Finite Group Databasebeta

← #11870695

Subgroups — #11870695

Order 1152.

1284 conjugacy classes of subgroups.

The subgroup lattice has 423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
2#10596067C211yesmaximal, characteristic
3C32×#448C211yesmaximal, characteristic, complemented
4#10592926C211yesmaximal, characteristic, complemented
5#10592862C212yesmaximal, complemented
6SD16×C3⋊Dic3C212yesmaximal, complemented
7#10592733C211yesmaximal, characteristic, complemented
8#10592490C212yesmaximal, complemented
9#10592487C212yesmaximal, complemented
10#10592434C211yesmaximal, characteristic, complemented
11#10592417C211yesmaximal, characteristic, complemented
12#80028—34nomaximal
13C22×C32×Q8C2211yescharacteristic
14C2×#3830—21no—
15C2×C32×SD16C2212yes—
16C32×#121C2211yescharacteristic
17Q8×C3⋊Dic3—21no—
18Q8×C3⋊Dic3—21no—
19Q8×C3⋊Dic3C2212yes—
20Q8×C3⋊Dic3C2212yes—
21C2×#3755C2212yes—
22#64149C2211yescharacteristic
23#64148—21no—
24D4×C3⋊Dic3C2211yescharacteristic
25#64139C2211yescharacteristic
26C2×C4⋊(C3⋊Dic3)—21no—
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C2×C4×C3⋊Dic3—21no—
29C2×C4×C3⋊Dic3C2211yescharacteristic
30#64102C2211yescharacteristic
31#64097C2211yescharacteristic
32#64094—21no—
33#64090—21no—
34C32×#103C2212yes—
35C32×C22⋊C8C2211yescharacteristic
36#63662C2212yes—
37#63659C2212yes—
38#63657C2211yescharacteristic
39#63648C2212yes—
40#63644C2212yes—
41#63641C2212yes—
42C8×C3⋊Dic3C2212yes—
43#63635C2212yes—
44C2×Q8×Dic3—34no—
45#5596—34no—
46C3×#448D314yescomplemented
47#5227—34no—
48#5163—38no—
49Dic3×SD16—38no—
50#5034—34no—
51#4791—38no—
52#4788—38no—
53#4735—34no—
54#4718—34no—
55C2×C32×Q8—24no—
56C2×C32×Q8—21no—
57C2×C32×Q8C2312yes—
58C2×C32×D4—21no—
59C2×C32×D4C2311yescharacteristic
60C22×C32×C4—21no—
61C22×C32×C4C2311yescharacteristic
62C2×#638—21no—
63C2×#638—21no—
64C2×#638—21no—
65C22×C3⋊Dic3—21no—
66C22×C3⋊Dic3—21no—
67C22×C3⋊Dic3D411yescharacteristic
68C22×C3⋊Dic3D411yescharacteristic
69#3830—44no—
70C2×C4⋊(C3⋊D3)C2311yescharacteristic
71C2×C4×C3⋊D3—21no—
72C2×#634—21no—
73C32×SD16—24no—
74C2×C32×C8C2312yes—
75C32×C4⋊C4C2311yescharacteristic
76C32×C22⋊C4—21no—
77#3757—21no—
78#3755—24no—
79#3752—21no—
80#3752—21no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)—22no—
83C4⋊(C3⋊Dic3)—22no—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85C4⋊(C3⋊Dic3)C2312yes—
86#3750—21no—
87C4×C3⋊Dic3—22no—
88C4×C3⋊Dic3—22no—
89C4×C3⋊Dic3D411yescharacteristic
90C4×C3⋊Dic3D411yescharacteristic
91C4×C3⋊Dic3C2311yescharacteristic
92C4×C3⋊Dic3C2311yescharacteristic
93C2×C3⋊(C3⋊C8)C2312yes—
94#3103—91noSylow
95C22×C3×Q8C2×D314yes—
96C2×#237—64no—
97C2×C3×SD16C2×D318yes—
98C3×#121C2×D314yes—
99Q8×Dic3—38no—
100Q8×Dic3—38no—
101Q8×Dic3—64no—
102Q8×Dic3—64no—
103C2×#215—38no—
104#940—34no—
105#939—64no—
106D4×Dic3—34no—
107#930—34no—
108C2×C4⋊Dic3—34no—
109C2×C4⋊Dic3—64no—
110C2×C4×Dic3—34no—
111C2×C4×Dic3—64no—
112#893—34no—
113#888—34no—
114#885—64no—
115#67⋊C4—64no—
116C3×#103C2×D318yes—
117C3×C22⋊C8C2×D314yes—
118#835—38no—
119#832—38no—
120#830—34no—
121#821—38no—
122#817—38no—
123Dic3⋊C8—38no—
124C8×Dic3—38no—
125#808—38no—
126C23×C32—21no—
