Finite Group Databasebeta

← #11794258

Subgroups — #11794258

Order 1152.

547 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595051C211yesmaximal, characteristic
2C3×#4935C211yesmaximal, characteristic
3#10591139C211yesmaximal, characteristic
4#10591130C211yesmaximal, characteristic
5#10589389C211yesmaximal, characteristic
6C3×#4523C211yesmaximal, characteristic
7#10589167C211yesmaximal, characteristic
8#69573—31nomaximal
9#68735—31nomaximal
10C2×C32×C42C2211yescharacteristic
11#64135C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4⋊Dic3—22no—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18#63964—22no—
19#63919—21no—
20#63918—21no—
21#63872—21no—
22#63869—21no—
23#63576—21no—
24#63575—21no—
25#63574—21no—
26#63573—21no—
27#5519—31no—
28#5500—31no—
29C3×#384—31no—
30#5121—31no—
31#4995—31no—
32#4964—31no—
33#4964—31no—
34#4935D311yescharacteristic
35C3×#339—31no—
36#4554—31no—
37#4530—31no—
38#4523—31no—
39#4523—31no—
40#4523—61no—
41#4523D311yescharacteristic
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3×Dic3—21no—
45C22×C3×Dic3D412yes—
46C2×#627—22no—
47C32×C42—21no—
48C32×C42Q812yescomplemented
49#3757—21no—
50C4⋊(C3⋊Dic3)D411yescharacteristic
51C4⋊(C3⋊Dic3)D411yescharacteristic
52C4×C3⋊Dic3—21no—
53#3748—21no—
54#3748Q812yescomplemented
55C2×C3⋊(C3⋊C8)—21no—
56C3×#217—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—44no—
62C3×C4⋊Dic3D411yescharacteristic
63C3×C4⋊Dic3D411yescharacteristic
64C3×C4×Dic3—21no—
65C3×#208—21no—
66C3×#208Q812yescomplemented
67C2×C3×C3⋊C8—21no—
68#3724—22no—
69Dic3⋊Dic3—22no—
70Dic3⋊Dic3—22no—
71#2060—91noSylow
72C2×C3×M16—31no—
73C3×#117—31no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4—62no—
77C2×C3×C42—21no—
78C2×C3×C42C2×D311yescharacteristic
79C2×C3×C42C2×D311yescharacteristic
80#926—31no—
81#926—31no—
82#926—61no—
83#926C2×D311yescharacteristic
84C2×C4⋊Dic3—22no—
85C2×C4⋊Dic3C2×D311yescharacteristic
86C2×C4⋊Dic3C2×D311yescharacteristic
87#924—62no—
88C2×#208—31no—
89C2×#208—31no—
90C2×#208—61no—
91C2×#208C2×D311yescharacteristic
92#890—61no—
93#890—61no—
94#890—61no—
95#888—61no—
96#888—61no—
97#888—61no—
98#878—62no—
99#870—61no—
100#869—61no—
101#818—61no—
102#817—61no—
103#808—61no—
104#808—61no—
105#808—61no—
106#807—61no—
107#807—61no—
108#807—61no—
109C23×C32C2×D411yescharacteristic
110C2×C32×C4—22no—
111C2×C32×C4—22no—
112C2×C32×C4—22no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×Q811yescharacteristic
116C2×C32×C4C2×Q811yescharacteristic
117C2×C32×C4C2×Q811yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—22no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—42no—
125C2×C3×Dic3—42no—
126C2×C3×Dic3—41no—
127#627—82no—
128C3⋊(C3⋊C8)—22no—
129C3×C3⋊C8—22no—
130#544—91no—
131#428—91no—
132#428—91no—
133#384—31no—
134#343—91no—
135#339—31no—
136#339—91no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—32no—
141C22×C3×C4—41no—
142C22×C3×C4—61no—
143C22×C3×C4C22×D311yescharacteristic
144C22×C3×C4C22×D311yescharacteristic
145C22×Dic3—21no—
