Finite Group Databasebeta

← #25013660

Subgroups — #25013660

Order 11008.

526 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063270C211yesmaximal, characteristic
2C2×C4×Dic172C211yesmaximal, characteristic, complemented
3C2×#14582704C211yesmaximal, characteristic, complemented
4C2×#14582701C211yesmaximal, characteristic
5#19135461C211yesmaximal, characteristic
6#19132687C211yesmaximal, characteristic, complemented
7C43×#1374C211yesmaximal, characteristic, complemented
8C22×Dic172C2211yescharacteristic
9C22×D344C2211yescharacteristic
10C2×C4×Dic86—21no—
11C2×#13063270—22no—
12C2×#13063270—22no—
13C2×#13063270C414yescomplemented
14C4×Dic172—22no—
15C4×Dic172—22no—
16C2×#13063259C2211yescharacteristic
17C2×#13063259C2211yescharacteristic
18C2×#13063250—21no—
19C2×#13063247—21no—
20#14582801—21no—
21#14582704—22no—
22#14582701—22no—
23C22×C16×C43C2211yescharacteristic
24C22×C16×C43C2211yescharacteristic
25C2×C4×C8×C43C2211yescharacteristic
26C22×Dic86—21no—
27C22×D172—21no—
28C2×Dic172—21no—
29C2×Dic172—21no—
30C2×Dic172—21no—
31C2×Dic172C2×C412yes—
32C2×Dic172D412yes—
33C2×Dic172D412yes—
34C2×D344—21no—
35C2×D344—21no—
36C2×D344—21no—
37C2×D344—21no—
38C2×D344—21no—
39C2×D344C2×C412yes—
40C4×Dic86—24no—
41C4×Dic86—42no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—21no—
44C2×Dic43⋊C4—41no—
45C2×(C2×D43)⋊C4—41no—
46C2×(C2×D43)⋊C4—41no—
47C2×C4×Dic43—41no—
48#13063270—28no—
49#13063259—21no—
50#13063259—21no—
51#13063259—21no—
52#13063259D412yes—
53#13063250—24no—
54#13063247—42no—
55C22×C8×C43D411yescharacteristic
56C22×C8×C43C2311yescharacteristic
57C2×C42×C43D411yescharacteristic
58C2×C16×C43—21no—
59C2×C16×C43—21no—
60C2×C16×C43—21no—
61C2×C16×C43—21no—
62C2×C16×C43—21no—
63C2×C16×C43C2×C412yes—
64C4×C8×C43—21no—
65C4×C8×C43—21no—
66C23×D43—41no—
67C22×C4×C43D811yescharacteristic
68C22×C4×C43D811yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—41no—
71C22×Dic43—41no—
72C22×Dic43—41no—
73C2×D172—22no—
74C2×D172—41no—
75C2×D172—41no—
76C2×D172—41no—
77C2×D172—41no—
78C2×D172—41no—
79C2×Dic86—22no—
80C2×Dic86—22no—
81C2×Dic86—22no—
82C2×Dic86—41no—
83C2×Dic86—41no—
84C2×Dic86—41no—
85C2×C8×C43—21no—
86C2×C8×C43—21no—
87C2×C8×C43—21no—
88C2×C8×C43C22×C411yescharacteristic
89C2×C8×C43C2×D411yescharacteristic
90C2×C8×C43C2×D411yescharacteristic
91C2×C8×C43C2×D411yescharacteristic
92C2×C8×C43#4111yescharacteristic
93C2×C8×C43#4111yescharacteristic
94C42×C43—21no—
95C42×C43—21no—
96(C2×D43)⋊C4—82no—
97(C2×D43)⋊C4—82no—
98C4⋊Dic43—22no—
99C4⋊Dic43—41no—
100C4⋊Dic43—41no—
101C4⋊Dic43—41no—
102Dic43⋊C4—44no—
103C4×Dic43—44no—
104Dic172—22no—
105Dic172—22no—
106Dic172—22no—
107Dic172C22⋊C414yescomplemented
108D344—22no—
109D344—22no—
110D344—41no—
111D344—41no—
112C16×C43—22no—
113C16×C43—41no—
114C23×C43C2×D811yescharacteristic
115C22×D43—42no—
116C22×D43—81no—
117C22×D43—81no—
118C22×D43—81no—
119C22×D43—81no—
120C22×D43—81no—
121C22×D43—81no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43SD3212yescomplemented
128C2×C4×C43C4×D411yescharacteristic
