Finite Group Databasebeta

← #25007290

Subgroups — #25007290

Order 11008.

448 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 69 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#19140336C211yesmaximal, characteristic
2#19134674C211yesmaximal, characteristic, complemented
3#19132923C211yesmaximal, characteristic, complemented
4#19132602C211yesmaximal, characteristic, complemented
5#19132600C211yesmaximal, characteristic, complemented
6#19132598C211yesmaximal, characteristic, complemented
7C43×#1345C211yesmaximal, characteristic, complemented
8C2×#13063307—21no—
9C2×#13063296C411yescharacteristic
10C2×C4⋊C4×D43C2211yescharacteristic
11#14582862—21no—
12#14582861—21no—
13#14582831C411yescharacteristic
14#14582829C2211yescharacteristic
15#14582822—21no—
16#14582822—21no—
17#14582813C411yescharacteristic
18#14582775—21no—
19#14582758C411yescharacteristic
20#14582668C2211yescharacteristic
21#14582667—21no—
22#14582625C2211yescharacteristic
23#14582624—21no—
24C43×#394C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×C22⋊D43—21no—
28C22×C4×D43C2×C411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C2×#10621877—21no—
32C2×#10621872—41no—
33#13063307—42no—
34#13063307—42no—
35#13063296—41no—
36#13063296—41no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43C2×C411yescharacteristic
39C2×C4⋊Dic43D411yescharacteristic
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4C2×C411yescharacteristic
43C2×Dic43⋊C4D411yescharacteristic
44C4⋊C4×D43—41no—
45C4⋊C4×D43—41no—
46C2×C22⋊Dic43—21no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43—21no—
49C2×(C2×D43)⋊C4—21no—
50C22⋊(C43⋊C8)—21no—
51(C2×D43)⋊C8—41no—
52(C2×D43)⋊C8—41no—
53(C2×D43)⋊C8—41no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95C2×C411yescharacteristic
57C22×D4×C43C2×C411yescharacteristic
58C2×M16×C43—21no—
59C2×C4⋊C4×C43C2311yescharacteristic
60C2×C22⋊C4×C43—21no—
61C2×C22⋊C4×C43—21no—
62C22⋊C8×C43—21no—
63#95×C43C2×C411yescharacteristic
64C24×C43—21no—
65C23×D43C22⋊C411yescharacteristic
66C2×D4×C43—41no—
67C2×D4×C43—81no—
68C22×C4×C43—21no—
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C2×C22⋊D43—42no—
73C2×C22⋊D43—42no—
74C2×C22⋊D43—41no—
75C2×C22⋊D43—41no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43C22⋊C411yescharacteristic
79C22×Dic43C22⋊C411yescharacteristic
80C22×Dic43C22⋊C411yescharacteristic
81C2×C4×D43—21no—
82C2×C4×D43—21no—
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—41no—
90C2×C4×D43—81no—
91C2×C4×D43—81no—
92M16×C43—41no—
93M16×C43—41no—
94C2×C8×C43—41no—
95C2×C8×C43—41no—
96C4⋊C4×C43—41no—
97C22⋊C4×C43—41no—
98C22⋊C4×C43—41no—
99C22⋊C4×C43—81no—
100C22⋊Dic43—42no—
101C22⋊Dic43—42no—
102C22⋊Dic43—81no—
103(C2×D43)⋊C4—42no—
104C4⋊Dic43—41no—
105C4⋊Dic43—42no—
106C4⋊Dic43—41no—
107Dic43⋊C4—41no—
108Dic43⋊C4—41no—
109Dic43⋊C4—41no—
110Dic43⋊C4—41no—
111Dic43⋊C4—81no—
112#10621877—41no—
113#10621877—41no—
114C2×C43⋊C8—41no—
115C2×C43⋊C8—41no—
116#10621872—82no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43—41no—
120C23×C43—41no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43C2×C22⋊C411yescharacteristic
125C22×D43—21no—
126C22×D43—21no—
127C22×D43—41no—
128C22×D43—41no—
129C22×D43#9911yescharacteristic
130C22×D43#9911yescharacteristic
131D4×C43—82no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
143C22⋊D43—82no—
144C22⋊D43—82no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C4×D43—41no—
159C4×D43—41no—
160C4×D43—41no—
161C4×D43—41no—
162C4×D43—42no—
163C4×D43—81no—
164C4×D43—81no—
165C4×D43—81no—
166C8×C43—81no—
167C8×C43—81no—
168C43⋊C8—81no—
169C43⋊C8—81no—
170#11805—431nomaximal, Sylow
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—81no—
174C22×C43—81no—
175C22×C43—81no—
176C22×C43—81no—
177C22×C43—81no—
178C22×C43—81no—
179C22×C43—81no—
180C22×C43C2×#9911yescharacteristic
181C22×C43#41811yescharacteristic
182C22×C43#42111yescharacteristic
183C2×D43—21no—
184C2×D43—21no—
185C2×D43—21no—
186C2×D43—21no—
187C2×D43—21no—
188C2×D43—21no—
189C2×D43—42no—
190C2×D43—42no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—41no—
194C4×C43—41no—
195C4×C43—81no—
196Dic43—41no—
197Dic43—41no—
198Dic43—41no—
199Dic43—81no—
200Dic43—81no—
201#2618—431no—
202#1821—431no—
203#1463—431no—
