Finite Group Databasebeta

← #11781714

Subgroups — #11781714

Order 1152.

466 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 92 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#10592714C211yesmaximal, characteristic, complemented
2C3×#5015C211yesmaximal, characteristic, complemented
3C3×#5012C211yesmaximal, characteristic, complemented
4#10590350C211yesmaximal, characteristic, complemented
5#10589097C211yesmaximal, characteristic, complemented
6#10589091C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#71009—31nomaximal
9#70868—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C2×#3753—21no—
12#64083C2211yescharacteristic
13C2×C3×#213—21no—
14C2×C3×#208—21no—
15C3×#874C2211yescharacteristic
16C2×#3714—21no—
17C2×#3714—21no—
18#63636—21no—
19C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
20C3×#830—21no—
21C3×#809—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#459—31no—
26C3×#436—31no—
27#5073—31no—
28#5015—31no—
29#5015—31no—
30#5015—61no—
31#5015D311yescharacteristic, complemented
32#5012D311yescharacteristic, complemented
33#4695—31no—
34#4544—31no—
35#4485—31no—
36#4485—31no—
37#4485—31no—
38#4480—31no—
39#4457—31no—
40C2×C32×D4D411yescharacteristic
41C22×C32×C4—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C32×C4⋊C4D411yescharacteristic
49C32×C22⋊C4—21no—
50C32×C42C2311yescharacteristic
51#3753—42no—
52C2×C3⋊(C3⋊C8)—21no—
53C3×#213—42no—
54C3×#208—42no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8D411yescharacteristic
58C2×C3×C3⋊C8D411yescharacteristic
59#3714—42no—
60#3714—42no—
61#1687—91noSylow
62C2×C3×D8—61no—
63C2×C3×M16—61no—
64C3×#127—31no—
65C3×C4×D4—21no—
66C3×C4×D4C2×D311yescharacteristic
67C3×C4×D4C2×D311yescharacteristic
68C2×#213—21no—
69C2×#213—62no—
70C2×#213—61no—
71C2×#213—61no—
72C2×#213—61no—
73C2×#213—61no—
74C2×#208—21no—
75C2×D24—61no—
76C2×D24—61no—
77#874—31no—
78#874—31no—
79#874—61no—
80#874C2×D311yescharacteristic
81C3×C4⋊C8—31no—
82C3×C4⋊C8—31no—
83C3×#102—61no—
84C3×C22⋊C8—61no—
85C3×C4×C8—31no—
86#830—21no—
87#809—21no—
88#809—62no—
89#809—61no—
90#809—61no—
91C4⋊(C3⋊C8)—31no—
92C4⋊(C3⋊C8)—31no—
93C4⋊(C3⋊C8)—61no—
94C4⋊(C3⋊C8)C2×D311yescharacteristic
95C4⋊(C3⋊C8)C2×D311yescharacteristic
96C4×C3⋊C8C2×D311yescharacteristic
97C23×C32—21no—
98C22×C3⋊D3—41no—
99C22×C3×D3—41no—
100C32×D4—21no—
101C32×D4—21no—
102C2×C32×C4—21no—
103C2×C32×C4—41no—
104C2×C32×C4—41no—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C4⋊(C3⋊D3)—41no—
109C4⋊(C3⋊D3)—41no—
110C4⋊(C3⋊D3)—41no—
111C4⋊(C3⋊D3)—41no—
112C4⋊(C3⋊D3)—81no—
113C3×D12—41no—
114C3×D12—41no—
115C3×D12—41no—
116C3×D12—41no—
117C3×D12—81no—
118C3⋊(C3⋊C8)—41no—
119C3×C3⋊C8—21no—
120C3×C3⋊C8—41no—
121C3×C3⋊C8—41no—
122C3×C3⋊C8D812yescomplemented
123#493—91no—
124#459—31no—
125#459—91no—
126#436—31no—
127#334—91no—
128#331—91no—
129#331—91no—
130C2×C3×D4—21no—
131C2×C3×D4—61no—
132C2×C3×D4—61no—
133C2×C3×D4—61no—
134C2×C3×D4D1211yescharacteristic
135C2×C3×D4#6711yescharacteristic
