Finite Group Databasebeta

← #25009383

Subgroups — #25009383

Order 11008.

578 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 63 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#19135759C211yesmaximal, characteristic
2#19133619C211yesmaximal, characteristic, complemented
3#19133551C211yesmaximal, characteristic, complemented
4#19132619C211yesmaximal, characteristic, complemented
5#19132616C211yesmaximal, characteristic, complemented
6#19132523C211yesmaximal, characteristic
7C43×#2437C211yesmaximal, characteristic
8#14583525C2211yescharacteristic
9#14583234—21no—
10#14583055—21no—
11#14582755—21no—
12#14582666C2211yescharacteristic
13#14582665—21no—
14#14582635—21no—
15#14582635—21no—
16#14582623C2211yescharacteristic
17#14582623C2211yescharacteristic
18C2×C22⋊Q8×C43—21no—
19C22×C22⋊C4×C43—21no—
20C43×#399C2211yescharacteristic
21C43×#396—21no—
22C43×#393C2211yescharacteristic
23C43×#385—21no—
24C43×#385—21no—
25C43×#380—21no—
26C43×#379C2211yescharacteristic
27C2×#10621885—41no—
28#13063304—21no—
29#13063304—21no—
30#13063302—41no—
31#13063302—41no—
32C2×C22⋊Dic43—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—41no—
35C2×C22⋊Dic43—41no—
36#13063258—41no—
37#13063249—41no—
38#13063248—41no—
39C22⋊(C43⋊C8)—21no—
40C22⋊(C43⋊C8)—21no—
41C25×C43D411yescharacteristic
42C22×Q8×C43D411yescharacteristic
43C23×C4×C43—21no—
44C23×C4×C43—21no—
45C22⋊Q8×C43—44no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43D411yescharacteristic
51C2×C22⋊C4×C43—21no—
52C2×C22⋊C4×C43—21no—
53C2×C22⋊C4×C43—21no—
54C2×C22⋊C4×C43—21no—
55C2×C22⋊C4×C43—21no—
56C2×C22⋊C4×C43—21no—
57C2×C22⋊C4×C43—44no—
58C2×C22⋊C4×C43D411yescharacteristic
59C2×C22⋊C4×C43C2311yescharacteristic
60#95×C43—21no—
61#95×C43—21no—
62#95×C43D411yescharacteristic
63#95×C43D411yescharacteristic
64C24×C43—21no—
65C24×C43—21no—
66C24×C43—42no—
67C24×C43—42no—
68C24×C43—41no—
69C24×C43—41no—
70C24×C43Q1612yescomplemented
71C24×C43C2×D411yescharacteristic
72C2×Q8×C43—42no—
73C2×Q8×C43—41no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—42no—
80C22×C4×C43—42no—
81C22×C4×C43—42no—
82C22×C4×C43—42no—
83C22×C4×C43—81no—
84C22×C4×C43—81no—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×Dic43—21no—
88C22×Dic43—21no—
89C22×Dic43—41no—
90C2×Dic86—21no—
91C2×Dic86—21no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43—42no—
94C4⋊C4×C43—42no—
95C4⋊C4×C43—42no—
96C4⋊C4×C43—81no—
97C22⋊C4×C43—24no—
98C22⋊C4×C43—41no—
99C22⋊C4×C43—41no—
100C22⋊C4×C43—42no—
101C22⋊C4×C43—42no—
102C22⋊C4×C43—42no—
103C22⋊C4×C43—42no—
104C22⋊C4×C43—42no—
105C22⋊Dic43—41no—
106C22⋊Dic43—41no—
107C22⋊Dic43—41no—
108C22⋊Dic43—41no—
109C22⋊Dic43—82no—
110C22⋊Dic43—82no—
111#10621885—82no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114Dic43⋊C4—41no—
115Dic43⋊C4—41no—
116C2×C43⋊C8—41no—
117C2×C43⋊C8—41no—
