Finite Group Databasebeta

← #11790011

Subgroups — #11790011

Order 1152.

523 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592701C211yesmaximal, characteristic
2C3×#4999C211yesmaximal, characteristic, complemented
3C2×#63570C211yesmaximal, characteristic
4#10591073C211yesmaximal, characteristic
5C2×#63554C211yesmaximal, characteristic, complemented
6C3×#4532C211yesmaximal, characteristic, complemented
7#10589165C211yesmaximal, characteristic, complemented
8#70536—31nomaximal
9#68746—31nomaximal
10C2×#3828C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×C3×C4×Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63637C412yescomplemented
18#63636C412yescomplemented
19C3×C4⋊(C3⋊C8)—22no—
20#63570—22no—
21#63557—22no—
22#63554—22no—
23C3×#424—31no—
24C2×#825—31no—
25#5129—31no—
26#5110—31no—
27C2×#815—31no—
28#5002—31no—
29#5002—31no—
30#5002—61no—
31#4999D311yescharacteristic, complemented
32C2×#805—31no—
33C2×#803—31no—
34C3×#339—31no—
35#4558—31no—
36#4558—31no—
37#4532D311yescharacteristic, 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×C4⋊C4C2×C412yes—
49C32×C22⋊C4—21no—
50C32×C42—21no—
51C2×C3⋊(C3⋊C8)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C2×C3⋊(C3⋊C8)C2×C412yes—
54C3×C4×Dic3—21no—
55C3×C4×Dic3D412yes—
56C3×#208—21no—
57C3×#208—21no—
58C3×#208—21no—
59C3×#208—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8D412yes—
65#1938—91noSylow
66C2×#235—31no—
67C2×#235—31no—
68C2×#235—61no—
69C2×C3×M16—31no—
70C2×C3×M16—31no—
71C22×C3×C8—31no—
72C3×#117—21no—
73C3×#117C2×D311yescharacteristic
74C3×#117C2×D311yescharacteristic
75C2×C3×C42—31no—
76C2×C4×Dic3C2×D311yescharacteristic
77C2×#208C2×D311yescharacteristic
78C2×#208C2×D311yescharacteristic
79C22×C3⋊C8—31no—
80C22×C3⋊C8—31no—
81C22×C3⋊C8—61no—
82C22×C3⋊C8C2×D311yescharacteristic
83C3×C4⋊C8—62no—
84#825—62no—
85(C2×D3)⋊C8—62no—
86(C2×D3)⋊C8—62no—
87#815—62no—
88#810—32no—
89#810—32no—
90#810—62no—
91#809—32no—
92#809—32no—
93#809—62no—
94#805—62no—
95C4⋊(C3⋊C8)—22no—
96#803—62no—
97C23×C32#4111yescharacteristic
98C22×C3⋊D3—21no—
99C2×C32×C4—22no—
100C2×C32×C4C22×C411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C32×C4#4111yescharacteristic
106#638—41no—
107#638—41no—
108C2×C3⋊Dic3—21no—
109C4⋊(C3⋊D3)—21no—
110C4⋊(C3⋊D3)—21no—
111C4×C3⋊D3—41no—
112C4×C3⋊D3—41no—
113#634—21no—
114#634—21no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—42no—
117C3⋊(C3⋊C8)—22no—
118C3×C3⋊C8—22no—
119C3×C3⋊C8—41no—
120C3×C3⋊C8—41no—
121#424—31no—
122C2×#104—91no—
123#416—91no—
124#408—91no—
125C2×#97—91no—
126#341—91no—
127#339—31no—
128C22×C3×C4—21no—
129C22×C3×C4—61no—
130C22×C3×C4C22×D311yescharacteristic
131C22×C3×C4C22×D311yescharacteristic
132C2×#67—61no—
133C2×#67—61no—
134C2×#67—121no—
135C22×Dic3—21no—
136#235—62no—
137#235—62no—
138#235—61no—
139#235—61no—
140#235—61no—
141#235—61no—
142#235—61no—
143#235—61no—
144#235—61no—
