Finite Group Databasebeta

← #11776137

Subgroups — #11776137

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
1C3×#5716C211yesmaximal, characteristic
2D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
3#10590248C211yesmaximal, characteristic, complemented
4#10589410C211yesmaximal, characteristic, complemented
5C3×#4544C211yesmaximal, characteristic, complemented
6#10589093C211yesmaximal, characteristic, complemented
7#10589092C211yesmaximal, characteristic, complemented
8#71804—31nomaximal
9#68381—31nomaximal
10C2×C3×#237—21no—
11C32×#127C2211yescharacteristic
12C3×#938—21no—
13C3×#938C412yes—
14C3×#936—21no—
15C3×D4×Dic3—21no—
16C3×D4×Dic3C412yes—
17C3×C42×D3C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C2×D3×C3⋊C8—21no—
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24Dic3⋊(C3⋊C8)—21no—
25(C2×D3)⋊(C3⋊C8)—21no—
26Dic3×C3⋊C8—21no—
27C3×#532—31no—
28#5716D311yescharacteristic
29#4925—31no—
30C2×C4⋊(C3⋊C8)—31no—
31#4833—31no—
32D3×C4⋊C8—31no—
33C3×#331—31no—
34#4547—31no—
35#4547—31no—
36#4544—31no—
37#4544—31no—
38#4544—61no—
39#4544D311yescharacteristic, complemented
40#4486—31no—
41#4482—31no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4C2×C412yes—
45C2×C3×#67—22no—
46C22×C3×Dic3—22no—
47C3×#237—42no—
48C3×#237—42no—
49C2×C3×C4×D3C2×C411yescharacteristic
50C2×C3×C4×D3D411yescharacteristic
51C2×C3×C4×D3D411yescharacteristic
52C2×C3×Dic6—21no—
53C32×C42C2311yescharacteristic
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×#217—22no—
57C3×#217—22no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3C2×C412yes—
60C3×C4×Dic3C2×C411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C3×C4×Dic3D411yescharacteristic
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65D3×C3⋊C8—42no—
66#1540—91noSylow
67C2×C3×#41—61no—
68C2×#237—21no—
69C3×C4⋊Q8—31no—
70C3×#127—21no—
71C3×#127C2×D311yescharacteristic
72C3×#127C2×D311yescharacteristic
73C3×#124—61no—
74C3×#121—32no—
75C3×#121—61no—
76C3×C4×D4—32no—
77C3×C4×D4—61no—
78C2×C3×C42—31no—
79#938—21no—
80#938Dic312yes—
81#936—21no—
82D4×Dic3—21no—
83D4×Dic3Dic312yes—
84C22×C3⋊C8—61no—
85C2×D3×C8—61no—
86C42×D3C2×D311yescharacteristic
87#869C2×D311yescharacteristic
88C3×C4⋊C8—31no—
89C3×C4⋊C8—31no—
90#830—61no—
91(C2×D3)⋊C8—61no—
92Dic3⋊C8—61no—
93C8×Dic3—61no—
94C4⋊(C3⋊C8)—31no—
95C4⋊(C3⋊C8)—31no—
96C4⋊(C3⋊C8)—31no—
97C4⋊(C3⋊C8)—31no—
98C4⋊(C3⋊C8)—61no—
99C4⋊(C3⋊C8)—61no—
100C4⋊(C3⋊C8)—61no—
101C4⋊(C3⋊C8)C2×D311yescharacteristic
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C4×C3⋊C8—61no—
104C23×C32—22no—
105C22×C3×D3C22⋊C411yescharacteristic
106C32×D4—42no—
107C32×D4—41no—
108C32×D4—41no—
109C32×D4—41no—
110C32×D4—41no—
111C2×C32×C4C22×C411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C3×#67—44no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—44no—
117C2×C3×Dic3C22⋊C411yescharacteristic
118C2×C3×Dic3C22⋊C411yescharacteristic
119C2×C3×Dic3C22⋊C411yescharacteristic
120C3×C4×D3—21no—
121C3×C4×D3—21no—
122C3×C4×D3—41no—
123C3×C4×D3D812yes—
124C3×C4×D3SD1612yes—
125C3×Dic6—41no—
