Finite Group Databasebeta

← #11780446

Subgroups — #11780446

Order 1152.

540 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 90 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#10593896C211yesmaximal, characteristic
2#10592540C211yesmaximal, characteristic, complemented
3#10590303C211yesmaximal, characteristic, complemented
4#10590272C211yesmaximal, characteristic, complemented
5C3×#4486C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#68439—31nomaximal
9#68185—31nomaximal
10C2×#3796—21no—
11C2×#3744—21no—
12C4×C4⋊(C3⋊D3)C2211yescharacteristic
13#64078C2211yescharacteristic
14C3×C4×D12C2211yescharacteristic
15C3×#869C2211yescharacteristic
16#63909—21no—
17#63890—22no—
18D3×C4⋊Dic3—21no—
19#63871—21no—
20C32×C4⋊C8C2211yescharacteristic
21#63643—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63575—21no—
25#63573—22no—
26#63563—21no—
27#5726—31no—
28#5555—31no—
29#5080—31no—
30#5007—31no—
31#4846—31no—
32#4841—31no—
33#4841—31no—
34#4841—61no—
35#4680—31no—
36C3×#332—31no—
37C3×D4⋊C8—31no—
38#4486D311yescharacteristic, complemented
39#4483—31no—
40#4483D311yescharacteristic, complemented
41#4459—31no—
42C2×C4⋊(C3⋊D3)D411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×#634—21no—
45C2×C3×D12D411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×Dic6—21no—
48C2×#626—22no—
49C2×D3×Dic3—22no—
50#3796—42no—
51#3796—42no—
52C2×C32×C8—21no—
53C32×C42C2311yescharacteristic
54#3752—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58#3744—42no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D412yes—
62C3×C4⋊Dic3D411yescharacteristic
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65Dic3⋊Dic3—22no—
66#3722—22no—
67#1654—91noSylow
68C2×#239—61no—
69C2×#237—61no—
70C3×C4⋊Q8—31no—
71C3×C4×D4—31no—
72#946—61no—
73#930—61no—
74C2×C4⋊Dic3—61no—
75C2×#204—61no—
76C2×#204—61no—
77C2×#204—62no—
78#897—61no—
79#895—61no—
80#894—62no—
81D3×C4⋊C4—61no—
82#886—62no—
83C4×D12—31no—
84C4×D12—31no—
85C4×D12—61no—
86C4×D12C2×D311yescharacteristic
87#869—31no—
88#869—31no—
89#869—61no—
90#869C2×D311yescharacteristic
91C3×C4⋊C8—21no—
92C3×C4⋊C8—31no—
93C3×C4⋊C8C2×D311yescharacteristic
94C3×C4⋊C8C2×D311yescharacteristic
95C3×C4×C8—31no—
96#832—61no—
97#821—61no—
98#818—61no—
99#817—62no—
100#816—61no—
101#816—61no—
102#816—62no—
103#808—62no—
104#807—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4×C3⋊C8C2×D311yescharacteristic
107C22×C3⋊D3—21no—
108C22×C3×D3—21no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3—41no—
114C4⋊(C3⋊D3)—21no—
115C4⋊(C3⋊D3)—21no—
116C4×C3⋊D3—41no—
117C4×C3⋊D3—41no—
118#634—41no—
119#634—41no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—22no—
122C3×D12—21no—
123C3×D12SD1612yescomplemented
124C3×C4×D3—41no—
125C3×C4×D3—41no—
126C3×Dic6—41no—
127C3×Dic6—41no—
128#626—44no—
129D3×Dic3—44no—
130C32×C8—41no—
131C3×C3⋊C8—22no—
132C3×C3⋊C8—41no—
133#547—91no—
134#498—91no—
135#474—91no—
136#461—91no—
137#332—31no—
138D4⋊C8—31no—
139D4⋊C8—91no—
140C2×C3×Q8—61no—
141C2×C3×D4—31no—
