Finite Group Databasebeta

← #24993930

Subgroups — #24993930

Order 11008.

582 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143014C211yesmaximal, characteristic, complemented
2#19140282C211yesmaximal, characteristic
3#19133194C212yesmaximal, complemented
4#19132487C212yesmaximal, complemented
5C43×#1464C211yesmaximal, characteristic, complemented
6C22×#10621877—21no—
7C2×#13063313C2211yescharacteristic
8#14582855—24no—
9C4×#10621877—21no—
10C4×#10621877C2212yes—
11#14582819C411yescharacteristic
12#14582816C411yescharacteristic
13#14582811C411yescharacteristic
14#14582808C411yescharacteristic
15#14582799—21no—
16#14582790—21no—
17#14582789—21no—
18#14582778—21no—
19#14582745C2211yescharacteristic
20#14582638—24no—
21C2×#117×C43C2211yescharacteristic
22C43×#432C2212yes—
23C43×#324—21no—
24C43×#323—21no—
25C22×Dic86C2×C411yescharacteristic
26C22×D172C2×C411yescharacteristic
27C22×C22⋊D43—21no—
28C2×#10621877—22no—
29C2×#10621877—24no—
30C2×#10621877—24no—
31C2×#10621877—22no—
32C22×C43⋊C8—22no—
33#13063313—22no—
34#13063313—22no—
35C2×Dic43⋊C4—21no—
36C2×C22⋊Dic43—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×C4×Dic43—21no—
43#13063236—22no—
44#13063236D414yescomplemented
45C4×C43⋊C8—22no—
46C4×C43⋊C8—22no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95C2×C411yescharacteristic
51C43⋊#95C2×C411yescharacteristic
52C23×C4×C43D411yescharacteristic
53#117×C43—22no—
54#117×C43—22no—
55C2×C4⋊C4×C43C2×C411yescharacteristic
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C22⋊C4×C43C2×C411yescharacteristic
58C2×C22⋊C4×C43D411yescharacteristic
59C2×C42×C43D411yescharacteristic
60C2×C42×C43C2311yescharacteristic
61C4⋊C8×C43—22no—
62C22⋊C8×C43—22no—
63#97×C43—22no—
64C24×C43C22⋊C411yescharacteristic
65C23×D43—21no—
66C22×C4×C43—22no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—22no—
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22⋊C411yescharacteristic
73C22×C4×C43C22×C411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C2×C22⋊D43—42no—
77C2×C22⋊D43—42no—
78C2×C22⋊D43—81no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C2×D172—22no—
83C2×D172—81no—
84C2×Dic86—22no—
85C2×Dic86—81no—
86C2×C8×C43—42no—
87C4⋊C4×C43—22no—
88C4⋊C4×C43—22no—
89C22⋊C4×C43—22no—
90C22⋊C4×C43—22no—
91C42×C43—21no—
92C42×C43—21no—
93C42×C43C2×D412yes—
94C42×C43#4112yes—
95C22⋊Dic43—81no—
96(C2×D43)⋊C4—42no—
97(C2×D43)⋊C4—42no—
98(C2×D43)⋊C4—41no—
99(C2×D43)⋊C4—42no—
100(C2×D43)⋊C4—41no—
101(C2×D43)⋊C4—81no—
102Dic43⋊C4—81no—
103C4×Dic43—42no—
104#10621877—28no—
105#10621877—24no—
106#10621877—24no—
107C2×C43⋊C8—28no—
108C2×C43⋊C8—24no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43#10412yes—
114C23×C43C2×C22⋊C411yescharacteristic
115C22×D43—41no—
116C22×D43—41no—
117C22×D43—41no—
118C22×D43—41no—
119C22×D43—41no—
120C22×D43—41no—
121C22×D43—41no—
122C2×C4×C43—22no—
123C2×C4×C43—22no—
124C2×C4×C43—24no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43#10412yes—
136C2×C4×C43C4×D412yes—
137C2×C4×C43#12011yescharacteristic
138C2×C4×C43#12112yes—
139C2×C4×C43#12311yescharacteristic
140C22⋊D43—84no—
141C2×Dic43—22no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150D172—82no—
151Dic86—82no—
152C8×C43—82no—
153C43⋊C8—28no—
154#9387—431nomaximal, Sylow
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—22no—
158C22×C43—42no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—81no—
162C22×C43#38611yescharacteristic
163C22×C43C2×#10411yescharacteristic
164C22×C43C2×#10411yescharacteristic
165C2×D43—81no—
166C2×D43—81no—
167C2×D43—81no—
168C2×D43—81no—
169C2×D43—81no—
170C2×D43—81no—
171C2×D43—81no—
172C4×C43—22no—
173C4×C43—21no—
174C4×C43—22no—
175C4×C43—21no—
176C4×C43—22no—
177C4×C43—41no—
178C4×C43—41no—
179Dic43—42no—
180Dic43—81no—
181Dic43—81no—
182#2873—431no—
183#2610—431no—
184#1527—432no—
185#1464D4311yescharacteristic, complemented
