Finite Group Databasebeta

← #11787921

Subgroups — #11787921

Order 1152.

1734 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1734 conjugacy classes of subgroups — too many to draw. Only its 191 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
1C2×#64162C211yesmaximal, characteristic
2#10595957C211yesmaximal, characteristic, complemented
3C32×#379C211yesmaximal, characteristic, complemented
4#10592946C211yesmaximal, characteristic, complemented
5C2×#63633C211yesmaximal, characteristic, complemented
6#10589393C211yesmaximal, characteristic, complemented
7#10589392C211yesmaximal, characteristic, complemented
8#69499—34nomaximal
9C25×C32C2211yescharacteristic
10C22×#638—21no—
11C22×#638C2211yescharacteristic
12C2×C32×C22⋊C4—22no—
13C2×C32×C22⋊C4C2211yescharacteristic
14C2×C32×C22⋊C4C2211yescharacteristic
15#64162—22no—
16#64162C414yescomplemented
17C2×#3757—21no—
18C2×#3757—22no—
19C2×#3757C2211yescharacteristic
20C2×#3757C2211yescharacteristic
21C2×#3757C2211yescharacteristic
22C4×#638—22no—
23#64090—22no—
24C22⋊C4×C3⋊D3—21no—
25#64086—21no—
26#63633—22no—
27C2×#953—34no—
28#5486—34no—
29C3×#379D314yescomplemented
30#5247—34no—
31C2×#806—34no—
32#4527—34no—
33#4526—34no—
34C24×C32—21no—
35C24×C32—21no—
36C24×C32—21no—
37C24×C32—21no—
38C24×C32—21no—
39C24×C32—21no—
40C24×C32—44no—
41C24×C32C2×C412yescomplemented
42C24×C32C2311yescharacteristic
43C23×C3⋊D3D411yescharacteristic
44C22×C32×C4—21no—
45C22×C32×C4D412yescomplemented
46C2×#638—21no—
47C2×#638—21no—
48C2×#638—21no—
49C2×#638—21no—
50C2×#638—24no—
51C2×#638—44no—
52C2×#638C2×C412yes—
53C2×#638D412yes—
54C22×C3⋊Dic3—21no—
55C22×C3⋊Dic3—21no—
56C22×C3⋊Dic3D411yescharacteristic
57C22×C3⋊Dic3D412yescomplemented
58C2×C4×C3⋊D3—22no—
59C32×C22⋊C4—21no—
60C32×C22⋊C4—21no—
61C32×C22⋊C4—21no—
62C32×C22⋊C4—21no—
63C32×C22⋊C4—44no—
64#3757—21no—
65#3757—21no—
66#3757—21no—
67#3757—24no—
68#3757—21no—
69#3757—21no—
70#3757—44no—
71#3757C2×C412yescomplemented
72#3752—22no—
73#3750—22no—
74C4×C3⋊Dic3—22no—
75#1889—91noSylow
76C25×C3C2×D314yes—
77C22×#67—34no—
78C22×#67—64no—
79C2×C3×C22⋊C4—28no—
80C2×C3×C22⋊C4C2×D314yes—
81C2×C3×C22⋊C4C2×D314yes—
82#953—316no—
83#953—68no—
84C2×#217—34no—
85C2×#217—34no—
86C2×#217—34no—
87C2×#217—64no—
88C2×#217—68no—
89C4×#67—68no—
90#67⋊C4—68no—
91D3×C22⋊C4—64no—
92#877—64no—
93#806—68no—
94C23×C32—24no—
95C23×C32—24no—
96C23×C32—24no—
97C23×C32—22no—
98C23×C32—22no—
99C23×C32—22no—
100C23×C32—44no—
101C23×C32—42no—
102C23×C32—42no—
103C23×C32—42no—
104C23×C32—42no—
105C23×C32—44no—
106C23×C32—44no—
107C23×C32—44no—
108C23×C32—41no—
