Finite Group Databasebeta

← #11779139

Subgroups — #11779139

Order 1152.

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

normal subgroups only

This group has 544 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#10593895C211yesmaximal, characteristic, complemented
2C3×#4843C211yesmaximal, characteristic, complemented
3#10590347C211yesmaximal, characteristic, complemented
4#10590273C211yesmaximal, characteristic, complemented
5#10589352C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71012—31nomaximal
9#68200—31nomaximal
10C2×#3795—21no—
11#64078C2211yescharacteristic
12C2×C3×D24—21no—
13C3×#874C2211yescharacteristic
14C3×C4×D12C2211yescharacteristic
15C3×C4×D12C2211yescharacteristic
16#63908—21no—
17#63891—22no—
18D3×C4⋊Dic3—21no—
19#63857—21no—
20C2×#3713—21no—
21C32×C4⋊C8C2211yescharacteristic
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×#821—21no—
24C3×C4×C3⋊C8C2211yescharacteristic
25#63563—22no—
26#63562—21no—
27#5555—31no—
28#5551—31no—
29C3×#459—31no—
30#5072—31no—
31#5070—31no—
32#5015—31no—
33#4843D311yescharacteristic, complemented
34#4694—31no—
35C3×D4⋊C8—31no—
36D4⋊(C3⋊C8)—31no—
37#4486—31no—
38#4486—31no—
39#4486—61no—
40#4483D311yescharacteristic, complemented
41#4459—31no—
42C2×#634—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12D411yescharacteristic
47C2×C3×D12D411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3—21no—
50C2×#625—22no—
51C2×D3×Dic3—22no—
52#3795—42no—
53#3795—42no—
54C2×C32×C8—21no—
55C32×C42C2311yescharacteristic
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)D412yes—
58C2×C3⋊(C3⋊C8)—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×C4⋊Dic3D411yescharacteristic
63C2×C3×C3⋊C8—21no—
64C3×D24—42no—
65Dic3⋊Dic3—22no—
66(C2×D3)⋊Dic3—22no—
67#3713—42no—
68#1625—91noSylow
69C2×#237—61no—
70C2×#235—61no—
71C2×C3×D8—61no—
72C3×#127—31no—
73C3×C4×D4—31no—
74C3×C4×D4—31no—
75#938—61no—
76C2×#213—61no—
77C2×#213—61no—
78#930—61no—
79C2×C4⋊Dic3—61no—
80#924—61no—
81C2×D24—21no—
82#897—61no—
83D3×C4⋊C4—61no—
84#886—62no—
85#883—62no—
86#874C2×D311yescharacteristic
87C4×D12C2×D311yescharacteristic
88C4×D12C2×D311yescharacteristic
89#869—31no—
90#869—31no—
91#869—61no—
92C3×C4⋊C8—21no—
93C3×C4⋊C8C2×D311yescharacteristic
94C3×C4⋊C8C2×D311yescharacteristic
95C3×#102—61no—
96C3×C4×C8—31no—
97#832—62no—
98#832—61no—
99#821—21no—
100#821—62no—
101#809—61no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—31no—
104C4⋊(C3⋊C8)—61no—
105C4×C3⋊C8C2×D311yescharacteristic
106C22×C3×D3—21no—
107C22×C3×D3—21no—
108C22×C3×D3—41no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3—22no—
113#634—41no—
114#634—41no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—21no—
117C3×D12—21no—
118C3×D12—21no—
119C3×D12—21no—
120C3×D12—42no—
121C3×D12—41no—
122C3×D12—41no—
123C3×D12—41no—
124C3×D12—41no—
125C3×D12D812yescomplemented
126C3×C4×D3—41no—
127C3×C4×D3—41no—
128C3×C4×D3—41no—
129C3×C4×D3—41no—
130#625—44no—
131D3×Dic3—44no—
132C32×C8—41no—
133C3⋊(C3⋊C8)—41no—
134C3×C3⋊C8—41no—
135#547—91no—
136#486—91no—
137#459—31no—
138#459—91no—
139#332—91no—
140D4⋊C8—31no—
141D4⋊C8—91no—
142C2×C3×D4—31no—
