Finite Group Databasebeta

← #11787927

Subgroups — #11787927

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×#64091C211yesmaximal, characteristic
2#10595957C211yesmaximal, characteristic, complemented
3#10592654C211yesmaximal, characteristic, complemented
4#10592654C211yesmaximal, characteristic, complemented
5C2×#63633C211yesmaximal, characteristic, complemented
6C32×#342C211yesmaximal, characteristic, complemented
7#10589393C211yesmaximal, characteristic, complemented
8#68962—34nomaximal
9C24×C3⋊D3C2211yescharacteristic
10C22×#638C2211yescharacteristic
11C22×C4⋊(C3⋊D3)—21no—
12C2×C32×C22⋊C4C2211yescharacteristic
13C2×C32×C22⋊C4C2211yescharacteristic
14C2×C32×C22⋊C4C2211yescharacteristic
15C2×#3757C2211yescharacteristic
16C2×#3757C2211yescharacteristic
17C4×#638—22no—
18C2×#3752—21no—
19C2×#3752—22no—
20C2×#3752—22no—
21#64091—22no—
22#64091C414yescomplemented
23#64090—22no—
24C22⋊C4×C3⋊D3—21no—
25#64086—21no—
26#63633—22no—
27C2×#882—34no—
28#5486—34no—
29#4955—34no—
30#4955—34no—
31C2×#806—34no—
32C3×#342D314yescomplemented
33#4527—34no—
34C24×C32C2311yescharacteristic
35C23×C3⋊D3—21no—
36C23×C3⋊D3—21no—
37C23×C3⋊D3—21no—
38C23×C3⋊D3—21no—
39C23×C3⋊D3—21no—
40C23×C3⋊D3—21no—
41C23×C3⋊D3—44no—
42C23×C3⋊D3C2×C412yescomplemented
43C23×C3⋊D3D411yescharacteristic
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4D412yescomplemented
47C2×#638—21no—
48C2×#638—21no—
49C2×#638—21no—
50C2×#638—21no—
51C2×#638C2×C412yes—
52C2×#638D412yes—
53C22×C3⋊Dic3—21no—
54C22×C3⋊Dic3D411yescharacteristic
55C22×C3⋊Dic3D412yescomplemented
56C2×C4⋊(C3⋊D3)—24no—
57C2×C4⋊(C3⋊D3)—44no—
58C2×C4×C3⋊D3—22no—
59C32×C22⋊C4—21no—
60C32×C22⋊C4—21no—
61C32×C22⋊C4—21no—
62C32×C22⋊C4—21no—
63C32×C22⋊C4—21no—
64C32×C22⋊C4C2×C412yescomplemented
65#3757—21no—
66#3757—21no—
67#3757—21no—
68#3757—21no—
69#3752—22no—
70#3752—24no—
71#3752—44no—
72#3752—44no—
73#3750—22no—
74C4×C3⋊Dic3—22no—
75#1889—91noSylow
76C24×D3—34no—
77C22×#67—34no—
78C22×D12—64no—
79C2×C3×C22⋊C4C2×D314yes—
80C2×C3×C22⋊C4C2×D314yes—
81C2×C3×C22⋊C4C2×D314yes—
82C2×#217—34no—
83C2×#217—34no—
84C4×#67—68no—
85C2×(C2×D3)⋊C4—64no—
86C2×(C2×D3)⋊C4—68no—
87C2×(C2×D3)⋊C4—68no—
88#882—316no—
89#882—68no—
90#67⋊C4—68no—
91D3×C22⋊C4—64no—
92#877—64no—
93#806—68no—
94C23×C32—42no—
95C23×C32C22×C411yescharacteristic
96C23×C32C2×D411yescharacteristic
97C23×C32C2×D411yescharacteristic
98C23×C32C2×D411yescharacteristic
99C23×C32C2×D411yescharacteristic
100C23×C32#4111yescharacteristic
101C23×C32#4111yescharacteristic
102C22×C3⋊D3—24no—
103C22×C3⋊D3—24no—
