Finite Group Databasebeta

← #11861297

Subgroups — #11861297

Order 1152.

949 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic
2C3×#5024C212yesmaximal, complemented
3#10590331C212yesmaximal
4#10590331C211yesmaximal, characteristic
5#10590322C212yesmaximal
6C4×#3710C211yesmaximal, characteristic
7#10590296C212yesmaximal, complemented
8#10590255C214yesmaximal, complemented
9D3×#446—32nomaximal
10C2×Q8×C3⋊D3C411yescharacteristic
11C32×C4×Q8C2211yescharacteristic
12Q8×C3⋊Dic3C411yescharacteristic
13C4⋊C4×C3⋊D3C412yes—
14C4⋊C4×C3⋊D3C411yescharacteristic
15#64096C411yescharacteristic
16#64096C412yes—
17C42×C3⋊D3C2211yescharacteristic
18C42×C3⋊D3C2212yes—
19C4×#634C2212yes—
20C4×#634C2211yescharacteristic
21C2×#3710C2211yescharacteristic
22C2×#3710C2212yes—
23C2×#3710C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2214yes—
25C3×C4⋊(C3⋊C8)C2212yes—
26C3×#803C2214yes—
27C3×C4×C3⋊C8C2212yes—
28#63572C2212yes—
29#63572C2214yes—
30#63555C2214yes—
31#63553C2212yes—
32C4×D3×Q8—32no—
33C4×D3×Q8—61no—
34C3×#446—32no—
35#5024D312yescomplemented
36D3×C4⋊C8—32no—
37D3×C4⋊C8—34no—
38#4831—32no—
39#4828—34no—
40D3×#97—34no—
41#4701—34no—
42C4×D3×C8—32no—
43#4679—32no—
44C2×C32×Q8C2×C411yescharacteristic
45Q8×C3⋊D3—24no—
46C2×C4×C3⋊D3C2×C411yescharacteristic
47C2×C4×C3⋊D3C2×C412yes—
48C2×C4×C3⋊D3C2×C412yes—
49C2×C4×C3⋊D3C2×C411yescharacteristic
50C2×C4×C3⋊D3C2311yescharacteristic
51C2×#634C2×C411yescharacteristic
52C2×#634C2×C412yes—
53C32×C4⋊C4C2×C412yes—
54C32×C4⋊C4C2×C411yescharacteristic
55C32×C42C2311yescharacteristic
56C32×C42C2312yes—
57C4⋊(C3⋊Dic3)C2×C412yes—
58C4⋊(C3⋊Dic3)C2×C411yescharacteristic
59#3750C2×C412yes—
60#3750C2×C412yes—
61#3750C2×C412yes—
62C4×C3⋊Dic3C2×C412yes—
63C4×C3⋊Dic3C2×C411yescharacteristic
64C4×C3⋊Dic3C2×C412yes—
65C4×C3⋊Dic3C2×C411yescharacteristic
66C4×C3⋊Dic3C2311yescharacteristic
67C4×C3⋊Dic3C2312yes—
68C2×C3×C3⋊C8C2312yes—
69C2×C3×C3⋊C8C2314yes—
70C2×C3×C3⋊C8C2312yes—
71#3710—22no—
72#3710—24no—
73#3710Q814yescomplemented
74C2×#446—91noSylow
75C2×D3×Q8—32no—
76C2×D3×Q8—61no—
77C3×C4×Q8—21no—
78C3×C4×Q8C2×D312yes—
79Q8×Dic3—32no—
80Q8×Dic3—61no—
81C2×D3×C8—32no—
82C2×D3×C8—32no—
83C2×D3×C8—34no—
84D3×C4⋊C4—32no—
85D3×C4⋊C4—34no—
86D3×C4⋊C4—61no—
87D3×C4⋊C4—62no—
88#887—34no—
89#887—32no—
90#887—62no—
91#887—61no—
92C42×D3—32no—
93C42×D3—34no—
94C42×D3—61no—
95C42×D3—62no—
96C4×Dic6—32no—
97C4×Dic6—34no—
98C4×Dic6—62no—
99C4×Dic6—61no—
100C3×C4⋊C8—34no—
101C3×C4⋊C8—32no—
102C3×#97—34no—
103C3×C4×C8—32no—
104#815—34no—
105#815—34no—
106Dic3⋊C8—34no—
107Dic3⋊C8—34no—
108Dic3⋊C8—34no—
109C8×Dic3—32no—
110C8×Dic3—32no—
111C4⋊(C3⋊C8)C2×D312yes—
112C4⋊(C3⋊C8)C2×D314yes—
113#803C2×D314yes—
114C4×C3⋊C8C2×D312yes—
115C22×C3⋊D3C22×C411yescharacteristic
116C32×Q8—22no—
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C22×C412yes—
119C2×C32×C4C22×C412yes—
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2411yescharacteristic
