Finite Group Databasebeta

← #25006880

Subgroups — #25006880

Order 11008.

592 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 107 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#19140400C211yesmaximal, characteristic
2C2×#14582623C211yesmaximal, characteristic
3#19132618C212yesmaximal, complemented
4#19132615C212yesmaximal, complemented
5C2×C43×#342C211yesmaximal, characteristic
6C2×#13063304C411yescharacteristic, complemented
7C2×C22⋊(C43⋊C8)—21no—
8#14582835C411yescharacteristic, complemented
9#14582835C2211yescharacteristic
10#14582822—21no—
11#14582822—21no—
12#14582811C411yescharacteristic, complemented
13#14582811C2211yescharacteristic
14#14582772—21no—
15#14582759C411yescharacteristic, complemented
16#14582755—21no—
17#14582623—21no—
18#14582623C2212yes—
19C22×C22⋊C4×C43—21no—
20C22×C22⋊C4×C43C2211yescharacteristic
21C43×#342—21no—
22C43×#342C2212yes—
23C22×Dic86C2×C411yescharacteristic, complemented
24C22×C43⋊C8—41no—
25#13063304—41no—
26#13063304—41no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43C2×C411yescharacteristic, complemented
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×C22⋊Dic43—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37C2×C22⋊Dic43—21no—
38C22⋊(C43⋊C8)—22no—
39C22⋊(C43⋊C8)—41no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95C2×C411yescharacteristic, complemented
43C43⋊#95C2×C411yescharacteristic, complemented
44C25×C43D411yescharacteristic
45C23×C4×C43—41no—
46C23×C4×C43C2×C411yescharacteristic
47C23×C4×C43D411yescharacteristic
48C2×C22⋊C4×C43—24no—
49C2×C22⋊C4×C43—22no—
50C2×C22⋊C4×C43—41no—
51C2×C22⋊C4×C43—41no—
52C2×C22⋊C4×C43—41no—
53C2×C22⋊C4×C43—42no—
54C2×C22⋊C4×C43C2×C411yescharacteristic
55C2×C22⋊C4×C43D411yescharacteristic
56C2×C22⋊C4×C43D411yescharacteristic
57C2×C22⋊C4×C43C2311yescharacteristic
58C24×C43—21no—
59C24×C43—21no—
60C24×C43—22no—
61C24×C43—81no—
62C24×C43—81no—
63C24×C43C22⋊C411yescharacteristic
64C24×C43C22⋊C411yescharacteristic
65C24×C43SD1612yes—
66C24×C43Q1612yes—
67C24×C43C2×D411yescharacteristic
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—44no—
73C22×C4×C43—42no—
74C22×C4×C43—81no—
75C22×C4×C43—81no—
76C22×C4×C43—82no—
77C22×C4×C43—82no—
78C22×C4×C43C22⋊C411yescharacteristic
79C22×C4×C43C22⋊C411yescharacteristic
80C22×C4×C43C22×C411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×Dic43—21no—
83C22×Dic43—21no—
84C22×Dic43—21no—
85C22×Dic43—21no—
86C2×Dic86—41no—
87C2×Dic86—81no—
88C22⋊C4×C43—24no—
89C22⋊C4×C43—41no—
90C22⋊C4×C43—41no—
91C22⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—44no—
94C22⋊C4×C43—42no—
95C22⋊Dic43—41no—
96C22⋊Dic43—41no—
97C22⋊Dic43—42no—
98C22⋊Dic43—81no—
99C22⋊Dic43—81no—
100C22⋊Dic43—81no—
101C22⋊Dic43—81no—
102C4⋊Dic43—41no—
103C4⋊Dic43—81no—
104Dic43⋊C4—42no—
105Dic43⋊C4—81no—
106Dic43⋊C4—81no—
107C2×C43⋊C8—42no—
108C2×C43⋊C8—82no—
109C23×C43—22no—
110C23×C43—22no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—22no—
114C23×C43—22no—
115C23×C43—21no—
116C23×C43—21no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43—42no—
120C23×C43—42no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43—81no—
126C23×C43—81no—
127C23×C43—82no—
128C23×C43—82no—
129C23×C43—84no—
130C23×C43#9911yescharacteristic
131C23×C43#9911yescharacteristic
132C23×C43#10312yes—
133C23×C43#10312yes—
134C23×C43#10412yes—
135C23×C43C2×C22⋊C411yescharacteristic
136C23×C43C2×SD1611yescharacteristic
137C23×C43C2×Q1611yescharacteristic
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—42no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—44no—
148C2×C4×C43—81no—
149C2×C4×C43—81no—
150C2×C4×C43—81no—
151C2×C4×C43—88no—
152C2×C4×C43—82no—
153C2×C4×C43—82no—
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—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166Dic86—82no—
167C43⋊C8—82no—
168#11716—431nomaximal, Sylow
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#32812yes—
194C22×C43#32812yes—
195C22×C43C2×#9911yescharacteristic
196C22×C43C2×#10311yescharacteristic
197C22×C43C2×#10411yescharacteristic
198C4×C43—41no—
199C4×C43—41no—
200C4×C43—41no—
201C4×C43—41no—
202C4×C43—84no—
203Dic43—81no—
204Dic43—81no—
205Dic43—81no—
206Dic43—81no—
207#2626—431no—
208C2×#342D4311yescharacteristic
209C2×#323—431no—
210#1352—432no—
211#1351—432no—
212C2×C43—21no—
213C2×C43—22no—
214C2×C43—21no—
215C2×C43—22no—
216C2×C43—41no—
217C2×C43—42no—
