Finite Group Databasebeta

← #11785924

Subgroups — #11785924

Order 1152.

637 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594996C211yesmaximal, characteristic
2C2×#63650C211yesmaximal, characteristic
3C2×#63559C211yesmaximal, characteristic
4C3×#4559C211yesmaximal, characteristic, complemented
5C3×#4556C211yesmaximal, characteristic, complemented
6#10589170C211yesmaximal, characteristic, complemented
7#10589169C211yesmaximal, characteristic, complemented
8#69026—31nomaximal
9#69026—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63974C414yes—
18#63894—22no—
19#63894—22no—
20#63650—22no—
21#63559—22no—
22#5521—31no—
23#5521—31no—
24C2×#823—31no—
25C2×#823—31no—
26C2×#823—31no—
27C2×#823—31no—
28C2×#823—61no—
29C3×#344—31no—
30C3×#344—31no—
31#4559—31no—
32#4559D311yescharacteristic, complemented
33#4556—31no—
34#4556D311yescharacteristic, complemented
35#4533—31no—
36#4533—31no—
37C23×C3⋊D3C2×C412yes—
38C22×C32×C4C2311yescharacteristic
39C2×C4⋊(C3⋊D3)—21no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)D412yes—
44C2×C4⋊(C3⋊D3)D412yes—
45C2×#624—24no—
46C32×M16—21no—
47C32×M16—21no—
48C2×C32×C8—21no—
49#3748—21no—
50#3748—21no—
51C2×C3⋊(C3⋊C8)—21no—
52C3×#217C2×C412yes—
53C3×#217C2×C412yes—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3—21no—
56C3×C4×Dic3—21no—
57C3×C4×Dic3—21no—
58C3×#208—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#3722—24no—
65#1829—91noSylow
66C22×D12—31no—
67C22×D12—31no—
68C22×D12—61no—
69C2×C3×M16—21no—
70C2×C3×M16—31no—
71C2×C3×M16—31no—
72C2×C3×M16C2×D311yescharacteristic
73C2×C3×M16C2×D311yescharacteristic
74C3×#117—31no—
75C3×#117—31no—
76#926C2×D311yescharacteristic
77#926C2×D311yescharacteristic
78C2×#208—31no—
79C2×#208—31no—
80C2×#208—61no—
81C2×#208C2×D311yescharacteristic
82C2×#208C2×D311yescharacteristic
83#893—62no—
84#893—62no—
85D3×C22⋊C4—34no—
86D3×C22⋊C4—34no—
87C4×D12—62no—
88C4×D12—62no—
89#823—62no—
90#823—62no—
91#823—62no—
92#823—62no—
93#823—64no—
94C23×C32C22×C411yescharacteristic
95C22×C3⋊D3—22no—
96C22×C3⋊D3—22no—
97C22×C3⋊D3—82no—
98C22×C3⋊D3C22⋊C414yes—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C4⋊(C3⋊D3)—22no—
106C4⋊(C3⋊D3)—22no—
107C4⋊(C3⋊D3)—22no—
108C4⋊(C3⋊D3)—22no—
109C2×C3×Dic3—22no—
110C2×C3×Dic3—22no—
111#624—84no—
112C32×C8—41no—
113C3⋊(C3⋊C8)—41no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8—41no—
116#518—91no—
117C2×#100—91no—
118C2×#100—91no—
119#344—31no—
120#344—31no—
121#344—91no—
122#344—91no—
123C23×D3—32no—
124C23×D3—32no—
125C23×D3—62no—
126C22×C3×C4—21no—
127C22×C3×C4C22×D311yescharacteristic
128C22×C3×C4C22×D311yescharacteristic
129C2×D12—32no—
130C2×D12—32no—
131C2×D12—32no—
132C2×D12—32no—
133C2×D12—62no—
134C2×D12—62no—
135C2×D12—61no—
136C2×D12—61no—
137C2×D12—61no—
138C2×D12—61no—
139C2×D12—61no—
140C2×D12—61no—
