Finite Group Databasebeta

← #25006150

Subgroups — #25006150

Order 11008.

496 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 71 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#19139065C211yesmaximal, characteristic
2#19132923C211yesmaximal, characteristic, complemented
3#324×D43C211yesmaximal, characteristic, complemented
4#19132540C211yesmaximal, characteristic, complemented
5#19132540C211yesmaximal, characteristic, complemented
6#19132527C211yesmaximal, characteristic, complemented
7C43×#1318C211yesmaximal, characteristic, complemented
8C2×#13063307—21no—
9C2×#13063307—21no—
10C2×#13063296C411yescharacteristic
11C2×C4⋊C4×D43C2211yescharacteristic
12#14582861—21no—
13C22⋊C8×D43—21no—
14#14582835—21no—
15#14582835—21no—
16#14582802C411yescharacteristic
17#14582769C411yescharacteristic
18#14582768C2211yescharacteristic
19C4×(C2×D43)⋊C4C411yescharacteristic
20#14582625C2211yescharacteristic
21#14582625C2211yescharacteristic
22#14582624—21no—
23#14582624—21no—
24C43×#390C2211yescharacteristic
25C43×#324C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×C22⋊D43—21no—
28C22×C4×D43C2×C411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C2×#10621872—41no—
32C2×C8×D43—41no—
33#13063307—44no—
34#13063307—44no—
35#13063296—41no—
36#13063296—41no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43C2×C411yescharacteristic
40C2×C4⋊Dic43C2×C411yescharacteristic
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4D411yescharacteristic
44C2×Dic43⋊C4D411yescharacteristic
45C4⋊C4×D43—41no—
46C4⋊C4×D43—41no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43—21no—
49C2×C22⋊Dic43—21no—
50C2×(C2×D43)⋊C4—21no—
51C2×C4×Dic43C2×C411yescharacteristic
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54(C2×D43)⋊C8—41no—
55(C2×D43)⋊C8—41no—
56C43⋊#95—21no—
57C22×D4×C43C2×C411yescharacteristic
58C2×C4⋊C4×C43C2311yescharacteristic
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43—21no—
61C2×C42×C43C2×C411yescharacteristic
62C22⋊C8×C43—21no—
63C22⋊C8×C43—21no—
64C24×C43—21no—
65C23×D43C22⋊C411yescharacteristic
66C2×D4×C43—21no—
67C2×D4×C43—21no—
68C2×D4×C43—41no—
69C2×D4×C43—41no—
70C22×C4×C43—21no—
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C2×C22⋊D43—42no—
75C2×C22⋊D43—42no—
76C2×C22⋊D43—41no—
77C2×C22⋊D43—41no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43C22⋊C411yescharacteristic
81C22×Dic43C22⋊C411yescharacteristic
82C22×Dic43C22⋊C411yescharacteristic
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86C2×C4×D43—21no—
87C2×C4×D43—21no—
88C2×C4×D43—21no—
89C2×C4×D43—21no—
90C2×C4×D43—21no—
91C2×C4×D43—41no—
92C2×C4×D43—42no—
93C2×C4×D43—42no—
94C2×C8×C43—41no—
95C2×C8×C43—41no—
96C4⋊C4×C43—41no—
97C22⋊C4×C43—42no—
98C22⋊C4×C43—42no—
99C42×C43—41no—
100C22⋊Dic43—42no—
101C22⋊Dic43—42no—
102C22⋊Dic43—42no—
103(C2×D43)⋊C4—24no—
104C4⋊Dic43—41no—
105C4⋊Dic43—42no—
106C4⋊Dic43—42no—
107C4⋊Dic43—41no—
108Dic43⋊C4—41no—
109Dic43⋊C4—41no—
110Dic43⋊C4—42no—
111Dic43⋊C4—42no—
112C4×Dic43—21no—
113C4×Dic43—21no—
114C2×C43⋊C8—41no—
115C2×C43⋊C8—41no—
116#10621872—82no—
117C8×D43—82no—
118C23×C43—41no—
119C23×C43—41no—
120C23×C43—41no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43C2×C22⋊C411yescharacteristic
126C22×D43—21no—
127C22×D43—21no—
128C22×D43—22no—
129C22×D43—41no—
130C22×D43#9911yescharacteristic
131C22×D43#9911yescharacteristic
132D4×C43—81no—
133D4×C43—81no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—22no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43#13111yescharacteristic
144C2×C4×C43#13111yescharacteristic
145C22⋊D43—82no—
146C22⋊D43—82no—
147C2×Dic43—22no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C4×D43—41no—
161C4×D43—41no—
162C4×D43—41no—
163C4×D43—41no—
164C4×D43—42no—
165C4×D43—42no—
166C4×D43—81no—
167C4×D43—81no—
168C8×C43—81no—
169C8×C43—81no—
170C43⋊C8—81no—
171C43⋊C8—81no—
172#11549—431nomaximal, Sylow
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—81no—
176C22×C43—81no—
177C22×C43—81no—
178C22×C43—81no—
179C22×C43—81no—
180C22×C43—81no—
181C22×C43—81no—
182C22×C43#40811yescharacteristic
183C22×C43C2×#9911yescharacteristic
184C22×C43#41311yescharacteristic
185C2×D43—21no—
186C2×D43—21no—
187C2×D43—21no—
188C2×D43—21no—
189C2×D43—21no—
190C2×D43—42no—
191C2×D43—42no—
192C2×D43#35312yes—
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—42no—
196C4×C43—41no—
197C4×C43—41no—
198Dic43—42no—
199Dic43—41no—
200Dic43—41no—
201Dic43—41no—