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—41no—
139C2×D12—21no—
140C2×D12—21no—
141C2×D12—21no—
142C2×D12—62no—
143C2×D12—61no—
144C2×D12—61no—
145C2×D12—61no—
146C2×D12—61no—
147C2×D12—61no—
148C2×D12—61no—
149C2×D12—121no—
150C2×D12—121no—
151C3×D8—122no—
152C3×M16—122no—
153C2×C3×C8—31no—
154C2×C3×C8—31no—
155C2×C3×C8—61no—
156C2×C3×C8—61no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4D1211yescharacteristic
159C3×C4⋊C4#6711yescharacteristic
160C3×C22⋊C4—21no—
161C3×C22⋊C4—21no—
162C3×C22⋊C4—41no—
163C3×C42—21no—
164C3×C42C22×D311yescharacteristic
165C3×C42C22×D311yescharacteristic
166#213—42no—
167#213—122no—
168#213—124no—
169#213—122no—
170#213—122no—
171#213—122no—
172#208—42no—
173C2×C3⋊C8—21no—
174C2×C3⋊C8—21no—
175C2×C3⋊C8—62no—
176C2×C3⋊C8—61no—
177C2×C3⋊C8—61no—
178C2×C3⋊C8#6711yescharacteristic
179C2×C3⋊C8#6711yescharacteristic
180D24—122no—
181D24—122no—
182C22×C32—41no—
183C22×C32—41no—
184C22×C32—41no—
185C22×C32#12111yescharacteristic
186C2×C3⋊D3—81no—
187C2×C3⋊D3—81no—
188C2×C3⋊D3—81no—
189C2×C3×D3—81no—
190C2×C3×D3—81no—
191C2×C3×D3—81no—
192C32×C4—21no—
193C32×C4—41no—
194C32×C4C2×D811yescharacteristic
195C32×C4AGL(1,ℤ/8)11yescharacteristic
196C32×C4AGL(1,ℤ/8)11yescharacteristic
197C32×C4AGL(1,ℤ/8)11yescharacteristic
198C2×D8—61no—
199C2×D8—181no—
200C2×D8—181no—
201C2×D8—181no—
202C2×M16—61no—
203#127—31no—
204#127—91no—
205C4×D4D3211yescharacteristic
206C4⋊C8—31no—
207C4⋊C8—31no—
208C4⋊C8—91no—
209#102—61no—
210#102—181no—
211C22⋊C8—61no—
212C4×C8—31no—
213C23×C3—21no—
214C23×C3—21no—
215C23×C3—41no—
216C23×C3—121no—
217C22×D3—41no—
218C22×D3—122no—
219C22×D3—121no—
220C22×D3—121no—
221C3×D4—22no—
222C3×D4—21no—
223C3×D4—21no—
224C3×D4—21no—
225C3×D4—21no—
226C3×D4—41no—
227C3×D4—121no—
228C3×D4—121no—
229C3×D4—121no—
230C3×D4—121no—
231C3×D4—241no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4—81no—
243C2×C3×C4—81no—
244C2×C3×C4C2×D1211yescharacteristic
245C2×C3×C4#23511yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4#23711yescharacteristic
248C2×C3×C4C2×#6711yescharacteristic
249C2×C3×C4C2×#6711yescharacteristic
250D12—41no—
251D12—41no—
252D12—41no—
253D12—41no—
254D12—81no—
255D12—122no—
256D12—122no—
257D12—121no—
258D12—121no—
259D12—121no—
260D12—121no—
261D12—121no—
262D12—121no—
263D12—121no—
264D12—121no—
265D12—241no—
266D12—241no—
267D12—241no—
268D12—241no—
269D12—242no—
270C3×C8—32no—
271C3×C8—61no—
272C3×C8—121no—
273C3×C8—121no—
274C3⋊C8—21no—
275C3⋊C8—41no—
276C3⋊C8—41no—
277C3⋊C8—122no—
278C3⋊C8—121no—
279C3⋊C8—121no—
280C3⋊C8#21312yescomplemented
281C2×C32—81no—
282C2×C32#45911yescharacteristic
283C2×C32#46911yescharacteristic
284C2×C32#47211yescharacteristic
285C3⋊D3—161no—
286C3×D3—161no—
287C2×D4—61no—
288C2×D4—61no—
289C2×D4—61no—
290C2×D4—181no—
291C2×D4—181no—
292C2×D4—181no—
293C2×D4#62611yescharacteristic
294C22×C4—21no—
295D8—122no—
296D8—362no—
297D8—362no—
298D8—362no—
299M16—122no—
300C2×C8—31no—
