Finite Group Databasebeta

← #11776136

Subgroups — #11776136

Order 1152.

544 conjugacy classes of subgroups.

The subgroup lattice has 421 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593897C211yesmaximal, characteristic
2C3×#4833C211yesmaximal, characteristic, complemented
3D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4#10589352C211yesmaximal, characteristic, complemented
5C3×#4485C211yesmaximal, characteristic, complemented
6#10589094C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#70772—31nomaximal
9#68381—31nomaximal
10C2×#3795—21no—
11#64078C2211yescharacteristic
12C3×#874C2211yescharacteristic
13C3×C42×D3C2211yescharacteristic
14#63908—21no—
15#63908C412yes—
16Dic3×D12—21no—
17Dic3×D12C412yes—
18#63860—21no—
19C2×D3×C3⋊C8—21no—
20C32×C4⋊C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×(C2×D3)⋊C8—21no—
23C3×C8×Dic3—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26Dic3⋊(C3⋊C8)—21no—
27#5716—31no—
28#5477—31no—
29C3×#431—31no—
30C2×C4⋊(C3⋊C8)—31no—
31#4833D311yescharacteristic, complemented
32D3×C4⋊C8—31no—
33C3×#331—31no—
34#4544—31no—
35#4486—31no—
36#4486—31no—
37#4486—31no—
38#4486—61no—
39#4485—31no—
40#4485D311yescharacteristic, complemented
41#4482—31no—
42C2×#634—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12C2×C412yes—
46C2×C3×C4×D3C2×C411yescharacteristic
47C2×C3×C4×D3D411yescharacteristic
48C2×C3×C4×D3D411yescharacteristic
49C2×#625—22no—
50C2×D3×Dic3—22no—
51#3795—42no—
52#3795—42no—
53C2×C32×C8—21no—
54C32×C42C2311yescharacteristic
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)C2×C412yes—
57C2×C3⋊(C3⋊C8)—21no—
58C3×C4×Dic3C2×C411yescharacteristic
59C3×C4×Dic3D411yescharacteristic
60C3×C4×Dic3D411yescharacteristic
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63(C2×D3)⋊Dic3—22no—
64(C2×D3)⋊Dic3—22no—
65D3×C3⋊C8—42no—
66#1540—91noSylow
67C2×#237—61no—
68C2×#235—61no—
69C3×#127—31no—
70C2×C3×C42—31no—
71#938—32no—
72#938—61no—
73#936—61no—
74D4×Dic3—32no—
75D4×Dic3—61no—
76#930—32no—
77#930—61no—
78C22×C3⋊C8—61no—
79C2×D3×C8—61no—
80#875—61no—
81#874C2×D311yescharacteristic
82C4×D12—32no—
83C4×D12—61no—
84C42×D3C2×D311yescharacteristic
85#869—31no—
86#869—31no—
87#869—61no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8—31no—
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4⋊C8C2×D311yescharacteristic
93C3×C22⋊C8—61no—
94C3×C4×C8—61no—
95(C2×D3)⋊C8—21no—
96Dic3⋊C8—61no—
97C8×Dic3—21no—
98C4⋊(C3⋊C8)—31no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—61no—
101C4⋊(C3⋊C8)—61no—
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C22×C3×D3—22no—
105C22×C3×D3C22⋊C411yescharacteristic
106C2×C32×C4C22×C411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C3⋊Dic3—22no—
110#634—41no—
111#634—41no—
112C2×C3×Dic3C22⋊C411yescharacteristic
113C2×C3×Dic3C22⋊C411yescharacteristic
114C2×C3×Dic3C22⋊C411yescharacteristic
115C3×D12—42no—
116C3×D12—41no—
117C3×D12—41no—
118C3×D12—41no—
119C3×D12—41no—
120C3×C4×D3—21no—
121C3×C4×D3—21no—
122C3×C4×D3—41no—
123C3×C4×D3D812yes—
124C3×C4×D3SD1612yes—
125#625—44no—
126D3×Dic3—44no—
127C32×C8—41no—
