Finite Group Databasebeta

← #11790004

Subgroups — #11790004

Order 1152.

499 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5129C211yesmaximal, characteristic
2#10591119C211yesmaximal, characteristic, complemented
3C2×#63568C211yesmaximal, characteristic
4#10591084C211yesmaximal, characteristic
5C2×#63555C211yesmaximal, characteristic, complemented
6#10589421C211yesmaximal, characteristic, complemented
7C3×#4558C211yesmaximal, characteristic, complemented
8#69998—31nomaximal
9#68919—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C22×C3×C3⋊C8C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C3×(C2×D3)⋊C8—22no—
18#63572—22no—
19#63568—22no—
20#63566C412yescomplemented
21#63563C412yescomplemented
22#63555—22no—
23C3×#408—31no—
24C2×#837—31no—
25#5233—31no—
26C2×#825—31no—
27#5129D311yescharacteristic
28#5119—31no—
29#5113—31no—
30#5102—31no—
31C2×#815—31no—
32C2×#815—31no—
33C3×#341—31no—
34#4558D311yescharacteristic, complemented
35#4555—31no—
36#4555—31no—
37#4555—61no—
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3—21no—
40C2×C3×#67—21no—
41C3×#235—21no—
42C3×#235—21no—
43C3×#235—21no—
44C3×#235—21no—
45C2×C3×D12C2×C411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×Dic6C2×C411yescharacteristic
48C32×M16—21no—
49C32×M16—21no—
50C2×C32×C8—21no—
51#3757—21no—
52C4⋊(C3⋊Dic3)C2×C412yes—
53C4×C3⋊Dic3—21no—
54C4×C3⋊Dic3—21no—
55C4×C3⋊Dic3D412yes—
56C3×#208—21no—
57C3×#208—21no—
58C2×C3×C3⋊C8—21no—
59C2×C3×C3⋊C8—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8C2×C412yes—
64C2×C3×C3⋊C8D412yes—
65#1938—91noSylow
66C2×C3×#41—31no—
67C2×#235C2×D311yescharacteristic
68C2×C3×M16—21no—
69C2×C3×M16—31no—
70C2×C3×M16C2×D311yescharacteristic
71C2×C3×M16C2×D311yescharacteristic
72C22×C3×C8—31no—
73C22×C3×C8—31no—
74#926—31no—
75#926—31no—
76#926—61no—
77C2×C4×Dic3—31no—
78C2×C4×Dic3—31no—
79C2×C4×Dic3—61no—
80C2×#208C2×D311yescharacteristic
81C22×C3⋊C8C2×D311yescharacteristic
82C22×C3⋊C8C2×D311yescharacteristic
83C3×C22⋊C8—62no—
84#837—62no—
85#835—32no—
86#832—32no—
87#825—62no—
88#821—32no—
89(C2×D3)⋊C8—22no—
90#816—32no—
91#815—62no—
92#815—62no—
93Dic3⋊C8—62no—
94Dic3⋊C8—62no—
95C23×C32#4111yescharacteristic
96C22×C3×D3—21no—
97C2×C32×C4C22×C411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—42no—
106C3×#67—41no—
107C3×#67—41no—
108C2×C3×Dic3—21no—
109C3×D12—21no—
110C3×D12—21no—
111C3×C4×D3—41no—
112C3×C4×D3—41no—
113C3×Dic6—21no—
114C3×Dic6—21no—
115C32×C8—41no—
116C3×C3⋊C8—22no—
117C3×C3⋊C8—22no—
118C3×C3⋊C8—41no—
119#424—91no—
120C2×#104—91no—
121#416—91no—
122#408—31no—
123C2×#97—91no—
124#341—31no—
125#339—91no—
126C3×#41—61no—
127C3×#41—61no—
128C3×#41—61no—
129C3×#41—61no—
130C2×C3×Q8—31no—
131C2×C3×D4—31no—
132C2×C3×D4—61no—
133C22×C3×C4—21no—
134C22×C3×C4—61no—
135C22×C3×C4C22×D311yescharacteristic
