Finite Group Databasebeta

← #11775123

Subgroups — #11775123

Order 1152.

833 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 833 conjugacy classes of subgroups — too many to draw. Only its 96 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
1#10596077C211yesmaximal, characteristic
2#10591370C211yesmaximal, characteristic, complemented
3#10591159C211yesmaximal, characteristic, complemented
4C3×#4537C212yesmaximal, complemented
5#10589154C212yesmaximal, complemented
6#68302—32nomaximal
7C2×#3830C411yescharacteristic, complemented
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×#624—21no—
10C32×#121C2211yescharacteristic
11#64147C411yescharacteristic, complemented
12#64146—21no—
13D4×C3⋊Dic3—21no—
14#64133C2211yescharacteristic
15#64106C411yescharacteristic, complemented
16#64101C411yescharacteristic, complemented
17#64092—21no—
18#64090—21no—
19C2×#3712—21no—
20C3×C3⋊#95C2212yes—
21C3×#830C2212yes—
22#63579—21no—
23#63557—21no—
24#5606—32no—
25#5606—61no—
26#4726—32no—
27D3×#95—32no—
28C3×#327—32no—
29#4537D312yescomplemented
30#4467—32no—
31#4452—32no—
32C23×C3⋊D3D411yescharacteristic
33C2×C32×D4—21no—
34C2×C32×D4C2×C411yescharacteristic, complemented
35C22×C32×C4C2311yescharacteristic
36C2×#638—21no—
37C2×#638—21no—
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3D411yescharacteristic
40#3830—42no—
41C2×C4×C3⋊D3—42no—
42C2×C4×C3⋊D3C2×C411yescharacteristic
43C2×C4×C3⋊D3C2×C411yescharacteristic
44C2×C4×C3⋊D3D411yescharacteristic
45C2×C4×C3⋊D3D411yescharacteristic
46C2×#634C2×C411yescharacteristic, complemented
47C22×C3×Dic3—22no—
48C2×#624—24no—
49C2×#624—42no—
50C2×#624—42no—
51C32×C4⋊C4C2×C411yescharacteristic, complemented
52C32×C22⋊C4—21no—
53#3757—21no—
54#3757—21no—
55#3752—21no—
56#3752—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)C2×C411yescharacteristic, complemented
59#3750—21no—
60C4×C3⋊Dic3—21no—
61C2×C3×C3⋊C8—22no—
62#3712—42no—
63#1504—91noSylow
64C2×#237—32no—
65C2×#237—61no—
66C22×C4×D3—32no—
67C22×C4×D3—61no—
68C22×C4×D3—62no—
69C3×#121—21no—
70C3×#121C2×D312yes—
71#938—32no—
72#938—61no—
73#937—62no—
74#937—62no—
75D4×Dic3—62no—
76D4×Dic3—62no—
77#924—32no—
78#924—61no—
79C2×ΓL(1,𝔽25)—62no—
80#897—32no—
81#897—61no—
82#892—32no—
83#892—61no—
84#883—62no—
85#883—62no—
86#67⋊C4—62no—
87#67⋊C4—62no—
88C3×C22⋊C8—32no—
89C3×#95—32no—
90C3⋊#95—62no—
91C3⋊#95C2×D312yes—
92#830C2×D312yes—
93(C2×D3)⋊C8—62no—
94C23×C32—21no—
95C23×C32C2×D411yescharacteristic
96C22×C3⋊D3—21no—
97C22×C3⋊D3—21no—
98C22×C3⋊D3—22no—
99C22×C3⋊D3—22no—
100C22×C3⋊D3C22⋊C411yescharacteristic
101C22×C3⋊D3C22⋊C411yescharacteristic
102C32×D4—41no—
103C32×D4—41no—
104C32×D4—41no—
105C2×C32×C4—21no—
106C2×C32×C4—41no—
107C2×C32×C4C22×C411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109#638—42no—
110#638—42no—
111C2×C3⋊Dic3—21no—
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3—41no—
114C2×C3⋊Dic3—42no—
115C2×C3⋊Dic3C22⋊C411yescharacteristic
116C2×C3⋊Dic3C22⋊C411yescharacteristic
117C4×C3⋊D3—22no—
118C4×C3⋊D3—22no—
119C4×C3⋊D3—41no—
120C4×C3⋊D3—41no—
121#634—41no—
122C2×C3×Dic3—24no—
123C2×C3×Dic3—42no—
124C2×C3×Dic3—42no—
125#624—48no—
126C3×C3⋊C8—42no—
127#525—91no—
128#407—91no—
129C2×#95—91no—
130#328—92no—
131#327—32no—
132C23×D3—32no—
133C23×D3—61no—
134C2×C3×D4—22no—
135C2×C3×D4—22no—
136C2×C3×D4—21no—
