Finite Group Databasebeta

← #11783443

Subgroups — #11783443

Order 1152.

718 conjugacy classes of subgroups.

The subgroup lattice has 389 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64283C211yesmaximal, characteristic
2C2×#64283C211yesmaximal, characteristic
3C3⋊D3×#117C211yesmaximal, characteristic
4#10590156C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×#3792C2212yes—
7C2×#3792C2212yes—
8#64283—21no—
9#64283—21no—
10#64283—21no—
11#64283—21no—
12#64283—21no—
13#64283—21no—
14#64283C412yescomplemented
15#64283C412yescomplemented
16C2×#3788—21no—
17C2×#3788C412yescomplemented
18C2×#3787—21no—
19C2×#3787C412yescomplemented
20C32×#117C411yescharacteristic
21#64135C411yescharacteristic
22#64101—21no—
23C4⋊C4×C3⋊D3—21no—
24C22⋊C4×C3⋊D3C412yes—
25#64086C2212yes—
26#64081—21no—
27C42×C3⋊D3—21no—
28D3×#117—62no—
29C23×C3⋊D3C2×C411yescharacteristic
30C22×C32×C4C2×C411yescharacteristic
31C22×C3⋊Dic3C2311yescharacteristic
32C2×C4×C3⋊D3—22no—
33C2×C4×C3⋊D3C2×C411yescharacteristic
34C2×C4×C3⋊D3C2×C411yescharacteristic
35C2×C4×C3⋊D3C2×C411yescharacteristic
36C2×C4×C3⋊D3C2×C411yescharacteristic
37C2×C4×C3⋊D3D411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C2×C4×C3⋊D3D411yescharacteristic
40C2×C4×C3⋊D3D411yescharacteristic
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3D411yescharacteristic
43C2×C4×C3⋊D3Q811yescharacteristic
44C2×C4×C3⋊D3Q811yescharacteristic
45#3792—22no—
46#3792—22no—
47#3792—22no—
48#3792C2×C414yescomplemented
49C2×#622—22no—
50C2×#622C2×C414yescomplemented
51#3788—22no—
52#3788—22no—
53#3788—22no—
54#3788—22no—
55#3787—22no—
56#3787—22no—
57#3787—22no—
58#3787—22no—
59C32×C4⋊C4—21no—
60C32×C22⋊C4C2×C412yes—
61C32×C42—21no—
62#3757C2×C412yes—
63#3752—22no—
64C4⋊(C3⋊Dic3)—21no—
65#3750—22no—
66C4×C3⋊Dic3—21no—
67C4×C3⋊Dic3—22no—
68C2×#344—91nomaximal, Sylow
69C22×C4×D3—62no—
70C3×#117—22no—
71#926—62no—
72#892—64no—
73D3×C4⋊C4—64no—
74D3×C22⋊C4—64no—
75#877—64no—
76#872—64no—
77C42×D3—64no—
78C23×C32C22×C411yescharacteristic
79C22×C3⋊D3—42no—
80C22×C3⋊D3C4211yescharacteristic
81C22×C3⋊D3C4211yescharacteristic
82C22×C3⋊D3C22⋊C411yescharacteristic
83C22×C3⋊D3C22⋊C411yescharacteristic
84C22×C3⋊D3C4⋊C411yescharacteristic
85C22×C3⋊D3C4⋊C411yescharacteristic
86C2×C32×C4—22no—
87C2×C32×C4C4211yescharacteristic
88C2×C32×C4C4211yescharacteristic
89C2×C32×C4C22⋊C411yescharacteristic
90C2×C32×C4C22⋊C411yescharacteristic
91C2×C32×C4C4⋊C411yescharacteristic
92C2×C32×C4C4⋊C411yescharacteristic
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3C22×C411yescharacteristic
95C2×C3⋊Dic3C22×C411yescharacteristic
96C2×C3⋊Dic3C2×D411yescharacteristic
97C2×C3⋊Dic3C2×D411yescharacteristic
98C2×C3⋊Dic3C2×D411yescharacteristic
99C2×C3⋊Dic3C2×Q811yescharacteristic
100C4×C3⋊D3—44no—
101C4×C3⋊D3C22⋊C411yescharacteristic
102C4×C3⋊D3C22⋊C411yescharacteristic
103C4×C3⋊D3C22⋊C411yescharacteristic
104C4×C3⋊D3C22⋊C411yescharacteristic
105C4×C3⋊D3C22⋊C411yescharacteristic
