Finite Group Databasebeta

← #24994588

Subgroups — #24994588

Order 11008.

478 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 89 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#19143230C211yesmaximal, characteristic
2#19138882C211yesmaximal, characteristic
3#19134676C211yesmaximal, characteristic
4#19132925C211yesmaximal, characteristic
5#19132504C211yesmaximal, characteristic
6#19132504C211yesmaximal, characteristic
7C43×#1463C211yesmaximal, characteristic
8C2×#13063284C2211yescharacteristic
9#14582957—22no—
10#14582957—22no—
11#14582922—21no—
12#14582863C2211yescharacteristic
13#14582863C2211yescharacteristic
14M16×Dic43—21no—
15#14582838—21no—
16#14582829—21no—
17#14582780—21no—
18#14582780—21no—
19#14582772C411yescharacteristic
20#14582772C411yescharacteristic
21#14582762C411yescharacteristic
22#14582762C411yescharacteristic
23#14582762C2211yescharacteristic
24#14582667—21no—
25#14582667—21no—
26#14582625—22no—
27C22×C4⋊C4×C43C2211yescharacteristic
28C43×#407C2211yescharacteristic
29C43×#407C2211yescharacteristic
30C43×#324—22no—
31C2×#10621877—21no—
32C2×#10621877—21no—
33#13063284—21no—
34#13063284—21no—
35#13063284—21no—
36#13063284—21no—
37C2×C4⋊Dic43D411yescharacteristic
38C2×C4⋊Dic43D411yescharacteristic
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×C22⋊Dic43C2×C411yescharacteristic
42C2×C22⋊Dic43C2×C411yescharacteristic
43C2×C22⋊Dic43C2×C411yescharacteristic
44C2×C22⋊Dic43C2×C411yescharacteristic
45C2×C4×Dic43D411yescharacteristic
46C2×C4×Dic43D411yescharacteristic
47Dic43⋊C8—24no—
48C22⋊(C43⋊C8)—21no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)D412yes—
52#13063235—22no—
53C8×Dic43—22no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C23×C4×C43C2×C411yescharacteristic
63C23×C4×C43C2×C411yescharacteristic
64C23×C4×C43C2311yescharacteristic
65C2×M16×C43—21no—
66C2×M16×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C22⋊C8×C43—21no—
74C22⋊C8×C43—21no—
75C22⋊C8×C43—21no—
76C22⋊C8×C43D412yes—
77C24×C43C22×C411yescharacteristic
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43—42no—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43#4111yescharacteristic
94C22×C4×C43#4111yescharacteristic
95C22×Dic43—21no—
96C22×Dic43—21no—
97C22×Dic43C22⋊C411yescharacteristic
98C22×Dic43C22⋊C411yescharacteristic
99C22×Dic43C22⋊C411yescharacteristic
100C22×Dic43C22⋊C411yescharacteristic
101M16×C43—41no—
102M16×C43—41no—
103M16×C43—41no—
104M16×C43—41no—
105C2×C8×C43—22no—
106C2×C8×C43—41no—
107C4⋊C4×C43—41no—
108C4⋊C4×C43—41no—
109C4⋊C4×C43—41no—
110C4⋊C4×C43—41no—
111C22⋊Dic43—21no—
112C22⋊Dic43—21no—
113C22⋊Dic43—21no—
114C22⋊Dic43—21no—
115C22⋊Dic43—41no—
116C22⋊Dic43—41no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121Dic43⋊C4—42no—
122Dic43⋊C4—42no—
123C4×Dic43—21no—
124C4×Dic43—21no—
125C4×Dic43—21no—
126C4×Dic43—21no—
127#10621877—41no—
128#10621877—41no—
129#10621877—41no—
130#10621877—41no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8—41no—
133C23×C43—21no—
134C23×C43—21no—
135C23×C43—41no—
136C23×C43—41no—
137C23×C43C2×C22⋊C411yescharacteristic
138C23×C43C4×D411yescharacteristic
139C23×C43C4×D411yescharacteristic
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—22no—
145C2×C4×C43—22no—
146C2×C4×C43—22no—
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—81no—
159C2×C4×C43—81no—
160C2×C4×C43#12011yescharacteristic
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43#12111yescharacteristic
163C2×C4×C43#12311yescharacteristic
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43—41no—
178C8×C43—42no—
179C8×C43—81no—
180C43⋊C8—42no—
181C43⋊C8—81no—
182#9514—431nomaximal, Sylow
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—42no—
192C22×C43—42no—
193C22×C43#38611yescharacteristic
194C22×C43#41011yescharacteristic
195C22×C43#41011yescharacteristic
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—42no—
201C4×C43—81no—
202Dic43—41no—
203Dic43—41no—
204Dic43—41no—
205Dic43—41no—
206Dic43—81no—
207Dic43—81no—
