Finite Group Databasebeta

← #11869621

Subgroups — #11869621

Order 1152.

830 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 121 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
2#10594925C211yesmaximal, characteristic
3#10593800C211yesmaximal, characteristic
4#10593500C214yesmaximal, complemented
5#10593396C212yesmaximal, complemented
6#10593375C212yesmaximal, complemented
7#10593372C214yesmaximal, complemented
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×#624—21no—
10C2×#3797C2211yescharacteristic
11C2×#3787C2212yes—
12C2×C3×C4⋊Dic3—21no—
13C3×#924—21no—
14#63982C2212yes—
15#63974—21no—
16C2×#3724C2212yes—
17#63900—21no—
18#63900—21no—
19#63900C2212yes—
20#63900C2212yes—
21#63900C2211yescharacteristic
22#63883—21no—
23#63871—21no—
24#63865C2212yes—
25C22⋊#622C2212yes—
26#63778C2212yes—
27#63743C2218yescomplemented
28#63740C2218yescomplemented
29D3×C22⋊Q8—61no—
30C2×D3×C4⋊C4—61no—
31C23×C3⋊D3D411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C3⋊Dic3C2311yescharacteristic
34C2×C4×C3⋊D3—24no—
35C2×C4×C3⋊D3D411yescharacteristic
36C2×C4×C3⋊D3D411yescharacteristic
37C2×C4×C3⋊D3C2311yescharacteristic
38C2×C4×C3⋊D3C2311yescharacteristic
39C22×C3×Dic3—22no—
40C2×C3×Dic6—21no—
41C2×#627C2312yes—
42C2×#624—21no—
43C2×#624—22no—
44C2×#624—22no—
45C2×#624—21no—
46C2×#624—44no—
47#3797—24no—
48C2×#622C2314yes—
49#3787—24no—
50C3×#217—22no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—22no—
53C3×C4⋊Dic3—22no—
54C3×Dic3⋊C4—22no—
55#3724—22no—
56#3724C2312yes—
57#3724C2314yes—
58Dic3⋊Dic3—22no—
59#3722—22no—
60C2×#484—91nomaximal, Sylow
61C2×D3×Q8—61no—
62C22×C4×D3—61no—
63C22×C4×D3—61no—
64C22×C4×D3—62no—
65C3×C22⋊Q8—61no—
66C2×C3×C4⋊C4—61no—
67#946—61no—
68C2×C4⋊Dic3—21no—
69#924—21no—
70C2×Dic3⋊C4—62no—
71#897—61no—
72#896—62no—
73D3×C4⋊C4—62no—
74D3×C4⋊C4—62no—
75D3×C4⋊C4—61no—
76D3×C4⋊C4—62no—
77D3×C4⋊C4—62no—
78D3×C4⋊C4—62no—
79D3×C22⋊C4—62no—
80#878—62no—
81C23×C32C2×D411yescharacteristic
82C22×C3⋊D3—22no—
83C22×C3⋊D3—22no—
84C22×C3⋊D3Q1614yes—
85C22×C3⋊D3C2×D411yescharacteristic
86C22×C3⋊D3C2×D411yescharacteristic
87C2×C32×C4—22no—
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×D411yescharacteristic
90C2×C3⋊Dic3—22no—
91C2×C3⋊Dic3C2×D411yescharacteristic
92C2×C3⋊Dic3C2411yescharacteristic
93C4×C3⋊D3—22no—
94C4×C3⋊D3—22no—
95C4×C3⋊D3—22no—
96C4×C3⋊D3#4114yes—
97C2×C3×Dic3—22no—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—24no—
100C2×C3×Dic3—44no—
101C3×Dic6—42no—
102#627—24no—
103#624—44no—
104#624—42no—
105#624—42no—
106#624—44no—
107#622—24no—
108C2×C22⋊Q8—91no—
