Finite Group Databasebeta

← #11865636

Subgroups — #11865636

Order 1152.

1105 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
2C2×#63944C212yesmaximal
3C4×#3797C211yesmaximal, characteristic
4C3×#5090C212yesmaximal, complemented
5#10591580C214yesmaximal, complemented
6#10591552C212yesmaximal
7#10590385C212yesmaximal, complemented
8#10590331C211yesmaximal, characteristic
9D3×#462—32nomaximal
10C2×Q8×C3⋊D3C2212yes—
11C2×#3797C2211yescharacteristic
12C32×C4⋊Q8C2211yescharacteristic
13#64153C2212yes—
14C4⋊C4×C3⋊D3—21no—
15C4⋊C4×C3⋊D3—21no—
16#64097—21no—
17#64097—21no—
18C42×C3⋊D3C2211yescharacteristic
19#64078C2211yescharacteristic
20C2×C3×#216C2214yes—
21C3×C4×Dic6C2212yes—
22#63944—28no—
23C4×#627—21no—
24#63900C2211yescharacteristic
25#63883—21no—
26C4×#624—21no—
27#63843C2212yes—
28#63838—21no—
29C2×#3719C2214yes—
30C2×#3710C2212yes—
31C3×#835C2214yes—
32C3×C4⋊(C3⋊C8)C2212yes—
33#63572C2212yes—
34#63567C2214yes—
35C2×D3×Q16—34no—
36D3×C4⋊Q8—32no—
37D3×C4⋊Q8—61no—
38C4×D3×Q8—32no—
39C3×#462—32no—
40#5182—34no—
41#5090D312yescomplemented
42#5031—32no—
43#4849—32no—
44D3×C4⋊C8—32no—
45D3×#103—34no—
46#4795—34no—
47C2×C32×Q8C2312yes—
48Q8×C3⋊D3—24no—
49Q8×C3⋊D3—24no—
50C2×C4×C3⋊D3—22no—
51C2×C4×C3⋊D3D411yescharacteristic
52C2×C4×C3⋊D3D411yescharacteristic
53C2×C4×C3⋊D3C2311yescharacteristic
54C2×#634—22no—
55C2×#634C2312yes—
56C2×C3×Dic6C2312yes—
57C2×#627—21no—
58C2×#624—21no—
59C2×#624—21no—
60#3797—22no—
61#3797D414yes—
62C32×C4⋊C4—21no—
63C32×C4⋊C4—21no—
64C32×C42C2311yescharacteristic
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67#3750—22no—
68#3750—22no—
69C4×C3⋊Dic3D411yescharacteristic
70C4×C3⋊Dic3D411yescharacteristic
71C4×C3⋊Dic3C2311yescharacteristic
72C3×#216—28no—
73C3×C4⋊Dic3C2312yes—
74C3×Dic3⋊C4—22no—
75C3×C4×Dic3—22no—
76C2×C3×C3⋊C8C2314yes—
77#3724—21no—
78Dic3⋊Dic3—22no—
79Dic32—22no—
80#3719—28no—
81#3710—24no—
82C2×#462—91noSylow
83C2×D3×Q8—34no—
84C2×D3×Q8—32no—
85C2×D3×Q8—62no—
86C2×C3×Q16—34no—
87C3×C4⋊Q8—21no—
88C3×C4⋊Q8C2×D312yes—
89C3×C4×Q8—32no—
90Q8×Dic3—32no—
91#944—34no—
92#944—62no—
93C2×#216—34no—
94C2×#216C2×D314yes—
95D3×Q16—616no—
96C2×Dic12—34no—
97C2×D3×C8—34no—
98D3×C4⋊C4—32no—
99D3×C4⋊C4—62no—
100D3×C4⋊C4—62no—
101D3×C4⋊C4—62no—
102D3×C4⋊C4—62no—
103D3×C4⋊C4—62no—
104#888—62no—
105#888—62no—
106#888—62no—
107#888—62no—
108#887—32no—
109#887—62no—
110C42×D3—32no—
111C42×D3—61no—
112C42×D3—62no—
113#869—32no—
114#869—61no—
115C4×Dic6—62no—
116C4×Dic6C2×D312yes—
117C3×C4⋊C8—32no—
118C3×#103—34no—
119#835C2×D314yes—
120#816—34no—
121Dic3⋊C8—34no—
122#810—34no—
123C4⋊(C3⋊C8)C2×D312yes—
124C22×C3⋊D3C2×D411yescharacteristic
125C32×Q8—22no—
126C32×Q8—22no—
127C2×C32×C4—22no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2411yescharacteristic
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3C2×D411yescharacteristic
133C2×C3⋊Dic3C2×D411yescharacteristic
134C2×C3⋊Dic3C2×D411yescharacteristic
135C4×C3⋊D3—22no—
136C4×C3⋊D3—44no—
