Finite Group Databasebeta

← #25006979

Subgroups — #25006979

Order 11008.

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

normal subgroups only

This group has 470 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#19140479C211yesmaximal, characteristic
2#19132913C211yesmaximal, characteristic, complemented
3#19132621C212yesmaximal, complemented
4#19132597C212yesmaximal, complemented
5C4×#100×C43C211yesmaximal, characteristic, complemented
6C2×#13063299C411yescharacteristic
7C2×C22⋊(C43⋊C8)—21no—
8#14582838C2211yescharacteristic
9#14582835C411yescharacteristic
10#14582816C2211yescharacteristic
11#14582814—21no—
12#14582808C411yescharacteristic
13#14582807—21no—
14#14582790—21no—
15#14582778—21no—
16#14582762C411yescharacteristic
17#14582625C2212yes—
18#14582623—21no—
19C2×C4×D4×C43C2211yescharacteristic
20C2×#100×C43—21no—
21C4×M16×C43—21no—
22C43×#343C2212yes—
23C22×D172C2×C411yescharacteristic
24C22×C22⋊D43—21no—
25C22×C22⋊D43—21no—
26C22×C43⋊C8—41no—
27#13063299—41no—
28#13063299—41no—
29C2×C4⋊Dic43C2×C411yescharacteristic
30C2×Dic43⋊C4—21no—
31C2×C22⋊Dic43—21no—
32C2×C22⋊Dic43—21no—
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C22⋊(C43⋊C8)—22no—
38C22⋊(C43⋊C8)—41no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95C2×C411yescharacteristic
43C43⋊#95C2×C411yescharacteristic
44C22×D4×C43D411yescharacteristic
45C23×C4×C43C2×C411yescharacteristic
46C23×C4×C43D411yescharacteristic
47C2×M16×C43—22no—
48C4×D4×C43—41no—
49C4×D4×C43—41no—
50C2×C4⋊C4×C43C2311yescharacteristic
51C2×C22⋊C4×C43C2×C411yescharacteristic
52C2×C22⋊C4×C43D411yescharacteristic
53C2×C42×C43D411yescharacteristic
54#100×C43—24no—
55#97×C43—41no—
56C4×C8×C43—41no—
57C24×C43C22⋊C411yescharacteristic
58C24×C43C22⋊C411yescharacteristic
59C23×D43—21no—
60C2×D4×C43—22no—
61C2×D4×C43—22no—
62C2×D4×C43—41no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—81no—
68C22×C4×C43—81no—
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C2×C22⋊D43—42no—
75C2×C22⋊D43—42no—
76C2×C22⋊D43—81no—
77C2×C22⋊D43—81no—
78C2×C22⋊D43—81no—
79C2×C22⋊D43—81no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C22×Dic43—21no—
83C2×D172—41no—
84C2×D172—81no—
85M16×C43—24no—
86M16×C43—42no—
87C2×C8×C43—42no—
88C4⋊C4×C43—41no—
89C22⋊C4×C43—41no—
90C22⋊C4×C43—41no—
91C42×C43—21no—
92C42×C43—21no—
93C22⋊Dic43—81no—
94C22⋊Dic43—81no—
95(C2×D43)⋊C4—41no—
96(C2×D43)⋊C4—41no—
97(C2×D43)⋊C4—42no—
98(C2×D43)⋊C4—81no—
99(C2×D43)⋊C4—81no—
100C4⋊Dic43—41no—
101Dic43⋊C4—81no—
102C2×C43⋊C8—42no—
103C2×C43⋊C8—82no—
104C23×C43—21no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43—41no—
110C23×C43—41no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43#10412yes—
114C23×C43C2×C22⋊C411yescharacteristic
115C22×D43—41no—
116C22×D43—41no—
117C22×D43—41no—
118C22×D43—41no—
119C22×D43—41no—
120C22×D43—41no—
121C22×D43—41no—
122D4×C43—44no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—41no—
129C2×C4×C43—42no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—81no—
134C2×C4×C43—81no—
135C2×C4×C43—81no—
136C2×C4×C43#9911yescharacteristic
137C2×C4×C43#9911yescharacteristic
138C2×C4×C43#13512yes—
139C22⋊D43—84no—
140C22⋊D43—84no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150D172—82no—
151C8×C43—44no—
152C43⋊C8—82no—
153#11737—431nomaximal, Sylow
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—22no—
157C22×C43—42no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—81no—
164C22×C43—81no—
165C22×C43—81no—
166C22×C43C2×#9911yescharacteristic
167C22×C43#41611yescharacteristic
168C22×C43C2×#10411yescharacteristic
169C2×D43—81no—
170C2×D43—81no—
171C2×D43—81no—
172C2×D43—81no—
173C2×D43—81no—
174C2×D43—81no—
175C2×D43—81no—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—22no—
179C4×C43—41no—
180C4×C43—41no—
181C4×C43—41no—
182Dic43—81no—
183Dic43—81no—
184Dic43—81no—
185#2635—431no—
186C4×#100D4311yescharacteristic, complemented
187#1459—431no—