301C2×C8—31no—
302C2×C8—61no—
303C2×C8—61no—
304C2×C8—181no—
305C4⋊C4#62611yescharacteristic
306C22⋊C4—21no—
307C42C2×D3211yescharacteristic
308C22×C3—21no—
309C22×C3—42no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3—41no—
316C22×C3—81no—
317C22×C3—81no—
318C22×C3—241no—
319C22×C3—241no—
320C22×C3—241no—
321C22×C3#93011yescharacteristic
322C22×C3#93911yescharacteristic
323C2×D3—81no—
324C2×D3—81no—
325C2×D3—81no—
326C2×D3—242no—
327C2×D3—242no—
328C2×D3—242no—
329C2×D3—241no—
330C2×D3—241no—
331C2×D3—241no—
332C2×D3—241no—
333C2×D3—241no—
334C2×D3—241no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—41no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—81no—
345C3×C4#90811yescharacteristic
346C3×C4#90811yescharacteristic
347C3×C4D3×D811yescharacteristic
348C3×C4#91111yescharacteristic
349C3×C4C2×#21311yescharacteristic
350C3×C4#93211yescharacteristic
351C3×C4#94911yescharacteristic
352C3×C4#94911yescharacteristic
353C32#168711yescharacteristic, complemented, Sylow
354C23—21no—
355C23—121no—
356C23—361no—
357D4—21no—
358D4—21no—
359D4—121no—
360D4—121no—
361D4—121no—
362D4—121no—
363D4—241no—
364D4—361no—
365D4—361no—
366D4—361no—
367D4—361no—
368D4—721no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4#380411yescharacteristic
373C2×C4C2×#62611yescharacteristic
374C2×C4D3×#6711yescharacteristic
375C8—32no—
376C8—61no—
377C8—121no—
378C8—121no—
379C8—361no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—82no—
384C2×C3—81no—
385C2×C3—81no—
386C2×C3—481no—
387C2×C3#501511yescharacteristic
388C2×C3#503911yescharacteristic
389C2×C3#513511yescharacteristic
390C2×C3#514211yescharacteristic
391C2×C3#515011yescharacteristic
392C2×C3#519911yescharacteristic
393D3—161no—
394D3—482no—
395D3—481no—
396D3—481no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—241no—
401C22—241no—
402C22—241no—
403C22—721no—
404C22—721no—
405C22—721no—
406C22#6397811yescharacteristic
407C4—21no—
408C4—41no—
409C4#6382511yescharacteristic
410C4#6383011yescharacteristic
411C4D3×#21311yescharacteristic
412C4#6392511yescharacteristic
413C3—21no—
414C3#7086811yescharacteristic, complemented
415C3#7100911yescharacteristic, complemented
416C2—81no—
417C2—481no—
418C2—1441no—
419C2#1059116511yescharacteristic
420C2#1059148111yescharacteristic
421C2#1059167711yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
hypercenterC4×D4D32
hypocenterC32#1687
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10592714C2semidirect
2. C3×#5015C2semidirect
3. C3×#5012C2semidirect
4. #10590350C2semidirect
5. #10589097C2semidirect
6. #10589091C2semidirect
7. #10589090C2semidirect
31. #5015D3semidirect
32. #5012D3semidirect
122. C3×C3⋊C8D8semidirect
280. C3⋊C8#213semidirect
353. C32#1687semidirect
414. C3#70868semidirect
415. C3#71009semidirect

Maximal subgroups

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

subgroupindex
#105927142
C3×#50152
C3×#50122
#105903502
#105890972
#105890912
#105890902
#710093
#708683