142C22×C3×C4—61no—
143C2×#67—62no—
144C22×Dic3—62no—
145#239—122no—
146#239—122no—
147#237—122no—
148#237—122no—
149C2×D12—31no—
150C2×D12—31no—
151C2×D12—61no—
152C2×D12—62no—
153C2×D12D1211yescharacteristic
154C2×C4×D3—21no—
155C2×C4×D3—62no—
156C2×C4×D3—61no—
157C2×C4×D3—61no—
158C2×C4×D3—121no—
159C2×Dic6—21no—
160C2×Dic6—62no—
161C2×Dic6—61no—
162C2×Dic6—61no—
163C2×C3×C8—22no—
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—32no—
170C3×C4⋊C4—61no—
171C3×C22⋊C4—61no—
172C3×C42—21no—
173C3×C42C22×D311yescharacteristic
174C3×C42C22×D311yescharacteristic
175(C2×D3)⋊C4—21no—
176(C2×D3)⋊C4—62no—
177(C2×D3)⋊C4—62no—
178(C2×D3)⋊C4—61no—
179(C2×D3)⋊C4—61no—
180(C2×D3)⋊C4—121no—
181C4⋊Dic3—21no—
182C4⋊Dic3—31no—
183C4⋊Dic3—31no—
184C4⋊Dic3—61no—
185C4⋊Dic3—62no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—121no—
191C4⋊Dic3—121no—
192C4⋊Dic3D1212yes—
193C4⋊Dic3D1211yescharacteristic
194Dic3⋊C4—62no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197#204—124no—
198#204—122no—
199#204—122no—
200C22×C32#12011yescharacteristic
201C2×C3⋊D3—41no—
202C2×C3⋊D3—41no—
203C2×C3⋊D3—41no—
204C2×C3×D3—22no—
205C2×C3×D3—41no—
206C2×C3×D3—41no—
207C32×C4—21no—
208C32×C4C2×SD1611yescharacteristic
209C32×C4#13511yescharacteristic
210C32×C4AGL(1,ℤ/8)11yescharacteristic
211C32×C4AGL(1,ℤ/8)11yescharacteristic
212C3⋊Dic3—41no—
213C3⋊Dic3—81no—
214C3×Dic3—41no—
215C3×Dic3—42no—
216C2×#41—181no—
217C2×SD16—181no—
218C4⋊Q8—31no—
219C4⋊Q8—91no—
220#123—182no—
221C22⋊Q8—181no—
222#121—181no—
223C4×D4—31no—
224C4×D4—91no—
225C2×C4⋊C4—181no—
226#107—181no—
227#106—182no—
228C4⋊C8—31no—
229C4⋊C8D3211yescharacteristic
230#103—181no—
231#102—181no—
232C4×C8—31no—
233C23×C3—61no—
234C22×D3—21no—
235C22×D3—61no—
236C22×D3—61no—
237C22×D3—121no—
238C3×Q8—121no—
239C3×Q8—121no—
240C3×D4—32no—
241C3×D4—61no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—62no—
246C2×C3×C4—61no—
247C2×C3×C4—121no—
248C2×C3×C4—121no—
249C2×C3×C4C2×D1211yescharacteristic
250C2×C3×C4C2×D1211yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255#67—124no—
256C2×Dic3—21no—
257C2×Dic3—22no—
258C2×Dic3—61no—
259C2×Dic3—61no—
260C2×Dic3—121no—
261C2×Dic3—124no—
262C2×Dic3—122no—
263C2×Dic3—121no—
264C2×Dic3—121no—
265D12—21no—
266D12—62no—
267D12—61no—
268D12—61no—
269D12—61no—
270D12—61no—
271D12—121no—
272D12—124no—
273D12#20412yescomplemented
274C4×D3—41no—
275C4×D3—41no—
276C4×D3—124no—
277C4×D3—121no—
278C4×D3—121no—
279C4×D3—121no—
280C4×D3—121no—
281C4×D3—241no—
282C4×D3—241no—
283Dic6—41no—
284Dic6—41no—
285Dic6—122no—
286Dic6—122no—
287Dic6—121no—
288Dic6—121no—
289Dic6—121no—
290Dic6—121no—
291C3×C8—42no—
292C3×C8—41no—
293C3×C8—41no—
294C3×C8—62no—
295C3×C8—121no—
296C3⋊C8—22no—
297C3⋊C8—41no—
298C2×C32#44911yescharacteristic
299C2×C32#45011yescharacteristic
300C2×C32#45611yescharacteristic
301C3⋊D3—81no—
302C3×D3—42no—
303#41—362no—
304#41—362no—
305C2×Q8—61no—
306C2×Q8—181no—
307C2×D4—31no—
308C2×D4—91no—
309C2×D4—182no—
310C22×C4—61no—
