Finite Group Databasebeta

← #24991679

Subgroups — #24991679

Order 11008.

516 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143680C211yesmaximal, characteristic, complemented
2#19137878C211yesmaximal, characteristic
3#19133039C212yesmaximal
4#19132489C212yesmaximal, complemented
5C4×#101×C43C211yesmaximal, characteristic, complemented
6C2×C4×D172C2211yescharacteristic
7#14583030—24no—
8#14582956—21no—
9#14582956C2212yes—
10#14582952—21no—
11#14582838C411yescharacteristic
12#14582838C411yescharacteristic
13#14582825—21no—
14#14582816C411yescharacteristic
15#14582816C411yescharacteristic
16#14582810—21no—
17C4×(C2×D43)⋊C4—21no—
18C4×(C2×D43)⋊C4—21no—
19#14582745C2211yescharacteristic
20#14582628—24no—
21C2×C4×Q8×C43C2211yescharacteristic
22C2×#101×C43—21no—
23C4×M16×C43C2212yes—
24C43×#343—21no—
25C22×D172C2×C411yescharacteristic
26C22×C4×D43—21no—
27C4×D172—22no—
28C4×D172—22no—
29C2×C4⋊Dic43C2×C411yescharacteristic
30C2×(C2×D43)⋊C4—21no—
31C2×(C2×D43)⋊C4—21no—
32C2×(C2×D43)⋊C4—21no—
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×C4×Dic43—21no—
36C4⋊(C43⋊C8)—22no—
37C4⋊(C43⋊C8)—22no—
38C4⋊(C43⋊C8)D414yes—
39C22⋊(C43⋊C8)—22no—
40#13063236—22no—
41#13063236—22no—
42C4×C43⋊C8—22no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95C2×C411yescharacteristic
49C43⋊#95C2×C411yescharacteristic
50C22×Q8×C43D411yescharacteristic
51C2×M16×C43—22no—
52C4×Q8×C43—22no—
53C4×Q8×C43—22no—
54C2×C4⋊C4×C43C2×C411yescharacteristic
55C2×C4⋊C4×C43C2×C411yescharacteristic
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C42×C43D411yescharacteristic
58C2×C42×C43D411yescharacteristic
59C2×C42×C43C2311yescharacteristic
60#101×C43—24no—
61#97×C43—22no—
62C4×C8×C43—22no—
63C23×D43—21no—
64C2×Q8×C43—22no—
65C2×Q8×C43—22no—
66C2×Q8×C43—41no—
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C2×D172—22no—
78C2×D172—42no—
79C2×C4×D43—42no—
80C2×C4×D43—42no—
81C2×C4×D43—41no—
82C2×C4×D43—41no—
83M16×C43—24no—
84M16×C43—42no—
85C2×C8×C43—42no—
86C4⋊C4×C43—22no—
87C4⋊C4×C43—22no—
88C4⋊C4×C43—22no—
89C42×C43—21no—
90C42×C43—21no—
91C42×C43—21no—
92C42×C43—21no—
93C42×C43C2×D412yes—
94C42×C43#4112yes—
95(C2×D43)⋊C4—42no—
96(C2×D43)⋊C4—42no—
97(C2×D43)⋊C4—42no—
98(C2×D43)⋊C4—42no—
99(C2×D43)⋊C4—42no—
100C4⋊Dic43—22no—
101C4×Dic43—42no—
102C2×C43⋊C8—24no—
103C23×C43C2×C22⋊C411yescharacteristic
104C22×D43—22no—
105C22×D43—41no—
106C22×D43—41no—
107C22×D43—41no—
108C22×D43—41no—
109C22×D43—41no—
110C22×D43—41no—
111Q8×C43—44no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—22no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43#10412yes—
126C2×C4×C43C4×D412yes—
127C2×C4×C43#12011yescharacteristic
128C2×C4×C43#12112yes—
129C2×C4×C43#12311yescharacteristic
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139D172—24no—
140D172—42no—
141C4×D43—82no—
142C4×D43—82no—
143C8×C43—44no—
144C43⋊C8—44no—
145#9032—431nomaximal, Sylow
146C22×C43—21no—
147C22×C43—21no—
148C22×C43#38611yescharacteristic
149C22×C43C2×#10411yescharacteristic
150C22×C43#42111yescharacteristic
151C2×D43—42no—
152C2×D43—42no—
153C2×D43—42no—
154C2×D43—81no—
155C2×D43—81no—
156C2×D43—81no—
157C2×D43—81no—
158C4×C43—22no—
159C4×C43—22no—
160C4×C43—21no—
161C4×C43—22no—
162C4×C43—41no—
163C4×C43—41no—
164C4×C43—41no—
165C4×C43#45412yes—
166Dic43—81no—
167Dic43—81no—
168Dic43—81no—
169#2983—431no—
170#2398—431no—
171C4×#101D4311yescharacteristic, complemented
172#1490—432no—
173#1300—432no—
174C2×C43—21no—
175C2×C43—21no—
176C2×C43#187111yescharacteristic
177C2×C43#188811yescharacteristic
