Finite Group Databasebeta

← #11868822

Subgroups — #11868822

Order 1152.

987 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C3⋊Dic3C211yesmaximal, characteristic
2C2×#63919C211yesmaximal, characteristic, complemented
3C3×#5232C212yesmaximal
4#10591631C212yesmaximal, complemented
5#10591630C212yesmaximal, complemented
6#10591495C212yesmaximal, complemented
7#10591494C212yesmaximal, complemented
8#10591130C212yesmaximal, complemented
9#10591120C211yesmaximal, characteristic, complemented
10#78870—32nomaximal
11C2×C32×#41C2211yescharacteristic
12C22×#627—21no—
13Q8×C3⋊Dic3C2211yescharacteristic
14Q8×C3⋊Dic3C2211yescharacteristic
15D4×C3⋊Dic3—21no—
16D4×C3⋊Dic3—21no—
17D4×C3⋊Dic3C2211yescharacteristic
18D4×C3⋊Dic3C2211yescharacteristic
19#64135—21no—
20#64135C2211yescharacteristic
21C2×C4×C3⋊Dic3—21no—
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×#208C2212yes—
25C2×#3724—21no—
26#63919—21no—
27#63919—21no—
28#63919C2212yes—
29#63919C2212yes—
30C3×#835C2214yes—
31C3×#832C2214yes—
32#63575C2214yes—
33#63573C2214yes—
34#63572C2212yes—
35#63572C2212yes—
36Dic3×#41—32no—
37Dic3×#41—61no—
38C2×#888—32no—
39C3×#417—32no—
40#5232D312yes—
41#5121—32no—
42#5118—32no—
43#4964—32no—
44#4793—34no—
45#4791—34no—
46#4761—34no—
47#4759—34no—
48C32×#41—22no—
49C32×#41Q814yescomplemented
50C2×C32×Q8C2311yescharacteristic
51C2×C32×D4—21no—
52C2×C32×D4C2311yescharacteristic
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C22×C3⋊Dic3—21no—
57C22×C3⋊Dic3D411yescharacteristic
58C22×C3⋊Dic3D411yescharacteristic
59C22×C3×Dic3—22no—
60C2×#627—22no—
61C2×#627—22no—
62C2×#627—44no—
63#3757—21no—
64#3757—21no—
65#3757—21no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)C2311yescharacteristic
69C4⋊(C3⋊Dic3)C2311yescharacteristic
70C4×C3⋊Dic3—21no—
71C4×C3⋊Dic3—21no—
72C4×C3⋊Dic3—21no—
73C4×C3⋊Dic3D411yescharacteristic
74C4×C3⋊Dic3D411yescharacteristic
75C4×C3⋊Dic3C2311yescharacteristic
76C4×C3⋊Dic3C2311yescharacteristic
77C3×C4⋊Dic3—22no—
78C3×C4⋊Dic3C2314yes—
79C3×#208—24no—
80C2×C3×C3⋊C8C2314yes—
81#3724—22no—
82#3724—22no—
83#3079—91noSylow
84C2×C3×#41—21no—
85C2×C3×#41C2×D312yes—
86C22×Dic6—62no—
87C2×C3×M16—32no—
88C2×C3×C4⋊C4—32no—
89Q8×Dic3—32no—
90Q8×Dic3—32no—
91Q8×Dic3—61no—
92Q8×Dic3—61no—
93D4×Dic3—32no—
94D4×Dic3—32no—
95D4×Dic3—61no—
96D4×Dic3—61no—
97D4×Dic3—62no—
98D4×Dic3—62no—
99D4×Dic3—62no—
100D4×Dic3—62no—
101#926—32no—
102#926—61no—
103#926—62no—
104#926—62no—
105C2×C4⋊Dic3C2×D312yes—
106C2×Dic3⋊C4—62no—
107C2×C4×Dic3—32no—
108C2×C4×Dic3—61no—
109C2×C4×Dic3—62no—
110C2×C4×Dic3—62no—
111C2×#208C2×D312yes—
112#888—34no—
113#888—34no—
114#888—62no—
115#888—62no—
116C3×#103—34no—
117C3×#102—34no—
118#835C2×D314yes—
119#832C2×D314yes—
120#818—34no—
121#817—34no—
122Dic3⋊C8—34no—
123Dic3⋊C8—34no—
124#808—34no—
125#807—34no—
126C23×C32—21no—
127C23×C32C2×D411yescharacteristic
128C32×Q8—21no—
129C32×Q8C2×Q812yescomplemented
130C32×D4—24no—
131C32×D4—21no—
132C32×D4C2×Q812yescomplemented
133C2×C32×C4—21no—
134C2×C32×C4—24no—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×Q812yes—
137C2×C32×C4#4112yes—
138C2×C32×C4C2411yescharacteristic
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—42no—
144C2×C3⋊Dic3—42no—
145C2×C3⋊Dic3C2×D411yescharacteristic
146C2×C3⋊Dic3C2×D411yescharacteristic
