Finite Group Databasebeta

← #11790565

Subgroups — #11790565

Order 1152.

861 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×C4×#625C211yesmaximal, characteristic
2C2×#63641C211yesmaximal, characteristic, complemented
3C2×C3×(C2×D3)⋊C8C212yesmaximal, complemented
4C2×(C2×D3)⋊(C3⋊C8)C212yesmaximal, complemented
5C2×#63553C211yesmaximal, characteristic, complemented
6#69916—32nomaximal
7C22×C3×C4×D3C2212yes—
8C22×#625C411yescharacteristic
9C22×C32×C8C2211yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C22×C3⋊(C3⋊C8)C2211yescharacteristic
12C22×C3×C3⋊C8C2212yes—
13C2×#3724C411yescharacteristic
14C2×(C2×D3)⋊Dic3C412yes—
15C4×#625—22no—
16C4×#625—22no—
17#63641—22no—
18C3×(C2×D3)⋊C8—24no—
19(C2×D3)⋊(C3⋊C8)—24no—
20#63553—22no—
21C2×C4×#67—32no—
22C2×C3×C22⋊C8—32no—
23C2×#830—32no—
24C2×(C2×D3)⋊C8—32no—
25C2×(C2×D3)⋊C8D312yescomplemented
26C2×Dic3⋊C8—32no—
27C2×Dic3⋊C8—61no—
28C2×C8×Dic3—32no—
29C23×C3×D3C2×C412yes—
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3C2×C411yescharacteristic
32C22×C3⋊Dic3C2×C411yescharacteristic
33C22×C3×Dic3C2×C412yes—
34C2×C3×C4×D3—22no—
35C2×C3×C4×D3—22no—
36C2×C3×C4×D3—22no—
37C2×C3×C4×D3—22no—
38C2×C3×C4×D3—22no—
39C2×C3×C4×D3—22no—
40C2×#625—22no—
41C2×#625—22no—
42C2×#625C814yescomplemented
43C2×C32×C8—21no—
44C2×C32×C8—22no—
45C4×C3⋊Dic3D412yes—
46C4×C3⋊Dic3D412yes—
47C2×C3⋊(C3⋊C8)—21no—
48C2×C3⋊(C3⋊C8)—22no—
49C2×C3×C3⋊C8—22no—
50C2×C3×C3⋊C8—22no—
51C2×C3×C3⋊C8D414yescomplemented
52#3724—22no—
53(C2×D3)⋊Dic3—24no—
54#1954—91noSylow
55C23×C3×C4—32no—
56C22×#67—32no—
57C22×C4×D3C2×D312yes—
58C22×C3×C8—21no—
59C22×C3×C8—32no—
60C22×C3×C8C2×D312yes—
61C2×#217—32no—
62C4×#67—64no—
63C4×#67—64no—
64C2×(C2×D3)⋊C4—32no—
65C2×Dic3⋊C4—32no—
66C2×C4×Dic3—32no—
67C2×C4×Dic3—61no—
68C22×C3⋊C8—32no—
69C22×C3⋊C8—61no—
70C22×C3⋊C8C2×D312yes—
71C3×C22⋊C8—64no—
72#830—64no—
73(C2×D3)⋊C8—24no—
74(C2×D3)⋊C8—64no—
75Dic3⋊C8—64no—
76Dic3⋊C8—64no—
77C8×Dic3—64no—
78C23×C32C22×C411yescharacteristic
79C22×C3×D3—22no—
80C22×C3×D3—22no—
81C22×C3×D3—22no—
82C22×C3×D3—22no—
83C22×C3×D3—22no—
84C22×C3×D3—22no—
85C22×C3×D3C2×C814yes—
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×D412yes—
89C2×C32×C4#4112yes—
90C2×C3⋊Dic3—22no—
91C2×C3⋊Dic3C22⋊C412yes—
92C2×C3⋊Dic3C22⋊C412yes—
93C2×C3⋊Dic3C2×C812yes—
94C2×C3⋊Dic3M1612yes—
95C2×C3×Dic3—22no—
96C2×C3×Dic3—22no—
97C2×C3×Dic3—22no—
98C3×C4×D3—42no—
99C3×C4×D3—42no—
100C3×C4×D3—42no—
101C3×C4×D3—42no—
102#625—28no—
103C32×C8—41no—
104C3⋊(C3⋊C8)—41no—
105C3×C3⋊C8—24no—
106C2×C4×D4—91no—
107C2×C4⋊C8—91no—
108C2×C22⋊C8—32no—
109C2×C22⋊C8—92no—
110C2×C4×C8—91no—
111C24×C3—32no—
112C23×D3C4×D312yes—
113C22×C3×C4—21no—
114C22×C3×C4—32no—
115C22×C3×C4—62no—
116C22×C3×C4—62no—
117C22×C3×C4—62no—
118C22×C3×C4—62no—
119C22×C3×C4—62no—
120C22×C3×C4—62no—
121C22×C3×C4C22×D312yes—
