Finite Group Databasebeta

← #11780447

Subgroups — #11780447

Order 1152.

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

normal subgroups only

This group has 521 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×#4841C211yesmaximal, characteristic, complemented
3#10590313C211yesmaximal, characteristic, complemented
4#10590309C211yesmaximal, characteristic, complemented
5#10589349C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71051—31nomaximal
9#68439—31nomaximal
10C2×#3799—21no—
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C3×#204—21no—
13C3×C4×D12C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C3×#869C2211yescharacteristic
16#63916—21no—
17#63900—21no—
18#63856—21no—
19#63854—22no—
20C32×C4⋊C8C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#816—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24#63575—21no—
25#63574—22no—
26#63564—21no—
27#5726—31no—
28#5551—31no—
29C3×#461—31no—
30#5087—31no—
31#5080—31no—
32#5080—31no—
33#4846—31no—
34#4841D311yescharacteristic, 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—
64C3×#204—42no—
65#3724—22no—
66(C2×D3)⋊Dic3—22no—
67#1654—91noSylow
68C2×#239—61no—
69C2×#235—61no—
70C2×C3×SD16—61no—
71C3×C4⋊Q8—31no—
72C3×C4⋊Q8—31no—
73C3×C4×D4—31no—
74#946—61no—
75#938—61no—
76#924—61no—
77C2×#204—21no—
78#895—61no—
79#894—62no—
80D3×C4⋊C4—61no—
81D3×C4⋊C4—61no—
82#883—62no—
83C4×D12—31no—
84C4×D12—31no—
85C4×D12—61no—
86C4×D12C2×D311yescharacteristic
87#869C2×D311yescharacteristic
88#869C2×D311yescharacteristic
89C3×C4⋊C8—21no—
90C3×C4⋊C8—31no—
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4⋊C8C2×D311yescharacteristic
93C3×#103—61no—
94#821—61no—
95#818—61no—
96#816—21no—
97#809—61no—
98#808—62no—
99#808—62no—
100#807—61no—
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—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C3⋊Dic3—21no—
111C4⋊(C3⋊D3)—21no—
112C4⋊(C3⋊D3)SD1612yescomplemented
113C4×C3⋊D3—41no—
114C4×C3⋊D3—41no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—21no—
117C2×C3×Dic3—41no—
118C3×D12—21no—
119C3×D12—21no—
120C3×C4×D3—41no—
121C3×C4×D3—41no—
122C3×Dic6—41no—
123C3×Dic6—41no—
124C3×Dic6—41no—
125C3×Dic6—41no—
126#626—44no—
127#624—44no—
128C32×C8—41no—
129C3⋊(C3⋊C8)—22no—
130C3×C3⋊C8—41no—
131#547—91no—
132#498—91no—
133#474—91no—
134#461—31no—
135#332—31no—
136D4⋊C8—91no—
137D4⋊C8—91no—
138C2×C3×Q8—61no—
139C2×C3×Q8—61no—
140C2×C3×D4—31no—
141C22×C3×C4—61no—
142C2×#67—62no—
143#239—122no—
144#239—122no—
145#235—122no—
146#235—122no—
147C2×D12—31no—
148C2×D12—31no—
149C2×D12—61no—
150C2×D12—62no—
151C2×D12#6711yescharacteristic
152C2×C4×D3—21no—
153C2×C4×D3—62no—
154C2×C4×D3—62no—
155C2×C4×D3—61no—
156C2×C4×D3—61no—
157C2×C4×D3—121no—
158C2×Dic6—21no—
159C2×Dic6—21no—
160C3×SD16—122no—
