Finite Group Databasebeta

← #24994468

Subgroups — #24994468

Order 11008.

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

normal subgroups only

This group has 522 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#19143678C211yesmaximal, characteristic, complemented
2#19139504C211yesmaximal, characteristic
3#19134588C211yesmaximal, characteristic, complemented
4#19133020C211yesmaximal, characteristic
5#19132455C211yesmaximal, characteristic, complemented
6#19132454C211yesmaximal, characteristic, complemented
7C43×#1486C211yesmaximal, characteristic
8C2×#13063304—21no—
9C2×C4×Dic86C2211yescharacteristic
10#14583029—22no—
11#14583026—22no—
12#14582953—22no—
13#14582952C2211yescharacteristic
14#14582923C2211yescharacteristic
15C2×#13063243—21no—
16#14582830C412yes—
17#14582813C412yes—
18#14582787—22no—
19#14582765C2211yescharacteristic
20#14582759—21no—
21#14582667—21no—
22D4⋊(C43⋊C8)—22no—
23C2×C4×D4×C43C2211yescharacteristic
24C43×#431C2211yescharacteristic
25C43×#423C2211yescharacteristic
26C43×D4⋊C8—22no—
27C22×Dic86D411yescharacteristic
28C2×#10621877—21no—
29#13063304—42no—
30#13063304—42no—
31C4×Dic86—21no—
32C4×Dic86—21no—
33C4×Dic86—21no—
34C4×Dic86—21no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43D411yescharacteristic
37C2×Dic43⋊C4—22no—
38C2×Dic43⋊C4C2×C412yes—
39C2×C22⋊Dic43—22no—
40C2×C22⋊Dic43—22no—
41C2×C4×Dic43D412yes—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)—21no—
45Dic43⋊C8—24no—
46#13063243—42no—
47C22⋊(C43⋊C8)—21no—
48#13063235—24no—
49C4×C43⋊C8D412yes—
50C43⋊#95—21no—
51C43⋊#95—22no—
52C43⋊#95C2×C412yes—
53C22×D4×C43C2×C411yescharacteristic
54C23×C4×C43—21no—
55C2×M16×C43—21no—
56C4×D4×C43—21no—
57C4×D4×C43—21no—
58C4×D4×C43—21no—
59C4×D4×C43—21no—
60C2×C4⋊C4×C43C2×C411yescharacteristic
61C2×C22⋊C4×C43—21no—
62C2×C42×C43C2311yescharacteristic
63C4⋊C8×C43—21no—
64C4⋊C8×C43—21no—
65C4⋊C8×C43—21no—
66C22⋊C8×C43—21no—
67C4×C8×C43D412yes—
68C24×C43—21no—
69C2×D4×C43—21no—
70C2×D4×C43—21no—
71C2×D4×C43—42no—
72C22×C4×C43—21no—
73C22×C4×C43—41no—
74C22×C4×C43—41no—
75C22×C4×C43—41no—
76C22×C4×C43—41no—
77C22×C4×C43—41no—
78C22×C4×C43—41no—
79C22×C4×C43C22×C411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×Dic43—22no—
83C22×Dic43C22⋊C412yes—
84C22×Dic43C22⋊C412yes—
85C2×Dic86—21no—
86C2×Dic86—21no—
87C2×Dic86—21no—
88C2×Dic86—21no—
89C2×Dic86—21no—
90C2×Dic86—21no—
91M16×C43—41no—
92M16×C43—41no—
93C2×C8×C43—22no—
94C2×C8×C43—41no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—21no—
97C22⋊C4×C43—41no—
98C22⋊C4×C43—41no—
99C42×C43C2×D411yescharacteristic
100C42×C43C2×D411yescharacteristic
101C42×C43#4111yescharacteristic
102C42×C43#4111yescharacteristic
103C22⋊Dic43—44no—
104C22⋊Dic43—44no—
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107C4⋊Dic43—41no—
108C4⋊Dic43—41no—
109Dic43⋊C4—22no—
110Dic43⋊C4—22no—
111Dic43⋊C4—44no—
112C4×Dic43—22no—
113C4×Dic43—22no—
114#10621877—41no—
115#10621877—41no—
116C2×C43⋊C8—22no—
117C2×C43⋊C8—41no—
118C23×C43—22no—
119C23×C43—41no—
120C23×C43—41no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43C2×C22⋊C411yescharacteristic
126D4×C43—22no—
127D4×C43—22no—
128D4×C43—41no—
129D4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—81no—
136C2×C4×C43—81no—
137C2×C4×C43—81no—
138C2×C4×C43—81no—
139C2×C4×C43C4×D411yescharacteristic
140C2×C4×C43C4×D411yescharacteristic
141C2×C4×C43#12011yescharacteristic
142C2×C4×C43#12111yescharacteristic
143C2×C4×C43#12111yescharacteristic
144C2×C4×C43#12311yescharacteristic
145C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C43#13711yescharacteristic
149C2×Dic43—22no—
150C2×Dic43—22no—
151C2×Dic43—22no—
152C2×Dic43—22no—
153C2×Dic43—42no—
154C2×Dic43—42no—
155C2×Dic43—42no—
156C2×Dic43—42no—
157Dic86—41no—
158Dic86—41no—
159Dic86—41no—
160Dic86—41no—
161C8×C43—42no—
162C8×C43—81no—
163C43⋊C8—42no—
164C43⋊C8—81no—
165#9490—431nomaximal, Sylow
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—42no—
169C22×C43—42no—
170C22×C43—42no—
171C22×C43—81no—
172C22×C43—81no—
173C22×C43—81no—
174C22×C43—81no—
175C22×C43#38611yescharacteristic
176C22×C43#41711yescharacteristic
177C22×C43#41811yescharacteristic
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—81no—
183C4×C43#46811yescharacteristic
184C4×C43#46811yescharacteristic
185C4×C43#46911yescharacteristic