141C2×D12—61no—
142C2×D12—61no—
143C2×D12—121no—
144C2×D12—121no—
145C2×D12—121no—
146C2×D12—121no—
147C2×C4×D3—64no—
148C2×C4×D3—64no—
149C3×M16—22no—
150C3×M16—21no—
151C3×M16—21no—
152C3×M16—21no—
153C3×M16—21no—
154C3×M16—41no—
155C3×M16—61no—
156C3×M16—61no—
157C3×M16—61no—
158C3×M16—61no—
159C2×C3×C8—21no—
160C2×C3×C8—21no—
161C2×C3×C8—41no—
162C2×C3×C8—61no—
163C2×C3×C8—61no—
164C3×C4⋊C4—61no—
165C3×C4⋊C4—61no—
166C3×C22⋊C4—32no—
167C3×C22⋊C4—32no—
168C3×C42—61no—
169C3×C42—61no—
170#217C4×D312yes—
171#217C4×D312yes—
172(C2×D3)⋊C4—64no—
173(C2×D3)⋊C4—64no—
174C4⋊Dic3—21no—
175C4⋊Dic3—21no—
176C4×Dic3—21no—
177C4×Dic3—21no—
178#208—21no—
179#208—21no—
180#208—21no—
181#208—21no—
182#208—62no—
183#208—61no—
184#208—61no—
185#208—61no—
186#208—61no—
187#208—121no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—121no—
193C22×C32—41no—
194C22×C32C2×C22⋊C411yescharacteristic
195C22×C32#11711yescharacteristic
196C22×C32#11711yescharacteristic
197C2×C3⋊D3—24no—
198C2×C3⋊D3—44no—
199C2×C3⋊D3—82no—
200C2×C3⋊D3—82no—
201C32×C4#12311yescharacteristic
202C32×C4#12311yescharacteristic
203C32×C4#12311yescharacteristic
204C32×C4#12311yescharacteristic
205C3×Dic3—42no—
206C3×Dic3—42no—
207C22×D4—91no—
208C2×M16—31no—
209C2×M16—31no—
210C2×M16—91no—
211C2×M16D3211yescharacteristic
212C4×D4—182no—
213C4×D4—182no—
214#117—31no—
215#117—31no—
216C2×C22⋊C4—94no—
217#100—182no—
218#100—182no—
219C23×C3—21no—
220C23×C3C2×C4×D311yescharacteristic
221C23×C3C2×C4×D311yescharacteristic
222C22×D3—34no—
223C22×D3—34no—
224C22×D3—64no—
225C22×D3—62no—
226C22×D3—62no—
227C22×D3—62no—
228C22×D3—62no—
229C22×D3—122no—
230C22×D3—122no—
231C22×D3—242no—
232C22×D3—242no—
233C22×D3—244no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—62no—
241C2×C3×C4—62no—
242C2×C3×C4#23511yescharacteristic
243C2×C3×C4#23511yescharacteristic
244C2×C3×C4#23511yescharacteristic
245C2×C3×C4#23511yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4#23711yescharacteristic
251C2×C3×C4#23711yescharacteristic
252C2×C3×C4#23911yescharacteristic
253C2×C3×C4#23911yescharacteristic
254C2×Dic3—22no—
255C2×Dic3—22no—
256D12—62no—
257D12—62no—
258D12—62no—
259D12—62no—
260D12—62no—
261D12—62no—
262D12—62no—
263D12—62no—
264D12—122no—
265D12—122no—
266D12—122no—
267D12—122no—
268C4×D3—244no—
269C4×D3—244no—
270C3×C8—42no—
271C3×C8—41no—
272C3×C8—41no—
273C3×C8—121no—
274C3×C8—121no—
275C3⋊C8—41no—
276C3⋊C8—41no—
277C3⋊C8—122no—
278C3⋊C8—121no—
279C3⋊C8—121no—
280C2×C32—21no—
281C2×C32—21no—
282C2×C32—21no—
283C2×C32#38111yescharacteristic
284C3⋊D3—44no—
285C24—92no—
286C2×D4—92no—
287C2×D4—92no—
288C2×D4—181no—
289C2×D4—181no—
290C2×D4—181no—
291C2×D4—181no—
292C22×C4—184no—
293C22×C4C2×D3211yescharacteristic
294M16—21no—
295M16—21no—
296M16—61no—
297M16—61no—
298M16—61no—
299M16—61no—
300M16—181no—
