Finite Group Databasebeta

← #25013659

Subgroups — #25013659

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×#13063268C211yesmaximal, characteristic
2C2×Q16×Dic43C211yesmaximal, characteristic, complemented
3C2×#14582701C211yesmaximal, characteristic
4#19135459C211yesmaximal, characteristic
5#19132686C211yesmaximal, characteristic, complemented
6#19132672C211yesmaximal, characteristic, complemented
7C2×C43×#358C211yesmaximal, characteristic, complemented
8C22×D344C2211yescharacteristic
9C2×Q8×Dic43—21no—
10C2×#13063268—22no—
11C2×#13063268—22no—
12C2×#13063268C414yescomplemented
13C22×C43⋊C16C2211yescharacteristic
14Q16×Dic43—22no—
15Q16×Dic43—22no—
16C2×#13063259C2211yescharacteristic
17C2×#13063249—21no—
18C2×#13063245—21no—
19C2×C8×Dic43C2211yescharacteristic
20#14582800—21no—
21#14582701—22no—
22C22×Q16×C43C2211yescharacteristic
23C22×C16×C43C2211yescharacteristic
24C2×#107×C43C2211yescharacteristic
25C43×#358—22no—
26C22×D172—21no—
27C2×D344—21no—
28C2×D344—21no—
29C2×D344—21no—
30C2×D344—21no—
31C2×D344—21no—
32C2×D344C2×C412yes—
33C22×C43⋊C8D411yescharacteristic
34Q8×Dic43—24no—
35Q8×Dic43—42no—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43—41no—
38C2×(C2×D43)⋊C4—41no—
39C2×(C2×D43)⋊C4—41no—
40C2×C4×Dic43—41no—
41C2×C4×Dic43D411yescharacteristic
42#13063268—28no—
43C2×C43⋊C16—21no—
44C2×C43⋊C16—21no—
45C2×C43⋊C16C2×C412yes—
46#13063259—21no—
47#13063259D412yes—
48#13063249—24no—
49#13063245—42no—
50C8×Dic43—21no—
51C8×Dic43—21no—
52C22×Q8×C43—21no—
53C2×Q16×C43—21no—
54C2×Q16×C43—21no—
55C2×Q16×C43—21no—
56C2×Q16×C43C2×C412yes—
57C2×Q16×C43D412yes—
58C2×Q16×C43D412yes—
59C22×C8×C43C2311yescharacteristic
60C2×C4⋊C4×C43—21no—
61C2×C16×C43—21no—
62C2×C16×C43—21no—
63C2×C16×C43—21no—
64#107×C43—21no—
65#107×C43—21no—
66C23×D43—41no—
67C2×Q8×C43—22no—
68C2×Q8×C43—22no—
69C2×Q8×C43—22no—
70C2×Q8×C43—41no—
71C2×Q8×C43—41no—
72C2×Q8×C43—41no—
73C22×C4×C43—41no—
74C22×C4×C43—41no—
75C22×C4×C43C2×D411yescharacteristic
76C22×Dic43—41no—
77C22×Dic43D811yescharacteristic
78C22×Dic43D811yescharacteristic
79C2×D172—22no—
80C2×D172—41no—
81C2×D172—41no—
82C2×D172—41no—
83C2×D172—41no—
84C2×D172—41no—
85Q16×C43—22no—
86Q16×C43—22no—
87Q16×C43—22no—
88Q16×C43C22⋊C414yescomplemented
89C2×C8×C43C22×C411yescharacteristic
90C2×C8×C43C2×D411yescharacteristic
91C2×C8×C43C2×D411yescharacteristic
92C2×C8×C43C2×D411yescharacteristic
93C2×C8×C43#4111yescharacteristic
94C2×C8×C43#4111yescharacteristic
95C4⋊C4×C43—41no—
96C4⋊C4×C43—41no—
97(C2×D43)⋊C4—82no—
98(C2×D43)⋊C4—82no—
99C4⋊Dic43—22no—
100C4⋊Dic43—44no—
101C4⋊Dic43—41no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43—44no—
105C2×C43⋊C8—21no—
106C2×C43⋊C8—21no—
107C2×C43⋊C8—21no—
108D344—22no—
109D344—22no—
110D344—41no—
111D344—41no—
112C16×C43—41no—
113C43⋊C16—22no—
114C23×C43C2×D811yescharacteristic
115C22×D43—42no—
116C22×D43—81no—