161C2×C3×C8—21no—
162C2×C3×C8—21no—
163C2×C3×C8—41no—
164C2×C3×C8—61no—
165C3×C4⋊C4—32no—
166C3×C4⋊C4—31no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169C3×C4⋊C4—61no—
170C3×C22⋊C4—61no—
171C3×C42—21no—
172C3×C42C22×D311yescharacteristic
173C3×C42C22×D311yescharacteristic
174#217—62no—
175(C2×D3)⋊C4—21no—
176(C2×D3)⋊C4—62no—
177(C2×D3)⋊C4—61no—
178(C2×D3)⋊C4—61no—
179(C2×D3)⋊C4—121no—
180C4⋊Dic3—21no—
181C4⋊Dic3—21no—
182C4⋊Dic3—21no—
183C4⋊Dic3—31no—
184C4⋊Dic3—31no—
185C4⋊Dic3—61no—
186C4⋊Dic3D1212yes—
187C4⋊Dic3#6711yescharacteristic
188Dic3⋊C4—62no—
189Dic3⋊C4—62no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—121no—
194#204—42no—
195C22×C32#12011yescharacteristic
196C2×C3⋊D3—22no—
197C2×C3⋊D3—41no—
198C2×C3⋊D3—41no—
199C2×C3×D3—41no—
200C2×C3×D3—41no—
201C2×C3×D3—41no—
202C32×C4—21no—
203C32×C4C2×SD1611yescharacteristic
204C32×C4#13511yescharacteristic
205C32×C4AGL(1,ℤ/8)11yescharacteristic
206C32×C4AGL(1,ℤ/8)11yescharacteristic
207C3⋊Dic3—41no—
208C3×Dic3—41no—
209C3×Dic3—42no—
210C3×Dic3—81no—
211C2×#41—181no—
212C2×SD16—61no—
213C4⋊Q8—31no—
214C4⋊Q8—31no—
215#123—182no—
216C22⋊Q8—181no—
217#121—181no—
218C4×D4—31no—
219C4×D4—91no—
220C2×C4⋊C4—181no—
221#107—181no—
222#106—182no—
223C4⋊C8—31no—
224C4⋊C8D3211yescharacteristic
225#103—61no—
226#102—181no—
227C4×C8—91no—
228C23×C3—61no—
229C22×D3—21no—
230C22×D3—61no—
231C22×D3—61no—
232C22×D3—121no—
233C3×Q8—121no—
234C3×Q8—121no—
235C3×Q8—121no—
236C3×Q8—121no—
237C3×D4—61no—
238C3×D4—61no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—61no—
243C2×C3×C4—62no—
244C2×C3×C4—121no—
245C2×C3×C4—121no—
246C2×C3×C4—121no—
247C2×C3×C4C2×D1211yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4C2×#6711yescharacteristic
253#67—124no—
254C2×Dic3—22no—
255C2×Dic3—21no—
256C2×Dic3—41no—
257C2×Dic3—61no—
258C2×Dic3—61no—
259C2×Dic3—121no—
260D12—21no—
261D12—21no—
262D12—32no—
263D12—32no—
264D12—62no—
265D12—61no—
266D12—61no—
267D12—121no—
268D12—124no—
269C4×D3—41no—
270C4×D3—41no—
271C4×D3—124no—
272C4×D3—124no—
273C4×D3—121no—
274C4×D3—121no—
275C4×D3—121no—
276C4×D3—121no—
277C4×D3—241no—
278C4×D3—241no—
279Dic6—41no—
280Dic6—41no—
281Dic6—41no—
282Dic6—41no—
283C3×C8—41no—
284C3×C8—41no—
285C3×C8—81no—
286C3×C8—121no—
287C3⋊C8—41no—
288C3⋊C8—62no—
289C3⋊C8—62no—
290C3⋊C8—122no—
291C2×C32#44911yescharacteristic
292C2×C32#45011yescharacteristic
293C2×C32#45611yescharacteristic
294C3⋊D3—42no—
295C3×D3—81no—
296#41—362no—
297#41—362no—
298C2×Q8—61no—
299C2×Q8—61no—
300C2×D4—31no—
301C2×D4—91no—
302C2×D4—182no—
303C22×C4—61no—
304C22×C4—182no—
305C22×C4—181no—
306SD16—122no—
307C2×C8—21no—
308C2×C8—61no—
309C2×C8—181no—
310C4⋊C4—32no—
311C4⋊C4—31no—
312C4⋊C4—61no—
313C4⋊C4—61no—
314C4⋊C4—61no—
315C4⋊C4—91no—
316C4⋊C4—182no—
317C22⋊C4—61no—
