Finite Group Databasebeta

← #11790006

Subgroups — #11790006

Order 1152.

523 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592828C211yesmaximal, characteristic
2#10591117C211yesmaximal, characteristic, complemented
3C2×#63570C211yesmaximal, characteristic
4#10591105C211yesmaximal, characteristic
5C2×#63554C211yesmaximal, characteristic, complemented
6C3×#4558C211yesmaximal, characteristic, complemented
7C3×#4555C211yesmaximal, characteristic, complemented
8#68919—31nomaximal
9#68746—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63647—22no—
18Dic3⋊(C3⋊C8)—22no—
19#63570—22no—
20#63567C412yescomplemented
21#63564C412yescomplemented
22#63554—22no—
23C2×#825—31no—
24#5129—31no—
25#5129—31no—
26#5129—61no—
27#5119—31no—
28#5113—31no—
29C2×#815—31no—
30#5002—31no—
31#4999—31no—
32C2×#805—31no—
33C2×#803—31no—
34C3×#341—31no—
35C3×#339—31no—
36#4558D311yescharacteristic, complemented
37#4555D311yescharacteristic, complemented
38C22×C32×C4C2311yescharacteristic
39C2×#638—21no—
40#3828—21no—
41#3828—21no—
42#3828—21no—
43#3828—21no—
44C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
45C2×C4×C3⋊D3—21no—
46C2×#634C2×C411yescharacteristic
47C22×C3×Dic3—21no—
48C32×M16—21no—
49C32×M16—21no—
50C2×C32×C8—21no—
51C2×C3⋊(C3⋊C8)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C2×C3⋊(C3⋊C8)D412yes—
54C3×#217—21no—
55C3×C4⋊Dic3C2×C412yes—
56C3×C4×Dic3—21no—
57C3×C4×Dic3—21no—
58C3×C4×Dic3D412yes—
59C3×#208—21no—
60C3×#208—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8C2×C412yes—
65#1938—91noSylow
66C2×#235—31no—
67C2×#235—31no—
68C2×#235—61no—
69C2×C3×M16—21no—
70C2×C3×M16—31no—
71C2×C3×M16C2×D311yescharacteristic
72C2×C3×M16C2×D311yescharacteristic
73C22×C3×C8—31no—
74C3×#117—31no—
75C2×C3×C42—31no—
76#926C2×D311yescharacteristic
77C2×C4×Dic3C2×D311yescharacteristic
78C2×#208C2×D311yescharacteristic
79C22×C3⋊C8—31no—
80C22×C3⋊C8—31no—
81C22×C3⋊C8—61no—
82C22×C3⋊C8C2×D311yescharacteristic
83#825—62no—
84#821—32no—
85(C2×D3)⋊C8—62no—
86(C2×D3)⋊C8—62no—
87(C2×D3)⋊C8—64no—
88#816—32no—
89#815—62no—
90Dic3⋊C8—62no—
91#810—32no—
92#809—32no—
93#805—62no—
94C4⋊(C3⋊C8)—62no—
95#803—62no—
96C23×C32#4111yescharacteristic
97C22×C3⋊D3—21no—
98C2×C32×C4C22×C411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C32×C4#4111yescharacteristic
104#638—41no—
105#638—41no—
106C2×C3⋊Dic3—21no—
107C4⋊(C3⋊D3)—21no—
108C4⋊(C3⋊D3)—21no—
109C4×C3⋊D3—41no—
110C4×C3⋊D3—41no—
111#634—21no—
112#634—21no—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—42no—
116C32×C8—41no—
117C3⋊(C3⋊C8)—22no—
118C3×C3⋊C8—22no—
119C3×C3⋊C8—41no—
120#424—91no—
121C2×#104—91no—
122#416—91no—
123#408—91no—
124C2×#97—91no—
125#341—31no—
126#339—31no—
127C22×C3×C4—21no—
128C22×C3×C4—61no—
129C22×C3×C4C22×D311yescharacteristic
130C22×C3×C4C22×D311yescharacteristic
131C2×#67—62no—
132C2×#67—61no—
133C2×#67—61no—
134C22×Dic3—21no—
135#235—61no—
136#235—61no—
137#235—61no—
