Finite Group Databasebeta

← #24991478

Subgroups — #24991478

Order 11008.

430 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144385C211yesmaximal, characteristic
2#19143263C211yesmaximal, characteristic
3#19133049C211yesmaximal, characteristic, complemented
4#19132999C211yesmaximal, characteristic, complemented
5#19132975C211yesmaximal, characteristic
6#19132429C211yesmaximal, characteristic, complemented
7C43×#1301C211yesmaximal, characteristic, complemented
8#14583456C2211yescharacteristic
9C4×#10621898C2211yescharacteristic
10#14583207—21no—
11#14583200—21no—
12#14583195C411yescharacteristic
13#14583190C411yescharacteristic
14#14583185C411yescharacteristic
15#14583180C411yescharacteristic
16#14582959—22no—
17#14582955—21no—
18#14582951—21no—
19#14582937—21no—
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21#14582896—21no—
22#14582867—21no—
23#14582857—21no—
24C2×C4×C43⋊C8C2211yescharacteristic
25#14582631—21no—
26#14582631—21no—
27#14582629—21no—
28#14582629—22no—
29#14582626—21no—
30C43×#431C2211yescharacteristic
31C43×#423C2211yescharacteristic
32C2×C4⋊C8×C43C2211yescharacteristic
33C2×#10621898D411yescharacteristic
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36#13063325C2×C411yescharacteristic
37#13063325C2×C411yescharacteristic
38#13063317—21no—
39#13063304—21no—
40#13063304—21no—
41C4×Dic86—21no—
42C4×Dic86—21no—
43C4×Dic86C2×C411yescharacteristic
44C4×Dic86D411yescharacteristic
45C4×D172C2×C411yescharacteristic
46C4×D172D411yescharacteristic
47C4×C22⋊D43—21no—
48C4×C22⋊D43—21no—
49#13063284—21no—
50#13063284D411yescharacteristic
51#13063282—21no—
52C42×D43—21no—
53#13063259—21no—
54#13063259—21no—
55#13063257—21no—
56#13063257—21no—
57C4⋊(C43⋊C8)—21no—
58C4⋊(C43⋊C8)D411yescharacteristic
59C4⋊(C43⋊C8)D411yescharacteristic
60#13063250—21no—
61#13063250—21no—
62#13063247—21no—
63#13063247—21no—
64(C2×D43)⋊C8—22no—
65(C2×D43)⋊C8—22no—
66#13063235—22no—
67C4×C43⋊C8—21no—
68C4×C43⋊C8—21no—
69C8×Dic43—22no—
70C2×M16×C43—21no—
71C22×C8×C43—21no—
72C2×C42×C43C2311yescharacteristic
73C4⋊C8×C43—21no—
74C4⋊C8×C43—21no—
75C4⋊C8×C43—21no—
76C4⋊C8×C43C2×C411yescharacteristic
77C4⋊C8×C43C2×C411yescharacteristic
78C4⋊C8×C43D412yes—
79C22⋊C8×C43—21no—
80C4×C8×C43—21no—
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43#4111yescharacteristic
83C22×C4×C43#4111yescharacteristic
84C2×C22⋊D43—21no—
85#10621898—21no—
86#10621898—21no—
87#10621898—21no—
88#10621898—21no—
89C2×D172C22⋊C411yescharacteristic
90C2×C4×D43—21no—
91C2×C4×D43—21no—
92C2×C4×D43—21no—
93C2×Dic86—21no—
94C2×Dic86—21no—
95C2×Dic86C22⋊C411yescharacteristic
96M16×C43—41no—
97M16×C43—41no—
98C2×C8×C43—21no—
99C2×C8×C43—21no—
100C2×C8×C43—22no—
101C2×C8×C43—41no—
102C2×C8×C43—41no—
103C2×C8×C43—41no—
104C42×C43C22×C411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43C2×D411yescharacteristic
107C42×C43C2×D411yescharacteristic
108C22⋊Dic43—21no—
109C22⋊Dic43—41no—
110(C2×D43)⋊C4—21no—
111(C2×D43)⋊C4—21no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115C4⋊Dic43—21no—
116C4⋊Dic43C22⋊C411yescharacteristic
