Finite Group Databasebeta

← #24997371

Subgroups — #24997371

Order 11008.

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

normal subgroups only

This group has 548 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#19144635C211yesmaximal, characteristic, complemented
2#19144392C211yesmaximal, characteristic
3#19139949C211yesmaximal, characteristic
4#19133160C211yesmaximal, characteristic, complemented
5#19133025C211yesmaximal, characteristic, complemented
6#19132454C211yesmaximal, characteristic, complemented
7C43×#1478C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9C2×C4×Dic86C2211yescharacteristic
10#14583235—21no—
11#14583199—22no—
12#14583195—21no—
13#14583189—21no—
14#14583179—21no—
15#14583110—21no—
16#14583057—21no—
17C4×Dic172—22no—
18#14582939—21no—
19#14582923C2211yescharacteristic
20#14582904—21no—
21#14582835—21no—
22#14582811—21no—
23#14582802—21no—
24#14582795—21no—
25#14582772—22no—
26#14582765C2211yescharacteristic
27#14582637—22no—
28#14582631—22no—
29C2×C4×D4×C43C2211yescharacteristic
30C43×#431C2211yescharacteristic
31C43×#431C2211yescharacteristic
32C43×D4⋊C8—22no—
33C22×Dic86D411yescharacteristic
34C2×Dic172—22no—
35C2×#10621877—21no—
36#13063325D411yescharacteristic
37#13063325D411yescharacteristic
38#13063317—21no—
39#13063304—21no—
40#13063304—21no—
41C4×Dic86—21no—
42C4×Dic86—21no—
43C4×Dic86—21no—
44C4×Dic86—21no—
45C4×Dic86—21no—
46C4×Dic86—21no—
47#13063284—21no—
48C2×C4⋊Dic43—21no—
49C2×C4⋊Dic43D411yescharacteristic
50C2×Dic43⋊C4—21no—
51C2×Dic43⋊C4—22no—
52C2×C22⋊Dic43—22no—
53C2×C22⋊Dic43—22no—
54C2×C4×Dic43—21no—
55#13063259—22no—
56#13063258—22no—
57#13063256—22no—
58C4⋊(C43⋊C8)—21no—
59C4⋊(C43⋊C8)D412yes—
60#13063250—22no—
61#13063250—22no—
62#13063246—22no—
63#13063246—22no—
64C43⋊#95—22no—
65C43⋊#95—21no—
66C43⋊#95D412yes—
67C22×D4×C43D411yescharacteristic
68C23×C4×C43—21no—
69C4×D4×C43—21no—
70C4×D4×C43—21no—
71C4×D4×C43—21no—
72C4×D4×C43—21no—
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C22⋊C4×C43—21no—
75C2×C42×C43C2311yescharacteristic
76C4⋊C8×C43—21no—
77C4⋊C8×C43—21no—
78C22⋊C8×C43—21no—
79C22⋊C8×C43—21no—
80C4×C8×C43—21no—
81C4×C8×C43D412yes—
82C24×C43—21no—
83C2×D4×C43—21no—
84C2×D4×C43—21no—
85C2×D4×C43—21no—
86C2×D4×C43—21no—
87C2×D4×C43—21no—
88C2×D4×C43Q1612yescomplemented
89C22×C4×C43—21no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43—82no—
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×Dic43—21no—
97C22×Dic43—22no—
98C22×Dic43—21no—
99C2×Dic86—21no—
100C2×Dic86—21no—
101C2×Dic86—21no—
102C2×Dic86—21no—
103C2×Dic86—42no—
104C2×C8×C43—22no—
105C2×C8×C43—41no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—21no—
108C22⋊C4×C43—41no—
109C22⋊C4×C43—41no—
110C42×C43C2×D411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43#4111yescharacteristic
114C22⋊Dic43—44no—
115C22⋊Dic43—41no—
116C22⋊Dic43—82no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121C4⋊Dic43—21no—
122C4⋊Dic43—21no—
123C4⋊Dic43—41no—
124C4⋊Dic43—41no—
125Dic43⋊C4—41no—
126Dic43⋊C4—41no—
127Dic43⋊C4—41no—
128Dic43⋊C4—41no—
129Dic43⋊C4—82no—
130C4×Dic43—41no—
