Finite Group Databasebeta

← #11807643

Subgroups — #11807643

Order 1152.

854 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#123C211yesmaximal, characteristic
2#10593827C211yesmaximal, characteristic
3#10593826C211yesmaximal, characteristic
4#10593812C212yesmaximal, complemented
5#10593759C212yesmaximal, complemented
6#10593758C212yesmaximal, complemented
7#10593747C212yesmaximal, complemented
8#10593747C212yesmaximal, complemented
9#10593746C212yesmaximal, complemented
10C23×#157C2211yescharacteristic
11C2×D4×C3⋊D3C2211yescharacteristic
12C22×C4×C3⋊D3C2211yescharacteristic
13C2×C22⋊#157C2212yes—
14C2×C22⋊#157C2212yes—
15C2×C22⋊#157C2211yescharacteristic
16C2×C22⋊#157C2212yes—
17C2×C4⋊#157C2212yes—
18C2×C4⋊#157C2212yes—
19C2×C4⋊#157C2211yescharacteristic
20C2×C4⋊#157C2212yes—
21C2×C4×#157C2211yescharacteristic
22C2×C4×#157C2212yes—
23C32×#123C411yescharacteristic, complemented
24#64144C411yescharacteristic, complemented
25#64138C411yescharacteristic, complemented
26#64103C412yescomplemented
27C4⋊C4×C3⋊D3C2212yes—
28#64095C411yescharacteristic, complemented
29#64092C412yescomplemented
30C22⋊C4×C3⋊D3C2212yes—
31C22⋊C4×C3⋊D3C2211yescharacteristic
32#63781C2212yes—
33#63781C2212yes—
34#63781C2212yes—
35#63781C2212yes—
36#63781C2212yes—
37D3×#123—62no—
38C23×C3⋊D3C2311yescharacteristic
39C23×C3⋊D3C2311yescharacteristic
40C22×#157—41no—
41C22×#157—42no—
42C22×#157C2312yes—
43C22×#157C2312yes—
44C22×#157C2312yes—
45C22×#157C2312yes—
46C2×C32×D4C2×C411yescharacteristic
47C22×C32×C4C2×C411yescharacteristic, complemented
48C2×#638C2×C411yescharacteristic
49C2×#638C2×C411yescharacteristic
50C22×C3⋊Dic3C2×C411yescharacteristic, complemented
51D4×C3⋊D3—41no—
52D4×C3⋊D3—41no—
53C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
54C2×C4×C3⋊D3—41no—
55C2×C4×C3⋊D3—41no—
56C2×C4×C3⋊D3C2×C412yescomplemented
57C2×C4×C3⋊D3C2312yes—
58C2×C4×C3⋊D3C2311yescharacteristic
59C2×C4×C3⋊D3C2312yes—
60C22⋊#157—42no—
61C22⋊#157—42no—
62C22⋊#157—41no—
63C22⋊#157—42no—
64C4⋊#157—42no—
65C4⋊#157—42no—
66C4⋊#157—42no—
67C4⋊#157—41no—
68C4×#157—42no—
69C4×#157—41no—
70C32×C4⋊C4C2×C412yescomplemented
71C32×C22⋊C4C2×C412yes—
72C32×C22⋊C4C2×C411yescharacteristic, complemented
73#3757C2×C412yes—
74#3757C2×C411yescharacteristic, complemented
75#3752C2×C412yes—
76#3752C2×C412yes—
77#3752C2×C412yescomplemented
78C4⋊(C3⋊Dic3)C2×C412yescomplemented
79#3750C2×C412yescomplemented
80#3750C2×C412yescomplemented
