Finite Group Databasebeta

← #11858745

Subgroups — #11858745

Order 1152.

986 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C42×C3⋊D3C211yesmaximal, characteristic
2#10593806C212yesmaximal, complemented
3#10593804C212yesmaximal, complemented
4#10593800C212yesmaximal
5#10593731C212yesmaximal, complemented
6#10593730C212yesmaximal, complemented
7#10593726C212yesmaximal, complemented
8#10593723C212yesmaximal, complemented
9C22×C4×C3⋊D3C411yescharacteristic
10C22×C4×C3⋊D3C411yescharacteristic
11C22×C4×C3⋊D3C2211yescharacteristic
12C2×#3787C2214yes—
13C2×C32×C42C411yescharacteristic
14C2×C4×C3⋊Dic3C411yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C42×C3⋊D3C411yescharacteristic
18C42×C3⋊D3C411yescharacteristic
19C42×C3⋊D3C411yescharacteristic
20C42×C3⋊D3C411yescharacteristic
21C42×C3⋊D3C2211yescharacteristic
22C42×C3⋊D3C2211yescharacteristic
23C42×C3⋊D3C2211yescharacteristic
24C42×C3⋊D3C2211yescharacteristic
25C22⋊#622C2214yes—
26#63779C2214yescomplemented
27#63778C2214yes—
28#63777C2214yescomplemented
29#63777C2214yescomplemented
30C4⋊#622C2214yescomplemented
31C2×C42×D3—62no—
32C23×C3⋊D3C2×C411yescharacteristic
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2×C411yescharacteristic
36C22×C3⋊Dic3C2×C411yescharacteristic
37C22×C3⋊Dic3C2×C411yescharacteristic
38C22×C3⋊Dic3C2311yescharacteristic
39C2×C4×C3⋊D3—24no—
40C2×C4×C3⋊D3—24no—
41C2×C4×C3⋊D3—24no—
42C2×C4×C3⋊D3C2×C411yescharacteristic
43C2×C4×C3⋊D3C2×C411yescharacteristic
44C2×C4×C3⋊D3C2×C411yescharacteristic
45C2×C4×C3⋊D3C2×C411yescharacteristic
46C2×C4×C3⋊D3C2×C411yescharacteristic
47C2×C4×C3⋊D3C2×C411yescharacteristic
48C2×C4×C3⋊D3C2×C411yescharacteristic
49C2×C4×C3⋊D3C2×C411yescharacteristic
50C2×C4×C3⋊D3C2×C411yescharacteristic
51C2×C4×C3⋊D3C2×C411yescharacteristic
52C2×C4×C3⋊D3C2311yescharacteristic
53C2×C4×C3⋊D3C2311yescharacteristic
54C2×#622C2318yes—
55#3787—28no—
56C32×C42C2×C411yescharacteristic
57C32×C42C2×C411yescharacteristic
58C32×C42C2×C411yescharacteristic
59C32×C42C2×C411yescharacteristic
60C4×C3⋊Dic3C2×C411yescharacteristic
61C4×C3⋊Dic3C2×C411yescharacteristic
62C4×C3⋊Dic3C2×C411yescharacteristic
63C4×C3⋊Dic3C2×C411yescharacteristic
64C4×C3⋊Dic3C2×C411yescharacteristic
65C4×C3⋊Dic3C2×C411yescharacteristic
66C4×C3⋊Dic3C2×C411yescharacteristic
67C4×C3⋊Dic3C2×C411yescharacteristic
68C4×C3⋊Dic3C2311yescharacteristic
69C4×C3⋊Dic3C2311yescharacteristic
70C4×C3⋊Dic3C2311yescharacteristic
71C4×C3⋊Dic3C2311yescharacteristic
72C2×#432—91nomaximal, Sylow
73C22×C4×D3—62no—
74C22×C4×D3—62no—
75C22×C4×D3—62no—
76C2×C3×C42—22no—
77C2×C4×Dic3—62no—
78C2×C4×Dic3—62no—
79C2×C4×Dic3—62no—
80C42×D3—62no—
81C42×D3—62no—
82C42×D3—62no—
83C42×D3—62no—
84C42×D3—62no—
85C42×D3—62no—
86C42×D3—62no—
87C42×D3—62no—
88C23×C32C22×C411yescharacteristic
89C22×C3⋊D3—22no—
90C22×C3⋊D3—22no—
91C22×C3⋊D3M1614yes—
92C22×C3⋊D3C22×C411yescharacteristic
93C22×C3⋊D3C22×C411yescharacteristic
94C2×C32×C4—22no—
95C2×C32×C4—22no—
96C2×C32×C4—22no—
97C2×C32×C4C22×C411yescharacteristic
98C2×C32×C4C22×C411yescharacteristic
99C2×C32×C4C22×C411yescharacteristic
