Finite Group Databasebeta

← #11779385

Subgroups — #11779385

Order 1152.

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

normal subgroups only

This group has 553 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#10593900C211yesmaximal, characteristic
2C3×#4693C211yesmaximal, characteristic, complemented
3#10590310C211yesmaximal, characteristic, complemented
4#10590300C211yesmaximal, characteristic, complemented
5#10589325C211yesmaximal, characteristic, complemented
6C3×#4456C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#71271—31nomaximal
9#68261—31nomaximal
10C2×#3796—21no—
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C3×#204—22no—
13C3×#874C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C3×C4×Dic6C2211yescharacteristic
16#63916—21no—
17#63911—21no—
18Dic3×D12—21no—
19#63886—22no—
20C32×C4×C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23#63576—21no—
24#63573—21no—
25#63565—21no—
26#63564—21no—
27#5718—31no—
28#5577—31no—
29C3×#492—31no—
30#5091—31no—
31#5084—31no—
32#5021—31no—
33#4842—31no—
34#4693D311yescharacteristic, complemented
35C3×Q8⋊C8—31no—
36#4544—31no—
37#4485—31no—
38#4459—31no—
39#4459—31no—
40#4459—61no—
41#4456D311yescharacteristic, complemented
42C2×C4⋊(C3⋊D3)D411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12D412yes—
47C2×C3×Dic6—21no—
48C2×C3×Dic6D411yescharacteristic
49C2×#626—22no—
50C2×#626—22no—
51C2×D3×Dic3—22no—
52#3796—42no—
53#3796—42no—
54C2×C32×C8—21no—
55C32×C42C2311yescharacteristic
56#3752—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58C2×C3⋊(C3⋊C8)—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—21no—
63C3×C4×Dic3—21no—
64C2×C3×C3⋊C8—21no—
65C3×#204—44no—
66(C2×D3)⋊Dic3—22no—
67#1631—91noSylow
68C2×#239—61no—
69C2×#237—61no—
70C2×C3×SD16—62no—
71C3×C4⋊Q8—31no—
72C3×#127—31no—
73C3×C4×Q8—31no—
74#940—61no—
75#939—62no—
76#938—61no—
77D4×Dic3—61no—
78C2×#204—22no—
79#895—61no—
80#895—62no—
81#874—61no—
82#874C2×D311yescharacteristic
83C4×D12—31no—
84C4×D12—31no—
85C4×D12—61no—
86C4×D12—61no—
87#869C2×D311yescharacteristic
88C4×Dic6C2×D311yescharacteristic
89C3×C4⋊C8—31no—
90C3×C4×C8—21no—
91C3×C4×C8C2×D311yescharacteristic
92C3×C4×C8C2×D311yescharacteristic
93#835—61no—
94#821—61no—
95#817—61no—
96#810—61no—
97#809—61no—
98#808—61no—
99#807—61no—
100#807—61no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—61no—
104C4⋊(C3⋊C8)C2×D311yescharacteristic
105C22×C3⋊D3—21no—
106C22×C3×D3—22no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C3⋊Dic3—21no—
111C4⋊(C3⋊D3)—21no—
112C4⋊(C3⋊D3)—21no—
113C4×C3⋊D3—41no—
114C4×C3⋊D3—41no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—21no—
117C2×C3×Dic3—41no—
118C3×D12—42no—
119C3×D12—41no—
120C3×D12—41no—
121C3×D12—41no—
122C3×D12—41no—
123C3×Dic6—21no—
124C3×Dic6—42no—
125C3×Dic6SD1612yescomplemented
126#626—44no—
127#626—82no—
128D3×Dic3—44no—
129C32×C8—22no—
130C3⋊(C3⋊C8)—41no—
131C3×C3⋊C8—41no—
132#550—91no—
133#492—31no—
134#477—91no—
135#476—91no—
136#331—91no—
137Q8⋊C8—31no—
138D4⋊C8—91no—