137C4×C3⋊D3Q1614yescomplemented
138C4×C3⋊D3C2×D412yes—
139C4×C3⋊D3#4112yes—
140#634—22no—
141#634—22no—
142#634—44no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C3×Dic6—22no—
146C3×Dic6C2×D414yes—
147#627—24no—
148#624—24no—
149#624—42no—
150C3×C3⋊C8—24no—
151C22×Q16—92no—
152C2×C4⋊Q8—91no—
153C2×C4×Q8—91no—
154#462—32no—
155#462—94no—
156#462—92no—
157C2×C4⋊C8—91no—
158C2×#103—92no—
159C2×C3×Q8—22no—
160C2×C3×Q8—32no—
161C2×C3×Q8C22×D314yes—
162D3×Q8—38no—
163D3×Q8—64no—
164D3×Q8—68no—
165D3×Q8—68no—
166D3×Q8—124no—
167D3×Q8—124no—
168C2×C4×D3—32no—
169C2×C4×D3—32no—
170C2×C4×D3—32no—
171C2×C4×D3—61no—
172C2×C4×D3—61no—
173C2×C4×D3—61no—
174C2×C4×D3—62no—
175C2×C4×D3—62no—
176C2×C4×D3—64no—
177C2×C4×D3—64no—
178C2×Dic6—34no—
179C2×Dic6—62no—
180C2×Dic6—62no—
181C2×Dic6—64no—
182C2×Dic6—64no—
183C2×Dic6C22×D312yes—
184C3×Q16—68no—
185C2×C3×C8—34no—
186C3×C4⋊C4—22no—
187C3×C4⋊C4—22no—
188C3×C4⋊C4—22no—
189C3×C4⋊C4—22no—
190C3×C4⋊C4—32no—
191C3×C4⋊C4—62no—
192C3×C42—21no—
193C3×C42—62no—
194C3×C42C22×D312yes—
195#216—28no—
196#216—68no—
197C4⋊Dic3—62no—
198C4⋊Dic3—62no—
199C4⋊Dic3—62no—
200C4⋊Dic3—62no—
201C4⋊Dic3—62no—
202C4⋊Dic3C22×D312yes—
203Dic3⋊C4—22no—
204Dic3⋊C4—62no—
205Dic3⋊C4—62no—
206Dic3⋊C4—64no—
207Dic3⋊C4—64no—
208Dic3⋊C4—64no—
209Dic3⋊C4—64no—
210C4×Dic3—22no—
211C4×Dic3—32no—
212C4×Dic3—32no—
213C4×Dic3—32no—
214C4×Dic3—61no—
215C4×Dic3—61no—
216C4×Dic3—61no—
217C4×Dic3—62no—
218C4×Dic3—62no—
219C2×C3⋊C8C22×D314yes—
220Dic12—68no—
221D3×C8—68no—
222C22×C32C22×D411yescharacteristic
223C2×C3⋊D3#12112yes—
224C2×C3⋊D3C2×Q1612yes—
225C2×C3⋊D3#13712yes—
226C32×C4—21no—
227C32×C4—42no—
228C32×C4C2×Q1612yescomplemented
229C32×C4C22×D411yescharacteristic
230C32×C4C2×#4111yescharacteristic
231C3⋊Dic3—21no—
232C3⋊Dic3—42no—
233C3⋊Dic3#12112yes—
234C3⋊Dic3C2×Q1612yescomplemented
235C3×Dic3—24no—
236C3×Dic3—42no—
237C22×Q8—91no—
238C22×Q8—92no—
239C2×Q16—34no—
240C2×Q16—94no—
241C2×Q16—188no—
242C22×C8—92no—
243C4⋊Q8—92no—
244C4⋊Q8—91no—
245C4⋊Q8—181no—
246C4⋊Q8—181no—
247C4⋊Q8D3211yescharacteristic
248C4×Q8—32no—
249C4×Q8—92no—
250C4×Q8—181no—
251C4×Q8—181no—
252C2×C4⋊C4—91no—
253C2×C4⋊C4—181no—
254C2×C4⋊C4—181no—
255C2×C4⋊C4—181no—
256C2×C42—91no—
257C2×C42—181no—
258C4⋊C8—32no—
259C4⋊C8—92no—
260#103—34no—
261#103—94no—
262C22×D3—32no—
263C22×D3—61no—
264C3×Q8—24no—
265C3×Q8—24no—
266C3×Q8—34no—
267C3×Q8—42no—
268C3×Q8—42no—
269C3×Q8—62no—
270C2×C3×C4—24no—
271C2×C3×C4—24no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—62no—
276C2×C3×C4—62no—
277C2×C3×C4D3×D412yes—
278C2×C3×C4D3×D412yes—
279C2×C3×C4C23×D312yes—
280C2×Dic3—22no—
281C2×Dic3—22no—
282C2×Dic3—32no—
283C2×Dic3—32no—
284C2×Dic3—32no—
285C2×Dic3—61no—
286C2×Dic3—61no—
287C2×Dic3—61no—
288C2×Dic3—64no—
289C2×Dic3—64no—
290C4×D3—38no—
291C4×D3—34no—
292C4×D3—34no—
293C4×D3—64no—
294C4×D3—62no—
295C4×D3—62no—
296C4×D3—68no—
297C4×D3—64no—
298C4×D3—64no—
299C4×D3—124no—
300C4×D3—128no—
301C4×D3—128no—
302Dic6—22no—
303Dic6—68no—
