Finite Group Databasebeta

← #25094633

Subgroups — #25094633

Order 11008.

1010 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582937C211yesmaximal, characteristic
2#19143013C212yesmaximal
3C2×#14582854C211yesmaximal, characteristic
4#19134482C214yesmaximal, complemented
5#19134477C214yesmaximal, complemented
6#19134306C212yesmaximal
7C22×#108×C43C211yesmaximal, characteristic
8C22×#10621877C2211yescharacteristic
9C2×#13063284C2212yes—
10C2×#13063284C2211yescharacteristic
11#14582937C412yescomplemented
12#14582937C412yescomplemented
13#14582937C2212yes—
14#14582937C2212yes—
15C2×#13063259C412yescomplemented
16C2×#13063257C412yescomplemented
17#14582857C2218yes—
18#14582854—24no—
19#14582854C418yescomplemented
20M16×Dic43—24no—
21C2×#13063235C2212yes—
22C2×C8×Dic43C2212yes—
23#14582660C2218yes—
24C22×M16×C43C2212yes—
25C23×C8×C43C2211yescharacteristic
26C2×#108×C43C418yescomplemented
27C2×#108×C43C2212yes—
28C2×#108×C43C2212yes—
29C2×#10621877C2×C414yes—
30C2×#10621877D412yes—
31C2×#10621877D412yes—
32C2×#10621877Q814yes—
33C22×C43⋊C8C2312yes—
34#13063284—22no—
35#13063284—22no—
36#13063284—22no—
37#13063284C2×C414yes—
38#13063284C2×C414yes—
39#13063284C2314yes—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43C2×C414yes—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—22no—
44C2×C4×Dic43—22no—
45C2×C4×Dic43C2312yes—
46#13063259C2×C414yes—
47#13063259C2×C414yes—
48#13063257C2×C414yes—
49#13063257C2×C414yes—
50#13063235—28no—
51#13063235C2×C418yescomplemented
52C8×Dic43—28no—
53C8×Dic43C2×C418yescomplemented
54C23×C4×C43C2311yescharacteristic
55C2×M16×C43—22no—
56C2×M16×C43—24no—
57C2×M16×C43C2×C418yes—
58C2×M16×C43C2314yes—
59C22×C8×C43—22no—
60C22×C8×C43C2×C414yes—
61C22×C8×C43C2×C411yescharacteristic
62C22×C8×C43C2×C411yescharacteristic
63C22×C8×C43C2×C411yescharacteristic
64C22×C8×C43C2×C411yescharacteristic
65C22×C8×C43C2×C414yes—
66C22×C8×C43C2311yescharacteristic
67C22×C8×C43C2311yescharacteristic
68#108×C43C2×C418yescomplemented
69#108×C43C2×C418yescomplemented
70C24×C43#4111yescharacteristic
71C22×C4×C43C22×C412yes—
72C22×C4×C43C22×C411yescharacteristic
73C22×C4×C43C22×C411yescharacteristic
74C22×C4×C43C22×C412yes—
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×Q812yes—
78C22×C4×C43#4112yes—
79C22×C4×C43#4111yescharacteristic
80C22×C4×C43C2411yescharacteristic
81C22×Dic43—24no—
82C22×Dic43—22no—
83M16×C43—28no—
84M16×C43—24no—
85M16×C43C22×C418yes—
86C2×C8×C43—28no—
87C2×C8×C43—24no—
88C2×C8×C43C4214yes—
89C2×C8×C43C4214yes—
90C2×C8×C43C4214yes—
91C2×C8×C43C4214yes—
92C2×C8×C43C22×C412yes—
93C2×C8×C43C22×C412yes—
94C2×C8×C43C22×C411yescharacteristic
95C2×C8×C43C22×C411yescharacteristic
96C2×C8×C43C22×C411yescharacteristic
97C2×C8×C43C22×C411yescharacteristic
98C2×C8×C43C22×C412yes—
99C2×C8×C43C22×C412yes—
100C22⋊Dic43—24no—
101C22⋊Dic43—24no—
102C22⋊Dic43—24no—
103C4⋊Dic43—24no—
104C4⋊Dic43—24no—
105C4⋊Dic43C22×C418yes—
106C4×Dic43—24no—
107C4×Dic43—24no—
108C4×Dic43—22no—
109C4×Dic43C22×C414yes—
110#10621877C4⋊C418yes—
111#10621877C4⋊C418yes—
112C2×C43⋊C8C22×C414yes—
113C2×C43⋊C8C2×D414yes—
114C2×C43⋊C8C2×Q814yes—
115C23×C43—42no—
116C23×C43#11712yes—
