Finite Group Databasebeta

← #11802665

Subgroups — #11802665

Order 1152.

1950 conjugacy classes of subgroups; only the 199 normal subgroups are shown.

normal subgroups only

This group has 1950 conjugacy classes of subgroups — too many to draw. Only its 199 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3802C211yesmaximal, characteristic
2C2×#64286C211yesmaximal, characteristic, complemented
3#10594969C211yesmaximal, characteristic, complemented
4#10593512C214yesmaximal, complemented
5#10593407C214yesmaximal, complemented
6#10593405C214yesmaximal, complemented
7C23×D32C2212yes—
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×C3×D12—21no—
10C22×#625—21no—
11C2×#3802—21no—
12C2×#3802—21no—
13C2×#3802—24no—
14C2×#3802C418yescomplemented
15C2×#3802C2212yes—
16C2×#3802C2212yes—
17C2×C22⋊#157C2212yes—
18#64286—24no—
19C2×C4⋊#157C2212yescomplemented
20C2×C4×#157C2212yescomplemented
21C2×D32⋊C4C22116yescomplemented
22C3×#926—21no—
23#63974C2212yes—
24#63957—21no—
25#63900C2212yescomplemented
26C4×#624C2212yescomplemented
27#63874—21no—
28#63849—21no—
29C22×D3×D4—61no—
30D3×#117—61no—
31C23×C3⋊D3C2311yescharacteristic
32C23×C3×D3—22no—
33C22×D32—22no—
34C22×D32—24no—
35C22×D32—48no—
36C22×D32C2×C418yes—
37C22×D32C2314yes—
38C22×#157C2314yes—
39C22×C32×C4D411yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41C2×C4×C3⋊D3C2×C414yes—
42C2×C4×C3⋊D3D411yescharacteristic
43C2×C4×C3⋊D3D411yescharacteristic
44C2×C4×C3⋊D3D414yes—
45C2×C4×C3⋊D3C2311yescharacteristic
46C2×C4×C3⋊D3C2311yescharacteristic
47C2×C3×D12—28no—
48C2×C3×D12—22no—
49C2×C3×D12—22no—
50C2×#625—28no—
51C2×#625—22no—
52C2×#625—22no—
53C2×#624C2314yes—
54#3802—28no—
55#3802—28no—
56#3802—24no—
57#3802—24no—
58#3802C2×C418yes—
59#3802C2×C418yes—
60C22⋊#157—24no—
61C4⋊#157—24no—
62C4×#157—24no—
63D32⋊C4—416no—
64C3×#217—22no—
65C3×C4⋊Dic3—22no—
66C3×C4×Dic3—22no—
67#3724—22no—
68#3722—22no—
69Dic32—22no—
70#2309—91nomaximal, Sylow
71C24×D3—62no—
72C22×C3×D4—61no—
73C22×#67—62no—
74C2×D3×D4—68no—
75C2×D3×D4—62no—
76C2×D3×D4—62no—
77C2×D3×D4—62no—
78C2×D3×D4—62no—
79C2×D3×D4—68no—
80C22×D12—21no—
81C22×C4×D3—61no—
82C22×C4×D3—61no—
83C3×#117—61no—
84#926—21no—
85#892—62no—
86D3×C4⋊C4—62no—
87D3×C22⋊C4—62no—
88#877—62no—
89#872—62no—
90C42×D3—62no—
91C23×C32C2×D411yescharacteristic
92C22×C3⋊D3—24no—
93C22×C3⋊D3C22×C412yes—
94C22×C3⋊D3C2×D411yescharacteristic
95C22×C3⋊D3C2×D412yes—
96C22×C3⋊D3C2411yescharacteristic
97C22×C3×D3—28no—
98C22×C3×D3—24no—
99C22×C3×D3—48no—
100C2×D32—28no—
101C2×D32—24no—
102C2×D32—216no—
103C2×D32—416no—
104C2×D32—48no—
105C2×D32—416no—
106C2×D32C22×C418yes—
107C2×#157—24no—
108C2×#157—28no—
109C2×C32×C4C22⋊C414yescomplemented
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3C22⋊C414yescomplemented
113C2×C3⋊Dic3C2×D411yescharacteristic
114C2×C3⋊Dic3C2×D411yescharacteristic
115C4×C3⋊D3C22⋊C414yescomplemented
116C4×C3⋊D3C22⋊C414yescomplemented
117C4×C3⋊D3C22×C412yes—
118C4×C3⋊D3C22×C412yes—
119C4×C3⋊D3C2×D412yes—
120C4×C3⋊D3C2×D412yes—
121C2×C3×Dic3—24no—
122C3×D12—28no—
123C3×D12—28no—
124#625—28no—
125#625—28no—
126#624—28no—
127C23×D4—91no—
