Finite Group Databasebeta

← #11789950

Subgroups — #11789950

Order 1152.

541 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
2C2×C3×#805C211yesmaximal, characteristic
3#10591117C211yesmaximal, characteristic, complemented
4#10591083C211yesmaximal, characteristic
5#10591071C211yesmaximal, characteristic
6C3×#4523C211yesmaximal, characteristic, complemented
7#10589165C211yesmaximal, characteristic, complemented
8#70371—31nomaximal
9#68745—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C4×C3⋊(C3⋊C8)—22no—
18C3×#805—22no—
19Dic3⋊(C3⋊C8)—22no—
20#63565C412yescomplemented
21#63562C412yescomplemented
22(C2×D3)⋊(C3⋊C8)—22no—
23C2×C3×#104—31no—
24#5234—31no—
25#5233—31no—
26#5129—31no—
27#5119—31no—
28#5002—31no—
29#4999—31no—
30C2×#805D311yescharacteristic
31C2×C4×C3⋊C8—31no—
32C2×C4×C3⋊C8—31no—
33C2×C4×C3⋊C8—61no—
34C3×#339—31no—
35#4558—31no—
36#4558—31no—
37#4523D311yescharacteristic, complemented
38C22×C32×C4—21no—
39C22×C32×C4C2311yescharacteristic
40C2×C3×#67—21no—
41C3×#235—21no—
42C3×#235—21no—
43C3×#235—21no—
44C3×#235—21no—
45C2×C3×D12C2×C411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×Dic6C2×C411yescharacteristic
48C32×C42—21no—
49C32×C42D412yes—
50C2×C3⋊(C3⋊C8)—21no—
51C2×C3⋊(C3⋊C8)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)C2×C412yes—
55C2×C3⋊(C3⋊C8)D412yes—
56C3×#217—21no—
57C3×C4⋊Dic3C2×C412yes—
58C3×C4×Dic3—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#1937—91noSylow
66C2×C3×#41—31no—
67C2×#235C2×D311yescharacteristic
68C2×C3×M16—31no—
69C2×C3×M16—31no—
70C3×#117—31no—
71C2×C3×C42—21no—
72C2×C3×C42C2×D311yescharacteristic
73C2×C3×C42C2×D311yescharacteristic
74#926C2×D311yescharacteristic
75C2×#208C2×D311yescharacteristic
76C2×#208C2×D311yescharacteristic
77C22×C3⋊C8—31no—
78C22×C3⋊C8—31no—
79C22×C3⋊C8—31no—
80C22×C3⋊C8—31no—
81C22×C3⋊C8—61no—
82C22×C3⋊C8—61no—
83C3×#104—62no—
84#835—32no—
85#832—32no—
86#830—62no—
87(C2×D3)⋊C8—62no—
88Dic3⋊C8—62no—
89#810—32no—
90#809—32no—
91#805—22no—
92C4⋊(C3⋊C8)—62no—
93C4×C3⋊C8—64no—
94C4×C3⋊C8—62no—
95C4×C3⋊C8—62no—
96C23×C32#4111yescharacteristic
97C22×C3×D3—21no—
98C2×C32×C4—24no—
99C2×C32×C4—22no—
100C2×C32×C4C22×C411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C32×C4#4111yescharacteristic
106C3×#67—41no—
107C3×#67—41no—
108C2×C3×Dic3—22no—
109C2×C3×Dic3—21no—
110C3×D12—21no—
111C3×D12—21no—
112C3×C4×D3—41no—
113C3×C4×D3—41no—
114C3×Dic6—21no—
115C3×Dic6—21no—
116C3⋊(C3⋊C8)—22no—
117C3⋊(C3⋊C8)—22no—
118C3×C3⋊C8—41no—
119C3×C3⋊C8—41no—
120#424—91no—
121C2×#104—31no—
122#416—91no—
123#408—91no—
124C2×C4×C8—91no—
125#341—91no—
126#339—31no—
127C3×#41—61no—
128C3×#41—61no—
129C3×#41—61no—
130C3×#41—61no—
131C2×C3×Q8—31no—
132C2×C3×D4—31no—
133C2×C3×D4—61no—
134C22×C3×C4—22no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—61no—
