Finite Group Databasebeta

← #24992665

Subgroups — #24992665

Order 11008.

622 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 131 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#19140337C211yesmaximal, characteristic
2#19133162C212yesmaximal
3C2×#14582625C211yesmaximal, characteristic, complemented
4#19132462C212yesmaximal, complemented
5C43×#2316C211yesmaximal, characteristic, complemented
6C2×#13063308—21no—
7C2×#13063299C2211yescharacteristic
8C2×C22⋊(C43⋊C8)C2212yes—
9#14582829C412yescomplemented
10#14582821—22no—
11#14582816C412yescomplemented
12#14582778—21no—
13#14582759C2211yescharacteristic
14#14582632—24no—
15#14582625—22no—
16C2×#117×C43—21no—
17C22×C4⋊C4×C43C2211yescharacteristic
18C43×#389—24no—
19C43×#380—21no—
20C43×#380C2212yes—
21C22×D172C2×C411yescharacteristic
22C22×C22⋊D43—21no—
23C22×C43⋊C8—22no—
24#13063308—42no—
25#13063308—42no—
26#13063299—22no—
27#13063299—22no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43C2×C411yescharacteristic
30C2×Dic43⋊C4—22no—
31C2×C22⋊Dic43—21no—
32C2×(C2×D43)⋊C4—22no—
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—22no—
35C22⋊(C43⋊C8)—22no—
36C22⋊(C43⋊C8)—22no—
37C43⋊#95—22no—
38C43⋊#95C2×C412yes—
39C23×C4×C43D411yescharacteristic
40C23×C4×C43D411yescharacteristic
41C23×C4×C43C2311yescharacteristic
42#117×C43—42no—
43#117×C43—42no—
44C2×C4⋊C4×C43—22no—
45C2×C4⋊C4×C43—22no—
46C2×C4⋊C4×C43—22no—
47C2×C4⋊C4×C43—22no—
48C2×C4⋊C4×C43—22no—
49C2×C4⋊C4×C43C2×C412yes—
50C2×C4⋊C4×C43D412yes—
51C2×C22⋊C4×C43—22no—
52C2×C42×C43—22no—
53#95×C43—22no—
54#95×C43D414yes—
55C24×C43C2×D411yescharacteristic
56C23×D43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—24no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—81no—
65C22×C4×C43—81no—
66C22×C4×C43C22⋊C412yes—
67C22×C4×C43C22⋊C412yes—
68C22×C4×C43D812yes—
69C22×C4×C43SD1612yes—
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D412yes—
73C22×C4×C43#4112yes—
74C2×C22⋊D43—41no—
75C2×C22⋊D43—41no—
76C2×C22⋊D43—41no—
77C2×C22⋊D43—41no—
78C2×C22⋊D43—41no—
79C2×C22⋊D43—41no—
80C22×Dic43—21no—
81C22×Dic43—22no—
82C2×D172—22no—
83C2×D172—81no—
84C4⋊C4×C43—24no—
85C4⋊C4×C43—24no—
86C4⋊C4×C43—44no—
87C4⋊C4×C43—82no—
88C4⋊C4×C43—82no—
89C22⋊C4×C43—42no—
90C22⋊C4×C43—42no—
91C42×C43—44no—
92C22⋊Dic43—41no—
93C22⋊Dic43—41no—
94(C2×D43)⋊C4—44no—
95(C2×D43)⋊C4—42no—
96(C2×D43)⋊C4—82no—
97C4⋊Dic43—22no—
98C4⋊Dic43—81no—
99Dic43⋊C4—44no—
100C2×C43⋊C8—42no—
101C2×C43⋊C8—82no—
102C23×C43—41no—
103C23×C43—41no—
104C23×C43C2×C22⋊C411yescharacteristic
105C23×C43#12011yescharacteristic
106C23×C43#12311yescharacteristic
107C23×C43C2×D811yescharacteristic
108C23×C43C2×SD1611yescharacteristic
109C23×C43AGL(1,ℤ/8)11yescharacteristic
110C23×C43#13711yescharacteristic
111C22×D43—42no—
112C22×D43—42no—
113C22×D43—41no—
114C22×D43—41no—
115C22×D43—41no—
116C2×C4×C43—22no—
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—22no—
121C2×C4×C43—22no—
122C2×C4×C43—22no—
123C2×C4×C43—42no—
124C2×C4×C43—41no—
125C2×C4×C43—42no—
126C2×C4×C43—41no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43—44no—
130C2×C4×C43—44no—
131C2×C4×C43—44no—
132C2×C4×C43—81no—
133C2×C4×C43#10214yes—
134C2×C4×C43C4×D412yes—
135C2×C4×C43#12112yes—
136C22⋊D43—81no—
137C22⋊D43—81no—
138C22⋊D43—81no—
139C22⋊D43—81no—
140C2×Dic43—42no—
141C2×Dic43—42no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—42no—
145C2×Dic43—41no—
146D172—82no—
147C43⋊C8—82no—
148#9204—431nomaximal, Sylow
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43#38611yescharacteristic
160C22×C43C2×#10211yescharacteristic
161C22×C43#41711yescharacteristic
162C22×C43#44711yescharacteristic
163C22×C43#44811yescharacteristic
164C22×C43#48011yescharacteristic
165C22×C43#48111yescharacteristic
166C2×D43—82no—
167C2×D43—82no—
168C2×D43—81no—
169C2×D43—81no—
170C2×D43—81no—
171C4×C43—24no—
172C4×C43—22no—
173C4×C43—22no—
174C4×C43—42no—
175C4×C43—84no—
176Dic43—82no—
177Dic43—81no—
178#2618—431no—
179#2316D4311yescharacteristic, complemented
