Finite Group Databasebeta

← #24992977

Subgroups — #24992977

Order 11008.

512 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583186C211yesmaximal, characteristic
2M16×D172C211yesmaximal, characteristic
3#19133280C211yesmaximal, characteristic, complemented
4#19133019C211yesmaximal, characteristic
5#19132469C211yesmaximal, characteristic, complemented
6#19132446C211yesmaximal, characteristic, complemented
7C43×#1997C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9C2×C4×D172C2211yescharacteristic
10#14583186—21no—
11#14583186—21no—
12#14583186—21no—
13#14583186—21no—
14#14582978—21no—
15#14582972—22no—
16C8×D172—21no—
17#14582952C2211yescharacteristic
18C2×#13063256C412yes—
19#14582923C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×#13063245C412yes—
22#14582862—21no—
23#14582645—22no—
24#14582626—21no—
25#14582626—21no—
26C2×C4⋊Q8×C43C2211yescharacteristic
27C43×#423C2211yescharacteristic
28C4×M16×C43C2211yescharacteristic
29C43×#343—21no—
30C43×#343—21no—
31C22×D172C2×C411yescharacteristic
32C22×C4×D43—21no—
33C2×#10621877—21no—
34C2×#10621872—22no—
35M16×D43—42no—
36M16×D43—42no—
37C22×C43⋊C8C2×C412yes—
38C2×C8×D43—22no—
39C4×D172—21no—
40C4×D172—21no—
41C4×D172D411yescharacteristic
42C4×D172D411yescharacteristic
43C4×D172D411yescharacteristic
44C4×D172D411yescharacteristic
45C2×C4⋊Dic43C2×C411yescharacteristic
46C2×(C2×D43)⋊C4—21no—
47#13063256—22no—
48#13063256—22no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)—21no—
51C4⋊(C43⋊C8)—21no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)D412yes—
54#13063245—22no—
55#13063245—22no—
56C22⋊(C43⋊C8)—21no—
57(C2×D43)⋊C8—22no—
58(C2×D43)⋊C8—22no—
59C4×C43⋊C8—21no—
60C22×Q8×C43—21no—
61C2×M16×C43—21no—
62C2×M16×C43D411yescharacteristic
63C2×M16×C43D411yescharacteristic
64C4⋊Q8×C43—21no—
65C4⋊Q8×C43—21no—
66C4⋊Q8×C43—21no—
67C4⋊Q8×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43C2×C412yes—
70C2×C42×C43C2311yescharacteristic
71C4⋊C8×C43—21no—
72C4⋊C8×C43—21no—
73#97×C43—21no—
74C4×C8×C43—21no—
75C23×D43—21no—
76C2×Q8×C43—41no—
77C2×Q8×C43—41no—
78C2×Q8×C43—82no—
79C22×C4×C43—22no—
80C22×C4×C43C22×C411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43#4111yescharacteristic
83C22×Dic43—21no—
84C2×D172—21no—
85C2×D172—22no—
86C2×D172—41no—
87C2×D172C22⋊C411yescharacteristic
88C2×D172C22⋊C411yescharacteristic
89C2×C4×D43—21no—
90C2×C4×D43—21no—
91C2×C4×D43—21no—
92C2×C4×D43—21no—
93C2×C4×D43—41no—
94C2×C4×D43—41no—
95C2×C4×D43—41no—
96C2×C4×D43—41no—
97M16×C43—21no—
98M16×C43—21no—
99M16×C43—21no—
100M16×C43—41no—
101M16×C43—41no—
102M16×C43SD1612yes—
103C2×C8×C43—21no—
104C2×C8×C43—21no—
105C2×C8×C43—41no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—41no—
109C4⋊C4×C43—41no—
110C42×C43C2×D411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43#4111yescharacteristic
114(C2×D43)⋊C4—21no—
115(C2×D43)⋊C4—21no—
116(C2×D43)⋊C4—21no—
117(C2×D43)⋊C4—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43C22⋊C411yescharacteristic
120C4⋊Dic43C22⋊C411yescharacteristic
121#10621877—41no—
122#10621877—41no—
123C2×C43⋊C8—22no—
124C2×C43⋊C8—22no—
125C2×C43⋊C8—42no—
126C2×C43⋊C8—41no—
127#10621872—44no—
128C8×D43—44no—