208#2921—431no—
209#2484—431no—
210#1822—431no—
211#1463—431no—
212#1463D4311yescharacteristic
213#1306—431no—
214#1306—431no—
215C2×C43—21no—
216C2×C43—21no—
217C2×C43—41no—
218C2×C43—41no—
219C2×C43#189111yescharacteristic
220C2×C43#189911yescharacteristic
221C2×C43#191511yescharacteristic
222C2×#117—431no—
223C22×C4⋊C4C2×D4311yescharacteristic
224#433—862no—
225#433—862no—
226#423—861no—
227#407—431no—
228#407—431no—
229#407C2×D4311yescharacteristic
230#407C2×D4311yescharacteristic
231C4×M16—861no—
232#400—861no—
233#398—861no—
234#387—861no—
235#387—861no—
236#385—431no—
237#385—431no—
238#381—431no—
239#381—431no—
240#381—431no—
241#343—861no—
242#343—861no—
243#324—22no—
244#324—862no—
245C43#951411yescharacteristic, complemented, Sylow
246C23×C4C4×D4311yescharacteristic
247C23×C4C4×D4311yescharacteristic
248C23×C4C22×D4311yescharacteristic
249C2×M16—21no—
250C2×M16—21no—
251C2×M16—861no—
252C2×M16—861no—
253#117—861no—
254#117—861no—
255#117—861no—
256#117—861no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—431no—
264C2×C4⋊C4—431no—
265C2×C4⋊C4—861no—
266C2×C4⋊C4—861no—
267C2×C22⋊C4—431no—
268C2×C22⋊C4—431no—
269C2×C22⋊C4—431no—
270C2×C22⋊C4—431no—
271C2×C42—431no—
272C2×C42—431no—
273C4⋊C8—864no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—432no—
278C22⋊C8—861no—
279C22⋊C8—861no—
280C22⋊C8—861no—
281C22⋊C8C22⋊D4312yes—
282#97—862no—
283C4×C8—862no—
284#95—861no—
285#95—861no—
286#95—861no—
287#95—861no—
288#95—861no—
289#95—861no—
290#95—861no—
291#95—861no—
292C24C2×C4×D4311yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—42no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—431no—
305C22×C4—431no—
306C22×C4—431no—
307C22×C4—431no—
308C22×C4—861no—
309C22×C4—861no—
310C22×C4#1062189811yescharacteristic
311C22×C4D4×D4311yescharacteristic
312C22×C4D4×D4311yescharacteristic
313C22×C4D4×D4311yescharacteristic
314C22×C4#1062190011yescharacteristic
315C22×C4C2×C22⋊D4311yescharacteristic
316M16—41no—
317M16—41no—
318M16—41no—
319M16—41no—
320M16—1721no—
321M16—1721no—
322M16—1721no—
323M16—1721no—
324C2×C8—22no—
325C2×C8—41no—
326C2×C8—862no—
327C2×C8—1721no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—861no—
333C4⋊C4—861no—
334C4⋊C4—861no—
335C4⋊C4—861no—
336C4⋊C4—1722no—
337C4⋊C4—1722no—
338C22⋊C4—861no—
339C22⋊C4—861no—
340C22⋊C4—861no—
341C22⋊C4—861no—
342C22⋊C4—1721no—
343C22⋊C4—1721no—
344C42—861no—
345C42—861no—
346C42—861no—
347C42—861no—
348C23—21no—
349C23—21no—
350C23—41no—
351C23—41no—
352C23C22⋊C4×D4311yescharacteristic
353C23(C22⋊D43)⋊C411yescharacteristic
354C23C4×C22⋊D4311yescharacteristic
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—861no—
376C2×C4—861no—
377C2×C4—861no—
378C2×C4—861no—
379C2×C4—1721no—
380C2×C4—1721no—
381C2×C4—1721no—
382C2×C4—1721no—
383C2×C4—1721no—
384C2×C4—1721no—
385C2×C4—1721no—
386C2×C4—1721no—
387C2×C4—1721no—
388C2×C4—1721no—
389C2×C4#1306329311yescharacteristic
390C2×C4#1306329611yescharacteristic
391C2×C4#1306329811yescharacteristic
392C2×C4#1306330711yescharacteristic
393C8—42no—
394C8—81no—
395C8—3441no—
396C8—1722no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—42no—
406C22—42no—
407C22#1458277511yescharacteristic
408C22#1458287111yescharacteristic
409C22#1458287111yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—42no—
415C4—81no—
416C4—3441no—
417C4—3441no—
418C4—1721no—
419C4—1721no—
420C4—1721no—
421C4—1721no—
422C2—21no—
423C2—21no—
424C2—41no—
425C2—41no—
426C2#1913501011yescharacteristic
427C2#1913505011yescharacteristic
428C2#1913514411yescharacteristic
subgroupG/H
centerC22#14582775
commutator, prime radicalC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1463C2
socleC22×C43#386
cosocleC23×C4×C43C23
hypercenter#1463D43
hypocenterC43#9514
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
245. C43#9514semidirect

Maximal subgroups

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

subgroupindex
#191432302
#191388822
#191346762
#191329252
#191325042
C43×#14632
#951443