Finite Group Databasebeta

← #11789731

Subgroups — #11789731

Order 1152.

487 conjugacy classes of subgroups.

The subgroup lattice has 427 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5132C211yesmaximal, characteristic
2C3×#5125C211yesmaximal, characteristic, complemented
3#10591110C211yesmaximal, characteristic
4C2×#63568C211yesmaximal, characteristic
5#10591060C211yesmaximal, characteristic, complemented
6#10589421C211yesmaximal, characteristic, complemented
7#10589171C211yesmaximal, characteristic, complemented
8#70727—31nomaximal
9#70130—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#824C412yescomplemented
18C3×#823C412yescomplemented
19C3×#819—22no—
20#63568—21no—
21#63568—21no—
22#63568—22no—
23#63555—21no—
24#63553—21no—
25C3×#430—31no—
26C3×#413—31no—
27#5236—31no—
28C2×#837—31no—
29#5139—31no—
30C2×#825—31no—
31#5132D311yescharacteristic
32#5125D311yescharacteristic, complemented
33Dic3×M16—31no—
34Dic3×M16—31no—
35#4559—31no—
36#4556—31no—
37#4555—31no—
38#4555—31no—
39#4555—61no—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3—21no—
42C2×C3×#67—21no—
43C3×#235—21no—
44C3×#235—21no—
45C3×#235—21no—
46C3×#235—21no—
47C2×C3×D12C2×C411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×Dic6C2×C411yescharacteristic
50C32×M16—21no—
51C32×M16C2×C412yes—
52C2×C32×C8—21no—
53#3757—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4×C3⋊Dic3—21no—
56C4×C3⋊Dic3—21no—
57C4×C3⋊Dic3D411yescharacteristic
58C4×C3⋊Dic3D411yescharacteristic
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208—21no—
63C3×#208C2×C412yes—
64C3×#208D412yes—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68#1932—91noSylow
69C2×C3×#41—31no—
70C2×#235C2×D311yescharacteristic
71C2×C3×M16—21no—
72C2×C3×M16—31no—
73C2×C3×M16—31no—
74C2×C3×M16—31no—
75C2×C3×M16C2×D311yescharacteristic
76C2×C3×M16C2×D311yescharacteristic
77#926—31no—
78#926—31no—
79#926—61no—
80C2×C4×Dic3—31no—
81C2×C4×Dic3—31no—
82C2×C4×Dic3—61no—
83C2×#208C2×D311yescharacteristic
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C3×#108—62no—
87C3×#101—32no—
88C3×#100—32no—
89#837—61no—
90#837—61no—
91#837—62no—
92#825—61no—
93#825—61no—
94#825—62no—
95#824Dic312yescomplemented
96#823Dic312yescomplemented
97#819—22no—
98#815—61no—
99#815—61no—
100C8×Dic3—61no—
101C8×Dic3—61no—
102C23×C32#4111yescharacteristic
103C22×C3×D3—21no—
104C2×C32×C4C22×C411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—21no—
112C2×C3⋊Dic3—42no—
113C2×C3⋊Dic3—41no—
114C3×#67—41no—
115C3×#67—41no—
116C2×C3×Dic3—21no—
117C3×D12—21no—
118C3×D12—21no—
119C3×C4×D3—41no—
120C3×C4×D3—41no—
121C3×Dic6—21no—
122C3×Dic6—21no—
123C32×C8—22no—
124C3×C3⋊C8—22no—
125C3×C3⋊C8—22no—
126C3×C3⋊C8—41no—
127#430—31no—
128#421—91no—
129C2×#104—91no—
130#413—31no—
131C4×M16—91no—
132#344—91no—
133#339—91no—
134C3×#41—61no—
135C3×#41—61no—
136C3×#41—61no—
137C3×#41—61no—
138C2×C3×Q8—31no—
139C2×C3×D4—31no—
140C2×C3×D4—61no—
141C22×C3×C4—21no—
142C22×C3×C4—61no—
143C22×C3×C4C22×D311yescharacteristic
