Finite Group Databasebeta

← #24996315

Subgroups — #24996315

Order 11008.

510 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583128C211yesmaximal, characteristic
2#19134633C211yesmaximal, characteristic, complemented
3#19133114C211yesmaximal, characteristic, complemented
4#19133110C211yesmaximal, characteristic
5#19132958C211yesmaximal, characteristic, complemented
6#19132954C211yesmaximal, characteristic
7C43×#1752C211yesmaximal, characteristic, complemented
8C22×#10621873C411yescharacteristic, complemented
9C2×#13063304C2211yescharacteristic
10C2×#13063299C2211yescharacteristic
11#14583128—21no—
12#14583128—21no—
13#14583128—21no—
14#14583128—21no—
15C2×#13063261—21no—
16C2×#13063257C411yescharacteristic, complemented
17C2×#13063250C411yescharacteristic, complemented
18C2×#13063247C411yescharacteristic, complemented
19#14582863C2211yescharacteristic
20#14582863C2211yescharacteristic
21#14582664—21no—
22#14582635—22no—
23#14582632—22no—
24#14582624—22no—
25#14582622—22no—
26C23×C8×C43C2211yescharacteristic
27C2×C22⋊C8×C43C2211yescharacteristic
28C2×#97×C43—21no—
29C4×C22⋊C4×C43C2211yescharacteristic
30C43×#336—21no—
31C22×Dic86C2×C411yescharacteristic
32C22×D172C2×C411yescharacteristic
33C22×C22⋊D43—21no—
34C2×#10621873—21no—
35C2×#10621873—21no—
36C2×#10621873—42no—
37C2×#10621877—21no—
38C2×#10621877—21no—
39#13063304—21no—
40#13063304—21no—
41#13063304—21no—
42#13063304—21no—
43#13063299—21no—
44#13063299—21no—
45#13063299—21no—
46#13063299—21no—
47C2×C4⋊Dic43C2×C411yescharacteristic
48C2×C4⋊Dic43C2×C411yescharacteristic
49C2×Dic43⋊C4—21no—
50C2×C22⋊Dic43—21no—
51C2×(C2×D43)⋊C4—21no—
52#13063261—42no—
53#13063257—21no—
54#13063257—21no—
55#13063250—21no—
56#13063250—21no—
57#13063247—21no—
58#13063247—21no—
59C22⋊(C43⋊C8)—21no—
60C22⋊(C43⋊C8)—21no—
61C22⋊(C43⋊C8)—21no—
62C22⋊(C43⋊C8)—21no—
63C23×C4×C43C2311yescharacteristic
64C22×C8×C43—21no—
65C22×C8×C43—42no—
66C22×C8×C43C2×C411yescharacteristic
67C22×C8×C43C2×C411yescharacteristic
68C22×C8×C43D411yescharacteristic
69C22×C8×C43D411yescharacteristic
70C22×C8×C43D411yescharacteristic
71C22×C8×C43D411yescharacteristic
72C2×C22⋊C4×C43—21no—
73C2×C42×C43—21no—
74C22⋊C8×C43—21no—
75C22⋊C8×C43D412yes—
76#97×C43—42no—
77#95×C43D412yes—
78C24×C43#4111yescharacteristic
79C23×D43—21no—
80C22×C4×C43—22no—
81C22×C4×C43—41no—
82C22×C4×C43—41no—
83C22×C4×C43C22×C411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43#4111yescharacteristic
89C2×C22⋊D43—41no—
90C2×C22⋊D43—41no—
91C2×C22⋊D43—82no—
92C22×Dic43—21no—
93C22×Dic43—21no—
94C22×Dic43—21no—
95C2×D172—21no—
96C2×D172—21no—
97C2×D172—41no—
98C2×D172—41no—
99C2×Dic86—21no—
100C2×Dic86—21no—
101C2×Dic86—41no—
102C2×Dic86—41no—
103C2×C8×C43—22no—
104C2×C8×C43—22no—
105C2×C8×C43—22no—
106C2×C8×C43—22no—
107C2×C8×C43—41no—
108C2×C8×C43—41no—
109C2×C8×C43—41no—
110C2×C8×C43—41no—
111C2×C8×C43—41no—
112C2×C8×C43C22⋊C411yescharacteristic
113C2×C8×C43C22⋊C411yescharacteristic
114C2×C8×C43C22⋊C411yescharacteristic
115C2×C8×C43C22⋊C411yescharacteristic
116C22⋊C4×C43—42no—
117C42×C43—41no—
118C42×C43—41no—
119C22⋊Dic43—41no—
120C22⋊Dic43—41no—
121(C2×D43)⋊C4—41no—
122(C2×D43)⋊C4—41no—
