Finite Group Databasebeta

← #11779531

Subgroups — #11779531

Order 1152.

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

normal subgroups only

This group has 517 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
2#10592778C211yesmaximal, characteristic, complemented
3C3×#5084C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5#10589094C211yesmaximal, characteristic, complemented
6#10589080C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71146—31nomaximal
9#71140—31nomaximal
10C2×#3795—21no—
11C32×C4⋊Q8C2211yescharacteristic
12#64078C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×C4×D12C2211yescharacteristic
15#63908—21no—
16#63891—22no—
17D3×C4⋊Dic3—21no—
18#63857—21no—
19#63662—22no—
20C4×C3⋊(C3⋊C8)C2211yescharacteristic
21C3×#809—21no—
22C3×#809—21no—
23C3×#808—21no—
24C3×#808—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27#5555—31no—
28#5551—31no—
29C3×#476—31no—
30C3×#476—31no—
31#5084D311yescharacteristic, complemented
32#5084D311yescharacteristic, complemented
33#5079—31no—
34#5079—31no—
35#5079—61no—
36D4⋊(C3⋊C8)—31no—
37D4⋊(C3⋊C8)—31no—
38#4486—31no—
39#4483—31no—
40#4483—31no—
41#4482—31no—
42C2×C32×Q8—21no—
43C2×#634—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×D12D411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3—21no—
48C2×#625—22no—
49C2×D3×Dic3—22no—
50#3795—42no—
51#3795—42no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C32×C42C2311yescharacteristic
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)D412yes—
57C2×C3⋊(C3⋊C8)—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×C4⋊Dic3D411yescharacteristic
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64Dic3⋊Dic3—22no—
65(C2×D3)⋊Dic3—22no—
66#1635—91noSylow
67C2×#237—61no—
68C2×#235—61no—
69C3×C4⋊Q8—21no—
70C3×C4⋊Q8C2×D311yescharacteristic
71C3×C4⋊Q8C2×D311yescharacteristic
72C3×C4×D4—31no—
73C3×C4×D4—31no—
74#938—61no—
75#930—61no—
76C2×C4⋊Dic3—61no—
77#924—61no—
78#897—61no—
79D3×C4⋊C4—61no—
80#886—62no—
81#883—62no—
82C4×D12C2×D311yescharacteristic
83C4×D12C2×D311yescharacteristic
84#869—31no—
85#869—31no—
86#869—61no—
87C3×#106—61no—
88C3×#106—61no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8—31no—
91C3×#102—61no—
92C3×#102—61no—
93#835—62no—
94#835—62no—
95#835—64no—
96#809—21no—
97#809—21no—
98#808—21no—
99#808—21no—
100C4⋊(C3⋊C8)C2×D311yescharacteristic
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—
107C32×Q8—42no—
108C2×C32×C4—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×D12SD1612yes—
121C3×C4×D3—41no—
122C3×C4×D3—41no—
123C3×C4×D3—41no—
124C3×C4×D3—41no—
125#625—44no—
126D3×Dic3—44no—
127C3⋊(C3⋊C8)—41no—
128C3×C3⋊C8—41no—
129C3×C3⋊C8—41no—
130#547—91no—
131#487—91no—
132#476—31no—
133#476—31no—
134#332—91no—
135D4⋊C8—91no—
136D4⋊C8—91no—
137C2×C3×Q8—22no—
138C2×C3×Q8—21no—
139C2×C3×Q8—21no—
140C2×C3×D4—31no—
141C2×C3×D4—31no—
142C22×C3×C4—61no—
143C22×C3×C4—61no—
144C2×#67—62no—
145C2×#67—62no—
146C22×Dic3—62no—
147#237—122no—
148#237—122no—
149#235—122no—
150#235—122no—
151C2×D12#6711yescharacteristic
152C2×D12#6711yescharacteristic
153C2×C4×D3—21no—
154C2×C4×D3—21no—
155C2×C4×D3—62no—
156C2×Dic6—61no—
157C2×Dic6—61no—
158C2×Dic6—121no—
159C2×C3×C8—61no—
160C2×C3×C8—61no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—31no—
166C3×C4⋊C4—31no—
167C3×C4⋊C4—41no—
168C3×C4⋊C4—41no—
169C3×C22⋊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—21no—
177(C2×D3)⋊C4—62no—
178C4⋊Dic3—32no—
179C4⋊Dic3—32no—
180C4⋊Dic3—62no—
181C4⋊Dic3—62no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—121no—
185C4⋊Dic3#6711yescharacteristic
186C4⋊Dic3#6711yescharacteristic
187Dic3⋊C4—62no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—62no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C22×C32#12011yescharacteristic
194C2×C3×D3—22no—
195C2×C3×D3—41no—
196C2×C3×D3—41no—
197C2×C3×D3—41no—
198C2×C3×D3—41no—
199C2×C3×D3—41no—
200C32×C4—21no—
201C32×C4—81no—
202C32×C4C2×SD1611yescharacteristic
203C32×C4#13511yescharacteristic
204C32×C4AGL(1,ℤ/8)11yescharacteristic
205C32×C4#13711yescharacteristic
206C3⋊Dic3—42no—
207C3×Dic3—41no—
208C3×Dic3—41no—
209C2×#41—181no—
210C4⋊Q8—91no—
211C4⋊Q8D3211yescharacteristic
212#123—182no—
213C22⋊Q8—181no—
214#121—181no—
215C4×D4—31no—
216C4×D4—31no—