104C22×C3⋊D3—24no—
105C22×C3⋊D3—22no—
106C22×C3⋊D3—22no—
107C22×C3⋊D3—22no—
108C22×C3⋊D3—21no—
109C22×C3⋊D3—21no—
110C22×C3⋊D3—44no—
111C22×C3⋊D3—44no—
112C22×C3⋊D3—44no—
113C22×C3⋊D3—44no—
114C22×C3⋊D3—42no—
115C22×C3⋊D3—42no—
116C22×C3⋊D3—42no—
117C22×C3⋊D3—41no—
118C22×C3⋊D3—41no—
119C22×C3⋊D3—41no—
120C22×C3⋊D3—41no—
121C22×C3⋊D3—42no—
122C22×C3⋊D3C22⋊C412yescomplemented
123C2×C32×C4—22no—
124C2×C32×C4—22no—
125C2×C32×C4—42no—
126C2×C32×C4—42no—
127C2×C32×C4—42no—
128C2×C32×C4—41no—
129#638—22no—
130#638—22no—
131#638—22no—
132#638—22no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—42no—
137C2×C3⋊Dic3—42no—
138C2×C3⋊Dic3—41no—
139C2×C3⋊Dic3C22⋊C412yescomplemented
140C4⋊(C3⋊D3)—48no—
141C4×C3⋊D3—82no—
142C2×#120—91no—
143#518—91no—
144C2×#99—91no—
145#379—91no—
146#379—91no—
147#342—91no—
148#342C3⋊D311yescharacteristic, complemented
149C24×C3C22×D314yes—
150C23×D3—34no—
151C23×D3—38no—
152C23×D3—64no—
153C23×D3—64no—
154C23×D3—64no—
155C23×D3—64no—
156C23×D3—64no—
157C23×D3—64no—
158C23×D3—1216no—
159C22×C3×C4—24no—
160C22×C3×C4—24no—
161C22×C3×C4D1218yescomplemented
162C2×#67—38no—
163C2×#67—38no—
164C2×#67—64no—
165C2×#67—64no—
166C2×#67—64no—
167C2×#67—64no—
168C22×Dic3—34no—
169C22×Dic3—38no—
170C22×Dic3—64no—
171C2×D12—616no—
172C2×D12—1216no—
173C2×C4×D3—68no—
174C3×C22⋊C4—24no—
175C3×C22⋊C4—24no—
176C3×C22⋊C4—24no—
177C3×C22⋊C4—24no—
178C3×C22⋊C4—24no—
179C3×C22⋊C4C4×D318yescomplemented
180#217—64no—
181#217—64no—
182#217—64no—
183#217—64no—
184(C2×D3)⋊C4—616no—
185(C2×D3)⋊C4—68no—
186(C2×D3)⋊C4—1216no—
187(C2×D3)⋊C4—1216no—
188Dic3⋊C4—68no—
189C4×Dic3—68no—
190C22×C32—22no—
191C22×C32—22no—
192C22×C32—22no—
193C22×C32—41no—
194C22×C32—41no—
195C22×C32—41no—
196C22×C32—41no—
197C22×C32C2×C22⋊C411yescharacteristic
198C22×C32C4×D411yescharacteristic
199C22×C32C4×D411yescharacteristic
200C22×C32#12011yescharacteristic
201C22×C32#12111yescharacteristic
202C22×C32#12111yescharacteristic
203C22×C32#12311yescharacteristic
204C2×C3⋊D3—24no—
205C2×C3⋊D3—24no—
206C2×C3⋊D3—24no—
207C2×C3⋊D3—22no—
208C2×C3⋊D3—44no—
209C2×C3⋊D3—42no—
210C2×C3⋊D3—44no—
211C2×C3⋊D3—42no—
212C2×C3⋊D3—42no—
213C2×C3⋊D3—44no—
214C2×C3⋊D3—42no—
215C2×C3⋊D3—42no—
216C2×C3⋊D3—44no—
217C2×C3⋊D3—42no—
218C2×C3⋊D3—81no—
219C32×C4—42no—
220C32×C4—42no—
221C32×C4—81no—
222C3⋊Dic3—22no—
223C3⋊Dic3—42no—
224C3⋊Dic3—81no—
225C25—91no—
226C22×D4—91no—
227C22×D4—181no—
228#120—94no—
229#120—182no—
230C4×D4—182no—
231C4×D4—182no—
232#117—181no—
233C2×C22⋊C4—91no—
234C2×C22⋊C4—91no—
235C2×C22⋊C4—181no—
236C2×C22⋊C4—181no—
