Finite Group Databasebeta

← #25012853

Subgroups — #25012853

Order 11008.

670 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 87 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#19137082C211yesmaximal, characteristic
2#19134511C212yesmaximal
3#19132720C211yesmaximal, characteristic, complemented
4#19132719C212yesmaximal, complemented
5C43×#1393C211yesmaximal, characteristic, complemented
6C22×#10621900C2211yescharacteristic
7C2×#13063283C411yescharacteristic, complemented
8C2×C42×D43C411yescharacteristic, complemented
9C2×#13063240C2212yes—
10C2×#13063239—22no—
11#14582805C411yescharacteristic, complemented
12#14582804C411yescharacteristic, complemented
13#14582802C2211yescharacteristic
14#14582775—22no—
15#14582760—22no—
16C22⋊C4×Dic43—22no—
17C2×#99×C43C2212yes—
18C43×#390C2211yescharacteristic
19C2×#10621900—22no—
20C2×#10621900—21no—
21C2×#10621900—21no—
22C2×#10621900—42no—
23C2×#10621900—42no—
24C22×Dic86C2×C411yescharacteristic
25C22×C22⋊D43D412yes—
26C23×Dic43D412yes—
27C22×C4×D43—21no—
28C22×C4×D43C2×C411yescharacteristic
29#13063283—42no—
30C2×C4⋊Dic43C2×C411yescharacteristic
31C2×C22⋊Dic43—22no—
32C2×C22⋊Dic43—22no—
33C2×(C2×D43)⋊C4—21no—
34C2×C4×Dic43—21no—
35C2×C4×Dic43—21no—
36C2×C4×Dic43C2×C411yescharacteristic
37C42×D43—42no—
38#13063240—22no—
39#13063240—22no—
40#13063239—44no—
41C43⋊#95—22no—
42C43⋊#95—22no—
43C43⋊#95—44no—
44C22×D4×C43C2311yescharacteristic
45C2×C4⋊C4×C43C2×C411yescharacteristic
46C2×C22⋊C4×C43—22no—
47C2×C22⋊C4×C43—22no—
48C2×C42×C43C2×C411yescharacteristic
49#99×C43—22no—
50#99×C43—22no—
51C24×C43C2×D412yes—
52C23×D43C22⋊C411yescharacteristic
53C2×D4×C43—41no—
54C2×D4×C43—41no—
55C2×D4×C43#4112yes—
56C2×D4×C43#4111yescharacteristic
57C2×D4×C43#4111yescharacteristic
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—42no—
61C22×C4×C43C22×C411yescharacteristic
62C2×C22⋊D43—22no—
63C2×C22⋊D43—22no—
64C2×C22⋊D43—24no—
65C2×C22⋊D43—42no—
66C22×Dic43—24no—
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43—22no—
70C22×Dic43—22no—
71C22×Dic43—42no—
72C22×Dic43—42no—
73C22×Dic43C22⋊C412yes—
74C22×Dic43C22⋊C411yescharacteristic
75#10621900—48no—
76#10621900—44no—
77#10621900—44no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—22no—
81C2×C4×D43—22no—
82C2×C4×D43—42no—
83C2×C4×D43—42no—
84C2×C4×D43—42no—
85C2×Dic86—21no—
86C2×Dic86—21no—
87C2×Dic86—41no—
88C2×Dic86—41no—
89C4⋊C4×C43—41no—
90C22⋊C4×C43—42no—
91C22⋊C4×C43—44no—
92C22⋊C4×C43—42no—
93C42×C43—41no—
94C22⋊Dic43—42no—
95C22⋊Dic43—44no—
96C22⋊Dic43—42no—
97(C2×D43)⋊C4—42no—
98C4⋊Dic43—41no—
99C4×Dic43—42no—
100C4×Dic43—42no—
101C4×Dic43—41no—
102C23×C43—22no—
103C23×C43—22no—
104C23×C43—42no—
105C23×C43—42no—
106C23×C43C2×C22⋊C411yescharacteristic
107C23×C43#12312yes—
108C23×C43#12312yes—
109C22×D43—21no—
110C22×D43—21no—
111C22×D43—41no—
112C22×D43—41no—
113C22×D43#9912yes—
114D4×C43—42no—
115D4×C43—41no—
116D4×C43—41no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—22no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—42no—
123C2×C4×C43—41no—
124C2×C4×C43—82no—
125C2×C4×C43—82no—
126C2×C4×C43—82no—
127C2×C4×C43#11711yescharacteristic
128C2×C4×C43#11711yescharacteristic
129C22⋊D43—44no—
130C22⋊D43—44no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—22no—
134C2×Dic43—22no—
135C2×Dic43—22no—
136C2×Dic43—22no—
137C2×Dic43—44no—
138C2×Dic43—44no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—42no—
142C2×Dic43—41no—
143C2×Dic43—82no—
144C2×Dic43—82no—
145C2×Dic43—82no—
146C2×Dic43#9912yes—
147C4×D43—24no—
148C4×D43—24no—
149C4×D43—48no—
150Dic86—42no—
151Dic86—42no—
152#12857—431nomaximal, Sylow
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—22no—
156C22×C43—22no—
157C22×C43—42no—
158C22×C43—42no—
159C22×C43—42no—
160C22×C43—42no—
161C22×C43—82no—
162C22×C43#38111yescharacteristic
163C22×C43C2×#9911yescharacteristic
164C22×C43C2×#9911yescharacteristic
165C2×D43—22no—
166C2×D43—42no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—42no—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43—42no—
173C4×C43—81no—
174C4×C43—162no—
175Dic43—22no—
176Dic43—42no—
177Dic43—42no—
178Dic43—81no—
179Dic43—162no—
180#2297—431no—
181#1782—432no—
