Finite Group Databasebeta

← #25070588

Subgroups — #25070588

Order 11008.

912 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148000C211yesmaximal, characteristic
2#19145543C212yesmaximal, complemented
3#19133568C214yesmaximal, complemented
4#19133551C214yesmaximal
5#19133158C212yesmaximal, complemented
6#19132909C211yesmaximal, characteristic
7C43×#2628C211yesmaximal, characteristic
8#14583530—21no—
9#14583530C2212yes—
10#14583527—22no—
11#14583527—22no—
12#14583525—21no—
13#14583525C2212yes—
14#14583456—21no—
15#14583456C2212yes—
16#14583452—24no—
17C2×#13063284—21no—
18#14583278—22no—
19#14583249—22no—
20#14583106—24no—
21#14583055C2218yes—
22#14582952C2212yes—
23#14582635C2218yes—
24#14582625C2212yes—
25#14582623C2212yes—
26C2×C4⋊Q8×C43C2211yescharacteristic
27C2×#117×C43C2211yescharacteristic
28C43×#400—21no—
29C43×#399—21no—
30C43×#395C2212yes—
31C43×#393C2212yes—
32C43×#389—21no—
33C43×#382C2211yescharacteristic
34C43×#380—21no—
35C2×#10621885—28no—
36#13063325—21no—
37#13063325—21no—
38#13063325D412yes—
39#13063325D412yes—
40#13063324—24no—
41#13063324—24no—
42#13063317—22no—
43#13063317—22no—
44#13063316—24no—
45#13063316—24no—
46#13063304—22no—
47#13063304—22no—
48#13063304—22no—
49#13063304C2314yes—
50#13063302—24no—
51#13063302—24no—
52#13063302—24no—
53#13063302—24no—
54C4×Dic86—22no—
55C4×Dic86—22no—
56C4×Dic86—22no—
57C4×Dic86D414yes—
58#13063284—22no—
59#13063284—22no—
60#13063284—22no—
61#13063284—22no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—21no—
64C2×C22⋊Dic43—22no—
65C2×C4×Dic43—22no—
66C4⋊(C43⋊C8)—22no—
67#13063249—28no—
68C22⋊(C43⋊C8)C2314yes—
69C4×C43⋊C8—22no—
70C22×Q8×C43C2312yes—
71C23×C4×C43D411yescharacteristic
72C4⋊Q8×C43—22no—
73C4⋊Q8×C43—22no—
74#117×C43—22no—
75#117×C43—22no—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43—22no—
80C2×C4⋊C4×C43D411yescharacteristic
81C2×C4⋊C4×C43C2311yescharacteristic
82C2×C22⋊C4×C43—22no—
83C2×C22⋊C4×C43D411yescharacteristic
84C2×C22⋊C4×C43C2311yescharacteristic
85C2×C42×C43D411yescharacteristic
86C2×C42×C43C2311yescharacteristic
87#95×C43—22no—
88#95×C43—21no—
89#95×C43—22no—
90#95×C43C2312yes—
91C24×C43C2×D411yescharacteristic
92C2×Q8×C43—24no—
93C2×Q8×C43—82no—
94C22×C4×C43—21no—
95C22×C4×C43—21no—
96C22×C4×C43—22no—
97C22×C4×C43—22no—
98C22×C4×C43—22no—
99C22×C4×C43Q1614yescomplemented
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2411yescharacteristic
106C22×Dic43—22no—
107C22×Dic43—22no—
108C2×Dic86—22no—
109C2×Dic86—22no—
110C2×Dic86—22no—
111C2×Dic86C2×D414yes—
112C4⋊C4×C43—22no—
113C4⋊C4×C43—22no—
114C4⋊C4×C43—42no—
115C4⋊C4×C43—41no—
116C4⋊C4×C43—41no—
117C4⋊C4×C43—42no—
118C4⋊C4×C43—82no—
119C22⋊C4×C43—22no—
120C22⋊C4×C43—22no—
121C22⋊C4×C43—82no—
122C42×C43—21no—
123C42×C43—21no—
124C42×C43C2×D412yes—
125C42×C43C2×D412yes—
126C22⋊Dic43—24no—
127C22⋊Dic43—24no—
128#10621885—88no—
129C4⋊Dic43—22no—
130C4⋊Dic43—22no—
131C4⋊Dic43—22no—
132C4⋊Dic43—22no—
