Finite Group Databasebeta

← #11791409

Subgroups — #11791409

Order 1152.

827 conjugacy classes of subgroups.

The subgroup lattice has 443 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595948C211yesmaximal, characteristic
2C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C3×C4×#208C211yesmaximal, characteristic, complemented
4C2×#63570C214yesmaximal, complemented
5#69867—31nomaximal
6#69492—31nomaximal
7C2×#3828C2212yes—
8C2×C32×C42C2211yescharacteristic
9#64139—21no—
10#64139—21no—
11#64084C412yescomplemented
12#64083C411yescharacteristic, complemented
13C4×C4⋊(C3⋊D3)—21no—
14C4×C4⋊(C3⋊D3)—21no—
15#64078C411yescharacteristic, complemented
16C2×C3×C4⋊Dic3—21no—
17C2×C3×C4×Dic3C2212yes—
18C2×C3×#208C2212yes—
19C3×C3⋊#95—21no—
20C3×#803—21no—
21C3×C4×C3⋊C8—21no—
22#63570—28no—
23#5477—31no—
24#5477—31no—
25#5477—61no—
26C3×C4×M16—31no—
27C3×C4×C4⋊C4—31no—
28C2×#825—34no—
29C4×C4⋊Dic3D311yescharacteristic, complemented
30C2×#805—34no—
31C4×#208D311yescharacteristic, complemented
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C2×#638—22no—
36#3828—24no—
37#3828—24no—
38C2×C4⋊(C3⋊D3)—21no—
39C2×C4⋊(C3⋊D3)—21no—
40C2×C4⋊(C3⋊D3)C2×C412yes—
41C2×C4×C3⋊D3—22no—
42C2×#634C2×C412yes—
43C22×C3×Dic3—22no—
44C32×C42C2×C411yescharacteristic
45C32×C42C2×C411yescharacteristic
46C32×C42D411yescharacteristic
47C32×C42D411yescharacteristic
48#3752—22no—
49#3752—22no—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—21no—
52C3×C4⋊Dic3—24no—
53C3×C4×Dic3—24no—
54C3×#208—22no—
55C3×#208D414yescomplemented
56C2×C3×C3⋊C8—22no—
57#1980—91noSylow
58C2×#235—32no—
59C2×#235—32no—
60C2×#235—62no—
61C2×C3×M16—32no—
62C2×C3×C4⋊C4—61no—
63C2×C3×C42—21no—
64C2×C3×C42—32no—
65C2×C3×C42C2×D311yescharacteristic
66C2×C3×C42C2×D311yescharacteristic
67#930—62no—
68#930—62no—
69#930—61no—
70#930—61no—
71#930—61no—
72#930—61no—
73C2×C4⋊Dic3—21no—
74C2×C4×Dic3C2×D312yes—
75C2×#208C2×D312yes—
76#875—32no—
77#875—32no—
78#875—62no—
79#874—31no—
80#874—31no—
81#874—61no—
82C4×D12—62no—
83C4×D12—62no—
84C4×D12—61no—
85C4×D12—61no—
86C4×D12—61no—
87C4×D12—61no—
88#869—31no—
89#869—31no—
90#869—61no—
91C3×#97—61no—
92C3×C4×C8—61no—
93C3×#95—61no—
94C3⋊#95—21no—
95#825—68no—
96#805—68no—
97#803—21no—
98C4×C3⋊C8—21no—
99C23×C32C2×D411yescharacteristic
100C22×C3⋊D3—22no—
101C2×C32×C4—22no—
102C2×C32×C4—41no—
103C2×C32×C4C22⋊C411yescharacteristic
104C2×C32×C4C22⋊C411yescharacteristic
105C2×C32×C4C22⋊C411yescharacteristic
106C2×C32×C4C22⋊C411yescharacteristic
107C2×C32×C4C22×C411yescharacteristic
108C2×C32×C4C2×D412yes—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4#4112yes—
111#638—42no—
112#638—42no—
113C2×C3⋊Dic3—22no—
114C4⋊(C3⋊D3)—24no—
115C4⋊(C3⋊D3)—42no—
116C4⋊(C3⋊D3)—42no—
117C4×C3⋊D3—44no—
118#634—24no—
119C2×C3×Dic3—24no—
120C2×C3×Dic3—42no—
121C2×C3×Dic3—42no—
122C3×C3⋊C8—24no—
123#532—91no—
124C2×#104—94no—
125C4×M16—31no—
126C4×C4⋊C4—31no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—62no—
131C22×C3×C4D1211yescharacteristic
132C22×C3×C4D1211yescharacteristic
133C22×C3×C4#6711yescharacteristic
134C22×C3×C4#6711yescharacteristic
135C22×C3×C4C22×D311yescharacteristic
136C22×C3×C4C22×D311yescharacteristic
137C2×#67—64no—
138C2×#67—62no—
139C2×#67—62no—
140C22×Dic3—22no—
141#235—64no—
142#235—64no—
143#235—64no—
144#235—64no—
145#235—124no—
