Finite Group Databasebeta

← #11790009

Subgroups — #11790009

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#10592809C211yesmaximal, characteristic
2C3×#5102C211yesmaximal, characteristic, complemented
3C2×C3×#815C211yesmaximal, characteristic, complemented
4C2×#63570C211yesmaximal, characteristic
5#10591105C211yesmaximal, characteristic
6#10589166C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#70536—31nomaximal
9#69843—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63647—22no—
18C3×#815—22no—
19C3×Dic3⋊C8—22no—
20#63570—22no—
21#63567C412yescomplemented
22#63564C412yescomplemented
23C3×#424—31no—
24C2×C3×#97—31no—
25C2×#825—31no—
26#5113—31no—
27#5110—31no—
28#5110—31no—
29#5110—61no—
30#5102D311yescharacteristic, complemented
31C2×#815D311yescharacteristic, complemented
32#5002—31no—
33C2×#805—31no—
34#4558—31no—
35#4552—31no—
36#4532—31no—
37#4523—31no—
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—
48C2×C32×C8—21no—
49C2×C32×C8—21no—
50C2×C32×C8D412yes—
51#3748—21no—
52#3748—21no—
53C2×C3⋊(C3⋊C8)—21no—
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—31no—
70C22×C3×C8—21no—
71C22×C3×C8—31no—
72C22×C3×C8C2×D311yescharacteristic
73C22×C3×C8C2×D311yescharacteristic
74C3×#117—31no—
75C2×C3×C42—31no—
76#926C2×D311yescharacteristic
77C2×C4×Dic3C2×D311yescharacteristic
78C2×#208—31no—
79C2×#208—31no—
80C2×#208—61no—
81C2×#208C2×D311yescharacteristic
82C22×C3⋊C8C2×D311yescharacteristic
83C3×C4⋊C8—62no—
84C3×#97—62no—
85#825—62no—
86#821—32no—
87(C2×D3)⋊C8—64no—
88(C2×D3)⋊C8—62no—
89(C2×D3)⋊C8—62no—
90#816—32no—
91#815—22no—
92Dic3⋊C8—22no—
93#810—32no—
94#809—32no—
95#805—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—22no—
117C3⋊(C3⋊C8)—41no—
118C3×C3⋊C8—22no—
119C3×C3⋊C8—41no—
120#424—31no—
121C2×#104—91no—
122#416—91no—
123#408—91no—
124C2×#97—31no—
125#341—91no—
126#339—91no—
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—61no—
157C3×M16—61no—
158C2×C3×C8—21no—
159C2×C3×C8—21no—
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—22no—
163C2×C3×C8—32no—
164C2×C3×C8—41no—
165C2×C3×C8—41no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C2×C3×C8—61no—
169C2×C3×C8D1212yes—
170C2×C3×C8#6712yes—
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×Dic3#6712yes—
181#208—21no—
182#208—21no—
183#208—61no—
184#208—61no—
185#208—61no—
186#208—61no—
187#208—121no—
188#208—121no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—62no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—61no—
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×M16—91no—
212C22×C8—31no—
213C22×C8D3211yescharacteristic
214#117—31no—
215C2×C42—31no—
216C4⋊C8—62no—
217#104—182no—
218#103—92no—
219#102—92no—
220C22⋊C8—182no—
221#97—62no—
222C23×C3—21no—
223C23×C3#23511yescharacteristic
224C23×C3#23511yescharacteristic
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×C4#23711yescharacteristic
245C2×C3×C4#23911yescharacteristic
246C2×C3×C4#23911yescharacteristic
247C2×C3×C4C2×#6711yescharacteristic
248C2×C3×C4C2×#6711yescharacteristic
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—22no—
280C3×C8—22no—
281C3×C8—42no—
282C3×C8—62no—
283C3×C8—121no—
284C3⋊C8—22no—
285C3⋊C8—41no—
286C3⋊C8—122no—
287C3⋊C8—121no—
288C3⋊C8—121no—
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—61no—
305M16—61no—
306M16—181no—
307M16—181no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—32no—
311C2×C8—61no—
312C2×C8—61no—
313C2×C8—61no—
314C2×C8—181no—
315C2×C8#62612yes—
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×C3C4×D1211yescharacteristic
328C22×C3#87611yescharacteristic
329C22×C3#89411yescharacteristic
330C22×C3#89811yescharacteristic
331C22×C3C4×#6711yescharacteristic
332C22×C3#92911yescharacteristic
333C2×D3—122no—
334C2×D3—124no—
335C2×D3—122no—
336C2×D3—121no—
337C2×D3—122no—
338C2×D3—121no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—122no—
344C3×C4—122no—
345C3×C4#87211yescharacteristic
346C3×C4#87511yescharacteristic
347C3×C4#89211yescharacteristic
348C3×C4#89311yescharacteristic
349C3×C4C4×#6711yescharacteristic
350C3×C4#93011yescharacteristic
351C3×C4#93911yescharacteristic
352C3×C4#94711yescharacteristic
353Dic3—42no—
354Dic3—42no—
355Dic3—122no—
356Dic3—121no—
357Dic3—121no—
358C32#193811yescharacteristic, complemented, Sylow
359C23—181no—
360C23#379811yescharacteristic
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×C4#379911yescharacteristic
375C2×C4C4×D3211yescharacteristic
376C2×C4#380411yescharacteristic
377C2×C4C2×#62611yescharacteristic
378C2×C4D3×#6711yescharacteristic
379C8—22no—
380C8—62no—
381C8—121no—
382C8—361no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—22no—
389C2×C3—41no—
390C2×C3—41no—
391C2×C3#471712yes—
392C2×C3#494011yescharacteristic
393C2×C3#499011yescharacteristic
394C2×C3#514512yes—
395D3—242no—
396D3—241no—
397D3—241no—
398C22—22no—
399C22—361no—
400C22—362no—
401C22#6385011yescharacteristic
402C22#6386811yescharacteristic
403C22C4×#62611yescharacteristic
404C4—122no—
405C4—122no—
406C4—361no—
407C4#6383611yescharacteristic
408C4#6386411yescharacteristic
409C4#6390411yescharacteristic
410C4#6397811yescharacteristic
411C3—21no—
412C3#6984311yescharacteristic, complemented
413C3#7053611yescharacteristic, complemented
414C2—21no—
415C2—21no—
416C2—721no—
417C2#1059092412yes—
418C2#1059128911yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32C4×D4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1938
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C3×#5102C2semidirect
3. C2×C3×#815C2semidirect
6. #10589166C2semidirect
7. #10589161C2semidirect
21. #63567C4semidirect
22. #63564C4semidirect
30. #5102D3semidirect
31. C2×#815D3semidirect
358. C32#1938semidirect
412. C3#69843semidirect
413. C3#70536semidirect

Maximal subgroups

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

subgroupindex
#105928092
C3×#51022
C2×C3×#8152
C2×#635702
#105911052
#105891662
#105891612
#705363
#698433