Finite Group Databasebeta

← #11776135

Subgroups — #11776135

Order 1152.

571 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 571 conjugacy classes of subgroups — too many to draw. Only its 106 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#10593907C211yesmaximal, characteristic
2#10592532C211yesmaximal, characteristic, complemented
3#10590331C211yesmaximal, characteristic, complemented
4C3×#4486C211yesmaximal, characteristic, complemented
5C3×#4485C211yesmaximal, characteristic, complemented
6#10589093C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#68417—31nomaximal
9#68381—31nomaximal
10C2×#3796—21no—
11C42×C3⋊D3C2211yescharacteristic
12C3×#874C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63916—21no—
15#63916C412yes—
16#63898—21no—
17#63898C412yes—
18#63863—21no—
19C2×#3710—21no—
20C32×C4⋊C8C2211yescharacteristic
21#63647—21no—
22C8×C3⋊Dic3—21no—
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26#63572—21no—
27#5725—31no—
28#5716—31no—
29#4833—31no—
30#4833—31no—
31#4833—61no—
32D3×C4⋊C8—31no—
33D3×C4⋊C8—31no—
34C3×#332—31no—
35C3×#331—31no—
36#4547—31no—
37#4544—31no—
38#4486D311yescharacteristic, complemented
39#4485—31no—
40#4485D311yescharacteristic, complemented
41#4482—31no—
42C2×C4×C3⋊D3C2×C411yescharacteristic
43C2×C4×C3⋊D3D411yescharacteristic
44C2×C4×C3⋊D3D411yescharacteristic
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12C2×C412yes—
48C2×C3×Dic6—21no—
49C2×#626—22no—
50C2×D3×Dic3—22no—
51#3796—42no—
52#3796—42no—
53C2×C32×C8—21no—
54C32×C42C2311yescharacteristic
55C4×C3⋊Dic3C2×C411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57C4×C3⋊Dic3D411yescharacteristic
58C2×C3⋊(C3⋊C8)—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3C2×C412yes—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63(C2×D3)⋊Dic3—22no—
64(C2×D3)⋊Dic3—22no—
65#3710—42no—
66#1540—91noSylow
67C2×#239—61no—
68C2×#237—61no—
69C3×C4⋊Q8—31no—
70C3×#127—31no—
71#947—61no—
72#938—32no—
73#938—61no—
74#936—61no—
75D4×Dic3—32no—
76D4×Dic3—61no—
77C2×D3×C8—61no—
78C2×D3×C8—61no—
79#895—32no—
80#895—61no—
81#893—32no—
82#893—61no—
83#874C2×D311yescharacteristic
84C42×D3—31no—
85C42×D3—31no—
86C42×D3—61no—
87#869C2×D311yescharacteristic
88C3×C4⋊C8—21no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8—31no—
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4⋊C8C2×D311yescharacteristic
93(C2×D3)⋊C8—61no—
94(C2×D3)⋊C8—61no—
95(C2×D3)⋊C8—62no—
96Dic3⋊C8—61no—
97Dic3⋊C8—61no—
98C8×Dic3—61no—
99C8×Dic3—61no—
100C8×Dic3—62no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—61no—
104C4⋊(C3⋊C8)C2×D311yescharacteristic
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C22×C3⋊D3C22⋊C411yescharacteristic
107C22×C3×D3—22no—
108C2×C32×C4C22×C411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3⋊Dic3C22⋊C411yescharacteristic
112C2×C3⋊Dic3C22⋊C411yescharacteristic
113C2×C3⋊Dic3C22⋊C411yescharacteristic
114C4×C3⋊D3—21no—
115C4×C3⋊D3—21no—
116C4×C3⋊D3—41no—
117C4×C3⋊D3D812yes—
118C4×C3⋊D3SD1612yes—
119C2×C3×Dic3—22no—
120C3×D12—42no—
121C3×D12—41no—
122C3×D12—41no—
123C3×D12—41no—
124C3×D12—41no—
125C3×Dic6—41no—
