Finite Group Databasebeta

← #11787261

Subgroups — #11787261

Order 1152.

774 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 774 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63900C211yesmaximal, characteristic
2C2×#63865C211yesmaximal, characteristic
3C2×#63778C211yesmaximal, characteristic
4C2×#63740C212yesmaximal, complemented
5#10590075C212yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C22×#627C2211yescharacteristic
8C22×#624—21no—
9C22×#622C2212yes—
10C2×C3×C4⋊Dic3—21no—
11C2×C3×Dic3⋊C4—21no—
12C2×#3724C2211yescharacteristic
13C2×#3724C2212yes—
14C2×#3722—21no—
15#63900—24no—
16#63865—22no—
17#63865C414yescomplemented
18#63778—22no—
19#63740—24no—
20C2×#896—61no—
21C2×D3×C4⋊C4—61no—
22C23×C3⋊D3D411yescharacteristic
23C22×C32×C4D411yescharacteristic
24C22×C3⋊Dic3C2311yescharacteristic
25C2×C4×C3⋊D3—22no—
26C2×C4×C3⋊D3—22no—
27C2×C4×C3⋊D3C2×C412yes—
28C2×C4×C3⋊D3D412yes—
29C22×C3×Dic3—21no—
30C22×C3×Dic3—21no—
31C22×C3×Dic3—22no—
32C2×#627—22no—
33C2×#627—22no—
34C2×#627—21no—
35C2×#627C2×C412yescomplemented
36C2×#624—24no—
37C2×#624—42no—
38C2×#624—42no—
39C2×#622—22no—
40C2×#622—22no—
41C2×#622—22no—
42C3×C4⋊Dic3—24no—
43C3×Dic3⋊C4—24no—
44#3724—21no—
45#3724—22no—
46#3724C2×C412yescomplemented
47#3724D414yes—
48#3722—24no—
49#1872—91nomaximal, Sylow
50C22×C4×D3—61no—
51C22×C4×D3—61no—
52C22×C4×D3—62no—
53C22×Dic6—61no—
54C2×C3×C4⋊C4—61no—
55C2×C3×C4⋊C4—61no—
56C2×(C2×D3)⋊C4—61no—
57C2×(C2×D3)⋊C4—61no—
58C2×C4⋊Dic3—21no—
59C2×Dic3⋊C4—21no—
60C2×Dic3⋊C4—62no—
61C2×Dic3⋊C4—61no—
62#896—64no—
63#896—64no—
64D3×C4⋊C4—68no—
65C23×C32C2×D411yescharacteristic
66C22×C3⋊D3—21no—
67C22×C3⋊D3—21no—
68C22×C3⋊D3—21no—
69C22×C3⋊D3—21no—
70C22×C3⋊D3C22⋊C412yes—
71C22×C3⋊D3SD1612yes—
72C22×C3⋊D3Q1612yes—
73C2×C32×C4—21no—
74C2×C32×C4—21no—
75C2×C32×C4C22⋊C412yes—
76C2×C3⋊Dic3C22×C411yescharacteristic
77C2×C3⋊Dic3C2×D412yes—
78C2×C3⋊Dic3C2×D411yescharacteristic
79C2×C3⋊Dic3#4112yes—
80C4×C3⋊D3—24no—
81C4×C3⋊D3—24no—
82C2×C3×Dic3—22no—
83C2×C3×Dic3—22no—
84C2×C3×Dic3—24no—
85C2×C3×Dic3—41no—
86C2×C3×Dic3—41no—
87C2×C3×Dic3—42no—
88C2×C3×Dic3—42no—
89C2×C3×Dic3—41no—
90C2×C3×Dic3—41no—
91#627—24no—
92#627—42no—
93#624—48no—
94#622—42no—
95C2×C22⋊Q8—91no—
96C22×C4⋊C4—91no—
97C2×#103—92no—
98C2×C22⋊C8—91no—
99#340—92no—
100C23×D3—61no—
101C23×D3—61no—
102C22×C3×C4—21no—
103C22×C3×C4—21no—
104C22×C3×C4—61no—
105C22×C3×C4—62no—
106C22×C3×C4—61no—
107C22×Dic3—21no—
108C22×Dic3—21no—
109C22×Dic3—22no—
110C22×Dic3—61no—
111C22×Dic3—61no—
112C2×C4×D3—62no—
