Finite Group Databasebeta

← #24985152

Subgroups — #24985152

Order 11008.

394 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 95 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#19142954C211yesmaximal, characteristic
2#19134737C211yesmaximal, characteristic
3#19134342C211yesmaximal, characteristic
4#19132419C211yesmaximal, characteristic
5#19132418C211yesmaximal, characteristic
6#19132417C211yesmaximal, characteristic
7C43×#1271C211yesmaximal, characteristic
8C2×#13063315—21no—
9C2×#13063235—21no—
10#14582798C411yescharacteristic
11#14582797C2211yescharacteristic
12#14582796—21no—
13#14582795C411yescharacteristic
14#14582794—21no—
15#14582768C411yescharacteristic
16#14582768C411yescharacteristic
17#14582763—21no—
18C42×Dic43C2211yescharacteristic
19#14582654C2211yescharacteristic
20#14582654C2211yescharacteristic
21#14582653—21no—
22#14582653—21no—
23#14582653—21no—
24C43×#389C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×C43⋊C8—21no—
28C22×C43⋊C8—21no—
29#13063315—42no—
30#13063315—42no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43C2×C411yescharacteristic
33C2×C4⋊Dic43C2×C411yescharacteristic
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×C4×Dic43C2×C411yescharacteristic
41C2×C4×Dic43C2×C411yescharacteristic
42C2×C4×Dic43D411yescharacteristic
43C2×C4×Dic43D411yescharacteristic
44C2×C4×Dic43D411yescharacteristic
45C2×C4×Dic43D411yescharacteristic
46#13063235—24no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C22×C8×C43—21no—
51C22×C8×C43—21no—
52C2×C4⋊C4×C43—21no—
53C2×C4⋊C4×C43C2×C411yescharacteristic
54C2×C4⋊C4×C43C2×C411yescharacteristic
55C2×C42×C43C2311yescharacteristic
56#95×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43C22×C411yescharacteristic
60C22×C4×C43C2×D411yescharacteristic
61C22×C4×C43C2×D411yescharacteristic
62C22×Dic43—21no—
63C22×Dic43—21no—
64C22×Dic43C22⋊C411yescharacteristic
65C22×Dic43C22⋊C411yescharacteristic
66C22×Dic43C22⋊C411yescharacteristic
67C22×Dic43C22⋊C411yescharacteristic
68C2×C8×C43—22no—
69C2×C8×C43—41no—
70C2×C8×C43—41no—
71C2×C8×C43—41no—
72C2×C8×C43—41no—
73C2×C8×C43—41no—
74C4⋊C4×C43—21no—
75C4⋊C4×C43—21no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C42×C43—41no—
80C4⋊Dic43—21no—
81C4⋊Dic43—21no—
82C4⋊Dic43—42no—
83C4⋊Dic43—41no—
84Dic43⋊C4—42no—
85Dic43⋊C4—42no—
86Dic43⋊C4—42no—
87Dic43⋊C4—42no—
88Dic43⋊C4—41no—
89Dic43⋊C4—41no—
90Dic43⋊C4—42no—
91C4×Dic43—21no—
92C4×Dic43—21no—
93C4×Dic43—21no—
94C4×Dic43—21no—
95C4×Dic43—21no—
96C4×Dic43—21no—
97C4×Dic43—22no—
98C4×Dic43—22no—
99C4×Dic43—41no—
100C2×C43⋊C8—22no—
101C2×C43⋊C8—41no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8—41no—
104C2×C43⋊C8—41no—
105C2×C43⋊C8—41no—
106C23×C43C2×C22⋊C411yescharacteristic
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43#13111yescharacteristic
120C2×C4×C43#13111yescharacteristic
121C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C43#13711yescharacteristic
124C2×C4×C43#13711yescharacteristic
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43#10112yes—
142C2×Dic43#10412yes—
143C8×C43—42no—
144C8×C43—81no—
145C43⋊C8—42no—
146C43⋊C8—81no—
147#7703—431nomaximal, Sylow
148C22×C43#40811yescharacteristic
149C22×C43#41011yescharacteristic
150C22×C43C2×#10111yescharacteristic
151C22×C43#41811yescharacteristic
152C22×C43#41911yescharacteristic
153C22×C43C2×#10411yescharacteristic
154C22×C43#42111yescharacteristic
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—81no—
162C4×C43—81no—
163Dic43—22no—
164Dic43—22no—
165Dic43—41no—
166Dic43—41no—
167Dic43—81no—
168Dic43—81no—
169#2859—431no—
170#1839—431no—
171#1745—431no—
172#1271—431no—
173#1271—431no—
174#1271—431no—
