Finite Group Databasebeta

← #25007611

Subgroups — #25007611

Order 11008.

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

normal subgroups only

This group has 776 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#19137951C211yesmaximal, characteristic
2#19132916C211yesmaximal, characteristic, complemented
3#19132591C214yesmaximal, complemented
4C43×#1799C211yesmaximal, characteristic, complemented
5C23×D172C411yescharacteristic, complemented
6C2×#13063299—21no—
7C2×#13063293—21no—
8#14582952—21no—
9#14582816C412yescomplemented
10#14582808C2212yes—
11#14582801—21no—
12#14582759C411yescharacteristic, complemented
13#14582754—21no—
14#14582623—21no—
15#14582623C2212yescomplemented
16C2×C4×D4×C43C2211yescharacteristic
17C2×#99×C43—21no—
18C43×#380—21no—
19C43×#342C2212yescomplemented
20C24×D43—21no—
21C22×D172—21no—
22C22×D172—44no—
23C22×D172—41no—
24C22×D172—41no—
25C22×D172C2×C412yes—
26C22×C22⋊D43—22no—
27#13063299—44no—
28#13063293—42no—
29#13063293—42no—
30C2×C4⋊Dic43—21no—
31C2×C22⋊Dic43—21no—
32C2×(C2×D43)⋊C4—22no—
33C2×(C2×D43)⋊C4—22no—
34C2×(C2×D43)⋊C4—22no—
35C4⋊(C43⋊C8)—41no—
36C22⋊(C43⋊C8)—22no—
37C4×C43⋊C8—41no—
38C43⋊#95C2×C412yes—
39C22×D4×C43D411yescharacteristic
40C23×C4×C43C2×C411yescharacteristic
41C23×C4×C43D411yescharacteristic
42C4×D4×C43—41no—
43C4×D4×C43—41no—
44C2×C4⋊C4×C43—41no—
45C2×C4⋊C4×C43C2×C411yescharacteristic
46C2×C22⋊C4×C43—22no—
47C2×C22⋊C4×C43D411yescharacteristic
48C2×C22⋊C4×C43C2311yescharacteristic
49C2×C42×C43D411yescharacteristic
50#99×C43—42no—
51#95×C43—41no—
52C24×C43C22⋊C411yescharacteristic
53C24×C43C2×D411yescharacteristic
54C23×D43—22no—
55C23×D43—44no—
56C23×D43—42no—
57C23×D43—42no—
58C23×D43—42no—
59C23×D43—82no—
60C2×D4×C43—41no—
61C2×D4×C43—41no—
62C2×D4×C43D812yes—
63C2×D4×C43SD1612yes—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—42no—
69C22×C4×C43—42no—
70C22×C4×C43—42no—
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22⋊C411yescharacteristic
73C22×C4×C43C22⋊C411yescharacteristic
74C22×C4×C43C22×C411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C2×C22⋊D43—44no—
77C2×C22⋊D43—42no—
78C2×C22⋊D43—42no—
79C2×C22⋊D43—82no—
80C22×Dic43—22no—
81C2×D172—24no—
82C2×D172—44no—
83C2×D172—42no—
84C2×D172—48no—
85C2×D172—44no—
86C2×D172—41no—
87C2×D172—41no—
88C2×D172—44no—
89C2×D172—42no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—82no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—42no—
95C22⋊C4×C43—42no—
96C42×C43—21no—
97C42×C43—21no—
98C22⋊Dic43—42no—
99(C2×D43)⋊C4—44no—
100(C2×D43)⋊C4—44no—
101(C2×D43)⋊C4—82no—
102C4⋊Dic43—42no—
103C2×C43⋊C8—42no—
104C23×C43—21no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—41no—
109C23×C43—41no—
110C23×C43—41no—
111C23×C43—41no—
112C23×C43#10212yes—
113C23×C43C2×C22⋊C411yescharacteristic
114C23×C43C2×D811yescharacteristic
115C23×C43C2×SD1611yescharacteristic
116C22×D43—24no—
117C22×D43—42no—
118C22×D43—42no—
119C22×D43—42no—
120C22×D43—48no—
121C22×D43—42no—
122C22×D43—42no—
123C22×D43—42no—
124C22×D43—88no—
125C22×D43—88no—
126C22×D43—84no—
127C22×D43—84no—
128D4×C43—42no—
129D4×C43—42no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—22no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—42no—
137C2×C4×C43—42no—
138C2×C4×C43—42no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—81no—
143C2×C4×C43—82no—
144C2×C4×C43—82no—
145C2×C4×C43—82no—
146C2×C4×C43#9911yescharacteristic
147C2×C4×C43#9911yescharacteristic
148C2×C4×C43#10212yes—
149C22⋊D43—84no—
150C22⋊D43—84no—
151C2×Dic43—42no—
152C2×Dic43—42no—
153C2×Dic43—42no—
154D172—44no—
155D172—44no—
156D172—44no—
157D172—44no—
158C43⋊C8—82no—
159#11873—431nomaximal, Sylow
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—22no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—42no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—42no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43—81no—
174C22×C43C2×#9911yescharacteristic
175C22×C43C2×#10211yescharacteristic
176C22×C43#42111yescharacteristic
177C2×D43—44no—
178C2×D43—44no—
179C2×D43—44no—
180C2×D43—82no—
181C2×D43—82no—
182C2×D43—816no—
183C2×D43—82no—
184C2×D43—82no—
185C4×C43—21no—
186C4×C43—22no—
187C4×C43—41no—
188C4×C43—41no—
189C4×C43—41no—
190C4×C43—162no—
191C4×C43AΣL(1,𝔽16)12yes—
192Dic43—82no—
193#2408—431no—
