Finite Group Databasebeta

← #25013652

Subgroups — #25013652

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063266C211yesmaximal, characteristic
2C2×D8×Dic43C211yesmaximal, characteristic, complemented
3C2×#14582701C211yesmaximal, characteristic, complemented
4#19135459C211yesmaximal, characteristic, complemented
5#19132686C211yesmaximal, characteristic, complemented
6#19132672C211yesmaximal, characteristic, complemented
7C2×C43×#357C211yesmaximal, characteristic, complemented
8C22×D344C2211yescharacteristic
9C2×D4×Dic43—21no—
10C2×#13063266—22no—
11C2×#13063266—22no—
12C2×#13063266C414yescomplemented
13C22×C43⋊C16C2211yescharacteristic
14D8×Dic43—22no—
15D8×Dic43—22no—
16C2×#13063259C2211yescharacteristic
17C2×#13063246—21no—
18C2×#13063245—21no—
19C2×C8×Dic43C2211yescharacteristic
20#14582800—21no—
21#14582701—22no—
22C22×D8×C43C2211yescharacteristic
23C22×C16×C43C2211yescharacteristic
24C2×#107×C43C2211yescharacteristic
25C43×#357—22no—
26C22×D172—21no—
27C23×Dic43—41no—
28C2×D344—21no—
29C2×D344—21no—
30C2×D344—21no—
31C2×D344—21no—
32C2×D344—21no—
33C2×D344C2×C412yescomplemented
34C22×C43⋊C8D411yescharacteristic
35D4×Dic43—24no—
36D4×Dic43—42no—
37C2×C4⋊Dic43—21no—
38C2×C22⋊Dic43—41no—
39C2×(C2×D43)⋊C4—41no—
40C2×(C2×D43)⋊C4—41no—
41C2×C4×Dic43D411yescharacteristic
42#13063266—28no—
43C2×C43⋊C16—21no—
44C2×C43⋊C16—21no—
45C2×C43⋊C16C2×C412yescomplemented
46#13063259—21no—
47#13063259D412yes—
48#13063246—24no—
49#13063245—42no—
50C8×Dic43—21no—
51C8×Dic43—21no—
52C22×D4×C43—21no—
53C2×D8×C43—21no—
54C2×D8×C43—21no—
55C2×D8×C43—21no—
56C2×D8×C43C2×C412yes—
57C2×D8×C43D412yes—
58C2×D8×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—
66C24×C43—41no—
67C23×D43—41no—
68C2×D4×C43—22no—
69C2×D4×C43—22no—
70C2×D4×C43—22no—
71C2×D4×C43—41no—
72C2×D4×C43—41no—
73C2×D4×C43—41no—
74C22×C4×C43—41no—
75C22×C4×C43C2×D411yescharacteristic
76C22×Dic43—44no—
77C22×Dic43—41no—
78C22×Dic43—82no—
79C22×Dic43—82no—
80C22×Dic43D811yescharacteristic
81C22×Dic43D811yescharacteristic
82C2×D172—22no—
83C2×D172—41no—
84C2×D172—41no—
85C2×D172—41no—
86C2×D172—41no—
87C2×D172—41no—
88D8×C43—22no—
89D8×C43—22no—
90D8×C43—22no—
91D8×C43C22⋊C414yescomplemented
92C2×C8×C43C22×C411yescharacteristic
93C2×C8×C43C2×D411yescharacteristic
94C2×C8×C43C2×D411yescharacteristic
95C2×C8×C43C2×D411yescharacteristic
96C2×C8×C43#4111yescharacteristic
97C2×C8×C43#4111yescharacteristic
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C22⋊Dic43—44no—
101(C2×D43)⋊C4—82no—
102(C2×D43)⋊C4—82no—
103C4⋊Dic43—22no—
104C4⋊Dic43—41no—
105C4×Dic43—21no—
106C4×Dic43—21no—
107C2×C43⋊C8—21no—
108C2×C43⋊C8—21no—
109C2×C43⋊C8—21no—
110D344—22no—
111D344—22no—
112D344—41no—
113D344—41no—
114C16×C43—41no—
115C43⋊C16—22no—
116C23×C43—42no—
117C23×C43—42no—
118C23×C43—42no—
119C23×C43—81no—
120C23×C43—81no—
121C23×C43—81no—
122C23×C43—81no—
123C23×C43C2×D811yescharacteristic
124C22×D43—42no—
125C22×D43—81no—
126C22×D43—81no—
127C22×D43—81no—
128C22×D43—81no—
129C22×D43—81no—
130C22×D43—81no—
131D4×C43—24no—
132D4×C43—42no—
133D4×C43—42no—
134D4×C43—42no—
135C2×C4×C43—81no—
136C2×C4×C43—81no—