106C4×C3⋊D3C22⋊C411yescharacteristic
107C4×C3⋊D3C22⋊C411yescharacteristic
108C4×C3⋊D3C22⋊C411yescharacteristic
109C4×C3⋊D3C4⋊C411yescharacteristic
110C4×C3⋊D3C4⋊C411yescharacteristic
111C4×C3⋊D3C4⋊C411yescharacteristic
112C4×C3⋊D3C4⋊C411yescharacteristic
113C4×C3⋊D3C4⋊C411yescharacteristic
114C4×C3⋊D3C4⋊C411yescharacteristic
115C4×C3⋊D3C4⋊C411yescharacteristic
116C4×C3⋊D3C4⋊C411yescharacteristic
117#622—24no—
118#622—24no—
119C22×M16—91no—
120C22×M16—91no—
121C2×#117—91no—
122#344—94no—
123C23×D3—62no—
124C22×C3×C4—22no—
125C22×Dic3—62no—
126C2×C4×D3—62no—
127C2×C4×D3—62no—
128C2×C4×D3—62no—
129C2×C4×D3—62no—
130C2×C4×D3—62no—
131C2×C4×D3—62no—
132C2×C4×D3—62no—
133C2×C4×D3—62no—
134C2×C4×D3—62no—
135C2×C4×D3—62no—
136C2×C4×D3—62no—
137C2×C4×D3—62no—
138C2×C4×D3—68no—
139C3×C4⋊C4—24no—
140C3×C22⋊C4—24no—
141C3×C42—24no—
142#217—64no—
143(C2×D3)⋊C4—68no—
144C4⋊Dic3—64no—
145Dic3⋊C4—68no—
146C4×Dic3—64no—
147C4×Dic3—68no—
148C22×C32—41no—
149C22×C32C2×C4211yescharacteristic
150C22×C32C2×C22⋊C411yescharacteristic
151C22×C32C2×C4⋊C411yescharacteristic
152C2×C3⋊D3—22no—
153C2×C3⋊D3—22no—
154C2×C3⋊D3—22no—
155C2×C3⋊D3—41no—
156C2×C3⋊D3—41no—
157C2×C3⋊D3—41no—
158C2×C3⋊D3#9511yescharacteristic
159C2×C3⋊D3#9511yescharacteristic
160C2×C3⋊D3#9511yescharacteristic
161C2×C3⋊D3#9511yescharacteristic
162C32×C4—42no—
163C32×C4#9511yescharacteristic
164C32×C4#9511yescharacteristic
165C32×C4#9511yescharacteristic
166C32×C4#9511yescharacteristic
167C3⋊Dic3—42no—
168C3⋊Dic3C2×C22⋊C411yescharacteristic
169C3⋊Dic3C2×C22⋊C411yescharacteristic
170C3⋊Dic3C2×C4⋊C411yescharacteristic
171C3⋊Dic3C2×C4⋊C411yescharacteristic
172C23×C4—91no—
173C2×M16—92no—
174C2×M16—92no—
175C2×M16—92no—
176C2×M16—92no—
177C2×M16—92no—
178C2×M16—181no—
179C2×M16—181no—
180C2×M16—181no—
181C2×M16—181no—
182C2×M16—181no—
183C2×M16—181no—
184C2×M16—181no—
185C22×C8—92no—
186C22×C8—181no—
187#117—91no—
188#117—92no—
189#117—181no—
190#117—181no—
191#117#15711yescharacteristic
192C2×C4⋊C4—181no—
193C2×C22⋊C4—92no—
194C2×C42—181no—
195C23×C3—22no—
196C22×D3—62no—
197C22×D3—62no—
198C22×D3—62no—
199C22×D3—62no—
200C22×D3—62no—
201C22×D3—62no—
202C22×D3—128no—
203C2×C3×C4—28no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×Dic3—62no—
211C2×Dic3—62no—
212C2×Dic3—62no—
213C2×Dic3—62no—
214C2×Dic3—62no—
215C2×Dic3—62no—
216C2×Dic3—68no—
217C4×D3—62no—
218C4×D3—62no—
219C4×D3—62no—
220C4×D3—62no—
221C4×D3—62no—
222C4×D3—62no—
223C4×D3—62no—
224C4×D3—62no—
225C4×D3—62no—
226C4×D3—62no—
227C4×D3—62no—
228C4×D3—62no—
229C4×D3—62no—
230C4×D3—62no—
231C4×D3—62no—
232C4×D3—62no—
233C4×D3—1216no—
234C2×C32—21no—
235C2×C32—21no—
236C2×C32—21no—
237C2×C32C2×#9511yescharacteristic
238C3⋊D3—21no—
239C3⋊D3—21no—
240C3⋊D3—21no—
241C3⋊D3#34412yescomplemented
242C24—91no—
243C22×C4—91no—
244C22×C4—91no—
245C22×C4—91no—
246C22×C4—91no—
247C22×C4—91no—
248C22×C4—91no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—91no—
252C22×C4—91no—