146C22×Dic3#6712yes—
147C2×Dic6—62no—
148C2×Dic6—62no—
149C3×M16—32no—
150C3×M16—61no—
151C2×C3×C8—61no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—31no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4—124no—
159C3×C22⋊C4—61no—
160C3×C42—21no—
161C3×C42—21no—
162C3×C42—22no—
163C3×C42—41no—
164C3×C42—61no—
165C3×C42Dic612yescomplemented
166C3×C42Dic612yescomplemented
167#217—21no—
168#217—61no—
169#217—61no—
170#217—121no—
171C4⋊Dic3—21no—
172C4⋊Dic3—21no—
173C4⋊Dic3—21no—
174C4⋊Dic3—21no—
175C4⋊Dic3—31no—
176C4⋊Dic3—31no—
177C4⋊Dic3—31no—
178C4⋊Dic3—31no—
179C4⋊Dic3—44no—
180C4⋊Dic3—61no—
181C4⋊Dic3—61no—
182C4⋊Dic3—62no—
183C4⋊Dic3—62no—
184C4⋊Dic3D1211yescharacteristic
185C4⋊Dic3D1211yescharacteristic
186Dic3⋊C4—62no—
187Dic3⋊C4—62no—
188Dic3⋊C4—62no—
189Dic3⋊C4—62no—
190C4×Dic3—21no—
191C4×Dic3—61no—
192C4×Dic3—61no—
193C4×Dic3—121no—
194#208—21no—
195#208—32no—
196#208—32no—
197#208—62no—
198#208—61no—
199#208—61no—
200#208—121no—
201#208Dic612yescomplemented
202C2×C3⋊C8—21no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—121no—
206C22×C32—21no—
207C22×C32—21no—
208C22×C32#12011yescharacteristic
209C22×C32C22⋊Q811yescharacteristic
210C22×C32C4⋊Q811yescharacteristic
211C32×C4—24no—
212C32×C4C22⋊Q811yescharacteristic
213C32×C4C22⋊Q811yescharacteristic
214C32×C4C4⋊Q811yescharacteristic
215C32×C4C4⋊Q811yescharacteristic
216C3⋊Dic3—41no—
217C3⋊Dic3—41no—
218C3×Dic3—41no—
219C3×Dic3—42no—
220C3×Dic3—41no—
221C3×Dic3—81no—
222C2×M16—31no—
223C2×M16—91no—
224C4⋊Q8—181no—
225C4⋊Q8—181no—
226#125—181no—
227#125—181no—
228C22⋊Q8—182no—
229#117—31no—
230#117—91no—
231C2×C4⋊C4—31no—
232C2×C4⋊C4—31no—
233C2×C4⋊C4—62no—
234C2×C42D3211yescharacteristic
235#107—181no—
236#107—181no—
237#106—181no—
238#106—181no—
239C23×C3—21no—
240C23×C3D3×D411yescharacteristic
241C23×C3C2×#6711yescharacteristic
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—42no—
255C2×C3×C4—42no—
256C2×C3×C4—42no—
257C2×C3×C4—62no—
258C2×C3×C4—61no—
259C2×C3×C4—61no—
260C2×C3×C4—122no—
261C2×C3×C4—122no—
262C2×C3×C4—121no—
263C2×C3×C4C2×Dic611yescharacteristic
264C2×C3×C4C2×Dic611yescharacteristic
265C2×C3×C4C2×Dic611yescharacteristic
266C2×C3×C4C2×D1211yescharacteristic
267C2×C3×C4#23511yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4#23711yescharacteristic
272C2×C3×C4D3×Q811yescharacteristic
273C2×C3×C4D3×Q811yescharacteristic
274C2×C3×C4D3×Q811yescharacteristic
275C2×Dic3—21no—
276C2×Dic3—21no—
277C2×Dic3—22no—
278C2×Dic3—42no—
279C2×Dic3—42no—
280C2×Dic3—41no—
281C2×Dic3—61no—
282C2×Dic3—61no—
283C2×Dic3—61no—
284C2×Dic3—61no—
285C2×Dic3—121no—
286C2×Dic3—121no—
287Dic6—242no—
288Dic6—242no—
289C3×C8—62no—
290C3⋊C8—22no—
291C3⋊C8—62no—
292C3⋊C8—62no—
293C3⋊C8—122no—
294C2×C32—21no—
295C2×C32—21no—
296C2×C32#39511yescharacteristic
297C2×C32#45311yescharacteristic
298C2×C32#45611yescharacteristic
299C2×Q8—182no—
300C22×C4—21no—
301C22×C4—32no—
302C22×C4—61no—
303C22×C4C2×D3211yescharacteristic
304M16—32no—
305M16—61no—
306M16—92no—