137C2×C4×C43—81no—
138C2×C4×C43C4×D411yescharacteristic
139C2×C4×C43#12011yescharacteristic
140C2×C4×C43#12111yescharacteristic
141C2×C4×C43#13511yescharacteristic
142C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—42no—
150C2×Dic43—88no—
151C2×Dic43—81no—
152C2×Dic43—81no—
153C2×Dic43D1612yescomplemented
154D172—42no—
155D172—42no—
156D172—81no—
157D172—81no—
158C8×C43C2×C22⋊C411yescharacteristic
159C8×C43C4×D411yescharacteristic
160C8×C43#12111yescharacteristic
161C8×C43#12311yescharacteristic
162C43⋊C8—41no—
163#13012—431nomaximal, Sylow
164C22×C43—44no—
165C22×C43—82no—
166C22×C43—82no—
167C22×C43—82no—
168C22×C43—82no—
169C22×C43—82no—
170C22×C43—82no—
171C22×C43C4×D811yescharacteristic
172C22×C43#44711yescharacteristic
173C22×C43#45911yescharacteristic
174C22×C43C2×D1611yescharacteristic
175C22×C43#50811yescharacteristic
176C22×C43#50911yescharacteristic
177C22×C43#50911yescharacteristic
178C2×D43—82no—
179C2×D43—82no—
180C2×D43—82no—
181C2×D43—161no—
182C2×D43—161no—
183C2×D43—161no—
184C2×D43—161no—
185C4×C43—161no—
186C4×C43#38611yescharacteristic
187C4×C43#44211yescharacteristic
188C4×C43#44911yescharacteristic
189C4×C43#46311yescharacteristic
190Dic43—22no—
191Dic43—41no—
192Dic43—82no—
193C22×D16—431no—
194C2×C4×D8—431no—
195C2×#357—431no—
196C2×#357D4311yescharacteristic, complemented
197#1970—431no—
198#1380—431no—
199#1374—431no—
200C2×C43—84no—
201C2×C43#187911yescharacteristic
202C2×C43C4×D1611yescharacteristic
203C2×C43#217711yescharacteristic
204C2×C43#218411yescharacteristic
205C2×C43#218611yescharacteristic
206C2×C43#220611yescharacteristic
207C2×C43#221011yescharacteristic
208D43—162no—
209C22×D8—431no—
210C22×D8C2×D4311yescharacteristic
211C2×C4×D4—861no—
212C2×D16—434no—
213C2×D16—862no—
214C2×D16—862no—
215C22×C16—431no—
216C22×C16C2×D4311yescharacteristic
217C4×D8—862no—
218C4×D8—862no—
219C2×#107—431no—
220C2×#107C2×D4311yescharacteristic
221C2×#102—861no—
222C2×#102—861no—
223C2×C4×C8—431no—
224#390—861no—
225#357—22no—
226#357—862no—
227C43#1301211yescharacteristic, complemented, Sylow
228C22×D4—21no—
229C22×D4—861no—
230C23×C4—1721no—
231C2×D8—21no—
232C2×D8—21no—
233C2×D8—21no—
234C2×D8—432no—
235C2×D8—861no—
236C2×D8—861no—
237C2×D8—861no—
238C2×D8—861no—
239C2×D8—861no—
240C2×D8C4×D4312yes—
241C2×D8D17212yes—
242C2×D8C22⋊D4312yes—
243C22×C8—431no—
244C22×C8C22×D4311yescharacteristic
245C4×D4—864no—
246C4×D4—1722no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—861no—
249C2×C22⋊C4—1721no—
250C2×C22⋊C4—1721no—
251C2×C22⋊C4—1721no—
252C2×C42—431no—
253D16—868no—
254C2×C16—21no—
255C2×C16—21no—
256C2×C16—21no—
257C2×C16—432no—
258C2×C16—861no—
259C2×C16—861no—
260#107—21no—
261#107—21no—
262#107—432no—
263#107—861no—
264#102—864no—
265#102—1722no—
266C4×C8—861no—
267C4×C8—861no—
268C24—41no—
269C24—1721no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—862no—
277C2×D4—1721no—
278C2×D4—1721no—
279C2×D4—1721no—
280C2×D4—1721no—
281C2×D4—1721no—
282C22×C4—41no—
283C22×C4—431no—
284C22×C4—431no—
285C22×C4—3442no—
286C22×C4—3442no—
287C22×C4—1724no—
288C22×C4—1721no—
289C22×C4D4×D4311yescharacteristic
