Finite Group Databasebeta

← #24992472

Subgroups — #24992472

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#19144404C211yesmaximal, characteristic
2#19143260C211yesmaximal, characteristic
3#19133280C211yesmaximal, characteristic, complemented
4#19132980C211yesmaximal, characteristic
5#19132492C211yesmaximal, characteristic, complemented
6#19132470C211yesmaximal, characteristic, complemented
7C2×C43×#333C211yesmaximal, characteristic, complemented
8C4×#10621898C2211yescharacteristic
9#14583191—21no—
10#14583186—21no—
11#14583181C412yes—
12#14583176C412yes—
13#14582959—22no—
14#14582955—21no—
15#14582952C2211yescharacteristic
16#14582951—21no—
17#14582939—21no—
18#14582923C2211yescharacteristic
19#14582923C2211yescharacteristic
20#14582898—21no—
21#14582865—21no—
22#14582854—21no—
23#14582645—22no—
24#14582629—21no—
25#14582626—21no—
26C2×C4⋊Q8×C43C2211yescharacteristic
27C2×C4⋊C8×C43C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C43×#333—21no—
30C43×#333—21no—
31C2×#10621898D411yescharacteristic
32C2×#10621877—21no—
33C2×#10621877—21no—
34C4×Dic86C2×C411yescharacteristic
35C4×Dic86D411yescharacteristic
36C4×D172C2×C411yescharacteristic
37C4×D172D411yescharacteristic
38C4×C22⋊D43—21no—
39C4×C22⋊D43—21no—
40#13063284D411yescharacteristic
41#13063282—21no—
42C42×D43—21no—
43#13063258—22no—
44#13063256—22no—
45C4⋊(C43⋊C8)—21no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)C2×C412yes—
49C4⋊(C43⋊C8)D412yes—
50#13063248—22no—
51#13063245—22no—
52C22⋊(C43⋊C8)—21no—
53(C2×D43)⋊C8—22no—
54(C2×D43)⋊C8—22no—
55#13063235—22no—
56C4×C43⋊C8—21no—
57C8×Dic43—22no—
58C22×Q8×C43—21no—
59C22×C8×C43—21no—
60C22×C8×C43—21no—
61C4⋊Q8×C43—21no—
62C4⋊Q8×C43—21no—
63C4⋊Q8×C43—21no—
64C4⋊Q8×C43C2×C412yes—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C42×C43C2311yescharacteristic
68C4⋊C8×C43—21no—
69C4⋊C8×C43—21no—
70C4⋊C8×C43—21no—
71C4⋊C8×C43D411yescharacteristic
72C4⋊C8×C43D411yescharacteristic
73C2×Q8×C43—22no—
74C2×Q8×C43—41no—
75C2×Q8×C43—82no—
76C22×C4×C43—41no—
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C22×C4×C43#4111yescharacteristic
80C2×C22⋊D43—21no—
81#10621898—21no—
82#10621898—21no—
83#10621898—21no—
84#10621898—21no—
85C2×D172C22⋊C411yescharacteristic
86C2×C4×D43—21no—
87C2×C4×D43—21no—
88C2×C4×D43—21no—
89C2×Dic86C22⋊C411yescharacteristic
90C2×C8×C43—21no—
91C2×C8×C43—21no—
92C2×C8×C43—41no—
93C2×C8×C43—41no—
94C2×C8×C43—41no—
95C2×C8×C43—81no—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C42×C43C22×C411yescharacteristic
101C42×C43C2×D411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C22⋊Dic43—21no—
105(C2×D43)⋊C4—21no—
106(C2×D43)⋊C4—21no—
107C4⋊Dic43C22⋊C411yescharacteristic
108C4⋊Dic43C22⋊C411yescharacteristic
109Dic43⋊C4—21no—
110Dic43⋊C4—21no—
111C4×Dic43—21no—
112C4×Dic43—21no—
113C4×Dic43—21no—
114#10621877—41no—
115#10621877—41no—
116#10621877—41no—
117#10621877—41no—
118C2×C43⋊C8—22no—
119C2×C43⋊C8—22no—
120C2×C43⋊C8—41no—
121C23×C43#12311yescharacteristic
122C22×D43—21no—
123Q8×C43—82no—
124Q8×C43—82no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—41no—
128C2×C4×C43—42no—
129C2×C4×C43—82no—
130C2×C4×C43C2×C22⋊C411yescharacteristic
131C2×C4×C43C4×D411yescharacteristic
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43#12011yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×C4×C43#13511yescharacteristic
137C2×C4×C43#13511yescharacteristic
138C2×C4×C43#13711yescharacteristic
139C2×C4×C43#13711yescharacteristic
140C22⋊D43—41no—
141C22⋊D43—41no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145D172—21no—
146D172—21no—
147C4×D43—41no—
148C4×D43—41no—
149C4×D43—41no—
150C4×D43—41no—
151C4×D43—81no—
152Dic86—21no—
153Dic86—21no—
154C8×C43—41no—
155C8×C43—41no—
156C8×C43—81no—
157C43⋊C8—42no—
158C43⋊C8—42no—
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—82no—
173C4×C43#41611yescharacteristic
174C4×C43#41911yescharacteristic
175C4×C43#45211yescharacteristic
176C4×C43#45211yescharacteristic
177C4×C43#47111yescharacteristic
