Finite Group Databasebeta

← #25070656

Subgroups — #25070656

Order 11008.

888 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148000C211yesmaximal, characteristic
2#19145746C212yesmaximal, complemented
3#19133636C214yesmaximal, complemented
4#19133619C214yesmaximal
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#14583302—22no—
19#14583251—22no—
20#14583234C2218yes—
21#14583191—24no—
22#14582952C2212yes—
23#14582635C2218yes—
24#14582625C2212yes—
25#14582623C2212yes—
26C2×C4⋊Q8×C43C2211yescharacteristic
27C2×#117×C43C2211yescharacteristic
28C43×#400C2212yes—
29C43×#399C2212yes—
30C43×#395—21no—
31C43×#393—21no—
32C43×#389—21no—
33C43×#382C2211yescharacteristic
34C43×#380—21no—
35#13063325—21no—
36#13063325—21no—
37#13063325D412yes—
38#13063325D412yes—
39#13063324—24no—
40#13063324—24no—
41#13063317—22no—
42#13063317—22no—
43#13063316—24no—
44#13063316—24no—
45#13063304—22no—
46#13063304—22no—
47#13063304—22no—
48#13063304C2314yes—
49#13063302—24no—
50#13063302—24no—
51#13063302—24no—
52#13063302—24no—
53C4×Dic86—22no—
54C4×Dic86—22no—
55C4×Dic86—22no—
56C4×Dic86D414yes—
57#13063284—22no—
58#13063284—22no—
59#13063284—22no—
60#13063284—22no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43—21no—
63C2×C22⋊Dic43—22no—
64C2×C4×Dic43—22no—
65#13063258—28no—
66C4⋊(C43⋊C8)—22no—
67#13063248—28no—
68C22⋊(C43⋊C8)C2314yes—
69C4×C43⋊C8—22no—
70C22×Q8×C43—21no—
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—22no—
79C2×C4⋊C4×C43D411yescharacteristic
80C2×C4⋊C4×C43C2312yes—
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—42no—
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×C43Q1614yes—
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—24no—
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—
128C4⋊Dic43—22no—
129C4⋊Dic43—22no—
130C4⋊Dic43—22no—
131C4⋊Dic43—22no—
132C4⋊Dic43—22no—
133C4⋊Dic43—22no—
134C4⋊Dic43—22no—
135C4⋊Dic43C2×D414yes—
136Dic43⋊C4—24no—
137Dic43⋊C4—24no—
138Dic43⋊C4—24no—
139Dic43⋊C4—24no—
140C4×Dic43—24no—
141C4×Dic43—24no—
142C2×C43⋊C8—24no—
143C23×C43—21no—
144C23×C43—21no—
145C23×C43—41no—
146C23×C43—41no—
147C23×C43C2×Q1612yes—
148C23×C43C22×D411yescharacteristic
149Q8×C43—84no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—24no—
153C2×C4×C43—24no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—42no—
161C2×C4×C43—42no—
162C2×C4×C43—42no—
163C2×C4×C43—42no—
164C2×C4×C43—42no—
165C2×C4×C43—42no—
166C2×C4×C43#12012yes—
167C2×C4×C43#12011yescharacteristic
168C2×C4×C43#12011yescharacteristic
169C2×C4×C43C2×Q1612yes—
170C2×C4×C43C2×Q1612yes—
171C2×C4×C43#13712yes—
172C2×C4×C43C22×D412yes—
173C2×Dic43—24no—
174C2×Dic43—24no—
175C2×Dic43—82no—
176C2×Dic43—82no—
177Dic86—44no—
178Dic86—82no—
179Dic86—82no—
180Dic86—82no—
181C43⋊C8—44no—
182#18311—431nomaximal, Sylow
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—22no—
186C22×C43—42no—
187C22×C43—41no—
188C22×C43—41no—
189C22×C43—81no—
190C22×C43C2×#12011yescharacteristic
191C22×C43C22×Q1611yescharacteristic
192C22×C43C2×#13711yescharacteristic
193C4×C43—22no—
194C4×C43—22no—
195C4×C43—22no—
196C4×C43—41no—
197C4×C43—41no—
198C4×C43—82no—
199C4×C43—82no—
200C4×C43#45112yes—
201C4×C43#45112yes—
202Dic43—44no—
203Dic43—44no—
204#3458—431no—
205#3230—432no—
206#2628D4311yescharacteristic
207#1617—434no—
208#1614—434no—
209#1518—432no—
210#1458—431no—
211C2×C43—21no—
212C2×C43—21no—
213C2×C43—42no—
214C2×C43C2×#45111yescharacteristic
215C2×C43#302111yescharacteristic
216C2×C43#302811yescharacteristic
217#544—432no—
218#544—862no—
219#544—862no—
220#544—861no—
221#543—432no—
222#543—861no—
223#533—432no—
224#533—864no—
225#533—861no—
226C2×C4⋊Q8C2×D4311yescharacteristic
227C2×#117—861no—
228C2×#117C2×D4311yescharacteristic
229#500—862no—
230#487—862no—
231#484—438no—
