Finite Group Databasebeta

← #24991715

Subgroups — #24991715

Order 11008.

468 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143643C211yesmaximal, characteristic
2#19134694C211yesmaximal, characteristic, complemented
3#19134666C211yesmaximal, characteristic, complemented
4#19133086C211yesmaximal, characteristic
5#19132483C211yesmaximal, characteristic, complemented
6#19132441C211yesmaximal, characteristic, complemented
7C43×#3091C211yesmaximal, characteristic
8#14582977—21no—
9#14582971—21no—
10#14582971—21no—
11D4×C43⋊C8—21no—
12#14582960—21no—
13#14582866—21no—
14#14582863C2211yescharacteristic
15C2×C22⋊(C43⋊C8)C2211yescharacteristic
16C2×C22⋊(C43⋊C8)C2211yescharacteristic
17C4×C22⋊Dic43C2211yescharacteristic
18#14582658—21no—
19#14582658—21no—
20#14582654—21no—
21#14582654—21no—
22#14582636—21no—
23#14582633—21no—
24C43×#525C2211yescharacteristic
25C2×#117×C43C2211yescharacteristic
26C43×#485—21no—
27C43×#484C411yescharacteristic, complemented
28C43×#483C411yescharacteristic, complemented
29C43×#482—21no—
30C43×#481C411yescharacteristic, complemented
31C43×#480C411yescharacteristic, complemented
32C43×#427—21no—
33C43×#416—21no—
34C2×C22⋊C8×C43C2211yescharacteristic
35C2×#10621877—21no—
36C2×#10621877D411yescharacteristic
37C2×#10621877D411yescharacteristic
38C22×C43⋊C8—21no—
39C22×C43⋊C8—21no—
40C22×C43⋊C8D411yescharacteristic
41C22×C43⋊C8D411yescharacteristic
42C2×C22⋊Dic43—21no—
43C2×C4×Dic43—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)—21no—
46C22⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)—21no—
48C22⋊(C43⋊C8)—21no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54#13063236—21no—
55C4×C43⋊C8—21no—
56C43⋊#95—21no—
57C2×#41×C43D411yescharacteristic
58C23×C4×C43C2311yescharacteristic
59C22×C8×C43—21no—
60#123×C43—21no—
61C22⋊Q8×C43C2×C411yescharacteristic
62C22⋊Q8×C43D411yescharacteristic
63#121×C43C2×C411yescharacteristic
64#121×C43D411yescharacteristic
65#120×C43—21no—
66C4×D4×C43—21no—
67C4×D4×C43—21no—
68#117×C43—21no—
69#117×C43—21no—
70#117×C43—21no—
71#117×C43—21no—
72#117×C43D411yescharacteristic
73C2×C4⋊C4×C43C2×C411yescharacteristic
74C2×C4⋊C4×C43C2×C411yescharacteristic
75C2×C22⋊C4×C43—21no—
76C2×C42×C43—21no—
77#107×C43—21no—
78#107×C43—21no—
79#106×C43—21no—
80#106×C43—21no—
81#103×C43—21no—
82#103×C43—21no—
83#102×C43—21no—
84#102×C43—21no—
85C22⋊C8×C43—21no—
86C22⋊C8×C43C2×C411yescharacteristic
87C22⋊C8×C43C2×C411yescharacteristic
88C24×C43#4111yescharacteristic
89#41×C43—41no—
90#41×C43—41no—
91C2×Q8×C43C22⋊C411yescharacteristic
92C2×D4×C43—21no—
93C2×D4×C43—21no—
94C2×D4×C43—21no—
95C2×D4×C43C22⋊C411yescharacteristic
96C22×C4×C43—21no—
97C22×C4×C43—21no—
98C22×C4×C43—21no—
99C22×C4×C43—41no—
100C22×C4×C43—41no—
101C22×C4×C43C22×C411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43#4111yescharacteristic
107C22×Dic43—41no—
108C2×C8×C43—21no—
109C2×C8×C43—21no—
110C2×C8×C43—41no—
111C2×C8×C43—41no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—21no—
116C4⋊C4×C43—21no—
117C4⋊C4×C43—21no—
118C4⋊C4×C43C22⋊C411yescharacteristic
119C4⋊C4×C43C22⋊C411yescharacteristic
120C22⋊C4×C43—21no—
121C22⋊C4×C43—21no—
122C22⋊C4×C43—21no—
123C22⋊C4×C43—21no—
124C22⋊C4×C43—21no—
125C22⋊C4×C43—41no—
126C22⋊C4×C43—41no—
127C42×C43—21no—
128C42×C43—41no—