100C2×C32×C4C22×C411yescharacteristic
101C2×C32×C4C22×C411yescharacteristic
102C2×C32×C4C22×C411yescharacteristic
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—22no—
106C2×C3⋊Dic3C22×C411yescharacteristic
107C2×C3⋊Dic3C22×C411yescharacteristic
108C2×C3⋊Dic3C22×C411yescharacteristic
109C2×C3⋊Dic3C22×C411yescharacteristic
110C2×C3⋊Dic3C22×C411yescharacteristic
111C2×C3⋊Dic3C2411yescharacteristic
112C4×C3⋊D3—22no—
113C4×C3⋊D3—22no—
114C4×C3⋊D3—22no—
115C4×C3⋊D3—22no—
116C4×C3⋊D3—22no—
117C4×C3⋊D3—22no—
118C4×C3⋊D3—22no—
119C4×C3⋊D3—22no—
120C4×C3⋊D3—22no—
121C4×C3⋊D3—22no—
122C4×C3⋊D3M1614yes—
123C4×C3⋊D3#4114yes—
124#622—28no—
125C22×C42—91no—
126#432—92no—
127#432—92no—
128#432—92no—
129#432—92no—
130C2×C4⋊C8—92no—
131C2×C22⋊C8—92no—
132C2×#97—92no—
133C23×D3—62no—
134C22×C3×C4—22no—
135C22×C3×C4—22no—
136C22×C3×C4—22no—
137C22×Dic3—62no—
138C22×Dic3—62no—
139C22×Dic3—62no—
140C2×C4×D3—62no—
141C2×C4×D3—62no—
142C2×C4×D3—62no—
143C2×C4×D3—62no—
144C2×C4×D3—62no—
145C2×C4×D3—62no—
146C2×C4×D3—62no—
147C2×C4×D3—62no—
148C2×C4×D3—62no—
149C2×C4×D3—62no—
150C2×C4×D3—62no—
151C2×C4×D3—62no—
152C2×C4×D3—616no—
153C2×C4×D3—616no—
154C2×C4×D3—616no—
155C3×C42—22no—
156C3×C42—22no—
157C3×C42—22no—
158C3×C42—22no—
159C4×Dic3—62no—
160C4×Dic3—62no—
161C4×Dic3—62no—
162C4×Dic3—62no—
163C4×Dic3—62no—
164C4×Dic3—62no—
165C4×Dic3—62no—
166C4×Dic3—62no—
167C4×Dic3—62no—
168C4×Dic3—62no—
169C4×Dic3—62no—
170C4×Dic3—62no—
171C22×C32—21no—
172C22×C32—21no—
173C22×C32C2×M1612yes—
174C22×C32C23×C411yescharacteristic
175C2×C3⋊D3—21no—
176C2×C3⋊D3—21no—
177C2×C3⋊D3—28no—
178C2×C3⋊D3#11712yes—
179C2×C3⋊D3C2×M1612yes—
180C2×C3⋊D3C2×M1612yes—
181C2×C3⋊D3C2×M1612yes—
182C32×C4—21no—
183C32×C4—21no—
184C32×C4—21no—
185C32×C4—21no—
186C32×C4#11712yes—
187C32×C4C2×M1612yes—
188C3⋊Dic3—21no—
189C3⋊Dic3—21no—
190C3⋊Dic3—21no—
191C3⋊Dic3—21no—
192C3⋊Dic3C2×M1612yes—
193C3⋊Dic3C2×#4112yes—
194C23×C4—91no—
195C23×C4—91no—
196C23×C4—91no—
197C22×C8—94no—
198C2×C42—91no—
199C2×C42—91no—
200C2×C42—91no—
201C2×C42—91no—
202C2×C42—91no—
203C2×C42—91no—
204C2×C42—91no—
205C2×C42—91no—
206C2×C42—91no—
207C2×C42—91no—
208C2×C42—91no—
209C2×C42#15711yescharacteristic
210C4⋊C8—94no—
211C4⋊C8—94no—
212C22⋊C8—94no—
213C22⋊C8—94no—
214#97—94no—
215#97—94no—
216C23×C3—22no—
217C22×D3—68no—
218C22×D3—62no—
219C22×D3—62no—
220C22×D3—68no—
221C22×D3—68no—
222C2×C3×C4—28no—
223C2×C3×C4—28no—
224C2×C3×C4—28no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—22no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×Dic3—62no—
232C2×Dic3—62no—
233C2×Dic3—62no—
234C2×Dic3—62no—
235C2×Dic3—62no—
236C2×Dic3—62no—
237C2×Dic3—68no—
238C2×Dic3—68no—
239C2×Dic3—68no—
240C4×D3—68no—
241C4×D3—68no—
242C4×D3—68no—
243C4×D3—68no—
244C4×D3—68no—
245C4×D3—68no—
246C4×D3—68no—
247C4×D3—68no—
248C4×D3—68no—
249C4×D3—68no—
250C4×D3—68no—
251C4×D3—68no—
252C2×C32—22no—
253C2×C32C2×#11711yescharacteristic
254C2×C32C22×M1611yescharacteristic
255C2×C32C22×M1611yescharacteristic
256C3⋊D3—22no—
257C3⋊D3#43214yescomplemented
258C24—91no—
259C22×C4—91no—
260C22×C4—91no—
261C22×C4—91no—