178C2×C43#189111yescharacteristic
179D43—82no—
180C2×C4×Q8C2×D4311yescharacteristic
181C2×C4×D4—431no—
182#446—864no—
183#432—432no—
184#432—861no—
185#431—861no—
186C2×#101—21no—
187C4×M16C2×D4312yes—
188#400—431no—
189#400—431no—
190#397—861no—
191#394—431no—
192#394—431no—
193#393—861no—
194C4×C22⋊C4—861no—
195C4×C22⋊C4—861no—
196#376—431no—
197#343—21no—
198D4⋊C8—864no—
199C43#903211yescharacteristic, complemented, Sylow
200C22×Q8C22⋊D4311yescharacteristic
201C22×D4—431no—
202C23×C4—861no—
203C2×M16—22no—
204C4×Q8—22no—
205C4×Q8—22no—
206C4×D4—862no—
207C4×D4—862no—
208C2×C4⋊C4—431no—
209C2×C4⋊C4C4×D4311yescharacteristic
210C2×C4⋊C4C4×D4311yescharacteristic
211C2×C4⋊C4C22⋊D4311yescharacteristic
212C2×C22⋊C4—861no—
213C2×C22⋊C4—861no—
214C2×C22⋊C4—861no—
215C2×C22⋊C4—861no—
216C2×C22⋊C4—861no—
217C2×C42—861no—
218C2×C42D17211yescharacteristic
219C2×C42D17211yescharacteristic
220C2×C42C22×D4311yescharacteristic
221C4⋊C8—434no—
222C4⋊C8—862no—
223C4⋊C8—862no—
224#101—24no—
225C22⋊C8—862no—
226#97—22no—
227#97—862no—
228#97—862no—
229C4×C8—22no—
230C4×C8—862no—
231#95—431no—
232#95—431no—
233#95—861no—
234#95—861no—
235#95—861no—
236#95—861no—
237#95—861no—
238C24—861no—
239C2×Q8—22no—
240C2×Q8—22no—
241C2×Q8—41no—
242C2×D4—862no—
243C2×D4—1722no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4—861no—
247C22×C4—1722no—
248C22×C4—1722no—
249C22×C4—1721no—
250C22×C4—1721no—
251C22×C4(C2×D43)⋊C411yescharacteristic
252C22×C4(C2×D43)⋊C411yescharacteristic
253C22×C4(C2×D43)⋊C411yescharacteristic
254C22×C4(C2×D43)⋊C411yescharacteristic
255C22×C4C2×C4×D4311yescharacteristic
256C22×C4C2×D17211yescharacteristic
257C22×C4C2×C22⋊D4311yescharacteristic
258M16—24no—
259M16—42no—
260C2×C8—42no—
261C2×C8—864no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—862no—
266C22⋊C4—1722no—
267C22⋊C4—1722no—
268C22⋊C4—1722no—
269C22⋊C4—1722no—
270C22⋊C4—1722no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42—1722no—
276C42D4×D4312yes—
277C42#1062190012yes—
278C23—862no—
279C23—1721no—
280C23—1721no—
281C23—1721no—
282C23—1721no—
283C23—1721no—
284C23—1721no—
285C23C2×(C2×D43)⋊C411yescharacteristic
286Q8—44no—
287D4—864no—
288D4—1722no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—3442no—
303C2×C4—3442no—
304C2×C4—1721no—
305C2×C4—1721no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4#1306325312yes—
314C2×C4(C22⋊D43)⋊C412yes—
315C2×C4#1306329511yescharacteristic
316C2×C4#1306329712yes—
317C2×C4#1306330911yescharacteristic
318C8—44no—
319C8—1724no—
320C22—21no—
321C22—21no—
322C22—3441no—
323C22—3441no—
324C22—3441no—
325C22—3441no—
326C22—1722no—
327C22—1722no—
328C22—1722no—
329C22#1458277611yescharacteristic
330C22C2×#1306325311yescharacteristic
331C22#1458291711yescharacteristic
332C4—21no—
333C4—22no—
334C4—22no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—3441no—
340C4—3441no—
341C4—3441no—
342C4#1458307412yes—
343C2—21no—
344C2—21no—
345C2—3442no—
346C2#1913489511yescharacteristic
347C2#1913499611yescharacteristic
348C2#1913501111yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC4×#101×C43C2
socleC22×C43#386
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenterC4×#101D43
hypocenterC43#9032
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
1. #19143680C2semidirect
4. #19132489C2semidirect
5. C4×#101×C43C2semidirect
171. C4×#101D43semidirect
199. C43#9032semidirect

Maximal subgroups

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

subgroupindex
#191436802
#191378782
#191330392
#191324892
C4×#101×C432
#903243