Finite Group Databasebeta

← #24992563

Subgroups — #24992563

Order 11008.

530 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 99 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#19143636C211yesmaximal, characteristic
2#19140512C211yesmaximal, characteristic
3#19133114C212yesmaximal, complemented
4#19132448C212yesmaximal, complemented
5C4×#99×C43C211yesmaximal, characteristic
6C2×#13063304C2211yescharacteristic
7#14582977—24no—
8#14582952—21no—
9#14582863—21no—
10#14582863C2212yes—
11#14582829C411yescharacteristic, complemented
12#14582827—21no—
13#14582824C411yescharacteristic, complemented
14#14582819C411yescharacteristic, complemented
15#14582813—21no—
16#14582811C411yescharacteristic, complemented
17#14582783—21no—
18#14582772—21no—
19#14582762C2211yescharacteristic
20#14582635—24no—
21C2×C4×D4×C43C2211yescharacteristic
22C2×#99×C43—21no—
23C4×C22⋊C4×C43C2212yes—
24C43×#342—21no—
25C22×Dic86C2×C411yescharacteristic
26C2×#10621877—22no—
27C2×#10621877—22no—
28#13063304—22no—
29#13063304—22no—
30C2×C4⋊Dic43C2×C411yescharacteristic
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×Dic43⋊C4—21no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37C2×C22⋊Dic43—21no—
38C4⋊(C43⋊C8)—22no—
39C22⋊(C43⋊C8)—22no—
40C22⋊(C43⋊C8)—22no—
41C22⋊(C43⋊C8)D414yes—
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×D4×C43D411yescharacteristic
51C23×C4×C43D411yescharacteristic
52C23×C4×C43C2311yescharacteristic
53C4×D4×C43—22no—
54C4×D4×C43—22no—
55C2×C4⋊C4×C43C2×C411yescharacteristic
56C2×C22⋊C4×C43—22no—
57C2×C22⋊C4×C43C2×C411yescharacteristic
58C2×C22⋊C4×C43D411yescharacteristic
59C2×C42×C43—22no—
60C2×C42×C43D411yescharacteristic
61#99×C43—24no—
62#95×C43—22no—
63C24×C43C22⋊C411yescharacteristic
64C24×C43C2×D411yescharacteristic
65C2×D4×C43—22no—
66C2×D4×C43—22no—
67C2×D4×C43—41no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—42no—
71C22×C4×C43—81no—
72C22×C4×C43—81no—
73C22×C4×C43C22⋊C411yescharacteristic
74C22×C4×C43C22⋊C411yescharacteristic
75C22×C4×C43C22⋊C411yescharacteristic
76C22×C4×C43C22×C411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D412yes—
79C22×C4×C43#4112yes—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C22×Dic43—21no—
83C22×Dic43—21no—
84C2×Dic86—22no—
85C2×Dic86—81no—
86C4⋊C4×C43—22no—
87C22⋊C4×C43—22no—
88C22⋊C4×C43—24no—
89C22⋊C4×C43—22no—
90C22⋊C4×C43—42no—
91C42×C43—21no—
92C42×C43—21no—
93C42×C43—82no—
94C22⋊Dic43—42no—
95C22⋊Dic43—42no—
96C22⋊Dic43—81no—
97C22⋊Dic43—81no—
98C4⋊Dic43—22no—
99Dic43⋊C4—42no—
100Dic43⋊C4—41no—
101Dic43⋊C4—41no—
102Dic43⋊C4—81no—
103#10621877—82no—
104#10621877—82no—
105C2×C43⋊C8—24no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43C2×C22⋊C411yescharacteristic
116C23×C43#12112yes—
117D4×C43—44no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—42no—
123C2×C4×C43—42no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—42no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—44no—
130C2×C4×C43—81no—
131C2×C4×C43—82no—
132C2×C4×C43—82no—
133C2×C4×C43#10412yes—
134C2×C4×C43C4×D412yes—
135C2×C4×C43#12011yescharacteristic
136C2×C4×C43#12311yescharacteristic
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149Dic86—82no—
150C43⋊C8—44no—
151#9184—431nomaximal, Sylow
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—22no—
155C22×C43—22no—
156C22×C43—22no—
157C22×C43—42no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—81no—
162C22×C43—81no—
163C22×C43—81no—
164C22×C43#38611yescharacteristic
165C22×C43C2×#10411yescharacteristic
166C22×C43#42111yescharacteristic
167C4×C43—22no—
168C4×C43—21no—
169C4×C43—22no—
170C4×C43—21no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43—84no—
174Dic43—81no—
175Dic43—81no—
176Dic43—81no—
177Dic43—81no—
178#2975—431no—
179#2638—431no—