117C22×D43—81no—
118C22×D43—81no—
119C22×D43—81no—
120C22×D43—81no—
121C22×D43—81no—
122Q8×C43—24no—
123Q8×C43—42no—
124Q8×C43—42no—
125Q8×C43—42no—
126C2×C4×C43—42no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43—81no—
130C2×C4×C43—81no—
131C2×C4×C43—81no—
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43#12011yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×C4×C43#13511yescharacteristic
136C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—42no—
144C2×Dic43—81no—
145C2×Dic43—81no—
146C2×Dic43SD3212yescomplemented
147D172—42no—
148D172—42no—
149D172—81no—
150D172—81no—
151C8×C43C2×C22⋊C411yescharacteristic
152C8×C43C4×D411yescharacteristic
153C8×C43#12111yescharacteristic
154C8×C43#12311yescharacteristic
155C43⋊C8—41no—
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—44no—
172C4×C43—161no—
173C4×C43#38611yescharacteristic
174C4×C43#44211yescharacteristic
175C4×C43#44911yescharacteristic
176C4×C43#46311yescharacteristic
177Dic43—22no—
178Dic43—41no—
179Dic43—82no—
180C22×SD32—431no—
181C2×C4×Q16—431no—
182C2×#358D4311yescharacteristic, complemented
183C2×#357—431no—
184#1970—431no—
185#1380—431no—
186#1374—431no—
187C2×C43#187911yescharacteristic
188C2×C43C4×SD3211yescharacteristic
189C2×C43#217511yescharacteristic
190C2×C43#218511yescharacteristic
191C2×C43#218611yescharacteristic
192C2×C43#220711yescharacteristic
193C2×C43#221111yescharacteristic
194D43—162no—
195C22×Q16C2×D4311yescharacteristic
196C22×D8—431no—
197C2×C4×Q8—861no—
198C2×SD32—434no—
199C2×SD32—862no—
200C2×SD32—862no—
201C22×C16—431no—
202C22×C16C2×D4311yescharacteristic
203C4×Q16—862no—
204C4×Q16—862no—
205C2×#107—431no—
206C2×#107C2×D4311yescharacteristic
207C2×#103—861no—
208C2×#102—861no—
209C2×C4×C8—431no—
210#390—861no—
211#358—22no—
212#357—862no—
213C43#1301311yescharacteristic, complemented, Sylow
214C22×Q8—21no—
215C22×D4—861no—
216C2×Q16—21no—
217C2×Q16—21no—
218C2×Q16—21no—
219C2×Q16C4×D4312yes—
220C2×Q16D17212yes—
221C2×Q16C22⋊D4312yes—
222C2×D8—432no—
223C2×D8—861no—
224C2×D8—861no—
225C2×D8—861no—
226C2×D8—861no—
227C2×D8—861no—
228C22×C8—431no—
229C22×C8C22×D4311yescharacteristic
230C4×Q8—864no—
231C4×Q8—1722no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—861no—
234C2×C4⋊C4—1721no—
235C2×C22⋊C4—1721no—
236C2×C22⋊C4—1721no—
237C2×C42—431no—
238C2×C42—1721no—
239SD32—868no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—21no—
243C2×C16—432no—
244C2×C16—861no—
245C2×C16—861no—
246#107—21no—
247#107—21no—
248#107—432no—
249#107—861no—
250#103—864no—
251#102—1722no—
252C4×C8—861no—
253C4×C8—861no—
254C24—1721no—
255C2×Q8—22no—
256C2×Q8—22no—
257C2×Q8—22no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×D4—862no—
262C2×D4—1721no—
263C2×D4—1721no—
264C2×D4—1721no—
265C2×D4—1721no—
266C2×D4—1721no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—431no—
270C22×C4—431no—
271C22×C4—1721no—