123C4⋊Dic43—21no—
124C4⋊Dic43—21no—
125C4⋊Dic43—21no—
126C4⋊Dic43—21no—
127Dic43⋊C4—41no—
128Dic43⋊C4—41no—
129#10621877—41no—
130#10621877—41no—
131#10621877—41no—
132#10621877—41no—
133C2×C43⋊C8—41no—
134C2×C43⋊C8—41no—
135#10621873—42no—
136#10621873—42no—
137C23×C43—22no—
138C23×C43—22no—
139C23×C43—41no—
140C23×C43C4×D411yescharacteristic
141C23×C43#12111yescharacteristic
142C23×C43#12411yescharacteristic
143C22×D43—41no—
144C22×D43—42no—
145C22×D43—81no—
146C22×D43—81no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—42no—
157C2×C4×C43—42no—
158C2×C4×C43—42no—
159C2×C4×C43C2×C22⋊C411yescharacteristic
160C2×C4×C43C4×D411yescharacteristic
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43#12711yescharacteristic
163C22⋊D43—82no—
164C22⋊D43—82no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—42no—
169C2×Dic43—81no—
170C2×Dic43—81no—
171D172—41no—
172D172—41no—
173D172—81no—
174Dic86—41no—
175Dic86—41no—
176Dic86—81no—
177C8×C43—21no—
178C8×C43—21no—
179C8×C43—21no—
180C8×C43—42no—
181C8×C43#9912yes—
182C43⋊C8—81no—
183C43⋊C8—81no—
184#9816—431nomaximal, Sylow
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—44no—
193C22×C43#39011yescharacteristic
194C22×C43#44412yes—
195C22×C43#47112yes—
196C2×D43—81no—
197C2×D43—81no—
198C2×D43—81no—
199C2×D43—162no—
200C4×C43—21no—
201C4×C43—21no—
202C4×C43—21no—
203C4×C43—82no—
204C4×C43C2×#9911yescharacteristic
205C4×C43#41011yescharacteristic
206Dic43—81no—
207Dic43—81no—
208Dic43—81no—
209C2×#465—431no—
210#1810—431no—
211#1752D4311yescharacteristic, complemented
212#1508—431no—
213#1507—431no—
214#1472—431no—
215#1471—431no—
216C2×C43—22no—
217C2×C43—22no—
218C2×C43—41no—
219C2×C43#196411yescharacteristic
220C2×C43#197511yescharacteristic
221C2×C43#197711yescharacteristic
222D43—161no—
223C22×SD16—431no—
224C23×C8C2×D4311yescharacteristic
225C2×C22⋊Q8—431no—
226C2×#121—431no—
227#465—861no—
228#465—861no—
229#465—861no—
230#465—861no—
231C2×#108—861no—
232C2×#106—431no—
233C2×#103—431no—
234C2×#102—431no—
235#407—431no—
236#407—431no—
237C2×C22⋊C8C2×D4311yescharacteristic
238C2×#97—21no—
239C4×C22⋊C4C2×D4311yescharacteristic
240#341—861no—
241#336—21no—
242#328—862no—
243#327—862no—
244#324—862no—
245#323—862no—
246C43#981611yescharacteristic, complemented, Sylow
247C22×Q8—431no—
248C22×D4—431no—
249C22×D4—861no—
250C23×C4C22×D4311yescharacteristic
251C2×SD16—861no—
252C2×SD16—861no—
253C2×SD16—1722no—
254C2×M16—861no—
255C2×M16—861no—
256C22×C8—21no—
257C22×C8—42no—
258C22×C8C4×D4311yescharacteristic
259C22×C8C4×D4311yescharacteristic
260C22×C8D17211yescharacteristic
261C22×C8D17211yescharacteristic
262C22×C8C22⋊D4311yescharacteristic
263C22×C8C22⋊D4311yescharacteristic
264C22⋊Q8—861no—
265C22⋊Q8—861no—
266C22⋊Q8—861no—
267C22⋊Q8—861no—
268#121—861no—
269#121—861no—
270#121—861no—
271#121—861no—
272C2×C4⋊C4—431no—
273C2×C4⋊C4—431no—
274C2×C4⋊C4—861no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—861no—
277C2×C22⋊C4—861no—
278C2×C42—21no—
279#108—1722no—
280#106—861no—
281#106—861no—
282#103—861no—
283#103—861no—
284#102—861no—
285#102—861no—
286C22⋊C8—21no—
287C22⋊C8—861no—
288C22⋊C8—861no—
289C22⋊C8—861no—
290C22⋊C8—861no—
