Finite Group Databasebeta

← #15674646

Subgroups — #15674646

Order 2944.

382 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 67 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
1#13092976C211yesmaximal, characteristic
2C2×#10625016C211yesmaximal, characteristic, complemented
3C2×#10624988C211yesmaximal, characteristic, complemented
4#13092296C211yesmaximal, characteristic, complemented
5#13092290C211yesmaximal, characteristic, complemented
6#13092183C211yesmaximal, characteristic, complemented
7C23×#386C211yesmaximal, characteristic, complemented
8C22×D4×C23C2211yescharacteristic
9C23×C4×C23C2211yescharacteristic
10C22×C22⋊D23C2211yescharacteristic
11C2×C22⋊C4×C23—21no—
12C2×C22⋊C4×C23C2211yescharacteristic
13#10625124—21no—
14C2×C22⋊Dic23C2211yescharacteristic
15C2×C22⋊Dic23C2211yescharacteristic
16C2×C22⋊Dic23C2211yescharacteristic
17#10625110—21no—
18#10625110—21no—
19#10625108—21no—
20#10625106—21no—
21#10625100—21no—
22C2×(C2×D23)⋊C4—21no—
23C2×Dic23⋊C4—21no—
24C23×#95—21no—
25#10625016—22no—
26C23⋊#95—21no—
27C23⋊#95—21no—
28#10624988—22no—
29C24×C23D411yescharacteristic
30C24×C23C2311yescharacteristic
31C23×D23D411yescharacteristic
32C2×D4×C23—21no—
33C2×D4×C23—21no—
34C2×D4×C23—21no—
35C2×D4×C23—21no—
36C2×D4×C23—21no—
37C2×D4×C23—21no—
38C22×C4×C23—21no—
39C22×C4×C23—21no—
40C22×C4×C23—21no—
41C22×C4×C23—21no—
42C22×C4×C23—42no—
43C22×C4×C23D411yescharacteristic
44C2×C22⋊D23—21no—
45C2×C22⋊D23—21no—
46C2×C22⋊D23—21no—
47C2×C22⋊D23—21no—
48C2×C22⋊D23—21no—
49C2×C22⋊D23—21no—
50C2×C22⋊D23—21no—
51C2×C22⋊D23—21no—
52C22×Dic23—21no—
53C22×Dic23—21no—
54C22×Dic23D411yescharacteristic
55C22×Dic23D411yescharacteristic
56C22×Dic23D411yescharacteristic
57C22⋊C4×C23—21no—
58C22⋊C4×C23—21no—
59C22⋊C4×C23—42no—
60C22⋊Dic23—21no—
61C22⋊Dic23—21no—
62C22⋊Dic23—21no—
63C22⋊Dic23—21no—
64C22⋊Dic23—21no—
65C22⋊Dic23—21no—
66C22⋊Dic23—21no—
67C22⋊Dic23D412yescomplemented
68(C2×D23)⋊C4—21no—
69(C2×D23)⋊C4—21no—
70(C2×D23)⋊C4—42no—
71Dic23⋊C4—21no—
72Dic23⋊C4—21no—
73Dic23⋊C4—42no—
74C23×C23—21no—
75C23×C23—21no—
76C23×C23—21no—
77C23×C23—41no—
78C23×C23—41no—
79C23×C23—41no—
80C23×C23—41no—
81C23×C23C2×D411yescharacteristic
82C23×C23C2×D411yescharacteristic
83C23×C23C2×D411yescharacteristic
84C23×C23C2×D411yescharacteristic
85C23×C23#4111yescharacteristic
86C23×C23#4111yescharacteristic
87C23×C23#4111yescharacteristic
88C22×D23—21no—
89C22×D23—21no—
90C22×D23—21no—
91C22×D23—41no—
92C22×D23—41no—
93D4×C23—41no—
94D4×C23—41no—
95D4×C23—41no—
96D4×C23—41no—
97C2×C4×C23—22no—
98C2×C4×C23—22no—
99C2×C4×C23—22no—
100C2×C4×C23—21no—
101C2×C4×C23—21no—
102C2×C4×C23—21no—
103C2×C4×C23—41no—
104C2×C4×C23—41no—
105C2×C4×C23—41no—
106C2×C4×C23—41no—
107C2×C4×C23—41no—
108C2×C4×C23—41no—
109C2×C4×C23—41no—
110C22⋊D23—41no—
111C22⋊D23—41no—
112C22⋊D23—41no—
113C22⋊D23—41no—
114C22⋊D23—81no—
115C22⋊D23—81no—
116C2×Dic23—21no—
117C2×Dic23—21no—
118C2×Dic23—21no—
119C2×Dic23—22no—
120C2×Dic23—21no—
121C2×Dic23—21no—
122C2×Dic23—41no—
123C2×Dic23—41no—
124C2×Dic23—41no—
125C2×Dic23—41no—
126C2×Dic23—41no—
127C2×Dic23—41no—
128C2×Dic23—41no—
129#2044—231nomaximal, Sylow
130C22×C23—21no—
131C22×C23—21no—
132C22×C23—21no—
133C22×C23—21no—
134C22×C23—21no—
135C22×C23—21no—
136C22×C23—41no—
137C22×C23—41no—
138C22×C23—41no—
139C22×C23—41no—
140C22×C23—42no—
141C22×C23—41no—
142C22×C23—41no—
143C22×C23—41no—
144C22×C23—81no—
145C22×C23#12011yescharacteristic
146C22×C23#12111yescharacteristic
147C22×C23#12111yescharacteristic
148C22×C23#12111yescharacteristic
149C22×C23#12311yescharacteristic
150C22×C23#12311yescharacteristic
151C22×C23#12411yescharacteristic
152C2×D23—42no—
153C2×D23—41no—
154C2×D23—41no—
155C2×D23—41no—
156C2×D23—81no—
157C4×C23—41no—
158C4×C23—42no—
159C4×C23—81no—
160Dic23—42no—