129C23×C43C4×D411yescharacteristic
130C22×D43—21no—
131C22×D43—21no—
132C22×D43—42no—
133C22×D43—41no—
134C22×D43—41no—
135C22×D43—81no—
136Q8×C43—82no—
137Q8×C43—82no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—41no—
141C2×C4×C43—42no—
142C2×C4×C43—82no—
143C2×C4×C43C2×C22⋊C411yescharacteristic
144C2×C4×C43C4×D411yescharacteristic
145C2×C4×C43#12011yescharacteristic
146C2×C4×C43#12111yescharacteristic
147C2×C4×C43#12111yescharacteristic
148C2×C4×C43#12311yescharacteristic
149C2×C4×C43C2×SD1611yescharacteristic
150C2×C4×C43#13511yescharacteristic
151C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C43#13711yescharacteristic
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157D172—21no—
158D172—21no—
159D172—21no—
160D172—42no—
161D172#10112yes—
162C4×D43—41no—
163C4×D43—41no—
164C4×D43—41no—
165C4×D43—41no—
166C4×D43—41no—
167C4×D43—41no—
168C4×D43—41no—
169C4×D43—41no—
170C8×C43—22no—
171C8×C43—41no—
172C8×C43—81no—
173C43⋊C8—42no—
174C43⋊C8—42no—
175C43⋊C8—81no—
176#9249—431nomaximal, Sylow
177C22×C43—21no—
178C22×C43—21no—
179C22×C43#38611yescharacteristic
180C22×C43C4×SD1611yescharacteristic
181C22×C43#44011yescharacteristic
182C2×D43—22no—
183C2×D43—41no—
184C2×D43—41no—
185C2×D43—41no—
186C2×D43—41no—
187C2×D43—41no—
188C2×D43—82no—
189C2×D43—82no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—82no—
194C4×C43C2×#10111yescharacteristic
195C4×C43#41311yescharacteristic
196C4×C43#45011yescharacteristic
197C4×C43#45211yescharacteristic
198C4×C43#46111yescharacteristic
199C4×C43#46311yescharacteristic
200Dic43—41no—
201Dic43—41no—
202C2×#476—431no—
203D4×M16—431no—
204#1997D4311yescharacteristic, complemented
205#1549—431no—
206#1486—431no—
207#1292—431no—
208#1283—431no—
209C2×C43—21no—
210C2×C43—21no—
211C2×C43#187711yescharacteristic
212C2×C43#190111yescharacteristic
213C2×C43#190311yescharacteristic
214D43—42no—
215D43—81no—
216C22×M16—861no—
217C2×C4⋊Q8C2×D4311yescharacteristic
218C2×C4×D4—431no—
219#476—861no—
220#476—861no—
221#476—861no—
222#476—861no—
223#436—861no—
224#435—862no—
225C8×D4—861no—
226#431—431no—
227C2×#106—432no—
228#423—431no—
229#423C2×D4311yescharacteristic
230C2×C4⋊C8—431no—
231C2×#102—432no—
232#407—861no—
233C4×M16C2×D4311yescharacteristic
234#343—21no—
235#343—21no—
236#332—862no—
237D4⋊C8—861no—
238D4⋊C8—861no—
239C43#924911yescharacteristic, complemented, Sylow
240C22×Q8—21no—
241C22×D4—431no—
242C23×C4—861no—
243C2×M16—21no—
244C2×M16—862no—
245C2×M16—861no—
246C2×M16—1722no—
247C2×M16—1722no—
248C2×M16C22⋊D4311yescharacteristic
249C2×M16C22⋊D4311yescharacteristic
250C22×C8—432no—
251C22×C8—862no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4×D4—431no—
257C4×D4—431no—
258C4×D4—431no—
259C4×D4—431no—
260C4×D4—861no—
261C4×D4—861no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—431no—
264C2×C4⋊C4C4×D4312yes—
265C2×C22⋊C4—861no—
266C2×C42C22×D4311yescharacteristic
267#106—862no—
268#106—862no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—432no—
272C4⋊C8—861no—
273C4⋊C8—861no—
274C4⋊C8—861no—
275C4⋊C8—861no—
276#102—862no—
277#102—862no—
278C22⋊C8—862no—
279C22⋊C8—862no—
280C22⋊C8—861no—
281#97—21no—
282C4×C8—21no—