127C23×C32C2×D411yescharacteristic
128C22×C3⋊D3—21no—
129C32×Q8—24no—
130C32×Q8—22no—
131C32×Q8#4114yescomplemented
132C32×D4—22no—
133C32×D4—42no—
134C2×C32×C4—24no—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4—21no—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2411yescharacteristic
140#638—42no—
141#638—42no—
142#638—42no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—41no—
146C2×C3⋊Dic3—42no—
147C2×C3⋊Dic3—42no—
148C2×C3⋊Dic3SD1614yescomplemented
149C2×C3⋊Dic3C2×D411yescharacteristic
150C2×C3⋊Dic3C2×D411yescharacteristic
151C2×C3⋊Dic3C2×D411yescharacteristic
152C2×C3⋊Dic3C2×D411yescharacteristic
153C4⋊(C3⋊D3)—22no—
154C4×C3⋊D3—42no—
155#634—42no—
156C32×C8—22no—
157C3⋊(C3⋊C8)—22no—
158#532—91no—
159C2×C4×Q8—91no—
160#481—91no—
161#481—91no—
162#475—92no—
163#460—92no—
164#448—91no—
165#448C3⋊D311yescharacteristic, complemented
166C4×SD16—92no—
167C4×SD16—92no—
168#431—91no—
169C2×C3×Q8—216no—
170C2×C3×Q8—24no—
171C2×C3×Q8C22×D318yes—
172C2×C3×D4—24no—
173C2×C3×D4C22×D314yes—
174C22×C3×C4—24no—
175C22×C3×C4C22×D314yes—
176C2×#67—64no—
177C2×#67—64no—
178C2×#67—64no—
179C22×Dic3—34no—
180C22×Dic3—34no—
181C22×Dic3—64no—
182C22×Dic3—64no—
183#237—1216no—
184C2×D12—34no—
185C2×C4×D3—64no—
186C2×Dic6—64no—
187C3×SD16—216no—
188C2×C3×C8C22×D318yes—
189C3×C4⋊C4C22×D314yes—
190C3×C22⋊C4—24no—
191#217—64no—
192#215—616no—
193(C2×D3)⋊C4—64no—
194(C2×D3)⋊C4—64no—
195C4⋊Dic3—38no—
196C4⋊Dic3—34no—
197C4⋊Dic3—68no—
198C4⋊Dic3—68no—
199C4⋊Dic3—64no—
200Dic3⋊C4—64no—
201C4×Dic3—34no—
202C4×Dic3—34no—
203C4×Dic3—34no—
204C4×Dic3—34no—
205C4×Dic3—68no—
206C4×Dic3—68no—
207C2×C3⋊C8—38no—
208C22×C32—21no—
209C22×C32—21no—
210C22×C32—41no—
211C22×C32—41no—
212C22×C32—41no—
213C22×C32C2×SD1612yes—
214C22×C32C22×D411yescharacteristic
215C2×C3⋊D3—41no—
216C2×C3⋊D3—41no—
217C2×C3⋊D3—41no—
218C32×C4—24no—
219C32×C4—21no—
220C32×C4—41no—
221C32×C4C2×#4112yes—
222C3⋊Dic3—21no—
223C3⋊Dic3—21no—
224C3⋊Dic3—41no—
225C3⋊Dic3—42no—
226C3⋊Dic3C2×SD1612yes—
227C3⋊Dic3C2×SD1612yes—
228C2×#41—181no—
229C22×Q8C2×C3⋊D311yescharacteristic
230C2×SD16—92no—
231C2×SD16C2×C3⋊D312yes—
232C4⋊Q8—91no—
233#127—91no—
234#124—181no—
235#121—91no—
236#121—181no—
237#121C2×C3⋊D311yescharacteristic
238C4×Q8—92no—
239C4×Q8—92no—
240C4×Q8—181no—
241C4×Q8—181no—
242C4×D4—91no—
243C4×D4—91no—
244C4×D4—181no—
245C2×C4⋊C4—91no—
246C2×C4⋊C4—181no—
247C2×C42—91no—
248C2×C42—181no—
249#106—92no—
250#106—92no—
251C4⋊C8—92no—
252#103—92no—
253#103C2×C3⋊D312yes—
254#102—92no—
255#102—92no—
256C22⋊C8—91no—
257C22⋊C8C2×C3⋊D311yescharacteristic
258C4×C8—92no—
259C23×C3—24no—
260C23×C3D3×D414yes—
261C22×D3—64no—
262C3×Q8—216no—
263C3×Q8—28no—
264C3×Q8#237116yescomplemented
265C3×D4—28no—
266C3×D4—48no—
267C2×C3×C4—216no—
268C2×C3×C4—28no—
269C2×C3×C4—28no—
270C2×C3×C4—24no—
271C2×C3×C4D3×D414yes—
272C2×C3×C4C23×D314yes—
273#67—128no—
274#67—128no—
275#67—128no—
276C2×Dic3—316no—
277C2×Dic3—34no—
278C2×Dic3—34no—
279C2×Dic3—34no—
280C2×Dic3—34no—
281C2×Dic3—68no—
282C2×Dic3—64no—
283C2×Dic3—128no—
284C2×Dic3—124no—
285C2×Dic3—128no—
286D12—68no—
287C4×D3—128no—
288Dic6—128no—
289C3×C8—28no—
290C3⋊C8—68no—