128C2×#117—91no—
129C2×#117—91no—
130#390—94no—
131#390—94no—
132#379—94no—
133C24×C3—62no—
134C23×D3—22no—
135C23×D3—68no—
136C23×D3—64no—
137C23×D3—61no—
138C23×D3—61no—
139C23×D3—64no—
140C23×D3—68no—
141C23×D3—1216no—
142C2×C3×D4—62no—
143C2×C3×D4—62no—
144C2×C3×D4—68no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C2×#67—616no—
148C2×#67—64no—
149C2×#67—64no—
150C22×Dic3—61no—
151C22×Dic3—61no—
152D3×D4—68no—
153D3×D4—68no—
154D3×D4—616no—
155D3×D4—616no—
156D3×D4—68no—
157D3×D4—68no—
158C2×D12—22no—
159C2×D12—22no—
160C2×D12—28no—
161C2×C4×D3—61no—
162C2×C4×D3—61no—
163C2×C4×D3—61no—
164C2×C4×D3—61no—
165C2×C4×D3—64no—
166C2×C4×D3—61no—
167C2×C4×D3—61no—
168C2×C4×D3—64no—
169C2×C4×D3—61no—
170C2×C4×D3—61no—
171C2×C4×D3—64no—
172C2×C4×D3—64no—
173C2×C4×D3—64no—
174C3×C4⋊C4—62no—
175C3×C22⋊C4—62no—
176C3×C42—62no—
177#217—22no—
178(C2×D3)⋊C4—64no—
179C4⋊Dic3—22no—
180Dic3⋊C4—64no—
181C4×Dic3—22no—
182C4×Dic3—64no—
183C22×C32—22no—
184C22×C32C2×C22⋊C412yes—
185C22×C32C22×D411yescharacteristic
186C2×C3⋊D3—22no—
187C2×C3⋊D3—24no—
188C2×C3⋊D3—24no—
189C2×C3⋊D3C2×C22⋊C412yes—
190C2×C3⋊D3C23×C411yescharacteristic
191C2×C3⋊D3C22×D411yescharacteristic
192C2×C3⋊D3H(5,𝔽2)14yes—
193C2×C3×D3—28no—
194C2×C3×D3—416no—
195C2×C3×D3—48no—
196D32—216no—
197D32—416no—
198D32—48no—
199#157—44no—
200C32×C4C2×C22⋊C412yes—
201C32×C4C2×C22⋊C412yes—
202C3⋊Dic3C2×C22⋊C412yes—
203C3⋊Dic3C2×C22⋊C412yes—
204C3×Dic3—44no—
205C25—92no—
206C22×D4—61no—
207C22×D4—92no—
208C22×D4—92no—
209C22×D4—98no—
210C22×D4—181no—
211C22×D4—181no—
212C22×D4—184no—
213C22×D4—181no—
214C23×C4—91no—
215#117—61no—
216#117—181no—
217#117—181no—
218#117—181no—
219#117—184no—
220C2×C4⋊C4—92no—
221C2×C4⋊C4—92no—
222C2×C22⋊C4—92no—
223C2×C22⋊C4—92no—
224C2×C22⋊C4—916no—
225C2×C42—92no—
226C2×C42—92no—
227C23×C3—21no—
228C23×C3—21no—
229C23×C3—64no—
230C23×C3—68no—
231C23×C3—128no—
232C22×D3—24no—
233C22×D3—28no—
234C22×D3—48no—
235C22×D3—68no—
236C22×D3—62no—
237C22×D3—61no—
238C22×D3—62no—
239C22×D3—61no—
240C22×D3—61no—
241C22×D3—62no—
242C22×D3—61no—
243C22×D3—62no—
244C22×D3—616no—
245C22×D3—68no—
246C22×D3—68no—
247C22×D3—1216no—
248C22×D3—124no—
249C22×D3—1232no—
250C22×D3—1232no—
251C22×D3—1216no—
252C3×D4—68no—
253C3×D4—68no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—24no—
259C2×C3×C4—24no—
260C2×C3×C4—64no—
261#67—616no—
262#67—616no—
263C2×Dic3—24no—
264C2×Dic3—64no—
265C2×Dic3—64no—
266C2×Dic3—61no—
267C2×Dic3—61no—
268C2×Dic3—61no—
269C2×Dic3—61no—
270D12—28no—
271D12—28no—
272C4×D3—64no—
273C4×D3—64no—
274C4×D3—64no—
275C4×D3—64no—
276C4×D3—62no—
277C4×D3—62no—
278C4×D3—62no—
279C4×D3—62no—
280C4×D3—62no—
281C4×D3—62no—
282C4×D3—62no—
283C4×D3—62no—
284C4×D3—128no—
285C2×C32—22no—
286C2×C32C22×C22⋊C411yescharacteristic
287C2×C32#53512yes—
288C3⋊D3—22no—
289C3⋊D3#51812yes—
290C3⋊D3#53512yes—
291C3×D3—48no—
292C24—62no—
293C24—94no—
294C24—98no—
295C24—91no—
296C24—182no—
297C24—184no—
298C24—368no—
299C2×D4—62no—
300C2×D4—62no—
301C2×D4—68no—
302C2×D4—98no—
303C2×D4—98no—
304C2×D4—184no—
305C2×D4—184no—
306C2×D4—188no—
307C2×D4—188no—
308C2×D4—182no—
309C2×D4—182no—
310C2×D4—188no—
