Finite Group Databasebeta

← #25015764

Subgroups — #25015764

Order 11008.

446 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583137C211yesmaximal, characteristic
2C2×#14582726C211yesmaximal, characteristic, complemented
3C2×#14582703C211yesmaximal, characteristic, complemented
4C2×(C2×D43)⋊C16C211yesmaximal, characteristic
5#19134621C211yesmaximal, characteristic
6#19132687C211yesmaximal, characteristic, complemented
7C2×C43×#358C211yesmaximal, characteristic, complemented
8C22×C8×D43C2211yescharacteristic
9C2×#13063301—21no—
10C22×C43⋊C16C2211yescharacteristic
11#14583137—22no—
12#14583137—22no—
13C2×#13063259C2211yescharacteristic
14C2×#13063259C2211yescharacteristic
15C2×#13063249—21no—
16#14582756—21no—
17#14582726—22no—
18#14582703—22no—
19(C2×D43)⋊C16—22no—
20#14582661—21no—
21C22×Q16×C43C2211yescharacteristic
22C22×C16×C43C2211yescharacteristic
23C2×#107×C43C2211yescharacteristic
24C43×#358—22no—
25C22×C4×D43D411yescharacteristic
26C22×C43⋊C8D411yescharacteristic
27C2×C8×D43—21no—
28C2×C8×D43—21no—
29C2×C8×D43—21no—
30C2×C8×D43—21no—
31C2×C8×D43—21no—
32C2×C8×D43—21no—
33#13063301—24no—
34#13063301—42no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43—21no—
37C2×Dic43⋊C4—41no—
38C2×(C2×D43)⋊C4—41no—
39C2×(C2×D43)⋊C4—41no—
40C2×C43⋊C16—21no—
41C2×C43⋊C16—21no—
42C2×C43⋊C16D412yes—
43#13063259—21no—
44#13063259—21no—
45#13063259—21no—
46#13063259D412yes—
47#13063249—24no—
48C43⋊#95—41no—
49C22×Q8×C43—21no—
50C2×Q16×C43—21no—
51C2×Q16×C43—21no—
52C2×Q16×C43—21no—
53C2×Q16×C43—21no—
54C2×Q16×C43—21no—
55C2×Q16×C43D412yes—
56C22×C8×C43C2311yescharacteristic
57C2×C4⋊C4×C43—21no—
58C2×C16×C43—21no—
59C2×C16×C43—21no—
60C2×C16×C43—21no—
61#107×C43—21no—
62#107×C43—21no—
63C23×D43D811yescharacteristic
64C2×Q8×C43—22no—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C2×Q8×C43—41no—
69C2×Q8×C43—41no—
70C22×C4×C43—41no—
71C22×C4×C43—41no—
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43—41no—
74C22×Dic43—41no—
75C22×Dic43D811yescharacteristic
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82Q16×C43—22no—
83Q16×C43—22no—
84Q16×C43—41no—
85Q16×C43—41no—
86C2×C8×C43C2×D411yescharacteristic
87C2×C8×C43C2×D411yescharacteristic
88C2×C8×C43C2×D411yescharacteristic
89C2×C8×C43#4111yescharacteristic
90C2×C8×C43#4111yescharacteristic
91C2×C8×C43#4111yescharacteristic
92C4⋊C4×C43—41no—
93C4⋊C4×C43—41no—
94(C2×D43)⋊C4—44no—
95(C2×D43)⋊C4—82no—
96C4⋊Dic43—22no—
97C4⋊Dic43—41no—
98C4⋊Dic43—41no—
99C4⋊Dic43—41no—
100Dic43⋊C4—44no—
101C2×C43⋊C8—21no—
102C2×C43⋊C8—21no—
103C2×C43⋊C8—21no—
104C8×D43—41no—
105C8×D43—41no—
106C8×D43—41no—
107C8×D43—41no—
108C16×C43—41no—
109C43⋊C16—22no—
110C23×C43C2×D811yescharacteristic
111C22×D43—21no—
112C22×D43—21no—
113C22×D43—21no—
114C22×D43—21no—
115C22×D43—21no—
116C22×D43—21no—
117C22×D43SD3212yes—
118Q8×C43—42no—
119Q8×C43—42no—
120Q8×C43—81no—
121Q8×C43—81no—
