Finite Group Databasebeta

← #24991295

Subgroups — #24991295

Order 11008.

600 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 119 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#19143624C211yesmaximal, characteristic
2C4×#13063306C211yesmaximal, characteristic
3#19134661C212yesmaximal, complemented
4#19132441C212yesmaximal, complemented
5C43×#1459C211yesmaximal, characteristic
6C2×#13063306C411yescharacteristic
7C22×C4×Dic43C2211yescharacteristic
8#14582971—24no—
9#14582956—21no—
10#14582863—21no—
11C2×C22⋊(C43⋊C8)C2212yes—
12#14582787—21no—
13#14582780—21no—
14#14582779C411yescharacteristic
15#14582771C411yescharacteristic
16#14582760C411yescharacteristic
17C4×Dic43⋊C4—21no—
18C4×C22⋊Dic43—21no—
19C4×C22⋊Dic43C2211yescharacteristic
20#14582653—24no—
21C2×C4×D4×C43C2211yescharacteristic
22C2×C22⋊C8×C43C2212yes—
23C43×#324—21no—
24C43×#323—21no—
25C23×Dic43C2×C411yescharacteristic
26C23×Dic43C2×C411yescharacteristic
27C2×#10621877—22no—
28C22×C43⋊C8D414yes—
29#13063306—22no—
30#13063306—22no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43C2×C411yescharacteristic
36C2×C22⋊Dic43C2×C411yescharacteristic
37C2×C4×Dic43—21no—
38C2×C4×Dic43—22no—
39C2×C4×Dic43—21no—
40C2×C4×Dic43—21no—
41C2×C4×Dic43—22no—
42C4⋊(C43⋊C8)—22no—
43C22⋊(C43⋊C8)—22no—
44C22⋊(C43⋊C8)—22no—
45C22⋊(C43⋊C8)—22no—
46#13063236—22no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C22×D4×C43C2×C411yescharacteristic
53C23×C4×C43D411yescharacteristic
54C23×C4×C43C2311yescharacteristic
55C22×C8×C43—22no—
56C4×D4×C43—22no—
57C4×D4×C43—22no—
58C2×C4⋊C4×C43D411yescharacteristic
59C2×C22⋊C4×C43C2×C411yescharacteristic
60C2×C22⋊C4×C43D411yescharacteristic
61C2×C42×C43D411yescharacteristic
62C22⋊C8×C43—22no—
63C22⋊C8×C43—22no—
64C24×C43C22⋊C411yescharacteristic
65C24×C43C22×C411yescharacteristic
66C2×D4×C43—22no—
67C2×D4×C43—21no—
68C2×D4×C43—21no—
69C2×D4×C43—22no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—42no—
73C22×C4×C43—42no—
74C22×C4×C43C22⋊C411yescharacteristic
75C22×C4×C43C22⋊C411yescharacteristic
76C22×C4×C43C22⋊C411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D412yes—
80C22×C4×C43#4112yes—
81C22×Dic43—21no—
82C22×Dic43—21no—
83C22×Dic43—21no—
84C22×Dic43—21no—
85C22×Dic43—22no—
86C22×Dic43—22no—
87C22×Dic43—21no—
88C22×Dic43—22no—
89C22×Dic43—42no—
90C22×Dic43M1612yescomplemented
91C2×C8×C43—44no—
92C2×C8×C43—42no—
93C4⋊C4×C43—22no—
94C22⋊C4×C43—22no—
95C22⋊C4×C43—22no—
96C42×C43—21no—
97C42×C43—21no—
98C22⋊Dic43—24no—
99C22⋊Dic43—21no—
100C22⋊Dic43—22no—
101C22⋊Dic43—42no—
102C22⋊Dic43M1612yescomplemented
103Dic43⋊C4—24no—
104Dic43⋊C4—42no—
105C4×Dic43—42no—
106C4×Dic43—41no—
107C4×Dic43—42no—
108C4×Dic43—41no—
109#10621877—82no—
110C2×C43⋊C8—24no—
111C2×C43⋊C8—44no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—21no—
115C23×C43—41no—
116C23×C43—41no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43C2×C22⋊C411yescharacteristic
120C23×C43C4×D412yes—
121C23×C43C2×M1611yescharacteristic
122C23×C43C2×M1611yescharacteristic
123C23×C43#13112yes—
124D4×C43—42no—
125D4×C43—42no—
126C2×C4×C43—24no—
127C2×C4×C43—22no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—41no—
134C2×C4×C43—42no—
135C2×C4×C43—42no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—81no—
139C2×C4×C43#12011yescharacteristic
140C2×C4×C43#12112yes—
141C2×C4×C43#12311yescharacteristic
142C2×Dic43—22no—
143C2×Dic43—24no—
144C2×Dic43—22no—
145C2×Dic43—22no—
146C2×Dic43—24no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—42no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—42no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C8×C43—82no—
159C43⋊C8—44no—
160#8968—431nomaximal, Sylow
161C22×C43—21no—
162C22×C43—22no—
163C22×C43—21no—
164C22×C43—22no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—42no—
168C22×C43—42no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—81no—
173C22×C43#38611yescharacteristic
174C22×C43#40711yescharacteristic
175C22×C43#40811yescharacteristic
176C22×C43#43512yes—
177C22×C43#43612yes—
178C4×C43—22no—
179C4×C43—21no—
180C4×C43—41no—
181C4×C43—41no—
182C4×C43—41no—
183C4×C43#45812yes—
184Dic43—42no—
185Dic43—42no—
186Dic43—42no—