283C4×C8—861no—
284C24—861no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—82no—
288C2×D4—431no—
289C2×D4—431no—
290C2×D4—862no—
291C2×D4—861no—
292C2×D4—1721no—
293C22×C4—22no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4—861no—
298C22×C4—861no—
299C22×C4—1721no—
300C22×C4—1721no—
301C22×C4—1721no—
302C22×C4—1721no—
303C22×C4C2×C4×D4311yescharacteristic
304C22×C4#1062189811yescharacteristic
305C22×C4C2×C22⋊D4311yescharacteristic
306M16—21no—
307M16—21no—
308M16—21no—
309M16—41no—
310M16—41no—
311M16—1724no—
312M16—1721no—
313M16—1721no—
314M16#1062188412yes—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—41no—
318C2×C8—862no—
319C2×C8—862no—
320C2×C8—1724no—
321C2×C8—1721no—
322C2×C8—1722no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—431no—
328C4⋊C4—431no—
329C4⋊C4—861no—
330C22⋊C4—861no—
331C22⋊C4—861no—
332C22⋊C4—861no—
333C22⋊C4—861no—
334C42D4×D4311yescharacteristic
335C42D4×D4311yescharacteristic
336C42D4×D4311yescharacteristic
337C42#1062190011yescharacteristic
338C23—861no—
339C23—861no—
340C23—3441no—
341C23—1722no—
342C23—1721no—
343C23—1721no—
344C23C4×C22⋊D4311yescharacteristic
345Q8—82no—
346Q8—82no—
347D4—432no—
348D4—861no—
349D4—861no—
350D4—861no—
351D4—1722no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—82no—
357C2×C4—861no—
358C2×C4—861no—
359C2×C4—1721no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4—1721no—
363C2×C4—1721no—
364C2×C4—1721no—
365C2×C4—1721no—
366C2×C4—1721no—
367C2×C4—1721no—
368C2×C4—1721no—
369C2×C4C22⋊C4×D4311yescharacteristic
370C2×C4(C22⋊D43)⋊C411yescharacteristic
371C2×C4#1306329311yescharacteristic
372C2×C4#1306329611yescharacteristic
373C2×C4#1306329811yescharacteristic
374C2×C4#1306330711yescharacteristic
375C2×C4C2×#1062188411yescharacteristic
376C2×C4#1306334511yescharacteristic
377C2×C4#1306335011yescharacteristic
378C2×C4#1306335611yescharacteristic
379C8—22no—
380C8—41no—
381C8—81no—
382C8—3441no—
383C8—1722no—
384C8—1722no—
385C22—21no—
386C22—21no—
387C22—862no—
388C22—3442no—
389C22—3442no—
390C22—1721no—
391C22—1721no—
392C22—1721no—
393C22—1721no—
394C22—1721no—
395C22#1458277511yescharacteristic
396C22C4×#1062188411yescharacteristic
397C22#1458299711yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—82no—
402C4—1721no—
403C4—1721no—
404C4#101×D4311yescharacteristic
405C4#1458288211yescharacteristic
406C4#1458304911yescharacteristic
407C4#1458305911yescharacteristic
408C4#1458310111yescharacteristic
409C4#1458311111yescharacteristic
410C2—21no—
411C2—21no—
412C2—3441no—
413C2—1722no—
414C2#1913493211yescharacteristic
415C2#1913506011yescharacteristic
416C2#1913507811yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1997C2
socleC22×C43#386
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#1997D43
hypocenterC43#9249
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
3. #19133280C2semidirect
5. #19132469C2semidirect
6. #19132446C2semidirect
7. C43×#1997C2semidirect
204. #1997D43semidirect
239. C43#9249semidirect

Maximal subgroups

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

subgroupindex
C2×#145831862
M16×D1722
#191332802
#191330192
#191324692
#191324462
C43×#19972
#924943