Finite Group Databasebeta

← #11773488

Subgroups — #11773488

Order 1152.

1326 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 1326 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C22×#3797C211yesmaximal, characteristic
2C2×#63781C211yesmaximal, characteristic
3C2×#63737C214yesmaximal
4#10591370C211yesmaximal, characteristic
5C23×#157C2212yes—
6C22×C4×C3⋊D3C2211yescharacteristic
7C22×C3×Dic6—21no—
8C22×#627—21no—
9C22×#624C2212yes—
10C22×#624C2212yes—
11C2×#3797—22no—
12C2×#3797—28no—
13C2×#3797C414yescomplemented
14#63781—22no—
15#63737—28no—
16C3×C3⋊#95—21no—
17#63579—21no—
18C22×D3×Q8—61no—
19D3×#95—61no—
20C23×C3⋊D3C2311yescharacteristic
21C22×#157—22no—
22C22×#157—24no—
23C22×#157—22no—
24C22×#157—24no—
25C22×#157Q814yescomplemented
26C22×C32×C4D411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C2×C4×C3⋊D3—24no—
29C2×C4×C3⋊D3C2×C412yes—
30C2×C4×C3⋊D3D412yes—
31C22×C3×Dic3—22no—
32C22×C3×Dic3—22no—
33C2×C3×Dic6—28no—
34C2×C3×Dic6—24no—
35C2×#627—28no—
36C2×#627—24no—
37C2×#624—24no—
38C2×#624—22no—
39C2×#624—24no—
40C2×#624—24no—
41C2×#624—22no—
42C2×#624C2×C414yes—
43C2×#624D418yes—
44C2×#624Q814yescomplemented
45#3797—216no—
46#3797—216no—
47#1446—91nomaximal, Sylow
48C22×C3×Q8—61no—
49C2×D3×Q8—64no—
50C2×D3×Q8—616no—
51C2×D3×Q8—64no—
52C22×C4×D3—62no—
53C22×C4×D3—61no—
54C22×C4×D3—62no—
55C22×C4×D3—61no—
56C22×Dic6—21no—
57C22×Dic6—62no—
58C3×#95—61no—
59C3⋊#95—21no—
60C3⋊#95—62no—
61C23×C32C2×D411yescharacteristic
62C22×C3⋊D3C22×C411yescharacteristic
63C22×C3⋊D3C2×D414yes—
64C22×C3⋊D3C2×D411yescharacteristic
65C22×C3⋊D3C2×Q812yes—
66C22×C3⋊D3C2×Q812yes—
67C22×C3⋊D3#4112yes—
68C22×C3⋊D3#4112yes—
69C2×#157—28no—
70C2×#157—24no—
71C2×#157—42no—
72C2×#157—44no—
73C2×#157—42no—
74C2×C32×C4—22no—
75C2×C32×C4C22⋊C412yes—
76C2×C3⋊Dic3—22no—
77C2×C3⋊Dic3C22⋊C412yes—
78C4×C3⋊D3—24no—
79C4×C3⋊D3—24no—
80C2×C3×Dic3—24no—
81C2×C3×Dic3—28no—
82C2×C3×Dic3—24no—
83C2×C3×Dic3—42no—
84C2×C3×Dic3—42no—
85C3×Dic6—216no—
86#627—216no—
87#624—24no—
88#624—28no—
89#624—28no—
90#624—44no—
91#624C22⋊C418yes—
92C23×Q8—91no—
93C2×#95—91no—
94C2×#95—91no—
95C2×#95—94no—
96C23×D3—61no—
97C23×D3—61no—
98C2×C3×Q8—68no—
99C2×C3×Q8—64no—
100C22×C3×C4—21no—
101C22×C3×C4—21no—
102C22×C3×C4—62no—
103C22×C3×C4—62no—
104C22×Dic3—22no—
105C22×Dic3—22no—
106C22×Dic3—61no—
107C22×Dic3—61no—
108D3×Q8—632no—
109D3×Q8—632no—
110C2×C4×D3—64no—
111C2×C4×D3—68no—
