Finite Group Databasebeta

← #25007291

Subgroups — #25007291

Order 11008.

448 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 79 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#19140337C211yesmaximal, characteristic
2#19132925C211yesmaximal, characteristic, complemented
3#19132600C212yesmaximal, complemented
4#19132597C212yesmaximal, complemented
5C43×#1821C211yesmaximal, characteristic, complemented
6C2×#13063308—21no—
7C2×#13063299C411yescharacteristic
8#14582863—21no—
9#14582829C411yescharacteristic
10#14582829C2211yescharacteristic
11#14582821—21no—
12#14582821—21no—
13#14582816C411yescharacteristic
14#14582816C2211yescharacteristic
15#14582778—21no—
16#14582759C411yescharacteristic
17#14582625—21no—
18#14582625C2212yes—
19C22×C4⋊C4×C43C2211yescharacteristic
20C43×#407—21no—
21C43×#343—21no—
22C43×#343C2212yes—
23C22×D172C2×C411yescharacteristic
24C22×C22⋊D43—21no—
25C2×#10621877—41no—
26#13063308—44no—
27#13063299—41no—
28#13063299—41no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43C2×C411yescharacteristic
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×C22⋊Dic43—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C22⋊(C43⋊C8)—22no—
40C22⋊(C43⋊C8)—41no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95C2×C411yescharacteristic
44C43⋊#95C2×C411yescharacteristic
45C23×C4×C43C2×C411yescharacteristic
46C23×C4×C43D411yescharacteristic
47C23×C4×C43D411yescharacteristic
48C2×M16×C43—22no—
49C2×C4⋊C4×C43—41no—
50C2×C4⋊C4×C43—41no—
51C2×C4⋊C4×C43C2×C411yescharacteristic
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C4⋊C4×C43D411yescharacteristic
54C2×C4⋊C4×C43C2311yescharacteristic
55C22⋊C8×C43—41no—
56C22⋊C8×C43—41no—
57C24×C43C22⋊C411yescharacteristic
58C23×D43—21no—
59C22×C4×C43—22no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—41no—
67C22×C4×C43—81no—
68C22×C4×C43—81no—
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22×C411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C2×C22⋊D43—42no—
76C2×C22⋊D43—42no—
77C2×C22⋊D43—41no—
78C2×C22⋊D43—41no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C2×D172—41no—
83C2×D172—81no—
84M16×C43—42no—
85M16×C43—42no—
86C2×C8×C43—42no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C22⋊Dic43—42no—
92(C2×D43)⋊C4—42no—
93(C2×D43)⋊C4—42no—
94(C2×D43)⋊C4—42no—
95(C2×D43)⋊C4—81no—
96(C2×D43)⋊C4—81no—
97C4⋊Dic43—41no—
98C4⋊Dic43—81no—
99Dic43⋊C4—42no—
100Dic43⋊C4—42no—
101#10621877—82no—
102C2×C43⋊C8—42no—
103C23×C43—21no—
104C23×C43—21no—
105C23×C43—41no—
106C23×C43—41no—
107C23×C43#9911yescharacteristic
108C23×C43#9911yescharacteristic
109C23×C43C2×C22⋊C411yescharacteristic
110C22×D43—41no—
111C22×D43—41no—
112C22×D43—41no—
113C22×D43—41no—
114C22×D43—41no—
115C22×D43—41no—
116C22×D43—41no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—42no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43—41no—
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×C43AGL(1,ℤ/8)12yes—
137C22⋊D43—82no—
138C22⋊D43—82no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148D172—82no—
149C8×C43—82no—
150C43⋊C8—82no—
151#11805—431nomaximal, Sylow
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—42no—
161C22×C43—42no—
162C22×C43C2×#9911yescharacteristic
163C22×C43#41811yescharacteristic
164C22×C43#42111yescharacteristic
165C2×D43—81no—
166C2×D43—81no—
167C2×D43—81no—
168C2×D43—81no—
169C2×D43—81no—
170C2×D43—81no—
171C2×D43—81no—
172C4×C43—22no—
173C4×C43—41no—
174C4×C43—41no—
175C4×C43—41no—
176C4×C43—41no—
177C4×C43—41no—
178Dic43—81no—
179Dic43—81no—
180Dic43—81no—
181#2618—431no—
182#1821D4311yescharacteristic, complemented
183#1463—431no—