188#1353—432no—
189#1345—432no—
190C2×C43—21no—
191C2×C43—21no—
192C2×C43—42no—
193C2×C43—81no—
194C2×C43#150111yescharacteristic
195C2×C43#212111yescharacteristic
196C2×C43#213411yescharacteristic
197D43—161no—
198C2×#121—431no—
199C2×C4×D4C2×D4311yescharacteristic
200C2×#100—21no—
201C2×C22⋊C8—861no—
202C4×M16—21no—
203#400—431no—
204#399—431no—
205#394—431no—
206#394—861no—
207#392—431no—
208#392—861no—
209#388—861no—
210#386—861no—
211#381—431no—
212#343C2×D4312yes—
213#324—432no—
214#323—861no—
215C43#1173711yescharacteristic, complemented, Sylow
216C22×D4—431no—
217C22×D4—861no—
218C22×D4—861no—
219C22×D4C22⋊D4311yescharacteristic
220C23×C4C4×D4311yescharacteristic
221C23×C4D17211yescharacteristic
222C2×M16—22no—
223C22×C8—1721no—
224#121—1721no—
225#121—1721no—
226C4×D4—41no—
227C4×D4—41no—
228C2×C4⋊C4—431no—
229C2×C4⋊C4—861no—
230C2×C4⋊C4C22×D4311yescharacteristic
231C2×C22⋊C4—861no—
232C2×C22⋊C4—861no—
233C2×C22⋊C4—861no—
234C2×C22⋊C4—861no—
235C2×C22⋊C4—861no—
236C2×C22⋊C4—861no—
237C2×C22⋊C4C4×D4311yescharacteristic
238C2×C22⋊C4D17211yescharacteristic
239C2×C42C22⋊D4311yescharacteristic
240#100—24no—
241C22⋊C8—862no—
242C22⋊C8—1721no—
243#97—41no—
244C4×C8—41no—
245#95—431no—
246#95—431no—
247#95—861no—
248#95—861no—
249#95—861no—
250C24—861no—
251C24(C2×D43)⋊C411yescharacteristic
252C24(C2×D43)⋊C411yescharacteristic
253C2×D4—22no—
254C2×D4—22no—
255C2×D4—41no—
256C2×D4—3441no—
257C2×D4—3441no—
258C2×D4—3441no—
259C2×D4—3441no—
260C2×D4—3441no—
261C2×D4—1721no—
262C2×D4—1722no—
263C2×D4—1722no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—81no—
269C22×C4—81no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4—861no—
273C22×C4(C2×D43)⋊C411yescharacteristic
274C22×C4(C2×D43)⋊C411yescharacteristic
275C22×C4C2×C4×D4311yescharacteristic
276C22×C4C2×D17211yescharacteristic
277C22×C4C2×C22⋊D4311yescharacteristic
278M16—24no—
279M16—42no—
280C2×C8—42no—
281C2×C8—3442no—
282C2×C8—1722no—
283C4⋊C4—41no—
284C4⋊C4—3441no—
285C4⋊C4—1721no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—3441no—
289C22⋊C4—3441no—
290C22⋊C4—3441no—
291C22⋊C4—3441no—
292C22⋊C4—1721no—
293C22⋊C4—1721no—
294C22⋊C4—1722no—
295C42—21no—
296C42—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—1721no—
307C23—1721no—
308C23—1721no—
309C23—1721no—
310C23—1721no—
311C23—1721no—
312C23—1721no—
313C23#1306325312yes—
314C23C2×(C2×D43)⋊C411yescharacteristic
315D4—44no—
316D4—3442no—
317D4—3444no—
318D4—3444no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—1721no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4—1721no—
336C2×C4—1721no—
337C2×C4—1721no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4—1721no—
341C2×C4#1306323911yescharacteristic
342C2×C4#1306323911yescharacteristic
343C2×C4#1306334512yes—
344C8—44no—
345C8—3442no—
346C22—21no—
347C22—21no—
348C22—22no—
349C22—42no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—3441no—
359C22—3441no—
360C22—3441no—
361C22—3441no—
362C22—3441no—
363C22—3441no—
364C22—3441no—
365C22C2×#1306323911yescharacteristic
366C22#1458289311yescharacteristic
367C22C2×#1306325311yescharacteristic
368C4—22no—
369C4—21no—
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—3441no—
375C4—3441no—
376C4—3441no—
377C2—21no—
378C2—21no—
379C2—42no—
380C2—81no—
381C2—6881no—
382C2#1913308411yescharacteristic
383C2#1913624211yescharacteristic
384C2#1913628611yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC4×#100×C43C2
socleC22×C43C2×#99
prime radical#19140479C2
cosocleC2×C4⋊C4×C43C23
hypercenterC4×#100D43
hypocenterC43#11737
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
2. #19132913C2semidirect
3. #19132621C2semidirect
4. #19132597C2semidirect
5. C4×#100×C43C2semidirect
186. C4×#100D43semidirect
215. C43#11737semidirect

Maximal subgroups

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

subgroupindex
#191404792
#191329132
#191326212
#191325972
C4×#100×C432
#1173743