Finite Group Databasebeta

← #11791389

Subgroups — #11791389

Order 1152.

1008 conjugacy classes of subgroups.

The subgroup lattice has 447 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596303C211yesmaximal, characteristic
2C2×C32×#104C211yesmaximal, characteristic, complemented
3C2×#63664C211yesmaximal, characteristic, complemented
4C2×#63652C211yesmaximal, characteristic, complemented
5M16×C3⋊Dic3C211yesmaximal, characteristic, complemented
6C4×#3750C211yesmaximal, characteristic, complemented
7C2×#63632C211yesmaximal, characteristic, complemented
8#70358—34nomaximal
9C2×C32×#41C2211yescharacteristic
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13#64156C411yescharacteristic, complemented
14#64153C411yescharacteristic, complemented
15#64149C411yescharacteristic, complemented
16#64148—21no—
17#64148—21no—
18#64145C411yescharacteristic, complemented
19C4×#638—21no—
20C4×#638—21no—
21C2×#3750—21no—
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×#3748C2211yescharacteristic
25C32×#104—22no—
26#63664—22no—
27#63658—21no—
28#63652—22no—
29#63642—21no—
30C8×C3⋊Dic3—21no—
31#63632—22no—
32#5832—34no—
33C2×C3×#104D314yescomplemented
34C2×#837—34no—
35C2×#825—34no—
36Dic3×M16—34no—
37C4×Dic3⋊C4—34no—
38C2×#805—34no—
39C32×#41—21no—
40C32×#41—21no—
41C32×#41—21no—
42C32×#41—21no—
43C2×C32×Q8C2×C411yescharacteristic
44C2×C32×D4—21no—
45C2×C32×D4C2×C411yescharacteristic
46C22×C32×C4—21no—
47C22×C32×C4—21no—
48C22×C32×C4C2311yescharacteristic
49C2×#638—21no—
50C2×#638—21no—
51C2×#638—21no—
52C22×C3⋊Dic3—21no—
53C22×C3⋊Dic3D411yescharacteristic
54C22×C3⋊Dic3D411yescharacteristic
55#3828—21no—
56#3828—21no—
57#3828—21no—
58#3828—21no—
59C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
60C2×C4×C3⋊D3—21no—
61C2×#634C2×C411yescharacteristic
62C32×M16—21no—
63C32×M16D412yescomplemented
64C2×C32×C8—21no—
65C32×C42—21no—
66C32×C42—21no—
67#3757—21no—
68#3757—21no—
69#3752—21no—
70#3752—21no—
71#3750—24no—
72#3750—21no—
73#3750—21no—
74C4×C3⋊Dic3—21no—
75C4×C3⋊Dic3—21no—
76C4×C3⋊Dic3C2×C411yescharacteristic
77C4×C3⋊Dic3C2×C411yescharacteristic
78C4×C3⋊Dic3D411yescharacteristic
79C4×C3⋊Dic3D411yescharacteristic
80#3748—21no—
81#3748D412yescomplemented
82C2×C3⋊(C3⋊C8)—21no—
83#1980—91noSylow
84C2×C3×#41C2×D314yes—
85C2×#235—34no—
86C2×C3×M16C2×D314yes—
87C2×C3×C42C2×D314yes—
88#947—34no—
89#944—34no—
90#940—34no—
91#939—64no—
92#939—64no—
93#936—34no—
94C4×#67—64no—
95C4×#67—64no—
96C2×Dic3⋊C4—64no—
97C2×C4×Dic3—34no—
98C2×C4×Dic3—34no—
99C2×#208—34no—
100C3×#104—28no—
101#837—68no—
102C3⋊#95—64no—
103#825—68no—
104#815—64no—
105C8×Dic3—64no—
106#805—68no—
107C23×C32—21no—
108C23×C32C2×D411yescharacteristic
109C22×C3⋊D3—21no—
110C32×Q8—21no—
111C32×Q8—21no—
112C32×D4—21no—
113C32×D4—21no—
114C32×D4—41no—
115C32×D4—41no—
116C2×C32×C4—22no—
117C2×C32×C4—21no—
118C2×C32×C4—41no—
119C2×C32×C4—41no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4C22×C411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C32×C4#4111yescharacteristic
128#638—42no—
129#638—41no—
130#638—41no—
131#638—42no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—41no—
136C2×C3⋊Dic3—41no—
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3C22⋊C411yescharacteristic
139C2×C3⋊Dic3C22⋊C411yescharacteristic
