Finite Group Databasebeta

← #11789672

Subgroups — #11789672

Order 1152.

529 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592821C211yesmaximal, characteristic, complemented
2C2×C3×#823C211yesmaximal, characteristic
3#10591130C211yesmaximal, characteristic, complemented
4#10591086C211yesmaximal, characteristic
5C2×#63562C211yesmaximal, characteristic
6C3×#4554C211yesmaximal, characteristic, complemented
7#10589165C211yesmaximal, characteristic, complemented
8#70072—31nomaximal
9#68983—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63642—21no—
18C8×C3⋊Dic3—21no—
19C3×#823C414yescomplemented
20#63575—21no—
21#63573—21no—
22#63563—21no—
23#63563—21no—
24#63562—21no—
25#63562—21no—
26C2×C3×#100—31no—
27#5215—31no—
28C2×#832—31no—
29#5131—31no—
30C2×#823D311yescharacteristic
31#5122—31no—
32#5122—31no—
33#5122—61no—
34#5121—31no—
35C2×#809—31no—
36#4964—31no—
37C3×#343—31no—
38#4558—31no—
39#4558—31no—
40#4554D311yescharacteristic, complemented
41C23×C3×D3—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3×Dic3—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12C2×C412yes—
50C32×M16—21no—
51C32×M16C2×C412yes—
52C2×C32×C8—21no—
53#3757—21no—
54C4⋊(C3⋊Dic3)D411yescharacteristic
55C4⋊(C3⋊Dic3)D411yescharacteristic
56C4×C3⋊Dic3—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)D411yescharacteristic
60C2×C3⋊(C3⋊C8)D411yescharacteristic
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×#208—21no—
64C3×#208—21no—
65C3×#208—21no—
66C3×#208C2×C412yes—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69#1931—91noSylow
70C22×C3×D4—31no—
71C22×D12C2×D311yescharacteristic
72C2×C3×M16—21no—
73C2×C3×M16—31no—
74C2×C3×M16—31no—
75C2×C3×M16C2×D311yescharacteristic
76C2×C3×M16C2×D311yescharacteristic
77C2×C3×C4⋊C4—31no—
78#926—31no—
79#926—31no—
80#926—61no—
81C2×C4⋊Dic3C2×D311yescharacteristic
82C2×#208C2×D311yescharacteristic
83C2×#208C2×D311yescharacteristic
84C22×C3⋊C8—31no—
85C22×C3⋊C8—31no—
86C22×C3⋊C8—61no—
87C3×#100—34no—
88#832—61no—
89#832—61no—
90#832—61no—
91#832—61no—
92#823Dic314yescomplemented
93#821—61no—
94#821—61no—
95#818—61no—
96#817—61no—
97#815—61no—
98#815—61no—
99#815—62no—
100C8×Dic3—61no—
101C8×Dic3—61no—
102C8×Dic3—62no—
103#809—61no—
104#809—61no—
105#808—61no—
106#807—61no—
107C23×C32#4111yescharacteristic
108C22×C3×D3—22no—
109C22×C3×D3—41no—
110C22×C3×D3—41no—
111C22×C3×D3—81no—
112C22×C3×D3—81no—
113C2×C32×C4C22×C411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3×Dic3—41no—
122C2×C3×Dic3—81no—
123C3×D12—22no—
124C3×D12—22no—
125C3×D12—41no—
126C3×D12—41no—
127C32×C8—22no—
128C3⋊(C3⋊C8)—21no—
129C3⋊(C3⋊C8)—21no—
130C3×C3⋊C8—22no—
131C3×C3⋊C8—41no—
132#428—91no—
133#418—91no—
134C2×#102—91no—
135C2×#100—31no—
136#405—91no—
137#343—31no—
138#341—91no—
139C24×C3—61no—
140C23×D3—21no—
141C2×C3×D4—32no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C2×C3×D4—61no—
145C2×C3×D4—61no—
146C2×C3×D4—61no—
147C22×C3×C4—21no—
148C22×C3×C4—61no—
149C22×C3×C4C22×D311yescharacteristic
150C22×C3×C4C22×D311yescharacteristic
151C22×Dic3—21no—
152C2×D12—21no—
153C2×D12—21no—