122C2×C4×C43—42no—
123C2×C4×C43—81no—
124C2×C4×C43—81no—
125C2×C4×C43—81no—
126C2×C4×C43—81no—
127C2×C4×C43—81no—
128C2×C4×C43#12011yescharacteristic
129C2×C4×C43#12111yescharacteristic
130C2×C4×C43#12311yescharacteristic
131C2×C4×C43#13511yescharacteristic
132C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C43#13711yescharacteristic
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—42no—
138C2×Dic43—81no—
139C2×Dic43—81no—
140C2×Dic43—81no—
141C2×Dic43—81no—
142C2×Dic43—81no—
143C4×D43—41no—
144C4×D43—41no—
145C4×D43—41no—
146C4×D43—41no—
147C8×C43#12111yescharacteristic
148C8×C43#12111yescharacteristic
149C8×C43#12311yescharacteristic
150C8×C43#12411yescharacteristic
151C43⋊C8—41no—
152#13382—431nomaximal, Sylow
153C22×C43#44711yescharacteristic
154C22×C43#46611yescharacteristic
155C22×C43#48011yescharacteristic
156C22×C43C2×SD3211yescharacteristic
157C22×C43#50811yescharacteristic
158C22×C43#51011yescharacteristic
159C22×C43#51011yescharacteristic
160C2×D43—22no—
161C2×D43—22no—
162C2×D43—22no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—41no—
167C4×C43—82no—
168C4×C43—161no—
169C4×C43#39411yescharacteristic
170C4×C43#45211yescharacteristic
171C4×C43#46811yescharacteristic
172C4×C43#48211yescharacteristic
173Dic43—41no—
174Dic43—82no—
175Dic43—161no—
176C2×#467—431no—
177C2×#367—431no—
178C2×#358—431no—
179C2×#358D4311yescharacteristic, complemented
180C2×C22⋊C16—431no—
181#1808—431no—
182#1380—431no—
183C2×C43#203311yescharacteristic
184C2×C43#218511yescharacteristic
185C2×C43#218911yescharacteristic
186C2×C43#221711yescharacteristic
187C2×C43#221911yescharacteristic
188C2×C43#223511yescharacteristic
189C2×C43#223711yescharacteristic
190D43—42no—
191C22×Q16C2×D4311yescharacteristic
192C23×C8—431no—
193C2×C22⋊Q8—861no—
194C22×C16—431no—
195C22×C16C2×D4311yescharacteristic
196#467—862no—
197#467—862no—
198C2×#107—431no—
199C2×#107—431no—
200C2×#107C2×D4311yescharacteristic
201C2×#103—861no—
202#380—861no—
203#367—862no—
204#358—22no—
205#358—862no—
206C22⋊C16—862no—
207#340—861no—
208C43#1338211yescharacteristic, complemented, Sylow
209C22×Q8—21no—
210C23×C4—431no—
211C2×Q16—21no—
212C2×Q16—21no—
213C2×Q16—21no—
214C2×Q16—21no—
215C2×Q16—21no—
216C2×Q16C22⋊D4312yes—
217C22×C8—431no—
218C22×C8—861no—
219C22×C8—861no—
220C22×C8—861no—
221C22×C8—861no—
222C22×C8—861no—
223C22×C8—861no—
224C22×C8C22×D4311yescharacteristic
225C22⋊Q8—864no—
226C22⋊Q8—1722no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—861no—
229C2×C4⋊C4—861no—
230C2×C4⋊C4—1721no—
231C2×C22⋊C4—1721no—
232C2×C22⋊C4—1721no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16—21no—
236C2×C16—432no—
237C2×C16—861no—
238C2×C16—861no—
239#107—21no—
240#107—21no—
241#107—432no—
242#107—861no—
243#107—861no—
244#107—861no—
245#103—864no—
246#95—1721no—
247C24—431no—
248C2×Q8—22no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—431no—
