Finite Group Databasebeta

← #25070591

Subgroups — #25070591

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#19145545C212yesmaximal, complemented
3#19140416C211yesmaximal, characteristic
4#19133571C214yesmaximal, complemented
5#19133554C214yesmaximal
6#19133160C212yesmaximal, complemented
7C43×#1458C211yesmaximal, 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×#13063325C2211yescharacteristic
18C2×#13063284—21no—
19#14583279—22no—
20#14583250—22no—
21#14583110—24no—
22#14583057C2218yes—
23#14582838—21no—
24#14582835—21no—
25#14582819C2212yes—
26#14582811C2212yes—
27#14582797—21no—
28#14582765C2211yescharacteristic
29#14582759—21no—
30#14582637C2218yes—
31C2×#117×C43C2211yescharacteristic
32C43×#431C2212yes—
33C43×#324C2212yes—
34C43×#323C2212yes—
35C22×Dic86C2312yes—
36C2×Dic172—28no—
37#13063325—21no—
38#13063325—21no—
39#13063325—22no—
40#13063325—22no—
41#13063325D412yes—
42#13063325D412yes—
43#13063324—24no—
44#13063324—24no—
45#13063317—22no—
46#13063317—22no—
47#13063316—24no—
48#13063316—24no—
49#13063304—22no—
50#13063304—22no—
51#13063304—22no—
52#13063304C2314yes—
53#13063302—24no—
54#13063302—24no—
55#13063302—24no—
56#13063302—24no—
57C4×Dic86—22no—
58C4×Dic86—22no—
59C4×Dic86—22no—
60C4×Dic86D414yes—
61#13063284—22no—
62#13063284—22no—
63#13063284—22no—
64#13063284—22no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×Dic43⋊C4—22no—
71C2×C22⋊Dic43—22no—
72C2×C22⋊Dic43—22no—
73C2×C4×Dic43—22no—
74#13063250—28no—
75C43⋊#95—22no—
76C43⋊#95—22no—
77C43⋊#95—21no—
78C43⋊#95C2312yes—
79C23×C4×C43D411yescharacteristic
80#117×C43—22no—
81#117×C43—22no—
82C2×C4⋊C4×C43D411yescharacteristic
83C2×C4⋊C4×C43C2311yescharacteristic
84C2×C22⋊C4×C43D411yescharacteristic
85C2×C22⋊C4×C43C2311yescharacteristic
86C2×C42×C43D411yescharacteristic
87C2×C42×C43C2311yescharacteristic
88C4⋊C8×C43—22no—
89C22⋊C8×C43C2314yes—
90C4×C8×C43—22no—
91C24×C43C2×D411yescharacteristic
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43—22no—
95C22×C4×C43Q1614yescomplemented
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2411yescharacteristic
102C22×Dic43—22no—
103C22×Dic43—22no—
104C22×Dic43—22no—
105C22×Dic43—22no—
106C2×Dic86—24no—
107C2×Dic86—22no—
108C2×Dic86—22no—
109C2×Dic86—22no—
110C2×Dic86—82no—
111C2×Dic86C2×D414yes—
112C2×C8×C43—24no—
113C4⋊C4×C43—22no—
114C4⋊C4×C43—22no—
115C22⋊C4×C43—22no—
116C22⋊C4×C43—22no—
117C42×C43—21no—
118C42×C43—21no—
119C42×C43C2×D412yes—
120C42×C43C2×D412yes—
121C22⋊Dic43—24no—
122C22⋊Dic43—24no—
123C22⋊Dic43—82no—
124C4⋊Dic43—22no—
125C4⋊Dic43—22no—
126C4⋊Dic43—22no—
127C4⋊Dic43—22no—
128C4⋊Dic43—22no—
129C4⋊Dic43—22no—
130C4⋊Dic43—22no—
131C4⋊Dic43—42no—
132C4⋊Dic43—41no—
133C4⋊Dic43—41no—
134C4⋊Dic43—42no—
135C4⋊Dic43C2×D414yes—
136Dic43⋊C4—24no—
137Dic43⋊C4—24no—
138Dic43⋊C4—24no—
139Dic43⋊C4—24no—
140Dic43⋊C4—82no—
141C4×Dic43—24no—
142C4×Dic43—24no—
143Dic172—88no—
144C23×C43—21no—
145C23×C43—21no—
146C23×C43—41no—
147C23×C43—41no—
148C23×C43C2×Q1612yes—
149C23×C43C22×D411yescharacteristic
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#12012yes—
161C2×C4×C43#12011yescharacteristic
162C2×C4×C43#12011yescharacteristic
163C2×C4×C43C2×Q1612yes—
164C2×C4×C43C2×Q1612yes—
165C2×C4×C43#13712yes—
166C2×C4×C43C22×D412yes—
167C2×Dic43—24no—
168C2×Dic43—24no—
169C2×Dic43—42no—
170C2×Dic43—42no—
171C2×Dic43—42no—
172C2×Dic43—42no—
173C2×Dic43—42no—
174C2×Dic43—42no—
175C2×Dic43—82no—
176C2×Dic43—82no—
177Dic86—44no—
178Dic86—48no—
179Dic86—82no—
180Dic86—82no—
181Dic86—82no—
182C8×C43—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#45112yes—
200C4×C43#45112yes—
201Dic43—44no—
202Dic43—44no—
203Dic43—82no—
204Dic43—82no—
205#3458—431no—
206#3209—432no—
207#2628—431no—
208#1605—434no—
209#1602—434no—
210#1518—432no—
211#1458D4311yescharacteristic
