Finite Group Databasebeta

← #25007371

Subgroups — #25007371

Order 11008.

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

normal subgroups only

This group has 446 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#19137879C211yesmaximal, characteristic
2#19132933C211yesmaximal, characteristic
3#19132615C212yesmaximal, complemented
4#19132594C212yesmaximal, complemented
5C43×#1799C211yesmaximal, characteristic
6C2×C4×Dic86C411yescharacteristic, complemented
7#14582863—21no—
8#14582837—21no—
9#14582824C411yescharacteristic, complemented
10#14582824C2211yescharacteristic
11#14582813—21no—
12#14582811C411yescharacteristic, complemented
13#14582811C2211yescharacteristic
14C4×C22⋊Dic43—21no—
15C4×C22⋊Dic43—21no—
16#14582745C411yescharacteristic, complemented
17#14582625—21no—
18#14582623C2212yes—
19C2×C4×D4×C43C2211yescharacteristic
20C2×#99×C43—21no—
21C43×#380—21no—
22C43×#342C2212yes—
23C22×Dic86C2×C411yescharacteristic
24C2×#10621877—41no—
25C4×Dic86—41no—
26C4×Dic86—41no—
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×Dic43⋊C4—21no—
29C2×C22⋊Dic43—21no—
30C2×C22⋊Dic43—21no—
31C2×C22⋊Dic43—21no—
32C2×C22⋊Dic43—21no—
33C2×C4×Dic43—21no—
34C2×C4×Dic43—21no—
35C22⋊(C43⋊C8)—22no—
36C22⋊(C43⋊C8)—41no—
37C43⋊#95—21no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95C2×C411yescharacteristic
43C43⋊#95C2×C411yescharacteristic
44C22×D4×C43D411yescharacteristic
45C23×C4×C43D411yescharacteristic
46C23×C4×C43D411yescharacteristic
47C4×D4×C43—41no—
48C4×D4×C43—41no—
49C2×C4⋊C4×C43—41no—
50C2×C4⋊C4×C43D411yescharacteristic
51C2×C22⋊C4×C43—22no—
52C2×C22⋊C4×C43C2×C411yescharacteristic
53C2×C22⋊C4×C43C2311yescharacteristic
54C2×C42×C43C2×C411yescharacteristic
55#99×C43—42no—
56#95×C43—41no—
57C24×C43C22⋊C411yescharacteristic
58C24×C43C2×D411yescharacteristic
59C2×D4×C43—21no—
60C2×D4×C43—21no—
61C2×D4×C43—41no—
62C2×D4×C43—41no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—42no—
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×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C2×Dic86—41no—
80C2×Dic86—42no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—82no—
83C22⋊C4×C43—41no—
84C22⋊C4×C43—41no—
85C22⋊C4×C43—42no—
86C22⋊C4×C43—42no—
87C42×C43—21no—
88C42×C43—21no—
89C22⋊Dic43—42no—
90C22⋊Dic43—42no—
91C22⋊Dic43—42no—
92C22⋊Dic43—41no—
93C22⋊Dic43—41no—
94C4⋊Dic43—41no—
95Dic43⋊C4—42no—
96C4×Dic43—42no—
97C4×Dic43—41no—
98C4×Dic43—41no—
99#10621877—82no—
100C2×C43⋊C8—42no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43—21no—
104C23×C43—21no—
105C23×C43—21no—
106C23×C43—41no—
107C23×C43—41no—
108C23×C43—41no—
109C23×C43—41no—
110C23×C43C2×C22⋊C411yescharacteristic
111C23×C43AGL(1,ℤ/8)11yescharacteristic
112C23×C43#13711yescharacteristic
113D4×C43—42no—
114D4×C43—42no—
115C2×C4×C43—22no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—42no—
123C2×C4×C43—42no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—81no—
128C2×C4×C43—81no—
129C2×C4×C43—82no—
130C2×C4×C43—82no—
131C2×C4×C43—82no—
132C2×C4×C43#9911yescharacteristic
133C2×C4×C43#9911yescharacteristic
134C2×Dic43—22no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146Dic86—42no—
147Dic86—42no—
148C43⋊C8—82no—
149#11823—431nomaximal, Sylow
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—41no—
155C22×C43—41no—
156C22×C43—42no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—81no—
163C22×C43—81no—
164C22×C43C2×#9911yescharacteristic
165C22×C43#41711yescharacteristic
166C22×C43#42111yescharacteristic
167C4×C43—21no—
168C4×C43—41no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43—162no—
173C4×C43#35412yes—
174Dic43—42no—
175Dic43—81no—
176Dic43—81no—
177Dic43—81no—
