic3—41no—
351Dic3—242no—
352Dic3—241no—
353Dic3—241no—
354C32#163511yescharacteristic, complemented, Sylow
355C23—61no—
356C23—61no—
357Q8—41no—
358Q8—41no—
359Q8—362no—
360D4—32no—
361D4—61no—
362D4—61no—
363D4—61no—
364D4—124no—
365C2×C4—22no—
366C2×C4—61no—
367C2×C4—61no—
368C2×C4—124no—
369C2×C4—121no—
370C2×C4—121no—
371C2×C4—121no—
372C2×C4—121no—
373C2×C4—361no—
374C2×C4C2×#62611yescharacteristic
375C2×C4D3×#6711yescharacteristic
376C2×C4D3×#6711yescharacteristic
377C8—121no—
378C8—121no—
379C8—361no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—122no—
384C2×C3—241no—
385C2×C3#475311yescharacteristic
386C2×C3#477611yescharacteristic
387C2×C3#480811yescharacteristic
388C2×C3#521811yescharacteristic
389C2×C3#523911yescharacteristic
390C2×C3#524511yescharacteristic
391D3—42no—
392D3—81no—
393C22—62no—
394C22—121no—
395C22—121no—
396C22—121no—
397C22—121no—
398C22—121no—
399C22#6397711yescharacteristic
400C4—21no—
401C4—42no—
402C4—121no—
403C4—121no—
404C4—721no—
405C4D3×#21411yescharacteristic
406C4#6393211yescharacteristic
407C4#6394311yescharacteristic
408C4#6394711yescharacteristic
409C3—21no—
410C3#6843411yescharacteristic, complemented
411C3#7191111yescharacteristic, complemented
412C2—122no—
413C2—241no—
414C2#1059145911yescharacteristic
415C2#1059159911yescharacteristic
416C2#1059164611yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radicalC3×#5726C2
hypercenterC4⋊Q8D32
hypocenterC32#1635
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10592792C2semidirect
3. #10590268C2semidirect
4. #10590268C2semidirect
5. C3×#4547C2semidirect
6. #10589080C2semidirect
7. #10589080C2semidirect
37. #4547D3semidirect
354. C32#1635semidirect
410. C3#68434semidirect
411. C3#71911semidirect

Maximal subgroups

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

subgroupindex
C3×#57262
#105927922
#105902682
C3×#45472
#105890802
#719113
#684343