144C22×C3×C4C22×D311yescharacteristic
145C2×#67—21no—
146C22×Dic3—61no—
147C22×Dic3—61no—
148C22×Dic3—121no—
149#235—21no—
150#235—21no—
151#235—21no—
152#235—21no—
153C2×D12C2×Dic311yescharacteristic
154C2×C4×D3—21no—
155C2×Dic6C2×Dic311yescharacteristic
156C3×M16—21no—
157C3×M16—21no—
158C3×M16—22no—
159C3×M16—32no—
160C3×M16—32no—
161C3×M16—41no—
162C3×M16—61no—
163C3×M16—61no—
164C3×M16—61no—
165C3×M16—61no—
166C3×M16C4×D312yes—
167C3×M16C2×Dic312yes—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C2×C3×C8—41no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C2×C3×C8—61no—
174#217—61no—
175#217—61no—
176#217—121no—
177C4⋊Dic3—62no—
178C4⋊Dic3—61no—
179C4⋊Dic3—61no—
180C4×Dic3—31no—
181C4×Dic3—31no—
182C4×Dic3—31no—
183C4×Dic3—31no—
184C4×Dic3—61no—
185C4×Dic3—61no—
186C4×Dic3—61no—
187C4×Dic3—61no—
188C4×Dic3—61no—
189C4×Dic3—61no—
190C4×Dic3—121no—
191C4×Dic3—121no—
192#208—21no—
193#208—21no—
194#208—21no—
195#208—21no—
196#208C2×Dic312yes—
197#208#6712yes—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—21no—
201C22×C32—41no—
202C22×C32#11711yescharacteristic
203C22×C32#12311yescharacteristic
204C22×C32#12411yescharacteristic
205C2×C3×D3—41no—
206C2×C3×D3—81no—
207C32×C4C4×D411yescharacteristic
208C32×C4C4×D411yescharacteristic
209C32×C4#12111yescharacteristic
210C32×C4#12611yescharacteristic
211C3⋊Dic3—22no—
212C3⋊Dic3—41no—
213C3⋊Dic3—81no—
214C3×Dic3—41no—
215C2×#41—31no—
216C2×M16—31no—
217C2×M16—31no—
218C2×M16—31no—
219C2×M16D3211yescharacteristic
220#117—91no—
221C2×C42—91no—
222#108—62no—
223#104—181no—
224#104—181no—
225#104—182no—
226#101—32no—
227#100—32no—
228#97—181no—
229C4×C8—181no—
230C23×C3—21no—
231C23×C3—61no—
232C23×C3#23511yescharacteristic
233C23×C3#23911yescharacteristic
234C22×D3—21no—
235C3×Q8—61no—
236C3×Q8—61no—
237C3×D4—61no—
238C3×D4—61no—
239C3×D4—121no—
240C3×D4—121no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—61no—
248C2×C3×C4—121no—
249C2×C3×C4—121no—
250C2×C3×C4C2×C4×D311yescharacteristic
251C2×C3×C4#23511yescharacteristic
252C2×C3×C4#23511yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4#23711yescharacteristic
257C2×C3×C4#23711yescharacteristic
258C2×C3×C4#23711yescharacteristic
259C2×C3×C4#23911yescharacteristic
260C2×C3×C4C22×Dic311yescharacteristic
261C2×C3×C4C2×#6711yescharacteristic
262#67—41no—
263#67—41no—
264C2×Dic3—21no—
265C2×Dic3—61no—
266C2×Dic3—61no—
267C2×Dic3—61no—
268C2×Dic3—61no—
269C2×Dic3—121no—
270C2×Dic3—121no—
271C2×Dic3—122no—
272C2×Dic3—122no—
273C2×Dic3—124no—
274C2×Dic3—122no—
275C2×Dic3—121no—
276C2×Dic3—121no—
277D12—21no—
278D12—21no—
279C4×D3—41no—
280C4×D3—41no—
281Dic6—21no—
282Dic6—21no—
283C3×C8—22no—
284C3×C8—22no—
285C3×C8—42no—
286C3×C8—62no—
287C3×C8—62no—
288C3×C8—121no—
289C3⋊C8—22no—
290C3⋊C8—22no—
291C3⋊C8—41no—
292C2×C32—21no—
293C2×C32—21no—
294C2×C32—21no—
295C2×C32#38811yescharacteristic
296C3×D3—81no—
297#41—61no—
298#41—61no—
299#41—61no—
300#41—61no—
301C2×Q8—31no—
302C2×D4—31no—
303C2×D4—61no—
304C22×C4—61no—