253C22×C4—91no—
254C22×C4—91no—
255C22×C4—91no—
256C22×C4—182no—
257C22×C4C2×#15711yescharacteristic
258M16—94no—
259M16—182no—
260M16—182no—
261M16—182no—
262M16—182no—
263M16—182no—
264M16—182no—
265M16—182no—
266C2×C8—94no—
267C2×C8—182no—
268C2×C8—182no—
269C2×C8—182no—
270C2×C8—182no—
271C2×C8—182no—
272C4⋊C4—21no—
273C4⋊C4—182no—
274C4⋊C4—181no—
275C22⋊C4—92no—
276C22⋊C4—182no—
277C22⋊C4C2×#15712yes—
278C42—21no—
279C42—182no—
280C42—181no—
281C22×C3—22no—
282C22×C3—22no—
283C22×C3—22no—
284C22×C3—44no—
285C2×D3—62no—
286C2×D3—62no—
287C2×D3—62no—
288C2×D3—62no—
289C2×D3—68no—
290C2×D3—124no—
291C2×D3—124no—
292C2×D3—124no—
293C2×D3—124no—
294C2×D3—124no—
295C3×C4—22no—
296C3×C4—22no—
297C3×C4—22no—
298C3×C4—22no—
299C3×C4—48no—
300Dic3—62no—
301Dic3—62no—
302Dic3—62no—
303Dic3—62no—
304Dic3—128no—
305C32C2×#34411yescharacteristic, complemented, Sylow
306C23—91no—
307C23—91no—
308C23—91no—
309C23—91no—
310C23—91no—
311C23—91no—
312C23—362no—
313C23C22×#15711yescharacteristic
314C2×C4—22no—
315C2×C4—91no—
316C2×C4—91no—
317C2×C4—91no—
318C2×C4—91no—
319C2×C4—91no—
320C2×C4—91no—
321C2×C4—91no—
322C2×C4—91no—
323C2×C4—91no—
324C2×C4—91no—
325C2×C4—91no—
326C2×C4—91no—
327C2×C4—91no—
328C2×C4—91no—
329C2×C4—91no—
330C2×C4—91no—
331C2×C4—91no—
332C2×C4—91no—
333C2×C4—91no—
334C2×C4—91no—
335C2×C4—91no—
336C2×C4—91no—
337C2×C4—182no—
338C2×C4—364no—
339C2×C4C4×#15711yescharacteristic
340C2×C4C4×#15711yescharacteristic
341C2×C4C4⋊#15711yescharacteristic
342C2×C4C4⋊#15711yescharacteristic
343C2×C4C22⋊#15711yescharacteristic
344C2×C4C22⋊#15711yescharacteristic
345C8—184no—
346C8—184no—
347C2×C3—24no—
348C2×C3—22no—
349C2×C3—42no—
350C2×C3—42no—
351D3—64no—
352D3—64no—
353D3—122no—
354D3—122no—
355C22—41no—
356C22—91no—
357C22—91no—
358C22—91no—
359C22—91no—
360C22—182no—
361C22—182no—
362C22—182no—
363C22—361no—
364C22—361no—
365C22—361no—
366C22C2×C4×#15711yescharacteristic
367C22C2×C4⋊#15711yescharacteristic
368C22C2×C22⋊#15711yescharacteristic
369C4—42no—
370C4—91no—
371C4—91no—
372C4—91no—
373C4—91no—
374C4—362no—
375C4#6378111yescharacteristic
376C4#6378111yescharacteristic
377C4#6378111yescharacteristic
378C4#6378111yescharacteristic
379C3—22no—
380C2—21no—
381C2—21no—
382C2—21no—
383C2—92no—
384C2—181no—
385C2—181no—
386C2—181no—
387C2C2×#6378111yescharacteristic
subgroupG/H
centerC4#63781
commutatorC22×C32C2×C42
FrattiniC23C22×#157
FittingC32×#117C4
socleC2×C32C2×#95
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C3⋊Dic3C23
hypercenter#117#157
hypocenterC32C2×#344
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #10590156C2semidirect
14. #64283C4semidirect
15. #64283C4semidirect
17. C2×#3788C4semidirect
19. C2×#3787C4semidirect
48. #3792C2×C4semidirect
50. C2×#622C2×C4semidirect
241. C3⋊D3#344semidirect
305. C32C2×#344semidirect

Maximal subgroups

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

subgroupindex
C2×#642832
C3⋊D3×#1172
#105901562
C2×#3449