311C22×C4—182no—
312C22×C4—181no—
313SD16—362no—
314C2×C8—21no—
315C2×C8—61no—
316C2×C8—61no—
317C4⋊C4—32no—
318C4⋊C4—31no—
319C4⋊C4—61no—
320C4⋊C4—91no—
321C4⋊C4—182no—
322C4⋊C4—181no—
323C4⋊C4—181no—
324C22⋊C4—61no—
325C22⋊C4—182no—
326C22⋊C4—181no—
327C42C2×D3211yescharacteristic
328C22×C3—21no—
329C22×C3—62no—
330C22×C3—121no—
331C22×C3—121no—
332C22×C3#88211yescharacteristic
333C22×C3#88211yescharacteristic
334C2×D3—22no—
335C2×D3—41no—
336C2×D3—41no—
337C2×D3—122no—
338C2×D3—121no—
339C2×D3—121no—
340C2×D3—121no—
341C2×D3—121no—
342C2×D3—121no—
343C2×D3—121no—
344C2×D3—241no—
345C2×D3—241no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—41no—
353C3×C4—122no—
354C3×C4—121no—
355C3×C4C2×#20411yescharacteristic
356C3×C4#90811yescharacteristic
357C3×C4#91111yescharacteristic
358C3×C4#91111yescharacteristic
359C3×C4D3×SD1611yescharacteristic
360C3×C4#91411yescharacteristic
361C3×C4#91611yescharacteristic
362C3×C4#91911yescharacteristic
363Dic3—42no—
364Dic3—41no—
365Dic3—121no—
366Dic3—121no—
367Dic3—241no—
368Dic3—242no—
369Dic3—241no—
370Dic3—241no—
371C32#165411yescharacteristic, complemented, Sylow
372C23—61no—
373C23—181no—
374Q8—121no—
375Q8—121no—
376Q8—361no—
377Q8—361no—
378D4—32no—
379D4—61no—
380D4—181no—
381D4—181no—
382D4—364no—
383C2×C4—61no—
384C2×C4—62no—
385C2×C4—121no—
386C2×C4—121no—
387C2×C4—181no—
388C2×C4—364no—
389C2×C4—361no—
390C2×C4—361no—
391C2×C4—361no—
392C2×C4D3×D1211yescharacteristic
393C2×C4D3×D1211yescharacteristic
394C2×C4#381111yescharacteristic
395C8—41no—
396C8—62no—
397C8—121no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—122no—
402C2×C3#473111yescharacteristic
403C2×C3#475211yescharacteristic
404C2×C3#477611yescharacteristic
405C2×C3#478111yescharacteristic
406C2×C3#481011yescharacteristic
407C2×C3#482611yescharacteristic
408D3—42no—
409D3—242no—
410D3—241no—
411D3—241no—
412C22—62no—
413C22—121no—
414C22—121no—
415C22—361no—
416C22—361no—
417C22—361no—
418C22#6392311yescharacteristic
419C4—21no—
420C4—121no—
421C4—122no—
422C4—361no—
423C4—721no—
424C4D3×#20411yescharacteristic
425C4#6379511yescharacteristic
426C4#6393711yescharacteristic
427C4#6395011yescharacteristic
428C3—21no—
429C3#6818511yescharacteristic, complemented
430C3#6843911yescharacteristic, complemented
431C2—122no—
432C2—721no—
433C2#1059061711yescharacteristic
434C2#1059094611yescharacteristic
435C2#1059102111yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10593896C2
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. #10592540C2semidirect
3. #10590303C2semidirect
4. #10590272C2semidirect
5. C3×#4486C2semidirect
6. C3×#4483C2semidirect
7. #10589082C2semidirect
38. #4486D3semidirect
40. #4483D3semidirect
123. C3×D12SD16semidirect
273. D12#204semidirect
371. C32#1654semidirect
429. C3#68185semidirect
430. C3#68439semidirect

Maximal subgroups

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

subgroupindex
#105938962
#105925402
#105903032
#105902722
C3×#44862
C3×#44832
#105890822
#684393
#681853