Finite Group Databasebeta

← #24988243

Subgroups — #24988243

Order 11008.

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

normal subgroups only

This group has 788 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×#14583609C211yesmaximal, characteristic
2#19133196C212yesmaximal, complemented
3#19133039C212yesmaximal
4#19132939C211yesmaximal, characteristic, complemented
5C4×#101×C43C211yesmaximal, characteristic, complemented
6#14583609—24no—
7#14583609—24no—
8C2×#13063325C411yescharacteristic
9C2×#13063317C411yescharacteristic
10C2×#13063317C2211yescharacteristic
11C2×#13063303—21no—
12C2×#13063303—21no—
13C2×#13063301—21no—
14C2×C4×D172C411yescharacteristic
15C2×C4×D172C411yescharacteristic
16C2×C4×D172C2211yescharacteristic
17C2×C4⋊C4×D43—21no—
18#14582956C2212yes—
19#14582640—24no—
20#14582628—24no—
21#14582625—21no—
22#14582625—21no—
23C2×C4×Q8×C43C2211yescharacteristic
24C2×#101×C43—21no—
25C4×M16×C43C2212yes—
26C43×#343—21no—
27C22×Dic86—21no—
28C22×D172C2×C411yescharacteristic
29C22×C4×D43—21no—
30C22×C4×D43—21no—
31C22×C4×D43—21no—
32#13063325—22no—
33#13063325—22no—
34#13063317—22no—
35#13063317—22no—
36#13063317—22no—
37#13063317D414yes—
38#13063303—28no—
39#13063303—28no—
40#13063301—28no—
41C4×D172—22no—
42C4×D172—22no—
43C4×D172—22no—
44C4×D172—22no—
45C4×D172—22no—
46C4×D172D414yes—
47C2×C4⋊Dic43—21no—
48C2×C4⋊Dic43C2×C411yescharacteristic
49C2×C4⋊Dic43C2×C411yescharacteristic
50C2×C4⋊Dic43C2×C411yescharacteristic
51C2×Dic43⋊C4—21no—
52C2×Dic43⋊C4—21no—
53C2×Dic43⋊C4—21no—
54C2×Dic43⋊C4—21no—
55C4⋊C4×D43—28no—
56C2×(C2×D43)⋊C4—21no—
57C2×(C2×D43)⋊C4—21no—
58C2×(C2×D43)⋊C4—21no—
59C4⋊(C43⋊C8)—22no—
60C22⋊(C43⋊C8)—22no—
61#13063236—22no—
62C22×Q8×C43D411yescharacteristic
63C2×M16×C43—22no—
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
72#101×C43—24no—
73#97×C43—22no—
74C4×C8×C43—22no—
75C23×D43—21no—
76C2×Q8×C43—22no—
77C2×Q8×C43—22no—
78C2×Q8×C43—41no—
79C22×C4×C43C22⋊C411yescharacteristic
80C22×C4×C43C22⋊C411yescharacteristic
81C22×C4×C43C22⋊C411yescharacteristic
82C22×C4×C43C22⋊C411yescharacteristic
83C22×C4×C43C22×C411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C2×D172—21no—
90C2×D172—24no—
91C2×D172C22⋊C412yes—
92C2×C4×D43—24no—
93C2×C4×D43—24no—
94C2×C4×D43—24no—
95C2×C4×D43—42no—
96C2×C4×D43—42no—
97C2×C4×D43—82no—
98C2×C4×D43—82no—
99C2×Dic86—24no—
100C2×Dic86—82no—
101M16×C43—24no—
102M16×C43—42no—
103C2×C8×C43—42no—
104C4⋊C4×C43—22no—
105C4⋊C4×C43—22no—
106C4⋊C4×C43—22no—
107C42×C43—21no—
108C42×C43—21no—
109C42×C43—21no—
110C42×C43—21no—
111C42×C43C2×D412yes—
112C42×C43C2×D412yes—
113(C2×D43)⋊C4—24no—
114(C2×D43)⋊C4—24no—
115(C2×D43)⋊C4—24no—
116C4⋊Dic43—24no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120C4⋊Dic43C22⋊C412yes—