180#1519—432no—
181C2×#324—431no—
182#1289—432no—
183C2×C43—21no—
184C2×C43—21no—
185C2×C43—21no—
186C2×C43—21no—
187C2×C43—21no—
188C2×C43—21no—
189C2×C43#187411yescharacteristic
190C2×C43#191211yescharacteristic
191C2×C43#191311yescharacteristic
192D43—161no—
193C2×#123—861no—
194C2×#121—431no—
195C2×#117—21no—
196C22×C4⋊C4C2×D4311yescharacteristic
197C2×C22⋊C8—432no—
198#398—432no—
199#396—862no—
200#394—432no—
201#389—24no—
202#386—861no—
203#380—21no—
204#380—431no—
205#380C2×D4312yes—
206#327—864no—
207#324—862no—
208C43#920411yescharacteristic, complemented, Sylow
209C22×D4—431no—
210C22×D4—861no—
211C23×C4C22⋊D4311yescharacteristic
212C23×C4C22⋊D4311yescharacteristic
213C23×C4C22×D4311yescharacteristic
214C22×C8—862no—
215#123—1722no—
216#123—1722no—
217#121—862no—
218#121—862no—
219#117—42no—
220#117—42no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—431no—
227C2×C4⋊C4—861no—
228C2×C4⋊C4—862no—
229C2×C4⋊C4C4×D4312yes—
230C2×C4⋊C4D17212yes—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—862no—
233C2×C22⋊C4—861no—
234C2×C22⋊C4—862no—
235C2×C22⋊C4—861no—
236C2×C42—22no—
237C22⋊C8—862no—
238C22⋊C8—862no—
239#95—22no—
240#95—432no—
241#95—862no—
242#95C22⋊D4314yes—
243C24—861no—
244C24C2×C22⋊D4311yescharacteristic
245C2×D4—862no—
246C2×D4—3441no—
247C2×D4—1721no—
248C2×D4—1721no—
249C2×D4—1721no—
250C2×D4—1721no—
251C2×D4—1721no—
252C2×D4—1721no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—24no—
260C22×C4—81no—
261C22×C4—81no—
262C22×C4—862no—
263C22×C4—861no—
264C22×C4(C2×D43)⋊C412yes—
265C22×C4(C2×D43)⋊C412yes—
266C22×C4#1062188212yes—
267C22×C4#1062188412yes—
268C22×C4C2×C4×D4311yescharacteristic
269C22×C4C2×D17211yescharacteristic
270C22×C4#1062189812yes—
271C22×C4C2×C22⋊D4312yes—
272C2×C8—3442no—
273C2×C8—1722no—
274C4⋊C4—24no—
275C4⋊C4—24no—
276C4⋊C4—44no—
277C4⋊C4—82no—
278C4⋊C4—82no—
279C4⋊C4—862no—
280C4⋊C4—3441no—
281C4⋊C4—1724no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—3442no—
285C22⋊C4—1721no—
286C22⋊C4—1721no—
287C22⋊C4—1724no—
288C22⋊C4—1722no—
289C42—44no—
290C23—41no—
291C23—41no—
292C23—1722no—
293C23—1722no—
294C23—1721no—
295C23—1721no—
296C23—1721no—
297C23C2×(C2×D43)⋊C411yescharacteristic
298C23#1306329411yescharacteristic
299C23#1306330811yescharacteristic
300C23C2×#1062188211yescharacteristic
301C23C2×#1062188411yescharacteristic
302C23#1306335111yescharacteristic
303C23#1306335611yescharacteristic
304D4—3442no—
305D4—3441no—
306D4—3441no—
307D4—3441no—
308D4—3441no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—81no—
326C2×C4—1722no—
327C2×C4—1722no—
328C2×C4—1722no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4#1306324514yes—
333C2×C4C4×C22⋊D4312yes—
334C2×C4#1306329912yes—
335C8—3442no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—3442no—
347C22—3442no—
348C22—3441no—
349C22—3441no—
350C22—3441no—
351C22#1458277811yescharacteristic
352C22C2×#1306324511yescharacteristic
353C22#1458289811yescharacteristic
354C22#1458303311yescharacteristic
355C22#1458303811yescharacteristic
356C22#1458321211yescharacteristic
357C22#1458321711yescharacteristic
358C4—22no—
359C4—22no—
360C4—24no—
361C4—42no—
362C4—84no—
363C4—3442no—
364C4—3441no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2—21no—
371C2—6881no—
372C2#1913491211yescharacteristic
373C2#1913513211yescharacteristic
374C2#1913513711yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2316C2
socleC22×C43#386
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#2316D43
hypocenterC43#9204
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2316

Complements

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

NH ≅ G/Ntype
3. C2×#14582625C2semidirect
4. #19132462C2semidirect
5. C43×#2316C2semidirect
9. #14582829C4semidirect
11. #14582816C4semidirect
179. #2316D43semidirect
208. C43#9204semidirect

Maximal subgroups

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

subgroupindex
#191403372
#191331622
C2×#145826252
#191324622
C43×#23162
#920443