Finite Group Databasebeta

← #11860786

Subgroups — #11860786

Order 1152.

794 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 794 conjugacy classes of subgroups — too many to draw. Only its 151 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×#3775C211yesmaximal, characteristic
2#10594245C211yesmaximal, characteristic, complemented
3#10594181C211yesmaximal, characteristic
4#10593738C211yesmaximal, characteristic, complemented
5#10593511C211yesmaximal, characteristic, complemented
6#10593503C211yesmaximal, characteristic, complemented
7#10593493C211yesmaximal, characteristic
8#10593433C212yesmaximal, complemented
9#10593432C212yesmaximal, complemented
10#10593431C212yesmaximal, complemented
11C4×#3775C212yesmaximal, complemented
12C22×#627C2211yescharacteristic
13C22×#625C2211yescharacteristic
14C2×#3792C2211yescharacteristic
15C22×#622C2211yescharacteristic
16C2×#3775C418yescomplemented
17C2×#3775C2211yescharacteristic
18C2×#3775C2211yescharacteristic
19C2×#3775C2211yescharacteristic
20C2×#3775C2211yescharacteristic
21#64086C2211yescharacteristic
22C3×D3×C22⋊C4—21no—
23C3×#877—21no—
24D3×#217—21no—
25#63957C2211yescharacteristic
26#63957C2211yescharacteristic
27#63955—21no—
28C4×#627C2212yescomplemented
29#63902C2212yes—
30C4×#625C2212yes—
31#63879—22no—
32#63838C2212yescomplemented
33#63837—22no—
34#63777C2212yescomplemented
35C4×#622C2212yescomplemented
36#63743C2212yescomplemented
37#63742C2212yescomplemented
38#63740C2212yescomplemented
39#63740C2212yescomplemented
40#63739C2212yes—
41#63739C2212yes—
42#5516—61no—
43#5486—61no—
44C23×C3×D3—21no—
45C22×C3⋊Dic3C2311yescharacteristic
46C22×C3×Dic3—21no—
47C2×C3×C4×D3—22no—
48C2×#627—21no—
49C2×#627—22no—
50C2×#627C2×C414yescomplemented
51C2×#627C2311yescharacteristic
52C2×#627C2311yescharacteristic
53C2×#625—21no—
54C2×#625—22no—
55C2×#625C2×C414yes—
56C2×#625C2311yescharacteristic
57C2×#625C2311yescharacteristic
58C2×D3×Dic3—22no—
59#3792—22no—
60C2×#622C2×C414yescomplemented
61C2×#622C2312yes—
62C2×#622C2311yescharacteristic
63C2×#622C2311yescharacteristic
64#3775C2×C414yescomplemented
65#3775C2×C414yescomplemented
66#3775C2×C414yescomplemented
67#3775C2×C414yescomplemented
68C32×C22⋊C4D411yescharacteristic
69#3757D411yescharacteristic
70#3750D412yes—
71C4×C3⋊Dic3C2312yes—
72C3×#217—21no—
73C3×#217—21no—
74C3×(C2×D3)⋊C4—22no—
75C3×Dic3⋊C4—22no—
76C3×C4×Dic3—22no—
77#3724C2312yes—
78#3724C2312yes—
79Dic3⋊Dic3—22no—
80(C2×D3)⋊Dic3—22no—
81Dic32—21no—
82Dic32—22no—
83Dic32—21no—
84#2949—91nomaximal, Sylow
85C22×#67—61no—
86C22×Dic6—61no—
87C3×#117—61no—
88C2×C3×C22⋊C4—61no—
89C2×#217—61no—
90C4×#67—62no—
91C4×#67—62no—
92#926—61no—
93#887—62no—
94#887—62no—
95#67⋊C4—62no—
96#67⋊C4—62no—
97D3×C22⋊C4—21no—
98D3×C22⋊C4—61no—
99#877—21no—
100#877—61no—
101#877—61no—
102#877—61no—
103#877—61no—
104#877—61no—
105C4×Dic6—62no—
106C4×Dic6—62no—
107C23×C32C2×D411yescharacteristic
108C22×C3×D3—21no—
109C22×C3×D3—21no—
110C22×C3×D3—24no—
111C22×C3×D3—82no—
112C2×C32×C4C2×D412yes—
113C2×C3⋊Dic3C22×C412yes—
114C2×C3⋊Dic3C2×D412yes—
115C2×C3⋊Dic3C2×D411yescharacteristic
116C2×C3⋊Dic3#4112yes—
117C2×C3⋊Dic3C2411yescharacteristic
