Finite Group Databasebeta

← #11794613

Subgroups — #11794613

Order 1152.

483 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592824C211yesmaximal, characteristic, complemented
2C2×C3×#823C211yesmaximal, characteristic
3C3×#5124C211yesmaximal, characteristic, complemented
4#10591143C211yesmaximal, characteristic, complemented
5C2×#63558C211yesmaximal, characteristic
6C2×#63558C211yesmaximal, characteristic
7#10589159C211yesmaximal, characteristic, complemented
8#70730—31nomaximal
9#70077—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63646—22no—
18C3×#823—22no—
19C3×#822—22no—
20#63578—22no—
21#63558—22no—
22#63558—22no—
23C3×#430—31no—
24C2×C3×#100—31no—
25C2×#833—31no—
26C2×#833—31no—
27C2×#823—31no—
28C2×#823—31no—
29C2×#823D311yescharacteristic
30#5125—31no—
31#5125—31no—
32#5125—61no—
33#5124—31no—
34#5124—31no—
35#5124D311yescharacteristic, complemented
36C3⋊#338—31no—
37C3⋊#338—31no—
38C23×C3×D3Q812yes—
39C22×C32×C4C2311yescharacteristic
40C2×C3×D12—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C32×M16—21no—
47C32×M16D412yes—
48C2×C32×C8—21no—
49#3748—21no—
50#3748—21no—
51#3748—21no—
52#3748D412yes—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C3×#208—21no—
56C3×#208—21no—
57C3×#208—21no—
58C3×#208—21no—
59C3×#208—21no—
60C3×#208D412yes—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#2069—91noSylow
65C22×C3×D4—31no—
66C22×D12C2×D311yescharacteristic
67C2×C3×M16—21no—
68C2×C3×M16—31no—
69C2×C3×M16—31no—
70C2×C3×M16—31no—
71C2×C3×M16C2×D311yescharacteristic
72C2×C3×M16C2×D311yescharacteristic
73C2×#208—31no—
74C2×#208—31no—
75C2×#208—31no—
76C2×#208—31no—
77C2×#208—61no—
78C2×#208—61no—
79C2×#208C2×D311yescharacteristic
80C2×#208C2×D311yescharacteristic
81C2×#208C2×D311yescharacteristic
82C3×#108—62no—
83C3×#100—62no—
84#833—62no—
85#833—62no—
86#823—22no—
87#823—62no—
88#823—62no—
89#822—22no—
90#822—62no—
91#822—62no—
92#819—62no—
93#819—62no—
94#819—64no—
95C23×C32C2×Q811yescharacteristic
96C22×C3×D3—22no—
97C22×C3×D3—22no—
98C22×C3×D3—22no—
99C22×C3×D3—82no—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C32×C4#4111yescharacteristic
106C3×D12—41no—
107C3×D12—41no—
108C3×D12—41no—
109C3×D12—41no—
110C32×C8—22no—
111C3⋊(C3⋊C8)—22no—
112C3⋊(C3⋊C8)—41no—
113C3×C3⋊C8—22no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8—41no—
116#430—31no—
117#430—91no—
118#430—91no—
119C2×#100—31no—
120C2×#100—91no—
121C2×#100—91no—
122#338—91no—
123C24×C3—32no—
124C23×D3Dic612yes—
125C2×C3×D4—61no—
126C2×C3×D4—61no—
127C2×C3×D4—61no—
128C2×C3×D4—61no—
129C2×C3×D4—61no—
130C2×C3×D4—61no—
131C22×C3×C4—21no—
132C22×C3×C4C22×D311yescharacteristic
133C22×C3×C4C22×D311yescharacteristic
134C2×D12—21no—
135C2×D12—21no—
136C2×D12—21no—
137C2×D12—21no—
138C2×D12—21no—
139C2×D12—21no—
140C3×M16—22no—
141C3×M16—21no—
142C3×M16—21no—
143C3×M16—22no—
144C3×M16—32no—
145C3×M16—61no—
146C3×M16—61no—
147C3×M16—61no—
148C3×M16—61no—
149C3×M16—61no—
150C3×M16#6712yes—
151C3×M16#6712yes—
152C2×C3×C8—22no—
153C2×C3×C8—21no—
154C2×C3×C8—21no—
155C2×C3×C8—61no—
156C2×C3×C8—61no—
157C2×C3×C8—61no—
158#208—21no—
159#208—21no—
160#208—21no—
161#208—21no—
162#208—21no—
163#208—32no—
164#208—32no—
165#208—62no—
166#208—61no—
167#208—61no—
168#208—62no—
169#208—61no—
170#208—61no—
171#208—61no—
172#208—61no—
173#208—121no—
174#208—121no—
175#208D1212yes—
176C2×C3⋊C8—21no—
177C2×C3⋊C8—21no—
178C2×C3⋊C8—21no—
179C2×C3⋊C8—61no—
180C2×C3⋊C8—61no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—61no—
183C2×C3⋊C8—121no—
184C2×C3⋊C8—121no—
185C22×C32—41no—
186C22×C32C22⋊Q811yescharacteristic
187C22×C32C22⋊Q811yescharacteristic
188C22×C32C22⋊Q811yescharacteristic
189C2×C3×D3—42no—
190C2×C3×D3—82no—
191C2×C3×D3—82no—
192C2×C3×D3—82no—
193C32×C4#12111yescharacteristic
194C32×C4#12111yescharacteristic
195C32×C4#12111yescharacteristic
196C32×C4#12611yescharacteristic
197C22×D4—31no—
198C2×M16—31no—
199C2×M16—31no—
200C2×M16—31no—
201C2×M16—91no—
202C2×M16—91no—
203C2×M16D3211yescharacteristic
