Finite Group Databasebeta

← #24992668

Subgroups — #24992668

Order 11008.

690 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 111 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#19140329C211yesmaximal, characteristic
2#19137193C211yesmaximal, characteristic, complemented
3#19133164C212yesmaximal, complemented
4#19132463C212yesmaximal, complemented
5C2×C43×#323C211yesmaximal, characteristic, complemented
6C2×#13063299C2211yescharacteristic
7C2×#13063294—21no—
8#14582824C412yescomplemented
9#14582815—22no—
10#14582808C412yescomplemented
11#14582792—24no—
12#14582778—21no—
13#14582759C2211yescharacteristic
14#14582759C2212yes—
15#14582755—21no—
16C4×C22⋊Dic43—21no—
17#14582634—24no—
18C22×C22⋊C4×C43C2211yescharacteristic
19C2×C22⋊C8×C43C2212yes—
20C43×#323—22no—
21C22×D172C2×C411yescharacteristic
22C22×C22⋊D43—21no—
23C22×C22⋊D43—22no—
24#13063299—22no—
25#13063299—22no—
26#13063294—44no—
27C2×C4⋊Dic43—22no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43C2×C411yescharacteristic
30C2×C22⋊Dic43—22no—
31C2×C22⋊Dic43—21no—
32C2×C22⋊Dic43—22no—
33C2×C22⋊Dic43—22no—
34C2×C22⋊Dic43—22no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—22no—
37C2×C4×Dic43—22no—
38C43⋊#95—22no—
39C43⋊#95—22no—
40C43⋊#95C2×C412yes—
41C43⋊#95D414yescomplemented
42C25×C43D411yescharacteristic
43C23×C4×C43D411yescharacteristic
44C23×C4×C43C2311yescharacteristic
45C22×C8×C43—22no—
46C2×C22⋊C4×C43—22no—
47C2×C22⋊C4×C43—22no—
48C2×C22⋊C4×C43C2×C412yes—
49C2×C22⋊C4×C43D412yes—
50C22⋊C8×C43—22no—
51C22⋊C8×C43—22no—
52C24×C43—21no—
53C24×C43—21no—
54C24×C43—22no—
55C24×C43—22no—
56C24×C43—81no—
57C24×C43—81no—
58C24×C43C22⋊C412yes—
59C24×C43C2×D411yescharacteristic
60C23×D43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—81no—
64C22×C4×C43—81no—
65C22×C4×C43C22⋊C412yes—
66C22×C4×C43C22×C411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D412yes—
69C22×C4×C43#4112yes—
70C2×C22⋊D43—44no—
71C2×C22⋊D43—41no—
72C2×C22⋊D43—41no—
73C2×C22⋊D43—42no—
74C2×C22⋊D43—42no—
75C2×C22⋊D43—82no—
76C2×C22⋊D43—82no—
77C22×Dic43—21no—
78C22×Dic43—22no—
79C22×Dic43—24no—
80C2×D172—22no—
81C2×D172—81no—
82C2×C8×C43—42no—
83C2×C8×C43—82no—
84C22⋊C4×C43—24no—
85C22⋊C4×C43—24no—
86C22⋊Dic43—44no—
87C22⋊Dic43—42no—
88C22⋊Dic43—42no—
89C22⋊Dic43—42no—
90C22⋊Dic43—82no—
91C22⋊Dic43—82no—
92(C2×D43)⋊C4—42no—
93(C2×D43)⋊C4—82no—
94C4⋊Dic43—22no—
95C4⋊Dic43—82no—
96C4⋊Dic43—81no—
97C4×Dic43—82no—
98C23×C43—22no—
99C23×C43—22no—
100C23×C43—22no—
101C23×C43—41no—
102C23×C43—41no—
103C23×C43—42no—
104C23×C43—42no—
105C23×C43—42no—
106C23×C43—42no—
107C23×C43—42no—
108C23×C43—42no—
109C23×C43—81no—
110C23×C43—81no—
111C23×C43—84no—
112C23×C43—84no—
113C23×C43C2×C22⋊C411yescharacteristic
114C23×C43#12011yescharacteristic
115C23×C43#12311yescharacteristic
116C23×C43#13512yes—
117C23×C43AGL(1,ℤ/8)12yes—
118C22×D43—42no—
119C22×D43—42no—
120C22×D43—41no—
121C22×D43—41no—
122C22×D43—41no—
123C2×C4×C43—22no—
124C2×C4×C43—42no—
125C2×C4×C43—41no—
126C2×C4×C43—42no—
127C2×C4×C43—41no—
128C2×C4×C43—42no—
129C2×C4×C43—42no—
130C2×C4×C43—81no—
131C2×C4×C43C4×D412yes—
132C2×C4×C43#12112yes—
133C22⋊D43—88no—
134C22⋊D43—82no—
135C22⋊D43—82no—
136C2×Dic43—44no—
137C2×Dic43—44no—
138C2×Dic43—42no—
139C2×Dic43—42no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—42no—
143C2×Dic43—41no—
144C2×Dic43—44no—
145D172—82no—
146C8×C43—82no—
147#9205—431nomaximal, Sylow
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—42no—
155C22×C43—42no—
156C22×C43—44no—
157C22×C43—42no—
158C22×C43—42no—
159C22×C43—42no—
160C22×C43—82no—
161C22×C43—84no—
162C22×C43—84no—
163C22×C43#38611yescharacteristic
164C22×C43#41611yescharacteristic
165C22×C43#41811yescharacteristic
166C22×C43#44912yes—
167C22×C43#48212yes—
168C2×D43—82no—
169C2×D43—82no—
170C2×D43—81no—
171C2×D43—81no—
172C2×D43—81no—
173C4×C43—22no—
174C4×C43—22no—
175C4×C43—42no—
176Dic43—84no—
177Dic43—82no—
178Dic43—81no—
179#2617—431no—
180#2312—431no—
181#1519—432no—
182C2×#323D4311yescharacteristic, complemented
