Finite Group Databasebeta

← #24993007

Subgroups — #24993007

Order 11008.

534 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583099C211yesmaximal, characteristic
2Q8×#10621877C211yesmaximal, characteristic, complemented
3#19135434C211yesmaximal, characteristic
4#19133262C211yesmaximal, characteristic
5#19132469C211yesmaximal, characteristic, complemented
6#19132444C211yesmaximal, characteristic, complemented
7C43×#1487C211yesmaximal, characteristic, complemented
8C22×#10621884C412yes—
9C2×#13063322C2211yescharacteristic
10#14583099—21no—
11#14583099—21no—
12#14583099—21no—
13#14583099—21no—
14#14583030—22no—
15#14583030—21no—
16Q8×C43⋊C8—21no—
17#14582923—21no—
18#14582923C2211yescharacteristic
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C2×#13063245C412yes—
21C2×#13063241—21no—
22C2×#13063241—21no—
23C4×#10621877—21no—
24C4×#10621877C2211yescharacteristic
25#14582642—22no—
26C2×C4×Q8×C43C2211yescharacteristic
27C43×#431C2211yescharacteristic
28C43×#423C2211yescharacteristic
29C43×Q8⋊C8—21no—
30C43×Q8⋊C8—21no—
31C22×D172—21no—
32C22×D172—21no—
33C22×D172C2×C412yes—
34C2×#10621884—22no—
35C2×#10621884—22no—
36C2×#10621884—44no—
37C2×#10621877—21no—
38C2×#10621877D411yescharacteristic
39C2×#10621877D411yescharacteristic
40C22×C43⋊C8C2×C412yes—
41#13063322—21no—
42#13063322—21no—
43#13063322—21no—
44#13063322—21no—
45C4⋊(C43⋊C8)—22no—
46C4⋊(C43⋊C8)—22no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)D412yes—
51#13063245—22no—
52#13063245—22no—
53#13063241—42no—
54#13063241—42no—
55#13063236—22no—
56#13063236—21no—
57C4×C43⋊C8—22no—
58C4×C43⋊C8—21no—
59C22×Q8×C43C2×C411yescharacteristic
60C2×M16×C43—21no—
61C4×Q8×C43—21no—
62C4×Q8×C43—21no—
63C4×Q8×C43D411yescharacteristic
64C4×Q8×C43D411yescharacteristic
65C4×Q8×C43D411yescharacteristic
66C4×Q8×C43D411yescharacteristic
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43C2×C411yescharacteristic
69C2×C42×C43—21no—
70C2×C42×C43C2311yescharacteristic
71C4⋊C8×C43—21no—
72C4⋊C8×C43—21no—
73C4⋊C8×C43—21no—
74C22⋊C8×C43—21no—
75C4×C8×C43—21no—
76C23×D43—22no—
77C2×Q8×C43—21no—
78C2×Q8×C43—22no—
79C2×Q8×C43—41no—
80C2×Q8×C43C22⋊C411yescharacteristic
81C2×Q8×C43C22⋊C411yescharacteristic
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43C22×C411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43#4111yescharacteristic
87C2×D172—22no—
88C2×D172—22no—
89C2×D172—41no—
90C2×D172—41no—
91C2×D172—41no—
92C2×D172—41no—
93C2×D172—41no—
94C2×D172—41no—
95C2×D172—41no—
96C2×D172—41no—
97C2×D172—42no—
98C2×D172—42no—
99C2×D172—82no—
100M16×C43—41no—
101M16×C43—41no—
102C2×C8×C43—41no—
103C2×C8×C43—41no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43C22⋊C411yescharacteristic
110C4⋊C4×C43C22⋊C411yescharacteristic
111C42×C43—21no—
112C42×C43—21no—
113C42×C43—21no—
114C42×C43—21no—
115C42×C43C2×D411yescharacteristic
116C42×C43C2×D411yescharacteristic
117C42×C43C2×D411yescharacteristic
118C42×C43#4111yescharacteristic
119#10621884—44no—
120#10621884—44no—
121#10621877—21no—
122#10621877—21no—
123#10621877—21no—
124#10621877—41no—
125#10621877—41no—
126#10621877SD1612yescomplemented