109C23×C32—41no—
110C23×C32—41no—
111C23×C32—41no—
112C23×C32C22×C411yescharacteristic
113C23×C32C2×D411yescharacteristic
114C23×C32C2×D411yescharacteristic
115C23×C32C2×D411yescharacteristic
116C23×C32C2×D411yescharacteristic
117C23×C32#4111yescharacteristic
118C23×C32#4111yescharacteristic
119C22×C3⋊D3—21no—
120C22×C3⋊D3—21no—
121C22×C3⋊D3—42no—
122C22×C3⋊D3C22⋊C412yescomplemented
123C2×C32×C4—22no—
124C2×C32×C4—42no—
125C2×C32×C4—42no—
126C2×C32×C4—41no—
127#638—22no—
128#638—22no—
129#638—22no—
130#638—22no—
131#638—48no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—42no—
137C2×C3⋊Dic3—42no—
138C2×C3⋊Dic3—42no—
139C2×C3⋊Dic3—41no—
140C2×C3⋊Dic3C22⋊C412yescomplemented
141C4×C3⋊D3—82no—
142C2×#120—91no—
143#518—91no—
144C2×#99—91no—
145#379—91no—
146#379C3⋊D311yescharacteristic, complemented
147#342—91no—
148#342—91no—
149C24×C3—24no—
150C24×C3—24no—
151C24×C3—24no—
152C24×C3—24no—
153C24×C3—24no—
154C24×C3—24no—
155C24×C3—416no—
156C24×C3C4×D318yescomplemented
157C24×C3C22×D314yes—
158C23×D3—34no—
159C22×C3×C4—24no—
160C22×C3×C4#6718yescomplemented
161C2×#67—38no—
162C2×#67—38no—
163C2×#67—64no—
164C2×#67—64no—
165C2×#67—64no—
166C2×#67—64no—
167C2×#67—616no—
168C2×#67—1216no—
169C22×Dic3—34no—
170C22×Dic3—38no—
171C22×Dic3—64no—
172C22×Dic3—64no—
173C2×C4×D3—68no—
174C3×C22⋊C4—24no—
175C3×C22⋊C4—24no—
176C3×C22⋊C4—24no—
177C3×C22⋊C4—24no—
178C3×C22⋊C4—416no—
179#217—38no—
180#217—616no—
181#217—64no—
182#217—64no—
183#217—64no—
184#217—64no—
185#217—64no—
186#217—1216no—
187(C2×D3)⋊C4—68no—
188Dic3⋊C4—68no—
189C4×Dic3—68no—
190C22×C32—22no—
191C22×C32—22no—
192C22×C32—22no—
193C22×C32—24no—
194C22×C32—24no—
195C22×C32—24no—
196C22×C32—41no—
197C22×C32—41no—
198C22×C32—41no—
199C22×C32—41no—
200C22×C32—42no—
201C22×C32—44no—
202C22×C32—44no—
203C22×C32—44no—
204C22×C32—42no—
205C22×C32—42no—
206C22×C32—42no—
207C22×C32—44no—
208C22×C32C2×C22⋊C411yescharacteristic
209C22×C32C4×D411yescharacteristic
210C22×C32C4×D411yescharacteristic
211C22×C32#12011yescharacteristic
212C22×C32#12111yescharacteristic
213C22×C32#12111yescharacteristic
214C22×C32#12311yescharacteristic
215C2×C3⋊D3—22no—
216C2×C3⋊D3—42no—
217C2×C3⋊D3—42no—
218C2×C3⋊D3—81no—
219C32×C4—42no—
220C32×C4—81no—
221C3⋊Dic3—22no—
222C3⋊Dic3—42no—
223C3⋊Dic3—42no—
224C3⋊Dic3—81no—
225C25C2×C3⋊D311yescharacteristic
226C22×D4—91no—
227C22×D4—181no—
228#120—94no—
229#120—182no—
230C4×D4—182no—
231C4×D4—182no—
232#117—181no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—91no—
235C2×C22⋊C4—91no—
236C2×C22⋊C4—91no—
237C2×C22⋊C4—181no—
238C2×C22⋊C4—181no—
