Finite Group Databasebeta

← #24988256

Subgroups — #24988256

Order 11008.

712 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C2×#14583627C211yesmaximal, characteristic
2C4×#13063244C211yesmaximal, characteristic
3#19133198C212yesmaximal
4#19133041C212yesmaximal
5C43×#1467C211yesmaximal, characteristic
6#14583627—24no—
7#14583627—24no—
8C2×#13063325C411yescharacteristic
9C2×#13063323—21no—
10C2×#13063317C411yescharacteristic
11C2×#13063317C2211yescharacteristic
12C2×#13063315—21no—
13C2×#13063315—21no—
14C2×C4×Dic86C411yescharacteristic
15C2×C4×Dic86C411yescharacteristic
16C2×C4×Dic86C2211yescharacteristic
17C2×#13063290—21no—
18C2×#13063244—21no—
19C4×#10621877C2212yes—
20#14582668—21no—
21#14582640—24no—
22#14582629—24no—
23C2×C4×Q8×C43C2211yescharacteristic
24C43×#432C2212yes—
25C43×#324—21no—
26C43×#324—21no—
27C22×Dic86—21no—
28C22×Dic86C2×C411yescharacteristic
29C2×#10621877—22no—
30#13063325—22no—
31#13063325—22no—
32#13063323—28no—
33#13063317—22no—
34#13063317—22no—
35#13063317—22no—
36#13063317D414yes—
37#13063315—28no—
38#13063315—28no—
39C4×Dic86—22no—
40C4×Dic86—22no—
41C4×Dic86—22no—
42C4×Dic86—22no—
43C4×Dic86—22no—
44C4×Dic86D414yes—
45#13063290—28no—
46C2×C4⋊Dic43—21no—
47C2×C4⋊Dic43C2×C411yescharacteristic
48C2×C4⋊Dic43C2×C411yescharacteristic
49C2×C4⋊Dic43C2×C411yescharacteristic
50C2×Dic43⋊C4—21no—
51C2×Dic43⋊C4—21no—
52C2×Dic43⋊C4—21no—
53C2×Dic43⋊C4—21no—
54C2×Dic43⋊C4—21no—
55C2×Dic43⋊C4—21no—
56C2×Dic43⋊C4—21no—
57C2×C4×Dic43—21no—
58C2×C4×Dic43—21no—
59C2×C4×Dic43—21no—
60#13063244—24no—
61#13063236—22no—
62C4×C43⋊C8—22no—
63C22×Q8×C43D411yescharacteristic
64C4×Q8×C43—22no—
65C4×Q8×C43—22no—
66C2×C4⋊C4×C43D411yescharacteristic
67C2×C4⋊C4×C43D411yescharacteristic
68C2×C4⋊C4×C43D411yescharacteristic
69C2×C42×C43C2×C411yescharacteristic
70C2×C42×C43C2×C411yescharacteristic
71C2×C42×C43C2311yescharacteristic
72C4⋊C8×C43—22no—
73C22⋊C8×C43—22no—
74#97×C43—22no—
75C2×Q8×C43—22no—
76C2×Q8×C43—22no—
77C2×Q8×C43—41no—
78C22×C4×C43C22⋊C411yescharacteristic
79C22×C4×C43C22⋊C411yescharacteristic
80C22×C4×C43C22⋊C411yescharacteristic
81C22×C4×C43C22⋊C411yescharacteristic
82C22×C4×C43C22×C411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C2×Dic86—21no—
90C2×Dic86—24no—
91C2×Dic86—24no—
92C2×Dic86—42no—
93C2×Dic86—42no—
94C2×Dic86C22⋊C412yes—
95C2×C8×C43—42no—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—22no—
99C42×C43—21no—
100C42×C43—21no—
101C42×C43—21no—
102C42×C43—21no—
103C42×C43C2×D412yes—
104C42×C43C2×D412yes—
105C4⋊Dic43—24no—
106C4⋊Dic43—21no—
107C4⋊Dic43—21no—
108C4⋊Dic43—21no—
109C4⋊Dic43C22⋊C412yes—
110C4⋊Dic43C22⋊C412yes—
111C4⋊Dic43C22⋊C412yes—
112Dic43⋊C4—24no—
113Dic43⋊C4—24no—
114Dic43⋊C4—24no—
115Dic43⋊C4—24no—
116Dic43⋊C4—24no—
117Dic43⋊C4—24no—
118Dic43⋊C4—24no—
119C4×Dic43—24no—
120C4×Dic43—24no—
121C4×Dic43—24no—
122#10621877—24no—
123#10621877—42no—
124C2×C43⋊C8—42no—
125C23×C43C2×C22⋊C411yescharacteristic
126Q8×C43—44no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—22no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43#10412yes—
141C2×C4×C43C2×C22⋊C411yescharacteristic
142C2×C4×C43C2×C22⋊C411yescharacteristic
143C2×C4×C43#12012yes—
144C2×C4×C43#12012yes—
145C2×Dic43—24no—
146C2×Dic43—22no—
147C2×Dic43—22no—
148C2×Dic43—22no—
149C2×Dic43—22no—
150C2×Dic43—42no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155Dic86—24no—
156Dic86—22no—
157Dic86—48no—
158Dic86#10114yescomplemented
159C8×C43—82no—
160C43⋊C8—44no—
161#8374—431nomaximal, Sylow
162C22×C43—21no—
163C22×C43—21no—
164C22×C43#37911yescharacteristic
165C22×C43C2×#10411yescharacteristic
166C22×C43#42111yescharacteristic
167C4×C43—22no—
168C4×C43—21no—
169C4×C43—22no—
170C4×C43—22no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43—41no—
174C4×C43C2×#10112yes—
175Dic43—24no—
176Dic43—42no—
177Dic43—42no—
178Dic43—42no—