137C2×C3×D4C4×D312yescomplemented
138C22×C3×C4—21no—
139C22×C3×C4—62no—
140C22×C3×C4C22×D312yes—
141C2×#67—62no—
142C2×#67—62no—
143C2×#67—62no—
144C2×#67—62no—
145C22×Dic3—22no—
146C22×Dic3—32no—
147C22×Dic3—61no—
148C22×Dic3—62no—
149C22×Dic3—62no—
150#237—124no—
151#237—124no—
152C2×C4×D3—32no—
153C2×C4×D3—32no—
154C2×C4×D3—32no—
155C2×C4×D3—32no—
156C2×C4×D3—61no—
157C2×C4×D3—61no—
158C2×C4×D3—61no—
159C2×C4×D3—61no—
160C2×C4×D3—68no—
161C2×C4×D3—124no—
162C2×C4×D3—124no—
163C2×C4×D3—124no—
164C2×C4×D3—124no—
165C2×Dic6—32no—
166C2×Dic6—61no—
167C2×C3×C8—62no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4C4×D312yescomplemented
170C3×C22⋊C4—22no—
171C3×C22⋊C4—22no—
172#217—62no—
173#217—62no—
174#217—62no—
175#217—62no—
176(C2×D3)⋊C4—62no—
177(C2×D3)⋊C4—62no—
178(C2×D3)⋊C4—62no—
179(C2×D3)⋊C4—62no—
180C4⋊Dic3—32no—
181C4⋊Dic3—61no—
182C4⋊Dic3—62no—
183C4⋊Dic3—62no—
184Dic3⋊C4—62no—
185Dic3⋊C4—62no—
186C4×Dic3—62no—
187C4×Dic3—62no—
188C2×C3⋊C8—22no—
189ΓL(1,𝔽25)—124no—
190C22×C32—21no—
191C22×C32—21no—
192C22×C32—41no—
193C22×C32—41no—
194C22×C32—41no—
195C22×C32C2×C22⋊C411yescharacteristic
196C22×C32AGL(1,ℤ/8)11yescharacteristic
197C22×C32#13711yescharacteristic
198C2×C3⋊D3—24no—
199C2×C3⋊D3—24no—
200C2×C3⋊D3—21no—
201C2×C3⋊D3—21no—
202C2×C3⋊D3—21no—
203C2×C3⋊D3—21no—
204C2×C3⋊D3#9912yes—
205C2×C3⋊D3#10412yes—
206C32×C4—21no—
207C32×C4—21no—
208C32×C4—41no—
209C3⋊Dic3—21no—
210C3⋊Dic3—21no—
211C3⋊Dic3—41no—
212C3⋊Dic3—41no—
213C3×Dic3—44no—
214C2×#41—91no—
215C23×C4—91no—
216C23×C4—181no—
217C2×M16—181no—
218#123—181no—
219C22⋊Q8—91no—
220C22⋊Q8—91no—
221#121—91no—
222#121D3211yescharacteristic
223#120—181no—
224C4×D4—181no—
225C4×D4—181no—
226#117—91no—
227C22⋊C8—32no—
228C22⋊C8—181no—
229#95—32no—
230#95—181no—
231C23×C3—22no—
232C23×C3—22no—
233C23×C3—21no—
234C23×C3D3×D412yes—
235C22×D3—32no—
236C22×D3—32no—
237C22×D3—61no—
238C22×D3—61no—
239C22×D3—64no—
240C22×D3—64no—
241C22×D3—62no—
242C22×D3—62no—
243C22×D3—122no—
244C22×D3—122no—
245C22×D3—121no—
246C22×D3—121no—
247C3×D4—42no—
248C3×D4—42no—
249C3×D4—42no—
250C3×D4—42no—
251C3×D4—42no—
252C3×D4—42no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—42no—
258C2×C3×C4—42no—
259C2×C3×C4—64no—
260C2×C3×C4—122no—
261C2×C3×C4—122no—
262C2×C3×C4C2×C4×D312yes—
263C2×C3×C4D3×D412yes—
264#67—124no—
265#67—124no—
266#67—124no—
267#67—124no—
268C2×Dic3—24no—
269C2×Dic3—32no—
270C2×Dic3—32no—
271C2×Dic3—42no—
272C2×Dic3—42no—
273C2×Dic3—61no—
274C2×Dic3—61no—
275C2×Dic3—62no—
276C2×Dic3—62no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279C2×Dic3—122no—
280C2×Dic3—122no—
281C2×Dic3—124no—
282C2×Dic3—124no—
283C4×D3—64no—
284C4×D3—64no—
285C4×D3—64no—
286C4×D3—122no—
287C4×D3—1216no—
288C4×D3—122no—
289C4×D3—122no—
290C4×D3—122no—
291C4×D3—122no—
292Dic6—122no—
293Dic6—122no—
294C3×C8—122no—
295C3⋊C8—42no—
296C2×C32—21no—
297C2×C32—21no—
298C2×C32—81no—
299C2×C32C2×#9911yescharacteristic
300C2×C32#41711yescharacteristic
301C2×C32C2×#10411yescharacteristic
302C3⋊D3—22no—
303C3⋊D3—22no—
304C24—91no—
305#41—362no—
306C2×Q8—91no—
307C2×D4—21no—
308C2×D4—181no—
309C2×D4—181no—
310C2×D4#62411yescharacteristic, complemented
311C22×C4—62no—
312C22×C4—91no—
313C22×C4—91no—
314C22×C4—91no—
315C22×C4—91no—
316C22×C4—91no—
317C22×C4—184no—
318C22×C4—181no—
319C22×C4—362no—