239C2×C22⋊C4—182no—
240C2×C22⋊C4C2×C3⋊D311yescharacteristic
241C2×C22⋊C4C2×C3⋊D311yescharacteristic
242#99—182no—
243C23×C3—216no—
244C23×C3—216no—
245C23×C3—216no—
246C23×C3—28no—
247C23×C3—28no—
248C23×C3—28no—
249C23×C3—416no—
250C23×C3—48no—
251C23×C3—48no—
252C23×C3—48no—
253C23×C3—48no—
254C23×C3—416no—
255C23×C3—416no—
256C23×C3—416no—
257C23×C3—44no—
258C23×C3—44no—
259C23×C3—44no—
260C23×C3—44no—
261C23×C3C2×C4×D314yes—
262C23×C3#23514yes—
263C23×C3D3×D414yes—
264C23×C3D3×D414yes—
265C23×C3D3×D414yes—
266C23×C3#23714yes—
267C23×C3C2×#6714yes—
268C22×D3—38no—
269C22×D3—64no—
270C22×D3—64no—
271C22×D3—128no—
272C2×C3×C4—28no—
273C2×C3×C4—48no—
274C2×C3×C4—48no—
275C2×C3×C4—44no—
276#67—68no—
277#67—68no—
278#67—68no—
279#67—68no—
280#67—1232no—
281C2×Dic3—38no—
282C2×Dic3—64no—
283C2×Dic3—64no—
284C2×Dic3—68no—
285C2×Dic3—68no—
286C2×Dic3—128no—
287C2×Dic3—128no—
288C2×Dic3—128no—
289C2×Dic3—124no—
290C4×D3—248no—
291C2×C32—21no—
292C2×C32—21no—
293C2×C32—21no—
294C2×C32—21no—
295C2×C32—21no—
296C2×C32—21no—
297C2×C32—44no—
298C2×C32#38611yescharacteristic
299C2×C32B(4,𝔽2)12yes—
300C3⋊D3—42no—
301C24—21no—
302C24—21no—
303C24—21no—
304C24—21no—
305C24—21no—
306C24—21no—
307C24—44no—
308C24—91no—
309C24C4×C3⋊D312yescomplemented
310C24C22×C3⋊D311yescharacteristic
311C2×D4—92no—
312C2×D4—92no—
313C2×D4—181no—
314C2×D4—181no—
315C2×D4—181no—
316C2×D4—181no—
317C2×D4—184no—
318C2×D4—364no—
319C22×C4—21no—
320C22×C4—91no—
321C22×C4—92no—
322C22×C4—182no—
323C22×C4—181no—
324C22×C4—181no—
325C22×C4#63812yescomplemented
326C4⋊C4—182no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—44no—
332C22⋊C4—92no—
333C22⋊C4—182no—
334C22⋊C4—184no—
335C22⋊C4—181no—
336C22⋊C4—181no—
337C22⋊C4—181no—
338C22⋊C4—181no—
339C22⋊C4—181no—
340C22⋊C4—364no—
341C42—182no—
342C22×C3—28no—
343C22×C3—28no—
344C22×C3—28no—
345C22×C3—216no—
346C22×C3—216no—
347C22×C3—216no—
348C22×C3—44no—
349C22×C3—44no—
350C22×C3—44no—
351C22×C3—44no—
352C22×C3—48no—
353C22×C3—416no—
354C22×C3—416no—
355C22×C3—416no—
356C22×C3—48no—
357C22×C3—48no—
358C22×C3—48no—
359C22×C3—416no—
360C22×C3D3×C22⋊C414yes—
361C22×C3#67⋊C414yes—
362C22×C3#88314yes—
363C22×C3#88414yes—
364C22×C3C4×#6714yes—
365C22×C3#93714yes—
366C22×C3#93814yes—
367C2×D3—68no—
368C2×D3—128no—
369C2×D3—128no—
370C2×D3—244no—
371C3×C4—48no—
372C3×C4—84no—
373Dic3—68no—
374Dic3—128no—
375Dic3—128no—
376Dic3—244no—
377C32#188911yescharacteristic, complemented, Sylow
378C23—24no—
379C23—24no—
380C23—24no—
381C23—22no—
382C23—22no—
383C23—22no—
384C23—44no—
385C23—42no—
386C23—42no—
387C23—42no—