311C22×C4—94no—
312C22×C4—91no—
313C22×C4—91no—
314C22×C4—91no—
315C22×C4—91no—
316C22×C4—91no—
317C22×C4—94no—
318C22×C4—94no—
319C22×C4—94no—
320C22×C4GO+(4,𝔽2)11yescharacteristic
321C4⋊C4—62no—
322C4⋊C4—182no—
323C4⋊C4—184no—
324C22⋊C4—62no—
325C22⋊C4—182no—
326C22⋊C4—184no—
327C22⋊C4—3616no—
328C42—62no—
329C42—182no—
330C42—184no—
331C22×C3—24no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—22no—
335C22×C3—22no—
336C22×C3—42no—
337C22×C3—68no—
338C22×C3—1216no—
339C22×C3—128no—
340C2×D3—28no—
341C2×D3—416no—
342C2×D3—48no—
343C2×D3—62no—
344C2×D3—61no—
345C2×D3—61no—
346C2×D3—61no—
347C2×D3—61no—
348C2×D3—64no—
349C2×D3—64no—
350C2×D3—62no—
351C2×D3—68no—
352C2×D3—68no—
353C2×D3—64no—
354C2×D3—1216no—
355C2×D3—124no—
356C2×D3—124no—
357C2×D3—122no—
358C2×D3—1216no—
359C2×D3—1232no—
360C3×C4—22no—
361C3×C4—22no—
362C3×C4—22no—
363C3×C4—22no—
364C3×C4—124no—
365Dic3—44no—
366Dic3—62no—
367Dic3—62no—
368Dic3—62no—
369Dic3—62no—
370C32#230911yescharacteristic, complemented, Sylow
371C23—64no—
372C23—68no—
373C23—98no—
374C23—91no—
375C23—91no—
376C23—92no—
377C23—92no—
378C23—128no—
379C23—184no—
380C23—184no—
381C23—188no—
382C23—1816no—
383C23—3616no—
384C23—3616no—
385C23—368no—
386C23C2×GO+(4,𝔽2)11yescharacteristic
387D4—68no—
388D4—68no—
389D4—188no—
390D4—188no—
391C2×C4—64no—
392C2×C4—91no—
393C2×C4—91no—
394C2×C4—94no—
395C2×C4—92no—
396C2×C4—92no—
397C2×C4—92no—
398C2×C4—92no—
399C2×C4—94no—
400C2×C4—94no—
401C2×C4—188no—
402C2×C4—184no—
403C2×C4—188no—
404C2×C4D32⋊C414yescomplemented
405C2×C4C2×GO+(4,𝔽2)11yescharacteristic
406C2×C4C2×GO+(4,𝔽2)11yescharacteristic
407C2×C3—24no—
408C2×C3—22no—
409C2×C3—22no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—42no—
413C2×C3—128no—
414D3—48no—
415D3—62no—
416D3—62no—
417D3—62no—
418D3—62no—
419D3—64no—
420D3—122no—
421C22—22no—
422C22—68no—
423C22—94no—
424C22—91no—
425C22—91no—
426C22—92no—
427C22—1216no—
428C22—128no—
429C22—184no—
430C22—184no—
431C22—1816no—
432C22—182no—
433C22—368no—
434C22—3616no—
435C22C2×D32⋊C412yes—
436C22C22×GO+(4,𝔽2)11yescharacteristic
437C4—92no—
438C4—92no—
439C4—124no—
440C4—364no—
441C4C2×D32⋊C412yes—
442C4C2×D32⋊C412yes—
443C3—21no—
444C3—21no—
445C2—22no—
446C2—92no—
447C2—92no—
448C2—128no—
449C2—182no—
450C2#1059651212yes—
451C2C22×D32⋊C411yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC2×C3⋊D3C23×C4
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC22×#3802C2
cosocleC22×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2309
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#64286C2semidirect
3. #10594969C2semidirect
4. #10593512C2semidirect
5. #10593407C2semidirect
6. #10593405C2semidirect
14. C2×#3802C4semidirect
19. C2×C4⋊#157C22semidirect
20. C2×C4×#157C22semidirect
21. C2×D32⋊C4C22semidirect
25. #63900C22semidirect
26. C4×#624C22semidirect
109. C2×C32×C4C22⋊C4semidirect
112. C2×C3⋊Dic3C22⋊C4semidirect
115. C4×C3⋊D3C22⋊C4semidirect
116. C4×C3⋊D3C22⋊C4semidirect
370. C32#2309semidirect
404. C2×C4D32⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#38022
C2×#642862
#105949692
#105935122
#105934072
#105934052
#23099