320C22×C4—362no—
321C22×C4—362no—
322C22×C4C2×D3211yescharacteristic
323M16—362no—
324C2×C8—62no—
325C4⋊C4—91no—
326C4⋊C4—181no—
327C4⋊C4—181no—
328C4⋊C4#62411yescharacteristic, complemented
329C22⋊C4—21no—
330C22⋊C4—181no—
331C22⋊C4—181no—
332C22⋊C4—181no—
333C22⋊C4—181no—
334C42—181no—
335C22×C3—22no—
336C22×C3—22no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3—42no—
343C22×C3—42no—
344C22×C3—42no—
345C22×C3—42no—
346C22×C3—42no—
347C22×C3—42no—
348C22×C3D3×C22⋊C412yes—
349C22×C3#91112yes—
350C22×C3#91512yes—
351C2×D3—34no—
352C2×D3—34no—
353C2×D3—62no—
354C2×D3—62no—
355C2×D3—68no—
356C2×D3—68no—
357C2×D3—62no—
358C2×D3—62no—
359C2×D3—62no—
360C2×D3—62no—
361C2×D3—121no—
362C2×D3—121no—
363C2×D3—121no—
364C2×D3—121no—
365C2×D3—124no—
366C2×D3—124no—
367C3×C4—22no—
368C3×C4—22no—
369C3×C4—22no—
370C3×C4—41no—
371C3×C4—42no—
372C3×C4—42no—
373C3×C4—124no—
374Dic3—44no—
375Dic3—62no—
376Dic3—62no—
377Dic3—62no—
378Dic3—121no—
379Dic3—122no—
380Dic3—122no—
381Dic3—122no—
382Dic3—122no—
383C32#150411yescharacteristic, complemented, Sylow
384C23—21no—
385C23—91no—
386C23—91no—
387C23—182no—
388C23—182no—
389C23—181no—
390C23—181no—
391C23#381111yescharacteristic
392Q8—361no—
393D4—41no—
394D4—41no—
395D4—41no—
396D4—362no—
397D4—362no—
398C2×C4—21no—
399C2×C4—41no—
400C2×C4—64no—
401C2×C4—91no—
402C2×C4—91no—
403C2×C4—122no—
404C2×C4—122no—
405C2×C4—182no—
406C2×C4—182no—
407C2×C4—181no—
408C2×C4—181no—
409C2×C4—361no—
410C2×C4—361no—
411C2×C4—368no—
412C2×C4—361no—
413C2×C4—362no—
414C2×C4C2×#62411yescharacteristic
415C2×C4#381111yescharacteristic
416C8—122no—
417C2×C3—22no—
418C2×C3—22no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—41no—
423C2×C3—41no—
424C2×C3—82no—
425C2×C3—82no—
426C2×C3D3×#9912yes—
427C2×C3#477112yes—
428C2×C3D3×#10412yes—
429D3—64no—
430D3—64no—
431D3—122no—
432D3—122no—
433C22—21no—
434C22—21no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—92no—
439C22—92no—
440C22—184no—
441C22—184no—
442C22—181no—
443C22—181no—
444C22—181no—
445C22—181no—
446C22#6392711yescharacteristic
447C22#6393111yescharacteristic
448C22#6397411yescharacteristic
449C4—21no—
450C4—21no—
451C4—41no—
452C4—124no—
453C4—181no—
454C4—181no—
455C4—361no—
456C4—361no—
457C3—21no—
458C3#6830212yescomplemented
459C2—21no—
460C2—21no—
461C2—81no—
462C2—182no—
463C2—182no—
464C2#1059141811yescharacteristic
465C2#1059152711yescharacteristic
466C2#1059167111yescharacteristic
subgroupG/H
centerC22#63974
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32C2×C22⋊C4
prime radical#10596077C2
cosocleC22×C32×C4C23
hypercenter#121D32
hypocenterC32#1504
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #10591370C2semidirect
3. #10591159C2semidirect
4. C3×#4537C2semidirect
5. #10589154C2semidirect
7. C2×#3830C4semidirect
11. #64147C4semidirect
15. #64106C4semidirect
16. #64101C4semidirect
29. #4537D3semidirect
34. C2×C32×D4C2×C4semidirect
46. C2×#634C2×C4semidirect
51. C32×C4⋊C4C2×C4semidirect
58. C4⋊(C3⋊Dic3)C2×C4semidirect
137. C2×C3×D4C4×D3semidirect
169. C3×C4⋊C4C4×D3semidirect
310. C2×D4#624semidirect
328. C4⋊C4#624semidirect
383. C32#1504semidirect
458. C3#68302semidirect

Maximal subgroups

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

subgroupindex
#105960772
#105913702
#105911592
C3×#45372
#105891542
#683023