184#1346—432no—
185#1345—432no—
186C2×C43—21no—
187C2×C43—21no—
188C2×C43—41no—
189C2×C43—41no—
190C2×C43#151011yescharacteristic
191C2×C43#212111yescharacteristic
192C2×C43#213311yescharacteristic
193D43—161no—
194C2×#123—861no—
195C2×#121—431no—
196C22×C4⋊C4C2×D4311yescharacteristic
197#407—21no—
198#407—861no—
199#398—431no—
200#398—431no—
201#396—861no—
202#396—861no—
203#394—431no—
204#394—431no—
205#386—861no—
206#380—431no—
207#343—21no—
208#343C2×D4312yes—
209#324—432no—
210#324—861no—
211C43#1180511yescharacteristic, complemented, Sylow
212C22×D4—431no—
213C22×D4—861no—
214C23×C4C4×D4311yescharacteristic
215C23×C4D17211yescharacteristic
216C23×C4C22⋊D4311yescharacteristic
217C2×M16—22no—
218C2×M16—1721no—
219#123—1724no—
220#121—1721no—
221#121—1721no—
222C2×C4⋊C4—41no—
223C2×C4⋊C4—41no—
224C2×C4⋊C4—431no—
225C2×C4⋊C4—861no—
226C2×C4⋊C4—861no—
227C2×C4⋊C4—861no—
228C2×C4⋊C4C4×D4311yescharacteristic
229C2×C4⋊C4D17211yescharacteristic
230C2×C4⋊C4C22⋊D4311yescharacteristic
231C2×C4⋊C4C22×D4311yescharacteristic
232C2×C22⋊C4—861no—
233C2×C22⋊C4—861no—
234C2×C22⋊C4—861no—
235C2×C22⋊C4—861no—
236C2×C22⋊C4—861no—
237C2×C22⋊C4—861no—
238C22⋊C8—41no—
239C22⋊C8—41no—
240C22⋊C8—862no—
241C22⋊C8—1721no—
242#95—431no—
243#95—431no—
244#95—861no—
245#95—861no—
246C24—861no—
247C24(C2×D43)⋊C411yescharacteristic
248C2×D4—3441no—
249C2×D4—1721no—
250C2×D4—1722no—
251C2×D4—1722no—
252C2×D4—1721no—
253C2×D4—1721no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—41no—
262C22×C4—81no—
263C22×C4—81no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4(C2×D43)⋊C411yescharacteristic
268C22×C4(C2×D43)⋊C411yescharacteristic
269C22×C4(C2×D43)⋊C411yescharacteristic
270C22×C4C2×C4×D4311yescharacteristic
271C22×C4C2×D17211yescharacteristic
272C22×C4C2×C22⋊D4311yescharacteristic
273M16—42no—
274M16—42no—
275M16—3442no—
276C2×C8—42no—
277C2×C8—1722no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—3441no—
283C4⋊C4—1721no—
284C4⋊C4—1722no—
285C4⋊C4—1722no—
286C22⋊C4—3441no—
287C22⋊C4—3441no—
288C22⋊C4—1722no—
289C22⋊C4—1722no—
290C22⋊C4—1722no—
291C22⋊C4—1722no—
292C23—21no—
293C23—21no—
294C23—41no—
295C23—41no—
296C23—1721no—
297C23—1721no—
298C23—1721no—
299C23—1721no—
300C23—1721no—
301C23—1721no—
302C23—1721no—
303C23#1306323911yescharacteristic
304C23#1306323911yescharacteristic
305C23C2×(C2×D43)⋊C411yescharacteristic
306D4—3442no—
307D4—3442no—
308D4—3442no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4—1721no—
336C2×C4—1721no—
337C2×C4#1306335012yes—
338C8—82no—
339C8—3442no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—42no—
349C22—42no—
350C22—3441no—
351C22—3441no—
352C22—3441no—
353C22—3441no—
354C22—3441no—
355C22—3441no—
356C22—3441no—
357C22C2×#1306323911yescharacteristic
358C22#1458290311yescharacteristic
359C22#1458291711yescharacteristic
360C4—22no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—3441no—
367C4—3441no—
368C4—3441no—
369C2—21no—
370C2—21no—
371C2—41no—
372C2—41no—
373C2—6881no—
374C2#1913312311yescharacteristic
375C2#1913624211yescharacteristic
376C2#1913628211yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1821C2
socleC22×C43C2×#99
prime radicalC2×#13063299C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1821D43
hypocenterC43#11805
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
2. #19132925C2semidirect
3. #19132600C2semidirect
4. #19132597C2semidirect
5. C43×#1821C2semidirect
182. #1821D43semidirect
211. C43#11805semidirect

Maximal subgroups

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

subgroupindex
#191403372
#191329252
#191326002
#191325972
C43×#18212
#1180543