122C2×#67—38no—
123C2×#67—64no—
124C2×#67—64no—
125C22×Dic3—32no—
126C22×Dic3—32no—
127C22×Dic3—61no—
128C22×Dic3—61no—
129C22×Dic3C4×D312yes—
130C2×C4×D3—22no—
131C2×C4×D3—22no—
132C2×C4×D3—22no—
133C2×C4×D3—22no—
134C2×C4×D3—22no—
135C2×C4×D3—22no—
136C2×C3×C8—22no—
137C2×C3×C8—22no—
138C2×C3×C8—22no—
139C2×C3×C8—22no—
140C2×C3×C8—34no—
141C2×C3×C8—42no—
142C2×C3×C8—62no—
143C2×C3×C8—62no—
144#217—64no—
145(C2×D3)⋊C4—64no—
146Dic3⋊C4—64no—
147C4×Dic3—34no—
148C4×Dic3—34no—
149C4×Dic3—62no—
150C4×Dic3—62no—
151C2×C3⋊C8—22no—
152C2×C3⋊C8—22no—
153C2×C3⋊C8—62no—
154C2×C3⋊C8—62no—
155C2×C3⋊C8—62no—
156C2×C3⋊C8—62no—
157C2×C3⋊C8—122no—
158C2×C3⋊C8#6714yescomplemented
159C22×C32C2×C22⋊C411yescharacteristic
160C22×C32C4×D412yes—
161C22×C32C22×C811yescharacteristic
162C22×C32C2×M1611yescharacteristic
163C22×C32#13112yes—
164C2×C3×D3—24no—
165C2×C3×D3—24no—
166C2×C3×D3—24no—
167C2×C3×D3—42no—
168C2×C3×D3—42no—
169C2×C3×D3—42no—
170C2×C3×D3—42no—
171C32×C4#12112yes—
172C32×C4#12411yescharacteristic
173C32×C4#12711yescharacteristic
174C3⋊Dic3—22no—
175C3⋊Dic3C22⋊C814yescomplemented
176C3×Dic3—42no—
177C22×D4—91no—
178C23×C4—32no—
179C22×C8—32no—
180C22×C8—91no—
181C22×C8D3211yescharacteristic
182C4×D4—182no—
183C4×D4—182no—
184C2×C4⋊C4—91no—
185C2×C22⋊C4—92no—
186C2×C42—91no—
187C4⋊C8—182no—
188C22⋊C8—64no—
189C22⋊C8—184no—
190C4×C8—182no—
191C23×C3—21no—
192C23×C3—34no—
193C23×C3—62no—
194C23×C3—62no—
195C23×C3—62no—
196C23×C3—62no—
197C23×C3—62no—
198C23×C3—62no—
199C23×C3C2×C4×D312yes—
200C22×D3—22no—
201C22×D3—22no—
202C22×D3—22no—
203C22×D3—22no—
204C22×D3—22no—
205C22×D3—22no—
206C22×D3D3×C814yes—
207C2×C3×C4—22no—
208C2×C3×C4—21no—
209C2×C3×C4—22no—
210C2×C3×C4—21no—
211C2×C3×C4—62no—
212C2×C3×C4—62no—
213C2×C3×C4—62no—
214C2×C3×C4—122no—
215C2×C3×C4—122no—
216C2×C3×C4—122no—
217C2×C3×C4—122no—
218C2×C3×C4#23512yes—
219C2×C3×C4D3×D412yes—
220C2×C3×C4D3×D412yes—
221C2×C3×C4D3×D412yes—
222C2×C3×C4#23712yes—
223C2×C3×C4C2×#6712yes—
224#67—616no—
225C2×Dic3—22no—
226C2×Dic3—22no—
227C2×Dic3—22no—
228C2×Dic3—34no—
229C2×Dic3—34no—
230C2×Dic3—34no—
231C2×Dic3—34no—
232C2×Dic3—62no—
233C2×Dic3—62no—
234C2×Dic3—62no—
235C2×Dic3—62no—
236C2×Dic3—62no—
237C2×Dic3—62no—
238C2×Dic3—122no—
239C4×D3—42no—
240C4×D3—42no—
241C4×D3—42no—
242C4×D3—42no—
243C3×C8—42no—
244C3×C8—42no—
245C3×C8—64no—
246C3⋊C8—24no—
247C3⋊C8—122no—
248C3⋊C8—122no—
249C2×C32#39011yescharacteristic
250C2×C32C2×C22⋊C811yescharacteristic
251C2×C32#40811yescharacteristic
252C2×C32C8×D412yes—
253C2×C32#43612yes—
254C3×D3—44no—
255C24—32no—
256C2×D4—94no—
257C2×D4—182no—
258C2×D4—182no—
259C22×C4—32no—
260C22×C4—62no—
261C22×C4—62no—
262C22×C4—62no—
263C22×C4—62no—
264C22×C4—62no—
265C22×C4—62no—
266C22×C4—91no—
267C22×C4—91no—
268C22×C4C2×D3211yescharacteristic
269C2×C8—22no—
270C2×C8—21no—