154C2×D12—21no—
155C2×D12—21no—
156C2×D12—21no—
157C2×D12C2×Dic312yes—
158C3×M16—22no—
159C3×M16—21no—
160C3×M16—21no—
161C3×M16—22no—
162C3×M16—32no—
163C3×M16—61no—
164C3×M16—61no—
165C3×M16—61no—
166C3×M16C4×D312yes—
167C3×M16C2×Dic312yes—
168C2×C3×C8—22no—
169C2×C3×C8—21no—
170C2×C3×C8—21no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175#217—62no—
176#217—61no—
177#217—61no—
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180C4⋊Dic3—31no—
181C4⋊Dic3—31no—
182C4⋊Dic3—31no—
183C4⋊Dic3—31no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C4×Dic3—62no—
187C4×Dic3—61no—
188C4×Dic3—61no—
189#208—21no—
190#208—21no—
191#208—21no—
192#208C2×Dic312yes—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—31no—
196C2×C3⋊C8—31no—
197C2×C3⋊C8—31no—
198C2×C3⋊C8—31no—
199C2×C3⋊C8—61no—
200C2×C3⋊C8—61no—
201C2×C3⋊C8—62no—
202C2×C3⋊C8—62no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—61no—
207C22×C32—21no—
208C22×C32—21no—
209C22×C32#11711yescharacteristic
210C22×C32#12111yescharacteristic
211C22×C32#12611yescharacteristic
212C2×C3×D3—42no—
213C2×C3×D3—82no—
214C2×C3×D3—81no—
215C2×C3×D3—81no—
216C2×C3×D3—82no—
217C32×C4C4×D411yescharacteristic
218C32×C4C4×D411yescharacteristic
219C32×C4#12311yescharacteristic
220C32×C4#12411yescharacteristic
221C3⋊Dic3—41no—
222C3⋊Dic3—41no—
223C3×Dic3—81no—
224C22×D4—31no—
225C2×M16—31no—
226C2×M16—31no—
227C2×M16D3211yescharacteristic
228C22×C8—91no—
229#117—91no—
230C2×C4⋊C4—31no—
231#107—181no—
232#106—181no—
233#102—181no—
234#102—181no—
235#102—181no—
236#102—181no—
237#100—34no—
238#97—181no—
239C4×C8—181no—
240C23×C3—21no—
241C23×C3—62no—
242C23×C3—121no—
243C23×C3—121no—
244C23×C3—241no—
245C23×C3—241no—
246C23×C3#23511yescharacteristic
247C23×C3#23511yescharacteristic
248C22×D3—22no—
249C22×D3—41no—
250C22×D3—41no—
251C22×D3—81no—
252C22×D3—81no—
253C3×D4—62no—
254C3×D4—62no—
255C3×D4—121no—
256C3×D4—121no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—121no—
264C2×C3×C4—241no—
265C2×C3×C4C2×C4×D311yescharacteristic
266C2×C3×C4#23511yescharacteristic
267C2×C3×C4#23511yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4D3×D411yescharacteristic
272C2×C3×C4#23711yescharacteristic
273C2×C3×C4#23711yescharacteristic
274C2×C3×C4#23711yescharacteristic
275C2×C3×C4#23911yescharacteristic
276C2×C3×C4C22×Dic311yescharacteristic
277C2×Dic3—41no—
278C2×Dic3—62no—
279C2×Dic3—62no—
280C2×Dic3—61no—
281C2×Dic3—61no—
282C2×Dic3—61no—
283C2×Dic3—61no—
284C2×Dic3—81no—
285D12—22no—
286D12—22no—
287D12—41no—
288D12—41no—
289C3×C8—24no—
290C3×C8—22no—
291C3×C8—22no—
292C3×C8—62no—
293C3×C8—121no—
294C3⋊C8—22no—
295C3⋊C8—41no—
296C3⋊C8—62no—
297C3⋊C8—62no—
298C3⋊C8—61no—
299C3⋊C8—61no—
300C3⋊C8—61no—
301C3⋊C8—61no—
302C2×C32—21no—
303C2×C32—21no—
304C2×C32#38811yescharacteristic
305C2×C32#47111yescharacteristic
306C2×C32#47211yescharacteristic
307C3×D3—82no—
308C24—61no—
309C2×D4—32no—
310C2×D4—61no—
311C2×D4—61no—
312C2×D4—61no—
313C2×D4—61no—
314C2×D4—61no—
315C22×C4—61no—
316C22×C4C2×D3211yescharacteristic
317M16—21no—
318M16—32no—
319M16—61no—
320M16—61no—