147C2×C3⋊Dic3C2×D411yescharacteristic
148C2×C3⋊Dic3C2×D411yescharacteristic
149C2×C3×Dic3—24no—
150C2×C3×Dic3—44no—
151#627—44no—
152#627—44no—
153C3×C3⋊C8—24no—
154C2×C4⋊Q8—91no—
155C4×#41—91no—
156#477—92no—
157#476—92no—
158#475—92no—
159#474—92no—
160#428—92no—
161#423—91no—
162#417—32no—
163C3×#41—24no—
164C3×#41—24no—
165C3×#41—24no—
166C3×#41Dic618yescomplemented
167C2×C3×Q8—21no—
168C2×C3×Q8C22×D312yes—
169C2×C3×D4—22no—
170C2×C3×D4—22no—
171C2×C3×D4—21no—
172C2×C3×D4C22×D312yes—
173C22×C3×C4—22no—
174C22×C3×C4—22no—
175C22×C3×C4—21no—
176C22×C3×C4—62no—
177C22×C3×C4C22×D312yes—
178C22×Dic3—22no—
179C22×Dic3—32no—
180C22×Dic3—32no—
181C22×Dic3—61no—
182C22×Dic3—61no—
183C22×Dic3—62no—
184C22×Dic3—62no—
185C22×Dic3—62no—
186C22×Dic3—62no—
187C2×Dic6—64no—
188C2×Dic6—64no—
189C2×Dic6—128no—
190C3×M16—64no—
191C2×C3×C8—34no—
192C3×C4⋊C4—34no—
193C3×C4⋊C4—62no—
194#217—62no—
195#217—62no—
196#217—62no—
197#217—62no—
198#217—62no—
199#217—62no—
200C4⋊Dic3—22no—
201C4⋊Dic3—32no—
202C4⋊Dic3—32no—
203C4⋊Dic3—61no—
204C4⋊Dic3—61no—
205C4⋊Dic3—62no—
206C4⋊Dic3—62no—
207C4⋊Dic3—62no—
208C4⋊Dic3—62no—
209C4⋊Dic3C22×D314yes—
210Dic3⋊C4—64no—
211Dic3⋊C4—64no—
212C4×Dic3—32no—
213C4×Dic3—32no—
214C4×Dic3—32no—
215C4×Dic3—32no—
216C4×Dic3—61no—
217C4×Dic3—61no—
218C4×Dic3—61no—
219C4×Dic3—61no—
220C4×Dic3—62no—
221C4×Dic3—62no—
222C4×Dic3—62no—
223C4×Dic3—62no—
224C4×Dic3—62no—
225C4×Dic3—62no—
226#208—24no—
227C2×C3⋊C8C22×D314yes—
228C22×C32—22no—
229C22×C32—21no—
230C22×C32—21no—
231C22×C32—41no—
232C22×C32—41no—
233C22×C32C22⋊Q812yes—
234C22×C32C22×D411yescharacteristic
235C32×C4—22no—
236C32×C4C22⋊Q812yes—
237C32×C4C22×Q811yescharacteristic
238C32×C4C2×#4111yescharacteristic
239C3⋊Dic3—21no—
240C3⋊Dic3—21no—
241C3⋊Dic3—41no—
242C3⋊Dic3—41no—
243C3⋊Dic3AGL(1,ℤ/8)12yes—
244C3⋊Dic3#13712yes—
245C3×Dic3—44no—
246C2×#41D3211yescharacteristic
247C22×Q8—181no—
248C2×M16—32no—
249C4⋊Q8—92no—
250C4⋊Q8—92no—
251C4⋊Q8—181no—
252C4⋊Q8—181no—
253C4×Q8—91no—
254C4×Q8—91no—
255C4×D4—91no—
256C4×D4—91no—
257C4×D4—181no—
258C4×D4—181no—
259#117—91no—
260#117—181no—
261C2×C4⋊C4—32no—
262C2×C4⋊C4—181no—
263C2×C42—91no—
264C2×C42—181no—
265#107—94no—
266#106—94no—
267C4⋊C8—92no—
268C4⋊C8—92no—
269#103—34no—
270#102—34no—
271C23×C3—22no—
272C23×C3—22no—
273C23×C3—21no—
274C23×C3D3×D412yes—
275C3×Q8—22no—
276C3×Q8—22no—
277C3×Q8—22no—
278C3×Q8C2×Dic614yescomplemented
279C3×D4—28no—
280C3×D4—22no—
281C3×D4—28no—
282C3×D4—22no—
283C3×D4—22no—
284C3×D4C2×Dic614yescomplemented
285C2×C3×C4—22no—
286C2×C3×C4—28no—
287C2×C3×C4—22no—
288C2×C3×C4—28no—
289C2×C3×C4—21no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—21no—
293C2×C3×C4—64no—
294C2×C3×C4—124no—
295C2×C3×C4C2×Dic614yes—
296C2×C3×C4D3×D412yes—
297C2×C3×C4#23714yes—
298C2×C3×C4C23×D312yes—
299C2×Dic3—24no—
300C2×Dic3—32no—
301C2×Dic3—32no—
302C2×Dic3—32no—
303C2×Dic3—32no—
304C2×Dic3—44no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308C2×Dic3—61no—
309C2×Dic3—64no—
310C2×Dic3—64no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—122no—
316C2×Dic3—122no—
317C2×Dic3—124no—
318C2×Dic3—124no—
319C2×Dic3—124no—
320C2×Dic3—124no—
321Dic6—128no—
322Dic6—128no—
323C3×C8—64no—
324C3⋊C8—24no—
325C2×C32—22no—
326C2×C32—42no—