232#477—864no—
233#431—432no—
234#400C2×D4312yes—
235#399C2×D4312yes—
236#395—21no—
237#393—21no—
238#389—21no—
239#382C2×D4311yescharacteristic
240#380—21no—
241#328—438no—
242#324—432no—
243#323—432no—
244C43#1831111yescharacteristic, complemented, Sylow
245C22×Q8—21no—
246C23×C4C22⋊D4311yescharacteristic
247C4⋊Q8—22no—
248C4⋊Q8—22no—
249C4⋊Q8—432no—
250C4⋊Q8—432no—
251C4⋊Q8—861no—
252C4⋊Q8—861no—
253C4⋊Q8—864no—
254C4⋊Q8—864no—
255#125—862no—
256#125—864no—
257#125—864no—
258#125—862no—
259C22⋊Q8—434no—
260C22⋊Q8—864no—
261C22⋊Q8—864no—
262C22⋊Q8—864no—
263C22⋊Q8—864no—
264C22⋊Q8—862no—
265C22⋊Q8—862no—
266C22⋊Q8—862no—
267C4×Q8—434no—
268C4×Q8—862no—
269C4×Q8—862no—
270C4×Q8—862no—
271#117—22no—
272#117—22no—
273#117—862no—
274#117—862no—
275#117—862no—
276#117—862no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—861no—
281C2×C4⋊C4—861no—
282C2×C4⋊C4C22⋊D4311yescharacteristic
283C2×C4⋊C4C22×D4312yes—
284C2×C4⋊C4C22×D4311yescharacteristic
285C2×C22⋊C4—22no—
286C2×C22⋊C4—862no—
287C2×C22⋊C4C22⋊D4311yescharacteristic
288C2×C22⋊C4C22×D4311yescharacteristic
289C2×C42—862no—
290C2×C42C22⋊D4311yescharacteristic
291C2×C42C22×D4311yescharacteristic
292#107—868no—
293C4⋊C8—862no—
294#103—868no—
295C22⋊C8—434no—
296C4×C8—862no—
297#95—22no—
298#95—21no—
299#95—22no—
300#95C22×D4312yes—
301C24C2×C22⋊D4311yescharacteristic
302C2×Q8—42no—
303C2×Q8—82no—
304C2×Q8—434no—
305C2×Q8—862no—
306C2×Q8—862no—
307C2×Q8—862no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—862no—
314C22×C4—862no—
315C22×C4#1062188514yes—
316C22×C4C2×C22⋊D4311yescharacteristic
317C22×C4C2×C22⋊D4311yescharacteristic
318C22×C4C2×C22⋊D4311yescharacteristic
319C22×C4C2×C22⋊D4311yescharacteristic
320C22×C4C2×C22⋊D4311yescharacteristic
321C22×C4C23×D4311yescharacteristic
322C2×C8—864no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—24no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—42no—
329C4⋊C4—82no—
330C4⋊C4—434no—
331C4⋊C4—862no—
332C4⋊C4—862no—
333C4⋊C4—864no—
334C4⋊C4—864no—
335C4⋊C4—862no—
336C4⋊C4—862no—
337C4⋊C4—862no—
338C4⋊C4—862no—
339C4⋊C4—864no—
340C4⋊C4—862no—
341C4⋊C4—864no—
342C22⋊C4—22no—
343C22⋊C4—22no—
344C22⋊C4—82no—
345C22⋊C4—864no—
346C22⋊C4—864no—
347C42—21no—
348C42—21no—
349C42—864no—
350C42—864no—
351C42D4×D4312yes—
352C42D4×D4312yes—
353C23—21no—
354C23—21no—
355C23—41no—
356C23—41no—
357C23C2×#1062188512yes—
358C23C22×C22⋊D4311yescharacteristic
359Q8—84no—
360Q8—3442no—
361Q8—3442no—
362Q8—3442no—
363Q8—1724no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—864no—
381C2×C4—864no—
382C2×C4—3442no—
383C2×C4—3442no—
384C2×C4#1306329312yes—
385C2×C4#1306329311yescharacteristic
386C2×C4#1306329311yescharacteristic
387C2×C4C2×#1062188512yes—
388C2×C4C2×#1062188512yes—
389C2×C4#1306335512yes—
390C2×C4C2×D4×D4312yes—
391C8—1724no—
392C22—21no—
393C22—21no—
394C22—22no—
395C22—42no—
396C22—41no—
397C22—41no—
398C22—81no—
399C22C2×#1306329311yescharacteristic
400C22C22×#1062188511yescharacteristic
401C22C2×#1306335511yescharacteristic
402C4—22no—
403C4—22no—
404C4—22no—
405C4—41no—
406C4—41no—
407C4—82no—
408C4—82no—
409C4—1724no—
410C4—1724no—
411C4#1458305412yes—
412C4#1458305412yes—
413C2—21no—
414C2—21no—
415C2—42no—
416C2C2×#1458305411yescharacteristic
417C2#1914396611yescharacteristic
418C2#1914400011yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2628C2
socleC22×C43C2×#120
prime radicalC24×C43C2×D4
hypercenter#2628D43
hypocenterC43#18311
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. #19145746C2semidirect
3. #19133636C2semidirect
5. #19133158C2semidirect
244. C43#18311semidirect

Maximal subgroups

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

subgroupindex
#191480002
#191457462
#191336362
#191336192
#191331582
#191329092
C43×#26282
#1831143