146#235—124no—
147C2×D12—32no—
148C2×D12—32no—
149C2×D12—62no—
150C2×D12—62no—
151C2×D12—62no—
152C2×D12—61no—
153C2×D12—61no—
154C2×D12—61no—
155C2×D12—61no—
156C2×C4×D3—64no—
157C2×C4×D3—62no—
158C2×C4×D3—62no—
159C2×Dic6—32no—
160C2×Dic6—32no—
161C2×Dic6—62no—
162C3×M16—34no—
163C3×M16—62no—
164C2×C3×C8—62no—
165C3×C4⋊C4—64no—
166C3×C42—21no—
167C3×C42—21no—
168C3×C42—21no—
169C3×C42—21no—
170C3×C42—64no—
171C3×C42C4×D311yescharacteristic
172C3×C42C4×D311yescharacteristic
173C3×C42C4×D311yescharacteristic
174C3×C42C4×D311yescharacteristic
175C3×C42D1211yescharacteristic
176C3×C42D1211yescharacteristic
177C3×C42#6711yescharacteristic
178C3×C42#6711yescharacteristic
179(C2×D3)⋊C4—64no—
180(C2×D3)⋊C4—64no—
181(C2×D3)⋊C4—62no—
182(C2×D3)⋊C4—62no—
183(C2×D3)⋊C4—62no—
184(C2×D3)⋊C4—62no—
185C4⋊Dic3—24no—
186C4⋊Dic3—62no—
187C4⋊Dic3—62no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192C4×Dic3—24no—
193#208—22no—
194#208D1214yescomplemented
195C2×C3⋊C8—22no—
196C22×C32—21no—
197C22×C32—21no—
198C22×C32C2×C22⋊C411yescharacteristic
199C22×C32#12411yescharacteristic
200C22×C32#12711yescharacteristic
201C2×C3⋊D3—42no—
202C2×C3⋊D3—42no—
203C2×C3⋊D3—42no—
204C32×C4—21no—
205C32×C4—21no—
206C32×C4—21no—
207C32×C4#10412yescomplemented
208C32×C4C4×D412yes—
209C32×C4#12112yes—
210C3⋊Dic3—42no—
211C3×Dic3—44no—
212C2×#41—92no—
213C2×M16—32no—
214C4⋊Q8—91no—
215#127—91no—
216#124—92no—
217#121—181no—
218#121—181no—
219C4×D4—181no—
220C4×D4—181no—
221C2×C4⋊C4—61no—
222C2×C42—32no—
223C2×C42D3211yescharacteristic
224#104—188no—
225#97—61no—
226C4×C8—61no—
227#95—61no—
228C23×C3—21no—
229C23×C3C2×D1211yescharacteristic
230C23×C3C2×#6711yescharacteristic
231C22×D3—64no—
232C22×D3—62no—
233C22×D3—62no—
234C2×C3×C4—22no—
235C2×C3×C4—22no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—22no—
241C2×C3×C4—22no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—42no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—42no—
248C2×C3×C4—64no—
249C2×C3×C4—122no—
250C2×C3×C4—122no—
251C2×C3×C4(C2×D3)⋊C411yescharacteristic
252C2×C3×C4(C2×D3)⋊C411yescharacteristic
253C2×C3×C4(C2×D3)⋊C411yescharacteristic
254C2×C3×C4(C2×D3)⋊C411yescharacteristic
255C2×C3×C4(C2×D3)⋊C411yescharacteristic
256C2×C3×C4(C2×D3)⋊C411yescharacteristic
257C2×C3×C4(C2×D3)⋊C411yescharacteristic
258C2×C3×C4(C2×D3)⋊C411yescharacteristic
259C2×C3×C4C2×C4×D311yescharacteristic
260C2×C3×C4C2×C4×D311yescharacteristic
261C2×C3×C4C2×D1212yes—
262C2×C3×C4C2×D1211yescharacteristic
263C2×C3×C4#23512yes—
264C2×C3×C4D3×D412yes—
265C2×C3×C4#23912yes—
266C2×C3×C4C2×#6711yescharacteristic
267#67—124no—
268#67—124no—
269#67—122no—
270#67—122no—
271#67—122no—
272#67—122no—
273C2×Dic3—24no—
274C2×Dic3—42no—
275C2×Dic3—42no—
276C2×Dic3—64no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279D12—64no—
280D12—64no—
281D12—124no—
282D12—124no—
283D12—122no—
284D12—122no—
285D12—124no—
286D12—122no—
287D12—122no—
288C4×D3—128no—
289C4×D3—124no—
290C4×D3—124no—
291Dic6—64no—
292Dic6—64no—
293Dic6—124no—
294C3×C8—64no—
295C3⋊C8—24no—
296C2×C32—21no—
297C2×C32—21no—
298C2×C32#39011yescharacteristic
299C2×C32C2×#10411yescharacteristic
300C2×C32#42111yescharacteristic
301C3⋊D3—82no—
302#41—184no—
303#41—184no—
304C2×Q8—92no—
305C2×D4—92no—
306C2×D4—182no—
307C2×D4—181no—
308C2×D4—181no—
309C22×C4—62no—