143C2×C3×D4—31no—
144C2×C3×D4—61no—
145C2×C3×D4—61no—
146C2×C3×D4—61no—
147C22×C3×C4—61no—
148C22×C3×C4—61no—
149C2×#67—62no—
150C2×#67—62no—
151C22×Dic3—62no—
152#237—122no—
153#237—122no—
154#235—122no—
155#235—122no—
156C2×D12—21no—
157C2×D12—21no—
158C2×D12—21no—
159C2×D12D1211yescharacteristic
160C2×D12#6711yescharacteristic
161C2×C4×D3—21no—
162C2×C4×D3—21no—
163C2×C4×D3—62no—
164C2×Dic6—61no—
165C2×Dic6—61no—
166C2×Dic6—121no—
167C3×D8—122no—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C2×C3×C8—41no—
171C2×C3×C8—61no—
172C3×C4⋊C4—31no—
173C3×C4⋊C4—31no—
174C3×C22⋊C4—61no—
175C3×C22⋊C4—61no—
176C3×C42—21no—
177C3×C42C22×D311yescharacteristic
178C3×C42C22×D311yescharacteristic
179#217—62no—
180#213—122no—
181#213—122no—
182(C2×D3)⋊C4—21no—
183(C2×D3)⋊C4—21no—
184(C2×D3)⋊C4—62no—
185C4⋊Dic3—32no—
186C4⋊Dic3—32no—
187C4⋊Dic3—62no—
188C4⋊Dic3—62no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—121no—
192C4⋊Dic3D1211yescharacteristic
193C4⋊Dic3#6711yescharacteristic
194Dic3⋊C4—62no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—121no—
199D24—42no—
200C22×C32#12011yescharacteristic
201C2×C3×D3—22no—
202C2×C3×D3—41no—
203C2×C3×D3—41no—
204C2×C3×D3—41no—
205C2×C3×D3—41no—
206C2×C3×D3—41no—
207C2×C3×D3—81no—
208C2×C3×D3—81no—
209C2×C3×D3—81no—
210C32×C4—21no—
211C32×C4C2×D811yescharacteristic
212C32×C4#13511yescharacteristic
213C32×C4AGL(1,ℤ/8)11yescharacteristic
214C32×C4AGL(1,ℤ/8)11yescharacteristic
215C3⋊Dic3—42no—
216C3×Dic3—41no—
217C3×Dic3—41no—
218C2×#41—181no—
219C2×D8—61no—
220C2×D8—181no—
221C4⋊Q8—91no—
222#127—31no—
223#123—182no—
224C22⋊Q8—181no—
225#121—181no—
226C4×D4—31no—
227C4×D4—31no—
228C2×C4⋊C4—181no—
229C4⋊C8—91no—
230C4⋊C8D3211yescharacteristic
231#102—61no—
232#102—181no—
233#102—182no—
234C4×C8—31no—
235C23×C3—61no—
236C23×C3—61no—
237C23×C3—121no—
238C22×D3—21no—
239C22×D3—21no—
240C22×D3—41no—
241C3×D4—32no—
242C3×D4—61no—
243C3×D4—61no—
244C3×D4—61no—
245C3×D4—122no—
246C3×D4—121no—
247C3×D4—121no—
248C3×D4—121no—
249C3×D4—121no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—61no—
254C2×C3×C4—61no—
255C2×C3×C4—121no—
256C2×C3×C4—121no—
257C2×C3×C4—121no—
258C2×C3×C4—121no—
259C2×C3×C4C2×D1211yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4C2×#6711yescharacteristic
265#67—124no—
266#67—124no—
267C2×Dic3—21no—
268C2×Dic3—21no—
269C2×Dic3—62no—
270C2×Dic3—62no—
271C2×Dic3—122no—
272C2×Dic3—124no—
273D12—21no—
274D12—21no—
275D12—21no—
276D12—42no—
277D12—41no—
278D12—41no—
279D12—41no—
280D12—41no—
281D12D2412yescomplemented
282C4×D3—41no—
283C4×D3—41no—
284C4×D3—41no—
285C4×D3—41no—
286C4×D3—124no—
287Dic6—121no—
288Dic6—121no—
289Dic6—121no—
290Dic6—121no—
291Dic6—241no—
292Dic6—241no—
293C3×C8—41no—
294C3×C8—41no—
295C3×C8—81no—
296C3×C8—121no—
297C3⋊C8—41no—
298C3⋊C8—121no—
299C3⋊C8—121no—
300C3⋊C8—241no—
301C2×C32#44711yescharacteristic
302C2×C32#44911yescharacteristic
303C2×C32#45411yescharacteristic
304C3×D3—42no—
305C3×D3—81no—
306C3×D3—161no—
307#41—362no—
308#41—362no—
309C2×Q8—181no—
310C2×D4—31no—
311C2×D4—31no—
312C2×D4—61no—
313C2×D4—61no—
314C2×D4—61no—
315C2×D4—182no—
316C22×C4—61no—