126C3×Dic6—41no—
127#626—44no—
128D3×Dic3—44no—
129C32×C8—41no—
130C3⋊(C3⋊C8)—41no—
131C3×C3⋊C8—41no—
132C3×C3⋊C8—41no—
133#532—91no—
134#431—91no—
135C2×C4⋊C8—91no—
136#332—31no—
137#332—91no—
138#331—31no—
139#331—91no—
140C2×C3×Q8—61no—
141C2×C3×D4—32no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C2×#67—62no—
145C22×Dic3—62no—
146#239—122no—
147#239—122no—
148#237—122no—
149#237—122no—
150C2×D12—21no—
151C2×D12—21no—
152C2×D12—62no—
153C2×D12C4×D312yes—
154C2×C4×D3—31no—
155C2×C4×D3—31no—
156C2×C4×D3—31no—
157C2×C4×D3—31no—
158C2×C4×D3—31no—
159C2×C4×D3—31no—
160C2×C4×D3—61no—
161C2×C4×D3—61no—
162C2×C4×D3—61no—
163C2×C4×D3—62no—
164C2×Dic6—21no—
165C2×C3×C8—22no—
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—61no—
169C2×C3×C8—61no—
170C3×C4⋊C4—32no—
171C3×C4⋊C4—61no—
172C3×C42—21no—
173C3×C42C22×D311yescharacteristic
174C3×C42C22×D311yescharacteristic
175#217—62no—
176#217—62no—
177(C2×D3)⋊C4—62no—
178(C2×D3)⋊C4—62no—
179C4⋊Dic3—21no—
180C4⋊Dic3C4×D312yes—
181C4×Dic3—31no—
182C4×Dic3—31no—
183C4×Dic3—31no—
184C4×Dic3—31no—
185C4×Dic3—31no—
186C4×Dic3—31no—
187C4×Dic3—61no—
188C4×Dic3—61no—
189C4×Dic3—61no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—62no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—61no—
195D3×C8—122no—
196D3×C8—122no—
197C22×C32C2×C22⋊C411yescharacteristic
198C2×C3⋊D3—21no—
199C2×C3⋊D3—21no—
200C2×C3⋊D3#10212yes—
201C2×C3×D3—42no—
202C2×C3×D3—42no—
203C2×C3×D3—42no—
204C32×C4—21no—
205C32×C4C2×D811yescharacteristic
206C32×C4C2×SD1611yescharacteristic
207C32×C4#13511yescharacteristic
208C32×C4#13511yescharacteristic
209C3⋊Dic3—21no—
210C3⋊Dic3—21no—
211C3⋊Dic3#10212yes—
212C3×Dic3—42no—
213C2×#41—181no—
214C22×C8—181no—
215C4⋊Q8—31no—
216#127—31no—
217#124—181no—
218#121—92no—
219#121—181no—
220C4×D4—92no—
221C4×D4—181no—
222C2×C42—91no—
223C4⋊C8—31no—
224C4⋊C8—31no—
225C4⋊C8—91no—
226C4⋊C8—181no—
227C4⋊C8D3211yescharacteristic
228C22⋊C8—181no—
229C4×C8—181no—
230C23×C3—62no—
231C22×D3—22no—
232C22×D3—31no—
233C22×D3—31no—
234C22×D3—61no—
235C3×Q8—121no—
236C3×Q8—121no—
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—62no—
246C2×C3×C4C2×C4×D311yescharacteristic
247C2×C3×C4C2×C4×D311yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252#67—124no—
253C2×Dic3—22no—
254C2×Dic3—31no—
255C2×Dic3—31no—
256C2×Dic3—31no—
257C2×Dic3—31no—
258C2×Dic3—31no—
259C2×Dic3—31no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—124no—
264D12—42no—
265D12—41no—
266D12—41no—
267D12—41no—
268D12—41no—
269D12—124no—
270C4×D3—32no—
271C4×D3—32no—
272C4×D3—32no—
273C4×D3—32no—
274C4×D3—62no—
275C4×D3—62no—
276C4×D3—61no—
277C4×D3—61no—
278C4×D3—61no—
279C4×D3—61no—
280C4×D3—121no—
281C4×D3—121no—
282C4×D3—124no—
283C4×D3—121no—
284C4×D3—121no—
285C4×D3—122no—
286Dic6—41no—
287Dic6—41no—
288C3×C8—42no—
289C3×C8—41no—
290C3×C8—41no—
291C3×C8—121no—
292C3×C8—121no—
293C3⋊C8—41no—
294C3⋊C8—41no—
295C3⋊C8—122no—
296C3⋊C8—121no—
297C3⋊C8—121no—
298C2×C32#41311yescharacteristic
299C2×C32C2×#10211yescharacteristic
300C2×C32#41611yescharacteristic
301C3⋊D3—22no—
302C3×D3—82no—
303#41—362no—
