Finite Group Databasebeta

← #25009647

Subgroups — #25009647

Order 11008.

378 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 57 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#19142560C211yesmaximal, characteristic
2#19135949C211yesmaximal, characteristic
3#19133622C211yesmaximal, characteristic
4#19133619C211yesmaximal, characteristic
5#19132618C211yesmaximal, characteristic
6#19132542C211yesmaximal, characteristic
7C43×#1352C211yesmaximal, characteristic
8#14583525C2211yescharacteristic
9#14583235—21no—
10#14583234—21no—
11#14582840—21no—
12#14582835C2211yescharacteristic
13#14582832—21no—
14#14582794—21no—
15#14582794—21no—
16#14582787—21no—
17#14582774—21no—
18#14582771—21no—
19#14582771C2211yescharacteristic
20#14582665—21no—
21#14582637—21no—
22#14582635—21no—
23#14582623C2211yescharacteristic
24C43×#399C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C23×Dic43D411yescharacteristic
28#13063304—21no—
29#13063304—21no—
30#13063302—41no—
31#13063302—41no—
32C2×C4⋊Dic43—41no—
33C2×C4⋊Dic43D411yescharacteristic
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×C22⋊Dic43—21no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43D411yescharacteristic
42C2×C4×Dic43—21no—
43#13063259—41no—
44#13063258—41no—
45#13063250—41no—
46#13063248—41no—
47C22⋊(C43⋊C8)—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—41no—
54C43⋊#95D411yescharacteristic
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43—21no—
59C2×C22⋊C4×C43C2311yescharacteristic
60C22⋊C8×C43—21no—
61#95×C43D411yescharacteristic
62C24×C43C2×D411yescharacteristic
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—41no—
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—41no—
75C22×Dic43—81no—
76C2×Dic86—21no—
77C2×Dic86—21no—
78C2×C8×C43—41no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—81no—
81C22⋊C4×C43—22no—
82C22⋊C4×C43—41no—
83C22⋊C4×C43—41no—
84C22⋊C4×C43—81no—
85C22⋊Dic43—21no—
86C22⋊Dic43—41no—
87C22⋊Dic43—42no—
88C22⋊Dic43—41no—
89C22⋊Dic43Q1612yes—
90C4⋊Dic43—21no—
91C4⋊Dic43—21no—
92C4⋊Dic43—41no—
93C4⋊Dic43—82no—
94Dic43⋊C4—42no—
95Dic43⋊C4—42no—
96Dic43⋊C4—41no—
97Dic43⋊C4—41no—
98Dic43⋊C4—81no—
99Dic43⋊C4—81no—
100Dic43⋊C4—81no—
101C4×Dic43—81no—
102C2×C43⋊C8—41no—
103C23×C43—21no—
104C23×C43—21no—
105C23×C43—41no—
106C23×C43—41no—
107C23×C43#12011yescharacteristic
108C23×C43C2×Q1611yescharacteristic
109C23×C43#13711yescharacteristic
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—42no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—81no—
122C2×C4×C43—81no—
123C2×Dic43—22no—
124C2×Dic43—22no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—42no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—81no—
139C2×Dic43—81no—
140C2×Dic43—81no—
141Dic86—81no—
142Dic86—81no—
143C8×C43—81no—
144C43⋊C8—81no—
145#12255—431nomaximal, Sylow
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43—81no—
155C22×C43#45111yescharacteristic
156C22×C43#45611yescharacteristic
157C22×C43B(4,𝔽2)11yescharacteristic
158C4×C43—41no—
159C4×C43—41no—
160C4×C43—81no—
161C4×C43—82no—
162C4×C43—81no—
163Dic43—42no—
164Dic43—42no—
165Dic43—81no—
166Dic43—81no—
167Dic43—81no—
168Dic43—81no—
169#2807—431no—
170#2062—431no—
171#1614—431no—
172#1614—431no—
173#1352—431no—
174#1352D4311yescharacteristic
175#1326—431no—
176C2×C43—21no—
177C2×C43—21no—
178C2×C43—41no—