175#1271D4311yescharacteristic
176C2×C43#147011yescharacteristic
177C2×C43#148411yescharacteristic
178C2×C43#149711yescharacteristic
179C2×C43#150611yescharacteristic
180C2×C43#151411yescharacteristic
181C2×C43#152811yescharacteristic
182C2×C43#155611yescharacteristic
183C2×#125—861no—
184C2×#97—861no—
185#389—431no—
186#389—431no—
187#389—431no—
188#389—861no—
189#389—861no—
190#389C2×D4311yescharacteristic
191#384—431no—
192#384—431no—
193#382—861no—
194C43—431no—
195#336—431no—
196#336—431no—
197#336—861no—
198#336—861no—
199#336—861no—
200#336C2×D4311yescharacteristic
201#336C2×D4311yescharacteristic
202C43#770311yescharacteristic, complemented, Sylow
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—861no—
206C22×C8—861no—
207#125—1722no—
208#125—1722no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—431no—
211C2×C4⋊C4—431no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4—861no—
214C2×C4⋊C4—861no—
215C2×C4⋊C4—861no—
216C2×C4⋊C4—861no—
217C2×C4⋊C4—861no—
218C2×C4⋊C4—861no—
219C2×C4⋊C4C4×D4311yescharacteristic
220C2×C4⋊C4C4×D4311yescharacteristic
221C2×C42—431no—
222C2×C42—431no—
223C2×C42—431no—
224C2×C42—431no—
225C2×C42—431no—
226C2×C42—431no—
227C2×C42C22×D4311yescharacteristic
228#97—864no—
229#95—21no—
230#95—861no—
231#95—861no—
232#95—861no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—431no—
236C22×C4—431no—
237C22×C4—431no—
238C22×C4—431no—
239C22×C4—861no—
240C22×C4—861no—
241C22×C4C2×C4×D4311yescharacteristic
242C22×C4D4×D4311yescharacteristic
243C22×C4D4×D4311yescharacteristic
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—862no—
251C2×C8—1721no—
252C2×C8—1721no—
253C2×C8—1721no—
254C2×C8—1721no—
255C2×C8—1721no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—861no—
262C4⋊C4—861no—
263C4⋊C4—1721no—
264C4⋊C4—1722no—
265C4⋊C4—1722no—
266C4⋊C4—1722no—
267C4⋊C4—1722no—
268C4⋊C4—1722no—
269C4⋊C4—1722no—
270C4⋊C4—1721no—
271C4⋊C4—1721no—
272C42—41no—
273C42—862no—
274C42—862no—
275C42—861no—
276C42—861no—
277C42—861no—
278C42—861no—
279C42—861no—
280C42—861no—
281C42—1721no—
282C23C22⋊C4×D4311yescharacteristic
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—432no—
296C2×C4—432no—
297C2×C4—861no—
298C2×C4—861no—
299C2×C4—861no—
300C2×C4—861no—
301C2×C4—861no—
302C2×C4—861no—
303C2×C4—861no—
304C2×C4—861no—
305C2×C4—861no—
306C2×C4—861no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4#1306333111yescharacteristic
314C2×C4#1306333311yescharacteristic
315C2×C4#1306334911yescharacteristic
316C2×C4#1306335211yescharacteristic
317C2×C4#1306335411yescharacteristic
318C2×C4#1306335711yescharacteristic
319C8—42no—
320C8—81no—
321C8—3441no—
322C8—1722no—
323C22#1458286411yescharacteristic
324C22#1458287111yescharacteristic
325C22#101×D4311yescharacteristic
326C22#1458290211yescharacteristic
327C22#1458290611yescharacteristic
328C22#104×D4311yescharacteristic
329C22#1458291411yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—81no—
337C4—81no—
338C4—862no—
339C4—862no—
340C4—3441no—
341C4—3441no—
342C4—1721no—
343C4—1721no—
344C2#1913294911yescharacteristic
345C2#1913301011yescharacteristic
346C2#1913306611yescharacteristic
347C2#1913310511yescharacteristic
348C2#1913314011yescharacteristic
349C2#1913319511yescharacteristic
350C2#1913331011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1271C2
socle, prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1271D43
hypocenterC43#7703
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
202. C43#7703semidirect

Maximal subgroups

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

subgroupindex
#191429542
#191347372
#191343422
#191324192
#191324182
#191324172
C43×#12712
#770343