Finite Group Databasebeta

← #24992056

Subgroups — #24992056

Order 11008.

488 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143678C211yesmaximal, characteristic, complemented
2C2×#14583001C211yesmaximal, characteristic
3#19132991C211yesmaximal, characteristic, complemented
4#19132985C211yesmaximal, characteristic
5#19132915C211yesmaximal, characteristic
6#19132426C211yesmaximal, characteristic, complemented
7C43×#1281C211yesmaximal, characteristic, complemented
8C22×#10621873C411yescharacteristic
9C2×C4×Dic86C2211yescharacteristic
10C2×C4×D172C2211yescharacteristic
11#14583029—22no—
12#14583026—22no—
13#14583001—22no—
14#14583001—22no—
15#14582953—22no—
16#14582952C2211yescharacteristic
17#14582952C2211yescharacteristic
18C2×#13063259C411yescharacteristic
19C2×#13063250C411yescharacteristic
20C2×#13063247C411yescharacteristic
21#14582631—22no—
22#14582626—22no—
23#14582622—22no—
24C43×#431C2211yescharacteristic
25C43×#431C2211yescharacteristic
26C2×#97×C43C2211yescharacteristic
27C22×Dic86C2×C411yescharacteristic
28C22×D172C2×C411yescharacteristic
29C22×C4×D43—21no—
30C2×#10621873—22no—
31C2×#10621873—22no—
32C2×#10621873—22no—
33C4×Dic86—21no—
34C4×Dic86—21no—
35C4×Dic86D412yes—
36C4×Dic86D412yes—
37C4×D172—21no—
38C4×D172—21no—
39C4×D172—21no—
40C4×D172—21no—
41C2×C4⋊Dic43C2×C411yescharacteristic
42C2×C4⋊Dic43C2×C411yescharacteristic
43C2×Dic43⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×C4×Dic43—21no—
46#13063259—22no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)—21no—
49Dic43⋊C8—24no—
50#13063250—22no—
51#13063247—22no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54#13063235—24no—
55C4×C43⋊C8—21no—
56C4×C43⋊C8D412yes—
57C22×C8×C43C2×C411yescharacteristic
58C22×C8×C43C2×C411yescharacteristic
59C2×C42×C43C2311yescharacteristic
60C4⋊C8×C43—21no—
61C4⋊C8×C43—21no—
62C22⋊C8×C43—21no—
63C22⋊C8×C43D412yes—
64#97×C43—21no—
65#97×C43—21no—
66C4×C8×C43—21no—
67C4×C8×C43—21no—
68C23×D43—21no—
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43#4111yescharacteristic
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C2×D172—21no—
76C2×D172—21no—
77C2×D172—21no—
78C2×D172—21no—
79C2×D172—21no—
80C2×D172M1612yes—
81C2×C4×D43—41no—
82C2×C4×D43—41no—
83C2×C4×D43—82no—
84C2×Dic86—21no—
85C2×Dic86—21no—
86C2×Dic86—21no—
87C2×Dic86—21no—
88C2×Dic86—21no—
89C2×Dic86C22⋊C412yes—
90C2×C8×C43—21no—
91C2×C8×C43—21no—
92C2×C8×C43—21no—
93C2×C8×C43—22no—
94C2×C8×C43—21no—
95C2×C8×C43—21no—
96C2×C8×C43—41no—
97C2×C8×C43M1612yes—
98C42×C43C2×D411yescharacteristic
99C42×C43C2×D411yescharacteristic
100C42×C43C2×D411yescharacteristic
101C42×C43#4111yescharacteristic
102(C2×D43)⋊C4—41no—
103(C2×D43)⋊C4—41no—
104C4⋊Dic43—21no—
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107C4⋊Dic43C22⋊C412yes—
108Dic43⋊C4—22no—
109Dic43⋊C4—22no—
110C4×Dic43—22no—
111C4×Dic43—22no—
112C2×C43⋊C8—22no—
113C2×C43⋊C8—41no—
114#10621873—28no—
115C23×C43C4×D411yescharacteristic
116C22×D43—22no—
117C22×D43—41no—
118C22×D43—41no—
119C22×D43—81no—
120C22×D43—81no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43C2×C22⋊C411yescharacteristic
124C2×C4×C43C4×D411yescharacteristic
125C2×C4×C43#12011yescharacteristic
126C2×C4×C43#12111yescharacteristic
127C2×C4×C43#12111yescharacteristic
128C2×C4×C43#12311yescharacteristic
129C2×C4×C43C2×M1611yescharacteristic
130C2×C4×C43C2×M1611yescharacteristic
131C2×C4×C43#13111yescharacteristic
132C2×C4×C43#13111yescharacteristic
133C2×Dic43—22no—
134C2×Dic43—22no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—81no—
139C2×Dic43—81no—
140D172—22no—
141D172—22no—
142D172—41no—
143D172—41no—
144C4×D43—82no—
145C4×D43—82no—
146Dic86—22no—
147Dic86—22no—
148Dic86—41no—
149Dic86—41no—
150C8×C43—22no—
151C8×C43—42no—
152C8×C43—41no—
153C8×C43—81no—
154C43⋊C8—42no—
155C43⋊C8—81no—
156#9094—431nomaximal, Sylow
157C22×C43—21no—
158C22×C43—21no—
159C22×C43#38611yescharacteristic
160C22×C43#43511yescharacteristic
161C22×C43#43611yescharacteristic
162C2×D43—42no—
163C2×D43—82no—
164C2×D43—81no—
165C2×D43—81no—
166C2×D43—82no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43#40711yescharacteristic
172C4×C43#40811yescharacteristic
173C4×C43#43511yescharacteristic
174C4×C43#43611yescharacteristic
175Dic43—42no—
176Dic43—42no—
177Dic43—81no—
178#2983—431no—
179C2×#440—431no—
180#1479—431no—