140C2×C3⋊Dic3C22⋊C411yescharacteristic
141C2×C3⋊Dic3C22⋊C411yescharacteristic
142C4⋊(C3⋊D3)—21no—
143C4⋊(C3⋊D3)—21no—
144C4×C3⋊D3—41no—
145C4×C3⋊D3—41no—
146#634—21no—
147#634—21no—
148C32×C8—22no—
149C3⋊(C3⋊C8)—22no—
150#532—91no—
151C2×#104—91no—
152C2×#104—91no—
153C2×#104—91no—
154C2×#104C3⋊D311yescharacteristic, complemented
155C4×M16—91no—
156C4×C4⋊C4—91no—
157C3×#41—24no—
158C3×#41—24no—
159C3×#41—24no—
160C3×#41—24no—
161C2×C3×Q8C4×D314yes—
162C2×C3×D4—24no—
163C2×C3×D4C4×D314yes—
164C22×C3×C4—24no—
165C22×C3×C4—24no—
166C22×C3×C4C22×D314yes—
167C2×#67—64no—
168C2×#67—64no—
169C2×#67—64no—
170C22×Dic3—34no—
171C22×Dic3—34no—
172C22×Dic3—64no—
173#235—64no—
174#235—64no—
175#235—64no—
176#235—64no—
177C2×D12—34no—
178C2×C4×D3—64no—
179C2×Dic6—34no—
180C3×M16—24no—
181C3×M16#6718yescomplemented
182C2×C3×C8—24no—
183C3×C42—24no—
184C3×C42—24no—
185#217—64no—
186#217—64no—
187(C2×D3)⋊C4—64no—
188(C2×D3)⋊C4—64no—
189Dic3⋊C4—64no—
190Dic3⋊C4—64no—
191Dic3⋊C4—616no—
192C4×Dic3—34no—
193C4×Dic3—34no—
194C4×Dic3—34no—
195C4×Dic3—34no—
196C4×Dic3—64no—
197C4×Dic3—64no—
198#208—38no—
199#208—64no—
200C2×C3⋊C8—64no—
201C22×C32—21no—
202C22×C32—21no—
203C22×C32—41no—
204C22×C32—41no—
205C22×C32—41no—
206C22×C32C2×C22⋊C411yescharacteristic
207C22×C32#12411yescharacteristic
208C22×C32#12711yescharacteristic
209C2×C3⋊D3—41no—
210C2×C3⋊D3—41no—
211C2×C3⋊D3—41no—
212C32×C4—42no—
213C32×C4—41no—
214C32×C4C4×D411yescharacteristic
215C32×C4C4×D411yescharacteristic
216C32×C4#12111yescharacteristic
217C32×C4#12111yescharacteristic
218C3⋊Dic3—21no—
219C3⋊Dic3—21no—
220C3⋊Dic3—21no—
221C3⋊Dic3—42no—
222C3⋊Dic3—41no—
223C3⋊Dic3#10412yescomplemented
224C2×#41—91no—
225C2×#41C2×C3⋊D311yescharacteristic
226C2×M16—91no—
227C2×M16C2×C3⋊D311yescharacteristic
228C4⋊Q8—91no—
229#127—91no—
230#124—91no—
231#124—91no—
232#121—181no—
233#121—181no—
234C4×D4—181no—
235C4×D4—181no—
236C2×C4⋊C4—181no—
237C2×C42—91no—
238C2×C42—91no—
239C2×C42C2×C3⋊D311yescharacteristic
240#104—22no—
241#104—182no—
242#104—182no—
243#104—182no—
244#97—181no—
245C4×C8—181no—
246#95—181no—
247C23×C3—24no—
248C23×C3D3×D414yes—
249C22×D3—64no—
250C3×Q8—24no—
251C3×Q8—24no—
252C3×D4—24no—
253C3×D4—24no—
254C3×D4—44no—
255C3×D4—44no—
256C2×C3×C4—28no—
257C2×C3×C4—24no—
258C2×C3×C4—44no—
259C2×C3×C4—44no—
260C2×C3×C4—44no—
261C2×C3×C4—44no—
262C2×C3×C4C2×C4×D314yes—
263C2×C3×C4#23514yes—
264C2×C3×C4D3×D414yes—
265C2×C3×C4D3×D414yes—
266C2×C3×C4#23714yes—
267C2×C3×C4C2×#6714yes—
268#67—128no—
269#67—128no—
270#67—124no—
271#67—124no—
272C2×Dic3—34no—
273C2×Dic3—34no—
274C2×Dic3—34no—
275C2×Dic3—34no—
276C2×Dic3—68no—
277C2×Dic3—68no—
278C2×Dic3—64no—
279C2×Dic3—124no—
280C2×Dic3—124no—
281C2×Dic3—124no—
282D12—64no—
283D12—64no—
284C4×D3—124no—
285C4×D3—124no—
286Dic6—64no—
287Dic6—64no—
288C3×C8—28no—
289C3⋊C8—68no—
290C2×C32—21no—
291C2×C32—21no—
292C2×C32—81no—
293C2×C32#39011yescharacteristic
294C2×C32C2×#10411yescharacteristic
295C2×C32#42111yescharacteristic
296C3⋊D3—81no—
297#41—21no—
298#41—21no—
299#41—21no—
300#41—21no—
301#41—181no—
302#41—181no—
303#41—181no—
304#41—181no—
305C2×Q8—91no—
306C2×Q8C4×C3⋊D311yescharacteristic
307C2×D4—21no—
308C2×D4—91no—
309C2×D4—181no—
310C2×D4—181no—
311C2×D4—181no—