139C22×C3×C4C22×D311yescharacteristic
140C22×C3×C4C22×D311yescharacteristic
141C2×#67—21no—
142#235—21no—
143#235—21no—
144#235—21no—
145#235—21no—
146C2×D12C4×D311yescharacteristic
147C2×C4×D3—21no—
148C2×Dic6C4×D311yescharacteristic
149C3×M16—61no—
150C3×M16—61no—
151C3×M16—61no—
152C3×M16—61no—
153C2×C3×C8—61no—
154C2×C3×C8—61no—
155C3×C4⋊C4—32no—
156C3×C22⋊C4—61no—
157C3×C42—22no—
158C3×C42—21no—
159C3×C42—21no—
160C3×C42—22no—
161C3×C42—61no—
162C3×C42D1212yes—
163C3×C42#6712yes—
164#217—21no—
165C4⋊Dic3C4×D312yes—
166C4×Dic3—21no—
167#208—21no—
168#208—21no—
169#208—21no—
170#208—21no—
171C2×C3⋊C8—21no—
172C2×C3⋊C8—21no—
173C2×C3⋊C8—32no—
174C2×C3⋊C8—32no—
175C2×C3⋊C8—32no—
176C2×C3⋊C8—32no—
177C2×C3⋊C8—62no—
178C2×C3⋊C8—62no—
179C2×C3⋊C8—62no—
180C2×C3⋊C8—62no—
181C2×C3⋊C8—62no—
182C2×C3⋊C8—62no—
183C2×C3⋊C8—61no—
184C2×C3⋊C8—61no—
185C2×C3⋊C8—61no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—61no—
189C2×C3⋊C8—61no—
190C2×C3⋊C8—61no—
191C22×C32—22no—
192C22×C32C4×D411yescharacteristic
193C22×C32#12311yescharacteristic
194C22×C32#12611yescharacteristic
195C2×C3×D3—41no—
196C2×C3×D3—42no—
197C32×C4—24no—
198C32×C4#11711yescharacteristic
199C32×C4C4×D411yescharacteristic
200C32×C4#12111yescharacteristic
201C32×C4#12411yescharacteristic
202C3×Dic3—41no—
203C3×Dic3—42no—
204C2×#41—31no—
205C2×M16—31no—
206C2×M16—31no—
207C22×C8—91no—
208C22×C8—91no—
209#117—31no—
210C2×C42D3211yescharacteristic
211C4⋊C8—182no—
212#104—62no—
213#103—92no—
214#102—92no—
215C22⋊C8—182no—
216C4×C8—182no—
217C23×C3—21no—
218C23×C3—61no—
219C23×C3#23711yescharacteristic
220C23×C3#23711yescharacteristic
221C22×D3—21no—
222C3×Q8—61no—
223C3×Q8—61no—
224C3×D4—61no—
225C3×D4—61no—
226C3×D4—121no—
227C3×D4—121no—
228C2×C3×C4—24no—
229C2×C3×C4—28no—
230C2×C3×C4—24no—
231C2×C3×C4—24no—
232C2×C3×C4—22no—
233C2×C3×C4—22no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—62no—
241C2×C3×C4—61no—
242C2×C3×C4—121no—
243C2×C3×C4—121no—
244C2×C3×C4C2×C4×D311yescharacteristic
245C2×C3×C4C2×C4×D311yescharacteristic
246C2×C3×C4C2×D1211yescharacteristic
247C2×C3×C4#23511yescharacteristic
248C2×C3×C4#23511yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4#23711yescharacteristic
252C2×C3×C4#23711yescharacteristic
253C2×C3×C4#23711yescharacteristic
254C2×C3×C4#23911yescharacteristic
255C2×C3×C4C2×#6711yescharacteristic
256#67—41no—
257#67—41no—
258C2×Dic3—22no—
259C2×Dic3—21no—
260D12—21no—
261D12—21no—
262C4×D3—41no—
263C4×D3—41no—
264Dic6—21no—
265Dic6—21no—
266C3×C8—121no—
267C3×C8—121no—
268C3⋊C8—41no—
269C3⋊C8—41no—
270C3⋊C8—64no—
271C3⋊C8—64no—
272C3⋊C8—62no—
273C3⋊C8—62no—
274C3⋊C8—62no—
275C3⋊C8—62no—
276C2×C32—21no—
277C2×C32—21no—
278C2×C32#38811yescharacteristic
279C2×C32#44312yes—
280C3×D3—81no—
281#41—61no—
282#41—61no—
283#41—61no—
284#41—61no—
285C2×Q8—31no—
