Finite Group Databasebeta

← #24991622

Subgroups — #24991622

Order 11008.

1224 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 135 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#19137193C211yesmaximal, characteristic, complemented
2#19134526C212yesmaximal, complemented
3C2×#14582623C211yesmaximal, characteristic, complemented
4#19132474C212yesmaximal, complemented
5C2×C43×#392C211yesmaximal, characteristic
6C2×#13063246—24no—
7C2×C22⋊(C43⋊C8)C2212yes—
8#14582792—24no—
9#14582759C2212yes—
10#14582755—21no—
11C4×C22⋊Dic43—21no—
12#14582623—22no—
13C23×D4×C43—21no—
14C23×D4×C43C2211yescharacteristic
15C22×C22⋊C4×C43—21no—
16C22×C22⋊C4×C43C2211yescharacteristic
17C43×#392—22no—
18C43×#392C414yescomplemented
19C2×#95×C43C2211yescharacteristic
20C22×C43⋊C8—22no—
21C2×C4⋊Dic43D414yescomplemented
22C2×C22⋊Dic43—22no—
23C2×C22⋊Dic43—22no—
24C2×C22⋊Dic43—22no—
25C2×C4×Dic43—22no—
26#13063246—48no—
27C22⋊(C43⋊C8)—22no—
28C22⋊(C43⋊C8)—22no—
29C43⋊#95—22no—
30C43⋊#95—22no—
31C25×C43—21no—
32C25×C43D411yescharacteristic
33C22×D4×C43—24no—
34C22×D4×C43—22no—
35C22×D4×C43—21no—
36C22×D4×C43—22no—
37C22×D4×C43—44no—
38C22×D4×C43—44no—
39C22×D4×C43—44no—
40C22×D4×C43—44no—
41C22×D4×C43C2×C412yes—
42C23×C4×C43—21no—
43C23×C4×C43D411yescharacteristic
44C23×C4×C43C2311yescharacteristic
45C2×C22⋊C4×C43—22no—
46C2×C22⋊C4×C43—22no—
47C2×C22⋊C4×C43—24no—
48C2×C22⋊C4×C43—44no—
49C2×C22⋊C4×C43C2×C412yes—
50C2×C22⋊C4×C43D412yes—
51#95×C43—21no—
52#95×C43C2×C412yes—
53C24×C43—24no—
54C24×C43—22no—
55C24×C43—21no—
56C24×C43—22no—
57C24×C43—21no—
58C24×C43—22no—
59C24×C43—42no—
60C24×C43—42no—
61C24×C43—42no—
62C24×C43—42no—
63C24×C43—42no—
64C24×C43—41no—
65C24×C43—41no—
66C24×C43—42no—
67C24×C43—42no—
68C24×C43C22⋊C412yes—
69C24×C43C2×D411yescharacteristic
70C2×D4×C43—28no—
71C2×D4×C43—24no—
72C2×D4×C43—44no—
73C2×D4×C43—48no—
74C2×D4×C43—44no—
75C2×D4×C43—48no—
76C2×D4×C43—48no—
77C2×D4×C43—44no—
78C2×D4×C43—48no—
79C2×D4×C43—432no—
80C2×D4×C43—42no—
81C22×C4×C43—24no—
82C22×C4×C43—22no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—42no—
86C22×C4×C43—42no—
87C22×C4×C43—42no—
88C22×C4×C43—42no—
89C22×C4×C43C22⋊C412yes—
90C22×C4×C43C22×C411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D412yes—
93C22×C4×C43#4112yes—
94C22×Dic43—24no—
95C22⋊C4×C43—24no—
96C22⋊C4×C43—24no—
97C22⋊C4×C43—48no—
98C22⋊Dic43—42no—
99C22⋊Dic43—42no—
100C22⋊Dic43—82no—
101C22⋊Dic43—82no—
102C4⋊Dic43—44no—
103C4×Dic43—82no—
104C2×C43⋊C8—44no—
105C2×C43⋊C8—42no—
106C23×C43—22no—
107C23×C43—22no—
108C23×C43—24no—
109C23×C43—22no—
110C23×C43—22no—
111C23×C43—22no—
112C23×C43—42no—
113C23×C43—42no—
114C23×C43—42no—
115C23×C43—48no—
116C23×C43—48no—
117C23×C43—42no—
118C23×C43—42no—
119C23×C43—44no—
120C23×C43—48no—
121C23×C43—42no—
122C23×C43—42no—
123C23×C43—42no—
124C23×C43—42no—
125C23×C43—42no—
126C23×C43—42no—
127C23×C43—44no—
