Finite Group Databasebeta

← #24987945

Subgroups — #24987945

Order 11008.

1238 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1238 conjugacy classes of subgroups — too many to draw. Only its 171 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#19134505C212yesmaximal, complemented
2C2×#14582625C212yesmaximal, complemented
3C2×#14582623C212yesmaximal, complemented
4C22×#123×C43C211yesmaximal, characteristic
5C2×C22⋊(C43⋊C8)—24no—
6C2×C22⋊(C43⋊C8)C2214yes—
7#14582625—24no—
8#14582623—24no—
9C23×D4×C43C411yescharacteristic
10C24×C4×C43C2211yescharacteristic
11C2×#123×C43—24no—
12C2×#123×C43—24no—
13C2×#123×C43—24no—
14C22×C4⋊C4×C43C411yescharacteristic
15C22×C4⋊C4×C43C2211yescharacteristic
16C22×C22⋊C4×C43C411yescharacteristic
17C22×C22⋊C4×C43C411yescharacteristic
18C22×C22⋊C4×C43C2211yescharacteristic
19C22×C43⋊C8—24no—
20C22⋊(C43⋊C8)—24no—
21C22⋊(C43⋊C8)—24no—
22C22⋊(C43⋊C8)—48no—
23C25×C43C2×C411yescharacteristic
24C25×C43C2×C411yescharacteristic
25C22×D4×C43—22no—
26C22×D4×C43—22no—
27C22×D4×C43—22no—
28C22×D4×C43—44no—
29C23×C4×C43—22no—
30C23×C4×C43—22no—
31C23×C4×C43—44no—
32C23×C4×C43C2×C411yescharacteristic
33C23×C4×C43C2×C411yescharacteristic
34C23×C4×C43C2×C411yescharacteristic
35C23×C4×C43C2×C411yescharacteristic
36C23×C4×C43D414yes—
37C23×C4×C43C2311yescharacteristic
38#123×C43—232no—
39C2×C4⋊C4×C43—22no—
40C2×C4⋊C4×C43—22no—
41C2×C4⋊C4×C43—22no—
42C2×C4⋊C4×C43—22no—
43C2×C4⋊C4×C43—22no—
44C2×C4⋊C4×C43D414yes—
45C2×C22⋊C4×C43—22no—
46C2×C22⋊C4×C43—22no—
47C2×C22⋊C4×C43—22no—
48C2×C22⋊C4×C43—22no—
49C2×C22⋊C4×C43—22no—
50C2×C22⋊C4×C43—22no—
51C2×C22⋊C4×C43—22no—
52C2×C22⋊C4×C43—22no—
53C2×C22⋊C4×C43D414yes—
54C24×C43—24no—
55C24×C43—21no—
56C24×C43—21no—
57C24×C43—21no—
58C24×C43—21no—
59C24×C43—24no—
60C24×C43—24no—
61C24×C43—42no—
62C24×C43—42no—
63C24×C43—42no—
64C24×C43C22⋊C412yes—
65C24×C43C22⋊C412yes—
66C24×C43C22×C411yescharacteristic
67C2×D4×C43—28no—
68C2×D4×C43—48no—
69C2×D4×C43—48no—
70C2×D4×C43—44no—
71C2×D4×C43—44no—
72C22×C4×C43—28no—
73C22×C4×C43—28no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—24no—
83C22×C4×C43—42no—
84C22×C4×C43—44no—
85C22×C4×C43—42no—
86C22×C4×C43—42no—
87C22×C4×C43—42no—
88C22×C4×C43—48no—
89C22×C4×C43—48no—
90C22×C4×C43C22⋊C412yes—
91C22×C4×C43C22⋊C412yes—
92C22×C4×C43C22⋊C412yes—
93C22×C4×C43C22⋊C412yes—
94C22×C4×C43C2×D412yes—
95C22×C4×C43C2×D412yes—
96C22×C4×C43C2×D412yes—
97C4⋊C4×C43—28no—
98C4⋊C4×C43—28no—
99C22⋊C4×C43—28no—
100C22⋊C4×C43—28no—
101C22⋊C4×C43—28no—
102C2×C43⋊C8—48no—
103C2×C43⋊C8—44no—
104C23×C43—22no—
105C23×C43—22no—
106C23×C43—24no—
107C23×C43—24no—
108C23×C43—22no—
109C23×C43—24no—
110C23×C43—22no—
111C23×C43—24no—
112C23×C43—22no—
113C23×C43—24no—
114C23×C43—416no—
115C23×C43—42no—
116C23×C43—42no—
117C23×C43—42no—
118C23×C43—42no—
119C23×C43—42no—
120C23×C43—42no—
121C23×C43—42no—
122C23×C43—42no—
123C23×C43—42no—
124C23×C43—42no—
125C23×C43—42no—
126C23×C43—42no—
127C23×C43—88no—
128C23×C43#9914yes—
129C23×C43C2×C22⋊C411yescharacteristic
130C23×C43C2×C22⋊C411yescharacteristic
131C23×C43C2×C22⋊C411yescharacteristic
132C23×C43#13114yes—
133D4×C43—416no—
134C2×C4×C43—24no—
135C2×C4×C43—22no—
136C2×C4×C43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—22no—
139C2×C4×C43—24no—
140C2×C4×C43—24no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43—416no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43—42no—
152C2×C4×C43—42no—
153C2×C4×C43—42no—
154C2×C4×C43#12014yes—
155C43⋊C8—84no—
156#8304—431nomaximal, Sylow
157C22×C43—28no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—28no—
163C22×C43—24no—
164C22×C43—48no—
165C22×C43—48no—
166C22×C43—44no—
167C22×C43—42no—
168C22×C43—42no—
169C22×C43—42no—
170C22×C43—42no—
171C22×C43—42no—
172C22×C43—84no—
173C22×C43—84no—
174C22×C43—84no—
175C22×C43#37911yescharacteristic
176C22×C43#40812yes—
177C22×C43#40812yes—
178C22×C43#40812yes—
179C22×C43C2×#9912yes—
180C22×C43#41312yes—
181C4×C43—24no—