133C4⋊Dic43—22no—
134C4⋊Dic43—22no—
135C4⋊Dic43—22no—
136C4⋊Dic43C2×D414yes—
137Dic43⋊C4—24no—
138Dic43⋊C4—24no—
139Dic43⋊C4—24no—
140Dic43⋊C4—24no—
141C4×Dic43—24no—
142C4×Dic43—24no—
143C2×C43⋊C8—24no—
144C23×C43—21no—
145C23×C43—21no—
146C23×C43—41no—
147C23×C43—41no—
148C23×C43C2×Q1612yes—
149C23×C43C22×D411yescharacteristic
150Q8×C43—48no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—24no—
154C2×C4×C43—24no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—42no—
162C2×C4×C43—42no—
163C2×C4×C43—42no—
164C2×C4×C43—42no—
165C2×C4×C43—42no—
166C2×C4×C43—42no—
167C2×C4×C43#12012yes—
168C2×C4×C43#12011yescharacteristic
169C2×C4×C43#12011yescharacteristic
170C2×C4×C43C2×Q1612yes—
171C2×C4×C43C2×Q1612yes—
172C2×C4×C43#13712yes—
173C2×C4×C43C22×D412yes—
174C2×Dic43—24no—
175C2×Dic43—24no—
176C2×Dic43—82no—
177C2×Dic43—82no—
178Dic86—44no—
179Dic86—82no—
180Dic86—82no—
181Dic86—82no—
182C43⋊C8—44no—
183#18303—431nomaximal, Sylow
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—22no—
187C22×C43—42no—
188C22×C43—41no—
189C22×C43—41no—
190C22×C43—81no—
191C22×C43C2×#12011yescharacteristic
192C22×C43C22×Q1611yescharacteristic
193C22×C43C2×#13711yescharacteristic
194C4×C43—22no—
195C4×C43—22no—
196C4×C43—22no—
197C4×C43—41no—
198C4×C43—41no—
199C4×C43—82no—
200C4×C43—82no—
201C4×C43#45112yes—
202C4×C43#45112yes—
203Dic43—44no—
204Dic43—44no—
205#3458—431no—
206#3209—432no—
207#2628D4311yescharacteristic
208#1605—434no—
209#1602—434no—
210#1518—432no—
211#1458—431no—
212C2×C43—21no—
213C2×C43—21no—
214C2×C43—42no—
215C2×C43C2×#45111yescharacteristic
216C2×C43#302211yescharacteristic
217C2×C43#302711yescharacteristic
218#544—432no—
219#544—862no—
220#544—862no—
221#544—861no—
222#543—432no—
223#543—861no—
224#533—432no—
225#533—864no—
226#533—861no—
227C2×C4⋊Q8C2×D4311yescharacteristic
228C2×#117—861no—
229C2×#117C2×D4311yescharacteristic
230#494—862no—
231#487—862no—
232#462—864no—
233#451—438no—
234#431—432no—
235#400—21no—
236#399—21no—
237#395C2×D4312yes—
238#393C2×D4312yes—
239#389—21no—
240#382C2×D4311yescharacteristic
241#380—21no—
242#328—438no—
243#324—432no—
244#323—432no—
245C43#1830311yescharacteristic, complemented, Sylow
246C22×Q8C22×D4312yes—
247C23×C4C22⋊D4311yescharacteristic
248C2×Q16—868no—
249C4⋊Q8—22no—
250C4⋊Q8—22no—
251C4⋊Q8—432no—
252C4⋊Q8—432no—
253C4⋊Q8—861no—
254C4⋊Q8—861no—
255C4⋊Q8—864no—
256C4⋊Q8—864no—
257#125—862no—
258#125—864no—
259#125—864no—
260#125—862no—
261C22⋊Q8—434no—
262C22⋊Q8—864no—
263C22⋊Q8—864no—
264C22⋊Q8—864no—
265C22⋊Q8—864no—
266C22⋊Q8—862no—
267C22⋊Q8—862no—
268C22⋊Q8—862no—
269C4×Q8—434no—
270C4×Q8—862no—
271C4×Q8—862no—
272C4×Q8—862no—
273#117—22no—
274#117—22no—
275#117—862no—
276#117—862no—
277#117—862no—
278#117—862no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—861no—
284C2×C4⋊C4—861no—
285C2×C4⋊C4C22⋊D4311yescharacteristic
286C2×C4⋊C4C22×D4311yescharacteristic
287C2×C22⋊C4—22no—
288C2×C22⋊C4—862no—