257C22×C4—861no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4—1721no—
264C22×C4—1721no—
265C22×C4D4×D4311yescharacteristic
266Q16—22no—
267Q16—22no—
268Q16—41no—
269Q16—41no—
270C2×C8—861no—
271C2×C8—861no—
272C2×C8—861no—
273C2×C8—1721no—
274C2×C8—1721no—
275C2×C8—1721no—
276C2×C8—1721no—
277C2×C8#1062189811yescharacteristic
278C2×C8#1062189811yescharacteristic
279C2×C8D4×D4311yescharacteristic
280C2×C8D4×D4311yescharacteristic
281C2×C8#1062190011yescharacteristic
282C2×C8C2×C22⋊D4311yescharacteristic
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—862no—
286C4⋊C4—1724no—
287C4⋊C4—1721no—
288C4⋊C4—1721no—
289C4⋊C4—1721no—
290C22⋊C4—3442no—
291C22⋊C4—1724no—
292C16—41no—
293C16—862no—
294C23—432no—
295C23—861no—
296C23—861no—
297C23—861no—
298C23—861no—
299C23—861no—
300C23—861no—
301C23D8×D4311yescharacteristic
302Q8—42no—
303Q8—42no—
304Q8—81no—
305Q8—81no—
306C2×C4—42no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—861no—
315C2×C4—3441no—
316C2×C4—3441no—
317C2×C4—3441no—
318C2×C4—3441no—
319C2×C4—3441no—
320C2×C4—1722no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4#1306329311yescharacteristic
326C2×C4#1306329811yescharacteristic
327C2×C4#1306330711yescharacteristic
328C2×C4#1306334611yescharacteristic
329C2×C4#1306334911yescharacteristic
330C2×C4#1306335411yescharacteristic
331C8—1721no—
332C8#1306329711yescharacteristic
333C8#1306329811yescharacteristic
334C8#1306330811yescharacteristic
335C8#1306331111yescharacteristic
336C22—862no—
337C22—862no—
338C22—862no—
339C22—1721no—
340C22—1721no—
341C22—1721no—
342C22—1721no—
343C22#1458303111yescharacteristic
344C22#1458313411yescharacteristic
345C22#1458321111yescharacteristic
346C22SD32×D4311yescharacteristic
347C22#1458333211yescharacteristic
348C22#1458333811yescharacteristic
349C22#1458334111yescharacteristic
350C4—82no—
351C4—161no—
352C4—3442no—
353C4—1721no—
354C4—6881no—
355C4#1458281411yescharacteristic
356C4#1458305811yescharacteristic
357C4#1458314411yescharacteristic
358C4#1458322211yescharacteristic
359C2—1722no—
360C2#1913577511yescharacteristic
361C2#1913651011yescharacteristic
362C2#1913653411yescharacteristic
363C2#1913669411yescharacteristic
364C2#1913670211yescharacteristic
365C2#1913679111yescharacteristic
366C2#1913680211yescharacteristic
subgroupG/H
centerC23D8×D43
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC2×C43×#358C2
socleC23×C43C2×D8
prime radicalC23×D43D8
hypercenterC2×#358D43
hypocenterC43#13382
LCSG ▷ C22×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×#14582726C2semidirect
3. C2×#14582703C2semidirect
6. #19132687C2semidirect
7. C2×C43×#358C2semidirect
179. C2×#358D43semidirect
208. C43#13382semidirect

Maximal subgroups

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

subgroupindex
C2×#145831372
C2×#145827262
C2×#145827032
C2×(C2×D43)⋊C162
#191346212
#191326872
C2×C43×#3582
#1338243