Finite Group Databasebeta

← #24991469

Subgroups — #24991469

Order 11008.

476 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
1#19144385C211yesmaximal, characteristic
2#19143160C211yesmaximal, characteristic
3#19133051C211yesmaximal, characteristic, complemented
4#19132997C211yesmaximal, characteristic, complemented
5#19132978C211yesmaximal, characteristic
6#19132492C211yesmaximal, characteristic, complemented
7C43×#1277C211yesmaximal, characteristic, complemented
8C2×#13063331—21no—
9#14583456C2211yescharacteristic
10C4×#10621898C2211yescharacteristic
11#14583207—21no—
12#14583200—21no—
13#14583195C411yescharacteristic
14#14583190C411yescharacteristic
15#14583185C411yescharacteristic
16#14583180C411yescharacteristic
17#14582952C2211yescharacteristic
18#14582937—21no—
19#14582925—21no—
20#14582924—22no—
21#14582923C2211yescharacteristic
22#14582921—21no—
23C4⋊C8×D43—21no—
24#14582896—21no—
25#14582631—21no—
26#14582631—22no—
27#14582629—21no—
28#14582629—21no—
29#14582628—21no—
30C2×C4⋊C8×C43C2211yescharacteristic
31C2×C4⋊C8×C43C2211yescharacteristic
32C2×C4×C8×C43C2211yescharacteristic
33C2×#10621898D411yescharacteristic
34#13063331—42no—
35#13063331—42no—
36C2×#10621877—21no—
37C2×#10621872—22no—
38C2×C8×D43—22no—
39#13063325C2×C411yescharacteristic
40#13063325C2×C411yescharacteristic
41#13063317—21no—
42#13063304—21no—
43#13063304—21no—
44C4×Dic86—21no—
45C4×Dic86—21no—
46C4×Dic86C2×C411yescharacteristic
47C4×Dic86D411yescharacteristic
48C4×D172C2×C411yescharacteristic
49C4×D172D411yescharacteristic
50C4×C22⋊D43—21no—
51C4×C22⋊D43—21no—
52#13063284—21no—
53#13063284D411yescharacteristic
54#13063282—21no—
55C42×D43—21no—
56#13063259—21no—
57#13063259—21no—
58#13063257—21no—
59#13063257—21no—
60C4⋊(C43⋊C8)—21no—
61C4⋊(C43⋊C8)—21no—
62C4⋊(C43⋊C8)D412yes—
63Dic43⋊C8—22no—
64Dic43⋊C8—22no—
65#13063250—21no—
66#13063250—21no—
67#13063247—21no—
68#13063247—21no—
69C22⋊(C43⋊C8)—21no—
70C4×C43⋊C8—21no—
71C22×C8×C43—21no—
72C22×C8×C43—21no—
73C22×C8×C43—21no—
74C2×C42×C43C2311yescharacteristic
75C4⋊C8×C43—21no—
76C4⋊C8×C43—21no—
77C4⋊C8×C43C2×C411yescharacteristic
78C4⋊C8×C43C2×C411yescharacteristic
79C4⋊C8×C43D411yescharacteristic
80C4⋊C8×C43D411yescharacteristic
81C4×C8×C43—21no—
82C4×C8×C43—21no—
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43#4111yescharacteristic
85C22×C4×C43#4111yescharacteristic
86C2×C22⋊D43—21no—
87#10621898—21no—
88#10621898—21no—
89#10621898SD1612yes—
90#10621898Q1612yes—
91C2×D172C22⋊C411yescharacteristic
92C2×C4×D43—21no—
93C2×C4×D43—21no—
94C2×C4×D43—21no—
95C2×Dic86—21no—
96C2×Dic86—21no—
97C2×Dic86C22⋊C411yescharacteristic
98C2×C8×C43—22no—
99C2×C8×C43—21no—
100C2×C8×C43—21no—
101C2×C8×C43—21no—
102C2×C8×C43—21no—
103C2×C8×C43—41no—
104C2×C8×C43—41no—
105C2×C8×C43—41no—
106C2×C8×C43—41no—
107C2×C8×C43—41no—
108C2×C8×C43—41no—
109C42×C43C22×C411yescharacteristic
110C42×C43C2×D411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C22⋊Dic43—21no—
114C22⋊Dic43—41no—
115(C2×D43)⋊C4—21no—
116(C2×D43)⋊C4—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121C4⋊Dic43C22⋊C411yescharacteristic
122C4⋊Dic43C22⋊C411yescharacteristic