128C23×C43—42no—
129C23×C43—81no—
130C23×C43—81no—
131C23×C43—84no—
132C23×C43—84no—
133C23×C43—84no—
134C23×C43—82no—
135C23×C43—82no—
136C23×C43—82no—
137C23×C43—82no—
138C23×C43C2×C22⋊C411yescharacteristic
139C23×C43#12011yescharacteristic
140C23×C43#12311yescharacteristic
141C23×C43#13512yes—
142C23×C43AGL(1,ℤ/8)12yes—
143D4×C43—28no—
144D4×C43—48no—
145D4×C43—44no—
146D4×C43—432no—
147C2×C4×C43—24no—
148C2×C4×C43—24no—
149C2×C4×C43—22no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—42no—
153C2×C4×C43—48no—
154C2×C4×C43—42no—
155C2×C4×C43—42no—
156C2×C4×C43—42no—
157C2×C4×C43—42no—
158C2×C4×C43—81no—
159C2×C4×C43C4×D412yes—
160C2×C4×C43#12112yes—
161C2×Dic43—44no—
162C2×Dic43—44no—
163C2×Dic43—44no—
164C43⋊C8—82no—
165#9020—431nomaximal, Sylow
166C22×C43—24no—
167C22×C43—24no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—44no—
173C22×C43—44no—
174C22×C43—44no—
175C22×C43—42no—
176C22×C43—42no—
177C22×C43—44no—
178C22×C43—42no—
179C22×C43—82no—
180C22×C43—82no—
181C22×C43—82no—
182C22×C43—84no—
183C22×C43—88no—
184C22×C43—84no—
185C22×C43—88no—
186C22×C43—82no—
187C22×C43—82no—
188C22×C43#38611yescharacteristic
189C22×C43#41611yescharacteristic
190C22×C43#41811yescharacteristic
191C22×C43#44912yes—
192C22×C43#45312yes—
193C22×C43B(4,𝔽2)12yes—
194C22×C43#48212yes—
195C4×C43—22no—
196C4×C43—22no—
197C4×C43—44no—
198C4×C43—42no—
199Dic43—84no—
200C2×#392D4311yescharacteristic
201#2312—431no—
202#1786—432no—
203C2×#323—431no—
204#1294—432no—
205C2×C43—21no—
206C2×C43—21no—
207C2×C43—22no—
208C2×C43—82no—
209C2×C43—84no—
210C2×C43#160014yes—
211C2×C43#187511yescharacteristic
212C2×C43#188711yescharacteristic
213C2×C43#188911yescharacteristic
214C23×D4—21no—
215C23×D4C2×D4311yescharacteristic
216C22×C22⋊C4—21no—
217C22×C22⋊C4C2×D4311yescharacteristic
218C2×#102—864no—
219C2×C22⋊C8—432no—
220#392—22no—
221#392Dic4314yescomplemented
222#388—864no—
223#380—432no—
224#379—861no—
225C4×C22⋊C4—861no—
226C2×#95C2×D4311yescharacteristic
227#323—862no—
228C43#902011yescharacteristic, complemented, Sylow
229C25—21no—
230C25C22⋊D4311yescharacteristic
231C22×D4—24no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—21no—
235C22×D4—44no—
236C22×D4—44no—
237C22×D4—44no—
238C22×D4—44no—
239C22×D4C2×Dic4312yes—
240C23×C4—21no—
241C23×C4C22⋊D4311yescharacteristic
242C23×C4C22×D4311yescharacteristic
243C22×C8—862no—
244C2×C4⋊C4—434no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—24no—
248C2×C22⋊C4—44no—
249C2×C22⋊C4—862no—
250C2×C22⋊C4—862no—
251C2×C22⋊C4—862no—
252C2×C22⋊C4C2×Dic4312yes—
253C2×C22⋊C4C22⋊D4312yes—
254C2×C42—862no—
255#102—1728no—
256C22⋊C8—862no—
257C22⋊C8—862no—
258#95—21no—
259#95—862no—
260#95—862no—
261#95C2×Dic4312yes—
262C24—24no—
263C24—22no—
264C24—21no—
265C24—22no—
266C24—21no—
267C24—22no—
268C24—42no—
269C24—42no—
270C24—42no—
271C24—42no—
272C24—42no—
273C24—41no—
274C24—41no—
275C24—42no—
