Finite Group Databasebeta

← #11789685

Subgroups — #11789685

Order 1152.

523 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#10592820C211yesmaximal, characteristic, complemented
2C2×C3×#823C211yesmaximal, characteristic
3#10591086C211yesmaximal, characteristic
4C2×#63563C211yesmaximal, characteristic
5#10591059C211yesmaximal, characteristic, complemented
6C3×#4558C211yesmaximal, characteristic, complemented
7#10589168C211yesmaximal, characteristic, complemented
8#70072—31nomaximal
9#68931—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63645—21no—
18#63644—21no—
19C3×#823C414yescomplemented
20#63563—21no—
21#63563—21no—
22#63563—21no—
23#63563—21no—
24#63555—21no—
25#63553—21no—
26C2×C3×#100—31no—
27#5215—31no—
28C2×#832—31no—
29#5131—31no—
30C2×#823D311yescharacteristic
31#5122—31no—
32#5121—31no—
33#5121—31no—
34#5121—61no—
35C2×#821—31no—
36#5101—31no—
37C3×#341—31no—
38#4558D311yescharacteristic, complemented
39#4554—31no—
40#4554—31no—
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)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)D411yescharacteristic
57C4⋊(C3⋊Dic3)D411yescharacteristic
58C4×C3⋊Dic3—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208C2×C412yes—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8D411yescharacteristic
68C2×C3×C3⋊C8D411yescharacteristic
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
77C22×C3×C8—31no—
78#926—31no—
79#926—31no—
80#926—61no—
81C2×C4⋊Dic3—31no—
82C2×C4⋊Dic3—31no—
83C2×C4⋊Dic3—61no—
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C22×C3⋊C8C2×D311yescharacteristic
87C3×#100—34no—
88#832—61no—
89#832—61no—
90#832—61no—
91#832—61no—
92#823Dic314yescomplemented
93#821—61no—
94#821—61no—
95#821—61no—
96#821—61no—
97#818—61no—
98#818—61no—
99#818—62no—
100#817—61no—
101#817—61no—
102#817—62no—
103#815—61no—
104#815—61no—
105C8×Dic3—61no—
106C8×Dic3—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—22no—
129C3×C3⋊C8—21no—
130C3×C3⋊C8—21no—
131C3×C3⋊C8—41no—
132#428—91no—
133#418—91no—
134C2×#102—91no—
135C2×#100—31no—
136#405—91no—
137#343—91no—
138#341—31no—
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×C4C22×D311yescharacteristic
149C22×C3×C4C22×D311yescharacteristic
150C22×Dic3—61no—
151C22×Dic3—61no—
152C22×Dic3—121no—
153C2×D12—21no—
154C2×D12—21no—
155C2×D12—21no—
156C2×D12—21no—
157C2×D12—21no—
158C2×D12C2×Dic312yes—
159C3×M16—22no—
160C3×M16—21no—
161C3×M16—21no—
162C3×M16—22no—
163C3×M16—32no—
164C3×M16—61no—
165C3×M16—61no—
166C3×M16—61no—
167C3×M16C4×D312yes—
168C3×M16C2×Dic312yes—
169C2×C3×C8—22no—
170C2×C3×C8—21no—
171C2×C3×C8—21no—
172C2×C3×C8—31no—
173C2×C3×C8—31no—
174C2×C3×C8—61no—
175C2×C3×C8—61no—
176C2×C3×C8—61no—
177C2×C3×C8—61no—
178#217—61no—
179#217—61no—
180#217—121no—
181C4⋊Dic3—31no—
182C4⋊Dic3—31no—
183C4⋊Dic3—31no—
184C4⋊Dic3—31no—
185C4⋊Dic3—61no—
186C4⋊Dic3—61no—
187C4⋊Dic3—62no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192C4⋊Dic3—121no—
193C4×Dic3—61no—
194C4×Dic3—61no—
195C4×Dic3—121no—
196#208—21no—
197#208—21no—
198#208—21no—
199#208C2×Dic312yes—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—21no—
204C2×C3⋊C8D1211yescharacteristic
205C2×C3⋊C8D1211yescharacteristic
206C22×C32—21no—
207C22×C32—21no—
208C22×C32#11711yescharacteristic
209C22×C32#12111yescharacteristic
210C22×C32#12611yescharacteristic
211C2×C3×D3—42no—
212C2×C3×D3—82no—
213C2×C3×D3—81no—
214C2×C3×D3—81no—
215C2×C3×D3—82no—
216C32×C4C4×D411yescharacteristic
217C32×C4C4×D411yescharacteristic
218C32×C4#12311yescharacteristic
219C32×C4#12411yescharacteristic
220C3⋊Dic3—41no—
221C3⋊Dic3—41no—
222C3⋊Dic3—81no—
223C22×D4—31no—
224C2×M16—31no—
225C2×M16—31no—
226C2×M16D3211yescharacteristic
227C22×C8—31no—
228#117—91no—
229C2×C4⋊C4—91no—
230#107—181no—
231#106—181no—
232#102—181no—
233#102—181no—
234#102—181no—
235#102—181no—
236#100—34no—
237#97—181no—
238C4×C8—181no—
239C23×C3—21no—
240C23×C3—62no—
241C23×C3—121no—
242C23×C3—121no—
243C23×C3—241no—
244C23×C3—241no—
245C23×C3#23511yescharacteristic
246C23×C3#23911yescharacteristic
247C22×D3—22no—
248C22×D3—41no—
249C22×D3—41no—
250C22×D3—81no—
251C22×D3—81no—
252C3×D4—62no—
253C3×D4—62no—
254C3×D4—121no—