123Dic43⋊C4—21no—
124Dic43⋊C4—21no—
125Dic43⋊C4—41no—
126Dic43⋊C4—41no—
127C4×Dic43—21no—
128C4×Dic43—21no—
129C4×Dic43—21no—
130C4×Dic43—41no—
131#10621877—41no—
132#10621877—41no—
133C2×C43⋊C8—22no—
134C2×C43⋊C8—41no—
135#10621872—44no—
136C8×D43—44no—
137C23×C43#12311yescharacteristic
138C22×D43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—41no—
142C2×C4×C43C2×C22⋊C411yescharacteristic
143C2×C4×C43C4×D411yescharacteristic
144C2×C4×C43C4×D411yescharacteristic
145C2×C4×C43#12011yescharacteristic
146C2×C4×C43#12111yescharacteristic
147C2×C4×C43#12111yescharacteristic
148C2×C4×C43C2×SD1611yescharacteristic
149C2×C4×C43C2×Q1611yescharacteristic
150C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C43#13711yescharacteristic
152C22⋊D43—22no—
153C22⋊D43—22no—
154C2×Dic43—21no—
155C2×Dic43—21no—
156C2×Dic43—21no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159D172—21no—
160D172#10312yes—
161C4×D43—22no—
162C4×D43—22no—
163C4×D43—41no—
164C4×D43—41no—
165C4×D43—81no—
166Dic86—21no—
167Dic86—42no—
168Dic86—41no—
169Dic86—41no—
170Dic86#10312yes—
171C8×C43—42no—
172C8×C43—41no—
173C8×C43—41no—
174C8×C43—41no—
175C8×C43—41no—
176C43⋊C8—42no—
177C43⋊C8—81no—
178#8993—431nomaximal, Sylow
179C22×C43—21no—
180C22×C43—21no—
181C22×C43#38611yescharacteristic
182C22×C43#48311yescharacteristic
183C22×C43#48411yescharacteristic
184C2×D43—22no—
185C2×D43—41no—
186C2×D43—41no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43C2×#10311yescharacteristic
191C4×C43#41711yescharacteristic
192C4×C43#44311yescharacteristic
193C4×C43#44411yescharacteristic
194C4×C43#45011yescharacteristic
195C4×C43#45111yescharacteristic
196Dic43—22no—
197Dic43—41no—
198Dic43—41no—
199Dic43—81no—
200Dic43—81no—
201#3076—431no—
202#2906—431no—
203#1493—431no—
204#1481—431no—
205#1476—431no—
206#1301—431no—
207#1277D4311yescharacteristic, complemented
208C2×C43—21no—
209C2×C43—21no—
210C2×C43#187211yescharacteristic
211C2×C43#187611yescharacteristic
212C2×C43#188111yescharacteristic
213D43—42no—
214C2×#131—861no—
215#533—431no—
216C4×#41—431no—
217#479—861no—
218#478—861no—
219#477—431no—
220#476—431no—
221#475—431no—
222#474—431no—
223#431—431no—
224#427—861no—
225#424—862no—
226#424—861no—
227#423—431no—
228#423—861no—
229C2×C4⋊C8—861no—
230C2×C4⋊C8C2×D4311yescharacteristic
231C2×C4⋊C8C2×D4311yescharacteristic
232#416—861no—
233C2×C4×C8C2×D4311yescharacteristic
234Q8⋊C8—862no—
235Q8⋊C8—861no—
236Q8⋊C8—861no—
237Q8⋊C8—861no—
238D4⋊C8—861no—
239C43#899311yescharacteristic, complemented, Sylow
240C2×#41—431no—
241#131—1722no—
242#131—1722no—
243C2×M16—862no—
244C2×M16—861no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—862no—
249C4⋊Q8—431no—
250C4⋊Q8—431no—
251#125—861no—
252C22⋊Q8—861no—
253C22⋊Q8—861no—
254C4×Q8—431no—
255C4×Q8—431no—
256C4×Q8—861no—
257C4×Q8—861no—
258C4×D4—431no—
259C4×D4—431no—
260C4×D4—861no—
261C4×D4—861no—
262#117—431no—
263#117—861no—
264#117—861no—
265C2×C42—861no—
266C2×C42C22×D4311yescharacteristic
267#107—861no—
268#107—861no—
269#106—861no—
270#106—861no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—432no—
274C4⋊C8—862no—
275C4⋊C8—862no—
276C4⋊C8—861no—