187Dic43—81no—
188#2973—431no—
189C4×#123—431no—
190#1817—432no—
191#1459D4311yescharacteristic
192#1282—432no—
193C2×C43—21no—
194C2×C43—21no—
195C2×C43—22no—
196C2×C43—22no—
197C2×C43—81no—
198C2×C43#187011yescharacteristic
199C2×C43#189011yescharacteristic
200C2×C43#189111yescharacteristic
201C2×#123—431no—
202C2×C4×D4C2×D4311yescharacteristic
203C22×C42—431no—
204#435—864no—
205#432—861no—
206#407—861no—
207C2×C22⋊C8—432no—
208C2×C22⋊C8C2×D4312yes—
209#388—861no—
210#387—861no—
211#386—431no—
212#385—431no—
213#381—431no—
214C4×C4⋊C4—861no—
215C4×C22⋊C4—431no—
216C4×C22⋊C4—861no—
217#336—864no—
218#324—21no—
219#323—21no—
220C43#896811yescharacteristic, complemented, Sylow
221C22×D4C4×D4311yescharacteristic
222C23×C4—431no—
223C23×C4—431no—
224C23×C4D17211yescharacteristic
225C23×C4C22×D4311yescharacteristic
226C2×M16—862no—
227C22×C8—22no—
228C22×C8—434no—
229#123—862no—
230#123—862no—
231C4×D4—22no—
232C4×D4—22no—
233C2×C4⋊C4—861no—
234C2×C4⋊C4—861no—
235C2×C4⋊C4C22⋊D4311yescharacteristic
236C2×C22⋊C4—431no—
237C2×C22⋊C4—431no—
238C2×C22⋊C4—861no—
239C2×C22⋊C4—861no—
240C2×C22⋊C4C4×D4311yescharacteristic
241C2×C22⋊C4C22⋊D4311yescharacteristic
242C2×C42—861no—
243C2×C42—861no—
244C2×C42—862no—
245C2×C42—862no—
246C2×C42—861no—
247C2×C42D17211yescharacteristic
248C4⋊C8—862no—
249C22⋊C8—22no—
250C22⋊C8—22no—
251C22⋊C8—862no—
252C22⋊C8—862no—
253C22⋊C8—862no—
254#97—862no—
255#95—861no—
256#95—861no—
257#95—861no—
258#95—861no—
259#95—861no—
260C24(C2×D43)⋊C411yescharacteristic
261C24C2×C4×D4311yescharacteristic
262C2×D4—22no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—432no—
271C22×C4—861no—
272C22×C4—861no—
273C22×C4—861no—
274C22×C4—862no—
275C22×C4—862no—
276C22×C4—861no—
277C22×C4—862no—
278C22×C4—861no—
279C22×C4—1722no—
280C22×C4(C2×D43)⋊C411yescharacteristic
281C22×C4(C2×D43)⋊C411yescharacteristic
282C22×C4(C2×D43)⋊C411yescharacteristic
283C22×C4C2×D17211yescharacteristic
284C22×C4D4×D4312yes—
285C22×C4#1062190012yes—
286C22×C4C2×C22⋊D4311yescharacteristic
287M16—3442no—
288C2×C8—44no—
289C2×C8—42no—
290C2×C8—864no—
291C2×C8—1724no—
292C4⋊C4—22no—
293C4⋊C4—864no—
294C4⋊C4—1722no—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—432no—
298C22⋊C4—864no—
299C22⋊C4—861no—
300C22⋊C4—862no—
301C22⋊C4—1722no—
302C42—21no—
303C42—21no—
304C42—1722no—
305C42—1721no—
306C42—1722no—
307C42—1721no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23C2×(C2×D43)⋊C411yescharacteristic
316C23(C22⋊D43)⋊C412yes—
317C23M16×D4311yescharacteristic
318C23M16×D4311yescharacteristic
319C23#1306333112yes—
320D4—42no—
321D4—42no—
322C2×C4—22no—
323C2×C4—24no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—862no—
336C2×C4—864no—
337C2×C4—862no—
338C2×C4—862no—
339C2×C4—864no—
340C2×C4—1721no—
341C2×C4—1721no—
342C2×C4—1721no—
343C2×C4—1721no—
344C2×C4—1721no—
345C2×C4—1721no—
346C2×C4—1722no—
347C2×C4—1721no—
348C2×C4—1722no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4#1306329511yescharacteristic
352C2×C4#1306329712yes—
353C2×C4#1306330911yescharacteristic
354C8—82no—
355C8—1724no—
356C22—21no—
357C22—22no—
358C22—21no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—42no—
363C22—42no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—81no—
368C22#1458277611yescharacteristic
369C22#1458286211yescharacteristic
370C22#1458286511yescharacteristic
371C22#1458297312yes—
372C22#1458297412yes—
373C4—22no—
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—3441no—
379C4—1722no—
380C4—1722no—
381C4—1722no—
382C4#1458309012yes—
383C2—21no—
384C2—21no—
385C2—22no—
386C2—22no—
387C2—81no—
388C2#1913489011yescharacteristic
389C2#1913500611yescharacteristic
390C2#1913501111yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1459C2
socleC22×C43#386
prime radicalC22×D4×C43C2×C4
cosocleC23×C4×C43C23
hypercenter#1459D43
hypocenterC43#8968
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #19134661C2semidirect
4. #19132441C2semidirect
90. C22×Dic43M16semidirect
102. C22⋊Dic43M16semidirect
220. C43#8968semidirect

Maximal subgroups

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

subgroupindex
#191436242
C4×#130633062
#191346612
#191324412
C43×#14592
#896843