Finite Group Databasebeta

← #25009701

Subgroups — #25009701

Order 11008.

468 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 59 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#19133585C211yesmaximal, characteristic, complemented
3#19133551C211yesmaximal, characteristic, complemented
4#19132616C211yesmaximal, characteristic, complemented
5#19132595C211yesmaximal, characteristic, complemented
6#19132523C211yesmaximal, characteristic
7C43×#2736C211yesmaximal, characteristic
8#14583525C2211yescharacteristic
9#14583229—21no—
10#14583055—21no—
11#14582755—21no—
12#14582666C2211yescharacteristic
13#14582665—21no—
14#14582635—21no—
15#14582635—21no—
16#14582623C2211yescharacteristic
17#14582623C2211yescharacteristic
18C43×#397—21no—
19C43×#397C2211yescharacteristic
20C43×#393—21no—
21C43×#393C2211yescharacteristic
22C43×#388—21no—
23C43×#388—21no—
24C43×#388—21no—
25C43×#379—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#13063256—41no—
37#13063249—41no—
38#13063248—41no—
39C22⋊(C43⋊C8)—21no—
40C22⋊(C43⋊C8)—21no—
41C25×C43D411yescharacteristic
42C22×Q8×C43D411yescharacteristic
43C2×C4⋊C4×C43—21no—
44C2×C4⋊C4×C43D411yescharacteristic
45C2×C22⋊C4×C43—21no—
46C2×C22⋊C4×C43—21no—
47C2×C22⋊C4×C43—21no—
48C2×C22⋊C4×C43—21no—
49C2×C22⋊C4×C43—21no—
50C2×C22⋊C4×C43—21no—
51C2×C22⋊C4×C43—21no—
52C2×C22⋊C4×C43—21no—
53C2×C22⋊C4×C43D411yescharacteristic
54C2×C22⋊C4×C43C2311yescharacteristic
55C2×C42×C43—21no—
56#95×C43—21no—
57#95×C43—21no—
58#95×C43—21no—
59#95×C43—21no—
60#95×C43D411yescharacteristic
61#95×C43D411yescharacteristic
62C24×C43—21no—
63C24×C43—21no—
64C24×C43—21no—
65C24×C43—41no—
66C24×C43—41no—
67C24×C43—42no—
68C24×C43—81no—
69C24×C43C2×D411yescharacteristic
70C2×Q8×C43—41no—
71C2×Q8×C43—81no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—41no—
82C2×Dic86—21no—
83C2×Dic86—21no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—81no—
86C22⋊C4×C43—41no—
87C22⋊C4×C43—41no—
88C22⋊C4×C43—42no—
89C22⋊C4×C43—42no—
90C22⋊C4×C43—41no—
91C22⋊C4×C43—41no—
92C22⋊C4×C43—81no—
93C22⋊C4×C43—81no—
94C22⋊C4×C43—81no—
95C22⋊C4×C43—81no—
96C22⋊C4×C43—81no—
97C42×C43—81no—
98C22⋊Dic43—41no—
99C22⋊Dic43—41no—
100C22⋊Dic43—41no—
101C22⋊Dic43—41no—
102C22⋊Dic43—82no—
103C22⋊Dic43—82no—
104#10621885—82no—
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107Dic43⋊C4—41no—
108Dic43⋊C4—41no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—41no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—22no—
114C23×C43—41no—
115C23×C43—41no—
116C23×C43—41no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43—42no—
120C23×C43—42no—
121C23×C43—42no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43—81no—
126C23×C43—82no—
127C23×C43—81no—
128C23×C43—82no—
129C23×C43—84no—
130C23×C43—81no—
131C23×C43#12011yescharacteristic
132C23×C43#13511yescharacteristic
133C23×C43#13711yescharacteristic
134Q8×C43—42no—
135Q8×C43—81no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
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×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—81no—
158C2×Dic43—81no—
159C2×Dic43—81no—
160C2×Dic43—81no—
161C2×Dic43—81no—
162Dic86—81no—
163Dic86—81no—
164C43⋊C8—81no—
165C43⋊C8—81no—
166#12264—431nomaximal, Sylow
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43—42no—
174C22×C43—42no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43—44no—
178C22×C43—42no—
179C22×C43—81no—
180C22×C43—81no—
181C22×C43—81no—
182C22×C43—82no—
183C22×C43—82no—
184C22×C43—82no—
185C22×C43—81no—
186C22×C43—81no—
187C22×C43#45211yescharacteristic
188C22×C43#45511yescharacteristic
189C22×C43B(4,𝔽2)11yescharacteristic
190C4×C43—41no—
191C4×C43—41no—
192C4×C43—81no—
193C4×C43—81no—
194C4×C43—81no—
195C4×C43—81no—
196C4×C43—81no—
197Dic43—81no—
198Dic43—81no—
199Dic43—161no—
200#2736D4311yescharacteristic
201#2029—431no—
202#1608—431no—
203#1602—431no—
