Finite Group Databasebeta

← #11794354

Subgroups — #11794354

Order 1152.

505 conjugacy classes of subgroups.

The subgroup lattice has 433 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#809C211yesmaximal, characteristic
2C3×#4964C211yesmaximal, characteristic, complemented
3C2×#63577C211yesmaximal, characteristic, complemented
4#10591116C211yesmaximal, characteristic, complemented
5#10591085C211yesmaximal, characteristic
6C2×#63558C211yesmaximal, characteristic
7#10589396C211yesmaximal, characteristic, complemented
8#70676—31nomaximal
9#70197—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C3×#809—22no—
18C3×#808—21no—
19C3×#807—21no—
20#63577—22no—
21Dic3⋊(C3⋊C8)—22no—
22#63562—21no—
23#63562—21no—
24#63558—22no—
25C3×#428—31no—
26C2×C3×#102—31no—
27C2×#833—31no—
28#5215—31no—
29C2×#823—31no—
30C2×#822—31no—
31C2×#819—31no—
32#5102—31no—
33#5001—31no—
34#4999—31no—
35C2×#809D311yescharacteristic
36#4964D311yescharacteristic, complemented
37#4530—31no—
38#4530—31no—
39#4530—61no—
40C23×C3×D3—21no—
41C22×C32×C4—21no—
42C22×C32×C4C2311yescharacteristic
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12Q812yes—
49C32×C4⋊C4—21no—
50C32×C4⋊C4—21no—
51#3748—21no—
52#3748—21no—
53#3748—21no—
54#3748—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×#217—21no—
58C3×C4⋊Dic3D411yescharacteristic
59C3×C4⋊Dic3D411yescharacteristic
60C3×C4×Dic3—21no—
61C3×#208—21no—
62C3×#208D412yes—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8D412yes—
67#2063—91noSylow
68C22×C3×D4—31no—
69C22×D12C2×D311yescharacteristic
70C2×C3×M16—31no—
71C22×C3×C8—31no—
72C3×#117—31no—
73C2×C3×C4⋊C4—21no—
74C2×C3×C4⋊C4C2×D311yescharacteristic
75C2×C3×C4⋊C4C2×D311yescharacteristic
76#926C2×D311yescharacteristic
77C2×#208—31no—
78C2×#208—31no—
79C2×#208—31no—
80C2×#208—31no—
81C2×#208—61no—
82C2×#208—61no—
83C2×#208C2×D311yescharacteristic
84C22×C3⋊C8C2×D311yescharacteristic
85C3×#107—61no—
86C3×#106—61no—
87C3×#102—62no—
88#833—62no—
89#832—61no—
90#832—61no—
91#823—62no—
92#822—62no—
93#819—62no—
94Dic3⋊C8—62no—
95#809—22no—
96#809—61no—
97#809—61no—
98#808—21no—
99#807—21no—
100C4⋊(C3⋊C8)—62no—
101C23×C32#4111yescharacteristic
102C22×C3×D3—22no—
103C22×C3×D3—41no—
104C22×C3×D3—41no—
105C22×C3×D3—81no—
106C22×C3×D3—81no—
107C2×C32×C4—41no—
108C2×C32×C4—81no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×Q811yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C3×Dic3—21no—
116C2×C3×Dic3—21no—
117C3×D12—22no—
118C3×D12—22no—
119C3×D12—41no—
120C3×D12—41no—
121C3⋊(C3⋊C8)—41no—
122C3⋊(C3⋊C8)—41no—
123C3×C3⋊C8—22no—
124C3×C3⋊C8—22no—
125C2×#108—91no—
126#428—31no—
127#424—91no—
128#418—91no—
129C2×#102—31no—
130C2×#100—91no—
131#343—91no—
132C24×C3—61no—
133C23×D3—21no—
134C2×C3×D4—32no—
135C2×C3×D4—61no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C2×C3×D4—61no—
139C2×C3×D4—61no—
140C22×C3×C4—22no—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4C22×D311yescharacteristic