81#2376—91nomaximal, Sylow
82C2×D3×D4—62no—
83C22×C4×D3—62no—
84C3×#123—22no—
85#935—62no—
86#929—62no—
87#894—64no—
88D3×C4⋊C4—64no—
89#886—62no—
90#883—64no—
91D3×C22⋊C4—64no—
92D3×C22⋊C4—62no—
93C23×C32C22×C411yescharacteristic
94C23×C32C22×C411yescharacteristic
95C22×C3⋊D3—21no—
96C22×C3⋊D3—21no—
97C22×C3⋊D3—22no—
98C22×C3⋊D3—21no—
99C22×C3⋊D3—22no—
100C22×C3⋊D3—21no—
101C22×C3⋊D3—22no—
102C22×C3⋊D3—22no—
103C22×C3⋊D3C22×C411yescharacteristic
104C22×C3⋊D3C22×C411yescharacteristic
105C22×C3⋊D3C2411yescharacteristic
106C2×#157—22no—
107C2×#157—22no—
108C2×#157—22no—
109C2×#157—22no—
110C2×#157—22no—
111C2×#157—22no—
112C2×#157—22no—
113C2×#157—22no—
114C2×#157—22no—
115C2×#157—22no—
116C2×#157—22no—
117C2×#157—22no—
118C2×#157—44no—
119C32×D4—41no—
120C2×C32×C4—41no—
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C22×C412yes—
123C2×C32×C4C22×C412yes—
124#638—41no—
125#638—41no—
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3C22×C411yescharacteristic
128C2×C3⋊Dic3C22×C412yes—
129C2×C3⋊Dic3C22×C412yes—
130C4⋊(C3⋊D3)—41no—
131C4×C3⋊D3—22no—
132C4×C3⋊D3—21no—
133C4×C3⋊D3—22no—
134C4×C3⋊D3—22no—
135C4×C3⋊D3—21no—
136C4×C3⋊D3—22no—
137C4×C3⋊D3—42no—
138C2×#123—91no—
139#390—91no—
140#389—92no—
141#388—92no—
142#388—92no—
143#387—92no—
144#386—91no—
145#385—92no—
146#380—92no—
147C23×D3—62no—
148C23×D3—62no—
149C2×C3×D4—22no—
150C22×C3×C4—22no—
151C2×#67—62no—
152C2×#67—62no—
153C22×Dic3—62no—
154D3×D4—124no—
155D3×D4—124no—
156C2×D12—62no—
157C2×C4×D3—64no—
158C2×C4×D3—64no—
159C2×C4×D3—64no—
160C2×C4×D3—62no—
161C2×C4×D3—124no—
162C2×C4×D3—124no—
163C3×C4⋊C4—24no—
164C3×C22⋊C4—24no—
165C3×C22⋊C4—22no—
166#217—64no—
167#217—62no—
168(C2×D3)⋊C4—64no—
169(C2×D3)⋊C4—64no—
170(C2×D3)⋊C4—64no—
171C4⋊Dic3—64no—
172Dic3⋊C4—64no—
173Dic3⋊C4—64no—
174C22×C32—21no—
175C22×C32—21no—
176C22×C32—22no—
177C22×C32—22no—
178C22×C32C23×C411yescharacteristic
179C2×C3⋊D3—21no—
180C2×C3⋊D3—21no—
181C2×C3⋊D3—22no—
182C2×C3⋊D3—22no—
183C2×C3⋊D3—41no—
184C2×C3⋊D3—42no—
185C2×C3⋊D3—41no—
186C2×C3⋊D3—41no—
187C2×C3⋊D3—42no—
188C2×C3⋊D3—41no—
189C2×C3⋊D3H(5,𝔽2)12yes—
190C2×C3⋊D3H(5,𝔽2)11yescharacteristic
191C2×C3⋊D3H(5,𝔽2)11yescharacteristic
192C2×C3⋊D32−1+412yes—
193#157—42no—
194#157—42no—
195#157—42no—
196#157—42no—
197C32×C4—22no—
198C32×C4—21no—
199C32×C4—22no—
200C3⋊Dic3—22no—
201C3⋊Dic3—21no—
202C3⋊Dic3—22no—
203C22×D4—91no—
204C23×C4—91no—
205C23×C4—91no—
206#123—91no—