131C4×Dic43—41no—
132C4×Dic43—41no—
133#10621877—41no—
134#10621877—41no—
135C2×C43⋊C8—22no—
136Dic172—44no—
137C23×C43—22no—
138C23×C43—42no—
139C23×C43—42no—
140C23×C43—41no—
141C23×C43—41no—
142C23×C43#12011yescharacteristic
143D4×C43—22no—
144D4×C43—22no—
145D4×C43—41no—
146D4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—42no—
150C2×C4×C43—41no—
151C2×C4×C43—82no—
152C2×C4×C43—82no—
153C2×C4×C43#12011yescharacteristic
154C2×C4×C43#12011yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12711yescharacteristic
159C2×C4×C43C2×Q1611yescharacteristic
160C2×C4×C43#13511yescharacteristic
161C2×C4×C43#13711yescharacteristic
162C2×C4×C43#13711yescharacteristic
163C2×Dic43—22no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—42no—
168C2×Dic43—42no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—42no—
174Dic86—22no—
175Dic86—22no—
176Dic86—41no—
177Dic86—41no—
178Dic86—42no—
179Dic86—81no—
180C8×C43—42no—
181C8×C43—81no—
182C43⋊C8—42no—
183#10002—431nomaximal, Sylow
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—44no—
187C22×C43—42no—
188C22×C43—82no—
189C22×C43—81no—
190C22×C43—81no—
191C22×C43#39211yescharacteristic
192C22×C43#45111yescharacteristic
193C22×C43#45211yescharacteristic
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—81no—
199C4×C43#45111yescharacteristic
200C4×C43#45211yescharacteristic
201C4×C43#46711yescharacteristic
202C4×C43#47011yescharacteristic
203Dic43—42no—
204Dic43—82no—
205Dic43—81no—
206Dic43—81no—
207Dic43—81no—
208#3104—431no—
209#3077—431no—
210#2580—431no—
211#1518—431no—
212#1487—431no—
213#1478D4311yescharacteristic
214#1286—431no—
215C2×C43—21no—
216C2×C43—21no—
217C2×C43—82no—
218C2×C43#200111yescharacteristic
219C2×C43#200811yescharacteristic
220C2×C43#201011yescharacteristic
221#533—431no—
222C2×C4×Q8—431no—
223C2×C4×D4C2×D4311yescharacteristic
224#484—861no—
225#478—862no—
226#477—861no—
227#476—861no—
228#474—861no—
229#462—861no—
230#451—861no—
231C4×Q16—862no—
232#431C2×D4311yescharacteristic
233#431C2×D4311yescharacteristic
234#428—861no—
235#423—431no—
236#418—861no—
237#399—861no—
238#393—861no—
239#390—861no—
240#389—861no—
241#385—862no—
242#382—431no—
243#328—862no—
244Q8⋊C8—862no—
245D4⋊C8—22no—
246C43#1000211yescharacteristic, complemented, Sylow
247C22×Q8—431no—
248C22×D4D17211yescharacteristic
249C23×C4—21no—
250C2×Q16—862no—
251C2×M16—861no—
252C4⋊Q8—431no—
253C4⋊Q8—431no—
254#125—861no—
255C22⋊Q8—861no—
256C22⋊Q8—861no—
257C4×Q8—861no—
258C4×Q8—861no—
259C4×Q8—861no—
260C4×Q8—861no—
261C4×Q8—861no—
262C4×Q8—861no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267#117—861no—
268C2×C4⋊C4—431no—
269C2×C4⋊C4—862no—
270C2×C4⋊C4—861no—
271C2×C4⋊C4—861no—
272C2×C4⋊C4D17211yescharacteristic
273C2×C22⋊C4—21no—
274C2×C22⋊C4—862no—
275C2×C22⋊C4—862no—
276C2×C42—861no—
277C2×C42C22×D4311yescharacteristic
278#107—862no—
279#107—862no—
280#106—862no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8—432no—
284C4⋊C8—861no—
285#103—862no—
286#103—862no—
287#102—862no—
288#102—862no—
289C22⋊C8—21no—
290C22⋊C8—21no—
291C4×C8—21no—
292C4×C8C22⋊D4312yes—