109C22×C4⋊C4—91no—
110#484—94no—
111#484—94no—
112C2×#107—92no—
113C2×#103—92no—
114C2×C22⋊C8—91no—
115C23×D3—61no—
116C23×D3—61no—
117C2×C3×Q8—61no—
118C22×C3×C4—21no—
119C22×C3×C4—21no—
120C22×C3×C4—62no—
121C22×Dic3—22no—
122C22×Dic3—61no—
123C22×Dic3—61no—
124D3×Q8—124no—
125C2×C4×D3—61no—
126C2×C4×D3—61no—
127C2×C4×D3—61no—
128C2×C4×D3—61no—
129C2×C4×D3—61no—
130C2×C4×D3—61no—
131C2×C4×D3—61no—
132C2×C4×D3—61no—
133C2×C4×D3—68no—
134C2×C4×D3—62no—
135C2×C4×D3—62no—
136C2×C4×D3—64no—
137C2×C4×D3—64no—
138C2×C4×D3—124no—
139C2×C4×D3—128no—
140C2×Dic6—21no—
141C2×Dic6—62no—
142C3×C4⋊C4—62no—
143C3×C4⋊C4—62no—
144C3×C4⋊C4—62no—
145C3×C4⋊C4—61no—
146C3×C22⋊C4—62no—
147#217—22no—
148(C2×D3)⋊C4—62no—
149(C2×D3)⋊C4—62no—
150C4⋊Dic3—22no—
151C4⋊Dic3—22no—
152C4⋊Dic3—21no—
153C4⋊Dic3—62no—
154Dic3⋊C4—22no—
155Dic3⋊C4—62no—
156Dic3⋊C4—64no—
157Dic3⋊C4—62no—
158Dic3⋊C4—64no—
159C22×C32—21no—
160C22×C32—21no—
161C22×C32C2×Q1612yes—
162C22×C32C22×D411yescharacteristic
163C2×C3⋊D3—21no—
164C2×C3⋊D3—21no—
165C2×C3⋊D3—28no—
166C2×C3⋊D3#12312yes—
167C2×C3⋊D3C2×Q1612yes—
168C2×C3⋊D3C2×Q1612yes—
169C2×C3⋊D3AGL(1,ℤ/8)12yes—
170C32×C4—21no—
171C32×C4#12312yes—
172C3⋊Dic3—21no—
173C3⋊Dic3C2×#4112yes—
174C3×Dic3—42no—
175C3×Dic3—44no—
176C3×Dic3—42no—
177C22×Q8—91no—
178C23×C4—91no—
179C23×C4—181no—
180C22×C8—92no—
181C22⋊Q8—61no—
182C22⋊Q8—92no—
183C22⋊Q8—92no—
184C22⋊Q8—181no—
185C2×C4⋊C4—61no—
186C2×C4⋊C4—92no—
187C2×C4⋊C4—92no—
188C2×C4⋊C4—91no—
189C2×C4⋊C4—92no—
190C2×C4⋊C4—181no—
191C2×C4⋊C4—181no—
192C2×C4⋊C4—181no—
193C2×C22⋊C4—181no—
194#107—98no—
195#103—98no—
196C22⋊C8—92no—
197C22⋊C8—92no—
198C23×C3—21no—
199C23×C3—21no—
200C22×D3—64no—
201C22×D3—61no—
202C22×D3—61no—
203C22×D3—61no—
204C22×D3—64no—
205C22×D3—61no—
206C22×D3—64no—
207C22×D3—64no—
208C22×D3—122no—
209C22×D3—122no—
210C3×Q8—122no—
211C2×C3×C4—24no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—42no—
217C2×C3×C4—64no—
218C2×C3×C4—62no—
219C2×C3×C4—62no—
220C2×C3×C4—124no—
221C2×Dic3—22no—
222C2×Dic3—22no—
223C2×Dic3—24no—
224C2×Dic3—44no—
225C2×Dic3—61no—
226C2×Dic3—61no—
227C2×Dic3—61no—
228C2×Dic3—61no—
229C2×Dic3—64no—
230C2×Dic3—122no—
231C4×D3—64no—
232C4×D3—64no—
233C4×D3—64no—
234C4×D3—64no—
235C4×D3—64no—
236C4×D3—122no—
237C4×D3—122no—
238C4×D3—122no—
239C4×D3—124no—
240C4×D3—128no—
241C4×D3—128no—
242C4×D3—124no—
243Dic6—42no—
244Dic6—124no—
245C2×C32—22no—
246C2×C32C2×#12311yescharacteristic
247C2×C32C22×Q1611yescharacteristic
248C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
249C3⋊D3—22no—
250C3⋊D3#48414yescomplemented
251C24—91no—
252C2×Q8—61no—