178C4×C43#47311yescharacteristic
179Dic43—41no—
180Dic43—41no—
181Dic43—41no—
182#3079—431no—
183#2925—431no—
184#1549—431no—
185C2×#333D4311yescharacteristic, complemented
186#1477—431no—
187#1301—431no—
188#1292—431no—
189C2×C43—21no—
190C2×C43—21no—
191C2×C43#187311yescharacteristic
192C2×C43#190311yescharacteristic
193C2×C43#190811yescharacteristic
194D43—81no—
195C2×C4⋊Q8C2×D4311yescharacteristic
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#423—431no—
207#423—431no—
208C2×C4⋊C8C2×D4311yescharacteristic
209C2×C4⋊C8C2×D4311yescharacteristic
210#417—861no—
211#408—861no—
212#405—861no—
213#333—21no—
214#333—21no—
215#332—862no—
216Q8⋊C8—861no—
217D4⋊C8—861no—
218C43#917011yescharacteristic, complemented, Sylow
219C2×#41—431no—
220C22×Q8—21no—
221C2×M16—861no—
222C2×M16—861no—
223C22×C8—21no—
224C22×C8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8C4×D4312yes—
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—21no—
238C2×C4⋊C4—21no—
239C2×C42—861no—
240C2×C42C22×D4311yescharacteristic
241#107—862no—
242#106—862no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—432no—
247C4⋊C8—432no—
248C4⋊C8—861no—
249C4⋊C8—861no—
250C4⋊C8—861no—
251C4⋊C8C22⋊D4311yescharacteristic
252C4⋊C8C22⋊D4311yescharacteristic
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—22no—
266C2×Q8—41no—
267C2×Q8—82no—
268C2×Q8—431no—
269C2×D4—431no—
270C2×D4—861no—
271C22×C4—41no—
272C22×C4—861no—
273C22×C4—861no—
274C22×C4—861no—
275C22×C4#1062189811yescharacteristic
276C22×C4D4×D4311yescharacteristic
277C22×C4#1062190011yescharacteristic
278M16—1721no—
279M16—1721no—
280M16—1721no—
281M16—1721no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—81no—
288C2×C8—862no—
289C2×C8—862no—
290C2×C8—1721no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—431no—
296C4⋊C4—431no—
297C4⋊C4—861no—
298C4⋊C4—861no—
299C22⋊C4—861no—
300C22⋊C4—861no—
301C22⋊C4—861no—
302C42—861no—
303C42—861no—
304C42—861no—
305C42C2×C4×D4311yescharacteristic
306C42D4×D4311yescharacteristic
307C42D4×D4311yescharacteristic
308C42C2×C22⋊D4311yescharacteristic
309C23—861no—
310C23#1306330711yescharacteristic
311Q8—82no—
312Q8—82no—
313Q8—861no—
314Q8—861no—
315D4—861no—
316D4—861no—
317D4—1721no—
318D4—1721no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—82no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—3441no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4C22⋊C4×D4311yescharacteristic
333C2×C4(C22⋊D43)⋊C411yescharacteristic
334C2×C4C4×C22⋊D4311yescharacteristic
335C2×C4#1306329311yescharacteristic
336C2×C4#1306329611yescharacteristic
337C2×C4#1306329811yescharacteristic
338C2×C4#1306334611yescharacteristic
339C2×C4#1306334811yescharacteristic
340C2×C4#1306335411yescharacteristic
341C2×C4#1306335711yescharacteristic
342C8—41no—
343C8—41no—
344C8—81no—
345C8—3441no—
346C8—1722no—
347C8—1722no—
348C22—21no—
349C22—21no—
350C22—1721no—
351C22—1721no—
352C22—1721no—
353C22#1458277511yescharacteristic
354C22#1458323811yescharacteristic
355C22#1458323911yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—82no—
360C4—1721no—
361C4—1721no—
362C4—1721no—
363C4#1458289411yescharacteristic
364C4#1458290611yescharacteristic
365C4#1458305811yescharacteristic
366C4#1458306011yescharacteristic
367C4#1458315911yescharacteristic
368C4#1458317111yescharacteristic
369C2—21no—
370C2—21no—
371C2—3441no—
372C2#1913490411yescharacteristic
373C2#1913507811yescharacteristic
374C2#1913511311yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#333C2
socleC22×C43#386
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenterC2×#333D43
hypocenterC43#9170
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
3. #19133280C2semidirect
5. #19132492C2semidirect
6. #19132470C2semidirect
7. C2×C43×#333C2semidirect
185. C2×#333D43semidirect
218. C43#9170semidirect

Maximal subgroups

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

subgroupindex
#191444042
#191432602
#191332802
#191329802
#191324922
#191324702
C2×C43×#3332
#917043