129C2×C4×C43#12011yescharacteristic
130C2×C4×C43#12111yescharacteristic
131C2×C4×C43#13511yescharacteristic
132C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
134C2×Dic43—42no—
135C2×Dic43—42no—
136C2×Dic43—42no—
137C2×Dic43—42no—
138C2×Dic43—81no—
139C2×Dic43—81no—
140C2×Dic43—81no—
141C2×Dic43—81no—
142C2×Dic43—81no—
143D172—42no—
144D172—42no—
145D172—81no—
146D172—81no—
147Dic86—24no—
148Dic86—42no—
149Dic86—42no—
150Dic86—42no—
151C8×C43—41no—
152C8×C43C2×C22⋊C411yescharacteristic
153C8×C43C4×D411yescharacteristic
154C8×C43#12111yescharacteristic
155C8×C43#12311yescharacteristic
156#13013—431nomaximal, Sylow
157C22×C43C4×D811yescharacteristic
158C22×C43#44711yescharacteristic
159C22×C43#45911yescharacteristic
160C22×C43C2×SD3211yescharacteristic
161C22×C43#50811yescharacteristic
162C22×C43#50911yescharacteristic
163C22×C43#51011yescharacteristic
164C2×D43—82no—
165C2×D43—82no—
166C2×D43—82no—
167C2×D43—161no—
168C2×D43—161no—
169C2×D43—161no—
170C2×D43—161no—
171C4×C43—22no—
172C4×C43—41no—
173C4×C43#38611yescharacteristic
174C4×C43#44211yescharacteristic
175C4×C43#44911yescharacteristic
176C4×C43#46311yescharacteristic
177Dic43—44no—
178Dic43—82no—
179Dic43—161no—
180C22×SD32—431no—
181C2×C4×Q16—431no—
182C2×#358—431no—
183C2×#357—431no—
184#1970—431no—
185#1380—431no—
186#1374D4311yescharacteristic, complemented
187C2×C43#187911yescharacteristic
188C2×C43C4×SD3211yescharacteristic
189C2×C43#217511yescharacteristic
190C2×C43#218511yescharacteristic
191C2×C43#218611yescharacteristic
192C2×C43#220711yescharacteristic
193C2×C43#221111yescharacteristic
194D43—162no—
195C22×Q16—431no—
196C22×D8—431no—
197C2×C4×Q8—861no—
198C2×SD32—434no—
199C2×SD32—862no—
200C2×SD32—862no—
201C22×C16C2×D4311yescharacteristic
202C22×C16C2×D4311yescharacteristic
203C4×Q16—862no—
204C4×Q16—862no—
205C2×#107—431no—
206C2×#107—431no—
207C2×#103—861no—
208C2×#102—861no—
209C2×C4×C8C2×D4311yescharacteristic
210#390—861no—
211#358—862no—
212#357—862no—
213C43#1301311yescharacteristic, complemented, Sylow
214C22×Q8—861no—
215C22×D4—861no—
216C2×Q16—432no—
217C2×Q16—432no—
218C2×Q16—432no—
219C2×Q16—861no—
220C2×Q16—861no—
221C2×Q16—861no—
222C2×D8—432no—
223C2×D8—861no—
224C2×D8—861no—
225C2×D8—861no—
226C2×D8—861no—
227C2×D8—861no—
228C22×C8D17211yescharacteristic
229C22×C8C22×D4311yescharacteristic
230C4×Q8—864no—
231C4×Q8—1722no—
232C2×C4⋊C4—861no—
233C2×C4⋊C4—861no—
234C2×C4⋊C4—1721no—
235C2×C22⋊C4—1721no—
236C2×C22⋊C4—1721no—
237C2×C42—1721no—
238C2×C42D17211yescharacteristic
239SD32—868no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16—21no—
245C2×C16C4×D4312yes—
246#107—432no—
247#107—861no—
248#107—861no—
249#107—861no—
250#103—864no—
251#102—1722no—
252C4×C8—21no—
253C4×C8—21no—
254C24—1721no—
255C2×Q8—862no—
256C2×Q8—862no—
257C2×Q8—862no—
258C2×Q8—1721no—
259C2×Q8—1721no—
260C2×Q8—1721no—
261C2×D4—862no—
262C2×D4—1721no—
263C2×D4—1721no—
264C2×D4—1721no—
265C2×D4—1721no—
266C2×D4—1721no—
267C22×C4—1721no—
268C22×C4—1721no—
269C22×C4—1721no—
270C22×C4D34411yescharacteristic