194#1799D4311yescharacteristic, complemented
195#1460—431no—
196#1343—434no—
197C2×C43—21no—
198C2×C43—21no—
199C2×C43—41no—
200C2×C43—42no—
201C2×C43—41no—
202C2×C43#151911yescharacteristic
203C2×C43C2×AΣL(1,𝔽16)11yescharacteristic
204C2×C43#212811yescharacteristic
205D43—84no—
206C23×D4—431no—
207C2×#121—861no—
208C2×#120—861no—
209C2×C4×D4C2×D4311yescharacteristic
210#431—861no—
211C2×#99—21no—
212#394—432no—
213#392—432no—
214#390—861no—
215#380—21no—
216#380—431no—
217#379—861no—
218#342C2×D4312yescomplemented
219#323—432no—
220#323—861no—
221C43#1187311yescharacteristic, complemented, Sylow
222C25—861no—
223C22×D4—432no—
224C22×D4—862no—
225C22×D4—861no—
226C22×D4—1721no—
227C22×D4—1721no—
228C22×D4—1724no—
229C22×D4C22⋊D4311yescharacteristic
230C23×C4C4×D4311yescharacteristic
231C23×C4C22⋊D4311yescharacteristic
232#121—1724no—
233#120—1722no—
234#120—1722no—
235C4×D4—41no—
236C4×D4—41no—
237C2×C4⋊C4—41no—
238C2×C4⋊C4—861no—
239C2×C4⋊C4C4×D4311yescharacteristic
240C2×C22⋊C4—22no—
241C2×C22⋊C4—862no—
242C2×C22⋊C4—861no—
243C2×C22⋊C4—862no—
244C2×C22⋊C4—862no—
245C2×C22⋊C4D17211yescharacteristic
246C2×C22⋊C4C22×D4311yescharacteristic
247C2×C42D17211yescharacteristic
248C4⋊C8—1721no—
249#99—42no—
250C22⋊C8—862no—
251C4×C8—1721no—
252#95—41no—
253#95—432no—
254C24—862no—
255C24—3442no—
256C24—1722no—
257C24—1722no—
258C24—1724no—
259C24—1722no—
260C24(C2×D43)⋊C411yescharacteristic
261C24C2×C22⋊D4311yescharacteristic
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—864no—
265C2×D4—3442no—
266C2×D4—1722no—
267C2×D4—1722no—
268C2×D4—1728no—
269C2×D4—1724no—
270C2×D4—1724no—
271C2×D4—1724no—
272C2×D4—1724no—
273C2×D4—1722no—
274C2×D4—1722no—
275C2×D4—1721no—
276C2×D4—1721no—
277C2×D4#1062188212yes—
278C2×D4#1062188412yes—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—862no—
287C22×C4(C2×D43)⋊C411yescharacteristic
288C22×C4(C2×D43)⋊C411yescharacteristic
289C22×C4(C2×D43)⋊C411yescharacteristic
290C22×C4C2×C4×D4311yescharacteristic
291C22×C4C2×D17211yescharacteristic
292C2×C8—1722no—
293C4⋊C4—41no—
294C4⋊C4—82no—
295C4⋊C4—1722no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—42no—
299C22⋊C4—42no—
300C22⋊C4—3442no—
301C22⋊C4—1724no—
302C22⋊C4—1722no—
303C22⋊C4—1724no—
304C42—21no—
305C42—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—864no—
315C23—3444no—
316C23—3444no—
317C23—3448no—
318C23—3448no—
319C23—1722no—
320C23—1722no—
321C23—1722no—
322C23—1728no—
323C23—1722no—
324C23—1722no—
325C23—1722no—
326C23#1306324512yes—
327C23C2×(C2×D43)⋊C411yescharacteristic
328C23C2×#1062188211yescharacteristic
329C23C2×#1062188411yescharacteristic
330D4—42no—
331D4—42no—
332D4—3444no—
333D4—3444no—
334D4—1724no—
335D4—1724no—
336D4—1724no—
337D4—1724no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—81no—
351C2×C4—82no—
352C2×C4—82no—
353C2×C4—82no—
354C2×C4—1722no—
355C2×C4—1722no—
356C2×C4—1722no—
357C2×C4#1306323911yescharacteristic
358C2×C4#1306323911yescharacteristic
359C2×C4#1306324512yes—
360C8—3442no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—21no—
366C22—41no—
367C22—41no—
368C22—42no—
369C22—42no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—81no—
375C22—3442no—
376C22—3442no—
377C22—34416no—
378C22—3442no—
379C22—3442no—
380C22—1724no—
381C22—1724no—
382C22—1724no—
383C22C2×#1306323911yescharacteristic
384C22C2×#1306324511yescharacteristic
385C22#1458291711yescharacteristic
386C4—21no—
387C4—22no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—162no—
392C4—3442no—
393C4#1458268512yes—
394C2—21no—
395C2—21no—
396C2—41no—
397C2—42no—
398C2—41no—
399C2—3444no—
400C2#1913316211yescharacteristic
401C2C2×#1458268511yescharacteristic
402C2#1913626611yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1799C2
socleC22×C43C2×#99
prime radical#19137951C2
cosocleC2×C22⋊C4×C43C23
hypercenter#1799D43
hypocenterC43#11873
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #19132916C2semidirect
3. #19132591C2semidirect
4. C43×#1799C2semidirect
5. C23×D172C4semidirect
9. #14582816C4semidirect
12. #14582759C4semidirect
15. #14582623C22semidirect
19. C43×#342C22semidirect
194. #1799D43semidirect
218. #342C2×D43semidirect
221. C43#11873semidirect

Maximal subgroups

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

subgroupindex
#191379512
#191329162
#191325912
C43×#17992
#1187343