139C2×C3×Q8—31no—
140C2×C3×Q8—61no—
141C2×C3×D4—32no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C2×#67—62no—
145C2×#67—62no—
146C22×Dic3—62no—
147#239—122no—
148#239—122no—
149#237—122no—
150#237—122no—
151C2×D12—21no—
152C2×D12—21no—
153C2×D12—31no—
154C2×D12—31no—
155C2×D12—61no—
156C2×D12—62no—
157C2×D12—62no—
158C2×D12#6712yes—
159C2×C4×D3—62no—
160C2×C4×D3—61no—
161C2×C4×D3—61no—
162C2×C4×D3—121no—
163C2×Dic6—21no—
164C2×Dic6D1211yescharacteristic
165C3×SD16—124no—
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—41no—
169C2×C3×C8—61no—
170C3×C4⋊C4—31no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4—61no—
174C3×C42—21no—
175C3×C42—61no—
176C3×C42C22×D311yescharacteristic
177C3×C42C22×D311yescharacteristic
178#217—62no—
179(C2×D3)⋊C4—62no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—121no—
183C4⋊Dic3—21no—
184C4⋊Dic3—21no—
185C4⋊Dic3—31no—
186C4⋊Dic3—31no—
187C4⋊Dic3—61no—
188C4⋊Dic3D1211yescharacteristic
189Dic3⋊C4—21no—
190C4×Dic3—21no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—121no—
195#204—44no—
196C22×C32#12011yescharacteristic
197C2×C3⋊D3—41no—
198C2×C3⋊D3—41no—
199C2×C3⋊D3—41no—
200C2×C3×D3—42no—
201C2×C3×D3—42no—
202C2×C3×D3—42no—
203C32×C4—21no—
204C32×C4C2×SD1611yescharacteristic
205C32×C4#13511yescharacteristic
206C32×C4AGL(1,ℤ/8)11yescharacteristic
207C32×C4#13711yescharacteristic
208C3⋊Dic3—41no—
209C3×Dic3—22no—
210C3×Dic3—41no—
211C3×Dic3—81no—
212C2×#41—181no—
213C2×SD16—62no—
214C4⋊Q8—31no—
215#127—31no—
216#127—181no—
217#121—181no—
218#121—182no—
219C4×Q8—31no—
220C4×D4—91no—
221C4×D4—181no—
222#107—181no—
223#106—181no—
224C4⋊C8—31no—
225C4⋊C8—91no—
226#103—181no—
227#102—181no—
228C4×C8D3211yescharacteristic
229C23×C3—62no—
230C22×D3—22no—
231C22×D3—61no—
232C22×D3—61no—
233C22×D3—121no—
234C3×Q8—32no—
235C3×Q8—61no—
236C3×Q8—122no—
237C3×D4—122no—
238C3×D4—121no—
239C3×D4—121no—
240C3×D4—121no—
241C3×D4—121no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—61no—
246C2×C3×C4—61no—
247C2×C3×C4—121no—
248C2×C3×C4C2×D1211yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4C2×#6711yescharacteristic
254#67—124no—
255#67—242no—
256C2×Dic3—21no—
257C2×Dic3—21no—
258C2×Dic3—41no—
259C2×Dic3—61no—
260C2×Dic3—61no—
261C2×Dic3—121no—
262C2×Dic3—124no—
263D12—42no—
264D12—41no—
265D12—41no—
266D12—41no—
267D12—41no—
268D12—62no—
269D12—61no—
270D12—61no—
271D12—61no—
272D12—61no—
273D12—121no—
274D12—124no—
275D12—242no—
276C4×D3—124no—
277C4×D3—121no—
278C4×D3—121no—
279C4×D3—121no—
280C4×D3—121no—
281C4×D3—241no—
282C4×D3—241no—
283Dic6—21no—
284Dic6—42no—
285Dic6#20412yescomplemented
286C3×C8—22no—
287C3×C8—22no—
288C3×C8—42no—
289C3×C8—121no—
290C3⋊C8—41no—
291C3⋊C8—121no—
292C3⋊C8—121no—
293C3⋊C8—241no—
294C2×C32#45011yescharacteristic
295C2×C32#45211yescharacteristic
296C2×C32#45311yescharacteristic
297C3⋊D3—81no—
298C3×D3—82no—
299#41—362no—
300#41—362no—
301C2×Q8—31no—
302C2×Q8—61no—
303C2×D4—32no—
304C2×D4—61no—
305C2×D4—61no—
306C2×D4—91no—
307C2×D4—182no—
308C2×D4—182no—