304#41—362no—
305C2×Q8—61no—
306C2×D4—32no—
307C2×D4—61no—
308C2×D4—61no—
309C2×D4—182no—
310C22×C4—91no—
311C22×C4—91no—
312C22×C4—91no—
313C22×C4—182no—
314C2×C8—21no—
315C2×C8—61no—
316C2×C8—61no—
317C2×C8—181no—
318C2×C8—362no—
319C4⋊C4—32no—
320C4⋊C4—61no—
321C22⋊C4—182no—
322C22⋊C4—182no—
323C42—91no—
324C42—91no—
325C42—91no—
326C42C2×D3211yescharacteristic
327C22×C3—21no—
328C22×C3—122no—
329C22×C3—122no—
330C22×C3—122no—
331C22×C3D3×C22⋊C411yescharacteristic
332C22×C3D3×C22⋊C411yescharacteristic
333C2×D3—32no—
334C2×D3—32no—
335C2×D3—42no—
336C2×D3—42no—
337C2×D3—42no—
338C2×D3—62no—
339C2×D3—61no—
340C2×D3—61no—
341C2×D3—61no—
342C2×D3—61no—
343C2×D3—121no—
344C2×D3—121no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—41no—
352C3×C4—122no—
353C3×C4D3×D811yescharacteristic
354C3×C4D3×D811yescharacteristic
355C3×C4#91211yescharacteristic
356C3×C4D3×SD1611yescharacteristic
357C3×C4D3×SD1611yescharacteristic
358C3×C4#91611yescharacteristic
359C3×C4#91611yescharacteristic
360C3×C4#91911yescharacteristic
361Dic3—32no—
362Dic3—32no—
363Dic3—42no—
364Dic3—62no—
365Dic3—62no—
366Dic3—61no—
367Dic3—61no—
368Dic3—61no—
369Dic3—61no—
370Dic3—121no—
371C32#154011yescharacteristic, complemented, Sylow
372C23—62no—
373C23—91no—
374Q8—121no—
375Q8—121no—
376D4—122no—
377D4—121no—
378D4—121no—
379D4—121no—
380D4—121no—
381D4—364no—
382C2×C4—62no—
383C2×C4—91no—
384C2×C4—92no—
385C2×C4—92no—
386C2×C4—91no—
387C2×C4—91no—
388C2×C4—181no—
389C2×C4—181no—
390C2×C4—361no—
391C2×C4—364no—
392C2×C4C4×D3211yescharacteristic
393C2×C4#380211yescharacteristic
394C2×C4#381111yescharacteristic
395C8—41no—
396C8—121no—
397C8—121no—
398C8—361no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—242no—
403C2×C3#474511yescharacteristic
404C2×C3#475111yescharacteristic
405C2×C3D3×#10211yescharacteristic
406C2×C3D3×#10211yescharacteristic
407C2×C3#477211yescharacteristic
408C2×C3#480411yescharacteristic
409D3—62no—
410D3—62no—
411D3—82no—
412D3—122no—
413C22—92no—
414C22—122no—
415C22—122no—
416C22—122no—
417C22—181no—
418C22—181no—
419C22#6392111yescharacteristic
420C4—21no—
421C4—92no—
422C4—122no—
423C4—181no—
424C4—181no—
425C4#6379611yescharacteristic
426C4#6379711yescharacteristic
427C4#6393611yescharacteristic
428C4#6395011yescharacteristic
429C3—21no—
430C3#6838111yescharacteristic, complemented
431C3#6841711yescharacteristic, complemented
432C2—182no—
433C2—242no—
434C2#1059061111yescharacteristic
435C2#1059094011yescharacteristic
436C2#1059101011yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#10593907C2
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1540
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592532C2semidirect
3. #10590331C2semidirect
4. C3×#4486C2semidirect
5. C3×#4485C2semidirect
6. #10589093C2semidirect
7. #10589090C2semidirect
38. #4486D3semidirect
40. #4485D3semidirect
371. C32#1540semidirect
430. C3#68381semidirect
431. C3#68417semidirect

Maximal subgroups

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

subgroupindex
#105939072
#105925322
#105903312
C3×#44862
C3×#44852
#105890932
#105890902
#684173
#683813