Finite Group Databasebeta

← #11794253

Subgroups — #11794253

Order 1152.

551 conjugacy classes of subgroups.

The subgroup lattice has 435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595051C211yesmaximal, characteristic
2#10592663C211yesmaximal, characteristic
3C3×#4975C211yesmaximal, characteristic
4C3×#4964C211yesmaximal, characteristic
5#10589167C211yesmaximal, characteristic
6#10589162C211yesmaximal, characteristic
7#10589161C211yesmaximal, characteristic
8#70666—31nomaximal
9#69573—31nomaximal
10C2×C32×C4⋊C4C2211yescharacteristic
11#64135C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×Dic3⋊C4—22no—
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18#63964—22no—
19#63919—21no—
20#63918—21no—
21#63872—21no—
22#63869—21no—
23#63635—21no—
24#63634—21no—
25C3×#808—21no—
26C3×#807—21no—
27#5519—31no—
28#5500—31no—
29C3×#428—31no—
30C3×#384—31no—
31#4975D311yescharacteristic
32#4964—31no—
33#4964—31no—
34#4964—61no—
35#4964D311yescharacteristic
36#4555—31no—
37#4554—31no—
38#4532—31no—
39#4530—31no—
40#4523—31no—
41#4523—31no—
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3×Dic3—21no—
45C22×C3×Dic3D412yes—
46C2×#627—22no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
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⋊Dic3D411yescharacteristic
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—44no—
62C3×C4×Dic3—21no—
63C3×C4×Dic3—21no—
64C3×C4×Dic3Q812yescomplemented
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—21no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4—62no—
77C2×C3×C4⋊C4C2×D311yescharacteristic
78C2×C3×C4⋊C4C2×D311yescharacteristic
79C2×C3×C42—31no—
80#926—31no—
81#926—31no—
82#926—61no—
83#926C2×D311yescharacteristic
84C2×C4⋊Dic3C2×D311yescharacteristic
85#924—62no—
86C2×Dic3⋊C4—22no—
87C2×C4×Dic3C2×D311yescharacteristic
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—
101C3×#107—61no—
102C3×#106—61no—
103#808—21no—
104#808—61no—
105#808—61no—
106#808—62no—
107#807—21no—
108#807—61no—
109#807—61no—
110#807—62no—
111C23×C32C2×D411yescharacteristic
112C2×C32×C4—41no—
113C2×C32×C4—42no—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×Q811yescharacteristic
117C2×C32×C4C2×Q811yescharacteristic
118C2×C32×C4C2×Q811yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—21no—
122C2×C3×Dic3—22no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—42no—
129#627—82no—
130C3⋊(C3⋊C8)—22no—
131C3×C3⋊C8—22no—
132#544—91no—
133#428—31no—
134#428—91no—
135#384—31no—
136#343—91no—
137#339—91no—
138#339—91no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—32no—
143C22×C3×C4—41no—
144C22×C3×C4—61no—
145C22×C3×C4C22×D311yescharacteristic
146C22×C3×C4C22×D311yescharacteristic
147C22×Dic3—21no—
148C22×Dic3#6712yes—
149C2×Dic6—62no—
150C2×Dic6—62no—
151C3×M16—32no—
152C3×M16—61no—
153C2×C3×C8—61no—
154C3×C4⋊C4—22no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4—31no—
160C3×C4⋊C4—31no—
161C3×C4⋊C4—41no—