207#123—91no—
208#123—92no—
209#123—92no—
210#123—91no—
211#123#15711yescharacteristic, complemented
212C2×C4⋊C4—92no—
213C2×C4⋊C4—92no—
214C2×C4⋊C4—92no—
215C2×C4⋊C4—92no—
216C2×C4⋊C4—91no—
217C2×C22⋊C4—92no—
218C2×C22⋊C4—91no—
219C2×C22⋊C4—92no—
220C2×C22⋊C4—92no—
221C2×C22⋊C4—92no—
222C2×C22⋊C4—91no—
223C2×C42—91no—
224C2×C42—92no—
225#95—92no—
226#95—92no—
227#95—92no—
228#95—92no—
229#95—92no—
230C23×C3—22no—
231C23×C3—22no—
232C22×D3—62no—
233C22×D3—62no—
234C22×D3—62no—
235C22×D3—64no—
236C22×D3—64no—
237C22×D3—124no—
238C22×D3—124no—
239C22×D3—122no—
240C22×D3—122no—
241C22×D3—124no—
242C22×D3—124no—
243C3×D4—44no—
244C2×C3×C4—22no—
245C2×C3×C4—24no—
246C2×C3×C4—24no—
247C2×C3×C4—44no—
248#67—124no—
249#67—124no—
250C2×Dic3—62no—
251C2×Dic3—64no—
252C2×Dic3—64no—
253C2×Dic3—124no—
254D12—124no—
255C4×D3—124no—
256C4×D3—124no—
257C4×D3—124no—
258C4×D3—124no—
259C4×D3—122no—
260C4×D3—122no—
261C4×D3—128no—
262C2×C32—41no—
263C2×C32—41no—
264C2×C32#51811yescharacteristic
265C2×C32#52012yes—
266C3⋊D3—41no—
267C3⋊D3—41no—
268C3⋊D3#56011yescharacteristic
269C3⋊D3#56212yes—
270C3⋊D3#56311yescharacteristic
271C24—91no—
272C24—91no—
273C2×D4—91no—
274C2×D4—91no—
275C2×D4—91no—
276C2×D4—361no—
277C2×D4—361no—
278C2×D4C2×#15711yescharacteristic
279C22×C4—91no—
280C22×C4—92no—
281C22×C4—91no—
282C22×C4—92no—
283C22×C4—92no—
284C22×C4—92no—
285C22×C4—92no—
286C22×C4—92no—
287C22×C4—92no—
288C22×C4—361no—
289C22×C4—361no—
290C22×C4—362no—
291C22×C4—361no—
292C22×C4C2×#15711yescharacteristic, complemented
293C4⋊C4—92no—
294C4⋊C4—92no—
295C4⋊C4—92no—
296C4⋊C4—362no—
297C4⋊C4—362no—
298C4⋊C4—362no—
299C4⋊C4—361no—
300C4⋊C4C2×#15712yescomplemented
301C22⋊C4—91no—
302C22⋊C4—92no—
303C22⋊C4—92no—
304C22⋊C4—92no—
305C22⋊C4—92no—
306C22⋊C4—362no—
307C22⋊C4—362no—
308C22⋊C4—362no—
309C22⋊C4—361no—
310C22⋊C4C2×#15712yes—
311C22⋊C4C2×#15711yescharacteristic, complemented
312C42—362no—
313C42—361no—
314C22×C3—24no—
315C22×C3—22no—
316C22×C3—44no—
317C22×C3—42no—
318C22×C3—44no—
319C2×D3—62no—
320C2×D3—62no—
321C2×D3—64no—
322C2×D3—64no—
323C2×D3—64no—
324C2×D3—124no—
325C2×D3—122no—
326C2×D3—124no—
327C2×D3—124no—
328C2×D3—128no—
329C2×D3—124no—
330C2×D3—242no—
331C2×D3—244no—
332C2×D3—242no—
333C3×C4—44no—
334C3×C4—42no—
335C3×C4—44no—
336Dic3—124no—
337Dic3—122no—
338Dic3—124no—
339C32#237611yescharacteristic, complemented, Sylow
340C23—91no—
341C23—91no—
342C23—91no—
343C23—182no—
