Finite Group Databasebeta

← #25007259

Subgroups — #25007259

Order 11008.

486 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 69 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#19137830C211yesmaximal, characteristic
2#19134671C211yesmaximal, characteristic, complemented
3#19132926C211yesmaximal, characteristic, complemented
4#19132596C211yesmaximal, characteristic, complemented
5#19132594C211yesmaximal, characteristic, complemented
6#19132592C211yesmaximal, characteristic
7C43×#1343C211yesmaximal, characteristic
8C2×D4×Dic43—21no—
9C2×D4×Dic43C411yescharacteristic, complemented
10C2×#13063281C2211yescharacteristic
11#14582953—21no—
12#14582831C411yescharacteristic, complemented
13#14582824C2211yescharacteristic
14#14582822—21no—
15#14582813—21no—
16#14582813C411yescharacteristic, complemented
17#14582760—21no—
18#14582750C411yescharacteristic, complemented
19C22⋊C4×Dic43—21no—
20#14582666C2211yescharacteristic
21#14582665—21no—
22#14582624—21no—
23#14582623C2211yescharacteristic
24C43×#392C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C23×Dic43—21no—
28C23×Dic43D411yescharacteristic
29D4×Dic43—41no—
30D4×Dic43—41no—
31D4×Dic43—42no—
32D4×Dic43—42no—
33#13063281—41no—
34#13063281—41no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43C2×C411yescharacteristic
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4C2×C411yescharacteristic
39C2×Dic43⋊C4D411yescharacteristic
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43D411yescharacteristic
46C2×C4×Dic43—21no—
47C2×C4×Dic43C2×C411yescharacteristic
48C2×C4×Dic43D411yescharacteristic
49Dic43⋊C8—41no—
50C22⋊(C43⋊C8)—21no—
51#13063235—41no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—41no—
55C43⋊#95—41no—
56C43⋊#95C2×C411yescharacteristic
57C22×D4×C43—21no—
58C22×D4×C43C2×C411yescharacteristic
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43—21no—
61C2×C22⋊C4×C43C2311yescharacteristic
62C22⋊C8×C43—21no—
63#95×C43C2×C411yescharacteristic
64C24×C43—21no—
65C24×C43C2×D411yescharacteristic
66C2×D4×C43—42no—
67C2×D4×C43—42no—
68C2×D4×C43—42no—
69C2×D4×C43—41no—
70C2×D4×C43—41no—
71C2×D4×C43—41no—
72C22×C4×C43—21no—
73C22×C4×C43—41no—
74C22×C4×C43C22×C411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C22×Dic43—41no—
83C22×Dic43—41no—
84C22×Dic43—42no—
85C22×Dic43—42no—
86C22×Dic43—41no—
87C22×Dic43—41no—
88C22×Dic43C22⋊C411yescharacteristic
89C22×Dic43C22⋊C411yescharacteristic
90C22×Dic43C22⋊C411yescharacteristic
91C22×Dic43C22⋊C411yescharacteristic
92C2×C8×C43—41no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—41no—
95C22⋊C4×C43—42no—
96C22⋊C4×C43—41no—
97C22⋊Dic43—41no—
98C22⋊Dic43—42no—
99C22⋊Dic43—41no—
100C22⋊Dic43—42no—
101C22⋊Dic43—42no—
102C22⋊Dic43—41no—
103C22⋊Dic43—41no—
104C22⋊Dic43—41no—
105C4⋊Dic43—42no—
106C4⋊Dic43—41no—
107Dic43⋊C4—41no—
108Dic43⋊C4—41no—
109Dic43⋊C4—42no—
110C4×Dic43—21no—
111C4×Dic43—21no—
112C4×Dic43—21no—
113C4×Dic43—21no—
114C4×Dic43—42no—
115C2×C43⋊C8—41no—
116C23×C43—21no—
117C23×C43—21no—
118C23×C43—22no—
119C23×C43—41no—
120C23×C43—41no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43—41no—
126C23×C43—41no—
127C23×C43C2×C22⋊C411yescharacteristic
128C23×C43AGL(1,ℤ/8)11yescharacteristic
129C23×C43AGL(1,ℤ/8)11yescharacteristic
130D4×C43—42no—
131D4×C43—44no—
132D4×C43—44no—
133D4×C43—42no—
134C2×C4×C43—22no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—81no—
142C2×C4×C43—81no—
143C2×C4×C43—81no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—82no—
164C2×Dic43—82no—
165C2×Dic43—81no—
166C2×Dic43—81no—
167C2×Dic43—81no—
168C2×Dic43#9911yescharacteristic
169C2×Dic43#9911yescharacteristic
170C8×C43—81no—
171C43⋊C8—81no—
172#11798—431nomaximal, Sylow
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—41no—
178C22×C43—41no—
179C22×C43—42no—
180C22×C43—42no—
181C22×C43—41no—
182C22×C43—41no—
183C22×C43—42no—
184C22×C43—81no—
185C22×C43—81no—
186C22×C43—81no—
187C22×C43—81no—
188C22×C43—81no—
189C22×C43C2×#9911yescharacteristic
190C22×C43#41811yescharacteristic
191C22×C43#42111yescharacteristic
192C4×C43—42no—
193C4×C43—41no—
194C4×C43—41no—
195C4×C43—161no—
196Dic43—21no—
197Dic43—21no—
198Dic43—41no—
199Dic43—41no—
200Dic43—41no—
201Dic43—81no—
202Dic43—81no—
203Dic43—161no—
204#2392—431no—
205#1820—431no—
206#1464—431no—
207#1344—431no—
208#1344—431no—
209#1343—431no—