117C23×C43C4×D411yescharacteristic
118C23×C43C4×D411yescharacteristic
119C23×C43C4×Q812yes—
120C23×C43C2×#4111yescharacteristic
121C2×C4×C43C2×C4212yes—
122C2×C4×C43C2×C4212yes—
123C2×C4×C43C2×C4⋊C412yes—
124C2×C4×C43C2×C4⋊C412yes—
125C2×C4×C43#11712yes—
126C2×C4×C43C4×D411yescharacteristic
127C2×C4×C43C4×D411yescharacteristic
128C2×C4×C43C4×D412yes—
129C2×C4×C43C4×D412yes—
130C2×C4×C43C4×Q812yes—
131C2×C4×C43C4×Q812yes—
132C2×C4×C43C4×Q812yes—
133C2×C4×C43C23×C411yescharacteristic
134C2×C4×C43C23×C411yescharacteristic
135C2×C4×C43C23×C411yescharacteristic
136C2×C4×C43C22×D411yescharacteristic
137C2×C4×C43C22×Q811yescharacteristic
138C2×C4×C43C2×#4111yescharacteristic
139C2×Dic43—24no—
140C2×Dic43—28no—
141C2×Dic43—44no—
142C2×Dic43—84no—
143C8×C43—28no—
144C8×C43C2×C4212yes—
145C8×C43C2×C4212yes—
146C8×C43C2×C4212yes—
147C8×C43C2×C4212yes—
148C43⋊C8C2×C4⋊C418yes—
149#20446—431nomaximal, Sylow
150C22×C43—22no—
151C22×C43—22no—
152C22×C43—22no—
153C22×C43—42no—
154C22×C43—42no—
155C22×C43C4×C4⋊C412yes—
156C22×C43C4×C4⋊C412yes—
157C22×C43C2×#11711yescharacteristic
158C22×C43C2×C4×D411yescharacteristic
159C22×C43C2×C4×Q811yescharacteristic
160C4×C43C4×C4⋊C412yes—
161C4×C43C4×C4⋊C412yes—
162C4×C43C22×C4211yescharacteristic
163C4×C43C22×C4⋊C411yescharacteristic
164C4×C43C2×C4×D411yescharacteristic
165C4×C43C2×C4×Q811yescharacteristic
166Dic43—44no—
167Dic43—48no—
168C22×#108D4311yescharacteristic
169C2×#427—431no—
170#2873—432no—
171C2×#405—431no—
172#1773—434no—
173#1772—434no—
174#1733—432no—
175C2×C43—21no—
176C2×C43—21no—
177C2×C43—22no—
178C2×C43—22no—
179C2×C43C2×C4×C4⋊C411yescharacteristic
180C2×C43#295712yes—
181C22×M16—431no—
182C22×M16C2×D4312yes—
183C23×C8C2×D4311yescharacteristic
184C2×#117—431no—
185C2×#117—432no—
186C2×#108Dic4318yescomplemented
187C2×#108C2×D4312yes—
188C2×#108C2×D4312yes—
189#427—432no—
190#427—432no—
191#427—432no—
192#427—432no—
193C2×#107—432no—
194C2×#106—432no—
195#405—438no—
196#405—438no—
197#405—864no—
198C4×M16—864no—
199C2×#97—432no—
200C2×C4×C8—432no—
201#339—438no—
202C43#2044611yescharacteristic, complemented, Sylow
203C23×C4C22×D4311yescharacteristic
204C2×M16—22no—
205C2×M16—24no—
206C2×M16—434no—
207C2×M16—432no—
208C2×M16—432no—
209C2×M16—434no—
210C2×M16C2×Dic4318yes—
211C2×M16C22×D4314yes—
212C22×C8—22no—
213C22×C8—432no—
214C22×C8C4×D4314yes—
215C22×C8C4×D4311yescharacteristic
216C22×C8C4×D4311yescharacteristic
217C22×C8C4×D4311yescharacteristic
218C22×C8C4×D4311yescharacteristic
219C22×C8C2×Dic4314yes—
220C22×C8C22×D4311yescharacteristic
221C22×C8C22×D4311yescharacteristic
222#117—434no—
223#117—434no—
224#117—434no—
225#117—862no—
226#117—862no—
227#117—862no—
228C2×C4⋊C4—434no—
229C2×C4⋊C4—861no—
230C2×C22⋊C4—861no—
231C2×C22⋊C4—862no—
232C2×C42—432no—
233C2×C42—862no—
234#108C2×Dic4318yescomplemented
235#108C2×Dic4318yescomplemented
236#107—434no—
237#107—434no—
238#106—434no—
239#106—434no—
240#97—438no—
241#97—868no—
242C4×C8—438no—
243C4×C8—868no—
244C24#1062190211yescharacteristic
245C22×C4—864no—
246C22×C4—862no—
247C22×C4C2×C4×D4312yes—
248C22×C4C2×C4×D4311yescharacteristic
249C22×C4C2×C4×D4311yescharacteristic
250C22×C4D4×D4311yescharacteristic