204#108—62no—
205#108—182no—
206#108—182no—
207#100—62no—
208#100—182no—
209#100—182no—
210C23×C3—21no—
211C23×C3—62no—
212C23×C3—62no—
213C23×C3—62no—
214C23×C3—242no—
215C23×C3C2×Dic611yescharacteristic
216C23×C3D3×Q811yescharacteristic
217C22×D3—22no—
218C22×D3—22no—
219C22×D3—22no—
220C22×D3—82no—
221C3×D4—121no—
222C3×D4—121no—
223C3×D4—121no—
224C3×D4—121no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4C2×D1211yescharacteristic
232C2×C3×C4#23511yescharacteristic
233C2×C3×C4#23511yescharacteristic
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4#23711yescharacteristic
238C2×C3×C4#23711yescharacteristic
239C2×C3×C4#23711yescharacteristic
240C2×C3×C4#23911yescharacteristic
241C2×C3×C4C2×#6711yescharacteristic
242C2×C3×C4C2×#6711yescharacteristic
243D12—41no—
244D12—41no—
245D12—41no—
246D12—41no—
247C3×C8—24no—
248C3×C8—22no—
249C3×C8—22no—
250C3×C8—62no—
251C3×C8—121no—
252C3×C8—121no—
253C3⋊C8—22no—
254C3⋊C8—41no—
255C3⋊C8—41no—
256C3⋊C8—62no—
257C3⋊C8—62no—
258C3⋊C8—122no—
259C3⋊C8—122no—
260C3⋊C8—121no—
261C3⋊C8—121no—
262C2×C32—21no—
263C2×C32—21no—
264C2×C32—21no—
265C2×C32#39611yescharacteristic
266C3×D3—82no—
267C24—32no—
268C2×D4—61no—
269C2×D4—61no—
270C2×D4—61no—
271C2×D4—61no—
272C2×D4—61no—
273C2×D4—61no—
274C22×C4C2×D3211yescharacteristic
275M16—21no—
276M16—32no—
277M16—61no—
278M16—61no—
279M16—61no—
280M16—61no—
281M16—61no—
282M16—92no—
283M16—181no—
284M16—181no—
285M16—181no—
286M16#62512yes—
287C2×C8—21no—
288C2×C8—61no—
289C2×C8—61no—
290C2×C8—61no—
291C2×C8—181no—
292C2×C8—181no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—41no—
297C22×C3—41no—
298C22×C3—81no—
299C22×C3—122no—
300C22×C3—242no—
301C22×C3—242no—
302C22×C3—242no—
303C22×C3#87811yescharacteristic
304C22×C3#87811yescharacteristic
305C22×C3#89611yescharacteristic
306C22×C3#89711yescharacteristic
307C22×C3#92411yescharacteristic
308C22×C3#94611yescharacteristic
309C2×D3—42no—
310C2×D3—82no—
311C2×D3—82no—
312C2×D3—82no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4#87911yescharacteristic
318C3×C4#88411yescharacteristic
319C3×C4#89511yescharacteristic
320C3×C4#89811yescharacteristic
321C3×C4#93011yescharacteristic
322C3×C4#93811yescharacteristic
323C3×C4#93911yescharacteristic
324C3×C4#93911yescharacteristic
325C32#206911yescharacteristic, complemented, Sylow
326C23—62no—
327C23—62no—
328C23—62no—
329C23—242no—
330C23D3×Dic611yescharacteristic
331D4—121no—
332D4—121no—
333D4—121no—
334D4—121no—
335C2×C4#379511yescharacteristic
336C2×C4#379911yescharacteristic
337C2×C4D3×D1211yescharacteristic
338C2×C4#380511yescharacteristic
339C2×C4C2×#62511yescharacteristic
340C2×C4#381111yescharacteristic
341C8—22no—
342C8—62no—
343C8—121no—
344C8—121no—
345C8—182no—
346C8—361no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—41no—
355C2×C3—41no—
356C2×C3—41no—
357C2×C3—242no—
358C2×C3#494811yescharacteristic
359C2×C3#499411yescharacteristic
360D3—82no—
361C22—41no—
362C22—122no—
363C22—242no—
364C22—242no—
365C22—242no—
366C22#6385611yescharacteristic
367C22#6389311yescharacteristic
368C22#6389611yescharacteristic
369C4#6386111yescharacteristic
370C4#6390811yescharacteristic
371C4#6391011yescharacteristic
372C4#6398011yescharacteristic
373C3—21no—
374C3#7007711yescharacteristic, complemented
375C3#7073011yescharacteristic, complemented
376C2—21no—
377C2—21no—
378C2—21no—
379C2—242no—
380C2#1059131911yescharacteristic
subgroupG/H
centerC2#10591319
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#396
prime radicalC22×C3×D12C22
hypercenterC2×M16D32
hypocenterC32#2069
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10592824C2semidirect
3. C3×#5124C2semidirect
4. #10591143C2semidirect
7. #10589159C2semidirect
35. #5124D3semidirect
325. C32#2069semidirect
374. C3#70077semidirect
375. C3#70730semidirect

Maximal subgroups

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

subgroupindex
#105928242
C2×C3×#8232
C3×#51242
#105911432
C2×#635582
#105891592
#707303
#700773