327C2×C32C2×C22⋊Q811yescharacteristic
328C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
329C2×C32C2×#13711yescharacteristic
330#41—22no—
331#41#62714yescomplemented
332C2×Q8—182no—
333C2×Q8—182no—
334C2×Q8—364no—
335C2×Q8C2×D3211yescharacteristic
336C2×D4—21no—
337C2×D4C2×D3211yescharacteristic
338C22×C4—21no—
339C22×C4—62no—
340C22×C4—91no—
341C22×C4—91no—
342C22×C4—181no—
343C22×C4—181no—
344C22×C4C2×D3211yescharacteristic
345M16—64no—
346C2×C8—34no—
347C4⋊C4—34no—
348C4⋊C4—62no—
349C4⋊C4—91no—
350C4⋊C4—91no—
351C4⋊C4—181no—
352C4⋊C4—181no—
353C4⋊C4—182no—
354C4⋊C4—182no—
355C22⋊C4—181no—
356C22⋊C4—181no—
357C22⋊C4—181no—
358C42—91no—
359C42—91no—
360C42—91no—
361C42—91no—
362C42—181no—
363C42—181no—
364C42—181no—
365C22×C3—22no—
366C22×C3—22no—
367C22×C3—24no—
368C22×C3—24no—
369C22×C3—21no—
370C22×C3—22no—
371C22×C3—41no—
372C22×C3—41no—
373C22×C3—42no—
374C22×C3—42no—
375C22×C3—42no—
376C22×C3—42no—
377C22×C3#87814yes—
378C22×C3C2×D3×D412yes—
379C3×C4—24no—
380C3×C4—24no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—22no—
384C3×C4—124no—
385C3×C4#87814yes—
386C3×C4C22×Dic612yes—
387C3×C4C2×#23712yes—
388Dic3—34no—
389Dic3—34no—
390Dic3—44no—
391Dic3—62no—
392Dic3—62no—
393Dic3—62no—
394Dic3—62no—
395Dic3—121no—
396Dic3—121no—
397Dic3—122no—
398Dic3—122no—
399Dic3—122no—
400Dic3—122no—
401C32#307911yescharacteristic, complemented, Sylow
402C23—21no—
403C23#381111yescharacteristic
404Q8—21no—
405Q8—364no—
406Q8—364no—
407Q8C2×#62712yescomplemented
408D4—24no—
409D4—21no—
410D4C2×#62712yescomplemented
411C2×C4—21no—
412C2×C4—24no—
413C2×C4—64no—
414C2×C4—91no—
415C2×C4—91no—
416C2×C4—91no—
417C2×C4—91no—
418C2×C4—124no—
419C2×C4—182no—
420C2×C4—182no—
421C2×C4—181no—
422C2×C4—181no—
423C2×C4—362no—
424C2×C4—362no—
425C2×C4#380512yes—
426C2×C4C2×#62712yes—
427C2×C4#381111yescharacteristic
428C2×C4C22×D3211yescharacteristic
429C8—64no—
430C2×C3—24no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—42no—
435C2×C3—44no—
436C2×C3—44no—
437C2×C3C2×#87812yes—
438C2×C3D3×AGL(1,ℤ/8)12yes—
439C2×C3D3×#13712yes—
440C22—21no—
441C22—21no—
442C22—22no—
443C22—41no—
444C22—41no—
445C22#6398212yes—
446C22C2×#381111yescharacteristic
447C4—22no—
448C4—92no—
449C4—92no—
450C4—124no—
451C4—181no—
452C4—181no—
453C4—361no—
454C4—361no—
455C4#6398212yes—
456C4C2×#380511yescharacteristic
457C4C22×#62711yescharacteristic
458C3—21no—
459C3#7887012yescomplemented
460C2—22no—
461C2—42no—
462C2#1059545811yescharacteristic
463C2#1059546811yescharacteristic
464C2C2×#6398211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3079
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#63919C2semidirect
4. #10591631C2semidirect
5. #10591630C2semidirect
6. #10591495C2semidirect
7. #10591494C2semidirect
8. #10591130C2semidirect
9. #10591120C2semidirect
49. C32×#41Q8semidirect
129. C32×Q8C2×Q8semidirect
132. C32×D4C2×Q8semidirect
166. C3×#41Dic6semidirect
278. C3×Q8C2×Dic6semidirect
284. C3×D4C2×Dic6semidirect
331. #41#627semidirect
401. C32#3079semidirect
407. Q8C2×#627semidirect
410. D4C2×#627semidirect
459. C3#78870semidirect

Maximal subgroups

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

subgroupindex
#41×C3⋊Dic32
C2×#639192
C3×#52322
#105916312
#105916302
#105914952
#105914942
#105911302
#105911202
#788703