183#1289—432no—
184C2×C43—21no—
185C2×C43—22no—
186C2×C43—21no—
187C2×C43—22no—
188C2×C43—82no—
189C2×C43#187511yescharacteristic
190C2×C43#191111yescharacteristic
191C2×C43#191311yescharacteristic
192D43—161no—
193C2×#121—431no—
194C2×#120—861no—
195C22×C22⋊C4C2×D4311yescharacteristic
196C2×C22⋊C8C2×D4312yes—
197#397—432no—
198#394—862no—
199#392—432no—
200#388—864no—
201#386—861no—
202#380—432no—
203#380—431no—
204#379—861no—
205C4×C22⋊C4—861no—
206#327—864no—
207#323—22no—
208C43#920511yescharacteristic, complemented, Sylow
209C25D17211yescharacteristic
210C22×D4—431no—
211C22×D4—862no—
212C22×D4—861no—
213C23×C4D17211yescharacteristic
214C23×C4C22×D4311yescharacteristic
215C22×C8—22no—
216#121—862no—
217#121—862no—
218#120—1724no—
219C2×C4⋊C4—431no—
220C2×C4⋊C4—862no—
221C2×C4⋊C4—861no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—862no—
225C2×C22⋊C4—862no—
226C2×C22⋊C4—862no—
227C2×C22⋊C4—862no—
228C2×C22⋊C4—861no—
229C2×C22⋊C4—862no—
230C2×C22⋊C4—861no—
231C2×C22⋊C4C4×D4312yes—
232C2×C22⋊C4C22⋊D4312yes—
233C2×C42—862no—
234C22⋊C8—22no—
235C22⋊C8—22no—
236#95—432no—
237#95—434no—
238#95—862no—
239#95—862no—
240C24—21no—
241C24—21no—
242C24—22no—
243C24—22no—
244C24—81no—
245C24—81no—
246C24—861no—
247C24(C2×D43)⋊C412yes—
248C24C2×D17211yescharacteristic
249C2×D4—862no—
250C2×D4—3441no—
251C2×D4—3442no—
252C2×D4—3442no—
253C2×D4—1724no—
254C2×D4—1721no—
255C2×D4—1721no—
256C2×D4—1722no—
257C2×D4—1722no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—81no—
261C22×C4—81no—
262C22×C4—862no—
263C22×C4—861no—
264C22×C4—864no—
265C22×C4(C2×D43)⋊C412yes—
266C22×C4C2×C4×D4311yescharacteristic
267C22×C4D4×D4312yes—
268C22×C4#1062190012yes—
269C22×C4C2×C22⋊D4311yescharacteristic
270C2×C8—42no—
271C2×C8—82no—
272C4⋊C4—862no—
273C4⋊C4—3442no—
274C4⋊C4—3441no—
275C22⋊C4—24no—
276C22⋊C4—24no—
277C22⋊C4—3442no—
278C22⋊C4—3442no—
279C22⋊C4—3442no—
280C22⋊C4—1724no—
281C22⋊C4—1722no—
282C22⋊C4—1722no—
283C22⋊C4—1722no—
284C22⋊C4—1722no—
285C42—3442no—
286C23—22no—
287C23—22no—
288C23—22no—
289C23—41no—
290C23—41no—
291C23—42no—
292C23—42no—
293C23—42no—
294C23—42no—
295C23—42no—
296C23—42no—
297C23—81no—
298C23—81no—
299C23—84no—
300C23—84no—
301C23—1722no—
302C23—1722no—
303C23—1721no—
304C23—1721no—
305C23—1721no—
306C23C2×(C2×D43)⋊C411yescharacteristic
307C23#1306329511yescharacteristic
308C23#1306330911yescharacteristic
309C23#1306334712yes—
310C23#1306335312yes—
311D4—3442no—
312D4—3448no—
313D4—3442no—
314D4—3442no—
315C2×C4—22no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—81no—
323C2×C4—1724no—
324C2×C4—1724no—
325C2×C4—1722no—
326C2×C4—1722no—
327C2×C4—1724no—
328C2×C4—1721no—
329C2×C4—1722no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4(C22⋊D43)⋊C412yes—
333C2×C4#1306329712yes—
334C8—82no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—42no—
342C22—42no—
343C22—44no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22—82no—
348C22—84no—
349C22—84no—
350C22—3442no—
351C22—3442no—
352C22—3441no—
353C22—3441no—
354C22—3441no—
355C22#1458277611yescharacteristic
356C22#1458289611yescharacteristic
357C22#1458290511yescharacteristic
358C22#1458304612yes—
359C22#1458322412yes—
360C4—22no—
361C4—22no—
362C4—42no—
363C4—3442no—
364C4—3444no—
365C4—3441no—
366C2—21no—
367C2—22no—
368C2—21no—
369C2—22no—
370C2—82no—
371C2—6881no—
372C2#1913491511yescharacteristic
373C2#1913512511yescharacteristic
374C2#1913513511yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#323C2
socleC22×C43#386
prime radical#19140329C2
cosocleC23×C4×C43C23
hypercenterC2×#323D43
hypocenterC43#9205
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. #19137193C2semidirect
3. #19133164C2semidirect
4. #19132463C2semidirect
5. C2×C43×#323C2semidirect
8. #14582824C4semidirect
10. #14582808C4semidirect
41. C43⋊#95D4semidirect
182. C2×#323D43semidirect
208. C43#9205semidirect

Maximal subgroups

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

subgroupindex
#191403292
#191371932
#191331642
#191324632
C2×C43×#3232
#920543