321M16—61no—
322M16D3×Dic312yes—
323C2×C8—21no—
324C2×C8—61no—
325C2×C8—61no—
326C2×C8—91no—
327C2×C8—91no—
328C2×C8—181no—
329C2×C8—181no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4—91no—
333C4⋊C4—91no—
334C22⋊C4—181no—
335C42—181no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—122no—
346C22×C3—242no—
347C22×C3—242no—
348C22×C3—241no—
349C22×C3—241no—
350C22×C3#87211yescharacteristic
351C22×C3#87911yescharacteristic
352C22×C3#88411yescharacteristic
353C22×C3#88411yescharacteristic
354C22×C3#89811yescharacteristic
355C22×C3#92611yescharacteristic
356C2×D3—42no—
357C2×D3—82no—
358C2×D3—81no—
359C2×D3—81no—
360C2×D3—82no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—241no—
366C3×C4#67⋊C411yescharacteristic
367C3×C4#88311yescharacteristic
368C3×C4#88511yescharacteristic
369C3×C4#88511yescharacteristic
370C3×C4#89311yescharacteristic
371C3×C4#89411yescharacteristic
372C3×C4D4×Dic311yescharacteristic
373C3×C4D4×Dic311yescharacteristic
374Dic3—81no—
375Dic3—122no—
376Dic3—122no—
377Dic3—121no—
378Dic3—121no—
379Dic3—121no—
380Dic3—121no—
381C32#193111yescharacteristic, complemented, Sylow
382C23—62no—
383C23—121no—
384C23—121no—
385C23—241no—
386C23—241no—
387C23#379811yescharacteristic
388D4—62no—
389D4—62no—
390D4—121no—
391D4—121no—
392C2×C4—121no—
393C2×C4—181no—
394C2×C4—181no—
395C2×C4—241no—
396C2×C4#379611yescharacteristic
397C2×C4#379811yescharacteristic
398C2×C4#380211yescharacteristic
399C2×C4C2×D3×Dic311yescharacteristic
400C2×C4#380511yescharacteristic
401C2×C4#381111yescharacteristic
402C8—22no—
403C8—62no—
404C8—121no—
405C8—181no—
406C8—181no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—41no—
415C2×C3—41no—
416C2×C3—242no—
417C2×C3#466911yescharacteristic
418C2×C3#474811yescharacteristic
419C2×C3#474911yescharacteristic
420C2×C3#474911yescharacteristic
421C2×C3#475411yescharacteristic
422C2×C3#495111yescharacteristic
423D3—82no—
424C22—21no—
425C22—21no—
426C22—122no—
427C22—242no—
428C22—242no—
429C22—241no—
430C22—241no—
431C22#6385511yescharacteristic
432C22#6386211yescharacteristic
433C22#6391211yescharacteristic
434C4—241no—
435C4—361no—
436C4—361no—
437C4#6385311yescharacteristic
438C4#6389811yescharacteristic
439C4#6391511yescharacteristic
440C4#67⋊Dic311yescharacteristic
441C3—21no—
442C3#6898311yescharacteristic, complemented
443C3#7007211yescharacteristic, complemented
444C2—21no—
445C2—21no—
446C2—242no—
447C2#1059098811yescharacteristic
448C2#1059099111yescharacteristic
449C2#1059128611yescharacteristic
subgroupG/H
centerC22#63912
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1931
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10592821C2semidirect
3. #10591130C2semidirect
6. C3×#4554C2semidirect
7. #10589165C2semidirect
19. C3×#823C4semidirect
40. #4554D3semidirect
92. #823Dic3semidirect
381. C32#1931semidirect
442. C3#68983semidirect
443. C3#70072semidirect

Maximal subgroups

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

subgroupindex
#105928212
C2×C3×#8232
#105911302
#105910862
C2×#635622
C3×#45542
#105891652
#700723
#689833