291C22⋊C8D17212yes—
292#97—42no—
293#95D17212yes—
294C24—861no—
295C24#1062189811yescharacteristic
296C2×Q8—861no—
297C2×Q8—861no—
298C2×Q8—1721no—
299C2×Q8—1721no—
300C2×D4—861no—
301C2×D4—861no—
302C2×D4—3442no—
303C2×D4—1721no—
304C2×D4—1721no—
305C2×D4—1721no—
306C2×D4—1721no—
307C22×C4—22no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—861no—
311C22×C4—861no—
312C22×C4—861no—
313C22×C4C2×C4×D4311yescharacteristic
314C22×C4C2×D17211yescharacteristic
315C22×C4C2×D17211yescharacteristic
316C22×C4C2×D17211yescharacteristic
317C22×C4#1062189811yescharacteristic
318C22×C4C2×C22⋊D4311yescharacteristic
319SD16—1722no—
320SD16—1722no—
321M16—1721no—
322M16—1721no—
323M16—1721no—
324M16—1721no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—1721no—
335C2×C8—1721no—
336C2×C8(C2×D43)⋊C411yescharacteristic
337C2×C8(C2×D43)⋊C411yescharacteristic
338C2×C8(C2×D43)⋊C411yescharacteristic
339C2×C8(C2×D43)⋊C411yescharacteristic
340C4⋊C4—861no—
341C4⋊C4—861no—
342C4⋊C4—861no—
343C4⋊C4—861no—
344C4⋊C4—1721no—
345C4⋊C4—1721no—
346C22⋊C4—42no—
347C22⋊C4—1721no—
348C22⋊C4—1721no—
349C22⋊C4—1721no—
350C22⋊C4—1721no—
351C42—41no—
352C42—41no—
353C23—22no—
354C23—22no—
355C23—41no—
356C23—3441no—
357C23—3441no—
358C23—1721no—
359C23—1722no—
360C23C4×D17211yescharacteristic
361C23#1306329911yescharacteristic
362C23#1306331311yescharacteristic
363Q8—3441no—
364Q8—1721no—
365Q8—1721no—
366D4—3441no—
367D4—3442no—
368D4—3442no—
369D4—1721no—
370D4—1721no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—3441no—
384C2×C4—3441no—
385C2×C4—1721no—
386C2×C4—1721no—
387C2×C4—1721no—
388C2×C4—1722no—
389C2×C4C2×(C2×D43)⋊C411yescharacteristic
390C2×C4C4×D17211yescharacteristic
391C2×C4#1306329911yescharacteristic
392C2×C4#1306332211yescharacteristic
393C8—21no—
394C8—21no—
395C8—21no—
396C8—42no—
397C8—3441no—
398C8—3441no—
399C8#1306323912yes—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—44no—
408C22—3441no—
409C22—3441no—
410C22—3441no—
411C22—6882no—
412C22#1458280111yescharacteristic
413C22#1458302212yes—
414C22#1458316212yes—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—82no—
419C4—3441no—
420C4—3441no—
421C4—3441no—
422C4C2×#1306323911yescharacteristic
423C4#1458287211yescharacteristic
424C2—22no—
425C2—22no—
426C2—41no—
427C2—6881no—
428C2#1913543111yescharacteristic
429C2#1913548811yescharacteristic
430C2#1913549811yescharacteristic
subgroupG/H
centerC22#14582801
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1752C2
socleC22×C43#390
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1752D43
hypocenterC43#9816
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1752

Complements

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

NH ≅ G/Ntype
2. #19134633C2semidirect
3. #19133114C2semidirect
5. #19132958C2semidirect
7. C43×#1752C2semidirect
8. C22×#10621873C4semidirect
16. C2×#13063257C4semidirect
17. C2×#13063250C4semidirect
18. C2×#13063247C4semidirect
211. #1752D43semidirect
246. C43#9816semidirect

Maximal subgroups

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

subgroupindex
C2×#145831282
#191346332
#191331142
#191331102
#191329582
#191329542
C43×#17522
#981643