128C3⋊(C3⋊C8)—41no—
129C3×C3⋊C8—41no—
130C3×C3⋊C8—41no—
131#532—91no—
132#431—31no—
133C2×C4⋊C8—91no—
134#332—91no—
135#332—91no—
136#331—31no—
137#331—91no—
138C2×C3×D4—32no—
139C2×C3×D4—61no—
140C2×C3×D4—61no—
141C22×C3×C4—31no—
142C22×C3×C4—31no—
143C22×C3×C4—31no—
144C2×#67—62no—
145C2×#67—62no—
146C22×Dic3—62no—
147#237—122no—
148#237—122no—
149#235—122no—
150#235—122no—
151C2×D12—21no—
152C2×D12—21no—
153C2×D12C4×D312yes—
154C2×C4×D3—62no—
155C2×C4×D3C4×D311yescharacteristic
156C2×C4×D3D1211yescharacteristic
157C2×C4×D3#6711yescharacteristic
158C2×Dic6—61no—
159C2×Dic6—61no—
160C2×Dic6—121no—
161C2×C3×C8—21no—
162C2×C3×C8—21no—
163C2×C3×C8—41no—
164C2×C3×C8—61no—
165C2×C3×C8—61no—
166C3×C42—21no—
167C3×C42—31no—
168C3×C42—31no—
169C3×C42—31no—
170C3×C42C22×D311yescharacteristic
171C3×C42C22×D311yescharacteristic
172#217—62no—
173#217—62no—
174(C2×D3)⋊C4—62no—
175(C2×D3)⋊C4—62no—
176C4⋊Dic3—32no—
177C4⋊Dic3—32no—
178C4⋊Dic3—62no—
179C4⋊Dic3—61no—
180C4⋊Dic3—61no—
181C4⋊Dic3—121no—
182C4×Dic3C4×D311yescharacteristic
183C4×Dic3D1211yescharacteristic
184C4×Dic3#6711yescharacteristic
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—61no—
189C2×C3⋊C8—121no—
190C2×C3⋊C8—122no—
191D3×C8—122no—
192C22×C32C2×C22⋊C411yescharacteristic
193C2×C3×D3—21no—
194C2×C3×D3—21no—
195C2×C3×D3—42no—
196C2×C3×D3—42no—
197C2×C3×D3—42no—
198C2×C3×D3#10212yes—
199C32×C4—21no—
200C32×C4C2×D811yescharacteristic
201C32×C4C2×SD1611yescharacteristic
202C32×C4#13511yescharacteristic
203C32×C4#13511yescharacteristic
204C3⋊Dic3—42no—
205C3×Dic3—21no—
206C3×Dic3—21no—
207C3×Dic3#10212yes—
208C2×#41—181no—
209C22×C8—181no—
210C4⋊Q8—91no—
211#127—31no—
212#124—181no—
213#121—92no—
214#121—181no—
215C4×D4—92no—
216C4×D4—181no—
217C2×C42—31no—
218C4⋊C8—31no—
219C4⋊C8—31no—
220C4⋊C8—91no—
221C4⋊C8—181no—
222C4⋊C8D3211yescharacteristic
223C22⋊C8—61no—
224C4×C8—61no—
225C23×C3—31no—
226C23×C3—62no—
227C22×D3—22no—
228C22×D3(C2×D3)⋊C411yescharacteristic
229C3×D4—122no—
230C3×D4—121no—
231C3×D4—121no—
232C3×D4—121no—
233C3×D4—121no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—31no—
238C2×C3×C4—32no—
239C2×C3×C4—32no—
240C2×C3×C4—31no—
241C2×C3×C4—31no—
242C2×C3×C4—61no—
243C2×C3×C4—61no—
244C2×C3×C4—121no—
245C2×C3×C4C2×C4×D311yescharacteristic
246C2×C3×C4C2×C4×D311yescharacteristic
247C2×C3×C4C2×D1211yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4C2×#6711yescharacteristic
251#67—124no—
252#67—124no—
253C2×Dic3—62no—
254C2×Dic3—62no—
255C2×Dic3—122no—
256C2×Dic3—124no—
257C2×Dic3(C2×D3)⋊C411yescharacteristic
258C2×Dic3(C2×D3)⋊C411yescharacteristic
259C2×Dic3(C2×D3)⋊C411yescharacteristic
260D12—42no—
261D12—41no—
262D12—41no—
263D12—41no—
264D12—41no—
265C4×D3—21no—
266C4×D3—21no—
267C4×D3—41no—
268C4×D3—124no—
269C4×D3#20412yes—
270C4×D3D2412yes—
271Dic6—121no—
272Dic6—121no—
273Dic6—121no—
274Dic6—121no—
275Dic6—241no—
276Dic6—241no—
277C3×C8—41no—
278C3×C8—41no—
279C3×C8—81no—
280C3×C8—121no—
281C3×C8—121no—
282C3⋊C8—41no—
283C3⋊C8—41no—
284C3⋊C8—121no—
285C3⋊C8—121no—
286C3⋊C8—241no—
287C2×C32#41311yescharacteristic
288C2×C32C2×#10211yescharacteristic