136C22×C3×C4C22×D311yescharacteristic
137C2×#67—21no—
138C22×Dic3—61no—
139C22×Dic3—61no—
140C22×Dic3—121no—
141#235—21no—
142#235—21no—
143#235—21no—
144#235—21no—
145C2×D12C4×D311yescharacteristic
146C2×C4×D3—21no—
147C2×Dic6C4×D311yescharacteristic
148C3×M16—22no—
149C3×M16—21no—
150C3×M16—21no—
151C3×M16—21no—
152C3×M16—21no—
153C3×M16—41no—
154C3×M16—61no—
155C3×M16—61no—
156C2×C3×C8—21no—
157C2×C3×C8—21no—
158C2×C3×C8—32no—
159C2×C3×C8—32no—
160C2×C3×C8—41no—
161C2×C3×C8—61no—
162C2×C3×C8—61no—
163C2×C3×C8—61no—
164C2×C3×C8—61no—
165C2×C3×C8—61no—
166#217—61no—
167#217—61no—
168#217—121no—
169C4⋊Dic3—32no—
170C4⋊Dic3—32no—
171C4⋊Dic3—62no—
172C4×Dic3—32no—
173C4×Dic3—32no—
174C4×Dic3—62no—
175C4×Dic3—61no—
176C4×Dic3—61no—
177C4×Dic3—61no—
178C4×Dic3—61no—
179C4×Dic3—121no—
180C4×Dic3—121no—
181#208—21no—
182#208—21no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8C4×D312yes—
189C2×C3⋊C8#6712yes—
190C22×C32—22no—
191C22×C32C4×D411yescharacteristic
192C22×C32#12311yescharacteristic
193C22×C32#12611yescharacteristic
194C2×C3×D3—41no—
195C2×C3×D3—42no—
196C32×C4#11711yescharacteristic
197C32×C4C4×D411yescharacteristic
198C32×C4#12111yescharacteristic
199C32×C4#12411yescharacteristic
200C3⋊Dic3—42no—
201C3⋊Dic3—42no—
202C3×Dic3—41no—
203C2×#41—31no—
204C2×M16—31no—
205C2×M16D3211yescharacteristic
206C22×C8—31no—
207C22×C8—31no—
208#117—91no—
209C2×C42—91no—
210C4⋊C8—182no—
211#104—182no—
212#103—92no—
213#102—92no—
214C22⋊C8—62no—
215#97—182no—
216C23×C3—21no—
217C23×C3—61no—
218C23×C3#23511yescharacteristic
219C23×C3#23911yescharacteristic
220C22×D3—21no—
221C3×Q8—61no—
222C3×Q8—61no—
223C3×D4—61no—
224C3×D4—61no—
225C3×D4—121no—
226C3×D4—121no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—61no—
234C2×C3×C4—121no—
235C2×C3×C4—121no—
236C2×C3×C4C2×C4×D311yescharacteristic
237C2×C3×C4C2×C4×D311yescharacteristic
238C2×C3×C4#23511yescharacteristic
239C2×C3×C4#23511yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4#23711yescharacteristic
244C2×C3×C4#23711yescharacteristic
245C2×C3×C4#23711yescharacteristic
246C2×C3×C4#23711yescharacteristic
247C2×C3×C4C2×#6711yescharacteristic
248#67—41no—
249#67—41no—
250C2×Dic3—21no—
251C2×Dic3—62no—
252C2×Dic3—62no—
253C2×Dic3—62no—
254C2×Dic3—62no—
255C2×Dic3—122no—
256C2×Dic3—122no—
257C2×Dic3—122no—
258C2×Dic3—122no—
259C2×Dic3—124no—
260D12—21no—
261D12—21no—
262C4×D3—41no—
263C4×D3—41no—
264Dic6—21no—
265Dic6—21no—
266C3×C8—42no—
267C3×C8—41no—
268C3×C8—41no—
269C3×C8—62no—
270C3×C8—62no—
271C3×C8—121no—
272C3⋊C8—22no—
273C3⋊C8—22no—
274C3⋊C8—41no—
275C2×C32—21no—
276C2×C32—21no—
277C2×C32#38811yescharacteristic
278C2×C32#44412yes—
279C3×D3—81no—
280#41—61no—
281#41—61no—
282#41—61no—
283#41—61no—
284C2×Q8—31no—
285C2×D4—31no—
286C2×D4—61no—
287C22×C4—61no—
288C22×C4—181no—