126C3×Dic6—41no—
127C3⋊(C3⋊C8)—41no—
128C3⋊(C3⋊C8)—41no—
129C3×C3⋊C8—41no—
130C3×C3⋊C8—41no—
131#532—31no—
132#431—91no—
133C2×C4⋊C8—91no—
134#332—91no—
135#332—91no—
136#331—31no—
137#331—91no—
138C3×#41—122no—
139C3×#41—122no—
140C2×C3×Q8—61no—
141C2×C3×D4—21no—
142C2×C3×D4—21no—
143C2×C3×D4—21no—
144C2×C3×D4—21no—
145C2×C3×D4—22no—
146C2×C3×D4—41no—
147C2×C3×D4—41no—
148C2×C3×D4—62no—
149C2×C3×D4C4×D312yes—
150C2×C3×D4C2×Dic312yes—
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—31no—
154C22×C3×C4—62no—
155C2×#67—22no—
156C22×Dic3—22no—
157#237—42no—
158#237—42no—
159C2×C4×D3C2×Dic311yescharacteristic
160C2×C4×D3#6711yescharacteristic
161C2×C4×D3#6711yescharacteristic
162C2×Dic6—21no—
163C2×C3×C8—61no—
164C2×C3×C8—61no—
165C3×C4⋊C4—32no—
166C3×C4⋊C4—61no—
167C3×C22⋊C4—62no—
168C3×C22⋊C4—62no—
169C3×C42—21no—
170C3×C42—31no—
171C3×C42—31no—
172C3×C42—31no—
173C3×C42C22×D311yescharacteristic
174C3×C42C22×D311yescharacteristic
175#217—22no—
176#217—22no—
177C4⋊Dic3—21no—
178C4⋊Dic3C2×Dic312yes—
179C4×Dic3C2×Dic311yescharacteristic
180C4×Dic3#6711yescharacteristic
181C4×Dic3#6711yescharacteristic
182C2×C3⋊C8—21no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—61no—
185C2×C3⋊C8—61no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—121no—
189C2×C3⋊C8—121no—
190C2×C3⋊C8—122no—
191D3×C8—122no—
192C22×C32—42no—
193C22×C32—42no—
194C22×C32—42no—
195C22×C32C2×C22⋊C411yescharacteristic
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—61no—
209C22×C8—181no—
210C4⋊Q8—31no—
211#127D3211yescharacteristic
212#124—61no—
213#121—32no—
214#121—61no—
215C4×D4—32no—
216C4×D4—61no—
217C2×C42—31no—
218C4⋊C8—31no—
219C4⋊C8—31no—
220C4⋊C8—91no—
221C4⋊C8—91no—
222C4⋊C8—181no—
223C22⋊C8—181no—
224C4×C8—181no—
225C23×C3—22no—
226C23×C3—22no—
227C23×C3—31no—
228C23×C3—42no—
229C22×D3#21711yescharacteristic
230C3×Q8—121no—
231C3×Q8—121no—
232C3×D4—42no—
233C3×D4—42no—
234C3×D4—41no—
235C3×D4—41no—
236C3×D4—41no—
237C3×D4—41no—
238C3×D4—41no—
239C3×D4—41no—
240C3×D4—41no—
241C3×D4—41no—
242C3×D4—81no—
243C3×D4—81no—
244C3×D4—81no—
245C3×D4—81no—
246C3×D4—82no—
247C3×D4—124no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—31no—
252C2×C3×C4—32no—
253C2×C3×C4—32no—
254C2×C3×C4—31no—
255C2×C3×C4—31no—
256C2×C3×C4—61no—
257C2×C3×C4—61no—
258C2×C3×C4—62no—
259C2×C3×C4—121no—
260C2×C3×C4—124no—
261C2×C3×C4C2×C4×D311yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4C22×Dic311yescharacteristic
265C2×C3×C4C2×#6711yescharacteristic
266C2×C3×C4C2×#6711yescharacteristic
267#67—44no—
268C2×Dic3—22no—
269C2×Dic3—44no—
270C2×Dic3#21711yescharacteristic
271C2×Dic3#21711yescharacteristic
272C2×Dic3#21711yescharacteristic
273C4×D3—21no—
274C4×D3—21no—
275C4×D3—41no—
276C4×D3#21312yes—
277C4×D3#21412yes—
278Dic6—41no—
279Dic6—41no—
280C3×C8—121no—
281C3×C8—121no—
282C3⋊C8—41no—
283C3⋊C8—41no—
284C3⋊C8—121no—
285C3⋊C8—121no—
286C3⋊C8—121no—
287C3⋊C8—121no—
288C3⋊C8—241no—
289C3⋊C8—241no—
290C2×C32—82no—
291C2×C32#41311yescharacteristic
292C2×C32C2×#10211yescharacteristic