145#235—61no—
146#235—121no—
147#235—121no—
148C2×D12—31no—
149C2×D12—31no—
150C2×D12—61no—
151C2×C4×D3—61no—
152C2×C4×D3—61no—
153C2×C4×D3—121no—
154C2×Dic6—31no—
155C2×Dic6—31no—
156C2×Dic6—61no—
157C3×M16—61no—
158C3×M16—61no—
159C3×M16—61no—
160C3×M16—61no—
161C2×C3×C8—32no—
162C2×C3×C8—61no—
163C2×C3×C8—61no—
164C2×C3×C8—61no—
165C2×C3×C8—61no—
166C3×C4⋊C4—22no—
167C3×C4⋊C4C4×D312yes—
168C3×C4⋊C4C4×D312yes—
169C3×C22⋊C4—21no—
170C3×C22⋊C4—21no—
171C3×C22⋊C4—41no—
172C3×C42—21no—
173C3×C42—21no—
174C3×C42—32no—
175C3×C42—41no—
176C3×C42—61no—
177C4×Dic3—21no—
178C4×Dic3D1212yes—
179#208—21no—
180#208—21no—
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—32no—
188C2×C3⋊C8—32no—
189C2×C3⋊C8—62no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—121no—
195C2×C3⋊C8—121no—
196C2×C3⋊C8#6712yes—
197C22×C32—22no—
198C22×C32C4×D411yescharacteristic
199C22×C32#12311yescharacteristic
200C22×C32#12611yescharacteristic
201C2×C3⋊D3—41no—
202C2×C3⋊D3—42no—
203C32×C4—42no—
204C32×C4#11711yescharacteristic
205C32×C4C4×D411yescharacteristic
206C32×C4#12111yescharacteristic
207C32×C4#12411yescharacteristic
208C3⋊Dic3—41no—
209C3×Dic3—42no—
210C2×#41—91no—
211C2×M16—31no—
212C2×M16—31no—
213C22×C8—31no—
214C22×C8—91no—
215#117D3211yescharacteristic
216C2×C42—31no—
217C4⋊C8—62no—
218#104—182no—
219#103—92no—
220#102—92no—
221C22⋊C8—182no—
222#97—182no—
223C23×C3—21no—
224C23×C3#23511yescharacteristic
225C23×C3#23711yescharacteristic
226C22×D3—61no—
227C22×D3—61no—
228C22×D3—121no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—42no—
238C2×C3×C4—62no—
239C2×C3×C4—122no—
240C2×C3×C4C2×C4×D311yescharacteristic
241C2×C3×C4C2×C4×D311yescharacteristic
242C2×C3×C4C2×D1211yescharacteristic
243C2×C3×C4#23511yescharacteristic
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4#23711yescharacteristic
247C2×C3×C4#23711yescharacteristic
248C2×C3×C4#23911yescharacteristic
249C2×C3×C4#23911yescharacteristic
250C2×C3×C4#23911yescharacteristic
251C2×C3×C4C2×#6711yescharacteristic
252#67—122no—
253#67—122no—
254#67—121no—
255#67—121no—
256#67—121no—
257#67—121no—
258C2×Dic3—22no—
259C2×Dic3—42no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—121no—
263D12—62no—
264D12—61no—
265D12—61no—
266D12—61no—
267D12—61no—
268D12—121no—
269C4×D3—122no—
270C4×D3—122no—
271C4×D3—121no—
272C4×D3—121no—
273C4×D3—121no—
274C4×D3—121no—
275Dic6—62no—
276Dic6—61no—
277Dic6—61no—
278Dic6—61no—
279Dic6—61no—
280Dic6—121no—
281C3×C8—62no—
282C3×C8—121no—
283C3×C8—121no—
284C3⋊C8—22no—
285C3⋊C8—41no—
286C3⋊C8—41no—
287C3⋊C8—62no—
288C3⋊C8—62no—
289C3⋊C8—122no—
290C2×C32—21no—
291C2×C32—21no—
292C2×C32#38811yescharacteristic
293C2×C32#44412yes—
294C3⋊D3—81no—
295#41—181no—
296#41—181no—
297#41—181no—
298#41—181no—
299C2×Q8—91no—
300C2×D4—91no—
301C2×D4—181no—
302C22×C4—61no—
303C22×C4—181no—
304C22×C4C2×D3211yescharacteristic
305M16—61no—