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⋊Q8—431no—
228C2×#117—861no—
229C2×#117C2×D4311yescharacteristic
230#494—862no—
231#487—862no—
232#462—864no—
233#451—438no—
234#431C2×D4312yes—
235#400—861no—
236#399—861no—
237#395—432no—
238#393—432no—
239#389—861no—
240#382—431no—
241#380—861no—
242#328—438no—
243#324C2×D4312yes—
244#323C2×D4312yes—
245C43#1830311yescharacteristic, complemented, Sylow
246C22×Q8—432no—
247C23×C4D17211yescharacteristic
248C2×Q16—868no—
249C4⋊Q8—432no—
250C4⋊Q8—432no—
251C4⋊Q8—861no—
252C4⋊Q8—861no—
253C4⋊Q8—864no—
254C4⋊Q8—864no—
255C4⋊Q8—862no—
256C4⋊Q8—862no—
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—861no—
280C2×C4⋊C4—861no—
281C2×C4⋊C4—862no—
282C2×C4⋊C4—861no—
283C2×C4⋊C4—861no—
284C2×C4⋊C4—861no—
285C2×C4⋊C4D17211yescharacteristic
286C2×C4⋊C4C22×D4311yescharacteristic
287C2×C22⋊C4—862no—
288C2×C22⋊C4—862no—
289C2×C22⋊C4D17211yescharacteristic
290C2×C22⋊C4C22×D4311yescharacteristic
291C2×C42—862no—
292C2×C42D17211yescharacteristic
293C2×C42C22×D4311yescharacteristic
294C4⋊C8—22no—
295#103—868no—
296C22⋊C8C22×D4314yes—
297C4×C8—22no—
298#95—432no—
299#95—862no—
300#95—861no—
301#95—862no—
302C24C2×D17211yescharacteristic
303C2×Q8—434no—
304C2×Q8—862no—
305C2×Q8—862no—
306C2×Q8—862no—
307C2×Q8—864no—
308C2×Q8—3442no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—862no—
313C22×C4—862no—
314C22×C4—862no—
315C22×C4—862no—
316C22×C4Dic17214yescomplemented
317C22×C4C2×D17211yescharacteristic
318C22×C4C2×D17211yescharacteristic
319C22×C4C2×D17211yescharacteristic
320C22×C4C2×D17211yescharacteristic
321C22×C4C2×D17211yescharacteristic
322C22×C4C23×D4311yescharacteristic
323Q16—3448no—
324C2×C8—24no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—434no—
328C4⋊C4—862no—
329C4⋊C4—862no—
330C4⋊C4—864no—
331C4⋊C4—864no—
332C4⋊C4—862no—
333C4⋊C4—862no—
334C4⋊C4—862no—
335C4⋊C4—862no—
336C4⋊C4—864no—
337C4⋊C4—862no—
338C4⋊C4—864no—
339C4⋊C4—3442no—
340C4⋊C4—1722no—
341C4⋊C4—1721no—
342C4⋊C4—1721no—
343C4⋊C4—1722no—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—864no—
347C22⋊C4—864no—
348C22⋊C4—3442no—
349C42—21no—
350C42—21no—
351C42—864no—
352C42—864no—
353C42D4×D4312yes—
354C42D4×D4312yes—
355C23—21no—
356C23—21no—
357C23—41no—
358C23—41no—
359C23C2×Dic17212yes—
360C23C22×D17211yescharacteristic
361Q8—3442no—
362Q8—3442no—
363Q8—3442no—
364Q8—1728no—
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—864no—
377C2×C4—864no—
378C2×C4—3442no—
379C2×C4—3442no—
380C2×C4—1722no—
381C2×C4—1722no—
382C2×C4—1722no—
383C2×C4—1722no—
384C2×C4—1722no—
385C2×C4—1722no—
386C2×C4#1306329512yes—
387C2×C4#1306329511yescharacteristic
388C2×C4#1306329511yescharacteristic
389C2×C4C2×Dic17212yes—
390C2×C4C2×Dic17212yes—
391C2×C4#1306335812yes—
392C2×C4C2×D4×D4312yes—
393C8—44no—
394C22—21no—
395C22—21no—
396C22—22no—
397C22—42no—
398C22—41no—
399C22—41no—
400C22—81no—
401C22C2×#1306329511yescharacteristic
402C22C22×Dic17211yescharacteristic
403C22C2×#1306335811yescharacteristic
404C4—22no—
405C4—22no—
406C4—22no—
407C4—41no—
408C4—41no—
409C4—3442no—
410C4—3442no—
411C4—1724no—
412C4—1724no—
413C4#1458305712yes—
414C4#1458305712yes—
415C2—21no—
416C2—21no—
417C2—42no—
418C2C2×#1458305711yescharacteristic
419C2#1914397611yescharacteristic
420C2#1914399811yescharacteristic
subgroupG/H
centerC22C2×#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1458C2
socleC22×C43C2×#120
prime radicalC24×C43C2×D4
hypercenter#1458D43
hypocenterC43#18303
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. #19145545C2semidirect
4. #19133571C2semidirect
6. #19133160C2semidirect
95. C22×C4×C43Q16semidirect
245. C43#18303semidirect
316. C22×C4Dic172semidirect

Maximal subgroups

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

subgroupindex
#191480002
#191455452
#191404162
#191335712
#191335542
#191331602
C43×#14582
#1830343