289C2×C22⋊C4C22⋊D4311yescharacteristic
290C2×C22⋊C4C22×D4311yescharacteristic
291C2×C42—862no—
292C2×C42C22⋊D4311yescharacteristic
293C2×C42C22×D4311yescharacteristic
294C4⋊C8—862no—
295#103—868no—
296C22⋊C8—434no—
297C4×C8—862no—
298#95—22no—
299#95—21no—
300#95—22no—
301#95C22×D4312yes—
302C24C2×C22⋊D4311yescharacteristic
303C2×Q8—24no—
304C2×Q8—82no—
305C2×Q8—434no—
306C2×Q8—862no—
307C2×Q8—862no—
308C2×Q8—862no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—862no—
315C22×C4—862no—
316C22×C4#1062188514yescomplemented
317C22×C4C2×C22⋊D4311yescharacteristic
318C22×C4C2×C22⋊D4311yescharacteristic
319C22×C4C2×C22⋊D4311yescharacteristic
320C22×C4C2×C22⋊D4311yescharacteristic
321C22×C4C2×C22⋊D4311yescharacteristic
322C22×C4C23×D4311yescharacteristic
323Q16—3448no—
324C2×C8—864no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—42no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—42no—
331C4⋊C4—82no—
332C4⋊C4—434no—
333C4⋊C4—862no—
334C4⋊C4—862no—
335C4⋊C4—864no—
336C4⋊C4—864no—
337C4⋊C4—862no—
338C4⋊C4—862no—
339C4⋊C4—862no—
340C4⋊C4—862no—
341C4⋊C4—864no—
342C4⋊C4—862no—
343C4⋊C4—864no—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—82no—
347C22⋊C4—864no—
348C22⋊C4—864no—
349C42—21no—
350C42—21no—
351C42—864no—
352C42—864no—
353C42D4×D4312yes—
354C42D4×D4312yes—
355C23—21no—
356C23—21no—
357C23—41no—
358C23—41no—
359C23C2×#1062188512yes—
360C23C22×C22⋊D4311yescharacteristic
361Q8—48no—
362Q8—3442no—
363Q8—3442no—
364Q8—3442no—
365Q8—1724no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—864no—
383C2×C4—864no—
384C2×C4—3442no—
385C2×C4—3442no—
386C2×C4#1306329312yes—
387C2×C4#1306329311yescharacteristic
388C2×C4#1306329311yescharacteristic
389C2×C4C2×#1062188512yes—
390C2×C4C2×#1062188512yes—
391C2×C4#1306335512yes—
392C2×C4C2×D4×D4312yes—
393C8—1724no—
394C22—21no—
395C22—21no—
396C22—22no—
397C22—42no—
398C22—41no—
399C22—41no—
400C22—81no—
401C22C2×#1306329311yescharacteristic
402C22C22×#1062188511yescharacteristic
403C22C2×#1306335511yescharacteristic
404C4—22no—
405C4—22no—
406C4—22no—
407C4—41no—
408C4—41no—
409C4—82no—
410C4—82no—
411C4—1724no—
412C4—1724no—
413C4#1458305412yes—
414C4#1458305412yes—
415C2—21no—
416C2—21no—
417C2—42no—
418C2C2×#1458305411yescharacteristic
419C2#1914397311yescharacteristic
420C2#1914399611yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2628C2
socleC22×C43C2×#120
prime radicalC24×C43C2×D4
hypercenter#2628D43
hypocenterC43#18303
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2628

Complements

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

NH ≅ G/Ntype
2. #19145543C2semidirect
3. #19133568C2semidirect
5. #19133158C2semidirect
99. C22×C4×C43Q16semidirect
245. C43#18303semidirect
316. C22×C4#10621885semidirect

Maximal subgroups

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

subgroupindex
#191480002
#191455432
#191335682
#191335512
#191331582
#191329092
C43×#26282
#1830343