121C4⋊Dic43C22⋊C412yes—
122C4⋊Dic43C22⋊C412yes—
123Dic43⋊C4—24no—
124Dic43⋊C4—24no—
125Dic43⋊C4—24no—
126Dic43⋊C4—24no—
127C2×C43⋊C8—42no—
128C23×C43C2×C22⋊C411yescharacteristic
129C22×D43—24no—
130C22×D43—22no—
131C22×D43—42no—
132C22×D43—41no—
133C22×D43—41no—
134Q8×C43—44no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—22no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43#10412yes—
149C2×C4×C43C2×C22⋊C411yescharacteristic
150C2×C4×C43C2×C22⋊C411yescharacteristic
151C2×C4×C43#12012yes—
152C2×C4×C43#12012yes—
153C2×Dic43—22no—
154C2×Dic43—22no—
155C2×Dic43—22no—
156C2×Dic43—42no—
157C2×Dic43—42no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160D172—24no—
161D172—22no—
162D172#10114yescomplemented
163C4×D43—48no—
164C4×D43—84no—
165C4×D43—84no—
166Dic86—84no—
167C8×C43—44no—
168C43⋊C8—82no—
169#8372—431nomaximal, Sylow
170C22×C43—21no—
171C22×C43—21no—
172C22×C43#37911yescharacteristic
173C22×C43C2×#10411yescharacteristic
174C22×C43#42111yescharacteristic
175C2×D43—24no—
176C2×D43—44no—
177C2×D43—44no—
178C2×D43—42no—
179C2×D43—42no—
180C4×C43—22no—
181C4×C43—21no—
182C4×C43—22no—
183C4×C43—22no—
184C4×C43—41no—
185C4×C43—41no—
186C4×C43—41no—
187C4×C43C2×#10112yes—
188Dic43—42no—
189Dic43—42no—
190Dic43—42no—
191C2×#554—431no—
192C4×#101D4311yescharacteristic, complemented
193#1528—432no—
194#1490—432no—
195#1467—431no—
196C2×C43—21no—
197C2×C43—21no—
198C2×C43#178411yescharacteristic
199C2×C43#178911yescharacteristic
200C2×C43#179511yescharacteristic
201D43—44no—
202#554—864no—
203#554—864no—
204C2×C4⋊Q8—431no—
205C2×#125—431no—
206C2×#125—431no—
207C2×C22⋊Q8—861no—
208C2×C22⋊Q8—861no—
209C2×C22⋊Q8—861no—
210C2×C4×Q8C2×D4311yescharacteristic
211C2×C4×D4—431no—
212C2×C4×D4—431no—
213C2×C4×D4—431no—
214C22×C4⋊C4—861no—
215#432—432no—
216C2×#101—21no—
217C4×M16C2×D4312yes—
218#343—21no—
219#330—864no—
220D4⋊C8—864no—
221#324—861no—
222#324—861no—
223C43#837211yescharacteristic, complemented, Sylow
224C22×Q8—861no—
225C22×Q8C22⋊D4311yescharacteristic
226C22×D4—431no—
227C23×C4—861no—
228C23×C4—861no—
229C23×C4—861no—
230C2×M16—22no—
231C4⋊Q8—862no—
232C4⋊Q8—862no—
233#125—434no—
234#125—862no—
235#125—862no—
236#125—862no—
237C22⋊Q8—868no—
238C22⋊Q8—868no—
239C22⋊Q8—868no—
240C4×Q8—22no—
241C4×Q8—22no—
242C4×D4—434no—
243C4×D4—862no—
244C4×D4—862no—
245C4×D4—862no—
246C4×D4—862no—
247C4×D4—862no—
248C2×C4⋊C4—431no—
249C2×C4⋊C4—431no—
250C2×C4⋊C4—431no—
251C2×C4⋊C4—868no—
252C2×C4⋊C4—861no—
253C2×C4⋊C4—861no—
254C2×C4⋊C4—861no—
255C2×C4⋊C4—861no—
256C2×C4⋊C4—861no—
257C2×C4⋊C4D17211yescharacteristic
258C2×C4⋊C4D17211yescharacteristic
259C2×C4⋊C4C22⋊D4311yescharacteristic
260C2×C22⋊C4—861no—
261C2×C22⋊C4—861no—
262C2×C22⋊C4—861no—
263C2×C42C4×D4311yescharacteristic
264C2×C42C4×D4311yescharacteristic