289C22×C4C2×D3211yescharacteristic
290M16—21no—
291M16—21no—
292M16—61no—
293M16—61no—
294C2×C8—21no—
295C2×C8—32no—
296C2×C8—32no—
297C2×C8—61no—
298C2×C8—61no—
299C2×C8—61no—
300C2×C8—61no—
301C2×C8—61no—
302C4⋊C4—92no—
303C22⋊C4—181no—
304C42—92no—
305C42—181no—
306C42—181no—
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—42no—
313C22×C3—122no—
314C22×C3—121no—
315C22×C3#87911yescharacteristic
316C22×C3#88311yescharacteristic
317C22×C3#89311yescharacteristic
318C22×C3#89411yescharacteristic
319C22×C3#89811yescharacteristic
320C22×C3C4×#6711yescharacteristic
321C2×D3—42no—
322C2×D3—41no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—121no—
328C3×C4#87211yescharacteristic
329C3×C4#87711yescharacteristic
330C3×C4#67⋊C411yescharacteristic
331C3×C4#67⋊C411yescharacteristic
332C3×C4#88411yescharacteristic
333C3×C4#88511yescharacteristic
334C3×C4#93611yescharacteristic
335C3×C4#93911yescharacteristic
336Dic3—41no—
337Dic3—122no—
338Dic3—122no—
339Dic3—124no—
340Dic3—122no—
341Dic3—122no—
342Dic3—242no—
343C32#193811yescharacteristic, complemented, Sylow
344C23—61no—
345C23#379911yescharacteristic
346Q8—61no—
347Q8—61no—
348D4—61no—
349D4—61no—
350D4—121no—
351D4—121no—
352C2×C4—61no—
353C2×C4—121no—
354C2×C4—121no—
355C2×C4—182no—
356C2×C4—182no—
357C2×C4—362no—
358C2×C4#379511yescharacteristic
359C2×C4C4×D3211yescharacteristic
360C2×C4#380211yescharacteristic
361C2×C4#380411yescharacteristic
362C2×C4#380511yescharacteristic
363C2×C4D3×#6711yescharacteristic
364C8—41no—
365C8—62no—
366C8—62no—
367C8—121no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—22no—
373C2×C3—21no—
374C2×C3—41no—
375C2×C3—41no—
376C2×C3—241no—
377C2×C3#466911yescharacteristic
378C2×C3#489412yes—
379C2×C3#494511yescharacteristic
380C2×C3#514512yes—
381D3—81no—
382C22—22no—
383C22—122no—
384C22—121no—
385C22#6385411yescharacteristic
386C22#6386111yescharacteristic
387C22#6390411yescharacteristic
388C4—121no—
389C4—362no—
390C4—362no—
391C4#6387711yescharacteristic
392C4#6388511yescharacteristic
393C4#6390211yescharacteristic
394C4#6395911yescharacteristic
395C3—21no—
396C3#6891911yescharacteristic, complemented
397C3#6999811yescharacteristic, complemented
398C2—21no—
399C2—21no—
400C2—241no—
401C2#1059099412yes—
402C2#1059128211yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1938
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10591119C2semidirect
5. C2×#63555C2semidirect
6. #10589421C2semidirect
7. C3×#4558C2semidirect
20. #63566C4semidirect
21. #63563C4semidirect
34. #4558D3semidirect
343. C32#1938semidirect
396. C3#68919semidirect
397. C3#69998semidirect

Maximal subgroups

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

subgroupindex
C3×#51292
#105911192
C2×#635682
#105910842
C2×#635552
#105894212
C3×#45582
#699983
#689193