162C3×C4⋊C4—61no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4—124no—
165C3×C22⋊C4—61no—
166C3×C42—32no—
167C3×C42—61no—
168C3×C42—61no—
169#217—21no—
170#217—61no—
171#217—61no—
172#217—121no—
173C4⋊Dic3—21no—
174C4⋊Dic3—21no—
175C4⋊Dic3—31no—
176C4⋊Dic3—31no—
177C4⋊Dic3—31no—
178C4⋊Dic3—31no—
179C4⋊Dic3—61no—
180C4⋊Dic3—61no—
181C4⋊Dic3—62no—
182C4⋊Dic3—62no—
183C4⋊Dic3#6711yescharacteristic
184C4⋊Dic3#6711yescharacteristic
185Dic3⋊C4—44no—
186Dic3⋊C4—62no—
187Dic3⋊C4—62no—
188Dic3⋊C4—62no—
189Dic3⋊C4—62no—
190C4×Dic3—21no—
191C4×Dic3—21no—
192C4×Dic3—61no—
193C4×Dic3—61no—
194C4×Dic3—121no—
195C4×Dic3Dic612yescomplemented
196#208—21no—
197#208—32no—
198#208—32no—
199#208—62no—
200#208—62no—
201#208—61no—
202#208—61no—
203#208Dic612yescomplemented
204C2×C3⋊C8—21no—
205C2×C3⋊C8—62no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—61no—
208C22×C32—21no—
209C22×C32—21no—
210C22×C32#12011yescharacteristic
211C22×C32C22⋊Q811yescharacteristic
212C22×C32C4⋊Q811yescharacteristic
213C32×C4—81no—
214C32×C4C22⋊Q811yescharacteristic
215C32×C4C22⋊Q811yescharacteristic
216C32×C4C4⋊Q811yescharacteristic
217C32×C4C4⋊Q811yescharacteristic
218C3⋊Dic3—41no—
219C3⋊Dic3—41no—
220C3×Dic3—24no—
221C3×Dic3—41no—
222C3×Dic3—42no—
223C3×Dic3—41no—
224C2×M16—31no—
225C2×M16—91no—
226C4⋊Q8—181no—
227C4⋊Q8—181no—
228#125—181no—
229#125—181no—
230C22⋊Q8—182no—
231#117—31no—
232#117—91no—
233C2×C4⋊C4—31no—
234C2×C4⋊C4—62no—
235C2×C4⋊C4D3211yescharacteristic
236C2×C42—31no—
237#107—61no—
238#107—181no—
239#106—61no—
240#106—181no—
241C23×C3—21no—
242C23×C3D3×D411yescharacteristic
243C23×C3C2×#6711yescharacteristic
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—42no—
251C2×C3×C4—42no—
252C2×C3×C4—42no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—62no—
256C2×C3×C4—62no—
257C2×C3×C4—62no—
258C2×C3×C4—61no—
259C2×C3×C4—62no—
260C2×C3×C4—61no—
261C2×C3×C4—82no—
262C2×C3×C4—122no—
263C2×C3×C4C2×Dic611yescharacteristic
264C2×C3×C4C2×Dic611yescharacteristic
265C2×C3×C4#23511yescharacteristic
266C2×C3×C4#23511yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4D3×Q811yescharacteristic
271C2×C3×C4D3×Q811yescharacteristic
272C2×C3×C4D3×Q811yescharacteristic
273C2×C3×C4D3×Q811yescharacteristic
274C2×C3×C4C2×#6711yescharacteristic
275C2×Dic3—22no—
276C2×Dic3—22no—
277C2×Dic3—22no—
278C2×Dic3—21no—
279C2×Dic3—21no—
280C2×Dic3—22no—
281C2×Dic3—42no—
282C2×Dic3—61no—
283C2×Dic3—61no—
284C2×Dic3—61no—
285C2×Dic3—61no—
286C2×Dic3—121no—
287C2×Dic3—121no—
288Dic6—242no—
289Dic6—242no—
290C3×C8—62no—
291C3⋊C8—22no—
292C3⋊C8—64no—
293C3⋊C8—62no—
294C3⋊C8—62no—
295C2×C32—21no—
296C2×C32—21no—
297C2×C32#39511yescharacteristic
298C2×C32#45311yescharacteristic
299C2×C32#45611yescharacteristic
300C2×Q8—182no—
301C22×C4—21no—
302C22×C4—32no—
303C22×C4—61no—
304C22×C4C2×D3211yescharacteristic
305M16—32no—
306M16—61no—
307M16—92no—
308M16—181no—
309C2×C8—61no—
