Finite Group Databasebeta

← #11776142

Subgroups — #11776142

Order 1152.

554 conjugacy classes of subgroups.

The subgroup lattice has 427 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593970C211yesmaximal, characteristic
2C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
3#10590248C211yesmaximal, characteristic, complemented
4#10589351C211yesmaximal, characteristic, complemented
5C3×#4482C211yesmaximal, characteristic, complemented
6#10589093C211yesmaximal, characteristic, complemented
7#10589091C211yesmaximal, characteristic, complemented
8#70431—31nomaximal
9#68417—31nomaximal
10C2×#3799—21no—
11#64083C2211yescharacteristic
12C2×C3×D3×C8—21no—
13C3×C42×D3C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63909—21no—
16#63909C412yes—
17#63894—21no—
18#63894C412yes—
19#63864—21no—
20C32×C4⋊C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×Dic3⋊C8—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25(C2×D3)⋊(C3⋊C8)—21no—
26Dic3×C3⋊C8—21no—
27#5725—31no—
28#5477—31no—
29C2×C3×C4⋊C8—31no—
30#4925—31no—
31#4833—31no—
32D3×C4⋊C8D311yescharacteristic, complemented
33C3×#332—31no—
34#4547—31no—
35#4485—31no—
36#4485—31no—
37#4485—31no—
38#4485—31no—
39#4485—61no—
40#4482—31no—
41#4482D311yescharacteristic, complemented
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)C2×C412yes—
45C2×C3×C4×D3C2×C411yescharacteristic
46C2×C3×C4×D3D411yescharacteristic
47C2×C3×C4×D3D411yescharacteristic
48C2×C3×Dic6—21no—
49C2×#626—22no—
50C2×#624—22no—
51#3799—42no—
52#3799—42no—
53C2×C32×C8—21no—
54C32×C42C2311yescharacteristic
55C2×C3⋊(C3⋊C8)—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3C2×C412yes—
58C3×C4×Dic3C2×C411yescharacteristic
59C3×C4×Dic3D411yescharacteristic
60C3×C4×Dic3D411yescharacteristic
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C3×D3×C8—42no—
64#3722—22no—
65#3722—22no—
66#1540—91noSylow
67C2×#239—61no—
68C2×#235—61no—
69C22×C3×C8—61no—
70C3×C4⋊Q8—31no—
71C2×C3×C42—31no—
72#947—61no—
73#930—32no—
74#930—61no—
75C2×D3×C8—21no—
76#895—32no—
77#895—61no—
78#893—32no—
79#893—61no—
80#875—61no—
81#874—31no—
82#874—31no—
83#874—61no—
84C4×D12—32no—
85C4×D12—61no—
86C42×D3C2×D311yescharacteristic
87#869C2×D311yescharacteristic
88C3×C4⋊C8—21no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8—31no—
91C3×C4⋊C8—61no—
92C3×C4⋊C8C2×D311yescharacteristic
93C3×C4⋊C8C2×D311yescharacteristic
94#830—61no—
95(C2×D3)⋊C8—61no—
96Dic3⋊C8—21no—
97C8×Dic3—61no—
98C4⋊(C3⋊C8)—31no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—61no—
101C4⋊(C3⋊C8)C2×D311yescharacteristic
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C4×C3⋊C8—61no—
104C22×C3⋊D3—22no—
105C22×C3×D3C22⋊C411yescharacteristic
106C2×C32×C4C22×C411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C4⋊(C3⋊D3)—42no—
110C4⋊(C3⋊D3)—41no—
111C4⋊(C3⋊D3)—41no—
112C4⋊(C3⋊D3)—41no—
113C4⋊(C3⋊D3)—41no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3C22⋊C411yescharacteristic
116C2×C3×Dic3C22⋊C411yescharacteristic
117C2×C3×Dic3C22⋊C411yescharacteristic
118C3×C4×D3—21no—
119C3×C4×D3—21no—
120C3×C4×D3—41no—
121C3×C4×D3D812yes—
122C3×C4×D3SD1612yes—
123C3×Dic6—41no—
124C3×Dic6—41no—
125#626—44no—