306M16—61no—
307M16—61no—
308M16—61no—
309C2×C8—32no—
310C2×C8—61no—
311C2×C8—61no—
312C2×C8—61no—
313C2×C8—61no—
314C2×C8—92no—
315C2×C8—181no—
316C2×C8—181no—
317C4⋊C4#62412yes—
318C22⋊C4—21no—
319C42—21no—
320C42—32no—
321C42—61no—
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—42no—
328C22×C3#67⋊C411yescharacteristic
329C22×C3#88611yescharacteristic
330C22×C3#89411yescharacteristic
331C22×C3#89811yescharacteristic
332C22×C3#89811yescharacteristic
333C22×C3C4×#6711yescharacteristic
334C2×D3—122no—
335C2×D3—122no—
336C2×D3—121no—
337C2×D3—121no—
338C2×D3—122no—
339C2×D3—242no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—42no—
345C3×C4—42no—
346C3×C4—82no—
347C3×C4—122no—
348C3×C4C4×D1211yescharacteristic
349C3×C4#88511yescharacteristic
350C3×C4#89211yescharacteristic
351C3×C4#89211yescharacteristic
352C3×C4#89311yescharacteristic
353C3×C4#89511yescharacteristic
354C3×C4#93911yescharacteristic
355C3×C4#94711yescharacteristic
356Dic3—42no—
357Dic3—122no—
358Dic3—121no—
359Dic3—121no—
360C32#193811yescharacteristic, complemented, Sylow
361C23—181no—
362C23#380411yescharacteristic
363Q8—181no—
364Q8—181no—
365D4—181no—
366D4—181no—
367D4—361no—
368D4—361no—
369C2×C4—22no—
370C2×C4—62no—
371C2×C4—122no—
372C2×C4—181no—
373C2×C4—361no—
374C2×C4—361no—
375C2×C4#379611yescharacteristic
376C2×C4#379611yescharacteristic
377C2×C4#379911yescharacteristic
378C2×C4D3×D1211yescharacteristic
379C2×C4C2×#62411yescharacteristic
380C2×C4D3×#6711yescharacteristic
381C8—62no—
382C8—121no—
383C8—121no—
384C8—182no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—22no—
391C2×C3—41no—
392C2×C3—41no—
393C2×C3#467011yescharacteristic
394C2×C3#482312yes—
395C2×C3#499011yescharacteristic
396C2×C3#514512yes—
397D3—242no—
398D3—241no—
399D3—241no—
400C22—22no—
401C22—361no—
402C22—362no—
403C22#6384811yescharacteristic
404C22#6389011yescharacteristic
405C22#6395211yescharacteristic
406C4—42no—
407C4—122no—
408C4—361no—
409C4#6384911yescharacteristic
410C4#6388611yescharacteristic
411C4#6389411yescharacteristic
412C4#6390711yescharacteristic
413C3—21no—
414C3#6874611yescharacteristic, complemented
415C3#7053611yescharacteristic, complemented
416C2—21no—
417C2—21no—
418C2—721no—
419C2#1059126611yescharacteristic
420C2#1059166312yes—
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32C4×D4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1938
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#4999C2semidirect
5. C2×#63554C2semidirect
6. C3×#4532C2semidirect
7. #10589165C2semidirect
17. #63637C4semidirect
18. #63636C4semidirect
31. #4999D3semidirect
37. #4532D3semidirect
360. C32#1938semidirect
414. C3#68746semidirect
415. C3#70536semidirect

Maximal subgroups

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

subgroupindex
#105927012
C3×#49992
C2×#635702
#105910732
C2×#635542
C3×#45322
#105891652
#705363
#687463