127C2×C43⋊C8—21no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—21no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—42no—
132C23×C43C4×D411yescharacteristic
133C22×D43—42no—
134C22×D43—42no—
135C22×D43—42no—
136C22×D43—82no—
137C22×D43—82no—
138Q8×C43—21no—
139Q8×C43—21no—
140Q8×C43—21no—
141Q8×C43—42no—
142Q8×C43#10012yescomplemented
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—41no—
150C2×C4×C43—42no—
151C2×C4×C43—81no—
152C2×C4×C43C2×C22⋊C411yescharacteristic
153C2×C4×C43C4×D411yescharacteristic
154C2×C4×C43#12011yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12311yescharacteristic
158C2×C4×C43C2×SD1611yescharacteristic
159C2×C4×C43#13511yescharacteristic
160C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C43#13711yescharacteristic
162D172—42no—
163D172—42no—
164D172—82no—
165D172—82no—
166D172—82no—
167D172—81no—
168D172—81no—
169D172—81no—
170D172—81no—
171C8×C43—81no—
172C8×C43—81no—
173C43⋊C8—22no—
174C43⋊C8—42no—
175C43⋊C8—41no—
176C43⋊C8—42no—
177#9254—431nomaximal, Sylow
178C22×C43—21no—
179C22×C43—21no—
180C22×C43#38611yescharacteristic
181C22×C43C4×SD1611yescharacteristic
182C22×C43#44011yescharacteristic
183C2×D43—82no—
184C2×D43—82no—
185C2×D43—82no—
186C2×D43—162no—
187C2×D43—162no—
188C4×C43—21no—
189C4×C43—22no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—41no—
193C4×C43—41no—
194C4×C43—41no—
195C4×C43C2×#10011yescharacteristic
196C4×C43#41311yescharacteristic
197C4×C43#44811yescharacteristic
198C4×C43#44911yescharacteristic
199C4×C43#46011yescharacteristic
200C4×C43#46411yescharacteristic
201C2×#460—431no—
202Q8×M16—431no—
203#1965—431no—
204#1545—431no—
205#1487D4311yescharacteristic, complemented
206#1292—431no—
207#1283—431no—
208C2×C43—21no—
209C2×C43—21no—
210C2×C43#188011yescharacteristic
211C2×C43#190011yescharacteristic
212C2×C43#190311yescharacteristic
213D43—162no—
214C22×SD16—432no—
215C2×#127—431no—
216C2×C4×Q8C2×D4311yescharacteristic
217#460—861no—
218#460—861no—
219#460—861no—
220#460—861no—
221#446—862no—
222#446—861no—
223C8×Q8—861no—
224#431C2×D4311yescharacteristic
225#423—431no—
226#423—861no—
227#423C2×D4311yescharacteristic
228C2×C4⋊C8—431no—
229C2×#102—432no—
230C2×#100—861no—
231C2×#100—861no—
232C4×M16—431no—
233C4×M16—861no—
234#331—862no—
235Q8⋊C8—21no—
236Q8⋊C8—21no—
237C43#925411yescharacteristic, complemented, Sylow
238C22×Q8C4×D4311yescharacteristic
239C22×D4—432no—
240C22×D4—861no—
241C22×D4—861no—
242C2×SD16—862no—
243C2×SD16—862no—
244C2×SD16—1724no—
245C2×M16—21no—
246C2×M16—431no—
247C2×M16—431no—
248C2×M16—861no—
249C22×C8—432no—
250#127—861no—
251#127—861no—
252#127—861no—
253#127—861no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×Q8D17211yescharacteristic
257C4×Q8D17211yescharacteristic
258C4×Q8C22⋊D4311yescharacteristic
259C4×Q8C22⋊D4311yescharacteristic
260C2×C4⋊C4—21no—
261C2×C4⋊C4C4×D4311yescharacteristic
262C2×C42—21no—
263C2×C42C22×D4311yescharacteristic
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—432no—
268C4⋊C8—862no—
269C4⋊C8—862no—
270C4⋊C8—861no—
271C4⋊C8—861no—
272C4⋊C8—861no—
273#102—862no—
274#102—862no—
275#100—1722no—
276#100—1722no—
277C22⋊C8—21no—
278#97—862no—
279#97—861no—
280C4×C8—21no—
281C4×C8—862no—
282C4×C8—861no—
283C24—862no—