388C23—42no—
389C23—44no—
390C23—44no—
391C23—44no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—92no—
397C23—181no—
398C23—181no—
399C23—362no—
400C23C2×C4×C3⋊D311yescharacteristic
401C23#382811yescharacteristic
402C23D4×C3⋊D311yescharacteristic
403C23D4×C3⋊D311yescharacteristic
404C23D4×C3⋊D311yescharacteristic
405C23#383011yescharacteristic
406C23C2×#63811yescharacteristic
407D4—182no—
408D4—182no—
409D4—182no—
410D4—182no—
411D4—368no—
412C2×C4—22no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—92no—
417C2×C4—181no—
418C2×C4—181no—
419C2×C4—182no—
420C2×C4—182no—
421C2×C4—362no—
422C2×C4—362no—
423C2×C4—362no—
424C2×C4—361no—
425C2×C4—722no—
426C2×C3—24no—
427C2×C3—24no—
428C2×C3—24no—
429C2×C3—24no—
430C2×C3—24no—
431C2×C3—24no—
432C2×C3—416no—
433C2×C3#495614yes—
434C2×C3#503218yes—
435D3—128no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—24no—
440C22—24no—
441C22—24no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—44no—
447C22—42no—
448C22—44no—
449C22—42no—
450C22—42no—
451C22—44no—
452C22—42no—
453C22—44no—
454C22—182no—
455C22—362no—
456C22—362no—
457C22—721no—
458C22C22⋊C4×C3⋊D311yescharacteristic
459C22#6409011yescharacteristic
460C22#6409211yescharacteristic
461C22#6409311yescharacteristic
462C22C4×#63811yescharacteristic
463C22#6414611yescharacteristic
464C22#6414711yescharacteristic
465C4—42no—
466C4—81no—
467C4—182no—
468C4—362no—
469C4—362no—
470C4—721no—
471C3#6949914yescomplemented
472C2—21no—
473C2—21no—
474C2—21no—
475C2—21no—
476C2—21no—
477C2—21no—
478C2—44no—
479C2—362no—
480C2#1059265511yescharacteristic
481C2#1059273112yes—
subgroupG/H
centerC22#64146
commutatorC23×C32C22×C4
FrattiniC24C22×C3⋊D3
FittingC32×#379C2
socleC22×C32#120
prime radicalC2×#64162C2
cosocleC24×C32C23
hypercenter#379C3⋊D3
hypocenterC32#1889
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
2. #10595957C2semidirect
3. C32×#379C2semidirect
4. #10592946C2semidirect
5. C2×#63633C2semidirect
6. #10589393C2semidirect
7. #10589392C2semidirect
16. #64162C4semidirect
29. C3×#379D3semidirect
41. C24×C32C2×C4semidirect
45. C22×C32×C4D4semidirect
57. C22×C3⋊Dic3D4semidirect
71. #3757C2×C4semidirect
122. C22×C3⋊D3C22⋊C4semidirect
140. C2×C3⋊Dic3C22⋊C4semidirect
146. #379C3⋊D3semidirect
156. C24×C3C4×D3semidirect
160. C22×C3×C4#67semidirect
309. C24C4×C3⋊D3semidirect
325. C22×C4#638semidirect
377. C32#1889semidirect
471. C3#69499semidirect

Maximal subgroups

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

subgroupindex
C2×#641622
#105959572
C32×#3792
#105929462
C2×#636332
#105893932
#105893922
#694993