Finite Group Databasebeta

← #11794346

Subgroups — #11794346

Order 1152.

509 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63649C211yesmaximal, characteristic, complemented
2C3×#5131C211yesmaximal, characteristic
3#10591139C211yesmaximal, characteristic, complemented
4#10591117C211yesmaximal, characteristic, complemented
5C2×#63562C211yesmaximal, characteristic
6C2×#63558C211yesmaximal, characteristic
7C3×#4554C211yesmaximal, characteristic, complemented
8#70317—31nomaximal
9#68996—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63649—22no—
18C3×#821—21no—
19C3×#821—21no—
20#63576—21no—
21#63574—21no—
22Dic3⋊(C3⋊C8)—22no—
23#63562—22no—
24#63558—22no—
25C3×#418—31no—
26C2×#833—31no—
27C2×#832—31no—
28#5131D311yescharacteristic
29C2×#823—31no—
30C2×#822—31no—
31C2×#822—31no—
32C2×#822—61no—
33#5119—31no—
34#4999—31no—
35#4995—31no—
36C2×#809—31no—
37#4964—31no—
38C3×#343—31no—
39#4554D311yescharacteristic, complemented
40C23×C3×D3—21no—
41C22×C32×C4C2311yescharacteristic
42C22×C3×Dic3—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12Q812yes—
49C32×M16—21no—
50C32×M16—21no—
51C2×C32×C8—21no—
52#3748—21no—
53#3748D412yes—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)D412yes—
58C3×#217—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×C4⋊Dic3D411yescharacteristic
63C3×C4×Dic3—21no—
64C3×#208—21no—
65C3×#208—21no—
66C2×C3×C3⋊C8—21no—
67#2063—91noSylow
68C22×C3×D4—31no—
69C22×D12C2×D311yescharacteristic
70C2×C3×M16—21no—
71C2×C3×M16—31no—
72C2×C3×M16C2×D311yescharacteristic
73C2×C3×M16C2×D311yescharacteristic
74C3×#117—31no—
75C2×C3×C4⋊C4—31no—
76#926C2×D311yescharacteristic
77C2×C4⋊Dic3C2×D311yescharacteristic
78C2×#208—31no—
79C2×#208—31no—
80C2×#208—61no—
81C2×#208C2×D311yescharacteristic
82C22×C3⋊C8—31no—
83C22×C3⋊C8—31no—
84C22×C3⋊C8—61no—
85C3×#102—61no—
86C3×#102—61no—
87#833—62no—
88#832—62no—
89#823—62no—
90#822—62no—
91#822—62no—
92#822—64no—
93#821—21no—
94#821—21no—
95Dic3⋊C8—62no—
96#809—62no—
97#808—61no—
98#808—61no—
99#807—61no—
100#807—61no—
101C4⋊(C3⋊C8)—62no—
102C23×C32#4111yescharacteristic
103C22×C3×D3—22no—
104C22×C3×D3—41no—
105C22×C3×D3—41no—
106C22×C3×D3—81no—
107C22×C3×D3—81no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×Q811yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C3×Dic3—21no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—41no—
117C2×C3×Dic3—81no—
118C3×D12—22no—
119C3×D12—22no—
120C3×D12—41no—
121C3×D12—41no—
122C32×C8—41no—
123C3⋊(C3⋊C8)—22no—
124C3⋊(C3⋊C8)—22no—
125C3×C3⋊C8—41no—
126C2×#108—91no—
127#428—91no—
128#424—91no—
129#418—31no—
130C2×#102—91no—
131C2×#100—91no—
132#343—31no—
133C24×C3—61no—
134C23×D3—21no—
135C2×C3×D4—32no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C2×C3×D4—61no—
139C2×C3×D4—61no—
140C2×C3×D4—61no—
141C22×C3×C4—21no—
142C22×C3×C4—61no—
143C22×C3×C4C22×D311yescharacteristic
144C22×C3×C4C22×D311yescharacteristic
145C22×Dic3—21no—
146C2×D12—21no—
147C2×D12—21no—
148C2×D12—21no—
149C2×D12—21no—
150C2×D12—21no—
151C2×D12Dic612yes—
152C3×M16—22no—
153C3×M16—21no—
154C3×M16—21no—
155C3×M16—21no—
156C3×M16—21no—
157C3×M16—41no—
158C3×M16—61no—
159C3×M16—61no—
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—41no—
163C2×C3×C8—61no—
164C3×C4⋊C4—31no—
165C3×C4⋊C4—31no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4—61no—
168C3×C22⋊C4—61no—
169C3×C42—61no—
170#217—21no—
171C4⋊Dic3—21no—
172C4⋊Dic3—21no—
173C4⋊Dic3#6711yescharacteristic
174C4⋊Dic3#6711yescharacteristic
175C4×Dic3—21no—
176#208—21no—
177#208—21no—
178#208—32no—
179#208—32no—
180#208—62no—
181#208—61no—
182#208—61no—
183#208—121no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—32no—
186C2×C3⋊C8—32no—
187C2×C3⋊C8—62no—
188C2×C3⋊C8—62no—
189C2×C3⋊C8—62no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—121no—
197C22×C32—21no—
198C22×C32—21no—
199C22×C32#12111yescharacteristic
200C22×C32C22⋊Q811yescharacteristic
201C22×C32#12611yescharacteristic
202C2×C3×D3—42no—
203C2×C3×D3—82no—
204C2×C3×D3—81no—
205C2×C3×D3—81no—
206C2×C3×D3—82no—
207C32×C4#12111yescharacteristic
208C32×C4#12111yescharacteristic
209C32×C4C22⋊Q811yescharacteristic
210C32×C4C22⋊Q811yescharacteristic
211C3×Dic3—41no—
212C3×Dic3—41no—