179C2×C43—41no—
180C2×C43#160511yescharacteristic
181C2×C43#219811yescharacteristic
182C2×C43#220011yescharacteristic
183#543—431no—
184#484—861no—
185#484—861no—
186#400—861no—
187#399—431no—
188#399C2×D4311yescharacteristic
189#398—861no—
190#389—861no—
191#389—861no—
192#388—861no—
193#385—431no—
194#385—861no—
195#385—861no—
196#342—861no—
197#342C2×D4311yescharacteristic
198#328—861no—
199#328—861no—
200#323—431no—
201#323C2×D4311yescharacteristic
202C43#1225511yescharacteristic, complemented, Sylow
203C23×C4—431no—
204C22⋊Q8—861no—
205C22⋊Q8—861no—
206C22⋊Q8—1721no—
207C22⋊Q8—1721no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—431no—
210C2×C4⋊C4—861no—
211C2×C4⋊C4—861no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4—861no—
214C2×C4⋊C4—861no—
215C2×C4⋊C4—1721no—
216C2×C4⋊C4D17211yescharacteristic
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—431no—
220C2×C22⋊C4—861no—
221C2×C22⋊C4—861no—
222C2×C22⋊C4C22×D4311yescharacteristic
223C2×C42—861no—
224#107—1721no—
225#107—1721no—
226#103—1721no—
227#103—1721no—
228C22⋊C8—21no—
229C22⋊C8—861no—
230#95—431no—
231#95—861no—
232#95—861no—
233#95—861no—
234#95—861no—
235#95—861no—
236#95—1721no—
237#95D17211yescharacteristic
238C24D4×D4311yescharacteristic
239C2×Q8—861no—
240C2×Q8—861no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—41no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4—861no—
247C22×C4—861no—
248C22×C4—861no—
249C22×C4—861no—
250C22×C4—3441no—
251C22×C4—1721no—
252C22×C4C2×D17211yescharacteristic
253C22×C4D4×D4311yescharacteristic
254C2×C8—41no—
255C2×C8—1721no—
256C4⋊C4—41no—
257C4⋊C4—81no—
258C4⋊C4—861no—
259C4⋊C4—861no—
260C4⋊C4—3441no—
261C4⋊C4—3441no—
262C4⋊C4—3441no—
263C4⋊C4—3442no—
264C4⋊C4—1721no—
265C4⋊C4—1721no—
266C4⋊C4—1721no—
267C4⋊C4—1722no—
268C4⋊C4—1722no—
269C22⋊C4—22no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—81no—
273C22⋊C4—432no—
274C22⋊C4—861no—
275C22⋊C4—1722no—
276C22⋊C4—1721no—
277C22⋊C4—1721no—
278C42—3441no—
279C23—21no—
280C23—21no—
281C23—41no—
282C23—41no—
283C23#1306329511yescharacteristic
284C23Q16×D4311yescharacteristic
285C23#1306335411yescharacteristic
286Q8—3441no—
287Q8—3441no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—862no—
302C2×C4—862no—
303C2×C4—3441no—
304C2×C4—3441no—
305C2×C4—3441no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1722no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C8—81no—
320C8—3441no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—81no—
330C22#1458305611yescharacteristic
331C22#1458308311yescharacteristic
332C22#1458308711yescharacteristic
333C4—41no—
334C4—41no—
335C4—81no—
336C4—82no—
337C4—81no—
338C4—3441no—
339C4—3441no—
340C4—3441no—
341C4—3441no—
342C4—1722no—
343C4—1722no—
344C2—21no—
345C2—21no—
346C2—41no—
347C2—41no—
348C2#1913357011yescharacteristic
349C2#1913659211yescharacteristic
350C2#1913660511yescharacteristic
subgroupG/H
centerC22#14583087
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1352C2
socleC22×C43B(4,𝔽2)
prime radicalC24×C43C2×D4
hypercenter#1352D43
hypocenterC43#12255
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
202. C43#12255semidirect

Maximal subgroups

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

subgroupindex
#191425602
#191359492
#191336222
#191336192
#191326182
#191325422
C43×#13522
#1225543