307M16—181no—
308C2×C8—61no—
309C2×C8—181no—
310C4⋊C4—31no—
311C4⋊C4—31no—
312C4⋊C4—61no—
313C4⋊C4—61no—
314C4⋊C4—61no—
315C4⋊C4—61no—
316C4⋊C4—91no—
317C4⋊C4—91no—
318C4⋊C4—124no—
319C4⋊C4—182no—
320C4⋊C4—182no—
321C4⋊C4—182no—
322C22⋊C4—61no—
323C22⋊C4—181no—
324C42—21no—
325C42—61no—
326C42—181no—
327C42#62712yescomplemented
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3#87811yescharacteristic
338C22×C3#88211yescharacteristic
339C22×C3#88811yescharacteristic
340C22×C3#92411yescharacteristic
341C22×C3#93711yescharacteristic
342C22×C3#94411yescharacteristic
343C3×C4—24no—
344C3×C4—24no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—44no—
350C3×C4—121no—
351C3×C4—122no—
352C3×C4—121no—
353C3×C4—241no—
354C3×C4#86911yescharacteristic
355C3×C4#87811yescharacteristic
356C3×C4#88811yescharacteristic
357C3×C4#88811yescharacteristic
358C3×C4#88811yescharacteristic
359C3×C4#89611yescharacteristic
360C3×C4#89611yescharacteristic
361C3×C4#89711yescharacteristic
362Dic3—42no—
363Dic3—41no—
364Dic3—41no—
365Dic3—81no—
366Dic3—121no—
367Dic3—121no—
368Dic3—121no—
369Dic3—121no—
370Dic3—241no—
371Dic3—241no—
372C32#206011yescharacteristic, complemented, Sylow
373C23D3×#6711yescharacteristic
374Q8—722no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—61no—
379C2×C4—61no—
380C2×C4—62no—
381C2×C4—122no—
382C2×C4—122no—
383C2×C4—121no—
384C2×C4—181no—
385C2×C4—181no—
386C2×C4D3×Dic611yescharacteristic
387C2×C4#379711yescharacteristic
388C2×C4D3×D1211yescharacteristic
389C2×C4#380211yescharacteristic
390C2×C4#380411yescharacteristic
391C2×C4C2×#62711yescharacteristic
392C8—62no—
393C8—182no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—41no—
402C2×C3—41no—
403C2×C3#465611yescharacteristic
404C2×C3#482211yescharacteristic
405C2×C3#482611yescharacteristic
406C2×C3#497911yescharacteristic
407C2×C3#507711yescharacteristic
408C2×C3#509511yescharacteristic
409C22—21no—
410C22—21no—
411C22#6383911yescharacteristic
412C22#6392211yescharacteristic
413C22#6396411yescharacteristic
414C4—24no—
415C4—122no—
416C4—121no—
417C4—121no—
418C4—241no—
419C4—361no—
420C4—361no—
421C4#6389511yescharacteristic
422C4#6389911yescharacteristic
423C4#6391811yescharacteristic
424C4#6391911yescharacteristic
425C3—21no—
426C3#6873511yescharacteristic, complemented
427C3#6957311yescharacteristic, complemented
428C2—21no—
429C2—21no—
430C2#1059039511yescharacteristic
431C2#1059039911yescharacteristic
432C2#1059133811yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC2×C42D32
hypocenterC32#2060
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
48. C32×C42Q8semidirect
54. #3748Q8semidirect
66. C3×#208Q8semidirect
165. C3×C42Dic6semidirect
166. C3×C42Dic6semidirect
201. #208Dic6semidirect
327. C42#627semidirect
372. C32#2060semidirect
426. C3#68735semidirect
427. C3#69573semidirect

Maximal subgroups

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

subgroupindex
#105950512
C3×#49352
#105911392
#105911302
#105893892
C3×#45232
#105891672
#695733
#687353