202Dic43—81no—
203#2501—431no—
204#1463—431no—
205C2×#324—431no—
206#1325—431no—
207#1325—431no—
208#1318—431no—
209#1318D4311yescharacteristic, complemented
210C2×C43—21no—
211C2×C43—21no—
212C2×C43—161no—
213C2×C43#146811yescharacteristic
214C2×C43C2×#35311yescharacteristic
215C2×C43#213311yescharacteristic
216D43—22no—
217D43—41no—
218C2×#123—861no—
219C2×#123—861no—
220C2×#121—431no—
221C22×C4⋊C4—431no—
222#407—861no—
223C2×C22⋊C8—861no—
224#399—861no—
225#399—861no—
226#390—431no—
227#390C2×D4311yescharacteristic
228#384—431no—
229#384—431no—
230C4×C22⋊C4—431no—
231#324—431no—
232#324—431no—
233#324—861no—
234#324—861no—
235#324C2×D4311yescharacteristic
236#324C2×D4311yescharacteristic
237C43#1154911yescharacteristic, complemented, Sylow
238C22×D4—861no—
239C22×D4C4×D4311yescharacteristic
240C23×C4—431no—
241C23×C4—431no—
242C23×C4—431no—
243C2×M16—1721no—
244C22×C8—1721no—
245#123—1724no—
246#123—1724no—
247#121—1721no—
248#121—1721no—
249C2×C4⋊C4—431no—
250C2×C4⋊C4—431no—
251C2×C4⋊C4—431no—
252C2×C4⋊C4—431no—
253C2×C4⋊C4—861no—
254C2×C4⋊C4—861no—
255C2×C4⋊C4—861no—
256C2×C4⋊C4—861no—
257C2×C4⋊C4—1721no—
258C2×C4⋊C4—1721no—
259C2×C4⋊C4C22×D4311yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—861no—
263C2×C22⋊C4—861no—
264C2×C22⋊C4—861no—
265C2×C22⋊C4—861no—
266C2×C42—431no—
267C2×C42C4×D4311yescharacteristic
268C22⋊C8—21no—
269C22⋊C8—21no—
270C22⋊C8—861no—
271C22⋊C8—861no—
272C22⋊C8—1721no—
273C22⋊C8—1721no—
274#95—861no—
275C24—21no—
276C24—431no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—1721no—
282C2×D4—1721no—
283C2×D4—1722no—
284C2×D4—1722no—
285C22×C4—21no—
286C22×C4—431no—
287C22×C4—431no—
288C22×C4—431no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4—861no—
292C22×C4—861no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4—861no—
298C22×C4—861no—
299C22×C4—1721no—
300C22×C4—1722no—
301C22×C4—1722no—
302C22×C4C2×C4×D4311yescharacteristic
303C22×C4D4×D4311yescharacteristic
304C22×C4D4×D4311yescharacteristic
305M16—3442no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—3442no—
309C2×C8—1721no—
310C2×C8—1721no—
311C4⋊C4—41no—
312C4⋊C4—1721no—
313C4⋊C4—1721no—
314C4⋊C4—1721no—
315C4⋊C4—1721no—
316C4⋊C4—1722no—
317C4⋊C4—1722no—
318C4⋊C4—1722no—
319C4⋊C4—1722no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4—864no—
323C22⋊C4—1722no—
324C22⋊C4—1722no—
325C22⋊C4—1722no—
326C42—41no—
327C42—861no—
328C42—861no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—431no—
337C23—431no—
338C23—862no—
339C23—861no—
340C23—861no—
341C23—1721no—
342C23C22⋊C4×D4311yescharacteristic
343D4—81no—
344D4—81no—
345D4—3442no—
346D4—3442no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—862no—
357C2×C4—861no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—861no—
361C2×C4—861no—
362C2×C4—3441no—
363C2×C4—3441no—
364C2×C4—1721no—
365C2×C4—1721no—
366C2×C4—1721no—
367C2×C4—1721no—
368C2×C4—1722no—
369C2×C4—1722no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4—1721no—
373C2×C4—1721no—
374C2×C4—1721no—
375C2×C4—1721no—
376C2×C4—1721no—
377C2×C4#1306333111yescharacteristic
378C2×C4#1306333311yescharacteristic
379C8—81no—
380C8—81no—
381C8—3441no—
382C8—3441no—
383C22—21no—
384C22—21no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—432no—
393C22—861no—
394C22—861no—
395C22—861no—
396C22—861no—
397C22—861no—
398C22—1722no—
399C22—1722no—
400C22#1458286411yescharacteristic
401C22#99×D4311yescharacteristic
402C22#1458288011yescharacteristic
403C4—21no—
404C4—21no—
405C4—42no—
406C4—41no—
407C4—41no—
408C4—3441no—
409C4—1722no—
410C4—1721no—
411C4—1721no—
412C4—1721no—
413C2—21no—
414C2—21no—
415C2—161no—
416C2—862no—
417C2—1721no—
418C2#1913294011yescharacteristic
419C2#353×D4311yescharacteristic
420C2#1913628111yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1318C2
socleC22×C43C2×#99
prime radicalC2×#13063296C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1318D43
hypocenterC43#11549
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1318

Complements

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

NH ≅ G/Ntype
2. #19132923C2semidirect
3. #324×D43C2semidirect
4. #19132540C2semidirect
5. #19132540C2semidirect
6. #19132527C2semidirect
7. C43×#1318C2semidirect
209. #1318D43semidirect
237. C43#11549semidirect

Maximal subgroups

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

subgroupindex
#191390652
#191329232
#324×D432
#191325402
#191325272
C43×#13182
#1154943