Finite Group Databasebeta

← #24993933

Subgroups — #24993933

Order 11008.

582 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 111 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#19133193C212yesmaximal, complemented
3#19132929C211yesmaximal, characteristic, complemented
4#19132488C212yesmaximal, complemented
5C43×#2610C211yesmaximal, characteristic
6C22×#10621877—21no—
7#14582956C2212yes—
8#14582855—24no—
9C4×#10621877—21no—
10C4×#10621877C2212yes—
11#14582639—24no—
12#14582625—21no—
13#14582623—21no—
14C2×#124×C43C2211yescharacteristic
15C2×#117×C43C2211yescharacteristic
16C43×#395C411yescharacteristic
17C43×#394C411yescharacteristic
18C43×#393C411yescharacteristic
19C43×#392C411yescharacteristic
20C43×#390—21no—
21C43×#388—21no—
22C43×#388—21no—
23C43×#386—21no—
24C43×#376C2211yescharacteristic
25C2×#10621877—22no—
26C2×#10621877—24no—
27C2×#10621877—24no—
28C2×#10621877—22no—
29C22×C43⋊C8—22no—
30C4⋊(C43⋊C8)—22no—
31C22⋊(C43⋊C8)—22no—
32#13063236—22no—
33#13063236—22no—
34#13063236D414yescomplemented
35C4×C43⋊C8—22no—
36C4×C43⋊C8—22no—
37C22×Q8×C43C2×C411yescharacteristic
38C22×D4×C43—21no—
39C22×D4×C43C2×C411yescharacteristic
40C23×C4×C43D411yescharacteristic
41#124×C43—22no—
42#124×C43—22no—
43#117×C43—22no—
44#117×C43—22no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43C2×C411yescharacteristic
47C2×C4⋊C4×C43D411yescharacteristic
48C2×C22⋊C4×C43—21no—
49C2×C22⋊C4×C43—21no—
50C2×C22⋊C4×C43—21no—
51C2×C22⋊C4×C43—21no—
52C2×C22⋊C4×C43—21no—
53C2×C22⋊C4×C43—21no—
54C2×C22⋊C4×C43C2×C411yescharacteristic
55C2×C22⋊C4×C43D411yescharacteristic
56C2×C42×C43—21no—
57C2×C42×C43D411yescharacteristic
58C2×C42×C43C2311yescharacteristic
59#95×C43—21no—
60#95×C43—21no—
61#95×C43—21no—
62#95×C43C2×C411yescharacteristic
63#95×C43C2×C411yescharacteristic
64C24×C43—21no—
65C24×C43C22⋊C411yescharacteristic
66C2×Q8×C43—22no—
67C2×Q8×C43—81no—
68C2×D4×C43—22no—
69C2×D4×C43—42no—
70C2×D4×C43—42no—
71C2×D4×C43—81no—
72C2×D4×C43—81no—
73C22×C4×C43—22no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—22no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43C22⋊C411yescharacteristic
81C22×C4×C43C22⋊C411yescharacteristic
82C22×C4×C43C22⋊C411yescharacteristic
83C22×C4×C43C22×C411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C4⋊C4×C43—22no—
87C4⋊C4×C43—22no—
88C4⋊C4×C43—81no—
89C22⋊C4×C43—22no—
90C22⋊C4×C43—22no—
91C22⋊C4×C43—42no—
92C22⋊C4×C43—42no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—42no—
95C22⋊C4×C43—41no—
96C22⋊C4×C43—81no—
97C22⋊C4×C43—81no—
98C42×C43—21no—
99C42×C43—21no—
100C42×C43—42no—
101C42×C43C2×D412yes—
102C42×C43#4112yes—
103#10621877—28no—
104#10621877—24no—
105#10621877—24no—
106C2×C43⋊C8—28no—
107C2×C43⋊C8—24no—
108C2×C43⋊C8—42no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43—41no—
116C23×C43—41no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43—41no—
120C23×C43#10412yes—
121C23×C43C2×C22⋊C411yescharacteristic
122Q8×C43—82no—
123D4×C43—82no—
124D4×C43—84no—
125C2×C4×C43—22no—
126C2×C4×C43—22no—
127C2×C4×C43—24no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—22no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43#10412yes—
148C2×C4×C43C4×D412yes—
149C2×C4×C43#12011yescharacteristic
150C2×C4×C43#12112yes—
151C2×C4×C43#12311yescharacteristic
152C43⋊C8—28no—
153C43⋊C8—82no—
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—81no—
163C22×C43—81no—
164C22×C43—81no—
165C22×C43—81no—
166C22×C43—81no—
167C22×C43—81no—
168C22×C43—81no—
169C22×C43#38611yescharacteristic
170C22×C43C2×#10411yescharacteristic
171C22×C43C2×#10411yescharacteristic
172C4×C43—22no—
173C4×C43—21no—
174C4×C43—22no—
175C4×C43—21no—
176C4×C43—22no—
177C4×C43—42no—
178C4×C43—41no—
179C4×C43—41no—
180C4×C43—81no—
181C4×C43—81no—
182#2873—431no—
183#2610D4311yescharacteristic