213C3×Dic3—81no—
214C22×D4—31no—
215C2×M16—31no—
216C2×M16—91no—
217C2×M16D3211yescharacteristic
218C22×C8—91no—
219#117—31no—
220C2×C4⋊C4—31no—
221#108—182no—
222#107—181no—
223#106—181no—
224C4⋊C8—182no—
225#102—61no—
226#102—61no—
227#102—182no—
228#100—182no—
229C23×C3—21no—
230C23×C3—62no—
231C23×C3—121no—
232C23×C3—121no—
233C23×C3—241no—
234C23×C3—241no—
235C23×C3#23511yescharacteristic
236C23×C3#23711yescharacteristic
237C22×D3—22no—
238C22×D3—41no—
239C22×D3—41no—
240C22×D3—81no—
241C22×D3—81no—
242C3×D4—62no—
243C3×D4—62no—
244C3×D4—121no—
245C3×D4—121no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—61no—
253C2×C3×C4—61no—
254C2×C3×C4—121no—
255C2×C3×C4—241no—
256C2×C3×C4C2×Dic611yescharacteristic
257C2×C3×C4#23511yescharacteristic
258C2×C3×C4#23511yescharacteristic
259C2×C3×C4#23511yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4#23711yescharacteristic
266C2×C3×C4D3×Q811yescharacteristic
267C2×C3×C4C2×#6711yescharacteristic
268C2×Dic3—21no—
269C2×Dic3—21no—
270C2×Dic3—41no—
271C2×Dic3—81no—
272D12—22no—
273D12—22no—
274D12—41no—
275D12—41no—
276C3×C8—42no—
277C3×C8—41no—
278C3×C8—41no—
279C3×C8—121no—
280C3⋊C8—41no—
281C3⋊C8—64no—
282C3⋊C8—62no—
283C3⋊C8—62no—
284C3⋊C8—62no—
285C3⋊C8—62no—
286C3⋊C8—122no—
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—61no—
301C22×C4C2×D3211yescharacteristic
302M16—21no—
303M16—21no—
304M16—61no—
305M16—61no—
306M16—92no—
307M16—181no—
308C2×C8—21no—
309C2×C8—61no—
310C2×C8—92no—
311C2×C8—181no—
312C2×C8—181no—
313C2×C8—181no—
314C4⋊C4—31no—
315C4⋊C4—31no—
316C4⋊C4—61no—
317C4⋊C4—61no—
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#87611yescharacteristic
335C22×C3#87811yescharacteristic
336C22×C3#87911yescharacteristic
337C22×C3#88411yescharacteristic
338C22×C3#89611yescharacteristic
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—121no—
350C3×C4—121no—
351C3×C4—241no—
352C3×C4#87811yescharacteristic
353C3×C4#88411yescharacteristic
354C3×C4#88411yescharacteristic
355C3×C4#88411yescharacteristic
356C3×C4#89611yescharacteristic
357C3×C4#89611yescharacteristic
358C3×C4#92411yescharacteristic
359C3×C4#93811yescharacteristic
360Dic3—41no—
361Dic3—41no—
362Dic3—81no—
363C32#206311yescharacteristic, complemented, Sylow
364C23—62no—
365C23—121no—
366C23—121no—
367C23—241no—
368C23—241no—
369C23#379511yescharacteristic
370D4—62no—
371D4—62no—
372D4—121no—
373D4—121no—
374C2×C4—61no—
375C2×C4—61no—
376C2×C4—121no—
377C2×C4—241no—
378C2×C4D3×Dic611yescharacteristic
379C2×C4#379811yescharacteristic
380C2×C4#380211yescharacteristic
381C2×C4#380411yescharacteristic
382C2×C4D3×#6711yescharacteristic
383C2×C4#381111yescharacteristic
384C8—41no—
385C8—121no—
386C8—182no—
387C8—182no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—41no—
396C2×C3—41no—
397C2×C3—242no—
398C2×C3#467611yescharacteristic
399C2×C3#474911yescharacteristic
400C2×C3#475411yescharacteristic
401C2×C3#494811yescharacteristic
402C2×C3#519911yescharacteristic
403C2×C3#520011yescharacteristic
404D3—82no—
405C22—21no—
406C22—21no—
407C22—122no—
408C22—242no—
409C22—242no—
410C22—241no—
411C22—241no—
412C22#6385911yescharacteristic
413C22#6388511yescharacteristic
414C22#6389611yescharacteristic
415C4—121no—
416C4—121no—
417C4—241no—
418C4#6385111yescharacteristic
419C4#6389911yescharacteristic
420C4#6391211yescharacteristic
421C4#6395811yescharacteristic
422C3—21no—
423C3#6899611yescharacteristic, complemented
424C3#7031711yescharacteristic, complemented
425C2—21no—
426C2—21no—
427C2—242no—
428C2#1059098011yescharacteristic
429C2#1059098211yescharacteristic
430C2#1059130911yescharacteristic
subgroupG/H
centerC22#63885
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC22×C3×D12C22
hypercenterC2×M16D32
hypocenterC32#2063
LCSG ▷ C22×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. C2×#63649C2semidirect
3. #10591139C2semidirect
4. #10591117C2semidirect
7. C3×#4554C2semidirect
39. #4554D3semidirect
363. C32#2063semidirect
423. C3#68996semidirect
424. C3#70317semidirect

Maximal subgroups

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

subgroupindex
C2×#636492
C3×#51312
#105911392
#105911172
C2×#635622
C2×#635582
C3×#45542
#703173
#689963