237C2×C22⋊C4—182no—
238C2×C22⋊C4—182no—
239C2×C22⋊C4C2×C3⋊D311yescharacteristic
240C2×C22⋊C4C2×C3⋊D311yescharacteristic
241C2×C22⋊C4C2×C3⋊D311yescharacteristic
242#99—182no—
243C23×C3—48no—
244C23×C3C2×C4×D314yes—
245C23×C3C2×D1214yes—
246C23×C3#23514yes—
247C23×C3D3×D414yes—
248C23×C3D3×D414yes—
249C23×C3D3×D414yes—
250C23×C3#23914yes—
251C22×D3—38no—
252C22×D3—616no—
253C22×D3—616no—
254C22×D3—616no—
255C22×D3—68no—
256C22×D3—68no—
257C22×D3—64no—
258C22×D3—68no—
259C22×D3—64no—
260C22×D3—1216no—
261C22×D3—1216no—
262C22×D3—1216no—
263C22×D3—1216no—
264C22×D3—128no—
265C22×D3—128no—
266C22×D3—128no—
267C22×D3—124no—
268C22×D3—124no—
269C22×D3—124no—
270C22×D3—124no—
271C22×D3—128no—
272C2×C3×C4—28no—
273C2×C3×C4—28no—
274C2×C3×C4—48no—
275C2×C3×C4—48no—
276C2×C3×C4—48no—
277C2×C3×C4—44no—
278#67—68no—
279#67—68no—
280#67—68no—
281#67—68no—
282C2×Dic3—38no—
283C2×Dic3—64no—
284C2×Dic3—64no—
285C2×Dic3—68no—
286C2×Dic3—128no—
287C2×Dic3—128no—
288C2×Dic3—124no—
289D12—1232no—
290C4×D3—248no—
291C2×C32—21no—
292C2×C32—21no—
293C2×C32—21no—
294C2×C32—21no—
295C2×C32—21no—
296C2×C32—21no—
297C2×C32#38611yescharacteristic
298C2×C32B(4,𝔽2)12yes—
299C3⋊D3—44no—
300C3⋊D3—42no—
301C24—91no—
302C24—92no—
303C24—181no—
304C24—181no—
305C24—181no—
306C24—181no—
307C24—181no—
308C24—181no—
309C24—364no—
310C24C22×C3⋊D311yescharacteristic
311C2×D4—92no—
312C2×D4—92no—
313C2×D4—184no—
314C2×D4—181no—
315C2×D4—181no—
316C2×D4—181no—
317C2×D4—181no—
318C2×D4—364no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—91no—
322C22×C4—92no—
323C22×C4—182no—
324C22×C4—181no—
325C22×C4C4⋊(C3⋊D3)12yescomplemented
326C4⋊C4—182no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—21no—
332C22⋊C4—184no—
333C22⋊C4—182no—
334C22⋊C4—181no—
335C22⋊C4—181no—
336C22⋊C4—181no—
337C22⋊C4—181no—
338C22⋊C4—364no—
339C22⋊C4—364no—
340C22⋊C4C4×C3⋊D312yescomplemented
341C42—182no—
342C22×C3—28no—
343C22×C3—28no—
344C22×C3—28no—
345C22×C3—44no—
346C22×C3—44no—
347C22×C3—44no—
348C22×C3—44no—
349C22×C3C4×D1214yes—
350C22×C3D3×C22⋊C414yes—
351C22×C3#88214yes—
352C22×C3#88414yes—
353C22×C3#89314yes—
354C22×C3#89414yes—
355C22×C3#89514yes—
356C2×D3—616no—
357C2×D3—616no—
358C2×D3—616no—
359C2×D3—68no—
360C2×D3—1216no—
361C2×D3—128no—
362C2×D3—1216no—
363C2×D3—128no—
364C2×D3—128no—
365C2×D3—1216no—
366C2×D3—128no—
367C2×D3—128no—
368C2×D3—1216no—
369C2×D3—128no—
370C2×D3—244no—
371C3×C4—48no—
372C3×C4—48no—
373C3×C4—84no—
374Dic3—68no—
375Dic3—128no—
376Dic3—244no—
377C32#188911yescharacteristic, complemented, Sylow
378C23—42no—