180C4×#99D4311yescharacteristic
181#1508—432no—
182#1284—432no—
183C2×C43—21no—
184C2×C43—21no—
185C2×C43—42no—
186C2×C43—81no—
187C2×C43#187111yescharacteristic
188C2×C43#190911yescharacteristic
189C2×C43#191311yescharacteristic
190C2×C22⋊Q8—431no—
191C2×C4×D4C2×D4311yescharacteristic
192#436—864no—
193#431—861no—
194C2×#99—21no—
195#407—432no—
196#407—861no—
197#398—431no—
198#397—431no—
199#397—861no—
200#395—431no—
201#394—861no—
202#393—431no—
203#387—861no—
204#385—861no—
205#381—431no—
206C4×C22⋊C4C2×D4312yes—
207#342—21no—
208#328—864no—
209C43#918411yescharacteristic, complemented, Sylow
210C22×Q8—431no—
211C22×D4C22⋊D4311yescharacteristic
212C23×C4D17211yescharacteristic
213C23×C4C22×D4311yescharacteristic
214C2×M16—862no—
215C2×M16—862no—
216C22⋊Q8—862no—
217C22⋊Q8—862no—
218C4×D4—22no—
219C4×D4—22no—
220C2×C4⋊C4—431no—
221C2×C4⋊C4—861no—
222C2×C4⋊C4—861no—
223C2×C4⋊C4—861no—
224C2×C4⋊C4C4×D4311yescharacteristic
225C2×C22⋊C4—22no—
226C2×C22⋊C4—861no—
227C2×C22⋊C4—861no—
228C2×C22⋊C4—861no—
229C2×C22⋊C4—861no—
230C2×C22⋊C4C4×D4311yescharacteristic
231C2×C22⋊C4C22⋊D4311yescharacteristic
232C2×C42—22no—
233C2×C42D17211yescharacteristic
234C4⋊C8—862no—
235#99—24no—
236C22⋊C8—434no—
237C22⋊C8—862no—
238C22⋊C8—862no—
239C4×C8—862no—
240#95—22no—
241#95—431no—
242#95—431no—
243#95—861no—
244#95—861no—
245#95—861no—
246#95—861no—
247#95—861no—
248C24(C2×D43)⋊C411yescharacteristic
249C24C2×C22⋊D4311yescharacteristic
250C2×Q8—862no—
251C2×Q8—3441no—
252C2×D4—22no—
253C2×D4—22no—
254C2×D4—41no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—42no—
258C22×C4—81no—
259C22×C4—81no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4(C2×D43)⋊C411yescharacteristic
265C22×C4(C2×D43)⋊C411yescharacteristic
266C22×C4(C2×D43)⋊C411yescharacteristic
267C22×C4C2×C4×D4311yescharacteristic
268C22×C4C2×D17211yescharacteristic
269C22×C4D4×D4312yes—
270C22×C4#1062190012yes—
271M16—3442no—
272M16—3442no—
273C2×C8—864no—
274C4⋊C4—22no—
275C4⋊C4—862no—
276C4⋊C4—3441no—
277C4⋊C4—1722no—
278C4⋊C4—1721no—
279C4⋊C4—1721no—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C22⋊C4—24no—
283C22⋊C4—42no—
284C22⋊C4—3441no—
285C22⋊C4—3441no—
286C22⋊C4—1722no—
287C22⋊C4—1722no—
288C42—21no—
289C42—21no—
290C42—82no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23C2×(C2×D43)⋊C411yescharacteristic
301C23#1306329712yes—
302Q8—3442no—
303D4—44no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—44no—
316C2×C4—81no—
317C2×C4—82no—
318C2×C4—82no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4—1721no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4#1306325312yes—
332C2×C4(C22⋊D43)⋊C412yes—
333C2×C4#1306329511yescharacteristic
334C2×C4#1306330911yescharacteristic
335C8—1724no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—42no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22#1458277611yescharacteristic
349C22C2×#1306325311yescharacteristic
350C22#1458291711yescharacteristic
351C4—21no—
352C4—21no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—84no—
358C4—3441no—
359C4—3441no—
360C4—3441no—
361C4—3441no—
362C2—21no—
363C2—21no—
364C2—42no—
365C2—81no—
366C2#1913489511yescharacteristic
367C2#1913511511yescharacteristic
368C2#1913513511yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC4×#99×C43C2
socleC22×C43#386
prime radicalC22×D4×C43D4
cosocleC23×C4×C43C23
hypercenterC4×#99D43
hypocenterC43#9184
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. #19133114C2semidirect
4. #19132448C2semidirect
11. #14582829C4semidirect
13. #14582824C4semidirect
14. #14582819C4semidirect
16. #14582811C4semidirect
209. C43#9184semidirect

Maximal subgroups

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

subgroupindex
#191436362
#191405122
#191331142
#191324482
C4×#99×C432
#918443