186#1300—432no—
187C2×C43—21no—
188C2×C43—21no—
189C2×C43—42no—
190C2×C43#188411yescharacteristic
191C2×C43#189611yescharacteristic
192C2×C43#191411yescharacteristic
193D43—161no—
194C22×M16—861no—
195C2×#124—431no—
196C2×#117C2×D4311yescharacteristic
197#432C2×D4312yes—
198#405—864no—
199C4×M16—432no—
200C4×M16—861no—
201#395—431no—
202#394—431no—
203#393—431no—
204#392—431no—
205#390—861no—
206#388—861no—
207#388—861no—
208#386—861no—
209#376—431no—
210#329—864no—
211#324—21no—
212#323—21no—
213C43#938711yescharacteristic, complemented, Sylow
214C22×Q8—431no—
215C22×D4—431no—
216C22×D4—861no—
217C23×C4D17211yescharacteristic
218C2×M16—862no—
219C2×M16—864no—
220C2×M16—864no—
221C2×M16—862no—
222C22×C8—862no—
223#124—862no—
224#124—862no—
225#117—22no—
226#117—22no—
227C2×C4⋊C4—861no—
228C2×C4⋊C4C4×D4311yescharacteristic
229C2×C4⋊C4C22⋊D4311yescharacteristic
230C2×C22⋊C4—861no—
231C2×C22⋊C4—861no—
232C2×C22⋊C4—861no—
233C2×C22⋊C4—861no—
234C2×C22⋊C4—861no—
235C2×C22⋊C4—861no—
236C2×C22⋊C4C4×D4311yescharacteristic
237C2×C22⋊C4C22⋊D4311yescharacteristic
238C2×C42—861no—
239C2×C42D17211yescharacteristic
240C2×C42C22×D4311yescharacteristic
241C4⋊C8—22no—
242C22⋊C8—22no—
243#97—22no—
244#97—434no—
245#97—862no—
246C4×C8—862no—
247C4×C8—862no—
248#95—431no—
249#95—431no—
250#95—861no—
251#95—861no—
252#95—861no—
253C24—861no—
254C24(C2×D43)⋊C411yescharacteristic
255C2×Q8—862no—
256C2×Q8—3441no—
257C2×D4—862no—
258C2×D4—3441no—
259C2×D4—3441no—
260C2×D4—1722no—
261C2×D4—1722no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4(C2×D43)⋊C411yescharacteristic
270C22×C4(C2×D43)⋊C411yescharacteristic
271C22×C4(C2×D43)⋊C411yescharacteristic
272C22×C4C2×C4×D4311yescharacteristic
273C22×C4C2×D17211yescharacteristic
274C22×C4C2×C22⋊D4311yescharacteristic
275M16—868no—
276M16—864no—
277M16—864no—
278C2×C8—42no—
279C2×C8—868no—
280C2×C8—864no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—3441no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—3441no—
287C22⋊C4—3441no—
288C22⋊C4—1722no—
289C22⋊C4—1722no—
290C22⋊C4—1721no—
291C22⋊C4—1722no—
292C22⋊C4—1721no—
293C42—21no—
294C42—21no—
295C42—1722no—
296C42D4×D4312yes—
297C42#1062190012yes—
298C23—21no—
299C23—21no—
300C23—41no—
301C23—41no—
302C23—1721no—
303C23—1721no—
304C23—1721no—
305C23—1721no—
306C23—1721no—
307C23—1721no—
308C23—1721no—
309C23#1306325112yes—
310C23C2×(C2×D43)⋊C411yescharacteristic
311Q8—3442no—
312D4—3442no—
313D4—3444no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—862no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4—1721no—
336C2×C4#1306325112yes—
337C2×C4(C22⋊D43)⋊C412yes—
338C2×C4#1306329511yescharacteristic
339C2×C4#1306329712yes—
340C2×C4#1306330911yescharacteristic
341C8—82no—
342C8—868no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—42no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—3441no—
351C22—3441no—
352C22—3441no—
353C22—3441no—
354C22—3441no—
355C22—3441no—
356C22—3441no—
357C22#1458277611yescharacteristic
358C22C2×#1306325111yescharacteristic
359C22C2×#1306325111yescharacteristic
360C4—22no—
361C4—21no—
362C4—22no—
363C4—21no—
364C4—22no—
365C4—41no—
366C4—41no—
367C4—3441no—
368C4—3441no—
369C4—1722no—
370C2—21no—
371C2—21no—
372C2—42no—
373C2—6881no—
374C2#1913497611yescharacteristic
375C2#1913503611yescharacteristic
376C2#1913514011yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1464C2
socleC22×C43#386
prime radical#14582808C4
cosocleC2×C42×C43C23
hypercenter#1464D43
hypocenterC43#9387
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
1. #19143014C2semidirect
3. #19133194C2semidirect
4. #19132487C2semidirect
5. C43×#1464C2semidirect
44. #13063236D4semidirect
185. #1464D43semidirect
213. C43#9387semidirect

Maximal subgroups

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

subgroupindex
#191430142
#191402822
#191331942
#191324872
C43×#14642
#938743