184#1527—432no—
185#1464—431no—
186#1300—432no—
187C2×C43—21no—
188C2×C43—21no—
189C2×C43—42no—
190C2×C43—161no—
191C2×C43#188411yescharacteristic
192C2×C43#189611yescharacteristic
193C2×C43#191411yescharacteristic
194C22×M16—861no—
195C2×#124C2×D4311yescharacteristic
196C2×#117C2×D4311yescharacteristic
197#432—432no—
198#405—864no—
199C4×M16—432no—
200C4×M16—861no—
201#395Dic4311yescharacteristic
202#394Dic4311yescharacteristic
203#393Dic4311yescharacteristic
204#392Dic4311yescharacteristic
205#390—21no—
206#388—21no—
207#388—21no—
208#386—21no—
209#376C2×D4311yescharacteristic
210#329—864no—
211#324—861no—
212#323—861no—
213C43#938711yescharacteristic, complemented, Sylow
214C22×Q8C2×Dic4311yescharacteristic
215C22×D4—21no—
216C22×D4C2×Dic4311yescharacteristic
217C23×C4C22⋊D4311yescharacteristic
218C2×M16—862no—
219C2×M16—864no—
220C2×M16—864no—
221C2×M16—862no—
222C22×C8—862no—
223#124—22no—
224#124—22no—
225#117—22no—
226#117—22no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4C2×Dic4311yescharacteristic
229C2×C4⋊C4C22⋊D4311yescharacteristic
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4C2×Dic4311yescharacteristic
237C2×C22⋊C4C22⋊D4311yescharacteristic
238C2×C42—21no—
239C2×C42C22⋊D4311yescharacteristic
240C2×C42C22×D4311yescharacteristic
241C4⋊C8—862no—
242C22⋊C8—862no—
243#97—434no—
244#97—862no—
245#97—862no—
246C4×C8—862no—
247C4×C8—862no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95C2×Dic4311yescharacteristic
252#95C2×Dic4311yescharacteristic
253C24—21no—
254C24C22⋊Dic4311yescharacteristic
255C2×Q8—22no—
256C2×Q8—81no—
257C2×D4—22no—
258C2×D4—42no—
259C2×D4—42no—
260C2×D4—81no—
261C2×D4—81no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4C22⋊Dic4311yescharacteristic
270C22×C4C22⋊Dic4311yescharacteristic
271C22×C4C22⋊Dic4311yescharacteristic
272C22×C4C22×Dic4311yescharacteristic
273C22×C4C2×C22⋊D4311yescharacteristic
274C22×C4C2×C22⋊D4311yescharacteristic
275M16—868no—
276M16—864no—
277M16—864no—
278C2×C8—868no—
279C2×C8—864no—
280C2×C8—1722no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—81no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—41no—
291C22⋊C4—81no—
292C22⋊C4—81no—
293C42—21no—
294C42—21no—
295C42—42no—
296C42D4×D4312yes—
297C42#1062190012yes—
298C23—21no—
299C23—21no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23#1306325212yes—
310C23C2×C22⋊Dic4311yescharacteristic
311Q8—82no—
312D4—82no—
313D4—84no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4#1306325212yes—
337C2×C4D4×Dic4312yes—
338C2×C4#1306329311yescharacteristic
339C2×C4#1306329712yes—
340C2×C4#1306330611yescharacteristic
341C8—868no—
342C8—3442no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—42no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22#1458277911yescharacteristic
358C22C2×#1306325211yescharacteristic
359C22C2×#1306325211yescharacteristic
360C4—22no—
361C4—21no—
362C4—22no—
363C4—21no—
364C4—22no—
365C4—42no—
366C4—41no—
367C4—41no—
368C4—81no—
369C4—81no—
370C2—21no—
371C2—21no—
372C2—42no—
373C2—161no—
374C2#1913497911yescharacteristic
375C2#1913503911yescharacteristic
376C2#1913514311yescharacteristic
subgroupG/H
centerC22#14582779
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2610C2
socleC22×C43#386
prime radicalC43×#392C4
cosocleC2×C42×C43C23
hypercenter#2610D43
hypocenterC43#9387
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2610

Complements

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

NH ≅ G/Ntype
1. #19143014C2semidirect
2. #19133193C2semidirect
3. #19132929C2semidirect
4. #19132488C2semidirect
34. #13063236D4semidirect
213. C43#9387semidirect

Maximal subgroups

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

subgroupindex
#191430142
#191331932
#191329292
#191324882
C43×#26102
#938743