Finite Group Databasebeta

← #11803457

Subgroups — #11803457

Order 1152.

1668 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64106C211yesmaximal, characteristic
2C2×#64081C211yesmaximal, characteristic
3C2×C4×#634C211yesmaximal, characteristic, complemented
4C32×C4×C4⋊C4C211yesmaximal, characteristic, complemented
5#10592686C211yesmaximal, characteristic
6#10592683C211yesmaximal, characteristic, complemented
7#10592672C211yesmaximal, characteristic, complemented
8#10592639C212yesmaximal
9#10592627C212yesmaximal, complemented
10#10592369C212yesmaximal
11#10592352C212yesmaximal, complemented
12#73762—34nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×#634C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C42C2212yes—
18C2×C32×C42C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×#3752C2211yescharacteristic
21C2×#3752C2212yes—
22C2×#3752C2212yes—
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2212yes—
25C2×C4⋊(C3⋊Dic3)C2212yes—
26C2×#3750C2211yescharacteristic
27C2×#3750C2212yes—
28C2×#3750C2211yescharacteristic
29C2×C4×C3⋊Dic3C2212yes—
30C2×C4×C3⋊Dic3C2211yescharacteristic
31#64106C418yescomplemented
32#64081—24no—
33C4×#634—24no—
34C32×#95C2212yes—
35#63658C2212yes—
36#63658C2212yes—
37#63658C2212yes—
38#63658C2212yes—
39C2×#897—34no—
40C2×#872—34no—
41C2×C4×Dic6—34no—
42C3×C4×C4⋊C4D314yescomplemented
43#4987—34no—
44#4984—34no—
45#4973—34no—
46#4940—38no—
47#4928—38no—
48#4670—38no—
49#4653—38no—
50C23×C3⋊D3C2311yescharacteristic
51C22×C32×C4C2312yes—
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3C2312yes—
57C22×C3⋊Dic3C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3⋊Dic3C2312yes—
60C22×C3⋊Dic3C2311yescharacteristic
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3—22no—
63C2×C4×C3⋊D3C2×C414yes—
64C2×#634—22no—
65C2×#634—22no—
66C2×#634C2×C414yes—
67C32×C4⋊C4—22no—
68C32×C4⋊C4C2×C414yes—
69C32×C42—42no—
70C32×C42D414yes—
71#3752—22no—
72#3752—22no—
73#3752—42no—
74#3752C2×C418yes—
75C4⋊(C3⋊Dic3)—22no—
76C4⋊(C3⋊Dic3)—42no—
77C4⋊(C3⋊Dic3)C2×C418yes—
78#3750—24no—
79#3750—22no—
80#3750—22no—
81C4×C3⋊Dic3—24no—
82C4×C3⋊Dic3—22no—
83#2323—91noSylow
84C22×C4×D3—34no—
85C22×Dic6—34no—
86C2×C3×C4⋊C4C2×D314yes—
87C2×C3×C4⋊C4C2×D314yes—
88C2×C3×C42C2×D318yes—
89C2×C3×C42C2×D314yes—
90C2×(C2×D3)⋊C4—38no—
91C2×(C2×D3)⋊C4—34no—
92C2×(C2×D3)⋊C4—34no—
93C2×(C2×D3)⋊C4—38no—
94C2×C4⋊Dic3—38no—
95C2×C4⋊Dic3—34no—
96C2×C4⋊Dic3—38no—
97C2×Dic3⋊C4—34no—
98C2×Dic3⋊C4—34no—
99C2×Dic3⋊C4—38no—
100C2×C4×Dic3—38no—
101C2×C4×Dic3—34no—
102#897—332no—
103#872—616no—
104C4×Dic6—616no—
105C3×#95C2×D318yes—
106C3⋊#95—38no—
107C3⋊#95—38no—
108C3⋊#95—38no—
109C3⋊#95—38no—
110C23×C32C2411yescharacteristic
111C22×C3⋊D3—21no—
112C22×C3⋊D3—21no—
113C22×C3⋊D3—21no—
114C22×C3⋊D3—21no—
115C22×C3⋊D3—21no—
116C22×C3⋊D3—21no—
117C22×C3⋊D3C22×C412yes—
118C2×C32×C4—22no—
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4—22no—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4—22no—
127C2×C32×C4C22×C414yes—
128C2×C32×C4C22×C412yes—
129C2×C32×C4C2×D412yes—
130C2×C32×C4C2×D412yes—
131C2×C32×C4C2×D412yes—
132C2×C32×C4#4112yes—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3C22×C412yes—