161Dic23—41no—
162Dic23—41no—
163Dic23—41no—
164Dic23—81no—
165#534—231no—
166C2×#99—231no—
167C2×#99—231no—
168#386—231no—
169#386D2311yescharacteristic, complemented
170#385—231no—
171#342—231no—
172C2×C23—21no—
173C2×C23—21no—
174C2×C23—21no—
175C2×C23—21no—
176C2×C23—21no—
177C2×C23—21no—
178C2×C23—81no—
179C2×C23#39411yescharacteristic
180C2×C23B(4,𝔽2)11yescharacteristic
181C2×C23#45811yescharacteristic
182D23—81no—
183C22×D4—231no—
184C22×D4C2×D2311yescharacteristic
185C23×C4C2×D2311yescharacteristic
186#123—461no—
187#123—461no—
188#121—461no—
189#121—461no—
190#120—461no—
191#120—461no—
192C2×C4⋊C4—461no—
193C2×C22⋊C4—21no—
194C2×C22⋊C4—231no—
195C2×C22⋊C4—231no—
196C2×C22⋊C4—231no—
197C2×C22⋊C4—461no—
198C2×C22⋊C4C2×D2311yescharacteristic
199#99—462no—
200#99—462no—
201#95—21no—
202#95—461no—
203#95—461no—
204C23#204411yescharacteristic, complemented, Sylow
205C24—231no—
206C24C22⋊D2311yescharacteristic
207C24C22×D2311yescharacteristic
208C2×D4—21no—
209C2×D4—21no—
210C2×D4—21no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—21no—
214C2×D4—461no—
215C2×D4—461no—
216C2×D4—461no—
217C2×D4—461no—
218C2×D4—461no—
219C2×D4—461no—
220C2×D4—461no—
221C2×D4—461no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—42no—
227C22×C4—231no—
228C22×C4—231no—
229C22×C4—231no—
230C22×C4—461no—
231C22×C4—461no—
232C22×C4C22⋊D2311yescharacteristic
233C4⋊C4—461no—
234C4⋊C4—461no—
235C4⋊C4—922no—
236C22⋊C4—21no—
237C22⋊C4—21no—
238C22⋊C4—42no—
239C22⋊C4—232no—
240C22⋊C4—461no—
241C22⋊C4—461no—
242C22⋊C4—461no—
243C22⋊C4—461no—
244C22⋊C4—461no—
245C22⋊C4—461no—
246C22⋊C4—461no—
247C22⋊C4—461no—
248C22⋊C4—461no—
249C22⋊C4—922no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23—461no—
258C23—461no—
259C23—461no—
260C23—921no—
261C23—921no—
262C23#6728811yescharacteristic
263C23#6728811yescharacteristic
264C23D4×D2311yescharacteristic
265C23D4×D2311yescharacteristic
266C23D4×D2311yescharacteristic
267C23#6729011yescharacteristic
268C23C2×C22⋊D2311yescharacteristic
269D4—41no—
270D4—41no—
271D4—41no—
272D4—41no—
273D4—921no—
274D4—921no—
275D4—921no—
276D4—921no—
277D4—1841no—
278D4—1841no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—461no—
293C2×C4—462no—
294C2×C4—461no—
295C2×C4—461no—
296C2×C4—461no—
297C2×C4—461no—
298C2×C4—921no—
299C2×C4—921no—
300C2×C4—921no—
301C2×C4—921no—
302C2×C4—921no—
303C2×C4—921no—
304C2×C4—921no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—42no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—81no—
320C22—922no—
321C22—921no—
322C22—921no—
323C22—921no—
324C22—1841no—
325C22#1062505411yescharacteristic
326C22#1062505511yescharacteristic
327C22#1062505511yescharacteristic
328C22#1062505611yescharacteristic
329C22#1062510011yescharacteristic
330C22#1062510811yescharacteristic
331C22#1062511011yescharacteristic
332C4—41no—
333C4—42no—
334C4—81no—
335C4—922no—
336C4—921no—
337C4—921no—
338C4—921no—
339C4—1841no—
340C2—21no—
341C2—21no—
342C2—21no—
343C2—21no—
344C2—21no—
345C2—21no—
346C2—81no—
347C2—1841no—
348C2#1309233211yescharacteristic
349C2#1309260311yescharacteristic
350C2#1309260611yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC24×C23C23
FrattiniC24C22×D23
FittingC23×#386C2
socleC22×C23#120
prime radical#13092976C2
hypercenter#386D23
hypocenterC23#2044
LCSG ▷ C24×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×#10625016C2semidirect
3. C2×#10624988C2semidirect
4. #13092296C2semidirect
5. #13092290C2semidirect
6. #13092183C2semidirect
7. C23×#386C2semidirect
67. C22⋊Dic23D4semidirect
169. #386D23semidirect
204. C23#2044semidirect

Maximal subgroups

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

subgroupindex
#130929762
C2×#106250162
C2×#106249882
#130922962
#130922902
#130921832
C23×#3862
#204423