Finite Group Databasebeta

← #11790567

Subgroups — #11790567

Order 1152.

873 conjugacy classes of subgroups.

The subgroup lattice has 419 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#625C211yesmaximal, characteristic
2C2×C8×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×(C2×D3)⋊C8C212yesmaximal, complemented
4C2×#63572C211yesmaximal, characteristic, complemented
5C2×(C2×D3)⋊(C3⋊C8)C212yesmaximal, 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—
17C8×C3⋊Dic3—22no—
18C3×(C2×D3)⋊C8—24no—
19#63572—22no—
20(C2×D3)⋊(C3⋊C8)—24no—
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×C8×Dic3—32no—
28C2×C8×Dic3—61no—
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—21no—
45C2×C32×C8D412yescomplemented
46C4×C3⋊Dic3D412yes—
47C4×C3⋊Dic3D412yes—
48C2×C3⋊(C3⋊C8)—21no—
49C2×C3⋊(C3⋊C8)—21no—
50C2×C3⋊(C3⋊C8)D412yescomplemented
51C2×C3×C3⋊C8—22no—
52C2×C3×C3⋊C8—22no—
53C2×C3×C3⋊C8—22no—
54#3724—22no—
55(C2×D3)⋊Dic3—24no—
56#1954—91noSylow
57C23×C3×C4—32no—
58C22×#67—32no—
59C22×C4×D3C2×D312yes—
60C22×C3×C8—21no—
61C22×C3×C8—32no—
62C22×C3×C8C2×D312yes—
63C2×#217—32no—
64C4×#67—64no—
65C4×#67—64no—
66C2×(C2×D3)⋊C4—32no—
67C2×Dic3⋊C4—32no—
68C2×C4×Dic3—32no—
69C2×C4×Dic3—61no—
70C22×C3⋊C8—32no—
71C22×C3⋊C8—61no—
72C22×C3⋊C8C2×D312yes—
73C3×C22⋊C8—64no—
74#830—64no—
75(C2×D3)⋊C8—24no—
76(C2×D3)⋊C8—64no—
77Dic3⋊C8—64no—
78C8×Dic3—64no—
79C8×Dic3—64no—
80C23×C32C22×C411yescharacteristic
81C22×C3×D3—22no—
82C22×C3×D3—22no—
83C22×C3×D3—22no—
84C22×C3×D3—22no—
85C22×C3×D3—22no—
86C22×C3×D3—22no—
87C22×C3×D3C2×C814yes—
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×D411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4#4111yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C3⋊Dic3—21no—
95C2×C3⋊Dic3—21no—
96C2×C3⋊Dic3C22⋊C412yes—
97C2×C3⋊Dic3C22⋊C412yes—
98C2×C3⋊Dic3C2×C812yes—
99C2×C3⋊Dic3M1612yes—
100C2×C3×Dic3—22no—
101C2×C3×Dic3—22no—
102C2×C3×Dic3—22no—
103C3×C4×D3—42no—
104C3×C4×D3—42no—
105C3×C4×D3—42no—
106C3×C4×D3—42no—
107#625—28no—
108C32×C8—22no—
109C3⋊(C3⋊C8)—22no—
110C3×C3⋊C8—42no—
111C2×C4×D4—91no—
112C2×C4⋊C8—91no—
113C2×C22⋊C8—32no—
114C2×C22⋊C8—92no—
115C2×C4×C8—91no—
116C24×C3—32no—
117C23×D3C4×D312yes—
118C22×C3×C4—21no—
119C22×C3×C4—32no—
120C22×C3×C4—62no—
121C22×C3×C4—62no—
122C22×C3×C4—62no—
123C22×C3×C4—62no—
124C22×C3×C4—62no—
125C22×C3×C4—62no—
126C22×C3×C4C22×D312yes—
127C2×#67—38no—
128C2×#67—64no—
129C2×#67—64no—
130C22×Dic3—32no—
131C22×Dic3—32no—
132C22×Dic3—61no—
133C22×Dic3—61no—
134C22×Dic3C4×D312yes—
135C2×C4×D3—22no—
136C2×C4×D3—22no—
137C2×C4×D3—22no—
138C2×C4×D3—22no—
139C2×C4×D3—22no—
140C2×C4×D3—22no—
141C2×C3×C8—22no—
142C2×C3×C8—22no—
143C2×C3×C8—22no—
144C2×C3×C8—22no—
145C2×C3×C8—22no—
146C2×C3×C8—62no—
147C2×C3×C8—62no—
148C2×C3×C8—62no—
149C2×C3×C8#6714yescomplemented
150#217—64no—
