Finite Group Databasebeta

← #25007084

Subgroups — #25007084

Order 11008.

586 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 87 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#19139753C211yesmaximal, characteristic
2C2×#14582666C211yesmaximal, characteristic
3#19132617C212yesmaximal, complemented
4#19132596C212yesmaximal, complemented
5C43×#1462C211yesmaximal, characteristic
6C2×#13063304C411yescharacteristic, complemented
7C22×C22⋊Dic43—21no—
8#14582824C411yescharacteristic, complemented
9#14582824C2211yescharacteristic
10#14582811C411yescharacteristic, complemented
11#14582811C2211yescharacteristic
12#14582793—21no—
13#14582793—21no—
14#14582762—21no—
15#14582755—21no—
16C4×C22⋊Dic43C411yescharacteristic, complemented
17#14582666—21no—
18#14582666C2212yes—
19C22×C22⋊C4×C43C2211yescharacteristic
20C43×#407—21no—
21C43×#323—21no—
22C43×#323C2212yes—
23C22×Dic86C2×C411yescharacteristic, complemented
24C23×Dic43—41no—
25#13063304—41no—
26#13063304—41no—
27C2×C4⋊Dic43C2×C411yescharacteristic, complemented
28C2×Dic43⋊C4—21no—
29C2×C22⋊Dic43—24no—
30C2×C22⋊Dic43—22no—
31C2×C22⋊Dic43—21no—
32C2×C22⋊Dic43—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37C2×C22⋊Dic43—41no—
38C2×C22⋊Dic43—42no—
39C2×C4×Dic43—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95C2×C411yescharacteristic, complemented
45C43⋊#95C2×C411yescharacteristic, complemented
46C25×C43D411yescharacteristic
47C23×C4×C43C2×C411yescharacteristic
48C23×C4×C43D411yescharacteristic
49C2×M16×C43—41no—
50C2×C22⋊C4×C43—41no—
51C2×C22⋊C4×C43—41no—
52C2×C22⋊C4×C43C2×C411yescharacteristic
53C2×C22⋊C4×C43D411yescharacteristic
54C2×C22⋊C4×C43D411yescharacteristic
55C2×C22⋊C4×C43C2311yescharacteristic
56C22⋊C8×C43—22no—
57C22⋊C8×C43—41no—
58C24×C43—21no—
59C24×C43—21no—
60C24×C43—22no—
61C24×C43—21no—
62C24×C43—21no—
63C24×C43—42no—
64C24×C43—81no—
65C24×C43C22⋊C411yescharacteristic
66C24×C43C22⋊C411yescharacteristic
67C24×C43C2×D411yescharacteristic
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—42no—
73C22×C4×C43—81no—
74C22×C4×C43C22⋊C411yescharacteristic
75C22×C4×C43C22⋊C411yescharacteristic
76C22×C4×C43C22×C411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C22×Dic43—44no—
83C22×Dic43—42no—
84C22×Dic43—82no—
85C22×Dic43—82no—
86C2×Dic86—41no—
87C2×Dic86—81no—
88M16×C43—82no—
89C2×C8×C43—42no—
90C22⋊C4×C43—41no—
91C22⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—41no—
94C22⋊Dic43—24no—
95C22⋊Dic43—42no—
96C22⋊Dic43—44no—
97C22⋊Dic43—41no—
98C22⋊Dic43—41no—
99C22⋊Dic43—42no—
100C22⋊Dic43—41no—
101C22⋊Dic43—42no—
102C22⋊Dic43—41no—
103C22⋊Dic43—81no—
104C22⋊Dic43—81no—
105C4⋊Dic43—41no—
106Dic43⋊C4—42no—
107C4×Dic43—81no—
108C23×C43—22no—
109C23×C43—22no—
110C23×C43—22no—
111C23×C43—22no—
112C23×C43—22no—
113C23×C43—21no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—21no—
117C23×C43—21no—
118C23×C43—21no—
119C23×C43—41no—
120C23×C43—42no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43—42no—
126C23×C43—81no—
127C23×C43—81no—
128C23×C43—84no—
129C23×C43—82no—
130C23×C43—82no—
131C23×C43#9911yescharacteristic
132C23×C43#9911yescharacteristic
133C23×C43#10412yes—
134C23×C43C2×C22⋊C411yescharacteristic
135C23×C43AGL(1,ℤ/8)11yescharacteristic
136C23×C43#13711yescharacteristic
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—42no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—81no—
147C2×C4×C43—81no—
148C2×C4×C43—81no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—44no—
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—88no—
163C2×Dic43—82no—
164C2×Dic43—82no—
165Dic86—82no—
166C8×C43—82no—
167#11759—431nomaximal, Sylow
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—22no—
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—42no—
179C22×C43—42no—
180C22×C43—42no—
181C22×C43—41no—
182C22×C43—41no—
183C22×C43—44no—
184C22×C43—44no—
185C22×C43—41no—
186C22×C43—41no—
187C22×C43—41no—
188C22×C43—41no—
189C22×C43—81no—
190C22×C43—81no—
191C22×C43—82no—
192C22×C43—82no—
193C22×C43#35412yes—
194C22×C43C2×#9911yescharacteristic
195C22×C43#41711yescharacteristic
196C22×C43C2×#10411yescharacteristic
197C4×C43—41no—
198C4×C43—41no—
199C4×C43—41no—
200C4×C43—41no—
201Dic43—81no—
202Dic43—81no—
203Dic43—84no—
204Dic43—81no—
205Dic43—81no—
206#2561—431no—
207C2×#342—431no—
208#1462D4311yescharacteristic
209#1351—432no—
210#1344—432no—