138#235—61no—
139#235—61no—
140#235—61no—
141#235—61no—
142#235—61no—
143#235—121no—
144#235—121no—
145#235—121no—
146#235—121no—
147C2×D12—31no—
148C2×D12—31no—
149C2×D12—61no—
150C2×C4×D3—62no—
151C2×C4×D3—61no—
152C2×C4×D3—61no—
153C2×Dic6—31no—
154C2×Dic6—31no—
155C2×Dic6—61no—
156C3×M16—21no—
157C3×M16—21no—
158C3×M16—21no—
159C3×M16—21no—
160C3×M16—41no—
161C3×M16—41no—
162C3×M16—61no—
163C3×M16—61no—
164C2×C3×C8—22no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—32no—
168C2×C3×C8—61no—
169C2×C3×C8—61no—
170C2×C3×C8—61no—
171C3×C4⋊C4—32no—
172C3×C22⋊C4—61no—
173C3×C42—32no—
174C3×C42—61no—
175C3×C42—61no—
176#217—21no—
177C4⋊Dic3C4×D312yes—
178C4×Dic3—21no—
179C4×Dic3—21no—
180C4×Dic3D1212yes—
181#208—21no—
182#208—21no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—32no—
187C2×C3⋊C8—32no—
188C2×C3⋊C8—62no—
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⋊C8C4×D312yes—
196C22×C32—22no—
197C22×C32C4×D411yescharacteristic
198C22×C32#12311yescharacteristic
199C22×C32#12611yescharacteristic
200C2×C3⋊D3—41no—
201C2×C3⋊D3—42no—
202C32×C4#11711yescharacteristic
203C32×C4C4×D411yescharacteristic
204C32×C4#12111yescharacteristic
205C32×C4#12411yescharacteristic
206C3⋊Dic3—41no—
207C3×Dic3—42no—
208C3×Dic3—42no—
209C2×#41—91no—
210C2×M16—31no—
211C2×M16D3211yescharacteristic
212C22×C8—31no—
213C22×C8—91no—
214#117—31no—
215C2×C42—31no—
216C4⋊C8—182no—
217#104—182no—
218#103—92no—
219#102—92no—
220C22⋊C8—182no—
221#97—182no—
222C23×C3—21no—
223C23×C3#23711yescharacteristic
224C23×C3#23911yescharacteristic
225C22×D3—62no—
226C22×D3—61no—
227C22×D3—61no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—62no—
235C2×C3×C4—62no—
236C2×C3×C4—122no—
237C2×C3×C4C2×C4×D311yescharacteristic
238C2×C3×C4C2×C4×D311yescharacteristic
239C2×C3×C4C2×D1211yescharacteristic
240C2×C3×C4#23511yescharacteristic
241C2×C3×C4#23511yescharacteristic
242C2×C3×C4#23511yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4#23711yescharacteristic
247C2×C3×C4#23711yescharacteristic
248C2×C3×C4#23911yescharacteristic
249#67—122no—
250#67—122no—
251#67—121no—
252#67—121no—
253#67—121no—
254#67—121no—
255C2×Dic3—22no—
256C2×Dic3—22no—
257C2×Dic3—42no—
258C2×Dic3—62no—
259C2×Dic3—61no—
260C2×Dic3—61no—
261D12—61no—
262D12—61no—
263D12—61no—
264D12—61no—
265D12—121no—
266D12—121no—
267C4×D3—122no—
268C4×D3—122no—
269C4×D3—121no—
270C4×D3—121no—
271C4×D3—121no—
272C4×D3—121no—
273Dic6—61no—
274Dic6—61no—
275Dic6—61no—
276Dic6—61no—
277Dic6—121no—
278Dic6—121no—
279C3×C8—42no—
280C3×C8—41no—
281C3×C8—41no—
282C3×C8—62no—
283C3×C8—121no—
284C3⋊C8—22no—
285C3⋊C8—41no—
286C3⋊C8—62no—
287C3⋊C8—62no—
288C3⋊C8—122no—
289C2×C32—21no—
290C2×C32—21no—
291C2×C32#38811yescharacteristic
292C2×C32#44412yes—
293C3⋊D3—81no—
294#41—181no—
295#41—181no—
296#41—181no—
297#41—181no—
298C2×Q8—91no—
299C2×D4—91no—
300C2×D4—181no—
301C22×C4—61no—
302C22×C4—181no—