151(C2×D3)⋊C4—64no—
152Dic3⋊C4—64no—
153C4×Dic3—34no—
154C4×Dic3—34no—
155C4×Dic3—62no—
156C4×Dic3—62no—
157C2×C3⋊C8—22no—
158C2×C3⋊C8—22no—
159C2×C3⋊C8—22no—
160C2×C3⋊C8—34no—
161C2×C3⋊C8—62no—
162C2×C3⋊C8—62no—
163C2×C3⋊C8—62no—
164C2×C3⋊C8—62no—
165C2×C3⋊C8—62no—
166C22×C32C2×C22⋊C411yescharacteristic
167C22×C32C4×D411yescharacteristic
168C22×C32C4×D411yescharacteristic
169C22×C32C22×C811yescharacteristic
170C22×C32C2×M1611yescharacteristic
171C22×C32#13111yescharacteristic
172C22×C32#13111yescharacteristic
173C2×C3×D3—24no—
174C2×C3×D3—24no—
175C2×C3×D3—24no—
176C2×C3×D3—42no—
177C2×C3×D3—42no—
178C2×C3×D3—42no—
179C2×C3×D3—42no—
180C32×C4#12111yescharacteristic
181C32×C4#12111yescharacteristic
182C32×C4#12411yescharacteristic
183C32×C4#12711yescharacteristic
184C3⋊Dic3—22no—
185C3⋊Dic3C22⋊C814yescomplemented
186C3×Dic3—42no—
187C22×D4—91no—
188C23×C4—32no—
189C22×C8—32no—
190C22×C8—91no—
191C22×C8D3211yescharacteristic
192C4×D4—182no—
193C4×D4—182no—
194C2×C4⋊C4—91no—
195C2×C22⋊C4—92no—
196C2×C42—91no—
197C4⋊C8—182no—
198C22⋊C8—64no—
199C22⋊C8—184no—
200C4×C8—182no—
201C23×C3—21no—
202C23×C3—34no—
203C23×C3—62no—
204C23×C3—62no—
205C23×C3—62no—
206C23×C3—62no—
207C23×C3—62no—
208C23×C3—62no—
209C23×C3C2×C4×D312yes—
210C22×D3—22no—
211C22×D3—22no—
212C22×D3—22no—
213C22×D3—22no—
214C22×D3—22no—
215C22×D3—22no—
216C22×D3D3×C814yes—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—62no—
224C2×C3×C4—62no—
225C2×C3×C4—62no—
226C2×C3×C4—122no—
227C2×C3×C4—122no—
228C2×C3×C4—122no—
229C2×C3×C4—122no—
230C2×C3×C4#23512yes—
231C2×C3×C4D3×D412yes—
232C2×C3×C4D3×D412yes—
233C2×C3×C4D3×D412yes—
234C2×C3×C4#23712yes—
235C2×C3×C4C2×#6712yes—
236#67—616no—
237C2×Dic3—22no—
238C2×Dic3—22no—
239C2×Dic3—22no—
240C2×Dic3—34no—
241C2×Dic3—34no—
242C2×Dic3—34no—
243C2×Dic3—34no—
244C2×Dic3—62no—
245C2×Dic3—62no—
246C2×Dic3—62no—
247C2×Dic3—62no—
248C2×Dic3—62no—
249C2×Dic3—62no—
250C2×Dic3—62no—
251C2×Dic3—62no—
252C4×D3—42no—
253C4×D3—42no—
254C4×D3—42no—
255C4×D3—42no—
256C3×C8—24no—
257C3×C8—24no—
258C3×C8—122no—
259C3⋊C8—42no—
260C3⋊C8—64no—
261C3⋊C8—64no—
262C2×C32#39011yescharacteristic
263C2×C32C2×C22⋊C811yescharacteristic
264C2×C32#40811yescharacteristic
265C2×C32C8×D411yescharacteristic
266C2×C32C8×D411yescharacteristic
267C2×C32#43611yescharacteristic
268C2×C32#43611yescharacteristic
269C3×D3—44no—
270C24—32no—
271C2×D4—94no—
272C2×D4—182no—
273C2×D4—182no—
274C22×C4—32no—
275C22×C4—62no—
276C22×C4—62no—
277C22×C4—62no—
278C22×C4—62no—
279C22×C4—62no—
280C22×C4—62no—
281C22×C4—91no—
282C22×C4—91no—
283C22×C4C2×D3211yescharacteristic
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—62no—
287C2×C8—62no—
288C2×C8—62no—
289C2×C8—92no—
290C2×C8—181no—
291C2×C8—181no—
292C2×C8#62512yescomplemented
293C4⋊C4—182no—
294C22⋊C4—184no—
295C42—92no—