211C2×C43—21no—
212C2×C43—21no—
213C2×C43—22no—
214C2×C43—41no—
215C2×C43—41no—
216C2×C43—42no—
217C2×C43—41no—
218C2×C43#150411yescharacteristic
219C2×C43#212111yescharacteristic
220C2×C43C2×#35411yescharacteristic
221C2×C22⋊Q8—431no—
222C22×C22⋊C4—861no—
223C22×C22⋊C4C2×D4311yescharacteristic
224#407—21no—
225#397—431no—
226#397—431no—
227#393—431no—
228#393—431no—
229#388—861no—
230#388—861no—
231#381—861no—
232#379—861no—
233C4×C22⋊C4—431no—
234#342—432no—
235#342—861no—
236#323—21no—
237#323C2×D4312yes—
238C43#1175911yescharacteristic, complemented, Sylow
239C25D17211yescharacteristic
240C22×Q8—431no—
241C23×C4—1721no—
242C23×C4C4×D4311yescharacteristic
243C23×C4C22⋊D4311yescharacteristic
244C2×M16—41no—
245C22⋊Q8—1721no—
246C22⋊Q8—1721no—
247C2×C4⋊C4—431no—
248C2×C4⋊C4—861no—
249C2×C22⋊C4—41no—
250C2×C22⋊C4—41no—
251C2×C22⋊C4—864no—
252C2×C22⋊C4—862no—
253C2×C22⋊C4—861no—
254C2×C22⋊C4—861no—
255C2×C22⋊C4—861no—
256C2×C22⋊C4—861no—
257C2×C22⋊C4—861no—
258C2×C22⋊C4—861no—
259C2×C22⋊C4—1721no—
260C2×C22⋊C4—1722no—
261C2×C22⋊C4C4×D4311yescharacteristic
262C2×C22⋊C4D17211yescharacteristic
263C2×C22⋊C4C22⋊D4311yescharacteristic
264C2×C22⋊C4C22×D4311yescharacteristic
265C2×C42—861no—
266C22⋊C8—22no—
267C22⋊C8—41no—
268#95—431no—
269#95—431no—
270#95—861no—
271#95—861no—
272#95—861no—
273#95—861no—
274C24—21no—
275C24—21no—
276C24—22no—
277C24—21no—
278C24—21no—
279C24—42no—
280C24—81no—
281C24(C2×D43)⋊C411yescharacteristic
282C24(C2×D43)⋊C411yescharacteristic
283C24C2×D17211yescharacteristic
284C2×Q8—3441no—
285C2×Q8—1721no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—42no—
291C22×C4—81no—
292C22×C4—861no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4—3442no—
297C22×C4—3442no—
298C22×C4—1724no—
299C22×C4—1722no—
300C22×C4(C2×D43)⋊C411yescharacteristic
301C22×C4(C2×D43)⋊C411yescharacteristic
302C22×C4C2×C4×D4311yescharacteristic
303C22×C4C2×C22⋊D4311yescharacteristic
304M16—82no—
305C2×C8—42no—
306C4⋊C4—1721no—
307C4⋊C4—1722no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—864no—
313C22⋊C4—3441no—
314C22⋊C4—3441no—
315C22⋊C4—1724no—
316C22⋊C4—1722no—
317C22⋊C4—1721no—
318C22⋊C4—1721no—
319C22⋊C4—1722no—
320C22⋊C4—1722no—
321C22⋊C4—1721no—
322C22⋊C4—1721no—
323C42—3441no—
324C23—22no—
325C23—22no—
326C23—22no—
327C23—22no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—22no—
333C23—21no—
334C23—21no—
335C23—41no—
336C23—42no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—42no—
342C23—81no—
343C23—81no—
344C23—84no—
345C23—82no—
346C23—82no—
347C23#1306323911yescharacteristic
348C23#1306323911yescharacteristic
349C23#1306325112yes—
350C23C2×(C2×D43)⋊C411yescharacteristic
351C23#1306335311yescharacteristic
352C23#1306335811yescharacteristic
353Q8—3442no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—3448no—
367C2×C4—3442no—
368C2×C4—3442no—
369C2×C4—1721no—
370C2×C4—1721no—
371C2×C4—1724no—
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—82no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—22no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—42no—
394C22—42no—
395C22—42no—
396C22—41no—
397C22—41no—
398C22—44no—
399C22—44no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—81no—
405C22—81no—
406C22—82no—
407C22—82no—
408C22#1458269312yes—
409C22C2×#1306323911yescharacteristic
410C22#1458290111yescharacteristic
411C22C2×#1306325111yescharacteristic
412C4—41no—
413C4—41no—
414C4—41no—
415C4—41no—
416C4—3441no—
417C4—3441no—
418C4—3444no—
419C4—3441no—
420C4—3441no—
421C2—21no—
422C2—21no—
423C2—22no—
424C2—41no—
425C2—41no—
426C2—42no—
427C2—41no—
428C2#1913310011yescharacteristic
429C2#1913624211yescharacteristic
430C2C2×#1458269311yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1462C2
socleC22×C43C2×#99
prime radicalC25×C43D4
cosocleC2×C22⋊C4×C43C23
hypercenter#1462D43
hypocenterC43#11759
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
3. #19132617C2semidirect
4. #19132596C2semidirect
6. C2×#13063304C4semidirect
8. #14582824C4semidirect
10. #14582811C4semidirect
16. C4×C22⋊Dic43C4semidirect
23. C22×Dic86C2×C4semidirect
27. C2×C4⋊Dic43C2×C4semidirect
44. C43⋊#95C2×C4semidirect
45. C43⋊#95C2×C4semidirect
238. C43#11759semidirect

Maximal subgroups

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

subgroupindex
#191397532
C2×#145826662
#191326172
#191325962
C43×#14622
#1175943