305C22×C4—181no—
306C22×C4C2×D3211yescharacteristic
307M16—21no—
308M16—32no—
309M16—32no—
310M16—61no—
311M16—61no—
312M16—61no—
313M16—61no—
314M16D3×Dic312yes—
315C2×C8—21no—
316C2×C8—61no—
317C2×C8—61no—
318C2×C8—61no—
319C4⋊C4—181no—
320C22⋊C4—181no—
321C42—91no—
322C42—91no—
323C42—181no—
324C42—181no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—42no—
331C22×C3—121no—
332C22×C3—241no—
333C22×C3#88311yescharacteristic
334C22×C3#88511yescharacteristic
335C22×C3#89211yescharacteristic
336C22×C3#89411yescharacteristic
337C22×C3#92611yescharacteristic
338C22×C3#94711yescharacteristic
339C2×D3—41no—
340C2×D3—81no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—121no—
346C3×C4#87911yescharacteristic
347C3×C4#88411yescharacteristic
348C3×C4#89311yescharacteristic
349C3×C4#89811yescharacteristic
350C3×C4C4×#6711yescharacteristic
351C3×C4D4×Dic311yescharacteristic
352C3×C4D4×Dic311yescharacteristic
353C3×C4#93911yescharacteristic
354Dic3—41no—
355Dic3—62no—
356Dic3—62no—
357Dic3—122no—
358Dic3—121no—
359Dic3—121no—
360Dic3—122no—
361Dic3—242no—
362Dic3—241no—
363Dic3—241no—
364C32#193211yescharacteristic, complemented, Sylow
365C23—61no—
366C23#379911yescharacteristic
367Q8—61no—
368Q8—61no—
369D4—61no—
370D4—61no—
371D4—121no—
372D4—121no—
373C2×C4—61no—
374C2×C4—121no—
375C2×C4—121no—
376C2×C4—181no—
377C2×C4—181no—
378C2×C4—362no—
379C2×C4—361no—
380C2×C4#379511yescharacteristic
381C2×C4#379611yescharacteristic
382C2×C4#380211yescharacteristic
383C2×C4C2×D3×Dic311yescharacteristic
384C2×C4#380411yescharacteristic
385C2×C4D3×#6711yescharacteristic
386C8—22no—
387C8—62no—
388C8—62no—
389C8—121no—
390C2×C3—22no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—41no—
399C2×C3—41no—
400C2×C3—241no—
401C2×C3#495111yescharacteristic
402C2×C3#499011yescharacteristic
403D3—81no—
404C22—41no—
405C22—121no—
406C22—241no—
407C22#6384111yescharacteristic
408C22#6385411yescharacteristic
409C22#6390711yescharacteristic
410C4—121no—
411C4—182no—
412C4—361no—
413C4—721no—
414C4#6385811yescharacteristic
415C4#6388511yescharacteristic
416C4#6389811yescharacteristic
417C4Dic3×#6711yescharacteristic
418C3—21no—
419C3#7013011yescharacteristic, complemented
420C3#7072711yescharacteristic, complemented
421C2—21no—
422C2—21no—
423C2—21no—
424C2—241no—
425C2#1059130711yescharacteristic
subgroupG/H
centerC4#63885
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#388
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1932
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C3×#5125C2semidirect
5. #10591060C2semidirect
6. #10589421C2semidirect
7. #10589171C2semidirect
17. C3×#824C4semidirect
18. C3×#823C4semidirect
32. #5125D3semidirect
95. #824Dic3semidirect
96. #823Dic3semidirect
364. C32#1932semidirect
419. C3#70130semidirect
420. C3#70727semidirect

Maximal subgroups

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

subgroupindex
C3×#51322
C3×#51252
#105911102
C2×#635682
#105910602
#105894212
#105891712
#707273
#701303