318C22⋊C4—182no—
319C22⋊C4—181no—
320C42C2×D3211yescharacteristic
321C22×C3—21no—
322C22×C3—121no—
323C22×C3—121no—
324C22×C3—121no—
325C22×C3#88211yescharacteristic
326C22×C3#93711yescharacteristic
327C2×D3—41no—
328C2×D3—41no—
329C2×D3—41no—
330C2×D3—62no—
331C2×D3—62no—
332C2×D3—122no—
333C2×D3—121no—
334C2×D3—121no—
335C2×D3—121no—
336C2×D3—121no—
337C2×D3—241no—
338C2×D3—241no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—41no—
346C3×C4—122no—
347C3×C4—121no—
348C3×C4—241no—
349C3×C4#91111yescharacteristic
350C3×C4D3×SD1611yescharacteristic
351C3×C4D3×SD1611yescharacteristic
352C3×C4#91411yescharacteristic
353C3×C4#91411yescharacteristic
354C3×C4#91911yescharacteristic
355C3×C4#93211yescharacteristic
356C3×C4#95011yescharacteristic
357Dic3—41no—
358Dic3—42no—
359Dic3—81no—
360Dic3—121no—
361Dic3—121no—
362Dic3—241no—
363C32#165411yescharacteristic, complemented, Sylow
364C23—61no—
365C23—181no—
366Q8—121no—
367Q8—121no—
368Q8—121no—
369Q8—121no—
370D4—61no—
371D4—61no—
372D4—92no—
373D4—181no—
374D4—364no—
375C2×C4—61no—
376C2×C4—62no—
377C2×C4—121no—
378C2×C4—121no—
379C2×C4—121no—
380C2×C4—181no—
381C2×C4—364no—
382C2×C4—361no—
383C2×C4—361no—
384C2×C4D3×D1211yescharacteristic
385C2×C4#380211yescharacteristic
386C2×C4D3×#6711yescharacteristic
387C8—41no—
388C8—121no—
389C8—182no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—241no—
394C2×C3#475211yescharacteristic
395C2×C3#477611yescharacteristic
396C2×C3#481011yescharacteristic
397C2×C3#503711yescharacteristic
398C2×C3#516911yescharacteristic
399C2×C3#520511yescharacteristic
400D3—81no—
401D3—122no—
402D3—122no—
403D3—242no—
404C22—121no—
405C22—121no—
406C22—121no—
407C22—182no—
408C22—361no—
409C22—361no—
410C22#6392211yescharacteristic
411C4—21no—
412C4—121no—
413C4—122no—
414C4—241no—
415C4—361no—
416C4#6379611yescharacteristic
417C4#6379811yescharacteristic
418C4#6393411yescharacteristic
419C4#6394911yescharacteristic
420C3—21no—
421C3#6843911yescharacteristic, complemented
422C3#7105111yescharacteristic, complemented
423C2—241no—
424C2—362no—
425C2#1059061511yescharacteristic
426C2#1059094311yescharacteristic
427C2#1059101811yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10593869C2
hypercenterC4⋊C8D32
hypocenterC32#1654
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×#4841C2semidirect
3. #10590313C2semidirect
4. #10590309C2semidirect
5. #10589349C2semidirect
6. C3×#4486C2semidirect
7. #10589080C2semidirect
34. #4841D3semidirect
37. #4486D3semidirect
112. C4⋊(C3⋊D3)SD16semidirect
363. C32#1654semidirect
421. C3#68439semidirect
422. C3#71051semidirect

Maximal subgroups

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

subgroupindex
#105938692
C3×#48412
#105903132
#105903092
#105893492
C3×#44862
#105890802
#710513
#684393