145C22×C3×C4C22×D311yescharacteristic
146C2×D12—21no—
147C2×D12—21no—
148C2×D12—21no—
149C2×D12—21no—
150C2×D12—21no—
151C2×D12Dic612yes—
152C3×M16—32no—
153C3×M16—61no—
154C2×C3×C8—32no—
155C2×C3×C8—61no—
156C2×C3×C8—61no—
157C2×C3×C8—61no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—31no—
163C3×C4⋊C4—31no—
164C3×C4⋊C4—41no—
165C3×C4⋊C4—41no—
166C3×C22⋊C4—61no—
167C3×C42—61no—
168#217—21no—
169C4⋊Dic3#6711yescharacteristic
170C4⋊Dic3#6711yescharacteristic
171C4×Dic3—21no—
172#208—21no—
173#208—62no—
174#208—62no—
175#208—61no—
176#208—61no—
177#208—61no—
178#208—61no—
179#208—61no—
180#208—61no—
181#208—61no—
182#208—61no—
183#208—121no—
184#208—121no—
185#208D1212yes—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—61no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—121no—
194C2×C3⋊C8—121no—
195C2×C3⋊C8#6712yes—
196C22×C32—21no—
197C22×C32—21no—
198C22×C32#12111yescharacteristic
199C22×C32C22⋊Q811yescharacteristic
200C22×C32#12611yescharacteristic
201C2×C3×D3—42no—
202C2×C3×D3—82no—
203C2×C3×D3—81no—
204C2×C3×D3—81no—
205C2×C3×D3—82no—
206C32×C4—81no—
207C32×C4#12111yescharacteristic
208C32×C4#12111yescharacteristic
209C32×C4C22⋊Q811yescharacteristic
210C32×C4C22⋊Q811yescharacteristic
211C3×Dic3—41no—
212C3×Dic3—41no—
213C22×D4—31no—
214C2×M16—31no—
215C2×M16—91no—
216C2×M16—91no—
217C22×C8—31no—
218#117—31no—
219C2×C4⋊C4D3211yescharacteristic
220#108—182no—
221#107—61no—
222#106—61no—
223C4⋊C8—182no—
224#102—62no—
225#102—181no—
226#102—181no—
227#100—182no—
228C23×C3—21no—
229C23×C3—62no—
230C23×C3—121no—
231C23×C3—121no—
232C23×C3—241no—
233C23×C3—241no—
234C23×C3#23711yescharacteristic
235C23×C3#23711yescharacteristic
236C22×D3—22no—
237C22×D3—41no—
238C22×D3—41no—
239C22×D3—81no—
240C22×D3—81no—
241C3×D4—62no—
242C3×D4—62no—
243C3×D4—121no—
244C3×D4—121no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—42no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—61no—
255C2×C3×C4—61no—
256C2×C3×C4—81no—
257C2×C3×C4—81no—
258C2×C3×C4—82no—
259C2×C3×C4C2×Dic611yescharacteristic
260C2×C3×C4C2×D1211yescharacteristic
261C2×C3×C4#23511yescharacteristic
262C2×C3×C4#23511yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4#23711yescharacteristic
267C2×C3×C4D3×Q811yescharacteristic
268C2×C3×C4#23911yescharacteristic
269C2×C3×C4C2×#6711yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×Dic3—21no—
272C2×Dic3—21no—
273D12—22no—
274D12—22no—
275D12—41no—
276D12—41no—
277C3×C8—62no—
278C3×C8—62no—
279C3⋊C8—22no—
280C3⋊C8—22no—
281C3⋊C8—122no—
282C3⋊C8—122no—
283C3⋊C8—121no—
284C3⋊C8—121no—
285C3⋊C8—121no—
286C3⋊C8—121no—
287C2×C32—21no—
288C2×C32—21no—
289C2×C32#39611yescharacteristic
290C2×C32#47111yescharacteristic
291C2×C32#47211yescharacteristic
292C3×D3—82no—
293C24—61no—
294C2×D4—32no—
295C2×D4—61no—
296C2×D4—61no—
297C2×D4—61no—
298C2×D4—61no—
299C2×D4—61no—
300C22×C4—21no—
301C22×C4C2×D3211yescharacteristic
302M16—32no—
303M16—61no—
304M16—181no—
305M16—181no—
306M16—181no—