312C2×D4C4×C3⋊D311yescharacteristic
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—91no—
316C22×C4—91no—
317C22×C4—181no—
318C22×C4—181no—
319C22×C4C22×C3⋊D311yescharacteristic
320M16—21no—
321M16—92no—
322M16—181no—
323M16#63812yescomplemented
324C2×C8—21no—
325C2×C8—181no—
326C4⋊C4—181no—
327C4⋊C4—181no—
328C4⋊C4—184no—
329C22⋊C4—181no—
330C22⋊C4—181no—
331C22⋊C4—181no—
332C22⋊C4—181no—
333C42—21no—
334C42—21no—
335C42—91no—
336C42—91no—
337C42—91no—
338C42—91no—
339C42—181no—
340C42—181no—
341C22×C3—24no—
342C22×C3—24no—
343C22×C3—44no—
344C22×C3—44no—
345C22×C3—44no—
346C22×C3D3×C22⋊C414yes—
347C22×C3#88514yes—
348C22×C3#94014yes—
349C2×D3—124no—
350C2×D3—124no—
351C2×D3—124no—
352C3×C4—48no—
353C3×C4—44no—
354C3×C4#67⋊C414yes—
355C3×C4#88414yes—
356C3×C4C4×#6714yes—
357C3×C4#93914yes—
358Dic3—38no—
359Dic3—64no—
360Dic3—64no—
361Dic3—64no—
362Dic3—128no—
363Dic3—124no—
364C32#198011yescharacteristic, complemented, Sylow
365C23—21no—
366C23—181no—
367C23D4×C3⋊D311yescharacteristic
368Q8—21no—
369Q8—21no—
370Q8—181no—
371Q8—181no—
372D4—21no—
373D4—21no—
374D4—41no—
375D4—41no—
376D4—181no—
377D4—181no—
378D4—362no—
379D4—362no—
380D4—361no—
381D4—361no—
382C2×C4—22no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—91no—
389C2×C4—91no—
390C2×C4—91no—
391C2×C4—91no—
392C2×C4—182no—
393C2×C4—182no—
394C2×C4—181no—
395C2×C4—361no—
396C2×C4—361no—
397C2×C4—361no—
398C2×C4—361no—
399C2×C4—361no—
400C2×C4C2×C4×C3⋊D311yescharacteristic
401C2×C4#382811yescharacteristic
402C2×C4D4×C3⋊D311yescharacteristic
403C2×C4D4×C3⋊D311yescharacteristic
404C2×C4#383011yescharacteristic
405C2×C4C2×#63811yescharacteristic
406C8—22no—
407C8—182no—
408C2×C3—24no—
409C2×C3—24no—
410C2×C3—84no—
411C2×C3D3×#10414yes—
412C2×C3#482114yes—
413C2×C3#495714yes—
414D3—244no—
415C22—21no—
416C22—21no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—361no—
421C22—361no—
422C22—361no—
423C22C22⋊C4×C3⋊D311yescharacteristic
424C22#6409411yescharacteristic
425C22#6414911yescharacteristic
426C4—42no—
427C4—41no—
428C4—92no—
429C4—181no—
430C4—181no—
431C4—181no—
432C4—362no—
433C4—361no—
434C4#6409011yescharacteristic
435C4#6409311yescharacteristic
436C4C4×#63811yescharacteristic
437C4#6414811yescharacteristic
438C3#7035814yescomplemented
439C2—21no—
440C2—21no—
441C2—81no—
442C2—721no—
443C2C3⋊D3×#10411yescharacteristic
444C2#1059252011yescharacteristic
445C2#1059265611yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#104C2
socleC22×C32C2×C22⋊C4
prime radical#10596303C2
cosocleC22×C32×C4C23
hypercenterC2×#104C3⋊D3
hypocenterC32#1980
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×C32×#104C2semidirect
3. C2×#63664C2semidirect
4. C2×#63652C2semidirect
5. M16×C3⋊Dic3C2semidirect
6. C4×#3750C2semidirect
7. C2×#63632C2semidirect
13. #64156C4semidirect
14. #64153C4semidirect
15. #64149C4semidirect
18. #64145C4semidirect
33. C2×C3×#104D3semidirect
63. C32×M16D4semidirect
81. #3748D4semidirect
154. C2×#104C3⋊D3semidirect
181. C3×M16#67semidirect
223. C3⋊Dic3#104semidirect
323. M16#638semidirect
364. C32#1980semidirect
438. C3#70358semidirect

Maximal subgroups

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

subgroupindex
#105963032
C2×C32×#1042
C2×#636642
C2×#636522
M16×C3⋊Dic32
C4×#37502
C2×#636322
#703583