Finite Group Databasebeta

← #25014784

Subgroups — #25014784

Order 11008.

424 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583014C211yesmaximal, characteristic
2C2×#14582719C211yesmaximal, characteristic, complemented
3#19136224C211yesmaximal, characteristic, complemented
4#19136216C211yesmaximal, characteristic, complemented
5#19136215C211yesmaximal, characteristic, complemented
6M32×Dic43C211yesmaximal, characteristic, complemented
7C43×#2117C211yesmaximal, characteristic, complemented
8C2×#13063345C411yescharacteristic
9C2×#13063331C2211yescharacteristic
10C2×#13063265C2211yescharacteristic
11C2×#13063265C2211yescharacteristic
12#14583014—21no—
13#14583014—21no—
14#14583014—21no—
15#14583014—21no—
16C2×#13063260C411yescharacteristic
17C2×#13063252C411yescharacteristic
18C2×#13063251C411yescharacteristic
19C2×C8×Dic43C2211yescharacteristic
20#14582719—21no—
21#14582719—21no—
22#14582684—22no—
23#14582681—22no—
24#14582680—22no—
25#14582674—21no—
26C16×Dic43—21no—
27C2×#131×C43C2211yescharacteristic
28C2×M32×C43C2211yescharacteristic
29C2×M32×C43C2211yescharacteristic
30C43×#350—22no—
31C2×#10621898C2×C411yescharacteristic
32#13063345—21no—
33#13063345—21no—
34#13063345—21no—
35#13063345—21no—
36C2×#10621885C811yescharacteristic
37C2×#10621883C811yescharacteristic
38C2×#10621884C811yescharacteristic
39C2×#10621882C811yescharacteristic
40#13063331—21no—
41#13063331—21no—
42#13063331—21no—
43#13063331—21no—
44C2×#10621877C2×C411yescharacteristic
45C2×#10621872—21no—
46C22×C43⋊C8C2×C411yescharacteristic
47C2×C8×D43—21no—
48C2×C4×Dic43C2×C411yescharacteristic
49#13063265—21no—
50#13063265—21no—
51#13063265—21no—
52#13063265D412yes—
53C2×C43⋊C16—21no—
54C2×C43⋊C16—21no—
55#13063260—21no—
56#13063260—21no—
57#13063252—21no—
58#13063252—21no—
59#13063251—21no—
60#13063251—21no—
61C8×Dic43D411yescharacteristic
62C8×Dic43D411yescharacteristic
63C8×Dic43D411yescharacteristic
64C8×Dic43D411yescharacteristic
65C2×#41×C43C2×C411yescharacteristic
66#131×C43—21no—
67#131×C43—21no—
68#131×C43—21no—
69#131×C43—21no—
70C2×M16×C43—21no—
71C2×M16×C43C2×C411yescharacteristic
72C22×C8×C43—21no—
73C22×C8×C43C2311yescharacteristic
74M32×C43—21no—
75M32×C43—21no—
76M32×C43—21no—
77M32×C43D412yes—
78C2×C16×C43—21no—
79C2×C16×C43—21no—
80#41×C43—21no—
81#41×C43—21no—
82#41×C43—21no—
83#41×C43—21no—
84C2×Q8×C43C2×C811yescharacteristic
85C2×D4×C43—21no—
86C2×D4×C43C2×C811yescharacteristic
87C22×C4×C43—21no—
88C22×C4×C43C22×C411yescharacteristic
89C2×C22⋊D43—21no—
90C22×Dic43—21no—
91#10621898—21no—
92#10621898—21no—
93#10621898—21no—
94#10621898—21no—
95C2×D172C2×C811yescharacteristic
96C2×C4×D43—21no—
97C2×Dic86C2×C811yescharacteristic
98M16×C43—21no—
99M16×C43—21no—
100M16×C43—41no—
101M16×C43—41no—
102C2×C8×C43—21no—
103C2×C8×C43—41no—
104C2×C8×C43—41no—
105C2×C8×C43C2×D411yescharacteristic
106C2×C8×C43C2×D411yescharacteristic
107C2×C8×C43C2×D411yescharacteristic
108C2×C8×C43C2×D411yescharacteristic
109C2×C8×C43#4111yescharacteristic
110C2×C8×C43#4111yescharacteristic
111#10621885—21no—
112#10621885—21no—
113#10621884—21no—
114#10621884—21no—
115#10621883—21no—
116#10621883—21no—
117#10621882—21no—
118#10621882—21no—
119C4×Dic43—21no—
120C4×Dic43C22⋊C411yescharacteristic