344C23—182no—
345C23—181no—
346C23—181no—
347C23—181no—
348C23—181no—
349C23—182no—
350C23—182no—
351C23C22×#15711yescharacteristic
352C23C22×#15711yescharacteristic
353D4—41no—
354D4—361no—
355D4—361no—
356D4—361no—
357C2×C4—41no—
358C2×C4—92no—
359C2×C4—92no—
360C2×C4—91no—
361C2×C4—182no—
362C2×C4—181no—
363C2×C4—182no—
364C2×C4—182no—
365C2×C4—181no—
366C2×C4—182no—
367C2×C4—182no—
368C2×C4—182no—
369C2×C4—182no—
370C2×C4—182no—
371C2×C4—182no—
372C2×C4—182no—
373C2×C4—182no—
374C2×C4—182no—
375C2×C4—182no—
376C2×C4—182no—
377C2×C4—182no—
378C2×C4—182no—
379C2×C4—362no—
380C2×C4—361no—
381C2×C4—364no—
382C2×C4C22×#15712yes—
383C2×C4C22×#15712yes—
384C2×C4C22×#15711yescharacteristic
385C2×C3—22no—
386C2×C3—24no—
387C2×C3—44no—
388C2×C3—82no—
389D3—62no—
390D3—64no—
391D3—62no—
392D3—124no—
393D3—242no—
394C22—21no—
395C22—21no—
396C22—22no—
397C22—22no—
398C22—91no—
399C22—91no—
400C22—92no—
401C22—92no—
402C22—181no—
403C22—181no—
404C22—182no—
405C22—182no—
406C22—361no—
407C22—361no—
408C22—362no—
409C22—361no—
410C22—362no—
411C22—361no—
412C22C23×#15711yescharacteristic
413C4—22no—
414C4—21no—
415C4—22no—
416C4—182no—
417C4—181no—
418C4—182no—
419C4—362no—
420C4—362no—
421C4—362no—
422C4—362no—
423C3—22no—
424C2—41no—
425C2—41no—
426C2—91no—
427C2—92no—
428C2—91no—
429C2—361no—
430C2—361no—
431C2#1059664211yescharacteristic
432C2#1059665012yes—
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×#123C4
prime radicalC2×D4×C3⋊D3C22
cosocleC22×C3⋊D3C24
hypercenter#123#157
hypocenterC32#2376
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
4. #10593812C2semidirect
5. #10593759C2semidirect
6. #10593758C2semidirect
7. #10593747C2semidirect
8. #10593747C2semidirect
9. #10593746C2semidirect
23. C32×#123C4semidirect
24. #64144C4semidirect
25. #64138C4semidirect
26. #64103C4semidirect
28. #64095C4semidirect
29. #64092C4semidirect
47. C22×C32×C4C2×C4semidirect
50. C22×C3⋊Dic3C2×C4semidirect
56. C2×C4×C3⋊D3C2×C4semidirect
70. C32×C4⋊C4C2×C4semidirect
72. C32×C22⋊C4C2×C4semidirect
74. #3757C2×C4semidirect
77. #3752C2×C4semidirect
78. C4⋊(C3⋊Dic3)C2×C4semidirect
79. #3750C2×C4semidirect
80. #3750C2×C4semidirect
211. #123#157semidirect
292. C22×C4C2×#157semidirect
300. C4⋊C4C2×#157semidirect
311. C22⋊C4C2×#157semidirect
339. C32#2376semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1232
#105938272
#105938262
#105938122
#105937592
#105937582
#105937472
#105937462
#23769