117C4⋊Dic43C22⋊C411yescharacteristic
118Dic43⋊C4—21no—
119Dic43⋊C4—21no—
120Dic43⋊C4—41no—
121Dic43⋊C4—41no—
122C4×Dic43—21no—
123C4×Dic43—21no—
124C4×Dic43—21no—
125C4×Dic43—41no—
126C2×C43⋊C8—22no—
127C2×C43⋊C8—21no—
128C2×C43⋊C8—21no—
129C2×C43⋊C8—41no—
130C2×C43⋊C8—41no—
131C2×C43⋊C8—41no—
132C2×C43⋊C8—41no—
133C23×C43#12311yescharacteristic
134C22×D43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—41no—
138C2×C4×C43C2×C22⋊C411yescharacteristic
139C2×C4×C43C4×D411yescharacteristic
140C2×C4×C43C4×D411yescharacteristic
141C2×C4×C43#12011yescharacteristic
142C2×C4×C43#12111yescharacteristic
143C2×C4×C43#12111yescharacteristic
144C2×C4×C43#13511yescharacteristic
145C2×C4×C43#13511yescharacteristic
146C2×C4×C43#13711yescharacteristic
147C2×C4×C43#13711yescharacteristic
148C22⋊D43—41no—
149C22⋊D43—41no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155D172—21no—
156D172—21no—
157C4×D43—41no—
158C4×D43—41no—
159C4×D43—41no—
160C4×D43—41no—
161C4×D43—81no—
162Dic86—21no—
163Dic86—21no—
164Dic86—42no—
165Dic86—41no—
166Dic86—41no—
167C8×C43—41no—
168C8×C43—41no—
169C8×C43—42no—
170C8×C43—81no—
171C43⋊C8—42no—
172C43⋊C8—41no—
173C43⋊C8—41no—
174#8994—431nomaximal, Sylow
175C22×C43—21no—
176C22×C43—21no—
177C22×C43#38611yescharacteristic
178C22×C43#48511yescharacteristic
179C22×C43#48511yescharacteristic
180C2×D43—41no—
181C2×D43—41no—
182C2×D43—41no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43#41611yescharacteristic
187C4×C43#41911yescharacteristic
188C4×C43#44311yescharacteristic
189C4×C43#44411yescharacteristic
190C4×C43#45211yescharacteristic
191C4×C43#45211yescharacteristic
192Dic43—41no—
193Dic43—41no—
194Dic43—41no—
195Dic43—81no—
196Dic43—81no—
197#3076—431no—
198#2925—431no—
199#1493—431no—
200#1481—431no—
201#1476—431no—
202#1301D4311yescharacteristic, complemented
203#1277—431no—
204C2×C43—21no—
205C2×C43—21no—
206C2×C43#187311yescharacteristic
207C2×C43#187611yescharacteristic
208C2×C43#188111yescharacteristic
209D43—81no—
210#533—431no—
211C4×#41—431no—
212#479—861no—
213#478—861no—
214#477—431no—
215#476—431no—
216#475—431no—
217#474—431no—
218#433—862no—
219#432—861no—
220#431—861no—
221#431C2×D4311yescharacteristic
222#427—861no—
223#423C2×D4311yescharacteristic
224C2×C4⋊C8—431no—
225C2×C4⋊C8C2×D4311yescharacteristic
226#416—861no—
227#408—861no—
228#405—861no—
229C2×C4×C8—431no—
230Q8⋊C8—861no—
231Q8⋊C8—861no—
232Q8⋊C8—861no—
233Q8⋊C8—862no—
234D4⋊C8—861no—
235C43#899411yescharacteristic, complemented, Sylow
236C2×#41—431no—
237C2×M16—21no—
238C22×C8—21no—
239C22×C8—861no—
240C22×C8—861no—
241C4⋊Q8—431no—
242C4⋊Q8—431no—
243#125—861no—
244C22⋊Q8—861no—
245C22⋊Q8—861no—
246C4×Q8—431no—
247C4×Q8—431no—
248C4×Q8—861no—
249C4×Q8—861no—
250C4×D4—431no—
251C4×D4—431no—
252C4×D4—861no—
253C4×D4—861no—
254#117—431no—
255#117—861no—
256#117—861no—
257C2×C42—861no—
258C2×C42C22×D4311yescharacteristic
259#107—861no—
260#107—861no—
261#106—861no—
262#106—861no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—431no—
267C4⋊C8—431no—
268C4⋊C8—861no—
269C4⋊C8C4×D4311yescharacteristic
270C4⋊C8C4×D4311yescharacteristic
