Finite Group Databasebeta

← #11780755

Subgroups — #11780755

Order 1152.

466 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 72 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#10596170C211yesmaximal, characteristic
2C3×#5069C211yesmaximal, characteristic, complemented
3#10590305C211yesmaximal, characteristic, complemented
4#10590294C211yesmaximal, characteristic
5C3×#4543C211yesmaximal, characteristic, complemented
6#10589089C211yesmaximal, characteristic, complemented
7#10589087C211yesmaximal, characteristic
8#71253—31nomaximal
9#68379—31nomaximal
10C32×#125C2211yescharacteristic
11#64107—21no—
12#64107—21no—
13#64106—21no—
14#64105—21no—
15#64103—21no—
16#64097—21no—
17#64084C2211yescharacteristic
18#64079C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×#810—21no—
21C3×#810—21no—
22C3×#803C2211yescharacteristic
23C3×#803C2211yescharacteristic
24C3×#803C2211yescharacteristic
25#63575—21no—
26#63573—21no—
27#63567—21no—
28#63564—21no—
29#5699—31no—
30#5699—31no—
31#5699—61no—
32C3×#491—31no—
33#5089—31no—
34#5081—31no—
35#5069D311yescharacteristic, complemented
36#4714—31no—
37#4702—31no—
38C3×#330—31no—
39#4543D311yescharacteristic, complemented
40#4465—31no—
41#4465—31no—
42#4464—31no—
43#4464—31no—
44C2×C4⋊(C3⋊D3)D411yescharacteristic
45C2×C4×C3⋊D3—21no—
46C2×#634—21no—
47C2×#634D411yescharacteristic
48C2×C3×Dic6—21no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4—21no—
51C32×C4⋊C4D411yescharacteristic
52C32×C4⋊C4D411yescharacteristic
53C32×C42C2311yescharacteristic
54#3752—21no—
55#3752—21no—
56#3752—21no—
57#3752—21no—
58#3752—21no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)D411yescharacteristic
61C4⋊(C3⋊Dic3)D411yescharacteristic
62#3750—21no—
63#3750—21no—
64#3750—21no—
65C4×C3⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#1664—91noSylow
72C3×C4⋊Q8—31no—
73C3×#125—21no—
74C3×#125C2×D311yescharacteristic
75C3×#125C2×D311yescharacteristic
76#898—61no—
77#898—61no—
78#898—62no—
79#898—62no—
80#898—61no—
81#898—61no—
82#897—61no—
83#897—61no—
84#897—62no—
85#896—62no—
86#896—61no—
87#896—61no—
88#894—61no—
89#894—61no—
90#894—62no—
91#888—61no—
92#888—61no—
93#888—62no—
94#875—31no—
95#875—31no—
96#875—61no—
97#870—31no—
98#870—31no—
99#870—61no—
100#869C2×D311yescharacteristic
101C3×#103—61no—
102C3×#103—61no—
103C3×#97—31no—
104C3×#97—31no—
105C3×#97—31no—
106#821—61no—
107#818—61no—
108#817—61no—
109#816—61no—
110#810—21no—
111#810—21no—
112#810—61no—
113#809—61no—
114#808—61no—
115#807—61no—
116#803C2×D311yescharacteristic
117#803C2×D311yescharacteristic
118#803C2×D311yescharacteristic
119C22×C3⋊D3—21no—
120C2×C32×C4—21no—
121C2×C32×C4—21no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—21no—
128C4⋊(C3⋊D3)—41no—
129C4×C3⋊D3—81no—
130#634—41no—
131#634—81no—
132C2×C3×Dic3—41no—
133C3×Dic6—42no—
134C3×C3⋊C8—22no—
135C3×C3⋊C8—41no—
136C3×C3⋊C8—41no—
137#563—91no—
138#501—91no—
139#491—31no—
140#489—91no—
141#330—31no—
142#330—91no—
143#329—91no—
144C2×C3×Q8—61no—
145C2×D12—31no—
146C2×D12—31no—
147C2×D12—61no—
148C2×C4×D3—62no—
149C2×C4×D3—61no—
150C2×C4×D3—61no—
151C2×Dic6—21no—
152C2×Dic6—31no—
153C2×Dic6—31no—
154C2×Dic6—61no—
155C2×Dic6—62no—
156C2×Dic6—61no—
157C2×Dic6—61no—
158C2×C3×C8—61no—
159C2×C3×C8—61no—
160C2×C3×C8—61no—
161C3×C4⋊C4—22no—
162C3×C4⋊C4—22no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4D1211yescharacteristic
172C3×C4⋊C4D1211yescharacteristic
173C3×C4⋊C4#6711yescharacteristic
174C3×C4⋊C4#6711yescharacteristic
175C3×C42—21no—
176C3×C42C22×D311yescharacteristic
177C3×C42C22×D311yescharacteristic
178(C2×D3)⋊C4—62no—
179(C2×D3)⋊C4—62no—
180(C2×D3)⋊C4—62no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—62no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4—61no—
186(C2×D3)⋊C4—62no—
187(C2×D3)⋊C4—61no—
188(C2×D3)⋊C4—61no—
189(C2×D3)⋊C4—61no—
190(C2×D3)⋊C4—61no—
191(C2×D3)⋊C4—61no—
192(C2×D3)⋊C4—61no—
193C4⋊Dic3—21no—
194C4⋊Dic3—21no—
195C4⋊Dic3—31no—
196C4⋊Dic3—31no—
197C4⋊Dic3—31no—
198C4⋊Dic3—31no—
199C4⋊Dic3—61no—
200C4⋊Dic3—61no—
201C4⋊Dic3—62no—
202C4⋊Dic3—61no—
203C4⋊Dic3—61no—
204Dic3⋊C4—62no—
205Dic3⋊C4—62no—
206Dic3⋊C4—62no—
207Dic3⋊C4—61no—
208Dic3⋊C4—61no—