112C2×C4×D3—62no—
113C2×C4×D3—62no—
114C2×C4×D3—64no—
115C2×C4×D3—62no—
116C2×C4×D3—62no—
117C2×C4×D3—64no—
118C2×C4×D3—68no—
119C2×C4×D3—68no—
120C2×C4×D3—64no—
121C2×C4×D3—124no—
122C2×C4×D3—124no—
123C2×C4×D3—124no—
124C2×Dic6—28no—
125C2×Dic6—24no—
126C2×Dic6—68no—
127C2×Dic6—616no—
128C22×C32C2×C22⋊C411yescharacteristic
129C22×C32#12012yes—
130C22×C32C22⋊Q812yes—
131C22×C32#12411yescharacteristic
132C22×C32C4⋊Q811yescharacteristic
133C2×C3⋊D3C2×C22⋊C412yes—
134C2×C3⋊D3C4×Q812yes—
135C2×C3⋊D3C4×Q812yes—
136C2×C3⋊D3#12012yes—
137C2×C3⋊D3C22⋊Q814yes—
138C2×C3⋊D3C22⋊Q814yes—
139C2×C3⋊D3C22⋊Q812yes—
140C2×C3⋊D3#12414yes—
141C2×C3⋊D3#12411yescharacteristic
142C2×C3⋊D3C4⋊Q814yes—
143C2×C3⋊D3C4⋊Q811yescharacteristic
144#157—44no—
145C32×C4—22no—
146C3⋊Dic3—22no—
147C3×Dic3—28no—
148C3×Dic3—44no—
149C22×Q8—61no—
150C22×Q8—94no—
151C22×Q8—181no—
152C22×Q8—188no—
153C22×Q8—182no—
154C23×C4—92no—
155C23×C4—92no—
156C23×C4—91no—
157C23×C4—92no—
158#95—61no—
159#95—181no—
160#95—182no—
161#95—188no—
162C23×C3—21no—
163C23×C3—21no—
164C22×D3—61no—
165C22×D3—61no—
166C22×D3—61no—
167C22×D3—64no—
168C22×D3—61no—
169C22×D3—64no—
170C22×D3—62no—
171C22×D3—62no—
172C22×D3—62no—
173C22×D3—62no—
174C22×D3—62no—
175C22×D3—62no—
176C22×D3—62no—
177C22×D3—62no—
178C3×Q8—616no—
179C2×C3×C4—24no—
180C2×C3×C4—22no—
181C2×C3×C4—22no—
182C2×C3×C4—42no—
183C2×C3×C4—64no—
184C2×C3×C4—68no—
185C2×C3×C4—64no—
186C2×C3×C4—122no—
187C2×C3×C4—122no—
188C2×Dic3—24no—
189C2×Dic3—28no—
190C2×Dic3—24no—
191C2×Dic3—42no—
192C2×Dic3—42no—
193C2×Dic3—62no—
194C2×Dic3—62no—
195C2×Dic3—64no—
196C2×Dic3—122no—
197C4×D3—68no—
198C4×D3—68no—
199C4×D3—616no—
200C4×D3—68no—
201C4×D3—68no—
202C4×D3—128no—
203C4×D3—124no—
204C4×D3—124no—
205C4×D3—128no—
206Dic6—216no—
207Dic6—632no—
208C2×C32#37911yescharacteristic
209C2×C32#39111yescharacteristic
210C2×C32#39111yescharacteristic
211C2×C32#39312yes—
212C2×C32#39512yes—
213C3⋊D3#39114yes—
214C3⋊D3#39312yes—
215C3⋊D3#39512yes—
216C24—91no—
217C2×Q8—68no—
218C2×Q8—64no—
219C2×Q8—184no—
220C2×Q8—188no—
221C2×Q8—1816no—
222C2×Q8—1816no—
223C22×C4—62no—
224C22×C4—62no—
225C22×C4—98no—
226C22×C4—94no—
227C22×C4—94no—
228C22×C4—91no—
229C22×C4—92no—
230C22×C4—92no—
231C22×C4—94no—
232C22×C4—184no—
233C22×C4—182no—
234C22×C4—184no—
235C22×C4—182no—
236C22×C4—184no—
237C22×C4—184no—
238C22×C4—182no—
239C22×C4—184no—
240C22×C4—184no—