147C2×C3⋊Dic3C22×C414yes—
148C4×C3⋊D3—28no—
149#634—28no—
150C2×C22⋊Q8—91no—
151C2×C4×Q8—91no—
152C2×#117—91no—
153#391—91no—
154#389—91no—
155#389—92no—
156#388—92no—
157#388—92no—
158#387—92no—
159#380—91no—
160C4×C4⋊C4C3⋊D311yescharacteristic, complemented
161C23×D3—34no—
162C22×C3×C4C22×D318yes—
163C22×C3×C4C22×D318yes—
164C22×C3×C4C22×D314yes—
165C22×C3×C4C22×D314yes—
166C22×C3×C4C22×D314yes—
167C22×Dic3—38no—
168C22×Dic3—34no—
169C22×Dic3—34no—
170C22×Dic3—38no—
171C22×Dic3—34no—
172C2×C4×D3—316no—
173C2×C4×D3—68no—
174C2×C4×D3—68no—
175C2×Dic6—316no—
176C2×Dic6—68no—
177C2×Dic6—68no—
178C3×C4⋊C4—28no—
179C3×C4⋊C4C4×D3116yes—
180C3×C42—48no—
181C3×C42D12116yes—
182(C2×D3)⋊C4—332no—
183(C2×D3)⋊C4—68no—
184(C2×D3)⋊C4—68no—
185(C2×D3)⋊C4—128no—
186C4⋊Dic3—332no—
187C4⋊Dic3—68no—
188C4⋊Dic3—128no—
189Dic3⋊C4—616no—
190Dic3⋊C4—68no—
191Dic3⋊C4—68no—
192C4×Dic3—616no—
193C4×Dic3—68no—
194C22×C32C23×C411yescharacteristic
195C22×C32C22×D411yescharacteristic
196C22×C32C2×#4111yescharacteristic
197C22×C32H(5,𝔽2)11yescharacteristic
198C22×C322−1+411yescharacteristic
199C22×C322−1+411yescharacteristic
200C22×C322−1+411yescharacteristic
201C2×C3⋊D3—22no—
202C2×C3⋊D3—22no—
203C2×C3⋊D3—22no—
204C2×C3⋊D3—41no—
205C2×C3⋊D3—41no—
206C2×C3⋊D3—41no—
207C2×C3⋊D3—41no—
208C32×C4—24no—
209C32×C4—22no—
210C32×C4—22no—
211C32×C4—42no—
212C32×C4C4×D414yes—
213C3⋊Dic3—24no—
214C3⋊Dic3—22no—
215C3⋊Dic3—41no—
216C3⋊Dic3—42no—
217C3⋊Dic3—41no—
218C22×Q8—91no—
219C23×C4—91no—
220C22⋊Q8—98no—
221C4×Q8—184no—
222#117—184no—
223C2×C4⋊C4—92no—
224C2×C4⋊C4—91no—
225C2×C4⋊C4—91no—
226C2×C4⋊C4—91no—
227C2×C4⋊C4—92no—
228C2×C4⋊C4—92no—
229C2×C4⋊C4C2×C3⋊D311yescharacteristic
230C2×C4⋊C4C2×C3⋊D311yescharacteristic
231C2×C22⋊C4—92no—
232C2×C22⋊C4—91no—
233C2×C22⋊C4—91no—
234C2×C22⋊C4—92no—
235C2×C42—91no—
236C2×C42—92no—
237C2×C42C2×C3⋊D312yes—
238C2×C42C2×C3⋊D311yescharacteristic
239#95—92no—
240#95—92no—
241#95—92no—
242#95—92no—
243#95C2×C3⋊D312yes—
244C23×C3C23×D314yes—
245C22×D3—38no—
246C22×D3—64no—
247C22×D3—64no—
248C22×D3—64no—
249C22×D3—64no—
250C22×D3—64no—
251C22×D3—64no—
252C2×C3×C4—28no—
253C2×C3×C4—24no—
254C2×C3×C4—24no—
255C2×C3×C4—24no—
256C2×C3×C4—24no—
257C2×C3×C4—28no—
258C2×C3×C4—28no—
259C2×C3×C4—28no—
260C2×C3×C4—28no—
261C2×C3×C4C2×C4×D3116yes—
262C2×C3×C4C2×C4×D318yes—
263C2×C3×C4C2×D1218yes—
264C2×C3×C4C2×D1218yes—
265C2×C3×C4C2×D1218yes—
266C2×C3×C4#23518yes—
267C2×Dic3—38no—
268C2×Dic3—316no—
269C2×Dic3—68no—
270C2×Dic3—64no—
271C2×Dic3—68no—
272C2×Dic3—64no—
273C2×Dic3—68no—
274C2×Dic3—64no—
275C2×Dic3—64no—
276C2×Dic3—64no—
277C2×Dic3—68no—
278C2×Dic3—68no—
279C2×Dic3—64no—
280C2×Dic3—64no—
281C2×Dic3—64no—
282C4×D3—632no—
283Dic6—632no—
284C2×C32C2×C4×D411yescharacteristic
285C2×C32#51911yescharacteristic
286C2×C32#52011yescharacteristic
287C2×C32#53611yescharacteristic
288C2×C32#53711yescharacteristic
289C2×C32#54111yescharacteristic
290C2×C32#54211yescharacteristic
291C3⋊D3—42no—
292C24—91no—
293C2×Q8—94no—
294C2×Q8—182no—
295C2×Q8—182no—
296C22×C4—92no—
297C22×C4—91no—
298C22×C4—94no—
299C22×C4—91no—
300C22×C4—91no—
301C22×C4—92no—
302C22×C4—182no—
