Finite Group Databasebeta

← #24992470

Subgroups — #24992470

Order 11008.

432 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144411C211yesmaximal, characteristic
2#19143263C211yesmaximal, characteristic
3#19133281C211yesmaximal, characteristic, complemented
4C2×#14582647C211yesmaximal, characteristic, complemented
5#19132980C211yesmaximal, characteristic
6#19132490C211yesmaximal, characteristic, complemented
7C43×#1292C211yesmaximal, characteristic, complemented
8C2×#13063325C2211yescharacteristic
9C4×#10621898C2211yescharacteristic
10#14583195—21no—
11#14583190—21no—
12#14583185C412yes—
13#14583180C412yes—
14#14582959—22no—
15#14582955—21no—
16#14582952C2211yescharacteristic
17#14582951—21no—
18#14582941—21no—
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20#14582901—21no—
21#14582867—21no—
22#14582857—21no—
23#14582647—21no—
24#14582647—21no—
25#14582644—22no—
26#14582629—21no—
27#14582626—21no—
28C43×#423C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C2×C4⋊C8×C43C2211yescharacteristic
31C2×#10621898D411yescharacteristic
32C22×Dic86—21no—
33C22×C43⋊C8—21no—
34#13063325—21no—
35#13063325—21no—
36#13063325—21no—
37#13063325C2×C412yes—
38C4×Dic86C2×C411yescharacteristic
39C4×Dic86D411yescharacteristic
40C4×D172C2×C411yescharacteristic
41C4×D172D411yescharacteristic
42C4×C22⋊D43—21no—
43C4×C22⋊D43—21no—
44#13063284D411yescharacteristic
45#13063282—21no—
46C2×C4⋊Dic43—21no—
47C2×C4⋊Dic43—21no—
48C42×D43—21no—
49#13063259—22no—
50#13063257—22no—
51C4⋊(C43⋊C8)—21no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)D411yescharacteristic
54C4⋊(C43⋊C8)D411yescharacteristic
55#13063250—22no—
56#13063247—22no—
57C22⋊(C43⋊C8)—21no—
58(C2×D43)⋊C8—22no—
59(C2×D43)⋊C8—22no—
60#13063235—22no—
61C4×C43⋊C8—21no—
62C8×Dic43—22no—
63C2×M16×C43—21no—
64C2×M16×C43—21no—
65C22×C8×C43—21no—
66C2×C42×C43C2311yescharacteristic
67C4⋊C8×C43—21no—
68C4⋊C8×C43—21no—
69C4⋊C8×C43—21no—
70C4⋊C8×C43—21no—
71C4⋊C8×C43C2×C412yes—
72C4⋊C8×C43D412yes—
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43#4111yescharacteristic
75C22×C4×C43#4111yescharacteristic
76C2×C22⋊D43—21no—
77C22×Dic43—41no—
78#10621898—21no—
79#10621898—21no—
80#10621898—21no—
81#10621898—21no—
82C2×D172C22⋊C411yescharacteristic
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86C2×Dic86—22no—
87C2×Dic86—41no—
88C2×Dic86—82no—
89C2×Dic86C22⋊C411yescharacteristic
90M16×C43—41no—
91M16×C43—41no—
92M16×C43—41no—
93M16×C43—41no—
94C2×C8×C43—22no—
95C2×C8×C43—22no—
96C2×C8×C43—41no—
97C2×C8×C43—81no—
98C42×C43C22×C411yescharacteristic
99C42×C43C2×D411yescharacteristic
100C42×C43C2×D411yescharacteristic
101C42×C43C2×D411yescharacteristic
102C22⋊Dic43—21no—
103(C2×D43)⋊C4—21no—
104(C2×D43)⋊C4—21no—
105C4⋊Dic43—22no—
106C4⋊Dic43—22no—
107C4⋊Dic43—41no—
108C4⋊Dic43—41no—
109C4⋊Dic43C22⋊C411yescharacteristic
110C4⋊Dic43C22⋊C411yescharacteristic
111Dic43⋊C4—21no—