217C2×C4⋊C4—181no—
218#106—61no—
219#106—61no—
220C4⋊C8—31no—
221C4⋊C8—31no—
222#103—182no—
223#102—61no—
224#102—61no—
225C4×C8—91no—
226C23×C3—61no—
227C23×C3—61no—
228C22×D3—21no—
229C22×D3—21no—
230C3×Q8—44no—
231C3×Q8—42no—
232C3×Q8—42no—
233C3×D4—32no—
234C3×D4—61no—
235C3×D4—61no—
236C3×D4—61no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—42no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4—61no—
244C2×C3×C4—61no—
245C2×C3×C4—121no—
246C2×C3×C4—121no—
247C2×C3×C4—121no—
248C2×C3×C4—121no—
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4C2×#6711yescharacteristic
254C2×C3×C4C2×#6711yescharacteristic
255#67—124no—
256#67—124no—
257C2×Dic3—21no—
258C2×Dic3—21no—
259C2×Dic3—62no—
260C2×Dic3—62no—
261C2×Dic3—122no—
262C2×Dic3—124no—
263D12—21no—
264D12—21no—
265D12—21no—
266D12#21512yes—
267C4×D3—41no—
268C4×D3—41no—
269C4×D3—41no—
270C4×D3—41no—
271C4×D3—124no—
272Dic6—121no—
273Dic6—121no—
274Dic6—121no—
275Dic6—121no—
276Dic6—241no—
277Dic6—241no—
278C3×C8—121no—
279C3×C8—121no—
280C3⋊C8—41no—
281C3⋊C8—41no—
282C3⋊C8—122no—
283C3⋊C8—121no—
284C3⋊C8—121no—
285C2×C32#45011yescharacteristic
286C2×C32#45211yescharacteristic
287C2×C32#45411yescharacteristic
288C3×D3—42no—
289C3×D3—81no—
290#41—362no—
291#41—362no—
292C2×Q8—21no—
293C2×Q8—181no—
294C2×D4—31no—
295C2×D4—31no—
296C2×D4—182no—
297C22×C4—61no—
298C22×C4—61no—
299C22×C4—182no—
300C2×C8—61no—
301C2×C8—61no—
302C2×C8—181no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—31no—
306C4⋊C4—31no—
307C4⋊C4—92no—
308C4⋊C4—182no—
309C4⋊C4—181no—
310C22⋊C4—61no—
311C22⋊C4—61no—
312C22⋊C4—182no—
313C42C2×D3211yescharacteristic
314C22×C3—21no—
315C22×C3—62no—
316C22×C3—121no—
317C22×C3—121no—
318C22×C3—121no—
319C22×C3—121no—
320C22×C3—121no—
321C22×C3#93711yescharacteristic
322C22×C3#93711yescharacteristic
323C2×D3—22no—
324C2×D3—41no—
325C2×D3—41no—
326C2×D3—41no—
327C2×D3—41no—
328C2×D3—41no—
329C3×C4—22no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—82no—
337C3×C4—81no—
338C3×C4—81no—
339C3×C4—121no—
340C3×C4—121no—
341C3×C4D3×SD1611yescharacteristic
342C3×C4#91411yescharacteristic
343C3×C4#91511yescharacteristic
344C3×C4#91611yescharacteristic
345C3×C4C2×#21511yescharacteristic
346C3×C4#94211yescharacteristic
347C3×C4#94911yescharacteristic
348C3×C4#95011yescharacteristic
349Dic3—41no—
350Dic3—41no—
351Dic3—122no—
352Dic3—122no—
353Dic3—242no—
354C32#163511yescharacteristic, complemented, Sylow
355C23—61no—
356C23—61no—
357Q8—42no—
358Q8—361no—
359Q8—361no—
360D4—32no—
361D4—61no—
362D4—61no—
363D4—61no—
364D4—364no—
365C2×C4—41no—
366C2×C4—61no—
367C2×C4—61no—
368C2×C4—121no—
369C2×C4—121no—
370C2×C4—121no—
371C2×C4—121no—
372C2×C4—182no—
373C2×C4—364no—
374C2×C4D3×#6711yescharacteristic
375C2×C4D3×#6711yescharacteristic
376C2×C4#381111yescharacteristic
377C8—121no—
378C8—121no—
379C8—361no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—122no—
384C2×C3—241no—
385C2×C3#504611yescharacteristic
386C2×C3#504711yescharacteristic
387C2×C3#516911yescharacteristic
388C2×C3#517311yescharacteristic
389C2×C3#520111yescharacteristic
390C2×C3#520111yescharacteristic
391D3—42no—
392D3—81no—
393C22—62no—
394C22—121no—
395C22—121no—
396C22—121no—
397C22—121no—
398C22—121no—
399C22#6398311yescharacteristic
400C4—21no—
401C4—81no—
402C4—121no—
403C4—121no—
404C4—362no—
405C4D3×#21511yescharacteristic
406C4#6393911yescharacteristic
407C4#6394611yescharacteristic
408C4#6394711yescharacteristic
409C3—21no—
410C3#7114011yescharacteristic, complemented
411C3#7114611yescharacteristic, complemented
412C2—122no—
413C2—241no—
414C2#1059152411yescharacteristic
415C2#1059165111yescharacteristic
416C2#1059165511yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radical#10593895C2
hypercenterC4⋊Q8D32
hypocenterC32#1635
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10592778C2semidirect
3. C3×#5084C2semidirect
4. C3×#5084C2semidirect
5. #10589094C2semidirect
6. #10589080C2semidirect
7. #10589080C2semidirect
31. #5084D3semidirect
32. #5084D3semidirect
354. C32#1635semidirect
410. C3#71140semidirect
411. C3#71146semidirect

Maximal subgroups

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

subgroupindex
#105938952
#105927782
C3×#50842
#105890942
#105890802
#711463
#711403