Finite Group Databasebeta

← #25006771

Subgroups — #25006771

Order 11008.

552 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 107 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#19137831C211yesmaximal, characteristic
2#19132909C211yesmaximal, characteristic, complemented
3#19132594C212yesmaximal, complemented
4#19132591C212yesmaximal
5C43×#1740C211yesmaximal, characteristic, complemented
6C2×C4×D172C411yescharacteristic, complemented
7C2×C4×C22⋊D43—21no—
8#14582952—21no—
9#14582829C411yescharacteristic, complemented
10#14582824C2211yescharacteristic
11#14582821—21no—
12#14582816C411yescharacteristic, complemented
13#14582815—21no—
14#14582808C2211yescharacteristic
15C4×C4⋊Dic43C411yescharacteristic, complemented
16C4×(C2×D43)⋊C4—21no—
17#14582625—21no—
18#14582623C2212yes—
19C2×#117×C43—21no—
20C2×#117×C43C2211yescharacteristic
21C43×#342—21no—
22C43×#342C2212yes—
23C22×D172C2×C411yescharacteristic
24C22×C22⋊D43—21no—
25C22×C4×D43—21no—
26C4×D172—41no—
27C4×D172—41no—
28C4×C22⋊D43—42no—
29C4×C22⋊D43—42no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43C2×C411yescharacteristic
32C2×Dic43⋊C4—21no—
33C2×C22⋊Dic43—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×C4×Dic43—21no—
39C4⋊(C43⋊C8)—41no—
40C22⋊(C43⋊C8)—22no—
41C4×C43⋊C8—41no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95C2×C411yescharacteristic
45C43⋊#95C2×C411yescharacteristic
46C23×C4×C43D411yescharacteristic
47#117×C43—24no—
48#117×C43—41no—
49#117×C43—41no—
50#117×C43—42no—
51C2×C4⋊C4×C43—41no—
52C2×C4⋊C4×C43C2×C411yescharacteristic
53C2×C4⋊C4×C43D411yescharacteristic
54C2×C22⋊C4×C43—22no—
55C2×C22⋊C4×C43D411yescharacteristic
56C2×C22⋊C4×C43C2311yescharacteristic
57C2×C42×C43—41no—
58C2×C42×C43C2×C411yescharacteristic
59C2×C42×C43D411yescharacteristic
60C24×C43C2×D411yescharacteristic
61C23×D43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—22no—
65C22×C4×C43—42no—
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43D812yes—
71C22×C4×C43SD1612yes—
72C22×C4×C43C22×C411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C2×C22⋊D43—42no—
75C2×C22⋊D43—42no—
76C2×C22⋊D43—41no—
77C2×C22⋊D43—41no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C2×D172—42no—
82C2×D172—41no—
83C2×C4×D43—41no—
84C2×C4×D43—41no—
85C2×C4×D43—42no—
86C2×C4×D43—42no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—44no—
90C22⋊C4×C43—24no—
91C22⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—42no—
94C42×C43—21no—
95C42×C43—21no—
96C42×C43—21no—
97C42×C43—21no—
98C42×C43—44no—
99C22⋊Dic43—41no—
100C22⋊Dic43—41no—
101(C2×D43)⋊C4—42no—
102(C2×D43)⋊C4—42no—
103(C2×D43)⋊C4—42no—
104(C2×D43)⋊C4—42no—
105C4⋊Dic43—42no—
106C4⋊Dic43—41no—
107Dic43⋊C4—42no—
108C4×Dic43—42no—
109C2×C43⋊C8—42no—
110C23×C43—21no—
111C23×C43—21no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43C2×C22⋊C411yescharacteristic
115C23×C43C2×D811yescharacteristic
116C23×C43C2×SD1611yescharacteristic
117C22×D43—22no—
118C22×D43—41no—
119C22×D43—41no—
120C22×D43—41no—
121C22×D43—41no—
122C22×D43—41no—
123C22×D43—41no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—22no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—44no—
139C2×C4×C43—82no—
140C2×C4×C43—82no—
141C2×C4×C43#9911yescharacteristic
142C2×C4×C43#9911yescharacteristic
143C2×C4×C43#10212yes—
144C2×C4×C43#10212yes—
145C2×C4×C43#10412yes—
146C22⋊D43—44no—
147C22⋊D43—44no—
148C2×Dic43—22no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157D172—42no—
158D172—42no—
159C4×D43—82no—
160C4×D43—82no—
161C43⋊C8—82no—
162#11691—431nomaximal, Sylow
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—81no—
172C22×C43C2×#9911yescharacteristic
173C22×C43C2×#10211yescharacteristic
174C22×C43C2×#10411yescharacteristic
175C2×D43—42no—
176C2×D43—42no—
177C2×D43—42no—
178C2×D43—81no—
179C2×D43—81no—
180C2×D43—81no—
181C2×D43—81no—
182C4×C43—22no—
183C4×C43—41no—
184C4×C43—41no—
185C4×C43—41no—
186C4×C43—41no—
187C4×C43—84no—
188C4×C43#32712yes—
189C4×C43#32712yes—
190Dic43—42no—
191Dic43—81no—
192Dic43—81no—
193#2392—431no—
194#1740D4311yescharacteristic, complemented
195#1458—431no—
196#1344—432no—
197#1343—432no—
198C2×C43—21no—
199C2×C43—21no—
200C2×C43—41no—
201C2×C43—41no—
202C2×C43C2×#32711yescharacteristic
203C2×C43#212011yescharacteristic
204C2×C43#212611yescharacteristic