182#1393—432no—
183#1393—431no—
184#1393D4311yescharacteristic, complemented
185C2×C43—21no—
186C2×C43—21no—
187C2×C43—42no—
188C2×C43—42no—
189C2×C43#181911yescharacteristic
190C2×C43#212611yescharacteristic
191C2×C43#212611yescharacteristic
192D43—42no—
193C22×#41—431no—
194C2×#117—431no—
195C22×C42—431no—
196C2×#99—432no—
197C2×#99—862no—
198C2×#99C2×D4312yes—
199#391—431no—
200#391—431no—
201#390—431no—
202#390C2×D4311yescharacteristic
203#386—862no—
204#381—862no—
205C4×C22⋊C4—862no—
206C43#1285711yescharacteristic, complemented, Sylow
207C2×#41—862no—
208C2×#41—861no—
209C2×#41—861no—
210C2×#41—1722no—
211C2×#41—1722no—
212C22×Q8—431no—
213C22×D4—432no—
214C22×D4C22×D4311yescharacteristic
215C23×C4—432no—
216C23×C4—431no—
217C23×C4—861no—
218#117—1722no—
219C2×C4⋊C4—431no—
220C2×C4⋊C4C4×D4311yescharacteristic
221C2×C22⋊C4—22no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—861no—
224C2×C22⋊C4—862no—
225C2×C22⋊C4—862no—
226C2×C42—431no—
227C2×C42—861no—
228C2×C42—861no—
229C2×C42—1722no—
230C2×C42C4×D4311yescharacteristic
231#99—22no—
232#99—22no—
233#99—862no—
234#99—862no—
235#99—1724no—
236#95—862no—
237#95—862no—
238#95—1724no—
239C24—431no—
240C24D4×D4312yes—
241#41—1728no—
242#41—1724no—
243#41—1724no—
244C2×Q8—861no—
245C2×Q8—861no—
246C2×Q8—1721no—
247C2×Q8—1721no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—864no—
251C2×D4—862no—
252C2×D4—862no—
253C2×D4—1722no—
254C2×D4#1062189812yes—
255C2×D4#1062190011yescharacteristic
256C2×D4#1062190211yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—42no—
260C22×C4—431no—
261C22×C4—432no—
262C22×C4—862no—
263C22×C4—862no—
264C22×C4—864no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—862no—
269C22×C4—862no—
270C22×C4—861no—
271C22×C4—1722no—
272C22×C4—1722no—
273C22×C4—1722no—
274C22×C4—1722no—
275C22×C4—1722no—
276C22×C4C2×C4×D4311yescharacteristic
277C4⋊C4—41no—
278C4⋊C4—1721no—
279C22⋊C4—44no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—1722no—
283C22⋊C4—1724no—
284C22⋊C4—1722no—
285C22⋊C4—1722no—
286C42—41no—
287C42—1721no—
288C42—1722no—
289C42—1722no—
290C23—22no—
291C23—22no—
292C23—42no—
293C23—42no—
294C23—432no—
295C23—861no—
296C23—861no—
297C23—1721no—
298C23—1721no—
299C23C22⋊C4×D4311yescharacteristic
300C23#1306330712yes—
301C23#1306331012yes—
302Q8—1722no—
303Q8—1722no—
304D4—42no—
305D4—41no—
306D4—41no—
307D4—1724no—
308D4—1724no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—82no—
317C2×C4—82no—
318C2×C4—82no—
319C2×C4—432no—
320C2×C4—864no—
321C2×C4—864no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—862no—
325C2×C4—862no—
326C2×C4—862no—
327C2×C4—862no—
328C2×C4—3442no—
329C2×C4—3442no—
330C2×C4—3442no—
331C2×C4—1728no—
332C2×C4—1724no—
333C2×C4—1724no—
334C2×C4—1722no—
335C2×C4—1721no—
336C2×C4—1721no—
337C2×C4—1721no—
338C2×C4#1306328211yescharacteristic
339C2×C4#1306328311yescharacteristic
340C22—21no—
341C22—21no—
342C22—22no—
343C22—22no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22—42no—
348C22—82no—
349C22—862no—
350C22—1722no—
351C22—1722no—
352C22—1721no—
353C22—1721no—
354C22#1458276111yescharacteristic
355C22#99×D4311yescharacteristic
356C22#99×D4311yescharacteristic
357C4—21no—
358C4—21no—
359C4—42no—
360C4—81no—
361C4—162no—
362C4—862no—
363C4—3441no—
364C4—1722no—
365C4—1722no—
366C4—6882no—
367C2—21no—
368C2—21no—
369C2—42no—
370C2—42no—
371C2—1722no—
372C2#1913466811yescharacteristic
373C2#1913625711yescharacteristic
374C2#1913625911yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC22×D4C22×D43
FittingC43×#1393C2
socleC22×C43C2×#99
prime radicalC22×#10621900C22
cosocleC22×D4×C43C23
hypercenter#1393D43
hypocenterC43#12857
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1393

Complements

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

NH ≅ G/Ntype
3. #19132720C2semidirect
4. #19132719C2semidirect
5. C43×#1393C2semidirect
7. C2×#13063283C4semidirect
8. C2×C42×D43C4semidirect
11. #14582805C4semidirect
12. #14582804C4semidirect
184. #1393D43semidirect
206. C43#12857semidirect

Maximal subgroups

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

subgroupindex
#191370822
#191345112
#191327202
#191327192
C43×#13932
#1285743