301M16—181no—
302C2×C8—21no—
303C2×C8—61no—
304C2×C8—61no—
305C2×C8—181no—
306C4⋊C4—61no—
307C4⋊C4—61no—
308C22⋊C4—32no—
309C22⋊C4—32no—
310C22⋊C4—184no—
311C42—61no—
312C42—61no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—41no—
317C22×C3—41no—
318C22×C3—42no—
319C22×C3#87211yescharacteristic
320C22×C3#87211yescharacteristic
321C22×C3D3×C22⋊C411yescharacteristic
322C22×C3D3×C22⋊C411yescharacteristic
323C22×C3#89211yescharacteristic
324C22×C3#89211yescharacteristic
325C2×D3—64no—
326C2×D3—64no—
327C2×D3—124no—
328C2×D3—124no—
329C2×D3—124no—
330C2×D3—244no—
331C2×D3—242no—
332C2×D3—242no—
333C2×D3—242no—
334C2×D3—242no—
335C2×D3—244no—
336C2×D3—244no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—122no—
342C3×C4—122no—
343C3×C4#88311yescharacteristic
344C3×C4#88311yescharacteristic
345C3×C4#88311yescharacteristic
346C3×C4#88311yescharacteristic
347C3×C4#89411yescharacteristic
348C3×C4#89411yescharacteristic
349C3×C4#89411yescharacteristic
350C3×C4#89411yescharacteristic
351Dic3—42no—
352Dic3—42no—
353C32#182911yescharacteristic, complemented, Sylow
354C23—94no—
355C23—182no—
356C23—182no—
357C23—722no—
358C23C4×D3211yescharacteristic
359D4—182no—
360D4—182no—
361D4—182no—
362D4—182no—
363C2×C4—62no—
364C2×C4—62no—
365C2×C4—724no—
366C2×C4#379911yescharacteristic
367C2×C4#379911yescharacteristic
368C2×C4#380211yescharacteristic
369C2×C4#380411yescharacteristic
370C2×C4#380411yescharacteristic
371C2×C4#381111yescharacteristic
372C8—41no—
373C8—121no—
374C8—121no—
375C8—361no—
376C2×C3—22no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—41no—
385C2×C3—41no—
386C2×C3#466411yescharacteristic
387C2×C3#466411yescharacteristic
388D3—124no—
389D3—124no—
390D3—244no—
391C22—41no—
392C22—184no—
393C22—364no—
394C22—722no—
395C22—722no—
396C22#6383611yescharacteristic
397C22#6383611yescharacteristic
398C22#6392111yescharacteristic
399C4—122no—
400C4—122no—
401C4#6385411yescharacteristic
402C4#6385411yescharacteristic
403C4#6389711yescharacteristic
404C4#6397511yescharacteristic
405C3—21no—
406C3#6902611yescharacteristic, complemented
407C3#6902611yescharacteristic, complemented
408C2—21no—
409C2—21no—
410C2—21no—
411C2—364no—
412C2#1059137111yescharacteristic
subgroupG/H
centerC2#10591371
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#381
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1829
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. C3×#4559C2semidirect
5. C3×#4556C2semidirect
6. #10589170C2semidirect
7. #10589169C2semidirect
32. #4559D3semidirect
34. #4556D3semidirect
353. C32#1829semidirect
406. C3#69026semidirect
407. C3#69026semidirect

Maximal subgroups

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

subgroupindex
#105949962
C2×#636502
C2×#635592
C3×#45592
C3×#45562
#105891702
#105891692
#690263