379C23—92no—
380C23—184no—
381C23—184no—
382C23—184no—
383C23—182no—
384C23—182no—
385C23—181no—
386C23—182no—
387C23—181no—
388C23—362no—
389C23—362no—
390C23—362no—
391C23—362no—
392C23—364no—
393C23—364no—
394C23—364no—
395C23—364no—
396C23—361no—
397C23—361no—
398C23—361no—
399C23—361no—
400C23C2×C4×C3⋊D311yescharacteristic
401C23C2×C4⋊(C3⋊D3)11yescharacteristic
402C23#382811yescharacteristic
403C23D4×C3⋊D311yescharacteristic
404C23D4×C3⋊D311yescharacteristic
405C23D4×C3⋊D311yescharacteristic
406C23#383211yescharacteristic
407D4—182no—
408D4—182no—
409D4—182no—
410D4—182no—
411D4—368no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—92no—
419C2×C4—181no—
420C2×C4—181no—
421C2×C4—182no—
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#466514yes—
433C2×C3#474118yes—
434D3—1216no—
435D3—128no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—184no—
444C22—184no—
445C22—184no—
446C22—182no—
447C22—362no—
448C22—362no—
449C22—364no—
450C22—364no—
451C22—362no—
452C22—362no—
453C22—364no—
454C22—362no—
455C22—362no—
456C22—364no—
457C22—721no—
458C22C4×C4⋊(C3⋊D3)11yescharacteristic
459C22C22⋊C4×C3⋊D311yescharacteristic
460C22#6409111yescharacteristic
461C22#6409311yescharacteristic
462C22#6410211yescharacteristic
463C22#6410311yescharacteristic
464C22#6410411yescharacteristic
465C4—42no—
466C4—42no—
467C4—81no—
468C4—182no—
469C4—362no—
470C4—721no—
471C3#6896214yescomplemented
472C2—21no—
473C2—21no—
474C2—21no—
475C2—21no—
476C2—21no—
477C2—21no—
478C2—364no—
479C2—362no—
480C2#1059236411yescharacteristic
481C2#1059244012yes—
subgroupG/H
centerC22#64091
commutatorC23×C32C22×C4
FrattiniC24C22×C3⋊D3
FittingC32×#342C2
socleC22×C32#120
prime radicalC2×#64091C2
cosocleC24×C32C23
hypercenter#342C3⋊D3
hypocenterC32#1889
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. #10595957C2semidirect
3. #10592654C2semidirect
4. #10592654C2semidirect
5. C2×#63633C2semidirect
6. C32×#342C2semidirect
7. #10589393C2semidirect
22. #64091C4semidirect
32. C3×#342D3semidirect
42. C23×C3⋊D3C2×C4semidirect
46. C22×C32×C4D4semidirect
55. C22×C3⋊Dic3D4semidirect
64. C32×C22⋊C4C2×C4semidirect
122. C22×C3⋊D3C22⋊C4semidirect
139. C2×C3⋊Dic3C22⋊C4semidirect
148. #342C3⋊D3semidirect
161. C22×C3×C4D12semidirect
179. C3×C22⋊C4C4×D3semidirect
325. C22×C4C4⋊(C3⋊D3)semidirect
340. C22⋊C4C4×C3⋊D3semidirect
377. C32#1889semidirect
471. C3#68962semidirect

Maximal subgroups

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

subgroupindex
C2×#640912
#105959572
#105926542
C2×#636332
C32×#3422
#105893932
#689623