265C2×C42C22×D4311yescharacteristic
266C4⋊C8—862no—
267#101—24no—
268C22⋊C8—862no—
269#97—22no—
270#97—862no—
271C4×C8—22no—
272C24—861no—
273C2×Q8—22no—
274C2×Q8—22no—
275C2×Q8—41no—
276C2×Q8—864no—
277C2×Q8—3442no—
278C2×D4—432no—
279C2×D4—864no—
280C2×D4—861no—
281C22×C4—864no—
282C22×C4—864no—
283C22×C4—861no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—864no—
287C22×C4—3442no—
288C22×C4—3442no—
289C22×C4—1722no—
290C22×C4—1722no—
291C22×C4(C2×D43)⋊C411yescharacteristic
292C22×C4(C2×D43)⋊C411yescharacteristic
293C22×C4(C2×D43)⋊C411yescharacteristic
294C22×C4(C2×D43)⋊C411yescharacteristic
295C22×C4C2×C4×D4311yescharacteristic
296C22×C4C2×D17211yescharacteristic
297C22×C4C2×C22⋊D4311yescharacteristic
298M16—24no—
299M16—42no—
300C2×C8—42no—
301C2×C8—1722no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—432no—
306C4⋊C4—432no—
307C4⋊C4—432no—
308C4⋊C4—864no—
309C4⋊C4—864no—
310C4⋊C4—864no—
311C4⋊C4—861no—
312C4⋊C4—861no—
313C4⋊C4—861no—
314C4⋊C4—864no—
315C4⋊C4—864no—
316C22⋊C4—864no—
317C22⋊C4—864no—
318C22⋊C4—864no—
319C42—21no—
320C42—21no—
321C42—21no—
322C42—21no—
323C42D4×D4312yes—
324C42D4×D4312yes—
325C23—864no—
326C23—862no—
327C23—1722no—
328C23—1721no—
329C23—1721no—
330C23C2×(C2×D43)⋊C411yescharacteristic
331Q8—44no—
332Q8—3444no—
333D4—434no—
334D4—864no—
335D4—862no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—862no—
350C2×C4—862no—
351C2×C4—862no—
352C2×C4—3444no—
353C2×C4—3444no—
354C2×C4—1728no—
355C2×C4—1722no—
356C2×C4—1722no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4#1306325312yes—
360C2×C4C22⋊C4×D4311yescharacteristic
361C2×C4C22⋊C4×D4311yescharacteristic
362C2×C4#1306329312yes—
363C2×C4#1306329512yes—
364C8—44no—
365C8—3442no—
366C22—21no—
367C22—21no—
368C22—864no—
369C22—1724no—
370C22—1724no—
371C22—1722no—
372C22—1722no—
373C22#1458275411yescharacteristic
374C22C2×#1306325311yescharacteristic
375C22#1458291711yescharacteristic
376C4—21no—
377C4—22no—
378C4—22no—
379C4—22no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—1722no—
384C4—1722no—
385C4—1722no—
386C4#101×D4312yes—
387C2—21no—
388C2—21no—
389C2—1724no—
390C2#1913451711yescharacteristic
391C2#1913454011yescharacteristic
392C2#1913456611yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC4×#101×C43C2
socleC22×C43#379
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenterC4×#101D43
hypocenterC43#8372
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
2. #19133196C2semidirect
4. #19132939C2semidirect
5. C4×#101×C43C2semidirect
162. D172#101semidirect
192. C4×#101D43semidirect
223. C43#8372semidirect

Maximal subgroups

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

subgroupindex
C2×#145836092
#191331962
#191330392
#191329392
C4×#101×C432
#837243