126#624—44no—
127C32×C8—41no—
128C3⋊(C3⋊C8)—41no—
129C3×C3⋊C8—41no—
130C3×C3⋊C8—41no—
131#532—91no—
132#431—91no—
133C2×C4⋊C8—31no—
134#332—31no—
135#332—91no—
136#331—91no—
137#331—91no—
138C2×C3×Q8—61no—
139C22×C3×C4—31no—
140C22×C3×C4—31no—
141C22×C3×C4—31no—
142C2×#67—62no—
143#239—122no—
144#239—122no—
145#235—122no—
146#235—122no—
147C2×D12—32no—
148C2×D12—32no—
149C2×D12—62no—
150C2×D12—62no—
151C2×D12—61no—
152C2×D12—61no—
153C2×D12—61no—
154C2×D12—61no—
155C2×D12—121no—
156C2×D12—121no—
157C2×C4×D3—62no—
158C2×C4×D3—62no—
159C2×C4×D3C4×D311yescharacteristic
160C2×C4×D3D1211yescharacteristic
161C2×C4×D3#6711yescharacteristic
162C2×Dic6—21no—
163C2×C3×C8—21no—
164C2×C3×C8—21no—
165C2×C3×C8—41no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C2×C3×C8—122no—
169C3×C4⋊C4—32no—
170C3×C4⋊C4—61no—
171C3×C42—21no—
172C3×C42—31no—
173C3×C42—31no—
174C3×C42—31no—
175C3×C42C22×D311yescharacteristic
176C3×C42C22×D311yescharacteristic
177(C2×D3)⋊C4—62no—
178(C2×D3)⋊C4—62no—
179(C2×D3)⋊C4—62no—
180(C2×D3)⋊C4—62no—
181C4⋊Dic3—21no—
182C4⋊Dic3C4×D312yes—
183C4×Dic3C4×D311yescharacteristic
184C4×Dic3D1211yescharacteristic
185C4×Dic3#6711yescharacteristic
186C2×C3⋊C8—21no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—61no—
189C2×C3⋊C8—61no—
190C2×C3⋊C8—121no—
191D3×C8—42no—
192C22×C32C2×C22⋊C411yescharacteristic
193C2×C3⋊D3—42no—
194C2×C3⋊D3—42no—
195C2×C3⋊D3—42no—
196C2×C3×D3—21no—
197C2×C3×D3—21no—
198C2×C3×D3#10212yes—
199C32×C4—21no—
200C32×C4C2×D811yescharacteristic
201C32×C4C2×SD1611yescharacteristic
202C32×C4#13511yescharacteristic
203C32×C4#13511yescharacteristic
204C3×Dic3—21no—
205C3×Dic3—21no—
206C3×Dic3—42no—
207C3×Dic3#10212yes—
208C2×#41—181no—
209C22×C8—61no—
210C4⋊Q8—31no—
211#127—91no—
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—61no—
221C4⋊C8—91no—
222C4⋊C8D3211yescharacteristic
223C22⋊C8—181no—
224C4×C8—181no—
225C23×C3—31no—
226C22×D3—62no—
227C22×D3—62no—
228C22×D3—122no—
229C22×D3(C2×D3)⋊C411yescharacteristic
230C3×Q8—121no—
231C3×Q8—121no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—31no—
236C2×C3×C4—32no—
237C2×C3×C4—32no—
238C2×C3×C4—31no—
239C2×C3×C4—31no—
240C2×C3×C4—61no—
241C2×C3×C4—61no—
242C2×C3×C4—62no—
243C2×C3×C4—121no—
244C2×C3×C4C2×C4×D311yescharacteristic
245C2×C3×C4C2×C4×D311yescharacteristic
246C2×C3×C4C2×D1211yescharacteristic
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249C2×C3×C4C2×#6711yescharacteristic
250#67—124no—
251C2×Dic3—22no—
252C2×Dic3(C2×D3)⋊C411yescharacteristic
253C2×Dic3(C2×D3)⋊C411yescharacteristic
254C2×Dic3(C2×D3)⋊C411yescharacteristic
255D12—122no—
256D12—122no—
257D12—124no—
258D12—121no—
259D12—121no—
260D12—121no—
261D12—121no—
262D12—121no—
263D12—121no—
264D12—121no—
265D12—121no—
266D12—241no—
267D12—241no—
268D12—241no—
269D12—241no—
270D12—242no—
271C4×D3—21no—
272C4×D3—21no—
273C4×D3—41no—
274C4×D3—124no—
275C4×D3—124no—
276C4×D3#21312yes—
277C4×D3#21512yes—
278Dic6—41no—
279Dic6—41no—
280C3×C8—41no—
281C3×C8—41no—
282C3×C8—81no—
283C3×C8—121no—
284C3×C8—121no—
285C3⋊C8—41no—
286C3⋊C8—41no—
287C3⋊C8—121no—
288C3⋊C8—121no—
289C3⋊C8—241no—
290C2×C32#41311yescharacteristic