291C2×C32—22no—
292C2×C32—81no—
293C2×C32#52511yescharacteristic
294C2×C32C22×SD1611yescharacteristic
295C2×C32#57511yescharacteristic
296C3⋊D3—81no—
297#41—364no—
298C2×Q8—24no—
299C2×Q8—21no—
300C2×Q8—181no—
301C2×Q8C22×C3⋊D312yes—
302C2×D4—21no—
303C2×D4—91no—
304C2×D4—181no—
305C2×D4—181no—
306C2×D4—181no—
307C2×D4C22×C3⋊D311yescharacteristic
308C22×C4—21no—
309C22×C4—91no—
310C22×C4—91no—
311C22×C4—181no—
312C22×C4—181no—
313C22×C4—181no—
314C22×C4C22×C3⋊D311yescharacteristic
315SD16—24no—
316SD16—184no—
317C2×C8—92no—
318C2×C8C22×C3⋊D312yes—
319C4⋊C4—92no—
320C4⋊C4—91no—
321C4⋊C4—182no—
322C4⋊C4—182no—
323C4⋊C4—181no—
324C4⋊C4—181no—
325C4⋊C4C22×C3⋊D311yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—181no—
328C22⋊C4—181no—
329C22⋊C4—181no—
330C42—91no—
331C42—91no—
332C42—91no—
333C42—91no—
334C42—182no—
335C42—182no—
336C22×C3—24no—
337C22×C3—24no—
338C22×C3—44no—
339C22×C3—44no—
340C22×C3—44no—
341C22×C3D3×SD1618yes—
342C22×C3C2×D3×D414yes—
343C2×D3—124no—
344C2×D3—124no—
345C2×D3—124no—
346C3×C4—216no—
347C3×C4—24no—
348C3×C4—44no—
349C3×C4C2×#23718yes—
350Dic3—38no—
351Dic3—38no—
352Dic3—64no—
353Dic3—64no—
354Dic3—124no—
355Dic3—128no—
356C32#310311yescharacteristic, complemented, Sylow
357C23—21no—
358C23—181no—
359C23D4×C3⋊D311yescharacteristic
360Q8—24no—
361Q8—22no—
362Q8—362no—
363Q8#383014yescomplemented
364D4—22no—
365D4—42no—
366D4—182no—
367D4—362no—
368D4—362no—
369D4—362no—
370C2×C4—24no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—21no—
374C2×C4—91no—
375C2×C4—91no—
376C2×C4—94no—
377C2×C4—91no—
378C2×C4—91no—
379C2×C4—182no—
380C2×C4—181no—
381C2×C4—362no—
382C2×C4—362no—
383C2×C4—361no—
384C2×C4—362no—
385C2×C4D4×C3⋊D311yescharacteristic
386C2×C4C23×C3⋊D311yescharacteristic
387C8—22no—
388C8—182no—
389C2×C3—28no—
390C2×C3—84no—
391C2×C3#558614yes—
392C2×C3C2×D3×SD1614yes—
393C2×C3#577714yes—
394D3—244no—
395C22—21no—
396C22—21no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—361no—
401C22—361no—
402C22—361no—
403C22SD16×C3⋊D312yes—
404C22C2×D4×C3⋊D311yescharacteristic
405C4—24no—
406C4—21no—
407C4—41no—
408C4—92no—
409C4—92no—
410C4—181no—
411C4—181no—
412C4—361no—
413C4—362no—
414C4C2×#383012yes—
415C3#8002814yescomplemented
416C2—22no—
417C2—81no—
418C2—721no—
419C2#1059605711yescharacteristic
420C2C2×SD16×C3⋊D311yescharacteristic
421C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#448C2
socleC22×C32C22×D4
prime radical#10596067C2
hypercenter#448C3⋊D3
hypocenterC32#3103
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C3⋊Dic3C2semidirect
3. C32×#448C2semidirect
4. #10592926C2semidirect
5. #10592862C2semidirect
6. SD16×C3⋊Dic3C2semidirect
7. #10592733C2semidirect
8. #10592490C2semidirect
9. #10592487C2semidirect
10. #10592434C2semidirect
11. #10592417C2semidirect
46. C3×#448D3semidirect
131. C32×Q8#41semidirect
148. C2×C3⋊Dic3SD16semidirect
165. #448C3⋊D3semidirect
264. C3×Q8#237semidirect
356. C32#3103semidirect
363. Q8#3830semidirect
415. C3#80028semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
#105960672
C32×#4482
#105929262
#105928622
SD16×C3⋊Dic32
#105927332
#105924902
#105924872
#105924342
#105924172
#800283