179C2×#557—431no—
180C4×#101—431no—
181#1528—432no—
182#1491—432no—
183#1467D4311yescharacteristic
184C2×C43—21no—
185C2×C43—21no—
186C2×C43#178411yescharacteristic
187C2×C43#178911yescharacteristic
188C2×C43#179611yescharacteristic
189#557—864no—
190#557—864no—
191C2×C4⋊Q8—431no—
192C2×C4⋊Q8—861no—
193C2×#125—431no—
194C2×#125—431no—
195C2×#125—861no—
196C2×#125—861no—
197C2×C4×Q8—431no—
198C2×C4×Q8—431no—
199C2×C4×Q8—431no—
200C2×C4×Q8—861no—
201C2×C4×Q8C2×D4311yescharacteristic
202#432C2×D4312yes—
203C2×#101—861no—
204C4×M16—432no—
205#343—861no—
206#330—864no—
207Q8⋊C8—864no—
208#324—21no—
209#324—21no—
210C43#837411yescharacteristic, complemented, Sylow
211C22×Q8—431no—
212C22×Q8—861no—
213C22×Q8D17211yescharacteristic
214C2×M16—862no—
215C4⋊Q8—862no—
216C4⋊Q8—862no—
217C4⋊Q8—868no—
218#125—434no—
219#125—862no—
220#125—862no—
221#125—868no—
222#125—868no—
223#125—862no—
224C4×Q8—22no—
225C4×Q8—22no—
226C4×Q8—434no—
227C4×Q8—862no—
228C4×Q8—862no—
229C4×Q8—862no—
230C4×Q8—862no—
231C4×Q8—868no—
232C4×Q8—862no—
233C2×C4⋊C4—431no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4—431no—
236C2×C4⋊C4—861no—
237C2×C4⋊C4—861no—
238C2×C4⋊C4—861no—
239C2×C4⋊C4—861no—
240C2×C4⋊C4—861no—
241C2×C4⋊C4—861no—
242C2×C4⋊C4—861no—
243C2×C4⋊C4—861no—
244C2×C4⋊C4D17211yescharacteristic
245C2×C4⋊C4C22⋊D4311yescharacteristic
246C2×C4⋊C4C22⋊D4311yescharacteristic
247C2×C42—861no—
248C2×C42—861no—
249C2×C42—861no—
250C2×C42C4×D4311yescharacteristic
251C2×C42C4×D4311yescharacteristic
252C2×C42C22×D4311yescharacteristic
253C4⋊C8—22no—
254#101—864no—
255C22⋊C8—22no—
256#97—22no—
257#97—862no—
258C4×C8—862no—
259C2×Q8—22no—
260C2×Q8—22no—
261C2×Q8—41no—
262C2×Q8—432no—
263C2×Q8—864no—
264C2×Q8—864no—
265C2×Q8—861no—
266C2×Q8—1722no—
267C2×Q8—1722no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4(C2×D43)⋊C411yescharacteristic
273C22×C4(C2×D43)⋊C411yescharacteristic
274C22×C4(C2×D43)⋊C411yescharacteristic
275C22×C4(C2×D43)⋊C411yescharacteristic
276C22×C4C2×C4×D4311yescharacteristic
277C22×C4C2×D17211yescharacteristic
278C22×C4C2×C22⋊D4311yescharacteristic
279M16—864no—
280M16—1722no—
281C2×C8—42no—
282C2×C8—1722no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—432no—
287C4⋊C4—432no—
288C4⋊C4—432no—
289C4⋊C4—864no—
290C4⋊C4—864no—
291C4⋊C4—864no—
292C4⋊C4—864no—
293C4⋊C4—864no—
294C4⋊C4—861no—
295C4⋊C4—861no—
296C4⋊C4—861no—
297C4⋊C4—864no—
298C4⋊C4—864no—
299C4⋊C4—864no—
300C42—21no—
301C42—21no—
302C42—21no—
303C42—21no—
304C42—864no—
305C42—864no—
306C42—864no—
307C42D4×D4312yes—
308C42D4×D4312yes—
309C23C2×(C2×D43)⋊C411yescharacteristic
310Q8—44no—
311Q8—434no—
312Q8—864no—
313Q8—862no—
314Q8—1728no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—864no—
329C2×C4—862no—
330C2×C4—862no—
331C2×C4—862no—
332C2×C4—862no—
333C2×C4—1722no—
334C2×C4—1721no—
335C2×C4—1721no—
336C2×C4—1721no—
337C2×C4—1721no—
338C2×C4#1306325112yes—
339C2×C4C22⋊C4×D4311yescharacteristic
340C2×C4C22⋊C4×D4311yescharacteristic
341C2×C4#1306329312yes—
342C2×C4#1306329512yes—
343C8—82no—
344C8—1724no—
345C22—21no—
346C22—21no—
347C22#1458275411yescharacteristic
348C22C2×#1306325111yescharacteristic
349C22#1458291511yescharacteristic
350C4—21no—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—864no—
358C4—1722no—
359C4—1722no—
360C4—1722no—
361C4#101×D4312yes—
362C2—21no—
363C2—21no—
364C2#1913451711yescharacteristic
365C2#1913453811yescharacteristic
366C2#1913456811yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1467C2
socleC22×C43#379
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1467D43
hypocenterC43#8374
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
158. Dic86#101semidirect
210. C43#8374semidirect

Maximal subgroups

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

subgroupindex
C2×#145836272
C4×#130632442
#191331982
#191330412
C43×#14672
#837443