Finite Group Databasebeta

← #24997501

Subgroups — #24997501

Order 11008.

576 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 81 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#19144981C211yesmaximal, characteristic, complemented
2#19144694C211yesmaximal, characteristic, complemented
3#19133219C211yesmaximal, characteristic, complemented
4#19133145C211yesmaximal, characteristic, complemented
5#19133038C211yesmaximal, characteristic, complemented
6#19132459C211yesmaximal, characteristic, complemented
7C43×#2631C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583258—21no—
10#14583258—21no—
11#14583253—22no—
12#14583234—21no—
13#14583179—21no—
14#14583104—21no—
15#14583050—21no—
16#14582999—22no—
17#14582956C2211yescharacteristic
18#14582956C2211yescharacteristic
19#14582908—21no—
20#14582904—21no—
21C4×#10621877C2211yescharacteristic
22#14582639—22no—
23#14582635—22no—
24D4⋊(C43⋊C8)—22no—
25C2×#124×C43C2211yescharacteristic
26C2×C4×D4×C43C2211yescharacteristic
27C43×#397—21no—
28C43×#393—21no—
29C43×#392—21no—
30C43×#392—21no—
31C43×#386—22no—
32C43×#383C2211yescharacteristic
33C2×#10621883—22no—
34C2×#10621877—21no—
35#13063325D411yescharacteristic, complemented
36#13063325D411yescharacteristic, complemented
37#13063317—21no—
38#13063304—21no—
39#13063304—21no—
40C4×Dic86—21no—
41C4×Dic86—21no—
42#13063284—21no—
43#13063258—22no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)—21no—
46#13063249—22no—
47#13063249—22no—
48#13063248—22no—
49#13063246—22no—
50#13063246—22no—
51#13063246—22no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54#13063236—21no—
55#13063236—21no—
56#13063236D412yescomplemented
57C4×C43⋊C8D412yescomplemented
58C22×Q8×C43D411yescharacteristic
59C22×D4×C43—22no—
60C22×D4×C43D411yescharacteristic
61C22×D4×C43D411yescharacteristic
62C23×C4×C43—21no—
63#124×C43—21no—
64#124×C43—21no—
65#124×C43—21no—
66#124×C43—21no—
67C4×D4×C43—21no—
68C4×D4×C43—21no—
69C4×D4×C43—21no—
70C4×D4×C43—21no—
71C2×C4⋊C4×C43D411yescharacteristic
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—22no—
76C2×C22⋊C4×C43—22no—
77C2×C42×C43C2311yescharacteristic
78#95×C43—22no—
79#95×C43—21no—
80#95×C43—21no—
81#95×C43D412yes—
82C24×C43—21no—
83C24×C43—21no—
84C2×Q8×C43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43—42no—
87C2×D4×C43—21no—
88C2×D4×C43—21no—
89C2×D4×C43—21no—
90C2×D4×C43—21no—
91C2×D4×C43—42no—
92C2×D4×C43—44no—
93C2×D4×C43—42no—
94C2×D4×C43—82no—
95C2×D4×C43—82no—
96C22×C4×C43—22no—
97C22×C4×C43—21no—
98C22×C4×C43—21no—
99C22×C4×C43—41no—
100C22×C4×C43—41no—
101C22×C4×C43—82no—
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C2×Dic86—21no—
106C2×Dic86—21no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C22⋊C4×C43—41no—
110C22⋊C4×C43—41no—
111C22⋊C4×C43—41no—
112C22⋊C4×C43—41no—
113C22⋊C4×C43—41no—
114C22⋊C4×C43—41no—
115C22⋊C4×C43—82no—
116C22⋊C4×C43—82no—
117C42×C43C2×D411yescharacteristic
118C42×C43C2×D411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43#4111yescharacteristic
121C22⋊Dic43—41no—
122#10621883—44no—
123C4⋊Dic43—21no—
124C4⋊Dic43—21no—
125C4⋊Dic43—21no—
126C4⋊Dic43—21no—
127Dic43⋊C4—41no—
128Dic43⋊C4—41no—
129C4×Dic43—41no—
130#10621877—42no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8—22no—
133C2×C43⋊C8—41no—
134C23×C43—22no—
135C23×C43—42no—
136C23×C43—41no—
137C23×C43—41no—
138C23×C43—42no—
139C23×C43—41no—
140C23×C43—41no—
141C23×C43—42no—
142C23×C43—41no—
143C23×C43—42no—
144C23×C43#12011yescharacteristic
145Q8×C43—42no—
146Q8×C43—81no—
147D4×C43—22no—
148D4×C43—22no—
149D4×C43—41no—
150D4×C43—41no—
151D4×C43—42no—
152D4×C43—81no—
153D4×C43—88no—
154C2×C4×C43—22no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—42no—
158C2×C4×C43—42no—
159C2×C4×C43—42no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—42no—
163C2×C4×C43—42no—
164C2×C4×C43—82no—
165C2×C4×C43—82no—
166C2×C4×C43#12011yescharacteristic
167C2×C4×C43#12011yescharacteristic
168C2×C4×C43#12111yescharacteristic
169C2×C4×C43#12111yescharacteristic
170C2×C4×C43#12111yescharacteristic
171C2×C4×C43#12711yescharacteristic
172C2×Dic43—41no—
173C2×Dic43—41no—
174Dic86—42no—
175Dic86—81no—
176C43⋊C8—42no—
177C43⋊C8—42no—
178C43⋊C8—81no—
179#10022—431nomaximal, Sylow
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—44no—
183C22×C43—42no—
184C22×C43—82no—
185C22×C43—82no—
186C22×C43—82no—
187C22×C43—81no—
188C22×C43—81no—
189C22×C43—81no—
190C22×C43—81no—
191C22×C43—81no—