276C24—42no—
277C24C22⋊Dic4312yes—
278C24C2×C22⋊D4311yescharacteristic
279C2×D4—28no—
280C2×D4—24no—
281C2×D4—44no—
282C2×D4—48no—
283C2×D4—44no—
284C2×D4—48no—
285C2×D4—44no—
286C2×D4—48no—
287C2×D4—48no—
288C2×D4—432no—
289C2×D4—42no—
290C22×C4—24no—
291C22×C4—22no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—864no—
299C22×C4C22⋊Dic4312yes—
300C22×C4D4×D4312yes—
301C22×C4#1062190012yes—
302C22×C4C22×Dic4311yescharacteristic
303C22×C4C2×C22⋊D4311yescharacteristic
304C2×C8—1724no—
305C2×C8—1722no—
306C4⋊C4—1724no—
307C22⋊C4—24no—
308C22⋊C4—24no—
309C22⋊C4—48no—
310C22⋊C4—3442no—
311C22⋊C4—3442no—
312C22⋊C4—1722no—
313C22⋊C4—1722no—
314C42—3442no—
315C23—22no—
316C23—22no—
317C23—24no—
318C23—22no—
319C23—22no—
320C23—22no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—44no—
327C23—48no—
328C23—48no—
329C23—48no—
330C23—42no—
331C23—42no—
332C23—42no—
333C23—44no—
334C23—42no—
335C23—42no—
336C23—42no—
337C23—42no—
338C23—81no—
339C23—81no—
340C23—84no—
341C23—82no—
342C23—84no—
343C23—84no—
344C23—82no—
345C23—82no—
346C23—82no—
347C23C2×C22⋊Dic4311yescharacteristic
348C23#1306329311yescharacteristic
349C23#1306330611yescharacteristic
350C23#1306334512yes—
351C23#1306335112yes—
352D4—28no—
353D4—48no—
354D4—44no—
355D4—432no—
356C2×C4—24no—
357C2×C4—24no—
358C2×C4—22no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—48no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—81no—
368C2×C4—1724no—
369C2×C4—1724no—
370C2×C4—1724no—
371C2×C4D4×Dic4312yes—
372C2×C4#1306329712yes—
373C8—3442no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—24no—
379C22—24no—
380C22—44no—
381C22—44no—
382C22—44no—
383C22—42no—
384C22—44no—
385C22—42no—
386C22—42no—
387C22—82no—
388C22—82no—
389C22—82no—
390C22—84no—
391C22—88no—
392C22—82no—
393C22—84no—
394C22—88no—
395C22—82no—
396C22#1458277911yescharacteristic
397C22#1458289511yescharacteristic
398C22#1458290411yescharacteristic
399C22#1458304212yes—
400C22#1458306612yes—
401C22#1458308512yes—
402C22#1458322012yes—
403C4—22no—
404C4—22no—
405C4—44no—
406C4—42no—
407C4—3444no—
408C2—21no—
409C2—21no—
410C2—22no—
411C2—82no—
412C2—84no—
413C2#1913353914yes—
414C2#1913491811yescharacteristic
415C2#1913499411yescharacteristic
416C2#1913500411yescharacteristic
subgroupG/H
centerC23#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
Fitting, prime radicalC2×C43×#392C2
socleC23×C43#120
cosocleC23×C4×C43C23
hypercenterC2×#392D43
hypocenterC43#9020
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. #19137193C2semidirect
2. #19134526C2semidirect
3. C2×#14582623C2semidirect
4. #19132474C2semidirect
18. C43×#392C4semidirect
21. C2×C4⋊Dic43D4semidirect
221. #392Dic43semidirect
228. C43#9020semidirect

Maximal subgroups

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

subgroupindex
#191371932
#191345262
C2×#145826232
#191324742
C2×C43×#3922
#902043