118C23×C43—22no—
119C23×C43—22no—
120C23×C43—22no—
121C23×C43—21no—
122C23×C43—21no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43—41no—
126C23×C43—44no—
127C23×C43—42no—
128C23×C43—41no—
129C23×C43—44no—
130C23×C43—41no—
131C23×C43—41no—
132C23×C43—42no—
133C23×C43—42no—
134C23×C43—81no—
135C23×C43—84no—
136C23×C43—81no—
137C23×C43—81no—
138C23×C43#12011yescharacteristic
139C23×C43C2×Q1611yescharacteristic
140C23×C43#13711yescharacteristic
141Q8×C43—42no—
142Q8×C43—81no—
143C2×C4×C43—22no—
144C2×C4×C43—22no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—84no—
163C2×C4×C43—84no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—81no—
167C2×Dic43—81no—
168C2×Dic43—81no—
169C2×Dic43—81no—
170C2×Dic43—81no—
171Dic86—81no—
172Dic86—81no—
173C43⋊C8—81no—
174C43⋊C8—81no—
175#12214—431nomaximal, Sylow
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—24no—
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—41no—
182C22×C43—41no—
183C22×C43—42no—
184C22×C43—42no—
185C22×C43—42no—
186C22×C43—44no—
187C22×C43—42no—
188C22×C43—41no—
189C22×C43—42no—
190C22×C43—42no—
191C22×C43—41no—
192C22×C43—81no—
193C22×C43—82no—
194C22×C43—82no—
195C22×C43—82no—
196C22×C43#45111yescharacteristic
197C22×C43#45511yescharacteristic
198C22×C43B(4,𝔽2)11yescharacteristic
199C4×C43—42no—
200C4×C43—41no—
201C4×C43—42no—
202C4×C43—41no—
203C4×C43—81no—
204C4×C43—81no—
205C4×C43—81no—
206Dic43—81no—
207Dic43—81no—
208Dic43—161no—
209#2437D4311yescharacteristic
210#2029—431no—
211#1614—431no—
212#1602—431no—
213#1352—431no—
214#1351—431no—
215#1316—431no—
216C2×C43—21no—
217C2×C43—21no—
218C2×C43—41no—
219C2×C43—44no—
220C2×C43—41no—
221C2×C43#160211yescharacteristic
222C2×C43#219611yescharacteristic
223C2×C43#219711yescharacteristic
224#543—431no—
225C2×C22⋊Q8—21no—
226C22×C22⋊C4—21no—
227#484—861no—
228#451—861no—
229#399C2×D4311yescharacteristic
230#396—21no—
231#393C2×D4311yescharacteristic
232#385—21no—
233#385—21no—
234#380—21no—
235#379—861no—
236#379C2×D4311yescharacteristic
237#342—431no—
238#342—861no—
239#328—861no—
240#328—861no—
241#323—431no—
242#323—431no—
243C43#1221411yescharacteristic, complemented, Sylow
244C25C22⋊D4311yescharacteristic
245C22×Q8C22⋊D4311yescharacteristic
246C23×C4—21no—
247C23×C4—21no—
248C2×Q16—1721no—
249C22⋊Q8—44no—
250C22⋊Q8—861no—
251C22⋊Q8—861no—
252C22⋊Q8—1721no—
253C22⋊Q8—1721no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4C22⋊D4311yescharacteristic
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—44no—
266C2×C22⋊C4—861no—
267C2×C22⋊C4—861no—
268C2×C22⋊C4—1721no—
269C2×C22⋊C4—1721no—
270C2×C22⋊C4C22⋊D4311yescharacteristic
271C2×C22⋊C4C22×D4311yescharacteristic
272#107—1721no—
273#103—1721no—
274#103—1721no—
275C22⋊C8—861no—
276C22⋊C8—861no—
277#95—21no—
278#95—21no—
279#95C22⋊D4311yescharacteristic