178#2398—431no—
179#1799D4311yescharacteristic
180#1465—431no—
181#1351—432no—
182#1344—432no—
183C2×C43—21no—
184C2×C43—21no—
185C2×C43—41no—
186C2×C43—41no—
187C2×C43—81no—
188C2×C43#151311yescharacteristic
189C2×C43#212011yescharacteristic
190C2×C43C2×#35411yescharacteristic
191C2×C4×Q8—431no—
192C2×C4×D4C2×D4311yescharacteristic
193C2×#99—21no—
194#407—861no—
195#400—861no—
196#397—431no—
197#397—431no—
198#394—861no—
199#393—431no—
200#393—431no—
201#380—21no—
202C4×C22⋊C4—861no—
203C4×C22⋊C4—861no—
204#376—431no—
205#342C2×D4312yes—
206#324—861no—
207#323—432no—
208C43#1182311yescharacteristic, complemented, Sylow
209C22×Q8—431no—
210C22×D4C22⋊D4311yescharacteristic
211C23×C4D17211yescharacteristic
212C23×C4C22⋊D4311yescharacteristic
213C2×M16—1721no—
214C4×Q8—1721no—
215C4×Q8—1721no—
216C4×D4—41no—
217C4×D4—41no—
218C2×C4⋊C4—41no—
219C2×C4⋊C4—431no—
220C2×C4⋊C4—861no—
221C2×C4⋊C4D17211yescharacteristic
222C2×C22⋊C4—22no—
223C2×C22⋊C4—861no—
224C2×C22⋊C4—861no—
225C2×C22⋊C4—861no—
226C2×C22⋊C4—861no—
227C2×C22⋊C4C4×D4311yescharacteristic
228C2×C22⋊C4C22×D4311yescharacteristic
229C2×C42—861no—
230C2×C42—861no—
231C2×C42C4×D4311yescharacteristic
232#99—42no—
233C22⋊C8—862no—
234C22⋊C8—1721no—
235#95—41no—
236#95—431no—
237#95—431no—
238#95—861no—
239#95—861no—
240#95—861no—
241#95—861no—
242#95—861no—
243C24(C2×D43)⋊C411yescharacteristic
244C24C2×C22⋊D4311yescharacteristic
245C2×Q8—1721no—
246C2×Q8—1722no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4—41no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4(C2×D43)⋊C411yescharacteristic
263C22×C4(C2×D43)⋊C411yescharacteristic
264C22×C4(C2×D43)⋊C411yescharacteristic
265C22×C4C2×C4×D4311yescharacteristic
266C22×C4C2×D17211yescharacteristic
267M16—3442no—
268C2×C8—1722no—
269C4⋊C4—41no—
270C4⋊C4—82no—
271C4⋊C4—1721no—
272C4⋊C4—1722no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—42no—
276C22⋊C4—42no—
277C22⋊C4—1722no—
278C22⋊C4—1722no—
279C22⋊C4—1722no—
280C22⋊C4—1721no—
281C22⋊C4—1721no—
282C42—21no—
283C42—21no—
284C42—1722no—
285C42—1721no—
286C42—1721no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23C2×(C2×D43)⋊C411yescharacteristic
297C23#1306335111yescharacteristic
298C23#1306335611yescharacteristic
299Q8—1722no—
300Q8—1722no—
301D4—42no—
302D4—42no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—82no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—862no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4—1721no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4#1306323911yescharacteristic
333C2×C4#1306323911yescharacteristic
334C8—3442no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—42no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—81no—
348C22—81no—
349C22C2×#1306323911yescharacteristic
350C22#1458289811yescharacteristic
351C22#1458291711yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—162no—
358C4—3441no—
359C4—3441no—
360C4—3441no—
361C4—1722no—
362C4#1458269312yes—
363C2—21no—
364C2—21no—
365C2—41no—
366C2—41no—
367C2—81no—
368C2#1913313611yescharacteristic
369C2#1913623411yescharacteristic
370C2C2×#1458269311yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1799C2
socleC22×C43C2×#99
prime radicalC22×D4×C43D4
cosocleC2×C22⋊C4×C43C23
hypercenter#1799D43
hypocenterC43#11823
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #19132615C2semidirect
4. #19132594C2semidirect
6. C2×C4×Dic86C4semidirect
9. #14582824C4semidirect
12. #14582811C4semidirect
16. #14582745C4semidirect
208. C43#11823semidirect

Maximal subgroups

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

subgroupindex
#191378792
#191329332
#191326152
#191325942
C43×#17992
#1182343