112Dic43⋊C4—21no—
113C4×Dic43—21no—
114C4×Dic43—21no—
115C4×Dic43—21no—
116C2×C43⋊C8—21no—
117C2×C43⋊C8—21no—
118C2×C43⋊C8—41no—
119C2×C43⋊C8—41no—
120C2×C43⋊C8—41no—
121C23×C43#12311yescharacteristic
122C22×D43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—41no—
126C2×C4×C43C2×C22⋊C411yescharacteristic
127C2×C4×C43C4×D411yescharacteristic
128C2×C4×C43C4×D411yescharacteristic
129C2×C4×C43#12011yescharacteristic
130C2×C4×C43#12111yescharacteristic
131C2×C4×C43#12111yescharacteristic
132C2×C4×C43#13511yescharacteristic
133C2×C4×C43#13511yescharacteristic
134C2×C4×C43#13711yescharacteristic
135C2×C4×C43#13711yescharacteristic
136C22⋊D43—41no—
137C22⋊D43—41no—
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—42no—
142C2×Dic43—82no—
143D172—21no—
144D172—21no—
145C4×D43—41no—
146C4×D43—41no—
147C4×D43—41no—
148C4×D43—41no—
149C4×D43—81no—
150Dic86—21no—
151Dic86—21no—
152Dic86—82no—
153Dic86—82no—
154C8×C43—42no—
155C8×C43—42no—
156C8×C43—81no—
157C43⋊C8—41no—
158C43⋊C8—41no—
159C43⋊C8—81no—
160#9170—431nomaximal, Sylow
161C22×C43—21no—
162C22×C43—21no—
163C22×C43#38611yescharacteristic
164C22×C43#48511yescharacteristic
165C22×C43#48511yescharacteristic
166C2×D43—41no—
167C2×D43—41no—
168C2×D43—41no—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43#41611yescharacteristic
173C4×C43#41911yescharacteristic
174C4×C43#45211yescharacteristic
175C4×C43#45211yescharacteristic
176C4×C43#47111yescharacteristic
177C4×C43#47311yescharacteristic
178Dic43—41no—
179Dic43—41no—
180Dic43—41no—
181Dic43—82no—
182#3079—431no—
183#2925—431no—
184#1549—431no—
185C2×#333—431no—
186#1477—431no—
187#1301—431no—
188#1292D4311yescharacteristic, complemented
189C2×C43—21no—
190C2×C43—21no—
191C2×C43#187311yescharacteristic
192C2×C43#190311yescharacteristic
193C2×C43#190811yescharacteristic
194D43—81no—
195C2×C4⋊Q8—431no—
196C4×#41—431no—
197#477—861no—
198#476—861no—
199#475—432no—
200#474—432no—
201#433—862no—
202#432—861no—
203#431—431no—
204#431—861no—
205#428—861no—
206#423C2×D4311yescharacteristic
207#423C2×D4311yescharacteristic
208C2×C4⋊C8—431no—
209C2×C4⋊C8C2×D4311yescharacteristic
210#417—861no—
211#408—861no—
212#405—861no—
213#333—861no—
214#333—861no—
215#332—862no—
216Q8⋊C8—861no—
217D4⋊C8—861no—
218C43#917011yescharacteristic, complemented, Sylow
219C2×#41—431no—
220C22×Q8—861no—
221C2×M16—21no—
222C2×M16—21no—
223C22×C8—21no—
224C22×C8—861no—
225C4⋊Q8—432no—
226C4⋊Q8—861no—
227C4⋊Q8—861no—
228C4⋊Q8—861no—
229C4×Q8—431no—
230C4×Q8—431no—
231C4×D4—431no—
232C4×D4—431no—
233C4×D4—861no—
234C4×D4—861no—
235#117—431no—
236#117—861no—
237C2×C4⋊C4—861no—
238C2×C4⋊C4—861no—
239C2×C42—861no—
240C2×C42C22×D4311yescharacteristic
241#107—862no—
242#106—862no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—431no—
248C4⋊C8—431no—
249C4⋊C8—861no—
250C4⋊C8—861no—
251C4⋊C8C4×D4312yes—
252C4⋊C8D17212yes—
253#103—862no—