291C2×C32C2×#10211yescharacteristic
292C2×C32#41611yescharacteristic
293C3⋊D3—82no—
294C3×D3—22no—
295#41—362no—
296#41—362no—
297C2×Q8—61no—
298C2×D4—92no—
299C2×D4—182no—
300C2×D4—181no—
301C2×D4—181no—
302C22×C4—31no—
303C22×C4—31no—
304C22×C4—31no—
305C22×C4—182no—
306C2×C8—21no—
307C2×C8—61no—
308C2×C8—61no—
309C2×C8—122no—
310C2×C8—181no—
311C4⋊C4—32no—
312C4⋊C4—61no—
313C22⋊C4—182no—
314C22⋊C4—182no—
315C42—31no—
316C42—31no—
317C42—31no—
318C42C2×D3211yescharacteristic
319C22×C3—21no—
320C22×C3—32no—
321C22×C3—61no—
322C22×C3—61no—
323C22×C3D3×C22⋊C411yescharacteristic
324C22×C3C2×(C2×D3)⋊C411yescharacteristic
325C2×D3—21no—
326C2×D3—21no—
327C2×D3—122no—
328C2×D3—122no—
329C2×D3—122no—
330C2×D3—122no—
331C2×D3—122no—
332C2×D3—122no—
333C2×D3—242no—
334C2×D3—242no—
335C2×D3—242no—
336C2×D3#80912yes—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—32no—
344C3×C4—41no—
345C3×C4—61no—
346C3×C4—61no—
347C3×C4—122no—
348C3×C4#90411yescharacteristic
349C3×C4#90411yescharacteristic
350C3×C4D3×D811yescharacteristic
351C3×C4D3×SD1611yescharacteristic
352C3×C4#91611yescharacteristic
353C3×C4#91911yescharacteristic
354C3×C4C2×#21311yescharacteristic
355C3×C4C2×#21511yescharacteristic
356Dic3—21no—
357Dic3—21no—
358Dic3—42no—
359Dic3#80912yes—
360C32#154011yescharacteristic, complemented, Sylow
361C23—31no—
362C23—182no—
363Q8—121no—
364Q8—121no—
365D4—362no—
366D4—364no—
367D4—361no—
368D4—361no—
369D4—361no—
370D4—361no—
371C2×C4—31no—
372C2×C4—32no—
373C2×C4—32no—
374C2×C4—31no—
375C2×C4—31no—
376C2×C4—61no—
377C2×C4—61no—
378C2×C4—62no—
379C2×C4—121no—
380C2×C4—364no—
381C2×C4C4×D3211yescharacteristic
382C2×C4D3×D1211yescharacteristic
383C2×C4D3×#6711yescharacteristic
384C8—41no—
385C8—121no—
386C8—121no—
387C8—361no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—62no—
392C2×C3#475111yescharacteristic
393C2×C3D3×#10211yescharacteristic
394C2×C3#480411yescharacteristic
395C2×C3C2×#80911yescharacteristic
396C2×C3#511311yescharacteristic
397C2×C3#513211yescharacteristic
398D3—22no—
399D3—242no—
400D3—242no—
401D3—482no—
402C22—32no—
403C22—61no—
404C22—61no—
405C22—362no—
406C22—362no—
407C22—362no—
408C22D3×(C2×D3)⋊C411yescharacteristic
409C4—21no—
410C4—32no—
411C4—61no—
412C4—61no—
413C4—122no—
414C4#6380611yescharacteristic
415C4#6380811yescharacteristic
416C4D3×#21311yescharacteristic
417C4D3×#21511yescharacteristic
418C3—21no—
419C3#6841711yescharacteristic, complemented
420C3#7043111yescharacteristic, complemented
421C2—62no—
422C2—722no—
423C2D3×#80911yescharacteristic
424C2#1059069011yescharacteristic
425C2#1059100711yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#10593970C2
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×D3×C4⋊C8C2semidirect
3. #10590248C2semidirect
4. #10589351C2semidirect
5. C3×#4482C2semidirect
6. #10589093C2semidirect
7. #10589091C2semidirect
32. D3×C4⋊C8D3semidirect
41. #4482D3semidirect
360. C32#1540semidirect
419. C3#68417semidirect
420. C3#70431semidirect

Maximal subgroups

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

subgroupindex
#105939702
C3×D3×C4⋊C82
#105902482
#105893512
C3×#44822
#105890932
#105890912
#704313
#684173