118C2×C3×Dic3—24no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—22no—
123C3×C4×D3—82no—
124#627—24no—
125#627—21no—
126#627—21no—
127#627C22×C412yes—
128#627C22×C412yes—
129#625—24no—
130#625—21no—
131#625—21no—
132#625C22×C412yes—
133#625C22×C412yes—
134D3×Dic3—82no—
135#622—22no—
136#622C22×C412yes—
137#622C22×C412yes—
138C22×SD16—91no—
139#519—91no—
140#518—91no—
141#440—92no—
142#440—92no—
143C4×SD16—92no—
144C4×SD16—92no—
145#427—91no—
146#419—91no—
147#418—91no—
148#405—91no—
149C24×C3—61no—
150C23×D3—21no—
151C22×C3×C4—62no—
152C22×C3×C4—61no—
153C2×#67—61no—
154C2×#67—61no—
155C2×#67—64no—
156C2×#67—61no—
157C2×#67—61no—
158C2×#67—64no—
159C22×Dic3—21no—
160C22×Dic3—61no—
161C22×Dic3—61no—
162C22×Dic3—62no—
163C2×C4×D3—22no—
164C2×C4×D3—62no—
165C2×Dic6—61no—
166C2×Dic6—61no—
167C2×Dic6—64no—
168C2×Dic6—61no—
169C2×Dic6—61no—
170C2×Dic6—64no—
171C3×C4⋊C4—62no—
172C3×C22⋊C4—21no—
173C3×C22⋊C4—21no—
174C3×C22⋊C4—62no—
175C3×C22⋊C4—61no—
176C3×C22⋊C4—61no—
177C3×C42—62no—
178#217—21no—
179#217—21no—
180#217—61no—
181#217—61no—
182#217—62no—
183(C2×D3)⋊C4—22no—
184(C2×D3)⋊C4—62no—
185C4⋊Dic3—62no—
186Dic3⋊C4—22no—
187Dic3⋊C4—62no—
188Dic3⋊C4—62no—
189Dic3⋊C4—62no—
190Dic3⋊C4—62no—
191Dic3⋊C4—62no—
192C4×Dic3—22no—
193C4×Dic3—62no—
194C4×Dic3—62no—
195C4×Dic3—62no—
196C4×Dic3—62no—
197C4×Dic3—62no—
198C4×Dic3—62no—
199C22×C32—22no—
200C22×C32C4×D412yes—
201C22×C32C22×D411yescharacteristic
202C2×C3×D3—22no—
203C2×C3×D3—22no—
204C2×C3×D3—42no—
205C2×C3×D3—42no—
206C2×C3×D3—84no—
207C32×C4—22no—
208C3⋊Dic3—22no—
209C3⋊Dic3C4×D412yes—
210C3⋊Dic3C23×C411yescharacteristic
211C3⋊Dic3C2×#4111yescharacteristic
212C3×Dic3—22no—
213C3×Dic3—22no—
214C3×Dic3—42no—
215C3×Dic3—42no—
216C22×Q8—91no—
217C22×D4—91no—
218C2×SD16—91no—
219C2×SD16—91no—
220C2×SD16—91no—
221C2×SD16—91no—
222C2×SD16—98no—
223C2×M16—91no—
224C22×C8—91no—
225C4×Q8—92no—
226C4×Q8—92no—
227C4×Q8—182no—
228C4×D4—92no—
229C4×D4—92no—
230C4×D4—182no—
231#117—61no—
232#117—91no—
233#117—91no—
234#117—91no—
235#117—181no—
236C2×C22⋊C4—61no—
237C2×C22⋊C4—181no—
238#107—92no—
239#106—92no—
240#103—92no—
241#103—92no—
242#102—92no—
243#102—92no—
244#97—92no—
245C4×C8—92no—
246C23×C3—21no—
247C23×C3—21no—
248C23×C3—61no—
249C23×C3—61no—
250C23×C3—64no—
251C23×C3—242no—
252C22×D3—21no—
253C22×D3—21no—
254C22×D3—24no—
255C22×D3—82no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—61no—
259C2×C3×C4—61no—
260C2×C3×C4—64no—
261C2×C3×C4—62no—
262C2×C3×C4—62no—
263C2×C3×C4—242no—
264#67—62no—
265#67—62no—
266#67—64no—
267#67—64no—
268#67—62no—
269#67—62no—
270C2×Dic3—21no—
271C2×Dic3—21no—
272C2×Dic3—24no—
273C2×Dic3—22no—
274C2×Dic3—22no—
275C2×Dic3—62no—
276C2×Dic3—62no—
277C2×Dic3—61no—
278C2×Dic3—61no—
279C2×Dic3—62no—
280C2×Dic3—62no—
281C2×Dic3—61no—
282C2×Dic3—61no—
283C2×Dic3—62no—
284C2×Dic3—62no—
285C2×Dic3—242no—
286C4×D3—82no—
287C4×D3—242no—
288Dic6—62no—
289Dic6—62no—
290Dic6—64no—
291Dic6—64no—
292Dic6—62no—
293Dic6—62no—
294C2×C32—22no—
295C2×C32C2×C4×D411yescharacteristic
296C2×C32#57712yes—
297C3×D3—42no—
298C3×D3—42no—
299C24—61no—
300C2×Q8—91no—
301C2×Q8—91no—
302C2×Q8—94no—
303C2×Q8—181no—
304C2×Q8—182no—
305C2×D4—91no—