307M16—181no—
308C2×C8—32no—
309C2×C8—61no—
310C2×C8—61no—
311C2×C8—61no—
312C2×C8—181no—
313C2×C8—181no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—31no—
317C4⋊C4—31no—
318C22⋊C4—61no—
319C42—61no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—122no—
330C22×C3—242no—
331C22×C3—242no—
332C22×C3—241no—
333C22×C3—241no—
334C22×C3#87811yescharacteristic
335C22×C3#87911yescharacteristic
336C22×C3#89711yescharacteristic
337C22×C3#89811yescharacteristic
338C22×C3#93811yescharacteristic
339C22×C3#93911yescharacteristic
340C2×D3—42no—
341C2×D3—82no—
342C2×D3—81no—
343C2×D3—81no—
344C2×D3—82no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—82no—
350C3×C4—81no—
351C3×C4—81no—
352C3×C4—121no—
353C3×C4—121no—
354C3×C4#87811yescharacteristic
355C3×C4#88411yescharacteristic
356C3×C4#89511yescharacteristic
357C3×C4#89611yescharacteristic
358C3×C4#92411yescharacteristic
359C3×C4#93011yescharacteristic
360C3×C4#93911yescharacteristic
361C3×C4#94611yescharacteristic
362Dic3—41no—
363Dic3—41no—
364C32#206311yescharacteristic, complemented, Sylow
365C23—62no—
366C23—121no—
367C23—121no—
368C23—241no—
369C23—241no—
370C23#380511yescharacteristic
371D4—62no—
372D4—62no—
373D4—121no—
374D4—121no—
375C2×C4—41no—
376C2×C4—61no—
377C2×C4—61no—
378C2×C4—81no—
379C2×C4D3×Dic611yescharacteristic
380C2×C4#379611yescharacteristic
381C2×C4#379811yescharacteristic
382C2×C4D3×D1211yescharacteristic
383C2×C4D3×#6711yescharacteristic
384C2×C4D3×#6711yescharacteristic
385C8—62no—
386C8—62no—
387C8—361no—
388C8—361no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—41no—
397C2×C3—41no—
398C2×C3—242no—
399C2×C3#494811yescharacteristic
400C2×C3#499411yescharacteristic
401C2×C3#516011yescharacteristic
402C2×C3#517711yescharacteristic
403C2×C3#519911yescharacteristic
404C2×C3#520311yescharacteristic
405D3—82no—
406C22—21no—
407C22—21no—
408C22—122no—
409C22—242no—
410C22—242no—
411C22—241no—
412C22—241no—
413C22#6386211yescharacteristic
414C22#6389311yescharacteristic
415C22#6397011yescharacteristic
416C4—81no—
417C4—121no—
418C4—121no—
419C4#6385111yescharacteristic
420C4#6388611yescharacteristic
421C4#6388711yescharacteristic
422C4#6390611yescharacteristic
423C3—21no—
424C3#7019711yescharacteristic, complemented
425C3#7067611yescharacteristic, complemented
426C2—21no—
427C2—21no—
428C2—242no—
429C2#1059130611yescharacteristic
430C2#1059150511yescharacteristic
431C2#1059164211yescharacteristic
subgroupG/H
centerC22#63970
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#121
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2063
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
2. C3×#4964C2semidirect
3. C2×#63577C2semidirect
4. #10591116C2semidirect
7. #10589396C2semidirect
36. #4964D3semidirect
364. C32#2063semidirect
424. C3#70197semidirect
425. C3#70676semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8092
C3×#49642
C2×#635772
#105911162
#105910852
C2×#635582
#105893962
#706763
#701973