303C22×C4C2×D3211yescharacteristic
304M16—21no—
305M16—21no—
306M16—61no—
307M16—61no—
308C2×C8—21no—
309C2×C8—32no—
310C2×C8—61no—
311C2×C8—61no—
312C2×C8—61no—
313C2×C8—92no—
314C2×C8—181no—
315C2×C8—181no—
316C4⋊C4—32no—
317C22⋊C4—61no—
318C42—32no—
319C42—61no—
320C42—61no—
321C22×C3—22no—
322C22×C3—22no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—42no—
327C22×C3#67⋊C411yescharacteristic
328C22×C3#88611yescharacteristic
329C22×C3#89311yescharacteristic
330C22×C3#89411yescharacteristic
331C22×C3#89811yescharacteristic
332C22×C3#89811yescharacteristic
333C2×D3—122no—
334C2×D3—124no—
335C2×D3—122no—
336C2×D3—121no—
337C2×D3—121no—
338C2×D3—122no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—122no—
344C3×C4—122no—
345C3×C4#87211yescharacteristic
346C3×C4C4×D1211yescharacteristic
347C3×C4#67⋊C411yescharacteristic
348C3×C4#88411yescharacteristic
349C3×C4#88511yescharacteristic
350C3×C4#88511yescharacteristic
351C3×C4#89211yescharacteristic
352C3×C4#89511yescharacteristic
353Dic3—42no—
354Dic3—42no—
355Dic3—122no—
356Dic3—121no—
357Dic3—121no—
358C32#193811yescharacteristic, complemented, Sylow
359C23—181no—
360C23#379611yescharacteristic
361Q8—181no—
362Q8—181no—
363D4—181no—
364D4—181no—
365D4—361no—
366D4—361no—
367C2×C4—62no—
368C2×C4—62no—
369C2×C4—122no—
370C2×C4—181no—
371C2×C4—361no—
372C2×C4—361no—
373C2×C4#379911yescharacteristic
374C2×C4C4×D3211yescharacteristic
375C2×C4D3×D1211yescharacteristic
376C2×C4#380411yescharacteristic
377C2×C4#380411yescharacteristic
378C2×C4#381111yescharacteristic
379C8—41no—
380C8—62no—
381C8—121no—
382C8—182no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—22no—
388C2×C3—21no—
389C2×C3—41no—
390C2×C3—41no—
391C2×C3#466911yescharacteristic
392C2×C3#467011yescharacteristic
393C2×C3#482312yes—
394C2×C3#489412yes—
395D3—242no—
396D3—241no—
397D3—241no—
398C22—22no—
399C22—362no—
400C22—361no—
401C22#6384811yescharacteristic
402C22#6388111yescharacteristic
403C22#6389011yescharacteristic
404C4—122no—
405C4—122no—
406C4—361no—
407C4#6383611yescharacteristic
408C4#6388011yescharacteristic
409C4#6391011yescharacteristic
410C4#6395311yescharacteristic
411C3—21no—
412C3#6874611yescharacteristic, complemented
413C3#6891911yescharacteristic, complemented
414C2—21no—
415C2—21no—
416C2—721no—
417C2#1059097812yes—
418C2#1059125911yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C4×D4
prime radicalC2×#3828C22
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. #10591117C2semidirect
5. C2×#63554C2semidirect
6. C3×#4558C2semidirect
7. C3×#4555C2semidirect
20. #63567C4semidirect
21. #63564C4semidirect
36. #4558D3semidirect
37. #4555D3semidirect
358. C32#1938semidirect
412. C3#68746semidirect
413. C3#68919semidirect

Maximal subgroups

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

subgroupindex
#105928282
#105911172
C2×#635702
#105911052
C2×#635542
C3×#45582
C3×#45552
#689193
#687463