254#102—862no—
255C22⋊C8—862no—
256C22⋊C8—862no—
257C22⋊C8—861no—
258#97—862no—
259C4×C8—862no—
260C4×C8—861no—
261#41—861no—
262#41—861no—
263#41—861no—
264#41—861no—
265C2×Q8—431no—
266C2×Q8—862no—
267C2×Q8—3442no—
268C2×Q8—1721no—
269C2×D4—431no—
270C2×D4—861no—
271C22×C4—861no—
272C22×C4—861no—
273C22×C4—861no—
274C22×C4—1721no—
275C22×C4#1062189811yescharacteristic
276C22×C4D4×D4311yescharacteristic
277C22×C4#1062190211yescharacteristic
278M16—41no—
279M16—41no—
280M16—41no—
281M16—41no—
282C2×C8—22no—
283C2×C8—22no—
284C2×C8—41no—
285C2×C8—81no—
286C2×C8—861no—
287C2×C8—861no—
288C2×C8—1721no—
289C2×C8—1721no—
290C2×C8—1721no—
291C4⋊C4—431no—
292C4⋊C4—431no—
293C4⋊C4—861no—
294C4⋊C4—861no—
295C4⋊C4—862no—
296C4⋊C4—862no—
297C4⋊C4—1721no—
298C4⋊C4—1721no—
299C22⋊C4—861no—
300C22⋊C4—861no—
301C22⋊C4—861no—
302C42—861no—
303C42—861no—
304C42—861no—
305C42C2×C4×D4311yescharacteristic
306C42C2×D17211yescharacteristic
307C42D4×D4311yescharacteristic
308C42D4×D4311yescharacteristic
309C23—861no—
310C23#1306331011yescharacteristic
311Q8—861no—
312Q8—861no—
313Q8—3442no—
314Q8—3442no—
315D4—861no—
316D4—861no—
317D4—1721no—
318D4—1721no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—3441no—
326C2×C4—3442no—
327C2×C4—1722no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4C22⋊C4×D4311yescharacteristic
333C2×C4#1306328711yescharacteristic
334C2×C4C4×D17211yescharacteristic
335C2×C4#1306329511yescharacteristic
336C2×C4#1306329811yescharacteristic
337C2×C4#1306330011yescharacteristic
338C2×C4#1306334411yescharacteristic
339C2×C4#1306334611yescharacteristic
340C2×C4#1306335411yescharacteristic
341C2×C4#1306335711yescharacteristic
342C8—42no—
343C8—42no—
344C8—81no—
345C8—3441no—
346C8—1721no—
347C8—1721no—
348C22—21no—
349C22—21no—
350C22—1721no—
351C22—1721no—
352C22—1721no—
353C22#1458277711yescharacteristic
354C22#1458324211yescharacteristic
355C22#1458324311yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—3442no—
360C4—1721no—
361C4—1721no—
362C4—1721no—
363C4#1458289211yescharacteristic
364C4#1458290611yescharacteristic
365C4#1458306211yescharacteristic
366C4#1458306411yescharacteristic
367C4#1458316111yescharacteristic
368C4#1458317311yescharacteristic
369C2—21no—
370C2—21no—
371C2—3441no—
372C2#1913490611yescharacteristic
373C2#1913507611yescharacteristic
374C2#1913511111yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1292C2
socleC22×C43#386
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1292D43
hypocenterC43#9170
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
3. #19133281C2semidirect
4. C2×#14582647C2semidirect
6. #19132490C2semidirect
7. C43×#1292C2semidirect
188. #1292D43semidirect
218. C43#9170semidirect

Maximal subgroups

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

subgroupindex
#191444112
#191432632
#191332812
C2×#145826472
#191329802
#191324902
C43×#12922
#917043