306C2×D4—91no—
307C2×D4—94no—
308C2×D4—181no—
309C2×D4—182no—
310C22×C4—61no—
311C22×C4—62no—
312C22×C4—91no—
313C22×C4—182no—
314SD16—94no—
315SD16—94no—
316SD16—94no—
317SD16—94no—
318M16—182no—
319C2×C8—91no—
320C2×C8—91no—
321C2×C8—94no—
322C2×C8—92no—
323C4⋊C4—62no—
324C4⋊C4—92no—
325C4⋊C4—92no—
326C4⋊C4—92no—
327C4⋊C4—182no—
328C22⋊C4—61no—
329C22⋊C4—61no—
330C22⋊C4—62no—
331C22⋊C4—91no—
332C22⋊C4—182no—
333C22⋊C4GO+(4,𝔽2)11yescharacteristic
334C42—62no—
335C42—92no—
336C42—181no—
337C42—181no—
338C42—182no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—22no—
342C22×C3—22no—
343C22×C3—42no—
344C22×C3—42no—
345C22×C3—62no—
346C22×C3—62no—
347C22×C3—122no—
348C22×C3—122no—
349C22×C3—244no—
350C2×D3—22no—
351C2×D3—22no—
352C2×D3—42no—
353C2×D3—42no—
354C2×D3—84no—
355C3×C4—42no—
356C3×C4—42no—
357C3×C4—62no—
358C3×C4—62no—
359C3×C4—122no—
360C3×C4—122no—
361Dic3—22no—
362Dic3—22no—
363Dic3—42no—
364Dic3—42no—
365Dic3—62no—
366Dic3—61no—
367Dic3—61no—
368Dic3—62no—
369Dic3—61no—
370Dic3—61no—
371Dic3—122no—
372Dic3—122no—
373C32#294911yescharacteristic, complemented, Sylow
374C23—61no—
375C23—61no—
376C23—64no—
377C23—242no—
378C23C2×GO+(4,𝔽2)11yescharacteristic
379Q8—92no—
380Q8—92no—
381Q8—181no—
382Q8—181no—
383Q8—184no—
384D4—92no—
385D4—92no—
386D4—181no—
387D4—181no—
388D4—184no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4—64no—
392C2×C4—62no—
393C2×C4—62no—
394C2×C4—91no—
395C2×C4—91no—
396C2×C4—92no—
397C2×C4—92no—
398C2×C4—92no—
399C2×C4—242no—
400C2×C4—722no—
401C2×C4C2×GO+(4,𝔽2)12yes—
402C8—92no—
403C8—92no—
404C8—182no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—22no—
408C2×C3—22no—
409C2×C3—42no—
410C2×C3—42no—
411C2×C3—122no—
412C2×C3—122no—
413D3—42no—
414D3—42no—
415C22—22no—
416C22—62no—
417C22—62no—
418C22—122no—
419C22—122no—
420C22—244no—
421C22C4×GO+(4,𝔽2)12yes—
422C22C22×GO+(4,𝔽2)11yescharacteristic
423C4—22no—
424C4—62no—
425C4—62no—
426C4—91no—
427C4—91no—
428C4—92no—
429C4—122no—
430C4—122no—
431C4—182no—
432C3—21no—
433C3—21no—
434C2—22no—
435C2—122no—
436C2—122no—
437C2C2×C4×GO+(4,𝔽2)11yescharacteristic
438C2#1059651512yes—
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC32×C22⋊C4D4
socleC22×C32C22×D4
prime radicalC22×#625C22
cosocleC2×C3⋊Dic3C24
hypercenterC22⋊C4GO+(4,𝔽2)
hypocenterC32#2949
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10594245C2semidirect
4. #10593738C2semidirect
5. #10593511C2semidirect
6. #10593503C2semidirect
8. #10593433C2semidirect
9. #10593432C2semidirect
10. #10593431C2semidirect
11. C4×#3775C2semidirect
16. C2×#3775C4semidirect
28. C4×#627C22semidirect
32. #63838C22semidirect
34. #63777C22semidirect
35. C4×#622C22semidirect
36. #63743C22semidirect
37. #63742C22semidirect
38. #63740C22semidirect
39. #63740C22semidirect
50. C2×#627C2×C4semidirect
60. C2×#622C2×C4semidirect
64. #3775C2×C4semidirect
65. #3775C2×C4semidirect
66. #3775C2×C4semidirect
67. #3775C2×C4semidirect
373. C32#2949semidirect

Maximal subgroups

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

subgroupindex
C22×#37752
#105942452
#105941812
#105937382
#105935112
#105935032
#105934932
#105934332
#105934322
#105934312
C4×#37752
#29499