304Dic6—64no—
305Dic6—64no—
306Dic6—122no—
307Dic6—122no—
308Dic6—128no—
309Dic6—128no—
310Dic6D3×D414yes—
311C3×C8—64no—
312C3⋊C8—24no—
313C2×C32C2×#12111yescharacteristic
314C2×C32C22×Q1611yescharacteristic
315C2×C32C2×#13711yescharacteristic
316C3⋊D3#46214yescomplemented
317C2×Q8—32no—
318C2×Q8—94no—
319C2×Q8—92no—
320C2×Q8—182no—
321C2×Q8—181no—
322C2×Q8—182no—
323C2×Q8—184no—
324C2×Q8—184no—
325C2×Q8C2×D3212yes—
326C22×C4—91no—
327C22×C4—91no—
328C22×C4—91no—
329C22×C4—182no—
330C22×C4—181no—
331C22×C4—181no—
332Q16—68no—
333Q16—188no—
334C2×C8—34no—
335C2×C8—184no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—32no—
339C4⋊C4—62no—
340C4⋊C4—182no—
341C4⋊C4—182no—
342C4⋊C4—181no—
343C4⋊C4—182no—
344C4⋊C4—181no—
345C4⋊C4—181no—
346C42—62no—
347C42—91no—
348C42—91no—
349C42—91no—
350C42—182no—
351C42C2×D3211yescharacteristic
352C22×C3—21no—
353C22×C3C2×D3×D412yes—
354C2×D3—34no—
355C2×D3—34no—
356C2×D3—34no—
357C2×D3—62no—
358C2×D3—62no—
359C2×D3—62no—
360C3×C4—22no—
361C3×C4—22no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—22no—
365C3×C4—44no—
366C3×C4—44no—
367C3×C4—64no—
368C3×C4—122no—
369C3×C4D3×Q1614yescomplemented
370C3×C4C2×D3×D412yes—
371C3×C4D3×#4112yes—
372Dic3—24no—
373Dic3—34no—
374Dic3—34no—
375Dic3—42no—
376Dic3—62no—
377Dic3—62no—
378Dic3—62no—
379Dic3—62no—
380Dic3—124no—
381Dic3—124no—
382C32C2×#46211yescharacteristic, complemented, Sylow
383C23—91no—
384Q8—22no—
385Q8—22no—
386Q8—34no—
387Q8—62no—
388Q8—184no—
389Q8—182no—
390Q8—182no—
391Q8—364no—
392C2×C4—22no—
393C2×C4—62no—
394C2×C4—62no—
395C2×C4—91no—
396C2×C4—91no—
397C2×C4—92no—
398C2×C4—92no—
399C2×C4—94no—
400C2×C4—91no—
401C2×C4—182no—
402C2×C4—184no—
403C2×C4—182no—
404C2×C4—364no—
405C2×C4—362no—
406C2×C4#381111yescharacteristic
407C2×C4#381111yescharacteristic
408C2×C4C22×D3211yescharacteristic
409C8—64no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3D3×#12112yes—
414C2×C3C2×D3×Q1612yes—
415C2×C3D3×#13712yes—
416D3—38no—
417D3—64no—
418C22—92no—
419C22—92no—
420C22—92no—
421C22C2×#381111yescharacteristic
422C4—21no—
423C4—42no—
424C4—64no—
425C4—92no—
426C4—92no—
427C4—122no—
428C4—181no—
429C4—362no—
430C4#6394412yescomplemented
431C4D32×D411yescharacteristic
432C4#6431211yescharacteristic
433C3—21no—
434C3D3×#46212yescomplemented
435C2—94no—
436C2#1059528211yescharacteristic
437C2#1059532211yescharacteristic
438C2C2×#6394411yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4⋊Q8D32
hypocenterC32C2×#462
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. C3×#5090C2semidirect
5. #10591580C2semidirect
7. #10590385C2semidirect
41. #5090D3semidirect
137. C4×C3⋊D3Q16semidirect
228. C32×C4C2×Q16semidirect
234. C3⋊Dic3C2×Q16semidirect
316. C3⋊D3#462semidirect
369. C3×C4D3×Q16semidirect
382. C32C2×#462semidirect
430. C4#63944semidirect
434. C3D3×#462semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
C2×#639442
C4×#37972
C3×#50902
#105915802
#105915522
#105903852
#105903312
D3×#4623