290D8—22no—
291D8—22no—
292D8—22no—
293D8—862no—
294D8—862no—
295D8—1721no—
296D8—1721no—
297D8(C2×D43)⋊C414yescomplemented
298C2×C8—861no—
299C2×C8—861no—
300C2×C8—861no—
301C2×C8C2×C4×D4311yescharacteristic
302C2×C8C2×D17211yescharacteristic
303C2×C8D4×D4311yescharacteristic
304C2×C8#1062190011yescharacteristic
305C2×C8#1062190011yescharacteristic
306C2×C8C2×C22⋊D4311yescharacteristic
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—862no—
310C4⋊C4—1721no—
311C22⋊C4—3442no—
312C22⋊C4—3442no—
313C22⋊C4—1724no—
314C42—861no—
315C42—861no—
316C16—41no—
317C16—862no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—81no—
324C23—81no—
325C23—3441no—
326C23—3441no—
327C23—3441no—
328C23—3441no—
329C23—3441no—
330C23—3441no—
331C23—1722no—
332C23D8×D4311yescharacteristic
333D4—24no—
334D4—42no—
335D4—42no—
336D4—42no—
337D4—3441no—
338D4—3441no—
339D4—1722no—
340D4—1722no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—432no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—861no—
350C2×C4—3448no—
351C2×C4—3441no—
352C2×C4—3441no—
353C2×C4—1722no—
354C2×C4(C22⋊D43)⋊C411yescharacteristic
355C2×C4#1306329511yescharacteristic
356C2×C4#1306329711yescharacteristic
357C2×C4#1306334611yescharacteristic
358C2×C4#1306334911yescharacteristic
359C2×C4#1306335211yescharacteristic
360C8—1721no—
361C8C2×(C2×D43)⋊C411yescharacteristic
362C8(C22⋊D43)⋊C411yescharacteristic
363C8#1306329711yescharacteristic
364C8#1306330911yescharacteristic
365C22—44no—
366C22—82no—
367C22—82no—
368C22—82no—
369C22—82no—
370C22—82no—
371C22—82no—
372C22—3442no—
373C22—3442no—
374C22—3442no—
375C22—6881no—
376C22—6881no—
377C22—6881no—
378C22—6881no—
379C22#1458297911yescharacteristic
380C22#1458303411yescharacteristic
381C22#1458309211yescharacteristic
382C22D16×D4311yescharacteristic
383C22#1458333011yescharacteristic
384C22#1458333311yescharacteristic
385C22#1458333611yescharacteristic
386C4—161no—
387C4—862no—
388C4—3442no—
389C4—1721no—
390C4#1458277611yescharacteristic
391C4#1458300811yescharacteristic
392C4#1458304511yescharacteristic
393C4#1458311611yescharacteristic
394C2—84no—
395C2—6882no—
396C2#1913494111yescharacteristic
397C2#1913643911yescharacteristic
398C2#1913646811yescharacteristic
399C2#1913650811yescharacteristic
400C2#1913651911yescharacteristic
401C2#1913662811yescharacteristic
402C2#1913665211yescharacteristic
subgroupG/H
centerC23D8×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#357C2
socleC23×C43C2×D8
prime radicalC22×#13063266C2
cosocleC22×C8×C43C23
hypercenterC2×#357D43
hypocenterC43#13012
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×D8×Dic43C2semidirect
3. C2×#14582701C2semidirect
4. #19135459C2semidirect
5. #19132686C2semidirect
6. #19132672C2semidirect
7. C2×C43×#357C2semidirect
12. C2×#13063266C4semidirect
33. C2×D344C2×C4semidirect
45. C2×C43⋊C16C2×C4semidirect
91. D8×C43C22⋊C4semidirect
153. C2×Dic43D16semidirect
196. C2×#357D43semidirect
227. C43#13012semidirect
297. D8(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130632662
C2×D8×Dic432
C2×#145827012
#191354592
#191326862
#191326722
C2×C43×#3572
#1301243