255C3×D4—121no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4C2×C4×D311yescharacteristic
263C2×C3×C4C2×D1211yescharacteristic
264C2×C3×C4#23511yescharacteristic
265C2×C3×C4#23511yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4#23711yescharacteristic
270C2×C3×C4#23711yescharacteristic
271C2×C3×C4#23711yescharacteristic
272C2×C3×C4#23711yescharacteristic
273C2×C3×C4C22×Dic311yescharacteristic
274C2×Dic3—61no—
275C2×Dic3—61no—
276C2×Dic3—61no—
277C2×Dic3—61no—
278C2×Dic3—121no—
279C2×Dic3—121no—
280C2×Dic3—122no—
281C2×Dic3—121no—
282C2×Dic3—121no—
283C2×Dic3—242no—
284C2×Dic3—241no—
285C2×Dic3—241no—
286D12—22no—
287D12—22no—
288D12—41no—
289D12—41no—
290C3×C8—24no—
291C3×C8—22no—
292C3×C8—22no—
293C3×C8—62no—
294C3×C8—61no—
295C3×C8—61no—
296C3×C8—121no—
297C3⋊C8—21no—
298C3⋊C8—21no—
299C3⋊C8—22no—
300C3⋊C8—41no—
301C2×C32—21no—
302C2×C32—21no—
303C2×C32#38811yescharacteristic
304C2×C32#47111yescharacteristic
305C2×C32#47211yescharacteristic
306C3×D3—82no—
307C24—61no—
308C2×D4—32no—
309C2×D4—61no—
310C2×D4—61no—
311C2×D4—61no—
312C2×D4—61no—
313C2×D4—61no—
314C22×C4—181no—
315C22×C4C2×D3211yescharacteristic
316M16—21no—
317M16—32no—
318M16—61no—
319M16—61no—
320M16—61no—
321M16D3×Dic312yes—
322C2×C8—21no—
323C2×C8—31no—
324C2×C8—31no—
325C2×C8—61no—
326C2×C8—61no—
327C2×C8—61no—
328C2×C8—61no—
329C4⋊C4—91no—
330C4⋊C4—91no—
331C4⋊C4—181no—
332C4⋊C4—181no—
333C22⋊C4—181no—
334C42—181no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3—122no—
345C22×C3—242no—
346C22×C3—242no—
347C22×C3—241no—
348C22×C3—241no—
349C22×C3#87911yescharacteristic
350C22×C3#88411yescharacteristic
351C22×C3#89211yescharacteristic
352C22×C3#89511yescharacteristic
353C22×C3#89811yescharacteristic
354C22×C3#92611yescharacteristic
355C2×D3—42no—
356C2×D3—82no—
357C2×D3—81no—
358C2×D3—81no—
359C2×D3—82no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4C4×D1211yescharacteristic
365C3×C4#67⋊C411yescharacteristic
366C3×C4#88311yescharacteristic
367C3×C4#88511yescharacteristic
368C3×C4#88511yescharacteristic
369C3×C4#88611yescharacteristic
370C3×C4D4×Dic311yescharacteristic
371C3×C4D4×Dic311yescharacteristic
372Dic3—121no—
373Dic3—121no—
374Dic3—121no—
375Dic3—121no—
376Dic3—241no—
377Dic3—241no—
378Dic3—242no—
379Dic3—241no—
380Dic3—241no—
381C32#193111yescharacteristic, complemented, Sylow
382C23—62no—
383C23—121no—
384C23—121no—
385C23—241no—
386C23—241no—
387C23#379911yescharacteristic
388D4—62no—
389D4—62no—
390D4—121no—
391D4—121no—
392C2×C4—181no—
393C2×C4—181no—
394C2×C4—361no—
395C2×C4—721no—
396C2×C4#379511yescharacteristic
397C2×C4#379511yescharacteristic
398C2×C4D3×D1211yescharacteristic
399C2×C4C2×D3×Dic311yescharacteristic
400C2×C4#380511yescharacteristic
401C2×C4#381111yescharacteristic
402C8—22no—
403C8—61no—
404C8—61no—
405C8—62no—
406C8—121no—
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#467011yescharacteristic
418C2×C3#474811yescharacteristic
419C2×C3#474911yescharacteristic
420C2×C3#489711yescharacteristic
421C2×C3#489811yescharacteristic
422C2×C3#495111yescharacteristic
423D3—82no—
424C22—21no—
425C22—21no—
426C22—122no—
427C22—242no—
428C22—242no—
429C22—241no—
430C22—241no—
431C22#6384111yescharacteristic
432C22#6386111yescharacteristic
433C22#6391011yescharacteristic
434C4—361no—
435C4—361no—
436C4—721no—
437C4#6389111yescharacteristic
438C4Dic3×D1211yescharacteristic
439C4#6391311yescharacteristic
440C4#67⋊Dic311yescharacteristic
441C3—21no—
442C3#6893111yescharacteristic, complemented
443C3#7007211yescharacteristic, complemented
444C2—21no—
445C2—21no—
446C2—242no—
447C2#1059098711yescharacteristic
448C2#1059098911yescharacteristic
449C2#1059131611yescharacteristic
subgroupG/H
centerC22#63910
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. #10592820C2semidirect
5. #10591059C2semidirect
6. C3×#4558C2semidirect
7. #10589168C2semidirect
19. C3×#823C4semidirect
38. #4558D3semidirect
92. #823Dic3semidirect
381. C32#1931semidirect
442. C3#68931semidirect
443. C3#70072semidirect

Maximal subgroups

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

subgroupindex
#105928202
C2×C3×#8232
#105910862
C2×#635632
#105910592
C3×#45582
#105891682
#700723
#689313