Finite Group Databasebeta

← #24994455

Subgroups — #24994455

Order 11008.

518 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 105 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#19143635C211yesmaximal, characteristic
2#19139954C211yesmaximal, characteristic
3#19134584C211yesmaximal, characteristic
4#19133025C211yesmaximal, characteristic, complemented
5#19133023C211yesmaximal, characteristic, complemented
6#19132453C211yesmaximal, characteristic, complemented
7C43×#1286C211yesmaximal, characteristic, complemented
8C2×C4×Dic86C2211yescharacteristic
9C2×C4×D172C2211yescharacteristic
10#14582978—22no—
11#14582976—22no—
12#14582952C2211yescharacteristic
13#14582923C2211yescharacteristic
14C2×#13063241—21no—
15#14582861—22no—
16#14582836C412yes—
17#14582812C412yes—
18#14582800—21no—
19#14582798—21no—
20#14582773—22no—
21#14582667—21no—
22#14582631—22no—
23#14582629—22no—
24C43×#431C2211yescharacteristic
25C43×#423C2211yescharacteristic
26C43×#382C2211yescharacteristic
27C22×Dic86C2×C411yescharacteristic
28C22×D172D411yescharacteristic
29C22×C4×D43D412yes—
30C2×#10621877—21no—
31C2×#10621872—24no—
32C4×Dic86—21no—
33C4×Dic86—21no—
34C4×Dic86—21no—
35C4×Dic86—21no—
36C4×D172—21no—
37C4×D172—21no—
38C4×D172—21no—
39C4×D172—21no—
40C2×C4⋊Dic43—22no—
41C2×C4⋊Dic43C2×C411yescharacteristic
42C2×C4⋊Dic43D411yescharacteristic
43C2×Dic43⋊C4—21no—
44C2×(C2×D43)⋊C4—22no—
45C2×(C2×D43)⋊C4—22no—
46C2×(C2×D43)⋊C4C2×C412yes—
47C2×C4×Dic43—21no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)—21no—
51#13063241—42no—
52C22⋊(C43⋊C8)—21no—
53(C2×D43)⋊C8—24no—
54C4×C43⋊C8D412yes—
55C43⋊#95—22no—
56C2×M16×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C42×C43C2311yescharacteristic
59C4⋊C8×C43—21no—
60C4⋊C8×C43—21no—
61C4⋊C8×C43—21no—
62C22⋊C8×C43—21no—
63C4×C8×C43D412yes—
64#95×C43—21no—
65#95×C43C2×C412yes—
66C23×D43C22⋊C412yes—
67C22×C4×C43—22no—
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43C22⋊C412yes—
74C2×D172—21no—
75C2×D172—21no—
76C2×D172—21no—
77C2×D172—21no—
78C2×D172—21no—
79C2×D172—21no—
80C2×C4×D43—22no—
81C2×C4×D43—22no—
82C2×C4×D43—82no—
83C2×Dic86—21no—
84C2×Dic86—21no—
85C2×Dic86—42no—
86M16×C43—41no—
87M16×C43—41no—
88C2×C8×C43—22no—
89C2×C8×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C42×C43C2×D411yescharacteristic
93C42×C43C2×D411yescharacteristic
94C42×C43#4111yescharacteristic
95C42×C43#4111yescharacteristic
96(C2×D43)⋊C4—22no—
97(C2×D43)⋊C4—22no—
98(C2×D43)⋊C4—44no—
99(C2×D43)⋊C4—82no—
100C4⋊Dic43—21no—
101C4⋊Dic43—21no—
102C4⋊Dic43—21no—
103C4⋊Dic43—21no—
104C4⋊Dic43—82no—
105Dic43⋊C4—41no—
106Dic43⋊C4—41no—
107C4×Dic43—41no—
108C4×Dic43—41no—
109#10621877—41no—
110#10621877—41no—
111C2×C43⋊C8—22no—
112C2×C43⋊C8—41no—
113#10621872—84no—
114C23×C43C2×C22⋊C411yescharacteristic
115C22×D43—22no—
116C22×D43—22no—
117C22×D43—22no—
118C22×D43—42no—
119C22×D43—42no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—42no—
123C2×C4×C43—42no—
124C2×C4×C43—42no—
125C2×C4×C43C4×D411yescharacteristic
126C2×C4×C43C4×D411yescharacteristic
127C2×C4×C43#12011yescharacteristic
128C2×C4×C43#12111yescharacteristic
129C2×C4×C43#12111yescharacteristic
130C2×C4×C43#12311yescharacteristic
131C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C43#13711yescharacteristic
133C2×C4×C43#13711yescharacteristic
134C2×C4×C43#13711yescharacteristic
135C2×Dic43—22no—
136C2×Dic43—22no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—42no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143D172—41no—
144D172—41no—
145D172—41no—
146D172—41no—
147C4×D43—44no—
148C4×D43—82no—
149Dic86—22no—
150Dic86—22no—
151Dic86—41no—
152Dic86—41no—
153C8×C43—42no—
154C8×C43—81no—
155C43⋊C8—42no—
156C43⋊C8—81no—
157#9487—431nomaximal, Sylow
158C22×C43—21no—
159C22×C43—21no—
160C22×C43#38611yescharacteristic
161C22×C43#41711yescharacteristic
162C22×C43#41911yescharacteristic
163C2×D43—44no—
164C2×D43—42no—
165C2×D43—42no—
166C2×D43—42no—
167C2×D43—82no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43—82no—
173C4×C43#46811yescharacteristic
174C4×C43#46811yescharacteristic
175C4×C43#47011yescharacteristic
176C4×C43#47011yescharacteristic
177Dic43—42no—
178Dic43—42no—
179Dic43—81no—
180#2975—431no—