271C22×C4D34411yescharacteristic
272C22×C4C2×D17211yescharacteristic
273Q16—434no—
274Q16—862no—
275Q16—862no—
276Q16—862no—
277D8—862no—
278D8—862no—
279D8—1721no—
280D8—1721no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8C2×C4×D4311yescharacteristic
285C2×C8#1062189811yescharacteristic
286C2×C8D4×D4311yescharacteristic
287C2×C8D4×D4311yescharacteristic
288C2×C8D4×D4311yescharacteristic
289C2×C8#1062190211yescharacteristic
290C4⋊C4—862no—
291C4⋊C4—1724no—
292C4⋊C4—1721no—
293C4⋊C4—1721no—
294C4⋊C4—1721no—
295C22⋊C4—3442no—
296C22⋊C4—3442no—
297C42—21no—
298C42—21no—
299C42—1724no—
300C16—22no—
301C16—41no—
302C23—3441no—
303C23—3441no—
304C23—3441no—
305C23—3441no—
306C23—3441no—
307C23—3441no—
308C23—1722no—
309C23C2×D34411yescharacteristic
310Q8—864no—
311Q8—1722no—
312Q8—1722no—
313Q8—1722no—
314D4—3441no—
315D4—3441no—
316D4—1722no—
317D4—1722no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—3441no—
324C2×C4—3441no—
325C2×C4—3441no—
326C2×C4—3441no—
327C2×C4—3441no—
328C2×C4—1722no—
329C2×C4—1722no—
330C2×C4—1722no—
331C2×C4—1722no—
332C2×C4#1306327012yescomplemented
333C2×C4C4×D17211yescharacteristic
334C2×C4#1306329511yescharacteristic
335C2×C4#1306330011yescharacteristic
336C2×C4#1306334711yescharacteristic
337C2×C4#1306335311yescharacteristic
338C2×C4#1306335311yescharacteristic
339C8—41no—
340C8C22⋊C4×D4311yescharacteristic
341C8#1306328711yescharacteristic
342C8#1306329811yescharacteristic
343C8#1306331011yescharacteristic
344C22—3442no—
345C22—3442no—
346C22—3442no—
347C22—6881no—
348C22—6881no—
349C22—6881no—
350C22—6881no—
351C22C4×D34411yescharacteristic
352C22#1458303511yescharacteristic
353C22#1458309511yescharacteristic
354C22C2×#1306327011yescharacteristic
355C22#1458333111yescharacteristic
356C22#1458333711yescharacteristic
357C22#1458334211yescharacteristic
358C4—22no—
359C4—41no—
360C4—3442no—
361C4—1724no—
362C4—6881no—
363C4#1458277711yescharacteristic
364C4#1458301211yescharacteristic
365C4#1458304611yescharacteristic
366C4#1458311511yescharacteristic
367C2—6882no—
368C2#1913494211yescharacteristic
369C2C4×#1306327011yescharacteristic
370C2#1913646111yescharacteristic
371C2#1913651411yescharacteristic
372C2#1913652011yescharacteristic
373C2#1913663611yescharacteristic
374C2#1913665811yescharacteristic
subgroupG/H
centerC23C2×D344
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#1374C2
socleC23×C43C2×D8
prime radicalC22×D344C22
cosocleC22×C8×C43C23
hypercenter#1374D43
hypocenterC43#13013
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1374

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic172C2semidirect
3. C2×#14582704C2semidirect
6. #19132687C2semidirect
7. C43×#1374C2semidirect
13. C2×#13063270C4semidirect
107. Dic172C22⋊C4semidirect
127. C2×C4×C43SD32semidirect
186. #1374D43semidirect
213. C43#13013semidirect
332. C2×C4#13063270semidirect

Maximal subgroups

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

subgroupindex
C22×#130632702
C2×C4×Dic1722
C2×#145827042
C2×#145827012
#191354612
#191326872
C43×#13742
#1301343