209Dic3⋊C4—61no—
210Dic3⋊C4—61no—
211Dic3⋊C4—61no—
212Dic3⋊C4—61no—
213C4×Dic3—62no—
214C4×Dic3—61no—
215C4×Dic3—61no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C22×C32#12011yescharacteristic
220C2×C3⋊D3—41no—
221C2×C3⋊D3—41no—
222C2×C3⋊D3—41no—
223C32×C4—21no—
224C32×C4—21no—
225C32×C4—21no—
226C32×C4—41no—
227C32×C4—41no—
228C3⋊Dic3—41no—
229C3⋊Dic3—41no—
230C3⋊Dic3—41no—
231C3×Dic3—81no—
232C4⋊Q8—31no—
233C4⋊Q8—181no—
234#126—181no—
235#126—181no—
236#125—91no—
237#125D3211yescharacteristic
238#124—91no—
239#123—181no—
240C22⋊Q8—181no—
241C22⋊Q8—181no—
242#107—181no—
243#106—181no—
244#103—61no—
245#103—61no—
246#103—181no—
247#102—181no—
248#97—31no—
249#97—31no—
250#97—31no—
251C22×D3—62no—
252C22×D3—61no—
253C22×D3—61no—
254C3×Q8—122no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—121no—
265C2×C3×C4C2×D1211yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×Dic3—41no—
272C2×Dic3—62no—
273C2×Dic3—62no—
274C2×Dic3—62no—
275C2×Dic3—61no—
276C2×Dic3—61no—
277C2×Dic3—61no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281D12—121no—
282D12—121no—
283D12—241no—
284C4×D3—242no—
285C4×D3—241no—
286C4×D3—241no—
287Dic6—42no—
288Dic6—121no—
289Dic6—121no—
290Dic6—241no—
291Dic6—242no—
292Dic6—241no—
293Dic6—241no—
294C3×C8—62no—
295C3×C8—121no—
296C3×C8—121no—
297C3⋊C8—22no—
298C3⋊C8—41no—
299C3⋊C8—41no—
300C2×C32#45411yescharacteristic
301C2×C32#45511yescharacteristic
302C2×C32#45611yescharacteristic
303C3⋊D3—81no—
304C2×Q8—61no—
305C2×Q8—91no—
306C2×Q8—181no—
307C2×D4—91no—
308C22×C4—181no—
309C2×C8—61no—
310C2×C8—61no—
311C2×C8—61no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—61no—
315C4⋊C4—61no—
316C4⋊C4—91no—
317C4⋊C4—91no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4#62611yescharacteristic
323C4⋊C4#62611yescharacteristic
324C22⋊C4—181no—
325C22⋊C4—181no—
326C22⋊C4—181no—
327C22⋊C4—181no—
328C22⋊C4—181no—
329C42—181no—
330C42C2×D3211yescharacteristic
331C22×C3—21no—
332C22×C3#88211yescharacteristic
333C22×C3#93711yescharacteristic
334C2×D3—122no—
335C2×D3—122no—
336C2×D3—122no—
337C2×D3—121no—
338C2×D3—121no—
339C2×D3—121no—
340C2×D3—121no—
341C2×D3—121no—
342C2×D3—121no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—41no—
350C3×C4—41no—
351C3×C4—41no—
352C3×C4—42no—
353C3×C4—42no—
354C3×C4—41no—
355C3×C4—41no—
356C3×C4—41no—
357C3×C4—41no—
358C3×C4—241no—
359Dic3—81no—
360Dic3—122no—
361Dic3—122no—
362Dic3—122no—
363Dic3—121no—
364Dic3—121no—
365Dic3—121no—
366Dic3—121no—
367Dic3—121no—
368Dic3—121no—
369C32#166411yescharacteristic, complemented, Sylow
370C23—181no—
371Q8—122no—
372Q8—361no—
373Q8—721no—
374D4—361no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—121no—
378C2×C4—181no—
379C2×C4—181no—
380C2×C4—181no—
381C2×C4—721no—
382C2×C4C2×#62611yescharacteristic
383C2×C4#381111yescharacteristic
384C2×C4#381111yescharacteristic
385C8—62no—
386C8—121no—
387C8—121no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3#475311yescharacteristic
392C2×C3#482511yescharacteristic
393C2×C3#482611yescharacteristic
394C2×C3#506211yescharacteristic
395C2×C3#520211yescharacteristic
396C2×C3#520511yescharacteristic
397D3—242no—
398D3—241no—
399D3—241no—
400C22—361no—
401C22—361no—
402C22—361no—
403C22#6398111yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—241no—
410C4—361no—
411C4—361no—
412C4—361no—
413C3—21no—
414C3#6837911yescharacteristic, complemented
415C3#7125311yescharacteristic, complemented
416C2—721no—
417C2#1059164711yescharacteristic
418C2#1059166811yescharacteristic
419C2#1059169011yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#125C22
socleC22×C32#120
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenter#125D32
hypocenterC32#1664
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
2. C3×#5069C2semidirect
3. #10590305C2semidirect
5. C3×#4543C2semidirect
6. #10589089C2semidirect
35. #5069D3semidirect
39. #4543D3semidirect
369. C32#1664semidirect
414. C3#68379semidirect
415. C3#71253semidirect

Maximal subgroups

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

subgroupindex
#105961702
C3×#50692
#105903052
#105902942
C3×#45432
#105890892
#105890872
#712533
#683793