113C2×C4×D3—62no—
114C2×C4×D3—62no—
115C2×C4×D3—62no—
116C2×C4×D3—64no—
117C2×C4×D3—64no—
118C2×C4×D3—68no—
119C2×C4×D3—122no—
120C2×C4×D3—122no—
121C2×C4×D3—124no—
122C2×C4×D3—124no—
123C2×Dic6—62no—
124C2×Dic6—62no—
125C2×Dic6—122no—
126C2×Dic6—122no—
127C3×C4⋊C4—64no—
128C3×C4⋊C4—64no—
129(C2×D3)⋊C4—64no—
130(C2×D3)⋊C4—64no—
131C4⋊Dic3—24no—
132Dic3⋊C4—24no—
133Dic3⋊C4—64no—
134Dic3⋊C4—62no—
135Dic3⋊C4—64no—
136Dic3⋊C4—62no—
137C22×C32C2×C22⋊C411yescharacteristic
138C22×C32#12011yescharacteristic
139C22×C32#12311yescharacteristic
140C22×C32C2×SD1611yescharacteristic
141C22×C32C2×Q1611yescharacteristic
142C22×C32AGL(1,ℤ/8)11yescharacteristic
143C22×C32#13711yescharacteristic
144C2×C3⋊D3—22no—
145C2×C3⋊D3—22no—
146C2×C3⋊D3—22no—
147C2×C3⋊D3—22no—
148C2×C3⋊D3—22no—
149C2×C3⋊D3—22no—
150C2×C3⋊D3#10314yescomplemented
151C32×C4—22no—
152C3⋊Dic3C4×D412yes—
153C3⋊Dic3#12112yes—
154C3×Dic3—42no—
155C3×Dic3—42no—
156C3×Dic3—44no—
157C22×Q8—91no—
158C23×C4—91no—
159C23×C4—181no—
160C22×C8—92no—
161C22⋊Q8—94no—
162C22⋊Q8—182no—
163C2×C4⋊C4—61no—
164C2×C4⋊C4—61no—
165C2×C4⋊C4—92no—
166C2×C4⋊C4—91no—
167C2×C4⋊C4—184no—
168C2×C22⋊C4—181no—
169#103—184no—
170C22⋊C8—182no—
171C23×C3—21no—
172C23×C3—21no—
173C22×D3—62no—
174C22×D3—62no—
175C22×D3—62no—
176C22×D3—62no—
177C22×D3—62no—
178C22×D3—62no—
179C22×D3—62no—
180C22×D3—62no—
181C22×D3—62no—
182C22×D3—62no—
183C22×D3—121no—
184C22×D3—121no—
185C22×D3—121no—
186C22×D3—121no—
187C2×C3×C4—22no—
188C2×C3×C4—22no—
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4—41no—
192C2×C3×C4—41no—
193C2×C3×C4—62no—
194C2×C3×C4—64no—
195C2×C3×C4—62no—
196C2×C3×C4—121no—
197C2×C3×C4—121no—
198C2×C3×C4—122no—
199C2×C3×C4—122no—
200C2×C3×C4—121no—
201C2×C3×C4—121no—
202C2×Dic3—22no—
203C2×Dic3—22no—
204C2×Dic3—24no—
205C2×Dic3—41no—
206C2×Dic3—41no—
207C2×Dic3—42no—
208C2×Dic3—42no—
209C2×Dic3—41no—
210C2×Dic3—41no—
211C2×Dic3—61no—
212C2×Dic3—61no—
213C2×Dic3—62no—
214C2×Dic3—61no—
215C2×Dic3—62no—
216C2×Dic3—61no—
217C2×Dic3—62no—
218C2×Dic3—62no—
219C4×D3—68no—
220C4×D3—68no—
221C4×D3—124no—
222C4×D3—124no—
223C4×D3—1216no—
224Dic6—124no—
225Dic6—124no—
226C2×C32#38611yescharacteristic
227C2×C32C2×#10311yescharacteristic
228C2×C32#41711yescharacteristic
229C2×C32#45011yescharacteristic
230C2×C32#45111yescharacteristic
231C2×C32#48311yescharacteristic
232C2×C32#48411yescharacteristic
233C3⋊D3—24no—
234C24—91no—
235C2×Q8—92no—
236C2×Q8—181no—
237C2×Q8—182no—
238C2×Q8—182no—
239C22×C4—61no—
240C22×C4—61no—
241C22×C4—62no—
242C22×C4—91no—