204#1346—431no—
205#1346—431no—
206#1345—431no—
207#1345D4311yescharacteristic, complemented
208C2×C43—21no—
209C2×C43—21no—
210C2×C43—161no—
211C2×C43#151011yescharacteristic
212C2×C43#212111yescharacteristic
213C2×C43#213311yescharacteristic
214D43—41no—
215D43—41no—
216C2×#123—861no—
217C2×#121—431no—
218C22×C4⋊C4—431no—
219#407—861no—
220#407—861no—
221#398—431no—
222#398—431no—
223#396—861no—
224#396—861no—
225#394—431no—
226#394C2×D4311yescharacteristic
227#386—861no—
228#380—431no—
229#343—431no—
230#343—861no—
231#343C2×D4311yescharacteristic
232#324—431no—
233#324—861no—
234#324C2×D4311yescharacteristic
235C43#1180511yescharacteristic, complemented, Sylow
236C22×D4—861no—
237C22×D4C4×D4311yescharacteristic
238C23×C4—431no—
239C23×C4—431no—
240C23×C4—431no—
241C2×M16—21no—
242C2×M16—861no—
243C2×M16—1721no—
244#123—1722no—
245#123—1722no—
246#121—1721no—
247#121—1721no—
248C2×C4⋊C4—431no—
249C2×C4⋊C4—431no—
250C2×C4⋊C4—431no—
251C2×C4⋊C4—431no—
252C2×C4⋊C4—861no—
253C2×C4⋊C4—861no—
254C2×C4⋊C4—861no—
255C2×C4⋊C4—1721no—
256C2×C4⋊C4—1721no—
257C2×C4⋊C4C22×D4311yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—861no—
261C2×C22⋊C4—861no—
262C2×C22⋊C4—861no—
263C2×C22⋊C4—861no—
264C22⋊C8—21no—
265C22⋊C8—861no—
266C22⋊C8—1721no—
267C22⋊C8—1721no—
268C22⋊C8—1721no—
269#95—431no—
270#95—861no—
271#95—861no—
272#95C4×D4311yescharacteristic
273C24—21no—
274C24—431no—
275C2×D4—41no—
276C2×D4—81no—
277C2×D4—1721no—
278C2×D4—1721no—
279C2×D4—1722no—
280C2×D4—1722no—
281C22×C4—21no—
282C22×C4—431no—
283C22×C4—431no—
284C22×C4—431no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4—861no—
292C22×C4—861no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—3441no—
296C22×C4—3441no—
297C22×C4—1721no—
298C22×C4C2×C4×D4311yescharacteristic
299C22×C4D4×D4311yescharacteristic
300C22×C4D4×D4311yescharacteristic
301M16—41no—
302M16—41no—
303M16—3442no—
304M16—1721no—
305M16—1721no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—1721no—
309C2×C8—1721no—
310C4⋊C4—41no—
311C4⋊C4—3441no—
312C4⋊C4—1721no—
313C4⋊C4—1721no—
314C4⋊C4—1721no—
315C4⋊C4—1721no—
316C4⋊C4—1722no—
317C4⋊C4—1721no—
318C4⋊C4—1721no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—81no—
322C22⋊C4—3441no—
323C22⋊C4—1722no—
324C22⋊C4—1722no—
325C22⋊C4—1722no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—431no—
334C23—431no—
335C23—861no—
336C23—861no—
337C23—1721no—
338C23—1721no—
339C23C22⋊C4×D4311yescharacteristic
340D4—82no—
341D4—3442no—
342D4—3442no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—3441no—
358C2×C4—3441no—
359C2×C4—3441no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4—1721no—
363C2×C4—1721no—
364C2×C4—1722no—
365C2×C4—1721no—
366C2×C4—1721no—
367C2×C4—1721no—
368C2×C4—1721no—
369C2×C4—1721no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4—1721no—
373C2×C4#1306334911yescharacteristic
374C2×C4#1306335211yescharacteristic
375C8—81no—
376C8—81no—
377C8—3441no—
378C8—3441no—
379C22—21no—
380C22—21no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—861no—
389C22—861no—
390C22—861no—
391C22—861no—
392C22—861no—
393C22—861no—
394C22—1722no—
395C22—1722no—
396C22#99×D4311yescharacteristic
397C22#1458290211yescharacteristic
398C22#1458291411yescharacteristic
399C4—21no—
400C4—21no—
401C4—41no—
402C4—41no—
403C4—81no—
404C4—3441no—
405C4—3441no—
406C4—1721no—
407C4—1721no—
408C4—1721no—
409C2—21no—
410C2—21no—
411C2—161no—
412C2—1721no—
413C2—1721no—
414C2#1913312211yescharacteristic
415C2#1913623811yescharacteristic
416C2#1913628111yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1345C2
socleC22×C43C2×#99
prime radicalC2×#13063296C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1345D43
hypocenterC43#11805
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1345

Complements

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

NH ≅ G/Ntype
2. #19134674C2semidirect
3. #19132923C2semidirect
4. #19132602C2semidirect
5. #19132600C2semidirect
6. #19132598C2semidirect
7. C43×#1345C2semidirect
207. #1345D43semidirect
235. C43#11805semidirect

Maximal subgroups

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

subgroupindex
#191403362
#191346742
#191329232
#191326022
#191326002
#191325982
C43×#13452
#1180543