122C2×C3⋊Dic3C22×C411yescharacteristic
123C2×C3⋊Dic3C22×C412yes—
124C2×C3⋊Dic3C22×C412yes—
125C2×C3⋊Dic3C22×C411yescharacteristic
126C2×C3⋊Dic3C22×C411yescharacteristic
127C4×C3⋊D3—24no—
128C4×C3⋊D3—22no—
129C4×C3⋊D3—24no—
130C4×C3⋊D3M1614yes—
131C4×C3⋊D3C2×Q812yes—
132C4×C3⋊D3#4112yes—
133#634—22no—
134#634—24no—
135C3×C3⋊C8—22no—
136C3×C3⋊C8—24no—
137C3×C3⋊C8C2×Q814yescomplemented
138C2×C4×Q8—91no—
139#446—32no—
140#446—92no—
141#446—94no—
142C2×C4⋊C8—91no—
143C2×C4⋊C8—92no—
144C2×#97—92no—
145C2×C4×C8—91no—
146C2×C3×Q8—21no—
147C2×C3×Q8C4×D312yes—
148D3×Q8—68no—
149D3×Q8—68no—
150C2×C4×D3—32no—
151C2×C4×D3—32no—
152C2×C4×D3—32no—
153C2×C4×D3—34no—
154C2×C4×D3—34no—
155C2×C4×D3—61no—
156C2×C4×D3—61no—
157C2×C4×D3—62no—
158C2×C4×D3—61no—
159C2×C4×D3—62no—
160C2×Dic6—34no—
161C2×Dic6—32no—
162C2×Dic6—62no—
163C2×Dic6—61no—
164C2×C3×C8—32no—
165C2×C3×C8—32no—
166C2×C3×C8—34no—
167C3×C4⋊C4—22no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4C4×D314yes—
170C3×C4⋊C4C4×D312yes—
171C3×C42—21no—
172C3×C42—22no—
173C3×C42C22×D312yes—
174C3×C42C22×D314yes—
175C4⋊Dic3—34no—
176C4⋊Dic3—32no—
177C4⋊Dic3—62no—
178C4⋊Dic3—61no—
179Dic3⋊C4—34no—
180Dic3⋊C4—34no—
181Dic3⋊C4—34no—
182Dic3⋊C4—62no—
183Dic3⋊C4—62no—
184Dic3⋊C4—62no—
185C4×Dic3—32no—
186C4×Dic3—34no—
187C4×Dic3—34no—
188C4×Dic3—32no—
189C4×Dic3—32no—
190C4×Dic3—34no—
191C4×Dic3—61no—
192C4×Dic3—62no—
193C4×Dic3—61no—
194C4×Dic3—62no—
195C4×Dic3—62no—
196C4×Dic3—61no—
197C2×C3⋊C8C22×D312yes—
198C2×C3⋊C8C22×D314yes—
199C2×C3⋊C8C22×D312yes—
200D3×C8—38no—
201D3×C8—64no—
202D3×C8—68no—
203C22×C32C23×C411yescharacteristic
204C2×C3⋊D3C4×Q812yes—
205C2×C3⋊D3C2×M1612yes—
206C2×C3⋊D3#13112yes—
207C32×C4—22no—
208C32×C4—21no—
209C32×C4—22no—
210C32×C4C2×M1612yes—
211C32×C4C22×Q811yescharacteristic
212C32×C4C2×#4111yescharacteristic
213C3⋊Dic3—22no—
214C3⋊Dic3—21no—
215C3⋊Dic3—22no—
216C3⋊Dic3C4×Q812yes—
217C3⋊Dic3C2×M1612yes—
218C22×Q8—91no—
219C22×C8—91no—
220C22×C8—91no—
221C22×C8—92no—
222C4×Q8—91no—
223C4×Q8—92no—
224C4×Q8—91no—
225C4×Q8—92no—
226C4×Q8—91no—
227C4×Q8D3211yescharacteristic
228C2×C4⋊C4—91no—
229C2×C4⋊C4—92no—
230C2×C42—91no—
231C2×C42—92no—
232C4⋊C8—32no—
233C4⋊C8—34no—
234C4⋊C8—92no—
235C4⋊C8—94no—
236#97—34no—
237#97—94no—
238C4×C8—32no—
239C4×C8—92no—
240C22×D3—32no—
241C22×D3—61no—
242C3×Q8—24no—
243C3×Q8—24no—
244C2×C3×C4—21no—
245C2×C3×C4—22no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—22no—
249C2×C3×C4C2×C4×D312yes—
250C2×C3×C4C2×C4×D314yes—
251C2×C3×C4C2×C4×D314yes—
252C2×C3×C4C2×C4×D312yes—
253C2×C3×C4C23×D312yes—
254C2×Dic3—32no—
255C2×Dic3—32no—
256C2×Dic3—32no—
257C2×Dic3—34no—
258C2×Dic3—34no—
259C2×Dic3—61no—
260C2×Dic3—61no—
261C2×Dic3—62no—
262C2×Dic3—61no—
263C2×Dic3—62no—
264C4×D3—38no—
265C4×D3—34no—
266C4×D3—34no—
267C4×D3—64no—
268C4×D3—62no—
269C4×D3—62no—
270C4×D3—64no—
271C4×D3—68no—
272C4×D3—68no—
273C4×D3—68no—