251C22×C4D4×D4311yescharacteristic
252C22×C4#1062190012yes—
253C22×C4Q8×D4312yes—
254C22×C4#1062190211yescharacteristic
255C22×C4C22×Dic4312yes—
256C22×C4C23×D4311yescharacteristic
257M16—28no—
258M16—24no—
259M16—438no—
260M16—438no—
261M16C22×Dic4318yes—
262C2×C8—28no—
263C2×C8—24no—
264C2×C8—434no—
265C2×C8—434no—
266C2×C8—434no—
267C2×C8C4×Dic4314yes—
268C2×C8C4×Dic4314yes—
269C2×C8C4×Dic4314yes—
270C2×C8C4×Dic4314yes—
271C2×C8C2×C4×D4312yes—
272C2×C8C2×C4×D4312yes—
273C2×C8C2×C4×D4311yescharacteristic
274C2×C8C2×C4×D4311yescharacteristic
275C2×C8C2×C4×D4311yescharacteristic
276C2×C8C2×C4×D4311yescharacteristic
277C2×C8C22×Dic4312yes—
278C2×C8C22×Dic4312yes—
279C4⋊C4—438no—
280C4⋊C4—864no—
281C4⋊C4—864no—
282C22⋊C4—864no—
283C22⋊C4—864no—
284C22⋊C4—864no—
285C42—434no—
286C42—864no—
287C42—864no—
288C42—862no—
289C23—42no—
290C23#1306328312yes—
291C23#1306328711yescharacteristic
292C23#1306328711yescharacteristic
293C23Q8×Dic4312yes—
294C23C2×#1062190211yescharacteristic
295C2×C4—864no—
296C2×C4—868no—
297C2×C4—3444no—
298C2×C4—1724no—
299C2×C4C2×C4×Dic4312yes—
300C2×C4C2×C4×Dic4312yes—
301C2×C4C4⋊C4×D4312yes—
302C2×C4C4⋊C4×D4312yes—
303C2×C4#1306328312yes—
304C2×C4#1306328711yescharacteristic
305C2×C4#1306328711yescharacteristic
306C2×C4D4×Dic4312yes—
307C2×C4D4×Dic4312yes—
308C2×C4#1306329012yes—
309C2×C4#1306329012yes—
310C2×C4Q8×Dic4312yes—
311C2×C4C22×C4×D4311yescharacteristic
312C2×C4C22×C4×D4311yescharacteristic
313C2×C4C23×Dic4311yescharacteristic
314C2×C4C2×D4×D4311yescharacteristic
315C2×C4C2×Q8×D4311yescharacteristic
316C2×C4C2×#1062190011yescharacteristic
317C8—28no—
318C8—438no—
319C8C2×C4×Dic4312yes—
320C8C2×C4×Dic4312yes—
321C8C2×C4×Dic4312yes—
322C8C2×C4×Dic4312yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—42no—
327C22—42no—
328C22C4⋊C4×Dic4312yes—
329C22C4⋊C4×Dic4312yes—
330C22C2×#1306328311yescharacteristic
331C22C2×#1306328711yescharacteristic
332C22C2×Q8×Dic4311yescharacteristic
333C4—1724no—
334C4—1728no—
335C4C4⋊C4×Dic4312yes—
336C4C4⋊C4×Dic4312yes—
337C4C22×C4×Dic4311yescharacteristic
338C4C2×C4⋊C4×D4311yescharacteristic
339C4C2×D4×Dic4311yescharacteristic
340C4C2×#1306329011yescharacteristic
341C2—21no—
342C2—21no—
343C2—22no—
344C2—22no—
345C2C2×C4⋊C4×Dic4311yescharacteristic
346C2#1914351112yes—
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC22×#108×C43C2
socleC22×C43C2×C4×D4
prime radicalC24×C43#41
cosocleC22×C4×C43C24
hypercenterC22×#108D43
hypocenterC43#20446
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#108

Complements

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

NH ≅ G/Ntype
4. #19134482C2semidirect
5. #19134477C2semidirect
11. #14582937C4semidirect
12. #14582937C4semidirect
15. C2×#13063259C4semidirect
16. C2×#13063257C4semidirect
19. #14582854C4semidirect
26. C2×#108×C43C4semidirect
51. #13063235C2×C4semidirect
53. C8×Dic43C2×C4semidirect
68. #108×C43C2×C4semidirect
69. #108×C43C2×C4semidirect
186. C2×#108Dic43semidirect
202. C43#20446semidirect
234. #108C2×Dic43semidirect
235. #108C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829372
#191430132
C2×#145828542
#191344822
#191344772
#191343062
C22×#108×C432
#2044643