182C4×C43—42no—
183C4×C43—42no—
184C4×C43—42no—
185C4×C43—42no—
186C22×#123D4311yescharacteristic
187#1779—432no—
188C2×#324—432no—
189C2×#323—432no—
190C2×C43—22no—
191C2×C43—22no—
192C2×C43—44no—
193C2×C43—82no—
194C2×C43#146814yes—
195C2×C43#178011yescharacteristic
196C2×C43#178111yescharacteristic
197C2×C43#178511yescharacteristic
198C23×D4Dic4311yescharacteristic
199C24×C4C2×D4311yescharacteristic
200C2×#123—24no—
201C2×#123—24no—
202C2×#123—24no—
203C22×C4⋊C4Dic4311yescharacteristic
204C22×C4⋊C4C2×D4311yescharacteristic
205C22×C22⋊C4Dic4311yescharacteristic
206C22×C22⋊C4Dic4311yescharacteristic
207C22×C22⋊C4C2×D4311yescharacteristic
208C2×C22⋊C8—434no—
209C2×C22⋊C8—864no—
210#324—864no—
211#323—864no—
212C43#830411yescharacteristic, complemented, Sylow
213C25C2×Dic4311yescharacteristic
214C25C2×Dic4311yescharacteristic
215C22×D4—22no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—44no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—44no—
222C23×C4C2×Dic4311yescharacteristic
223C23×C4C2×Dic4311yescharacteristic
224C23×C4C2×Dic4311yescharacteristic
225C23×C4C2×Dic4311yescharacteristic
226C23×C4C22⋊D4314yes—
227C23×C4C22×D4311yescharacteristic
228C22×C8—864no—
229#123—232no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4C22⋊D4314yes—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4C22⋊D4314yes—
245C22⋊C8—864no—
246C22⋊C8—864no—
247C22⋊C8—1728no—
248C24—24no—
249C24—21no—
250C24—21no—
251C24—21no—
252C24—21no—
253C24—24no—
254C24—24no—
255C24—42no—
256C24—42no—
257C24—42no—
258C24C22⋊Dic4312yes—
259C24C22⋊Dic4312yes—
260C24C22×Dic4311yescharacteristic
261C2×D4—28no—
262C2×D4—48no—
263C2×D4—44no—
264C2×D4—48no—
265C2×D4—44no—
266C22×C4—28no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—24no—
276C22×C4—28no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—44no—
280C22×C4—48no—
281C22×C4—48no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4C22⋊Dic4312yes—
285C22×C4C22⋊Dic4312yes—
286C22×C4C22⋊Dic4312yes—
287C22×C4C22⋊Dic4312yes—
288C22×C4C2×C22⋊D4312yes—
289C22×C4C2×C22⋊D4312yes—
290C22×C4C2×C22⋊D4312yes—
291C2×C8—1728no—
292C2×C8—1724no—
293C4⋊C4—28no—
294C4⋊C4—28no—
295C22⋊C4—28no—
296C22⋊C4—28no—
297C22⋊C4—28no—
298C23—22no—
299C23—22no—
300C23—24no—
301C23—24no—
302C23—24no—
303C23—22no—
304C23—24no—
305C23—22no—
306C23—22no—
307C23—24no—
308C23—416no—
309C23—42no—
310C23—42no—
311C23—42no—
312C23—42no—
313C23—42no—
314C23—42no—
315C23—42no—
316C23—42no—
317C23—42no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—88no—
322C23#1306324014yes—
323C23C2×C22⋊Dic4311yescharacteristic
324C23C2×C22⋊Dic4311yescharacteristic
325C23C2×C22⋊Dic4311yescharacteristic
326C23#1306333214yes—
327D4—416no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—416no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4#1306329414yes—
349C8—3444no—
350C22—28no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—28no—
356C22—24no—
357C22—48no—
358C22—48no—
359C22—44no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—42no—
364C22—42no—
365C22—84no—
366C22—84no—
367C22—84no—
368C22#1458275511yescharacteristic
369C22#1458286612yes—
370C22#1458286612yes—
371C22#1458286612yes—
372C22C2×#1306324012yes—
373C22#1458288312yes—
374C4—24no—
375C4—42no—
376C4—42no—
377C4—42no—
378C4—42no—
379C2—22no—
380C2—22no—
381C2—44no—
382C2—82no—
383C2#1913294314yes—
384C2#1913450711yescharacteristic
385C2#1913451011yescharacteristic
386C2#1913452311yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC22×#123×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D4×C43C4
cosocleC23×C4×C43C23
hypercenterC22×#123D43
hypocenterC43#8304
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. #19134505C2semidirect
2. C2×#14582625C2semidirect
3. C2×#14582623C2semidirect
212. C43#8304semidirect

Maximal subgroups

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

subgroupindex
#191345052
C2×#145826252
C2×#145826232
C22×#123×C432
#830443