253C2×Q8—92no—
254C2×Q8—184no—
255C22×C4—62no—
256C22×C4—91no—
257C22×C4—91no—
258C22×C4—91no—
259C22×C4—91no—
260C22×C4—91no—
261C22×C4—184no—
262C22×C4—181no—
263C22×C4—181no—
264C22×C4—182no—
265C22×C4—182no—
266C22×C4—364no—
267C22×C4GO+(4,𝔽2)11yescharacteristic
268C2×C8—94no—
269C2×C8—184no—
270C4⋊C4—62no—
271C4⋊C4—62no—
272C4⋊C4—61no—
273C4⋊C4—62no—
274C4⋊C4—94no—
275C4⋊C4—92no—
276C4⋊C4—182no—
277C4⋊C4—182no—
278C22⋊C4—62no—
279C22⋊C4—182no—
280C22×C3—22no—
281C22×C3—22no—
282C22×C3—21no—
283C22×C3—21no—
284C22×C3—22no—
285C22×C3—22no—
286C22×C3—41no—
287C22×C3—41no—
288C2×D3—62no—
289C2×D3—62no—
290C2×D3—62no—
291C2×D3—62no—
292C2×D3—62no—
293C2×D3—62no—
294C2×D3—62no—
295C2×D3—62no—
296C2×D3—62no—
297C2×D3—62no—
298C2×D3—616no—
299C2×D3—128no—
300C2×D3—121no—
301C2×D3—121no—
302C3×C4—22no—
303C3×C4—22no—
304C3×C4—22no—
305C3×C4—41no—
306C3×C4—122no—
307C3×C4—124no—
308C3×C4—122no—
309Dic3—42no—
310Dic3—44no—
311Dic3—42no—
312Dic3—62no—
313Dic3—62no—
314Dic3—62no—
315Dic3—121no—
316C32C2×#48411yescharacteristic, complemented, Sylow
317C23—91no—
318C23—91no—
319C23—94no—
320C23—182no—
321C23—182no—
322C23C2×GO+(4,𝔽2)11yescharacteristic
323Q8—122no—
324Q8—184no—
325C2×C4—22no—
326C2×C4—62no—
327C2×C4—62no—
328C2×C4—64no—
329C2×C4—91no—
330C2×C4—94no—
331C2×C4—91no—
332C2×C4—124no—
333C2×C4—182no—
334C2×C4—182no—
335C2×C4—182no—
336C2×C4—182no—
337C2×C4—364no—
338C2×C4—362no—
339C2×C4—362no—
340C2×C4—364no—
341C2×C4C2×GO+(4,𝔽2)11yescharacteristic
342C2×C4C2×GO+(4,𝔽2)11yescharacteristic
343C8—184no—
344C2×C3—24no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—42no—
352D3—64no—
353D3—64no—
354D3—64no—
355D3—122no—
356C22—21no—
357C22—21no—
358C22—92no—
359C22—92no—
360C22—92no—
361C22—92no—
362C22—188no—
363C22—181no—
364C22—181no—
365C22#6422812yes—
366C22C22×GO+(4,𝔽2)11yescharacteristic
367C4—21no—
368C4—92no—
369C4—124no—
370C4—122no—
371C4—122no—
372C4—181no—
373C4#6423312yes—
374C3—21no—
375C3—21no—
376C2—22no—
377C2—94no—
378C2—182no—
379C2#1059650111yescharacteristic
380C2C2×#6422811yescharacteristic
381C2C2×#6423311yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC23×C3⋊D3D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#484
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10593500C2semidirect
5. #10593396C2semidirect
6. #10593375C2semidirect
7. #10593372C2semidirect
27. #63743C22semidirect
28. #63740C22semidirect
250. C3⋊D3#484semidirect
316. C32C2×#484semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
#105949252
#105938002
#105935002
#105933962
#105933752
#105933722
C2×#4849