296C42—92no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—64no—
305C22×C3—64no—
306C22×C3—64no—
307C22×C3—122no—
308C22×C3—122no—
309C22×C3—122no—
310C22×C3—122no—
311C22×C3D3×C22⋊C412yes—
312C22×C3#67⋊C412yes—
313C22×C3C2×D3×C812yes—
314C22×C3#90112yes—
315C22×C3D3×M1612yes—
316C22×C3#90712yes—
317C22×C3C4×#6712yes—
318C2×D3—24no—
319C2×D3—24no—
320C2×D3—24no—
321C2×D3—42no—
322C2×D3—42no—
323C2×D3—42no—
324C2×D3—42no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—122no—
330C3×C4#88412yes—
331C3×C4#88512yes—
332C3×C4#93912yes—
333C3×C4#94012yes—
334Dic3—38no—
335Dic3—42no—
336Dic3—64no—
337Dic3—64no—
338Dic3—64no—
339C32#195411yescharacteristic, complemented, Sylow
340C23—34no—
341C23—62no—
342C23—62no—
343C23—62no—
344C23—62no—
345C23—62no—
346C23—62no—
347C23C4×D3211yescharacteristic
348D4—188no—
349C2×C4—62no—
350C2×C4—62no—
351C2×C4—62no—
352C2×C4—92no—
353C2×C4—92no—
354C2×C4—92no—
355C2×C4—92no—
356C2×C4—122no—
357C2×C4—122no—
358C2×C4—122no—
359C2×C4—122no—
360C2×C4—181no—
361C2×C4—181no—
362C2×C4#379811yescharacteristic
363C2×C4#380211yescharacteristic
364C2×C4#380211yescharacteristic
365C2×C4#380511yescharacteristic
366C2×C4C2×#62511yescharacteristic
367C2×C4#381111yescharacteristic
368C8—22no—
369C8—122no—
370C8—182no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—124no—
379C2×C3D3×C22⋊C812yes—
380C2×C3#67⋊C812yes—
381C2×C3#472712yes—
382C2×C3#472912yes—
383C2×C3#495712yes—
384C2×C3C8×#6712yes—
385C2×C3#512812yes—
386D3—44no—
387C22—64no—
388C22—64no—
389C22—64no—
390C22—122no—
391C22—122no—
392C22—122no—
393C22—122no—
394C22D32×C811yescharacteristic
395C22#6379111yescharacteristic
396C22#6380311yescharacteristic
397C22#6380511yescharacteristic
398C22C4×#62511yescharacteristic
399C22#6390211yescharacteristic
400C22#6392111yescharacteristic
401C4—94no—
402C4—122no—
403C4—182no—
404C4#6391211yescharacteristic
405C4#6391411yescharacteristic
406C4#6391511yescharacteristic
407C4#6398011yescharacteristic
408C3—21no—
409C3#6991612yescomplemented
410C2—124no—
411C2C8×#62511yescharacteristic
412C2#1059071811yescharacteristic
413C2#1059073311yescharacteristic
414C2#1059073411yescharacteristic
415C2#1059093511yescharacteristic
416C2#1059095811yescharacteristic
417C2#1059138511yescharacteristic
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×C8×C3⋊Dic3C2semidirect
3. C2×C3×(C2×D3)⋊C8C2semidirect
4. C2×#63572C2semidirect
5. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
25. C2×(C2×D3)⋊C8D3semidirect
42. C2×#625C8semidirect
45. C2×C32×C8D4semidirect
50. C2×C3⋊(C3⋊C8)D4semidirect
149. C2×C3×C8#67semidirect
185. C3⋊Dic3C22⋊C8semidirect
292. C2×C8#625semidirect
339. C32#1954semidirect
409. 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×C8×C3⋊Dic32
C2×C3×(C2×D3)⋊C82
C2×#635722
C2×(C2×D3)⋊(C3⋊C8)2
#699163