289C2×C32#41611yescharacteristic
290C3×D3—22no—
291C3×D3—82no—
292#41—362no—
293#41—362no—
294C2×Q8—181no—
295C2×D4—32no—
296C2×D4—61no—
297C2×D4—61no—
298C2×D4—182no—
299C22×C4—31no—
300C22×C4—31no—
301C22×C4—31no—
302C22×C4—182no—
303C2×C8—21no—
304C2×C8—61no—
305C2×C8—61no—
306C2×C8—181no—
307C2×C8—362no—
308C4⋊C4—92no—
309C4⋊C4—181no—
310C22⋊C4—182no—
311C22⋊C4—182no—
312C42—31no—
313C42—31no—
314C42—31no—
315C42C2×D3211yescharacteristic
316C22×C3—21no—
317C22×C3—32no—
318C22×C3—61no—
319C22×C3—61no—
320C22×C3—122no—
321C22×C3—122no—
322C22×C3—122no—
323C22×C3D3×C22⋊C411yescharacteristic
324C22×C3C2×(C2×D3)⋊C411yescharacteristic
325C2×D3—21no—
326C2×D3—21no—
327C2×D3—42no—
328C2×D3—42no—
329C2×D3—42no—
330C2×D3#82112yes—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—32no—
338C3×C4—41no—
339C3×C4—61no—
340C3×C4—61no—
341C3×C4C2×#20411yescharacteristic
342C3×C4C2×D2411yescharacteristic
343C3×C4D3×D811yescharacteristic
344C3×C4#91211yescharacteristic
345C3×C4D3×SD1611yescharacteristic
346C3×C4#91611yescharacteristic
347C3×C4#95011yescharacteristic
348C3×C4#95011yescharacteristic
349Dic3—21no—
350Dic3—21no—
351Dic3—122no—
352Dic3—122no—
353Dic3—242no—
354Dic3#82112yes—
355C32#154011yescharacteristic, complemented, Sylow
356C23—31no—
357C23—62no—
358Q8—361no—
359Q8—361no—
360D4—122no—
361D4—121no—
362D4—121no—
363D4—121no—
364D4—121no—
365D4—364no—
366C2×C4—31no—
367C2×C4—32no—
368C2×C4—32no—
369C2×C4—31no—
370C2×C4—31no—
371C2×C4—61no—
372C2×C4—61no—
373C2×C4—121no—
374C2×C4—182no—
375C2×C4—364no—
376C2×C4C4×D3211yescharacteristic
377C2×C4D3×D1211yescharacteristic
378C2×C4D3×#6711yescharacteristic
379C8—41no—
380C8—121no—
381C8—121no—
382C8—361no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—62no—
387C2×C3—242no—
388C2×C3#474511yescharacteristic
389C2×C3D3×#10211yescharacteristic
390C2×C3#477211yescharacteristic
391C2×C3#500211yescharacteristic
392C2×C3C2×#82111yescharacteristic
393C2×C3#513211yescharacteristic
394D3—22no—
395D3—82no—
396C22—32no—
397C22—61no—
398C22—61no—
399C22—122no—
400C22—122no—
401C22—122no—
402C22D3×(C2×D3)⋊C411yescharacteristic
403C4—21no—
404C4—32no—
405C4—61no—
406C4—61no—
407C4—362no—
408C4D3×#20411yescharacteristic
409C4D3×D2411yescharacteristic
410C4#6393311yescharacteristic
411C4#6394711yescharacteristic
412C3—21no—
413C3#6838111yescharacteristic, complemented
414C3#7077211yescharacteristic, complemented
415C2—62no—
416C2—242no—
417C2#1059060811yescharacteristic
418C2D3×#82111yescharacteristic
419C2#1059100611yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#10593897C2
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. C3×#4833C2semidirect
3. D3×C4⋊(C3⋊C8)C2semidirect
4. #10589352C2semidirect
5. C3×#4485C2semidirect
6. #10589094C2semidirect
7. #10589090C2semidirect
31. #4833D3semidirect
40. #4485D3semidirect
355. C32#1540semidirect
413. C3#68381semidirect
414. C3#70772semidirect

Maximal subgroups

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

subgroupindex
#105938972
C3×#48332
D3×C4⋊(C3⋊C8)2
#105893522
C3×#44852
#105890942
#105890902
#707723
#683813