286C2×D4—31no—
287C2×D4—61no—
288C22×C4—21no—
289C22×C4—61no—
290C22×C4C2×D3211yescharacteristic
291M16—61no—
292M16—61no—
293M16—61no—
294M16—61no—
295C2×C8—61no—
296C2×C8—61no—
297C2×C8—92no—
298C2×C8—92no—
299C2×C8—181no—
300C2×C8—181no—
301C2×C8—181no—
302C2×C8—181no—
303C4⋊C4—32no—
304C22⋊C4—61no—
305C42—21no—
306C42—61no—
307C42#62612yes—
308C22×C3—24no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—121no—
315C22×C3—122no—
316C22×C3#87911yescharacteristic
317C22×C3#67⋊C411yescharacteristic
318C22×C3#67⋊C411yescharacteristic
319C22×C3#88611yescharacteristic
320C22×C3#89811yescharacteristic
321C22×C3#93511yescharacteristic
322C2×D3—41no—
323C2×D3—42no—
324C3×C4—28no—
325C3×C4—24no—
326C3×C4—24no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—121no—
332C3×C4—122no—
333C3×C4C4×D1211yescharacteristic
334C3×C4#87711yescharacteristic
335C3×C4#88511yescharacteristic
336C3×C4#88511yescharacteristic
337C3×C4#89211yescharacteristic
338C3×C4#89511yescharacteristic
339C3×C4C4×#6711yescharacteristic
340C3×C4#93811yescharacteristic
341Dic3—41no—
342Dic3—42no—
343C32#193711yescharacteristic, complemented, Sylow
344C23—61no—
345C23#380511yescharacteristic
346Q8—61no—
347Q8—61no—
348D4—61no—
349D4—61no—
350D4—121no—
351D4—121no—
352C2×C4—24no—
353C2×C4—22no—
354C2×C4—62no—
355C2×C4—61no—
356C2×C4—121no—
357C2×C4—121no—
358C2×C4#379611yescharacteristic
359C2×C4#379811yescharacteristic
360C2×C4C4×D3211yescharacteristic
361C2×C4#380211yescharacteristic
362C2×C4#380511yescharacteristic
363C2×C4C2×#62611yescharacteristic
364C8—121no—
365C8—121no—
366C8—182no—
367C8—182no—
368C2×C3—22no—
369C2×C3—22no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—22no—
376C2×C3—241no—
377C2×C3#467011yescharacteristic
378C2×C3#482412yes—
379C2×C3#482412yes—
380C2×C3#494411yescharacteristic
381D3—81no—
382C22—22no—
383C22—121no—
384C22—122no—
385C22#6386211yescharacteristic
386C22#6390211yescharacteristic
387C22#6396211yescharacteristic
388C4—24no—
389C4—121no—
390C4—122no—
391C4#6387811yescharacteristic
392C4C4×#62611yescharacteristic
393C4#6391511yescharacteristic
394C4#6391611yescharacteristic
395C3—21no—
396C3#6874511yescharacteristic, complemented
397C3#7037111yescharacteristic, complemented
398C2—21no—
399C2—21no—
400C2—241no—
401C2#1059038912yes—
402C2#1059128711yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1937
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×C3⋊(C3⋊C8)C2semidirect
3. #10591117C2semidirect
6. C3×#4523C2semidirect
7. #10589165C2semidirect
20. #63565C4semidirect
21. #63562C4semidirect
37. #4523D3semidirect
343. C32#1937semidirect
396. C3#68745semidirect
397. C3#70371semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C3⋊(C3⋊C8)2
C2×C3×#8052
#105911172
#105910832
#105910712
C3×#45232
#105891652
#703713
#687453