293C2×C32#41611yescharacteristic
294C3×D3—22no—
295#41—122no—
296#41—122no—
297C2×Q8—61no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—62no—
301C2×D4D3×Dic312yes—
302C22×C4—31no—
303C22×C4—31no—
304C22×C4—31no—
305C22×C4—62no—
306C2×C8—61no—
307C2×C8—61no—
308C2×C8—181no—
309C2×C8—181no—
310C2×C8—362no—
311C4⋊C4—32no—
312C4⋊C4—61no—
313C22⋊C4—62no—
314C22⋊C4—62no—
315C42—31no—
316C42—31no—
317C42—31no—
318C42C2×D3211yescharacteristic
319C22×C3—21no—
320C22×C3—32no—
321C22×C3—42no—
322C22×C3—42no—
323C22×C3—42no—
324C22×C3—42no—
325C22×C3—42no—
326C22×C3—42no—
327C22×C3—61no—
328C22×C3—61no—
329C22×C3—82no—
330C22×C3—82no—
331C22×C3—82no—
332C22×C3D3×C22⋊C411yescharacteristic
333C22×C3C2×#21711yescharacteristic
334C2×D3—21no—
335C2×D3—21no—
336C2×D3#83212yes—
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×C4D3×D811yescharacteristic
349C3×C4#91211yescharacteristic
350C3×C4D3×SD1611yescharacteristic
351C3×C4#91611yescharacteristic
352C3×C4C2×#21311yescharacteristic
353C3×C4C2×#21411yescharacteristic
354C3×C4#95011yescharacteristic
355C3×C4#95011yescharacteristic
356Dic3—21no—
357Dic3—21no—
358Dic3—42no—
359Dic3#83212yes—
360C32#154011yescharacteristic, complemented, Sylow
361C23—22no—
362C23—31no—
363Q8—121no—
364Q8—121no—
365D4—42no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—41no—
370D4—124no—
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—124no—
381C2×C4C2×D3×Dic311yescharacteristic
382C2×C4D3×#6711yescharacteristic
383C2×C4D3×#6711yescharacteristic
384C8—121no—
385C8—121no—
386C8—361no—
387C8—361no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—62no—
392C2×C3—82no—
393C2×C3—82no—
394C2×C3—162no—
395C2×C3#474511yescharacteristic
396C2×C3D3×#10211yescharacteristic
397C2×C3#477211yescharacteristic
398C2×C3C2×#83211yescharacteristic
399C2×C3#523311yescharacteristic
400C2×C3#523711yescharacteristic
401D3—22no—
402C22—32no—
403C22—42no—
404C22—42no—
405C22—42no—
406C22—61no—
407C22—61no—
408C22D3×#21711yescharacteristic
409C4—21no—
410C4—32no—
411C4—61no—
412C4—61no—
413C4—122no—
414C4D3×#21311yescharacteristic
415C4D3×#21411yescharacteristic
416C4#6393311yescharacteristic
417C4#6393511yescharacteristic
418C3—21no—
419C3#6838111yescharacteristic, complemented
420C3#7180411yescharacteristic, complemented
421C2—62no—
422C2—82no—
423C2D3×#83211yescharacteristic
424C2#1059142011yescharacteristic
425C2#1059150111yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×#127C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5716C2
cosocleC32×C42C23
hypercenter#127D32
hypocenterC32#1540
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. D3×C4⋊(C3⋊C8)C2semidirect
3. #10590248C2semidirect
4. #10589410C2semidirect
5. C3×#4544C2semidirect
6. #10589093C2semidirect
7. #10589092C2semidirect
39. #4544D3semidirect
360. C32#1540semidirect
419. C3#68381semidirect
420. C3#71804semidirect

Maximal subgroups

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

subgroupindex
C3×#57162
D3×C4⋊(C3⋊C8)2
#105902482
#105894102
C3×#45442
#105890932
#105890922
#718043
#683813