284C2×Q8—21no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×Q8(C2×D43)⋊C411yescharacteristic
288C2×Q8(C2×D43)⋊C411yescharacteristic
289C2×D4—862no—
290C2×D4—862no—
291C2×D4—3442no—
292C2×D4—1722no—
293C2×D4—1722no—
294C2×D4—1721no—
295C2×D4—1721no—
296C2×D4—1721no—
297C2×D4—1721no—
298C2×D4—1721no—
299C2×D4—1721no—
300C2×D4—1721no—
301C2×D4—1721no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4C2×C4×D4311yescharacteristic
305C22×C4D4×D4311yescharacteristic
306C22×C4#1062190011yescharacteristic
307SD16—1724no—
308SD16—1724no—
309M16—41no—
310M16—41no—
311M16—432no—
312M16—861no—
313M16—861no—
314M16—861no—
315M16—1721no—
316M16—1721no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—861no—
320C2×C8—862no—
321C2×C8—862no—
322C2×C8—861no—
323C2×C8—1722no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4(C2×D43)⋊C411yescharacteristic
330C4⋊C4(C2×D43)⋊C411yescharacteristic
331C42—21no—
332C42—21no—
333C42—21no—
334C42—21no—
335C42C2×D17211yescharacteristic
336C42D4×D4311yescharacteristic
337C42#1062190011yescharacteristic
338C42C2×C22⋊D4311yescharacteristic
339C23—3442no—
340C23—3442no—
341C23—1722no—
342C23—1722no—
343C23—1722no—
344C23(C22⋊D43)⋊C411yescharacteristic
345Q8—21no—
346Q8—21no—
347Q8—21no—
348Q8—42no—
349Q8#1306324112yescomplemented
350D4—3442no—
351D4—3442no—
352D4—3442no—
353D4—3441no—
354D4—3441no—
355D4—3441no—
356D4—3441no—
357D4—1722no—
358D4—1722no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—81no—
368C2×C4C2×(C2×D43)⋊C411yescharacteristic
369C2×C4(C22⋊D43)⋊C411yescharacteristic
370C2×C4#1306329511yescharacteristic
371C2×C4#1306329711yescharacteristic
372C2×C4#1306329711yescharacteristic
373C2×C4#1306330911yescharacteristic
374C2×C4SD16×D4311yescharacteristic
375C2×C4#1306334811yescharacteristic
376C2×C4#1306335211yescharacteristic
377C2×C4#1306335711yescharacteristic
378C8—81no—
379C8—81no—
380C8—862no—
381C8—1721no—
382C8—1722no—
383C8—1722no—
384C22—21no—
385C22—21no—
386C22—3442no—
387C22—3442no—
388C22—3442no—
389C22—6882no—
390C22—6882no—
391C22#1458277611yescharacteristic
392C22#1458298411yescharacteristic
393C22#1458300211yescharacteristic
394C4—21no—
395C4—22no—
396C4—21no—
397C4—21no—
398C4—41no—
399C4—41no—
400C4—41no—
401C4C2×#1306324111yescharacteristic
402C4#1458288111yescharacteristic
403C4#1458303911yescharacteristic
404C4#1458304711yescharacteristic
405C4#1458309711yescharacteristic
406C4#1458312311yescharacteristic
407C2—21no—
408C2—21no—
409C2—6882no—
410C2#1913494811yescharacteristic
411C2#1913505611yescharacteristic
412C2#1913507311yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1487C2
socleC22×C43#386
prime radicalC2×#13063322C22
cosocleC2×C42×C43C23
hypercenter#1487D43
hypocenterC43#9254
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
2. Q8×#10621877C2semidirect
5. #19132469C2semidirect
6. #19132444C2semidirect
7. C43×#1487C2semidirect
126. #10621877SD16semidirect
142. Q8×C43#100semidirect
205. #1487D43semidirect
237. C43#9254semidirect
349. Q8#13063241semidirect

Maximal subgroups

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

subgroupindex
C2×#145830992
Q8×#106218772
#191354342
#191332622
#191324692
#191324442
C43×#14872
#925443