Finite Group Databasebeta

← #25006154

Subgroups — #25006154

Order 11008.

496 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 83 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#19139062C211yesmaximal, characteristic
2C2×#14582625C211yesmaximal, characteristic, complemented
3#19132540C212yesmaximal, complemented
4#19132526C212yesmaximal, complemented
5C43×#1463C211yesmaximal, characteristic, complemented
6C2×#13063308—21no—
7C2×#13063308—21no—
8C2×#13063299C411yescharacteristic
9C2×C22⋊(C43⋊C8)—21no—
10#14582834—21no—
11#14582834—21no—
12#14582800C411yescharacteristic
13#14582800C2211yescharacteristic
14#14582768C411yescharacteristic
15#14582768C2211yescharacteristic
16C4×C22⋊Dic43C411yescharacteristic
17#14582625—21no—
18#14582625C2212yes—
19C22×C4⋊C4×C43C2211yescharacteristic
20C43×#407—21no—
21C43×#324—21no—
22C43×#324C2212yes—
23C22×D172C2×C411yescharacteristic
24C22×C22⋊D43—21no—
25C22×C43⋊C8—41no—
26#13063308—44no—
27#13063308—44no—
28#13063299—41no—
29#13063299—41no—
30C2×C4⋊Dic43C2×C411yescharacteristic
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—21no—
35C2×C22⋊Dic43—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×C4×Dic43C2×C411yescharacteristic
42C2×C4×Dic43C2×C411yescharacteristic
43C22⋊(C43⋊C8)—22no—
44C22⋊(C43⋊C8)—41no—
45C43⋊#95—21no—
46C23×C4×C43C2×C411yescharacteristic
47C23×C4×C43D411yescharacteristic
48C23×C4×C43D411yescharacteristic
49C2×M16×C43—41no—
50C2×C4⋊C4×C43—41no—
51C2×C4⋊C4×C43—41no—
52C2×C4⋊C4×C43C2×C411yescharacteristic
53C2×C4⋊C4×C43D411yescharacteristic
54C2×C4⋊C4×C43D411yescharacteristic
55C2×C4⋊C4×C43C2311yescharacteristic
56C22⋊C8×C43—22no—
57C22⋊C8×C43—41no—
58C24×C43C22⋊C411yescharacteristic
59C23×D43—21no—
60C22×C4×C43—22no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—41no—
68C22×C4×C43—42no—
69C22×C4×C43—42no—
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—41no—
79C2×C22⋊D43—41no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C22×Dic43—21no—
83C2×D172—22no—
84C2×D172—41no—
85C2×D172—41no—
86M16×C43—82no—
87C2×C8×C43—42no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C22⋊Dic43—24no—
93(C2×D43)⋊C4—42no—
94(C2×D43)⋊C4—42no—
95(C2×D43)⋊C4—42no—
96(C2×D43)⋊C4—42no—
97(C2×D43)⋊C4—42no—
98C4⋊Dic43—41no—
99Dic43⋊C4—42no—
100Dic43⋊C4—42no—
101Dic43⋊C4—42no—
102Dic43⋊C4—42no—
103C4×Dic43—22no—
104C4×Dic43—41no—
105C2×C43⋊C8—42no—
106C2×C43⋊C8—82no—
107C23×C43—22no—
108C23×C43—21no—
109C23×C43—21no—
110C23×C43—41no—
111C23×C43#9911yescharacteristic
112C23×C43#9911yescharacteristic
113C23×C43C2×C22⋊C411yescharacteristic
114C22×D43—41no—
115C22×D43—41no—
116C22×D43—41no—
117C22×D43—41no—
118C22×D43—41no—
119C22×D43—41no—
120C22×D43—41no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—42no—
131C2×C4×C43—42no—
132C2×C4×C43—42no—
133C2×C4×C43—42no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—81no—
139C2×C4×C43—81no—
140C2×C4×C43#13112yes—
141C22⋊D43—82no—
142C22⋊D43—82no—
143C2×Dic43—22no—
144C2×Dic43—22no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152D172—82no—
153C8×C43—82no—
154C43⋊C8—82no—
155#11549—431nomaximal, Sylow
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—42no—
164C22×C43—42no—
165C22×C43#35312yes—
166C22×C43#40811yescharacteristic
167C22×C43C2×#9911yescharacteristic
168C22×C43#41311yescharacteristic
169C2×D43—81no—
170C2×D43—81no—
171C2×D43—81no—
172C2×D43—81no—
173C2×D43—81no—
174C2×D43—81no—
175C2×D43—81no—
176C4×C43—22no—
177C4×C43—41no—
178C4×C43—41no—
179C4×C43—41no—
180C4×C43—41no—
181C4×C43—41no—
182Dic43—42no—
183Dic43—42no—
184Dic43—81no—
185#2501—431no—
186#1463D4311yescharacteristic, complemented
187C2×#324—431no—
188#1325—432no—
189#1318—432no—
190C2×C43—21no—
191C2×C43—21no—
192C2×C43—22no—
193C2×C43—41no—
194C2×C43#146811yescharacteristic