271C4⋊C8D17212yes—
272#103—861no—
273#103—861no—
274#102—861no—
275#102—861no—
276C22⋊C8—21no—
277C22⋊C8—862no—
278C22⋊C8—862no—
279#97—862no—
280C4×C8—21no—
281C4×C8—862no—
282C4×C8—861no—
283C4×C8—861no—
284#41—861no—
285#41—861no—
286#41—861no—
287#41—861no—
288C2×Q8—431no—
289C2×Q8—861no—
290C2×Q8—861no—
291C2×D4—431no—
292C2×D4—861no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4#1062189811yescharacteristic
297C22×C4D4×D4311yescharacteristic
298C22×C4#1062190211yescharacteristic
299M16—41no—
300M16—41no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—22no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—862no—
308C2×C8—861no—
309C2×C8—861no—
310C2×C8—1721no—
311C2×C8—1721no—
312C2×C8—1721no—
313C2×C8—1721no—
314C4⋊C4—431no—
315C4⋊C4—431no—
316C4⋊C4—861no—
317C4⋊C4—861no—
318C4⋊C4—861no—
319C4⋊C4—861no—
320C4⋊C4—861no—
321C4⋊C4—861no—
322C4⋊C4—1721no—
323C4⋊C4—1721no—
324C22⋊C4—861no—
325C22⋊C4—861no—
326C22⋊C4—861no—
327C22⋊C4—1721no—
328C42—861no—
329C42—861no—
330C42—861no—
331C42—1721no—
332C42C2×C4×D4311yescharacteristic
333C42C2×D17211yescharacteristic
334C42D4×D4311yescharacteristic
335C42D4×D4311yescharacteristic
336C23—861no—
337C23#1306331011yescharacteristic
338Q8—861no—
339Q8—861no—
340Q8—1722no—
341Q8—1721no—
342Q8—1721no—
343D4—861no—
344D4—861no—
345D4—1721no—
346D4—1721no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—3441no—
354C2×C4—1721no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4C22⋊C4×D4311yescharacteristic
361C2×C4#1306328711yescharacteristic
362C2×C4C4×D17211yescharacteristic
363C2×C4#1306329511yescharacteristic
364C2×C4#1306329811yescharacteristic
365C2×C4#1306330011yescharacteristic
366C2×C4#1306334411yescharacteristic
367C2×C4#1306334611yescharacteristic
368C2×C4#1306335411yescharacteristic
369C2×C4#1306335711yescharacteristic
370C8—42no—
371C8—41no—
372C8—41no—
373C8—81no—
374C8—1722no—
375C8—1721no—
376C8—1721no—
377C22—21no—
378C22—21no—
379C22—1721no—
380C22—1721no—
381C22—1721no—
382C22#1458277711yescharacteristic
383C22#1458324211yescharacteristic
384C22#1458324311yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—3441no—
389C4—3441no—
390C4—1721no—
391C4—1721no—
392C4—1721no—
393C4#1458289211yescharacteristic
394C4#1458290611yescharacteristic
395C4#1458301511yescharacteristic
396C4#1458302011yescharacteristic
397C4#1458306211yescharacteristic
398C4#1458306411yescharacteristic
399C2—21no—
400C2—21no—
401C2—3441no—
402C2#1913490611yescharacteristic
403C2#1913492311yescharacteristic
404C2#1913495611yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1301C2
socleC22×C43#386
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1301D43
hypocenterC43#8994
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
3. #19133049C2semidirect
4. #19132999C2semidirect
6. #19132429C2semidirect
7. C43×#1301C2semidirect
202. #1301D43semidirect
235. C43#8994semidirect

Maximal subgroups

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

subgroupindex
#191443852
#191432632
#191330492
#191329992
#191329752
#191324292
C43×#13012
#899443