241C22×C4—182no—
242C22×C4GO+(4,𝔽2)11yescharacteristic
243C22×C3—22no—
244C22×C3—22no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—22no—
252C22×C3—22no—
253C2×D3—62no—
254C2×D3—62no—
255C2×D3—62no—
256C2×D3—62no—
257C2×D3—64no—
258C2×D3—64no—
259C2×D3—62no—
260C2×D3—62no—
261C2×D3—62no—
262C2×D3—62no—
263C2×D3—62no—
264C2×D3—62no—
265C2×D3—64no—
266C2×D3—64no—
267C2×D3—64no—
268C2×D3—61no—
269C2×D3—61no—
270C2×D3—64no—
271C2×D3—61no—
272C2×D3—61no—
273C2×D3—64no—
274C2×D3—64no—
275C3×C4—24no—
276C3×C4—42no—
277C3×C4—68no—
278C3×C4—124no—
279Dic3—28no—
280Dic3—44no—
281Dic3—64no—
282Dic3—122no—
283C32#144611yescharacteristic, complemented, Sylow
284C23—92no—
285C23—92no—
286C23—92no—
287C23—92no—
288C23—91no—
289C23—91no—
290C23—94no—
291C23C2×GO+(4,𝔽2)11yescharacteristic
292Q8—616no—
293Q8—1816no—
294C2×C4—22no—
295C2×C4—64no—
296C2×C4—68no—
297C2×C4—64no—
298C2×C4—98no—
299C2×C4—92no—
300C2×C4—122no—
301C2×C4—122no—
302C2×C4—184no—
303C2×C4—184no—
304C2×C4—184no—
305C2×C4—188no—
306C2×C4—188no—
307C2×C4—182no—
308C2×C4—184no—
309C2×C4—188no—
310C2×C4—364no—
311C2×C4—362no—
312C2×C4—364no—
313C2×C4—362no—
314C2×C4D32⋊C412yes—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—22no—
320C2×C3—22no—
321C2×C3—22no—
322C2×C3—22no—
323C2×C3—21no—
324C2×C3—21no—
325D3—64no—
326D3—64no—
327D3—62no—
328D3—62no—
329D3—62no—
330D3—62no—
331C22—91no—
332C22—91no—
333C22—92no—
334C22—92no—
335C22—92no—
336C22—94no—
337C22—94no—
338C22—94no—
339C22—94no—
340C22—92no—
341C22—92no—
342C22D32⋊Q812yes—
343C22#6422111yescharacteristic
344C22#6422211yescharacteristic
345C22C2×D32⋊C411yescharacteristic
346C22#6424112yes—
347C4—22no—
348C4—68no—
349C4—124no—
350C4—182no—
351C4—364no—
352C3—21no—
353C3—21no—
354C2—92no—
355C2—92no—
356C2—94no—
357C2#1059334111yescharacteristic
358C2#1059334211yescharacteristic
359C2#1059340212yes—
360C2#1059341112yes—
361C2#1059351211yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC22×C3⋊D3C22×C4
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radical, cosocleC23×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1446
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
13. C2×#3797C4semidirect
25. C22×#157Q8semidirect
44. C2×#624Q8semidirect
283. C32#1446semidirect

Maximal subgroups

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

subgroupindex
C22×#37972
C2×#637812
C2×#637372
#105913702
#14469