272C22×C4D4×D4311yescharacteristic
273Q16—22no—
274Q16—22no—
275Q16—22no—
276Q16(C2×D43)⋊C414yescomplemented
277D8—862no—
278D8—862no—
279D8—1721no—
280D8—1721no—
281C2×C8—861no—
282C2×C8—861no—
283C2×C8—861no—
284C2×C8C2×C4×D4311yescharacteristic
285C2×C8C2×D17211yescharacteristic
286C2×C8D4×D4311yescharacteristic
287C2×C8#1062190011yescharacteristic
288C2×C8#1062190011yescharacteristic
289C2×C8C2×C22⋊D4311yescharacteristic
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—862no—
293C4⋊C4—1724no—
294C4⋊C4—1721no—
295C22⋊C4—3442no—
296C22⋊C4—3442no—
297C42—861no—
298C42—861no—
299C42—1724no—
300C16—41no—
301C16—862no—
302C23—3441no—
303C23—3441no—
304C23—3441no—
305C23—3441no—
306C23—3441no—
307C23—3441no—
308C23—1722no—
309C23D8×D4311yescharacteristic
310Q8—24no—
311Q8—42no—
312Q8—42no—
313Q8—42no—
314D4—3441no—
315D4—3441no—
316D4—1722no—
317D4—1722no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—432no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—3441no—
331C2×C4—3441no—
332C2×C4—1722no—
333C2×C4(C22⋊D43)⋊C411yescharacteristic
334C2×C4#1306329511yescharacteristic
335C2×C4#1306329711yescharacteristic
336C2×C4#1306334611yescharacteristic
337C2×C4#1306334911yescharacteristic
338C2×C4#1306335211yescharacteristic
339C8—1721no—
340C8C2×(C2×D43)⋊C411yescharacteristic
341C8(C22⋊D43)⋊C411yescharacteristic
342C8#1306329711yescharacteristic
343C8#1306330911yescharacteristic
344C22—3442no—
345C22—3442no—
346C22—3442no—
347C22—6881no—
348C22—6881no—
349C22—6881no—
350C22—6881no—
351C22#1458297911yescharacteristic
352C22#1458303411yescharacteristic
353C22#1458309211yescharacteristic
354C22SD32×D4311yescharacteristic
355C22#1458333211yescharacteristic
356C22#1458333611yescharacteristic
357C22#1458334111yescharacteristic
358C4—44no—
359C4—161no—
360C4—862no—
361C4—3442no—
362C4—1721no—
363C4#1458277611yescharacteristic
364C4#1458300811yescharacteristic
365C4#1458304511yescharacteristic
366C4#1458311611yescharacteristic
367C2—6882no—
368C2#1913494111yescharacteristic
369C2#1913644411yescharacteristic
370C2#1913646211yescharacteristic
371C2#1913651311yescharacteristic
372C2#1913652111yescharacteristic
373C2#1913663311yescharacteristic
374C2#1913665911yescharacteristic
subgroupG/H
centerC23D8×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#358C2
socleC23×C43C2×D8
prime radicalC22×D344C22
cosocleC22×C8×C43C23
hypercenterC2×#358D43
hypocenterC43#13013
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. C2×Q16×Dic43C2semidirect
5. #19132686C2semidirect
6. #19132672C2semidirect
7. C2×C43×#358C2semidirect
12. C2×#13063268C4semidirect
88. Q16×C43C22⋊C4semidirect
146. C2×Dic43SD32semidirect
182. C2×#358D43semidirect
213. C43#13013semidirect
276. Q16(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130632682
C2×Q16×Dic432
C2×#145827012
#191354592
#191326862
#191326722
C2×C43×#3582
#1301343