243C22×C4—92no—
244C22×C4—92no—
245C22×C4—182no—
246C22×C4—182no—
247C22×C4—184no—
248C22×C4—362no—
249C22×C4—362no—
250C22×C4GO+(4,𝔽2)11yescharacteristic
251C2×C8—182no—
252C2×C8—182no—
253C2×C8—182no—
254C4⋊C4—64no—
255C4⋊C4—64no—
256C4⋊C4—94no—
257C4⋊C4—92no—
258C4⋊C4—182no—
259C4⋊C4—181no—
260C22⋊C4—184no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—21no—
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—21no—
273C22×C3—21no—
274C22×C3—21no—
275C2×D3—64no—
276C2×D3—64no—
277C2×D3—64no—
278C2×D3—64no—
279C2×D3—64no—
280C2×D3—64no—
281C2×D3—64no—
282C2×D3—64no—
283C2×D3—122no—
284C2×D3—122no—
285C2×D3—122no—
286C2×D3—122no—
287C2×D3—122no—
288C2×D3—122no—
289C3×C4—24no—
290C3×C4—42no—
291C3×C4—122no—
292C3×C4—124no—
293C3×C4—122no—
294Dic3—42no—
295Dic3—44no—
296Dic3—42no—
297Dic3—62no—
298Dic3—62no—
299Dic3—62no—
300Dic3—62no—
301C32#187211yescharacteristic, complemented, Sylow
302C23—92no—
303C23—92no—
304C23—92no—
305C23—181no—
306C23—181no—
307C23—181no—
308C23—181no—
309C23C2×GO+(4,𝔽2)11yescharacteristic
310Q8—184no—
311Q8—362no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—62no—
315C2×C4—62no—
316C2×C4—64no—
317C2×C4—91no—
318C2×C4—91no—
319C2×C4—92no—
320C2×C4—92no—
321C2×C4—122no—
322C2×C4—121no—
323C2×C4—121no—
324C2×C4—122no—
325C2×C4—121no—
326C2×C4—121no—
327C2×C4—184no—
328C2×C4—184no—
329C2×C4—368no—
330C2×C4D32⋊C412yes—
331C8—362no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—21no—
346D3—68no—
347D3—124no—
348C22—94no—
349C22—182no—
350C22—182no—
351C22—182no—
352C22—182no—
353C22—182no—
354C22—182no—
355C22#6422411yescharacteristic
356C22#6422611yescharacteristic
357C22#6422711yescharacteristic
358C22#6422811yescharacteristic
359C22C2×D32⋊C411yescharacteristic
360C22#6423311yescharacteristic
361C22#6424111yescharacteristic
362C4—22no—
363C4—92no—
364C4—92no—
365C4—124no—
366C4—122no—
367C4—122no—
368C3—21no—
369C3—21no—
370C2—184no—
371C2#1059335411yescharacteristic
372C2#1059336011yescharacteristic
373C2#1059337111yescharacteristic
374C2#1059337211yescharacteristic
375C2#1059337511yescharacteristic
376C2#1059338611yescharacteristic
377C2#1059351411yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1872
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. C2×#63740C2semidirect
5. #10590075C2semidirect
17. #63865C4semidirect
35. C2×#627C2×C4semidirect
46. #3724C2×C4semidirect
150. C2×C3⋊D3#103semidirect
301. C32#1872semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
C2×#638652
C2×#637782
C2×#637402
#105900752
#18729