274C4×D3—122no—
275C4×D3—124no—
276Dic6—68no—
277Dic6—68no—
278Dic6—64no—
279Dic6—64no—
280C3×C8—34no—
281C3×C8—62no—
282C3×C8—64no—
283C3⋊C8—22no—
284C3⋊C8—24no—
285C3⋊C8D3×Q814yescomplemented
286C2×C32C2×C4×Q811yescharacteristic
287C2×C32C22×M1611yescharacteristic
288C2×C32C2×#13111yescharacteristic
289C3⋊D3#44614yescomplemented
290C2×Q8—92no—
291C2×Q8—91no—
292C2×Q8—184no—
293C2×Q8#62411yescharacteristic
294C22×C4—91no—
295C22×C4—91no—
296C22×C4—91no—
297C22×C4—92no—
298C22×C4—92no—
299C2×C8—32no—
300C2×C8—32no—
301C2×C8—34no—
302C2×C8—94no—
303C2×C8—182no—
304C2×C8—184no—
305C4⋊C4—92no—
306C4⋊C4—92no—
307C4⋊C4—92no—
308C4⋊C4—92no—
309C4⋊C4—91no—
310C4⋊C4#62412yes—
311C4⋊C4#62411yescharacteristic
312C42—91no—
313C42—92no—
314C42—91no—
315C42—92no—
316C42—91no—
317C42—92no—
318C42C2×D3211yescharacteristic
319C42C2×D3212yes—
320C22×C3—21no—
321C22×C3C22×C4×D312yes—
322C2×D3—34no—
323C2×D3—34no—
324C2×D3—34no—
325C2×D3—62no—
326C2×D3—62no—
327C2×D3—62no—
328C3×C4—24no—
329C3×C4—24no—
330C3×C4—22no—
331C3×C4—24no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—22no—
335C3×C4—41no—
336C3×C4—42no—
337C3×C4D3×M1614yes—
338C3×C4C2×D3×Q812yes—
339C3×C4D3×#4112yes—
340Dic3—34no—
341Dic3—34no—
342Dic3—62no—
343Dic3—62no—
344Dic3—64no—
345Dic3—64no—
346Dic3—62no—
347Dic3—64no—
348Dic3—121no—
349Dic3—122no—
350C32C2×#44611yescharacteristic, complemented, Sylow
351C23—91no—
352Q8—22no—
353Q8—184no—
354Q8—182no—
355C2×C4—91no—
356C2×C4—91no—
357C2×C4—92no—
358C2×C4—92no—
359C2×C4—94no—
360C2×C4—91no—
361C2×C4—92no—
362C2×C4—92no—
363C2×C4—184no—
364C2×C4—182no—
365C2×C4—184no—
366C2×C4C2×#62411yescharacteristic
367C2×C4C2×#62412yes—
368C2×C4C2×#62412yes—
369C2×C4C2×#62411yescharacteristic
370C2×C4C22×D3211yescharacteristic
371C8—34no—
372C8—62no—
373C8—64no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3C4×D3×Q812yes—
378C2×C3C2×D3×M1612yes—
379C2×C3D3×#13112yes—
380D3—38no—
381D3—64no—
382C22—92no—
383C22—92no—
384C22—92no—
385C22C22×#62411yescharacteristic
386C4—21no—
387C4—22no—
388C4—22no—
389C4—92no—
390C4—92no—
391C4—181no—
392C4—182no—
393C4—182no—
394C4#6381812yes—
395C4D32×Q811yescharacteristic
396C4#6431911yescharacteristic
397C3—21no—
398C3D3×#44612yescomplemented
399C2—94no—
400C2C2×#6381811yescharacteristic
401C2Q8×#62411yescharacteristic
402C2#1059544211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4×Q8C22
prime radicalC22×C3⋊D3C22×C4
cosocleC2×C32×C4C24
hypercenterC4×Q8D32
hypocenterC32C2×#446
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5024C2semidirect
7. #10590296C2semidirect
8. #10590255C2semidirect
35. #5024D3semidirect
73. #3710Q8semidirect
137. C3×C3⋊C8C2×Q8semidirect
285. C3⋊C8D3×Q8semidirect
289. C3⋊D3#446semidirect
350. C32C2×#446semidirect
398. C3D3×#446semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
C3×#50242
#105903312
#105903222
C4×#37102
#105902962
#105902552
D3×#4463