317C22×C4—61no—
318C22×C4—182no—
319D8—122no—
320D8—362no—
321C2×C8—21no—
322C2×C8—61no—
323C2×C8—181no—
324C4⋊C4—31no—
325C4⋊C4—31no—
326C4⋊C4—92no—
327C4⋊C4—182no—
328C4⋊C4—181no—
329C22⋊C4—61no—
330C22⋊C4—61no—
331C22⋊C4—182no—
332C42C2×D3211yescharacteristic
333C22×C3—21no—
334C22×C3—62no—
335C22×C3—121no—
336C22×C3—121no—
337C22×C3—121no—
338C22×C3—121no—
339C22×C3—121no—
340C22×C3—241no—
341C22×C3—241no—
342C22×C3—241no—
343C22×C3#88211yescharacteristic
344C22×C3#93711yescharacteristic
345C2×D3—22no—
346C2×D3—41no—
347C2×D3—41no—
348C2×D3—41no—
349C2×D3—41no—
350C2×D3—41no—
351C2×D3—81no—
352C2×D3—81no—
353C2×D3—81no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—41no—
361C3×C4—121no—
362C3×C4—121no—
363C3×C4C2×D2411yescharacteristic
364C3×C4#90811yescharacteristic
365C3×C4D3×D811yescharacteristic
366C3×C4#91111yescharacteristic
367C3×C4#91111yescharacteristic
368C3×C4#91611yescharacteristic
369C3×C4#93211yescharacteristic
370C3×C4#95011yescharacteristic
371Dic3—41no—
372Dic3—41no—
373Dic3—122no—
374Dic3—122no—
375Dic3—242no—
376C32#162511yescharacteristic, complemented, Sylow
377C23—61no—
378C23—61no—
379C23—121no—
380Q8—361no—
381Q8—361no—
382D4—32no—
383D4—61no—
384D4—61no—
385D4—61no—
386D4—122no—
387D4—121no—
388D4—121no—
389D4—121no—
390D4—121no—
391D4—364no—
392C2×C4—61no—
393C2×C4—61no—
394C2×C4—121no—
395C2×C4—121no—
396C2×C4—121no—
397C2×C4—121no—
398C2×C4—182no—
399C2×C4—364no—
400C2×C4D3×D1211yescharacteristic
401C2×C4#380211yescharacteristic
402C2×C4D3×#6711yescharacteristic
403C8—41no—
404C8—121no—
405C8—361no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—122no—
410C2×C3—241no—
411C2×C3—481no—
412C2×C3#473211yescharacteristic
413C2×C3#478111yescharacteristic
414C2×C3#482711yescharacteristic
415C2×C3#503711yescharacteristic
416C2×C3#515611yescharacteristic
417C2×C3#520111yescharacteristic
418D3—42no—
419D3—81no—
420D3—161no—
421C22—62no—
422C22—121no—
423C22—121no—
424C22—121no—
425C22—121no—
426C22—121no—
427C22—241no—
428C22—241no—
429C22—241no—
430C22#6392211yescharacteristic
431C4—21no—
432C4—121no—
433C4—121no—
434C4—362no—
435C4D3×D2411yescharacteristic
436C4#6379511yescharacteristic
437C4#6393211yescharacteristic
438C4#6394711yescharacteristic
439C3—21no—
440C3#6820011yescharacteristic, complemented
441C3#7101211yescharacteristic, complemented
442C2—122no—
443C2—241no—
444C2—481no—
445C2#1059061311yescharacteristic
446C2#1059094411yescharacteristic
447C2#1059101911yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
hypercenterC4⋊C8D32
hypocenterC32#1625
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
1. #10593895C2semidirect
2. C3×#4843C2semidirect
3. #10590347C2semidirect
4. #10590273C2semidirect
5. #10589352C2semidirect
6. C3×#4483C2semidirect
7. #10589081C2semidirect
33. #4843D3semidirect
40. #4483D3semidirect
125. C3×D12D8semidirect
281. D12D24semidirect
376. C32#1625semidirect
440. C3#68200semidirect
441. C3#71012semidirect

Maximal subgroups

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

subgroupindex
#105938952
C3×#48432
#105903472
#105902732
#105893522
C3×#44832
#105890812
#710123
#682003