310C22×C4—182no—
311C22×C4#62611yescharacteristic
312C22×C4#62611yescharacteristic
313C22×C4C2×D3211yescharacteristic
314M16—34no—
315M16—62no—
316C2×C8—62no—
317C4⋊C4—64no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C22⋊C4—182no—
321C22⋊C4—182no—
322C42—64no—
323C42#62411yescharacteristic
324C42#62411yescharacteristic
325C42#62611yescharacteristic
326C42#62611yescharacteristic
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—41no—
335C22×C3—41no—
336C22×C3#87411yescharacteristic
337C22×C3#87511yescharacteristic
338C22×C3C2×(C2×D3)⋊C411yescharacteristic
339C22×C3C2×(C2×D3)⋊C411yescharacteristic
340C22×C3#94011yescharacteristic
341C22×C3#94711yescharacteristic
342C2×D3—124no—
343C2×D3—124no—
344C2×D3—124no—
345C2×D3—122no—
346C2×D3—122no—
347C2×D3—122no—
348C2×D3—122no—
349C2×D3—122no—
350C2×D3—122no—
351C3×C4—22no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—22no—
359C3×C4—22no—
360C3×C4—22no—
361C3×C4—41no—
362C3×C4—41no—
363C3×C4—124no—
364C3×C4#80512yescomplemented
365C3×C4#82512yescomplemented
366C3×C4C4×D1212yes—
367C3×C4#89312yes—
368C3×C4#89512yes—
369C3×C4#93012yes—
370Dic3—44no—
371Dic3—124no—
372Dic3—122no—
373Dic3—122no—
374C32#198011yescharacteristic, complemented, Sylow
375C23—182no—
376C23C2×#62611yescharacteristic
377Q8—184no—
378D4—184no—
379D4—362no—
380D4—362no—
381D4—362no—
382D4—362no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—64no—
386C2×C4—122no—
387C2×C4—122no—
388C2×C4—182no—
389C2×C4—364no—
390C2×C4#372211yescharacteristic
391C2×C4#372211yescharacteristic
392C2×C4#372211yescharacteristic
393C2×C4#372211yescharacteristic
394C2×C4#379912yes—
395C2×C4D3×D1212yes—
396C2×C4C2×#62411yescharacteristic
397C2×C4C2×#62611yescharacteristic
398C8—64no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—41no—
407C2×C3—41no—
408C2×C3C2×#80511yescharacteristic
409C2×C3#493911yescharacteristic
410C2×C3#498811yescharacteristic
411C2×C3#500511yescharacteristic
412C2×C3C2×#82511yescharacteristic
413C2×C3#513911yescharacteristic
414D3—244no—
415D3—242no—
416D3—242no—
417C22—21no—
418C22—21no—
419C22—362no—
420C22—362no—
421C22—362no—
422C22#6386411yescharacteristic
423C22#6391111yescharacteristic
424C22C2×#372211yescharacteristic
425C4—21no—
426C4—21no—
427C4—21no—
428C4—124no—
429C4—362no—
430C4#6357012yescomplemented
431C4#6389412yes—
432C4#6390912yes—
433C3—21no—
434C3#6949211yescharacteristic, complemented
435C3#6986711yescharacteristic, complemented
436C2—21no—
437C2—21no—
438C2—722no—
439C2C2×#6357011yescharacteristic
440C2#1059111311yescharacteristic
441C2#1059132011yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radical#10595948C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1980
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×C4×C4⋊Dic3C2semidirect
3. C3×C4×#208C2semidirect
4. C2×#63570C2semidirect
11. #64084C4semidirect
12. #64083C4semidirect
15. #64078C4semidirect
29. C4×C4⋊Dic3D3semidirect
31. C4×#208D3semidirect
55. C3×#208D4semidirect
194. #208D12semidirect
207. C32×C4#104semidirect
364. C3×C4#805semidirect
365. C3×C4#825semidirect
374. C32#1980semidirect
430. C4#63570semidirect
434. C3#69492semidirect
435. C3#69867semidirect

Maximal subgroups

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

subgroupindex
#105959482
C3×C4×C4⋊Dic32
C3×C4×#2082
C2×#635702
#698673
#694923