277C4⋊C8—861no—
278C4⋊C8C4×D4311yescharacteristic
279C4⋊C8C4×D4311yescharacteristic
280C4⋊C8D17211yescharacteristic
281C4⋊C8D17211yescharacteristic
282#103—861no—
283#103—861no—
284#102—861no—
285#102—861no—
286C22⋊C8—861no—
287C4×C8—21no—
288C4×C8—21no—
289C4×C8—861no—
290#41—432no—
291#41—432no—
292#41—861no—
293#41—861no—
294C2×Q8—431no—
295C2×Q8—861no—
296C2×Q8—861no—
297C2×D4—431no—
298C2×D4—861no—
299C22×C4—861no—
300C22×C4—861no—
301C22×C4—861no—
302C22×C4#1062189811yescharacteristic
303C22×C4D4×D4311yescharacteristic
304C22×C4#1062190211yescharacteristic
305M16—1724no—
306M16—1721no—
307M16—1721no—
308C2×C8—22no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—862no—
320C2×C8—1724no—
321C2×C8—1721no—
322C4⋊C4—431no—
323C4⋊C4—431no—
324C4⋊C4—861no—
325C4⋊C4—861no—
326C4⋊C4—861no—
327C4⋊C4—861no—
328C4⋊C4—861no—
329C4⋊C4—861no—
330C4⋊C4—1721no—
331C4⋊C4—1721no—
332C22⋊C4—861no—
333C22⋊C4—861no—
334C22⋊C4—861no—
335C22⋊C4—1721no—
336C42—861no—
337C42—861no—
338C42—861no—
339C42—1721no—
340C42C2×C4×D4311yescharacteristic
341C42C2×D17211yescharacteristic
342C42D4×D4311yescharacteristic
343C42D4×D4311yescharacteristic
344C23—861no—
345C23#1306331011yescharacteristic
346Q8—432no—
347Q8—861no—
348Q8—1722no—
349Q8—1721no—
350Q8—1721no—
351D4—432no—
352D4—862no—
353D4—862no—
354D4—861no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—41no—
358C2×C4—861no—
359C2×C4—862no—
360C2×C4—862no—
361C2×C4—861no—
362C2×C4—861no—
363C2×C4—3441no—
364C2×C4—1721no—
365C2×C4—1721no—
366C2×C4—1721no—
367C2×C4—1721no—
368C2×C4C22⋊C4×D4311yescharacteristic
369C2×C4#1306328711yescharacteristic
370C2×C4C4×D17211yescharacteristic
371C2×C4#1306329511yescharacteristic
372C2×C4#1306329811yescharacteristic
373C2×C4#1306330011yescharacteristic
374C2×C4SD16×D4311yescharacteristic
375C2×C4Q16×D4311yescharacteristic
376C2×C4#1306334911yescharacteristic
377C2×C4#1306335411yescharacteristic
378C8—42no—
379C8—41no—
380C8—41no—
381C8—41no—
382C8—41no—
383C8—3441no—
384C8—1722no—
385C22—21no—
386C22—21no—
387C22—862no—
388C22—1721no—
389C22—1721no—
390C22#1458277711yescharacteristic
391C22#1458323111yescharacteristic
392C22#1458323611yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—862no—
397C4—3441no—
398C4—3441no—
399C4—1721no—
400C4—1721no—
401C4#103×D4311yescharacteristic
402C4#1458289711yescharacteristic
403C4#1458301711yescharacteristic
404C4#1458302211yescharacteristic
405C4#1458305111yescharacteristic
406C4#1458305611yescharacteristic
407C2—21no—
408C2—21no—
409C2—1722no—
410C2#1913490111yescharacteristic
411C2#1913492111yescharacteristic
412C2#1913495811yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1277C2
socleC22×C43#386
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1277D43
hypocenterC43#8993
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
3. #19133051C2semidirect
4. #19132997C2semidirect
6. #19132492C2semidirect
7. C43×#1277C2semidirect
207. #1277D43semidirect
239. C43#8993semidirect

Maximal subgroups

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

subgroupindex
#191443852
#191431602
#191330512
#191329972
#191329782
#191324922
C43×#12772
#899343