181#1478—431no—
182#1460—431no—
183#1281D4311yescharacteristic, complemented
184#1275—431no—
185C2×C43—21no—
186C2×C43—21no—
187C2×C43#187011yescharacteristic
188C2×C43#190311yescharacteristic
189C2×C43#190511yescharacteristic
190D43—82no—
191C22×SD16—431no—
192C2×C4×Q8—431no—
193C2×C4×D4—431no—
194#446—862no—
195#446—862no—
196#440—862no—
197#440—862no—
198#432—862no—
199#431—431no—
200#431—431no—
201#431C2×D4311yescharacteristic
202#431C2×D4311yescharacteristic
203C2×#107—431no—
204C2×#103—431no—
205C2×#102—431no—
206C2×#97C2×D4311yescharacteristic
207Q8⋊C8—862no—
208D4⋊C8—862no—
209#323—862no—
210C43#909411yescharacteristic, complemented, Sylow
211C22×Q8—431no—
212C22×D4—431no—
213C23×C4—861no—
214C2×SD16—862no—
215C2×SD16—862no—
216C2×SD16—862no—
217C22×C8C4×D4311yescharacteristic
218C22×C8C4×D4311yescharacteristic
219C4×Q8—432no—
220C4×Q8—432no—
221C4×Q8—861no—
222C4×Q8—861no—
223C4×D4—861no—
224C4×D4—861no—
225C4×D4—861no—
226C4×D4—861no—
227C2×C4⋊C4—431no—
228C2×C4⋊C4—431no—
229C2×C4⋊C4—861no—
230C2×C22⋊C4—861no—
231C2×C42—861no—
232C2×C42C22×D4311yescharacteristic
233#107—862no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—864no—
237C4⋊C8—861no—
238C4⋊C8—861no—
239#103—862no—
240#102—862no—
241C22⋊C8—21no—
242C22⋊C8—861no—
243C22⋊C8—861no—
244C22⋊C8D17212yes—
245#97—21no—
246#97—21no—
247#97—864no—
248C4×C8—21no—
249C4×C8—21no—
250C4×C8—432no—
251C4×C8—861no—
252C24—861no—
253C2×Q8—432no—
254C2×Q8—861no—
255C2×Q8—861no—
256C2×Q8—861no—
257C2×Q8—861no—
258C2×Q8—861no—
259C2×D4—432no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—861no—
263C2×D4—861no—
264C2×D4—861no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—3442no—
269C22×C4—1721no—
270C22×C4—1721no—
271C22×C4C2×C4×D4311yescharacteristic
272C22×C4C2×D17211yescharacteristic
273C22×C4#1062189811yescharacteristic
274SD16—868no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—22no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—41no—
282C2×C8—862no—
283C2×C8—1721no—
284C2×C8#1062187212yes—
285C4⋊C4—432no—
286C4⋊C4—861no—
287C4⋊C4—862no—
288C4⋊C4—862no—
289C4⋊C4—861no—
290C4⋊C4—861no—
291C22⋊C4—1721no—
292C22⋊C4—1721no—
293C42—862no—
294C42—862no—
295C42D4×D4311yescharacteristic
296C42D4×D4311yescharacteristic
297C42D4×D4311yescharacteristic
298C42#1062190211yescharacteristic
299C23—862no—
300C23—3441no—
301C23—3441no—
302C23—1721no—
303C23—1721no—
304C23C4×D17211yescharacteristic
305Q8—862no—
306Q8—862no—
307Q8—1721no—
308Q8—1721no—
309D4—862no—
310D4—862no—
311D4—1721no—
312D4—1721no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—862no—
316C2×C4—862no—
317C2×C4—3442no—
318C2×C4—3442no—
319C2×C4—3441no—
320C2×C4—3441no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4C22⋊C4×D4311yescharacteristic
325C2×C4#1306328711yescharacteristic
326C2×C4#1306329511yescharacteristic
327C2×C4#1306329811yescharacteristic
328C2×C4#1306330011yescharacteristic
329C2×C4#1306331011yescharacteristic
330C2×C4M16×D4311yescharacteristic
331C2×C4C2×#1062187211yescharacteristic
332C2×C4#1306333111yescharacteristic
333C2×C4#1306333311yescharacteristic
334C8—22no—
335C8—42no—
336C8—41no—
337C8—81no—
338C8—3441no—
339C8—1722no—
340C22—21no—
341C22—21no—
342C22—3442no—
343C22—3442no—
344C22—3441no—
345C22—3441no—
346C22—1722no—
347C22#1458277711yescharacteristic
348C22#1458297211yescharacteristic
349C22#1458297811yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—3441no—
355C4—1722no—
356C4—1722no—
357C4#1458286111yescharacteristic
358C4#1458286411yescharacteristic
359C4#1458296911yescharacteristic
360C4#1458297611yescharacteristic
361C2—21no—
362C2—21no—
363C2—3442no—
364C2#1913489111yescharacteristic
365C2#1913507411yescharacteristic
366C2#1913508811yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1281C2
socleC22×C43#386
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#1281D43
hypocenterC43#9094
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1281

Complements

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

NH ≅ G/Ntype
1. #19143678C2semidirect
3. #19132991C2semidirect
6. #19132426C2semidirect
7. C43×#1281C2semidirect
183. #1281D43semidirect
210. C43#9094semidirect

Maximal subgroups

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

subgroupindex
#191436782
C2×#145830012
#191329912
#191329852
#191329152
#191324262
C43×#12812
#909443