205D43—82no—
206C2×C4×D4—431no—
207C2×C4×D4—861no—
208C2×#117—21no—
209C2×#117C2×D4311yescharacteristic
210#431—861no—
211#398—431no—
212#397—431no—
213#396—861no—
214#394—431no—
215#394—861no—
216#392—431no—
217C4×C4⋊C4—431no—
218C4×C22⋊C4—861no—
219#342—21no—
220#342C2×D4312yes—
221#324—861no—
222#323—432no—
223C43#1169111yescharacteristic, complemented, Sylow
224C22×D4—431no—
225C22×D4—861no—
226C23×C4—861no—
227C23×C4C22⋊D4311yescharacteristic
228C4×D4—1721no—
229C4×D4—1721no—
230C4×D4—1722no—
231C4×D4—1722no—
232#117—24no—
233#117—41no—
234#117—41no—
235#117—42no—
236C2×C4⋊C4—41no—
237C2×C4⋊C4—431no—
238C2×C4⋊C4—861no—
239C2×C4⋊C4—861no—
240C2×C4⋊C4C4×D4311yescharacteristic
241C2×C4⋊C4D17211yescharacteristic
242C2×C22⋊C4—22no—
243C2×C22⋊C4—861no—
244C2×C22⋊C4—861no—
245C2×C22⋊C4—861no—
246C2×C22⋊C4—861no—
247C2×C22⋊C4—861no—
248C2×C22⋊C4C22⋊D4311yescharacteristic
249C2×C22⋊C4C22×D4311yescharacteristic
250C2×C42—41no—
251C2×C42—861no—
252C2×C42C4×D4311yescharacteristic
253C2×C42D17211yescharacteristic
254C4⋊C8—1721no—
255C22⋊C8—862no—
256C4×C8—1721no—
257#95—431no—
258#95—431no—
259#95—861no—
260#95—861no—
261C24—861no—
262C24C2×C22⋊D4311yescharacteristic
263C2×D4—1721no—
264C2×D4—1722no—
265C2×D4—1722no—
266C2×D4—1722no—
267C2×D4—1721no—
268C2×D4—1721no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—42no—
273C22×C4—861no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—1721no—
277C22×C4—1721no—
278C22×C4—1722no—
279C22×C4—1722no—
280C22×C4(C2×D43)⋊C411yescharacteristic
281C22×C4(C2×D43)⋊C411yescharacteristic
282C22×C4(C2×D43)⋊C411yescharacteristic
283C22×C4(C2×D43)⋊C411yescharacteristic
284C22×C4#1062188212yes—
285C22×C4#1062188412yes—
286C22×C4C2×C4×D4311yescharacteristic
287C22×C4C2×D17211yescharacteristic
288C2×C8—1722no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—44no—
292C4⋊C4—1721no—
293C4⋊C4—1722no—
294C4⋊C4—1722no—
295C22⋊C4—24no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—42no—
299C22⋊C4—1722no—
300C22⋊C4—1722no—
301C22⋊C4—1722no—
302C22⋊C4—1721no—
303C22⋊C4—1721no—
304C22⋊C4—1722no—
305C42—21no—
306C42—21no—
307C42—21no—
308C42—21no—
309C42—44no—
310C42—1722no—
311C23—21no—
312C23—21no—
313C23—41no—
314C23—41no—
315C23—862no—
316C23—1721no—
317C23—1721no—
318C23—1721no—
319C23—1721no—
320C23—1721no—
321C23—1721no—
322C23C2×(C2×D43)⋊C411yescharacteristic
323C23C2×#1062188211yescharacteristic
324C23C2×#1062188411yescharacteristic
325D4—1722no—
326D4—1722no—
327D4—1724no—
328D4—1724no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—44no—
344C2×C4—82no—
345C2×C4—82no—
346C2×C4—862no—
347C2×C4—3442no—
348C2×C4—3442no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4—1721no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4—1721no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4#1306323911yescharacteristic
358C2×C4#1306323911yescharacteristic
359C2×C4#1306324512yes—
360C2×C4#1306324512yes—
361C2×C4#1306325312yes—
362C8—3442no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—81no—
372C22—3441no—
373C22—3441no—
374C22—3441no—
375C22—3441no—
376C22—1722no—
377C22—1722no—
378C22—1722no—
379C22C2×#1306323911yescharacteristic
380C22C2×#1306324511yescharacteristic
381C22C2×#1306325311yescharacteristic
382C4—22no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—84no—
388C4—3441no—
389C4—3441no—
390C4—1722no—
391C4#1458263212yes—
392C4#1458263212yes—
393C2—21no—
394C2—21no—
395C2—41no—
396C2—41no—
397C2—3442no—
398C2C2×#1458263211yescharacteristic
399C2#1913623411yescharacteristic
400C2#1913625811yescharacteristic
subgroupG/H
centerC2×C4#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1740C2
socleC22×C43C2×#99
prime radical#14582808C22
cosocleC2×C22⋊C4×C43C23
hypercenter#1740D43
hypocenterC43#11691
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#117 ◁ #1740

Complements

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

NH ≅ G/Ntype
2. #19132909C2semidirect
3. #19132594C2semidirect
5. C43×#1740C2semidirect
6. C2×C4×D172C4semidirect
9. #14582829C4semidirect
12. #14582816C4semidirect
15. C4×C4⋊Dic43C4semidirect
194. #1740D43semidirect
223. C43#11691semidirect

Maximal subgroups

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

subgroupindex
#191378312
#191329092
#191325942
#191325912
C43×#17402
#1169143