195C2×C43C2×#35311yescharacteristic
196C2×C43#213311yescharacteristic
197D43—161no—
198C2×#123—861no—
199C2×#123—861no—
200C2×#121—431no—
201C22×C4⋊C4C2×D4311yescharacteristic
202#407—21no—
203C2×C22⋊C8—861no—
204#399—861no—
205#399—861no—
206#390—431no—
207#390—431no—
208#384—431no—
209#384—431no—
210C4×C22⋊C4—431no—
211#324—21no—
212#324—432no—
213#324—861no—
214#324C2×D4312yes—
215C43#1154911yescharacteristic, complemented, Sylow
216C22×D4—431no—
217C22×D4—861no—
218C23×C4C4×D4311yescharacteristic
219C23×C4D17211yescharacteristic
220C23×C4C22⋊D4311yescharacteristic
221C2×M16—41no—
222C22×C8—1721no—
223#123—1724no—
224#123—1724no—
225#121—1721no—
226#121—1721no—
227C2×C4⋊C4—41no—
228C2×C4⋊C4—41no—
229C2×C4⋊C4—431no—
230C2×C4⋊C4—861no—
231C2×C4⋊C4—861no—
232C2×C4⋊C4—861no—
233C2×C4⋊C4—861no—
234C2×C4⋊C4C4×D4311yescharacteristic
235C2×C4⋊C4D17211yescharacteristic
236C2×C4⋊C4C22⋊D4311yescharacteristic
237C2×C4⋊C4C22×D4311yescharacteristic
238C2×C22⋊C4—861no—
239C2×C22⋊C4—861no—
240C2×C22⋊C4—861no—
241C2×C22⋊C4—861no—
242C2×C22⋊C4—861no—
243C2×C22⋊C4—861no—
244C2×C42—431no—
245C2×C42—431no—
246C22⋊C8—22no—
247C22⋊C8—41no—
248C22⋊C8—862no—
249C22⋊C8—1721no—
250#95—861no—
251C24—861no—
252C24(C2×D43)⋊C411yescharacteristic
253C2×D4—862no—
254C2×D4—1721no—
255C2×D4—1721no—
256C2×D4—1722no—
257C2×D4—1722no—
258C2×D4—1721no—
259C2×D4—1721no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—22no—
267C22×C4—41no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4—861no—
273C22×C4(C2×D43)⋊C411yescharacteristic
274C22×C4(C2×D43)⋊C411yescharacteristic
275C22×C4(C2×D43)⋊C411yescharacteristic
276C22×C4C2×C4×D4311yescharacteristic
277C22×C4C2×D17211yescharacteristic
278C22×C4C2×C22⋊D4311yescharacteristic
279M16—82no—
280C2×C8—42no—
281C2×C8—3442no—
282C2×C8—1722no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—1721no—
288C4⋊C4—1722no—
289C4⋊C4—1722no—
290C4⋊C4—1722no—
291C4⋊C4—1722no—
292C22⋊C4—864no—
293C22⋊C4—1722no—
294C22⋊C4—1722no—
295C22⋊C4—1722no—
296C22⋊C4—1722no—
297C22⋊C4—1722no—
298C42—862no—
299C42—1721no—
300C23—21no—
301C23—21no—
302C23—22no—
303C23—41no—
304C23—1721no—
305C23—1721no—
306C23—1721no—
307C23—1721no—
308C23—1721no—
309C23—1721no—
310C23—1721no—
311C23#1306323911yescharacteristic
312C23#1306323911yescharacteristic
313C23C2×(C2×D43)⋊C411yescharacteristic
314D4—3442no—
315D4—3442no—
316D4—3442no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—862no—
337C2×C4—862no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4—1721no—
341C2×C4—1721no—
342C2×C4—1721no—
343C2×C4—1721no—
344C2×C4—1721no—
345C2×C4#1306333312yes—
346C8—82no—
347C8—3442no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—42no—
356C22—42no—
357C22—3441no—
358C22—3441no—
359C22—3441no—
360C22—3441no—
361C22—3441no—
362C22—3441no—
363C22—3441no—
364C22#1458269112yes—
365C22#1458286711yescharacteristic
366C22C2×#1306323911yescharacteristic
367C22#1458288111yescharacteristic
368C4—22no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—3441no—
375C4—1722no—
376C4—1722no—
377C2—21no—
378C2—21no—
379C2—22no—
380C2—41no—
381C2—6881no—
382C2#1913294411yescharacteristic
383C2C2×#1458269111yescharacteristic
384C2#1913628211yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1463C2
socleC22×C43C2×#99
prime radicalC2×#13063299C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1463D43
hypocenterC43#11549
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
2. C2×#14582625C2semidirect
3. #19132540C2semidirect
4. #19132526C2semidirect
5. C43×#1463C2semidirect
186. #1463D43semidirect
215. C43#11549semidirect

Maximal subgroups

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

subgroupindex
#191390622
C2×#145826252
#191325402
#191325262
C43×#14632
#1154943