218C2×C43—41no—
219C2×C43C2×#32811yescharacteristic
220C2×C43#212111yescharacteristic
221C2×C43#212711yescharacteristic
222C2×C22⋊Q8—431no—
223C22×C22⋊C4—21no—
224C22×C22⋊C4C2×D4311yescharacteristic
225C2×C22⋊C8—861no—
226#399—431no—
227#399—431no—
228#396—861no—
229#396—861no—
230#393—431no—
231#393—431no—
232#385—861no—
233#380—431no—
234#379—861no—
235#342—21no—
236#342C2×D4312yes—
237#323—432no—
238#323—861no—
239C43#1171611yescharacteristic, complemented, Sylow
240C25C22⋊D4311yescharacteristic
241C22×Q8—431no—
242C23×C4—41no—
243C23×C4C4×D4311yescharacteristic
244C23×C4D17211yescharacteristic
245C22×C8—1721no—
246C22⋊Q8—1721no—
247C22⋊Q8—1721no—
248C2×C4⋊C4—431no—
249C2×C4⋊C4—861no—
250C2×C4⋊C4—861no—
251C2×C4⋊C4—861no—
252C2×C4⋊C4—861no—
253C2×C22⋊C4—24no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—41no—
256C2×C22⋊C4—41no—
257C2×C22⋊C4—41no—
258C2×C22⋊C4—42no—
259C2×C22⋊C4—861no—
260C2×C22⋊C4—861no—
261C2×C22⋊C4—861no—
262C2×C22⋊C4—861no—
263C2×C22⋊C4—861no—
264C2×C22⋊C4—861no—
265C2×C22⋊C4C4×D4311yescharacteristic
266C2×C22⋊C4D17211yescharacteristic
267C2×C22⋊C4C22⋊D4311yescharacteristic
268C2×C22⋊C4C22×D4311yescharacteristic
269C22⋊C8—862no—
270C22⋊C8—1721no—
271#95—431no—
272#95—431no—
273#95—861no—
274#95—861no—
275C24—21no—
276C24—21no—
277C24—22no—
278C24—81no—
279C24—81no—
280C24(C2×D43)⋊C411yescharacteristic
281C24(C2×D43)⋊C411yescharacteristic
282C24#1062188312yes—
283C24#1062188512yes—
284C24C2×C22⋊D4311yescharacteristic
285C2×Q8—3441no—
286C2×Q8—1721no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—42no—
292C22×C4—44no—
293C22×C4—81no—
294C22×C4—81no—
295C22×C4—82no—
296C22×C4—82no—
297C22×C4—861no—
298C22×C4—861no—
299C22×C4—861no—
300C22×C4—861no—
301C22×C4(C2×D43)⋊C411yescharacteristic
302C22×C4(C2×D43)⋊C411yescharacteristic
303C22×C4C2×C4×D4311yescharacteristic
304C22×C4C2×D17211yescharacteristic
305C2×C8—3442no—
306C2×C8—1722no—
307C4⋊C4—3441no—
308C4⋊C4—3441no—
309C4⋊C4—3441no—
310C4⋊C4—1721no—
311C4⋊C4—1722no—
312C22⋊C4—24no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—44no—
318C22⋊C4—42no—
319C22⋊C4—3441no—
320C22⋊C4—3441no—
321C22⋊C4—3441no—
322C22⋊C4—3441no—
323C22⋊C4—1721no—
324C22⋊C4—1721no—
325C22⋊C4—1722no—
326C23—21no—
327C23—21no—
328C23—22no—
329C23—22no—
330C23—22no—
331C23—22no—
332C23—21no—
333C23—21no—
334C23—41no—
335C23—41no—
336C23—42no—
337C23—42no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—81no—
343C23—81no—
344C23—82no—
345C23—82no—
346C23—84no—
347C23#1306323911yescharacteristic
348C23#1306323911yescharacteristic
349C23#1306324812yes—
350C23#1306324812yes—
351C23#1306325312yes—
352C23C2×(C2×D43)⋊C411yescharacteristic
353C23C2×#1062188311yescharacteristic
354C23C2×#1062188511yescharacteristic
355Q8—3442no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—44no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—88no—
370C2×C4—82no—
371C2×C4—82no—
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—
382C2×C4—1721no—
383C2×C4—1721no—
384C8—3442no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—22no—
393C22—21no—
394C22—42no—
395C22—42no—
396C22—42no—
397C22—41no—
398C22—41no—
399C22—44no—
400C22—44no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—81no—
406C22—81no—
407C22—82no—
408C22—82no—
409C22#1458263512yes—
410C22#1458263512yes—
411C22C2×#1306323911yescharacteristic
412C22C2×#1306324811yescharacteristic
413C22C2×#1306325311yescharacteristic
414C4—41no—
415C4—41no—
416C4—41no—
417C4—41no—
418C4—84no—
419C4—3441no—
420C4—3441no—
421C4—3441no—
422C4—3441no—
423C2—21no—
424C2—21no—
425C2—22no—
426C2—22no—
427C2—41no—
428C2—42no—
429C2—41no—
430C2C2×#1458263511yescharacteristic
431C2#1913623911yescharacteristic
432C2#1913626211yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC2×C43×#342C2
socleC22×C43C2×#99
prime radicalC25×C43D4
cosocleC2×C22⋊C4×C43C23
hypercenterC2×#342D43
hypocenterC43#11716
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
3. #19132618C2semidirect
4. #19132615C2semidirect
6. C2×#13063304C4semidirect
8. #14582835C4semidirect
12. #14582811C4semidirect
15. #14582759C4semidirect
23. C22×Dic86C2×C4semidirect
28. C2×C4⋊Dic43C2×C4semidirect
42. C43⋊#95C2×C4semidirect
43. C43⋊#95C2×C4semidirect
239. C43#11716semidirect

Maximal subgroups

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

subgroupindex
#191404002
C2×#145826232
#191326182
#191326152
C2×C43×#3422
#1171643