303C22×C4—182no—
304C22×C4C22×C3⋊D312yes—
305C22×C4C22×C3⋊D312yes—
306C22×C4C22×C3⋊D311yescharacteristic
307C22×C4C22×C3⋊D311yescharacteristic
308C22×C4C22×C3⋊D311yescharacteristic
309C4⋊C4—22no—
310C4⋊C4—98no—
311C4⋊C4—182no—
312C4⋊C4—182no—
313C4⋊C4—184no—
314C4⋊C4—182no—
315C4⋊C4—362no—
316C4⋊C4C4×C3⋊D314yes—
317C22⋊C4—98no—
318C22⋊C4—182no—
319C22⋊C4—182no—
320C22⋊C4—362no—
321C42—42no—
322C42—182no—
323C42—184no—
324C42C4⋊(C3⋊D3)14yes—
325C22×C3C22×C4×D314yes—
326C22×C3C22×D1214yes—
327C22×C3C2×#23514yes—
328C22×C3#100414yes—
329C22×C3#100714yes—
330C22×C3#101014yes—
331C22×C3#101014yes—
332C2×D3—68no—
333C2×D3—68no—
334C2×D3—68no—
335C2×D3—124no—
336C2×D3—124no—
337C2×D3—124no—
338C2×D3—124no—
339C3×C4—28no—
340C3×C4—28no—
341C3×C4—216no—
342C3×C4—48no—
343C3×C4C4×D12116yes—
344Dic3—616no—
345Dic3—68no—
346Dic3—128no—
347Dic3—124no—
348Dic3—124no—
349C32#232311yescharacteristic, complemented, Sylow
350C23—92no—
351C23—181no—
352C23—181no—
353C23—181no—
354C23—181no—
355C23—181no—
356C23—181no—
357C23C23×C3⋊D311yescharacteristic
358Q8—188no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—94no—
369C2×C4—92no—
370C2×C4—182no—
371C2×C4—181no—
372C2×C4—181no—
373C2×C4—182no—
374C2×C4—188no—
375C2×C4—181no—
376C2×C4—181no—
377C2×C4—182no—
378C2×C4—182no—
379C2×C4—181no—
380C2×C4—181no—
381C2×C4—182no—
382C2×C4—181no—
383C2×C4—181no—
384C2×C4C2×C4×C3⋊D314yes—
385C2×C4C2×C4×C3⋊D312yes—
386C2×C4C2×C4⋊(C3⋊D3)12yes—
387C2×C4C2×C4⋊(C3⋊D3)12yes—
388C2×C4C2×C4⋊(C3⋊D3)12yes—
389C2×C4#382812yes—
390C2×C3C2×C4×D1214yes—
391C2×C3#551014yes—
392C2×C3#552614yes—
393C2×C3#554614yes—
394C2×C3#556114yes—
395C2×C3#557214yes—
396C2×C3#558314yes—
397D3—128no—
398C22—182no—
399C22—182no—
400C22—182no—
401C22—361no—
402C22—361no—
403C22—361no—
404C22—361no—
405C22C22×C4×C3⋊D311yescharacteristic
406C22C22×C4⋊(C3⋊D3)11yescharacteristic
407C22C2×#382811yescharacteristic
408C22#6436111yescharacteristic
409C22#6436411yescharacteristic
410C22#6436711yescharacteristic
411C22#6436711yescharacteristic
412C4—22no—
413C4—22no—
414C4—24no—
415C4—42no—
416C4—182no—
417C4—184no—
418C4—361no—
419C4—362no—
420C4—361no—
421C4C4×C4⋊(C3⋊D3)14yes—
422C3#7376214yescomplemented
423C2—362no—
424C2C2×C4×C4⋊(C3⋊D3)11yescharacteristic
425C2#1059598111yescharacteristic
426C2#1059599711yescharacteristic
427C2#1059601711yescharacteristic
428C2#1059603211yescharacteristic
429C2#1059604311yescharacteristic
430C2#1059605411yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×C4×C4⋊C4C2
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC4×C4⋊C4C3⋊D3
hypocenterC32#2323
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×#634C2semidirect
4. C32×C4×C4⋊C4C2semidirect
6. #10592683C2semidirect
7. #10592672C2semidirect
9. #10592627C2semidirect
11. #10592352C2semidirect
31. #64106C4semidirect
42. C3×C4×C4⋊C4D3semidirect
160. C4×C4⋊C4C3⋊D3semidirect
349. C32#2323semidirect
422. C3#73762semidirect

Maximal subgroups

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

subgroupindex
C2×#641062
C2×#640812
C2×C4×#6342
C32×C4×C4⋊C42
#105926862
#105926832
#105926722
#105926392
#105926272
#105923692
#105923522
#737623