192C22×C43#39211yescharacteristic
193C22×C43#45512yes—
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—82no—
201C4×C43—81no—
202C4×C43—81no—
203Dic43—81no—
204Dic43—81no—
205#3140—431no—
206#3110—431no—
207#2631D4311yescharacteristic
208#1533—431no—
209#1515—431no—
210#1490—431no—
211#1288—431no—
212C2×C43—22no—
213C2×C43—82no—
214C2×C43—161no—
215C2×C43#200411yescharacteristic
216C2×C43#200811yescharacteristic
217C2×C43#201011yescharacteristic
218#533—431no—
219C2×#124C2×D4311yescharacteristic
220C2×C4×D4C2×D4311yescharacteristic
221#489—861no—
222#489—861no—
223#488—862no—
224#484—861no—
225#474—861no—
226#461—861no—
227#450—861no—
228#440—862no—
229#432—431no—
230#432—431no—
231#419—861no—
232#418—861no—
233C4×M16—431no—
234#397—21no—
235#393—21no—
236#392—21no—
237#392—21no—
238#386—22no—
239#383C2×D4311yescharacteristic
240#329—862no—
241#328—862no—
242D4⋊C8—862no—
243C43#1002211yescharacteristic, complemented, Sylow
244C22×Q8C22⋊D4311yescharacteristic
245C22×D4—22no—
246C22×D4C22⋊D4311yescharacteristic
247C22×D4C22⋊D4311yescharacteristic
248C23×C4—21no—
249C2×SD16—862no—
250C2×M16—861no—
251C4⋊Q8—431no—
252C4⋊Q8—431no—
253#125—861no—
254#124—21no—
255#124—21no—
256#124—21no—
257#124—21no—
258C22⋊Q8—861no—
259C22⋊Q8—861no—
260C4×Q8—861no—
261C4×Q8—861no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266#117—861no—
267C2×C4⋊C4C22⋊D4311yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C42C22×D4311yescharacteristic
274#107—862no—
275C4⋊C8—861no—
276C4⋊C8—861no—
277#103—862no—
278#103—862no—
279#103—862no—
280#102—862no—
281#102—862no—
282#102—862no—
283C22⋊C8—861no—
284C22⋊C8—861no—
285#97—432no—
286#97—861no—
287#97—861no—
288C4×C8—432no—
289#95—22no—
290#95—21no—
291#95—21no—
292#95C22⋊D4312yes—
293C24—21no—
294C24—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—42no—
298C2×Q8—861no—
299C2×Q8—861no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—42no—
305C2×D4—42no—
306C2×D4—44no—
307C2×D4—82no—
308C2×D4—82no—
309C22×C4—22no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—82no—
315C22×C4C2×C22⋊D4311yescharacteristic
316C22×C4C2×C22⋊D4311yescharacteristic
317C22×C4C2×C22⋊D4311yescharacteristic
318SD16—1724no—
319M16—1722no—
320C2×C8—862no—
321C2×C8—862no—
322C2×C8—1721no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—861no—
326C4⋊C4—861no—
327C4⋊C4—861no—
328C4⋊C4—861no—
329C4⋊C4—1721no—
330C4⋊C4—1721no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—82no—
338C22⋊C4—82no—
339C22⋊C4—1721no—
340C42—1721no—
341C42D4×D4311yescharacteristic
342C42D4×D4311yescharacteristic
343C42D4×D4311yescharacteristic
344C42#1062190011yescharacteristic
345C23—22no—
346C23—42no—
347C23—41no—
348C23—41no—
349C23—42no—
350C23—41no—
351C23—41no—
352C23—42no—
353C23—41no—
354C23—42no—
355C23#1306329411yescharacteristic
356Q8—42no—
357Q8—81no—
358Q8—3441no—
359Q8—1722no—
360D4—22no—
361D4—22no—
362D4—41no—
363D4—41no—
364D4—42no—
365D4—81no—
366D4—88no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4—1721no—
380C2×C4—1721no—
381C2×C4#1306329311yescharacteristic
382C2×C4#1306329311yescharacteristic
383C2×C4#1306329611yescharacteristic
384C2×C4#1306329711yescharacteristic
385C2×C4#1306329711yescharacteristic
386C2×C4#1306332111yescharacteristic
387C8—3441no—
388C8—1722no—
389C8—1722no—
390C22—21no—
391C22—21no—
392C22—44no—
393C22—42no—
394C22—82no—
395C22—82no—
396C22—82no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22#1458280711yescharacteristic
403C22#1458307712yes—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—82no—
411C4—81no—
412C4—81no—
413C4—3441no—
414C4—3441no—
415C2—22no—
416C2—82no—
417C2—161no—
418C2#1913562211yescharacteristic
419C2#1913564811yescharacteristic
420C2#1913566011yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#2631C2
socleC22×C43#392
hypercenter#2631D43
hypocenterC43#10022
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2631

Complements

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

NH ≅ G/Ntype
1. #19144981C2semidirect
2. #19144694C2semidirect
3. #19133219C2semidirect
4. #19133145C2semidirect
5. #19133038C2semidirect
6. #19132459C2semidirect
35. #13063325D4semidirect
36. #13063325D4semidirect
56. #13063236D4semidirect
57. C4×C43⋊C8D4semidirect
243. C43#10022semidirect

Maximal subgroups

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

subgroupindex
#191449812
#191446942
#191332192
#191331452
#191330382
#191324592
C43×#26312
#1002243