181#2580—431no—
182#1800—431no—
183#1487—431no—
184#1487—431no—
185#1286—431no—
186#1286D4311yescharacteristic, complemented
187C2×C43—21no—
188C2×C43—21no—
189C2×C43#189111yescharacteristic
190C2×C43#189411yescharacteristic
191C2×C43#191111yescharacteristic
192D43—82no—
193C2×C4×Q8—431no—
194C2×C4×D4—431no—
195#436—862no—
196#436—862no—
197#431—431no—
198#431C2×D4311yescharacteristic
199#423—431no—
200#423C2×D4311yescharacteristic
201C2×#100—861no—
202#407—862no—
203#399—432no—
204#393—432no—
205#390—861no—
206#389—861no—
207#385—862no—
208#382C2×D4311yescharacteristic
209#343—861no—
210Q8⋊C8—862no—
211Q8⋊C8—862no—
212C43#948711yescharacteristic, complemented, Sylow
213C22×Q8—431no—
214C22×D4—431no—
215C23×C4—432no—
216C2×M16—21no—
217C2×M16—864no—
218C2×M16—861no—
219C4×Q8—861no—
220C4×Q8—861no—
221C4×Q8—861no—
222C4×Q8—861no—
223C4×D4—861no—
224C4×D4—861no—
225C4×D4—861no—
226C4×D4—861no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—431no—
229C2×C4⋊C4—431no—
230C2×C4⋊C4—862no—
231C2×C4⋊C4—861no—
232C2×C22⋊C4—432no—
233C2×C22⋊C4—862no—
234C2×C22⋊C4—862no—
235C2×C42—861no—
236C2×C42C22×D4311yescharacteristic
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—861no—
241C4⋊C8—861no—
242C4⋊C8—861no—
243#100—1722no—
244C22⋊C8—21no—
245C22⋊C8—864no—
246C22⋊C8—861no—
247C4×C8—432no—
248C4×C8D17212yes—
249#95—21no—
250#95—862no—
251#95C4×D4312yes—
252C24—432no—
253C2×Q8—861no—
254C2×Q8—861no—
255C2×Q8—1722no—
256C2×D4—861no—
257C2×D4—861no—
258C2×D4—861no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4—861no—
262C22×C4—22no—
263C22×C4—432no—
264C22×C4—861no—
265C22×C4—862no—
266C22×C4—862no—
267C22×C4—861no—
268C22×C4—3442no—
269C22×C4C2×C4×D4311yescharacteristic
270C22×C4D4×D4311yescharacteristic
271C22×C4D4×D4311yescharacteristic
272M16—41no—
273M16—41no—
274M16—3444no—
275M16—1721no—
276M16—1721no—
277C2×C8—22no—
278C2×C8—41no—
279C2×C8—862no—
280C2×C8—1721no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4—861no—
287C4⋊C4—3442no—
288C4⋊C4—1721no—
289C4⋊C4—1721no—
290C22⋊C4—862no—
291C22⋊C4—862no—
292C22⋊C4—3442no—
293C22⋊C4—1724no—
294C42—1721no—
295C42—1721no—
296C42C2×D17211yescharacteristic
297C42#1062189811yescharacteristic
298C42D4×D4311yescharacteristic
299C42#1062190211yescharacteristic
300C23—862no—
301C23—862no—
302C23—862no—
303C23—1722no—
304C23—1722no—
305C23C22⋊C4×D4311yescharacteristic
306Q8—862no—
307Q8—862no—
308Q8—1721no—
309Q8—1721no—
310D4—1721no—
311D4—1721no—
312D4—1721no—
313D4—1721no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—862no—
320C2×C4—862no—
321C2×C4—3442no—
322C2×C4—1724no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4—1721no—
328C2×C4—1722no—
329C2×C4#1306328711yescharacteristic
330C2×C4C4×D17211yescharacteristic
331C2×C4#1306329511yescharacteristic
332C2×C4#1306329811yescharacteristic
333C2×C4#1306330011yescharacteristic
334C2×C4#1306331011yescharacteristic
335C2×C4#1306334911yescharacteristic
336C2×C4#1306335411yescharacteristic
337C2×C4#1306335411yescharacteristic
338C2×C4#1306335711yescharacteristic
339C8—42no—
340C8—81no—
341C8—3441no—
342C8—1722no—
343C22—21no—
344C22—21no—
345C22—3442no—
346C22—1724no—
347C22—1722no—
348C22—1722no—
349C22—1722no—
350C22#1458277711yescharacteristic
351C22#1458289711yescharacteristic
352C22#1458290611yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—82no—
358C4—3441no—
359C4—1722no—
360C4—1722no—
361C4#1458314411yescharacteristic
362C4#1458314611yescharacteristic
363C4#1458315611yescharacteristic
364C4#1458315811yescharacteristic
365C2—21no—
366C2—21no—
367C2—3442no—
368C2#1913501211yescharacteristic
369C2#1913502711yescharacteristic
370C2#1913512611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1286C2
socleC22×C43#386
prime radicalC22×D172D4
cosocleC2×C42×C43C23
hypercenter#1286D43
hypocenterC43#9487
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
4. #19133025C2semidirect
5. #19133023C2semidirect
6. #19132453C2semidirect
7. C43×#1286C2semidirect
186. #1286D43semidirect
212. C43#9487semidirect

Maximal subgroups

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

subgroupindex
#191436352
#191399542
#191345842
#191330252
#191330232
#191324532
C43×#12862
#948743