210#1343D4311yescharacteristic
211C2×C43—21no—
212C2×C43—21no—
213C2×C43—41no—
214C2×C43—41no—
215C2×C43—82no—
216C2×C43#151011yescharacteristic
217C2×C43#212011yescharacteristic
218C2×C43#212611yescharacteristic
219C2×C4×D4—431no—
220C2×C4×D4—861no—
221C2×#117—431no—
222#432—861no—
223#398—431no—
224#397—431no—
225#396—861no—
226#394—431no—
227#394—861no—
228#392C2×D4311yescharacteristic
229#381—861no—
230C4×C4⋊C4—431no—
231C4×C22⋊C4—861no—
232#342—431no—
233#342—861no—
234#342C2×D4311yescharacteristic
235#324—861no—
236#323—431no—
237#323C2×D4311yescharacteristic
238C43#1179811yescharacteristic, complemented, Sylow
239C22×D4—21no—
240C22×D4C4×D4311yescharacteristic
241C23×C4—431no—
242C23×C4—861no—
243C4×D4—1721no—
244C4×D4—1721no—
245C4×D4—1722no—
246C4×D4—1722no—
247#117—1721no—
248#117—1721no—
249C2×C4⋊C4—431no—
250C2×C4⋊C4—431no—
251C2×C4⋊C4—431no—
252C2×C4⋊C4—861no—
253C2×C4⋊C4—861no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—431no—
257C2×C22⋊C4—861no—
258C2×C22⋊C4—861no—
259C2×C22⋊C4—861no—
260C2×C22⋊C4—861no—
261C2×C22⋊C4—861no—
262C2×C22⋊C4C22×D4311yescharacteristic
263C2×C42—431no—
264C2×C42—431no—
265C2×C42—861no—
266C4⋊C8—1721no—
267C22⋊C8—21no—
268C22⋊C8—861no—
269#97—1721no—
270#95—431no—
271#95—861no—
272#95—861no—
273#95—1721no—
274#95—1721no—
275#95C4×D4311yescharacteristic
276C24—21no—
277C24D4×D4311yescharacteristic
278C2×D4—41no—
279C2×D4—42no—
280C2×D4—42no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—42no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—431no—
287C22×C4—431no—
288C22×C4—431no—
289C22×C4—431no—
290C22×C4—861no—
291C22×C4—861no—
292C22×C4—861no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4—1721no—
297C22×C4—1721no—
298C22×C4—1721no—
299C22×C4—1722no—
300C22×C4—1722no—
301C22×C4—1721no—
302C22×C4C2×C4×D4311yescharacteristic
303C22×C4D4×D4311yescharacteristic
304C2×C8—41no—
305C2×C8—1721no—
306C4⋊C4—1721no—
307C4⋊C4—1721no—
308C4⋊C4—1721no—
309C4⋊C4—1722no—
310C4⋊C4—1722no—
311C22⋊C4—41no—
312C22⋊C4—42no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—1721no—
316C22⋊C4—1722no—
317C22⋊C4—1722no—
318C22⋊C4—1721no—
319C22⋊C4—1721no—
320C22⋊C4—1722no—
321C22⋊C4—1721no—
322C22⋊C4—1721no—
323C42—861no—
324C42—861no—
325C42—861no—
326C42—861no—
327C42—1722no—
328C23—21no—
329C23—21no—
330C23—22no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23C22⋊C4×D4311yescharacteristic
340C23#1306334911yescharacteristic
341C23#1306335211yescharacteristic
342D4—42no—
343D4—44no—
344D4—44no—
345D4—42no—
346C2×C4—22no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—431no—
357C2×C4—431no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—861no—
361C2×C4—861no—
362C2×C4—861no—
363C2×C4—861no—
364C2×C4—861no—
365C2×C4—3442no—
366C2×C4—3442no—
367C2×C4—3441no—
368C2×C4—3441no—
369C2×C4—3441no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4—1721no—
373C2×C4—1721no—
374C2×C4—1721no—
375C2×C4—1721no—
376C2×C4—1721no—
377C2×C4—1721no—
378C2×C4—1721no—
379C2×C4—1721no—
380C2×C4—1721no—
381C2×C4—1721no—
382C8—81no—
383C8—3441no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—42no—
391C22—42no—
392C22—41no—
393C22—41no—
394C22—42no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22#99×D4311yescharacteristic
401C22#1458290211yescharacteristic
402C22#1458291411yescharacteristic
403C4—42no—
404C4—41no—
405C4—41no—
406C4—161no—
407C4—861no—
408C4—861no—
409C4—3441no—
410C4—3441no—
411C4—1721no—
412C4—1721no—
413C4—1721no—
414C4—6881no—
415C2—21no—
416C2—21no—
417C2—41no—
418C2—41no—
419C2—82no—
420C2#1913312211yescharacteristic
421C2#1913623311yescharacteristic
422C2#1913625711yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1343C2
socleC22×C43C2×#99
prime radicalC43×#392C22
cosocleC2×C22⋊C4×C43C23
hypercenter#1343D43
hypocenterC43#11798
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1343

Complements

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

NH ≅ G/Ntype
2. #19134671C2semidirect
3. #19132926C2semidirect
4. #19132596C2semidirect
5. #19132594C2semidirect
9. C2×D4×Dic43C4semidirect
12. #14582831C4semidirect
16. #14582813C4semidirect
18. #14582750C4semidirect
238. C43#11798semidirect

Maximal subgroups

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

subgroupindex
#191378302
#191346712
#191329262
#191325962
#191325942
#191325922
C43×#13432
#1179843