271C2×C8—34no—
272C2×C8—62no—
273C2×C8—62no—
274C2×C8—182no—
275C2×C8—181no—
276C4⋊C4—182no—
277C22⋊C4—184no—
278C42—92no—
279C42—92no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—22no—
283C22×C3—22no—
284C22×C3—21no—
285C22×C3—64no—
286C22×C3—64no—
287C22×C3—64no—
288C22×C3—122no—
289C22×C3—122no—
290C22×C3—122no—
291C22×C3—122no—
292C22×C3D3×C22⋊C412yes—
293C22×C3#67⋊C412yes—
294C22×C3C2×D3×C812yes—
295C22×C3#90112yes—
296C22×C3D3×M1612yes—
297C22×C3#90712yes—
298C22×C3C4×#6712yes—
299C2×D3—24no—
300C2×D3—24no—
301C2×D3—24no—
302C2×D3—42no—
303C2×D3—42no—
304C2×D3—42no—
305C2×D3—42no—
306C3×C4—22no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—122no—
310C3×C4#88412yes—
311C3×C4#88512yes—
312C3×C4#93912yes—
313C3×C4#94012yes—
314Dic3—38no—
315Dic3—42no—
316Dic3—64no—
317Dic3—64no—
318Dic3—122no—
319C32#195411yescharacteristic, complemented, Sylow
320C23—34no—
321C23—62no—
322C23—62no—
323C23—62no—
324C23—62no—
325C23—62no—
326C23—62no—
327C23C4×D3211yescharacteristic
328D4—188no—
329C2×C4—62no—
330C2×C4—62no—
331C2×C4—62no—
332C2×C4—92no—
333C2×C4—92no—
334C2×C4—92no—
335C2×C4—92no—
336C2×C4—122no—
337C2×C4—122no—
338C2×C4—122no—
339C2×C4—122no—
340C2×C4—182no—
341C2×C4#379512yes—
342C2×C4#380211yescharacteristic
343C2×C4D3×#6712yes—
344C2×C4#381111yescharacteristic
345C8—41no—
346C8—64no—
347C8—361no—
348C2×C3—22no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—22no—
353C2×C3—124no—
354C2×C3D3×C22⋊C812yes—
355C2×C3#67⋊C812yes—
356C2×C3#472712yes—
357C2×C3#472912yes—
358C2×C3#495712yes—
359C2×C3C8×#6712yes—
360C2×C3#512812yes—
361D3—44no—
362C22—64no—
363C22—64no—
364C22—64no—
365C22—122no—
366C22—122no—
367C22—122no—
368C22—122no—
369C22D32×C811yescharacteristic
370C22#6379111yescharacteristic
371C22#6380412yes—
372C22#6387912yes—
373C22#6392111yescharacteristic
374C4—94no—
375C4—122no—
376C4—182no—
377C4#6388512yes—
378C4#6391311yescharacteristic
379C4#6397911yescharacteristic
380C3—21no—
381C3#6991612yescomplemented
382C2—124no—
383C2#1059071712yes—
384C2#1059073512yes—
385C2#1059093511yescharacteristic
386C2#1059095911yescharacteristic
387C2#1059138611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC22×C32C22×C8
FittingC22×C32×C8C22
socleC23×C32C22×C4
prime radicalC22×#625C4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1954
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63641C2semidirect
3. C2×C3×(C2×D3)⋊C8C2semidirect
4. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
5. C2×#63553C2semidirect
25. C2×(C2×D3)⋊C8D3semidirect
42. C2×#625C8semidirect
51. C2×C3×C3⋊C8D4semidirect
158. C2×C3⋊C8#67semidirect
175. C3⋊Dic3C22⋊C8semidirect
319. C32#1954semidirect
381. C3#69916semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6252
C2×#636412
C2×C3×(C2×D3)⋊C82
C2×(C2×D3)⋊(C3⋊C8)2
C2×#635532
#699163