204#1351—431no—
205#1344—431no—
206#1316—431no—
207C2×C43—21no—
208C2×C43—21no—
209C2×C43—41no—
210C2×C43—41no—
211C2×C43—82no—
212C2×C43#160611yescharacteristic
213C2×C43#219711yescharacteristic
214C2×C43#219911yescharacteristic
215#543—431no—
216#483—861no—
217#451—861no—
218#397—21no—
219#397C2×D4311yescharacteristic
220#393—21no—
221#393C2×D4311yescharacteristic
222#388—21no—
223#388—21no—
224#388—21no—
225#379—21no—
226#379—861no—
227#379C2×D4311yescharacteristic
228#342—431no—
229#342—861no—
230#328—861no—
231#328—861no—
232#323—431no—
233#323—431no—
234C43#1226411yescharacteristic, complemented, Sylow
235C25C22⋊D4311yescharacteristic
236C22×Q8C22⋊D4311yescharacteristic
237C2×Q16—1721no—
238C22⋊Q8—861no—
239C22⋊Q8—861no—
240C22⋊Q8—1721no—
241C22⋊Q8—1721no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4C22⋊D4311yescharacteristic
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—861no—
253C2×C22⋊C4—861no—
254C2×C22⋊C4—1721no—
255C2×C22⋊C4—1721no—
256C2×C22⋊C4C22⋊D4311yescharacteristic
257C2×C22⋊C4C22×D4311yescharacteristic
258C2×C42—21no—
259#106—1721no—
260#103—1721no—
261#103—1721no—
262C22⋊C8—861no—
263C22⋊C8—861no—
264#95—21no—
265#95—21no—
266#95—21no—
267#95—21no—
268#95C22⋊D4311yescharacteristic
269#95C22⋊D4311yescharacteristic
270C24—21no—
271C24—21no—
272C24—21no—
273C24—41no—
274C24—41no—
275C24—42no—
276C24—81no—
277C24C2×C22⋊D4311yescharacteristic
278C2×Q8—41no—
279C2×Q8—81no—
280C2×Q8—861no—
281C2×Q8—861no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4—1721no—
290C22×C4C2×C22⋊D4311yescharacteristic
291C22×C4C2×C22⋊D4311yescharacteristic
292Q16—3442no—
293C2×C8—1721no—
294C2×C8—1721no—
295C4⋊C4—41no—
296C4⋊C4—81no—
297C4⋊C4—861no—
298C4⋊C4—861no—
299C4⋊C4—1721no—
300C4⋊C4—1721no—
301C22⋊C4—41no—
302C22⋊C4—42no—
303C22⋊C4—42no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—81no—
308C22⋊C4—81no—
309C22⋊C4—81no—
310C22⋊C4—81no—
311C22⋊C4—81no—
312C22⋊C4—3442no—
313C22⋊C4—3442no—
314C22⋊C4—1721no—
315C22⋊C4—1721no—
316C22⋊C4—1721no—
317C22⋊C4—1721no—
318C42—81no—
319C23—21no—
320C23—21no—
321C23—22no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—42no—
328C23—42no—
329C23—42no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—81no—
334C23—82no—
335C23—81no—
336C23—82no—
337C23—84no—
338C23—81no—
339C23#1306329411yescharacteristic
340C23#1306334511yescharacteristic
341C23#1306335511yescharacteristic
342Q8—42no—
343Q8—81no—
344Q8—3441no—
345Q8—3441no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—3441no—
366C2×C4—3441no—
367C2×C4—3441no—
368C2×C4—3441no—
369C2×C4—3441no—
370C2×C4—1721no—
371C2×C4—1721no—
372C8—3441no—
373C8—3441no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—42no—
381C22—42no—
382C22—41no—
383C22—41no—
384C22—44no—
385C22—42no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—82no—
390C22—82no—
391C22—82no—
392C22—81no—
393C22—81no—
394C22#1458306111yescharacteristic
395C22#1458307711yescharacteristic
396C22#1458308611yescharacteristic
397C4—41no—
398C4—41no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4—81no—
403C4—81no—
404C4—3441no—
405C4—3441no—
406C4—6881no—
407C2—21no—
408C2—21no—
409C2—41no—
410C2—41no—
411C2—82no—
412C2#1913357511yescharacteristic
413C2#1913658511yescharacteristic
414C2#1913659611yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#2736C2
socleC22×C43B(4,𝔽2)
prime radicalC25×C43D4
hypercenter#2736D43
hypocenterC43#12264
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2736

Complements

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

NH ≅ G/Ntype
2. #19133585C2semidirect
3. #19133551C2semidirect
4. #19132616C2semidirect
5. #19132595C2semidirect
234. C43#12264semidirect

Maximal subgroups

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

subgroupindex
#191357592
#191335852
#191335512
#191326162
#191325952
#191325232
C43×#27362
#1226443