262C22×C4—91no—
263C22×C4—91no—
264C22×C4—91no—
265C22×C4—91no—
266C22×C4—91no—
267C22×C4—91no—
268C22×C4—91no—
269C22×C4—91no—
270C22×C4—91no—
271C22×C4—91no—
272C22×C4—91no—
273C22×C4—91no—
274C22×C4—184no—
275C22×C4—184no—
276C22×C4—184no—
277C22×C4C2×#15711yescharacteristic
278C22×C4C2×#15711yescharacteristic
279C22×C4C2×#15711yescharacteristic
280C2×C8—98no—
281C2×C8—188no—
282C42—91no—
283C42—91no—
284C42—91no—
285C42—91no—
286C42—91no—
287C42—91no—
288C42—91no—
289C42—91no—
290C42—91no—
291C42—91no—
292C42—91no—
293C42—91no—
294C42C2×#15711yescharacteristic
295C42C2×#15711yescharacteristic
296C42C2×#15711yescharacteristic
297C42C2×#15711yescharacteristic
298C22×C3—24no—
299C22×C3—24no—
300C22×C3—24no—
301C22×C3—22no—
302C2×D3—64no—
303C2×D3—64no—
304C2×D3—64no—
305C2×D3—64no—
306C2×D3—64no—
307C2×D3—64no—
308C2×D3—632no—
309C3×C4—24no—
310C3×C4—24no—
311C3×C4—24no—
312C3×C4—24no—
313C3×C4—24no—
314C3×C4—24no—
315Dic3—64no—
316Dic3—64no—
317Dic3—64no—
318Dic3—64no—
319Dic3—64no—
320Dic3—64no—
321C32C2×#43211yescharacteristic, complemented, Sylow
322C23—91no—
323C23—94no—
324C23—91no—
325C23—182no—
326C23—182no—
327C23C22×#15711yescharacteristic
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—91no—
332C2×C4—91no—
333C2×C4—94no—
334C2×C4—94no—
335C2×C4—91no—
336C2×C4—91no—
337C2×C4—91no—
338C2×C4—91no—
339C2×C4—182no—
340C2×C4—182no—
341C2×C4—182no—
342C2×C4—182no—
343C2×C4—182no—
344C2×C4—182no—
345C2×C4—182no—
346C2×C4—182no—
347C2×C4—182no—
348C2×C4—182no—
349C2×C4—182no—
350C2×C4—182no—
351C2×C4—182no—
352C2×C4C22×#15711yescharacteristic
353C2×C4C22×#15711yescharacteristic
354C2×C4C22×#15711yescharacteristic
355C2×C4C22×#15711yescharacteristic
356C2×C4C22×#15711yescharacteristic
357C2×C4C22×#15711yescharacteristic
358C8—188no—
359C2×C3—28no—
360C2×C3—22no—
361C2×C3—22no—
362C2×C3—22no—
363D3—68no—
364D3—68no—
365C22—21no—
366C22—21no—
367C22—92no—
368C22—92no—
369C22—92no—
370C22—92no—
371C22—188no—
372C22—181no—
373C22—181no—
374C22#6428312yes—
375C22C23×#15711yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—92no—
381C4—92no—
382C4—181no—
383C4—181no—
384C4—181no—
385C4—181no—
386C4#6428312yes—
387C4#6428612yes—
388C3—22no—
389C2—22no—
390C2—94no—
391C2—182no—
392C2C2×#6428311yescharacteristic
393C2C2×#6428311yescharacteristic
394C2C2×#6428611yescharacteristic
subgroupG/H
centerC2×C4C22×#157
commutator, socleC22×C32C23×C4
FrattiniC22C23×#157
FittingC2×C32×C42C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C3⋊Dic3C24
hypercenterC2×C42#157
hypocenterC32C2×#432
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10593806C2semidirect
3. #10593804C2semidirect
5. #10593731C2semidirect
6. #10593730C2semidirect
7. #10593726C2semidirect
8. #10593723C2semidirect
26. #63779C22semidirect
28. #63777C22semidirect
29. #63777C22semidirect
30. C4⋊#622C22semidirect
257. C3⋊D3#432semidirect
321. C32C2×#432semidirect

Maximal subgroups

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

subgroupindex
C2×C42×C3⋊D32
#105938062
#105938042
#105938002
#105937312
#105937302
#105937262
#105937232
C2×#4329