121C4×Dic43C22⋊C411yescharacteristic
122#10621877—21no—
123#10621877—21no—
124C2×C43⋊C8—21no—
125C2×C43⋊C8C22⋊C411yescharacteristic
126C2×C43⋊C8C22⋊C411yescharacteristic
127C2×C43⋊C8C2×C811yescharacteristic
128C2×C43⋊C8C2×C811yescharacteristic
129C2×C43⋊C8M1611yescharacteristic
130C2×C43⋊C8M1611yescharacteristic
131#10621872—41no—
132#10621872—41no—
133C8×D43—41no—
134C8×D43—41no—
135C16×C43—22no—
136C16×C43—41no—
137C43⋊C16—22no—
138C43⋊C16—41no—
139C23×C43—21no—
140C23×C43#13111yescharacteristic
141C22×D43—21no—
142Q8×C43—21no—
143Q8×C43—21no—
144D4×C43—21no—
145D4×C43—21no—
146D4×C43—41no—
147D4×C43—41no—
148C2×C4×C43—21no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43C2×C22⋊C411yescharacteristic
152C2×C4×C43C4×D411yescharacteristic
153C2×C4×C43C4×D411yescharacteristic
154C2×C4×C43C22×C811yescharacteristic
155C2×C4×C43C2×M1611yescharacteristic
156C2×C4×C43#13111yescharacteristic
157C22⋊D43—41no—
158C22⋊D43—41no—
159C2×Dic43—21no—
160C2×Dic43—21no—
161C2×Dic43—21no—
162C2×Dic43—42no—
163D172—21no—
164D172—21no—
165C4×D43—41no—
166C4×D43—41no—
167Dic86—21no—
168Dic86—21no—
169C8×C43—41no—
170C8×C43#12111yescharacteristic
171C8×C43#12111yescharacteristic
172C8×C43#12411yescharacteristic
173C8×C43#12711yescharacteristic
174C43⋊C8—41no—
175C43⋊C8C22⋊C811yescharacteristic
176C43⋊C8C22⋊C811yescharacteristic
177C43⋊C8C22⋊C811yescharacteristic
178C43⋊C8C22⋊C811yescharacteristic
179#13197—431nomaximal, Sylow
180C22×C43—41no—
181C22×C43—41no—
182C22×C43—81no—
183C22×C43#40811yescharacteristic
184C22×C43C8×D411yescharacteristic
185C22×C43#43611yescharacteristic
186C2×D43—41no—
187C2×D43—81no—
188C4×C43—41no—
189C4×C43#39011yescharacteristic
190C4×C43C2×C22⋊C811yescharacteristic
191C4×C43C8×D411yescharacteristic
192C4×C43#43611yescharacteristic
193Dic43—22no—
194Dic43—41no—
195Dic43—41no—
196C2×#443—431no—
197C2×#364—431no—
198#2117—431no—
199#2117D4311yescharacteristic, complemented
200#2115—431no—
201#2115—431no—
202C4×M32—431no—
203C2×C43—21no—
204C2×C43—21no—
205C2×C43—21no—
206C2×C43—81no—
207C2×C43#195411yescharacteristic
208D43—81no—
209C2×#135—431no—
210C2×#131—431no—
211C2×#131C2×D4311yescharacteristic
212C2×M32—431no—
213C2×M32—431no—
214C2×M32C2×D4311yescharacteristic
215C2×M32C2×D4311yescharacteristic
216#443—861no—
217#443—861no—
218#443—861no—
219#443—861no—
220C2×#108—431no—
221C2×#104—431no—
222C2×#104—431no—
223C2×C4×C8—431no—
224#364—861no—
225#364—861no—
226#350—22no—
227#350—862no—
228#349—862no—
229#349—862no—
230#346—861no—
231C4×C16—861no—
232C43#1319711yescharacteristic, complemented, Sylow
233C2×#41—431no—
234C2×#41C4×D4311yescharacteristic
235#135—861no—
236#135—861no—
237#135—861no—
238#135—861no—
239C2×Q16—431no—
240C2×SD16—431no—
241C2×SD16—431no—
242C2×D8—431no—
243#131—21no—
244#131—21no—
245#131—21no—
246#131—21no—
247#131—861no—
248#131—861no—
249#131—861no—
250#131—861no—
251C2×M16—21no—
252C2×M16—431no—
253C2×M16—861no—
254C2×M16C4×D4311yescharacteristic
255C22×C8—21no—
256C22×C8—431no—
257C22×C8—861no—
258C22×C8C22×D4311yescharacteristic
259C2×C42—431no—
260M32—21no—
261M32—21no—
262M32—21no—
263M32—432no—
264M32—861no—
265M32—861no—
266M32—861no—
267M32C22⋊D4312yes—
268C2×C16—21no—
269C2×C16—21no—
270C2×C16—861no—
271C2×C16—861no—