293#95—432no—
294#95—862no—
295#95—861no—
296C24—21no—
297C2×Q8—861no—
298C2×Q8—861no—
299C2×Q8—861no—
300C2×Q8—861no—
301C2×Q8—1722no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4Dic17212yescomplemented
308C22×C4—21no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—82no—
312C22×C4—861no—
313C22×C4—862no—
314C22×C4—861no—
315C22×C4C2×D17211yescharacteristic
316C22×C4D4×D4311yescharacteristic
317C22×C4D4×D4311yescharacteristic
318Q16—1724no—
319M16—1721no—
320M16—1721no—
321C2×C8—22no—
322C2×C8—41no—
323C2×C8—862no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—861no—
327C4⋊C4—861no—
328C4⋊C4—861no—
329C4⋊C4—861no—
330C4⋊C4—861no—
331C4⋊C4—861no—
332C4⋊C4—3442no—
333C4⋊C4—1721no—
334C4⋊C4—1721no—
335C4⋊C4—1721no—
336C4⋊C4—1721no—
337C4⋊C4—1721no—
338C4⋊C4—1721no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—3442no—
342C22⋊C4—1724no—
343C22⋊C4—1721no—
344C42—1721no—
345C42—1721no—
346C42—1721no—
347C42#1062189811yescharacteristic
348C42D4×D4311yescharacteristic
349C42D4×D4311yescharacteristic
350C42C2×C22⋊D4311yescharacteristic
351C23—22no—
352C23—42no—
353C23—42no—
354C23—41no—
355C23—41no—
356C23#1306329511yescharacteristic
357Q8—862no—
358Q8—862no—
359Q8—3441no—
360Q8—1722no—
361Q8—1721no—
362Q8—1721no—
363D4—22no—
364D4—22no—
365D4—41no—
366D4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—82no—
372C2×C4—82no—
373C2×C4—862no—
374C2×C4—1721no—
375C2×C4—1722no—
376C2×C4—1722no—
377C2×C4—1721no—
378C2×C4—1722no—
379C2×C4—1721no—
380C2×C4—1721no—
381C2×C4—1721no—
382C2×C4—1721no—
383C2×C4—1721no—
384C2×C4#1306329311yescharacteristic
385C2×C4#1306329511yescharacteristic
386C2×C4#1306329811yescharacteristic
387C2×C4#1306329811yescharacteristic
388C2×C4#1306329911yescharacteristic
389C2×C4#1306332111yescharacteristic
390C2×C4C2×Dic17211yescharacteristic
391C2×C4#1306334711yescharacteristic
392C2×C4#1306335811yescharacteristic
393C2×C4#1306335811yescharacteristic
394C8—42no—
395C8—81no—
396C8—1722no—
397C22—21no—
398C22—21no—
399C22—44no—
400C22—42no—
401C22—82no—
402C22—81no—
403C22—81no—
404C22#1458280811yescharacteristic
405C22#1458305711yescharacteristic
406C22#1458306311yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—81no—
412C4—3442no—
413C4—3441no—
414C4—3441no—
415C4—3441no—
416C4—1722no—
417C4#1458305711yescharacteristic
418C4#1458306311yescharacteristic
419C4#1458314011yescharacteristic
420C4#1458315711yescharacteristic
421C2—21no—
422C2—21no—
423C2—82no—
424C2#1913560511yescharacteristic
425C2#1913565011yescharacteristic
426C2#1913566111yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1478C2
socleC22×C43#392
prime radicalC22×D4×C43D4
hypercenter#1478D43
hypocenterC43#10002
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
1. #19144635C2semidirect
4. #19133160C2semidirect
5. #19133025C2semidirect
6. #19132454C2semidirect
88. C2×D4×C43Q16semidirect
246. C43#10002semidirect
307. C2×D4Dic172semidirect

Maximal subgroups

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

subgroupindex
#191446352
#191443922
#191399492
#191331602
#191330252
#191324542
C43×#14782
#1000243