186C4×C43#46911yescharacteristic
187Dic43—42no—
188Dic43—42no—
189Dic43—82no—
190#2983—431no—
191#2536—431no—
192#1801—431no—
193#1486—431no—
194#1486D4311yescharacteristic
195#1286—431no—
196#1286—431no—
197C2×C43—21no—
198C2×C43—21no—
199C2×C43—82no—
200C2×C43#189111yescharacteristic
201C2×C43#189511yescharacteristic
202C2×C43#191211yescharacteristic
203C2×C22⋊Q8—861no—
204C2×C4×Q8—431no—
205C2×C4×D4C2×D4311yescharacteristic
206#446—862no—
207#446—862no—
208#432—862no—
209#431—431no—
210#431C2×D4311yescharacteristic
211#423—431no—
212#423C2×D4311yescharacteristic
213C2×#101—861no—
214#398—432no—
215#394—432no—
216#388—862no—
217#382—431no—
218#380—861no—
219#343—861no—
220D4⋊C8—22no—
221D4⋊C8—862no—
222C43#949011yescharacteristic, complemented, Sylow
223C22×Q8—431no—
224C22×D4C4×D4311yescharacteristic
225C23×C4—21no—
226C2×M16—21no—
227C2×M16—861no—
228C22⋊Q8—1722no—
229C22⋊Q8—1722no—
230C4×Q8—861no—
231C4×Q8—861no—
232C4×Q8—861no—
233C4×Q8—861no—
234C4×D4—21no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—21no—
238C2×C4⋊C4—432no—
239C2×C4⋊C4—431no—
240C2×C4⋊C4—862no—
241C2×C4⋊C4—861no—
242C2×C4⋊C4C4×D4311yescharacteristic
243C2×C22⋊C4—21no—
244C2×C22⋊C4—862no—
245C2×C22⋊C4—862no—
246C2×C42—432no—
247C2×C42C22×D4311yescharacteristic
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—864no—
252C4⋊C8—861no—
253C4⋊C8—861no—
254C4⋊C8—861no—
255#101—1722no—
256C22⋊C8—21no—
257C22⋊C8—861no—
258#97—864no—
259C4×C8—432no—
260C4×C8C22⋊D4312yes—
261#95—432no—
262#95—862no—
263#95—861no—
264C24—21no—
265C2×Q8—861no—
266C2×Q8—861no—
267C2×Q8—861no—
268C2×Q8—861no—
269C2×Q8—861no—
270C2×Q8—861no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—42no—
274C22×C4—21no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—432no—
282C22×C4—432no—
283C22×C4—862no—
284C22×C4C2×C4×D4311yescharacteristic
285C22×C4D4×D4311yescharacteristic
286C22×C4D4×D4311yescharacteristic
287M16—41no—
288M16—41no—
289M16—1721no—
290M16—1721no—
291C2×C8—22no—
292C2×C8—41no—
293C2×C8—862no—
294C2×C8—1721no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—862no—
298C4⋊C4—862no—
299C4⋊C4—861no—
300C4⋊C4—861no—
301C4⋊C4—1724no—
302C4⋊C4—1721no—
303C4⋊C4—1721no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—1724no—
307C22⋊C4—1724no—
308C42—862no—
309C42—862no—
310C42#1062189811yescharacteristic
311C42D4×D4311yescharacteristic
312C42#1062190011yescharacteristic
313C42C2×C22⋊D4311yescharacteristic
314C23—22no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23C22⋊C4×D4311yescharacteristic
322Q8—1721no—
323Q8—1721no—
324Q8—1721no—
325Q8—1721no—
326D4—22no—
327D4—22no—
328D4—41no—
329D4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—862no—
340C2×C4—862no—
341C2×C4—862no—
342C2×C4—862no—
343C2×C4—1722no—
344C2×C4—1722no—
345C2×C4—1722no—
346C2×C4—1722no—
347C2×C4(C22⋊D43)⋊C411yescharacteristic
348C2×C4C4×C22⋊D4311yescharacteristic
349C2×C4#1306329311yescharacteristic
350C2×C4#1306329611yescharacteristic
351C2×C4#1306329811yescharacteristic
352C2×C4#1306330711yescharacteristic
353C2×C4#1306334911yescharacteristic
354C2×C4#1306334911yescharacteristic
355C2×C4#1306335211yescharacteristic
356C2×C4#1306335411yescharacteristic
357C8—42no—
358C8—81no—
359C8—3441no—
360C8—1722no—
361C22—21no—
362C22—21no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22#1458277511yescharacteristic
371C22#1458289711yescharacteristic
372C22#1458290211yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—81no—
378C4—3442no—
379C4—1722no—
380C4—1722no—
381C4#1458314211yescharacteristic
382C4#1458314411yescharacteristic
383C4#1458314911yescharacteristic
384C4#1458315111yescharacteristic
385C2—21no—
386C2—21no—
387C2—82no—
388C2#1913501011yescharacteristic
389C2#1913503011yescharacteristic
390C2#1913512911yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1486C2
socleC22×C43#386
prime radicalC22×D4×C43C2×C4
cosocleC2×C42×C43C23
hypercenter#1486D43
hypocenterC43#9490
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
1. #19143678C2semidirect
3. #19134588C2semidirect
5. #19132455C2semidirect
6. #19132454C2semidirect
222. C43#9490semidirect

Maximal subgroups

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

subgroupindex
#191436782
#191395042
#191345882
#191330202
#191324552
#191324542
C43×#14862
#949043