280#95C22⋊D4311yescharacteristic
281C24—21no—
282C24—21no—
283C24—42no—
284C24—41no—
285C24—42no—
286C24—41no—
287C24#1062188512yescomplemented
288C24C2×C22⋊D4311yescharacteristic
289C2×Q8—42no—
290C2×Q8—41no—
291C2×Q8—861no—
292C2×Q8—861no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—81no—
303C22×C4—81no—
304C22×C4—861no—
305C22×C4—861no—
306C22×C4—1721no—
307C22×C4C2×C22⋊D4311yescharacteristic
308C22×C4C2×C22⋊D4311yescharacteristic
309Q16—3442no—
310C2×C8—1721no—
311C2×C8—1721no—
312C4⋊C4—41no—
313C4⋊C4—42no—
314C4⋊C4—42no—
315C4⋊C4—42no—
316C4⋊C4—81no—
317C4⋊C4—861no—
318C4⋊C4—861no—
319C4⋊C4—1721no—
320C4⋊C4—1721no—
321C22⋊C4—24no—
322C22⋊C4—41no—
323C22⋊C4—42no—
324C22⋊C4—42no—
325C22⋊C4—42no—
326C22⋊C4—42no—
327C22⋊C4—42no—
328C22⋊C4—41no—
329C22⋊C4—3442no—
330C22⋊C4—3442no—
331C22⋊C4—1721no—
332C22⋊C4—1721no—
333C22⋊C4—1721no—
334C22⋊C4—1721no—
335C23—22no—
336C23—22no—
337C23—22no—
338C23—21no—
339C23—21no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—44no—
344C23—42no—
345C23—41no—
346C23—44no—
347C23—41no—
348C23—41no—
349C23—42no—
350C23—42no—
351C23—81no—
352C23—84no—
353C23—81no—
354C23—81no—
355C23#1306329411yescharacteristic
356C23C2×#1062188511yescharacteristic
357C23#1306335611yescharacteristic
358Q8—42no—
359Q8—81no—
360Q8—3441no—
361Q8—3441no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—84no—
382C2×C4—84no—
383C2×C4—3441no—
384C2×C4—3441no—
385C2×C4—3441no—
386C2×C4—3441no—
387C2×C4—3441no—
388C2×C4—1721no—
389C2×C4—1721no—
390C8—3441no—
391C8—3441no—
392C22—21no—
393C22—21no—
394C22—24no—
395C22—21no—
396C22—21no—
397C22—41no—
398C22—41no—
399C22—42no—
400C22—42no—
401C22—42no—
402C22—44no—
403C22—42no—
404C22—41no—
405C22—41no—
406C22—42no—
407C22—42no—
408C22—81no—
409C22—82no—
410C22—82no—
411C22—82no—
412C22#1458305511yescharacteristic
413C22#1458307711yescharacteristic
414C22#1458308611yescharacteristic
415C4—42no—
416C4—41no—
417C4—42no—
418C4—41no—
419C4—81no—
420C4—81no—
421C4—81no—
422C4—3441no—
423C4—3441no—
424C4—6881no—
425C2—21no—
426C2—21no—
427C2—41no—
428C2—44no—
429C2—41no—
430C2#1913355211yescharacteristic
431C2#1913657911yescharacteristic
432C2#1913658511yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#2437C2
socleC22×C43B(4,𝔽2)
prime radicalC25×C43D4
hypercenter#2437D43
hypocenterC43#12214
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2437

Complements

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

NH ≅ G/Ntype
2. #19133619C2semidirect
3. #19133551C2semidirect
4. #19132619C2semidirect
5. #19132616C2semidirect
70. C24×C43Q16semidirect
243. C43#12214semidirect
287. C24#10621885semidirect

Maximal subgroups

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

subgroupindex
#191357592
#191336192
#191335512
#191326192
#191326162
#191325232
C43×#24372
#1221443