309C22×C4—182no—
310C22×C4—181no—
311SD16—124no—
312C2×C8—21no—
313C2×C8—61no—
314C2×C8—181no—
315C4⋊C4—31no—
316C4⋊C4—61no—
317C4⋊C4—61no—
318C4⋊C4—61no—
319C4⋊C4—91no—
320C22⋊C4—182no—
321C22⋊C4—181no—
322C42—61no—
323C42C2×D3211yescharacteristic
324C22×C3—21no—
325C22×C3—122no—
326C22×C3—122no—
327C22×C3—122no—
328C22×C3#88211yescharacteristic
329C22×C3#93711yescharacteristic
330C2×D3—42no—
331C2×D3—42no—
332C2×D3—42no—
333C2×D3—122no—
334C2×D3—121no—
335C2×D3—121no—
336C2×D3—121no—
337C2×D3—121no—
338C2×D3—121no—
339C2×D3—121no—
340C2×D3—241no—
341C2×D3—241no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—41no—
349C3×C4—62no—
350C3×C4—121no—
351C3×C4—241no—
352C3×C4C2×#20411yescharacteristic
353C3×C4#90811yescharacteristic
354C3×C4D3×SD1611yescharacteristic
355C3×C4#91411yescharacteristic
356C3×C4#91511yescharacteristic
357C3×C4#91611yescharacteristic
358C3×C4#91611yescharacteristic
359C3×C4#91811yescharacteristic
360Dic3—22no—
361Dic3—41no—
362Dic3—81no—
363Dic3—121no—
364Dic3—121no—
365Dic3—241no—
366C32#163111yescharacteristic, complemented, Sylow
367C23—62no—
368C23—181no—
369Q8—32no—
370Q8—61no—
371Q8—122no—
372D4—122no—
373D4—121no—
374D4—121no—
375D4—121no—
376D4—121no—
377D4—181no—
378D4—181no—
379D4—364no—
380D4—722no—
381C2×C4—61no—
382C2×C4—61no—
383C2×C4—121no—
384C2×C4—181no—
385C2×C4—364no—
386C2×C4—361no—
387C2×C4—361no—
388C2×C4D3×D1211yescharacteristic
389C2×C4#380211yescharacteristic
390C2×C4D3×#6711yescharacteristic
391C8—22no—
392C8—121no—
393C8—361no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—242no—
398C2×C3#473111yescharacteristic
399C2×C3#480811yescharacteristic
400C2×C3#482211yescharacteristic
401C2×C3#507711yescharacteristic
402C2×C3#516911yescharacteristic
403C2×C3#517311yescharacteristic
404D3—82no—
405D3—242no—
406D3—241no—
407D3—241no—
408C22—122no—
409C22—122no—
410C22—122no—
411C22—361no—
412C22—361no—
413C22—361no—
414C22#6392211yescharacteristic
415C4—21no—
416C4—62no—
417C4—121no—
418C4—241no—
419C4—361no—
420C4D3×#20411yescharacteristic
421C4#6379411yescharacteristic
422C4#6380911yescharacteristic
423C4#6381111yescharacteristic
424C3—21no—
425C3#6826111yescharacteristic, complemented
426C3#7127111yescharacteristic, complemented
427C2—242no—
428C2—721no—
429C2#1059039511yescharacteristic
430C2#1059094211yescharacteristic
431C2#1059096111yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#120
prime radical#10593900C2
hypercenterC4×C8D32
hypocenterC32#1631
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×#4693C2semidirect
3. #10590310C2semidirect
4. #10590300C2semidirect
5. #10589325C2semidirect
6. C3×#4456C2semidirect
7. #10589090C2semidirect
34. #4693D3semidirect
41. #4456D3semidirect
125. C3×Dic6SD16semidirect
285. Dic6#204semidirect
366. C32#1631semidirect
425. C3#68261semidirect
426. C3#71271semidirect

Maximal subgroups

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

subgroupindex
#105939002
C3×#46932
#105903102
#105903002
#105893252
C3×#44562
#105890902
#712713
#682613