272#108—861no—
273#108—861no—
274#104—861no—
275#104—861no—
276#104—861no—
277#104—861no—
278C4×C8—431no—
279C4×C8—431no—
280C4×C8—431no—
281C4×C8—431no—
282#41—21no—
283#41—21no—
284#41—21no—
285#41—21no—
286#41—861no—
287#41—861no—
288#41—861no—
289#41—861no—
290C2×Q8—431no—
291C2×Q8C8×D4311yescharacteristic
292C2×D4—21no—
293C2×D4—431no—
294C2×D4—861no—
295C2×D4C8×D4311yescharacteristic
296C22×C4—21no—
297C22×C4—861no—
298C22×C4—861no—
299C22×C4C2×C4×D4311yescharacteristic
300Q16—861no—
301Q16—861no—
302SD16—861no—
303SD16—861no—
304SD16—861no—
305SD16—861no—
306D8—861no—
307D8—861no—
308M16—21no—
309M16—21no—
310M16—41no—
311M16—41no—
312M16—861no—
313M16—861no—
314M16—1721no—
315M16—1721no—
316C2×C8—21no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—431no—
320C2×C8—431no—
321C2×C8—431no—
322C2×C8—431no—
323C2×C8—431no—
324C2×C8—431no—
325C2×C8—861no—
326C2×C8—1721no—
327C2×C8—1721no—
328C2×C8#1062189811yescharacteristic
329C2×C8D4×D4311yescharacteristic
330C2×C8D4×D4311yescharacteristic
331C2×C8D4×D4311yescharacteristic
332C2×C8#1062190011yescharacteristic
333C2×C8C2×C22⋊D4311yescharacteristic
334C42—431no—
335C42—431no—
336C42—861no—
337C16—22no—
338C16—41no—
339C16—862no—
340C16—1721no—
341C23—21no—
342C23—861no—
343C23#1306333311yescharacteristic
344Q8—21no—
345Q8—21no—
346Q8—861no—
347Q8—861no—
348D4—21no—
349D4—21no—
350D4—41no—
351D4—41no—
352D4—861no—
353D4—861no—
354D4—1721no—
355D4—1721no—
356C2×C4—21no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—861no—
360C2×C4—861no—
361C2×C4—861no—
362C2×C4—1722no—
363C2×C4—1721no—
364C2×C4—1721no—
365C2×C4C22⋊C4×D4311yescharacteristic
366C2×C4(C22⋊D43)⋊C411yescharacteristic
367C2×C4C4×C22⋊D4311yescharacteristic
368C2×C4C2×C8×D4311yescharacteristic
369C2×C4M16×D4311yescharacteristic
370C2×C4#1306333111yescharacteristic
371C8—41no—
372C8—431no—
373C8—431no—
374C8—431no—
375C8—431no—
376C8—1721no—
377C8#1306329711yescharacteristic
378C8#1306329811yescharacteristic
379C8#1306331111yescharacteristic
380C8#1306332111yescharacteristic
381C22—41no—
382C22—41no—
383C22—81no—
384C22—3441no—
385C22—1721no—
386C22#1458286411yescharacteristic
387C22(C22⋊D43)⋊C811yescharacteristic
388C22#1458297511yescharacteristic
389C4—41no—
390C4—862no—
391C4—1721no—
392C4—1721no—
393C4#1458279911yescharacteristic
394C4C22⋊C8×D4311yescharacteristic
395C4C8×C22⋊D4311yescharacteristic
396C4#1458297411yescharacteristic
397C2—21no—
398C2—21no—
399C2—21no—
400C2—81no—
401C2—3441no—
402C2#1913538711yescharacteristic
subgroupG/H
centerC8#13063297
commutatorC2×C4×C43C22×C8
FrattiniC22×C8C22×D43
FittingC43×#2117C2
socleC2×C43#1954
prime radicalC2×#13063345C4
cosocleC22×C8×C43C23
hypercenter#2117D43
hypocenterC43#13197
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2117

Complements

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

NH ≅ G/Ntype
2. C2×#14582719C2semidirect
3. #19136224C2semidirect
4. #19136216C2semidirect
5. #19136215C2semidirect
6. M32×Dic43C2semidirect
7. C43×#2117C2semidirect
199. #2117D43semidirect
232. C43#13197semidirect

Maximal subgroups

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

subgroupindex
C2×#145830142
C2×#145827192
#191362242
#191362162
#191362152
M32×Dic432
C43×#21172
#1319743