310C2×C8—181no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—31no—
314C4⋊C4—31no—
315C4⋊C4—61no—
316C4⋊C4—61no—
317C4⋊C4—91no—
318C4⋊C4—91no—
319C4⋊C4—124no—
320C4⋊C4—182no—
321C4⋊C4—182no—
322C4⋊C4—182no—
323C22⋊C4—61no—
324C22⋊C4—181no—
325C42—32no—
326C42—61no—
327C42—61no—
328C42—181no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—41no—
337C22×C3—41no—
338C22×C3#88811yescharacteristic
339C22×C3#89611yescharacteristic
340C22×C3#92411yescharacteristic
341C22×C3#93711yescharacteristic
342C22×C3#93711yescharacteristic
343C22×C3#94411yescharacteristic
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—64no—
349C3×C4—82no—
350C3×C4—81no—
351C3×C4—81no—
352C3×C4—122no—
353C3×C4—121no—
354C3×C4—121no—
355C3×C4#88811yescharacteristic
356C3×C4#88811yescharacteristic
357C3×C4#88811yescharacteristic
358C3×C4#89611yescharacteristic
359C3×C4#89611yescharacteristic
360C3×C4#89611yescharacteristic
361C3×C4#92411yescharacteristic
362C3×C4#94411yescharacteristic
363Dic3—24no—
364Dic3—41no—
365Dic3—41no—
366Dic3—42no—
367Dic3—121no—
368Dic3—121no—
369Dic3—121no—
370Dic3—121no—
371Dic3—241no—
372Dic3—241no—
373C32#206011yescharacteristic, complemented, Sylow
374C23D3×#6711yescharacteristic
375Q8—722no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—62no—
379C2×C4—62no—
380C2×C4—62no—
381C2×C4—61no—
382C2×C4—61no—
383C2×C4—62no—
384C2×C4—122no—
385C2×C4—181no—
386C2×C4—181no—
387C2×C4D3×Dic611yescharacteristic
388C2×C4D3×Dic611yescharacteristic
389C2×C4#379711yescharacteristic
390C2×C4#379811yescharacteristic
391C2×C4D3×#6711yescharacteristic
392C2×C4#381111yescharacteristic
393C8—62no—
394C8—182no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—41no—
403C2×C3—41no—
404C2×C3#497911yescharacteristic
405C2×C3#497911yescharacteristic
406C2×C3#507711yescharacteristic
407C2×C3#509511yescharacteristic
408C2×C3#519811yescharacteristic
409C2×C3#520511yescharacteristic
410C22—21no—
411C22—21no—
412C22#6383911yescharacteristic
413C22#6385111yescharacteristic
414C22#6398311yescharacteristic
415C4—64no—
416C4—81no—
417C4—122no—
418C4—121no—
419C4—121no—
420C4—361no—
421C4—361no—
422C4#6383911yescharacteristic
423C4#6384011yescharacteristic
424C4#6385111yescharacteristic
425C4#6386511yescharacteristic
426C3—21no—
427C3#6957311yescharacteristic, complemented
428C3#7066611yescharacteristic, complemented
429C2—21no—
430C2—21no—
431C2#1059119511yescharacteristic
432C2#1059152311yescharacteristic
433C2#1059166111yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#2060
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
54. #3748Q8semidirect
64. C3×C4×Dic3Q8semidirect
66. C3×#208Q8semidirect
195. C4×Dic3Dic6semidirect
203. #208Dic6semidirect
373. C32#2060semidirect
427. C3#69573semidirect
428. C3#70666semidirect

Maximal subgroups

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

subgroupindex
#105950512
#105926632
C3×#49752
C3×#49642
#105891672
#105891622
#105891612
#706663
#695733