129C42×C43—41no—
130C22⋊Dic43—22no—
131C22⋊Dic43—41no—
132C4×Dic43—41no—
133C4×Dic43—41no—
134#10621877—41no—
135#10621877—41no—
136#10621877—81no—
137C2×C43⋊C8—21no—
138C2×C43⋊C8—21no—
139C2×C43⋊C8—21no—
140C2×C43⋊C8—21no—
141C2×C43⋊C8—41no—
142C2×C43⋊C8—41no—
143C2×C43⋊C8—41no—
144C2×C43⋊C8—41no—
145C2×C43⋊C8—41no—
146C2×C43⋊C8—81no—
147C23×C43—21no—
148C23×C43—21no—
149C23×C43—21no—
150C23×C43—41no—
151C23×C43—41no—
152C23×C43C4×D411yescharacteristic
153C23×C43#12111yescharacteristic
154C23×C43#12311yescharacteristic
155Q8×C43—41no—
156D4×C43—41no—
157D4×C43—41no—
158D4×C43—41no—
159D4×C43—81no—
160D4×C43—81no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—21no—
164C2×C4×C43—21no—
165C2×C4×C43—21no—
166C2×C4×C43—21no—
167C2×C4×C43—21no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—42no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43C2×C22⋊C411yescharacteristic
181C2×C4×C43C4×D411yescharacteristic
182C2×C4×C43#12011yescharacteristic
183C2×C4×C43#12111yescharacteristic
184C2×Dic43—42no—
185C2×Dic43—81no—
186C2×Dic43—81no—
187C8×C43—41no—
188C8×C43—41no—
189C43⋊C8—41no—
190C43⋊C8—41no—
191C43⋊C8—41no—
192C43⋊C8—41no—
193C43⋊C8—81no—
194#9038—431nomaximal, Sylow
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—21no—
200C22×C43—21no—
201C22×C43—21no—
202C22×C43—21no—
203C22×C43—41no—
204C22×C43—41no—
205C22×C43—41no—
206C22×C43—81no—
207C22×C43—81no—
208C22×C43#38611yescharacteristic
209C22×C43#44311yescharacteristic
210C22×C43#44411yescharacteristic
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—21no—
214C4×C43—41no—
215C4×C43—41no—
216C4×C43—41no—
217C4×C43—81no—
218C4×C43—81no—
219C4×C43#45811yescharacteristic
220C4×C43#45811yescharacteristic
221Dic43—82no—
222#3091D4311yescharacteristic
223#2976—431no—
224#1826—431no—
225#1818—431no—
226#1501—431no—
227#1298—431no—
228#1282—431no—
229C2×C43—21no—
230C2×C43—21no—
231C2×C43—41no—
232C2×C43—41no—
233C2×C43—81no—
234C2×C43#187611yescharacteristic
235C2×C43#188111yescharacteristic
236C2×C43#189011yescharacteristic
237#525C2×D4311yescharacteristic
238C2×#117C2×D4311yescharacteristic
239#485—21no—
240#484Dic4311yescharacteristic, complemented
241#483Dic4311yescharacteristic, complemented
242#482—21no—
243#481Dic4311yescharacteristic, complemented
244#480Dic4311yescharacteristic, complemented
245#436—861no—
246#435—861no—
247#435—861no—
248C8×D4—861no—
249#433—861no—
250#427—21no—
251#416—21no—
252#408—861no—
253#407—431no—
254C2×C22⋊C8—431no—
255C2×C22⋊C8—431no—
256C2×C22⋊C8C2×D4311yescharacteristic
257C4×C22⋊C4—431no—
258#339—861no—
259#339—861no—
260#336—861no—
261#336—861no—
262#328—861no—
263#327—861no—
264C43#903811yescharacteristic, complemented, Sylow
265C2×#41C22⋊D4311yescharacteristic
266C23×C4C22×D4311yescharacteristic
267C2×M16—431no—
268C2×M16—431no—
269C2×M16—861no—
270C22×C8—21no—
271C22×C8—431no—
272C22×C8—431no—
273C22×C8—861no—
274C22×C8—861no—
275#123—21no—
276C22⋊Q8C2×Dic4311yescharacteristic
277C22⋊Q8C22⋊D4311yescharacteristic
278#121C2×Dic4311yescharacteristic
279#121C22⋊D4311yescharacteristic
280#120—21no—
281C4×D4—21no—
282C4×D4—21no—
283#117—21no—
284#117—21no—
285#117—21no—
286#117—21no—
287#117C22⋊D4311yescharacteristic
288C2×C4⋊C4C2×Dic4311yescharacteristic
289C2×C4⋊C4C2×Dic4311yescharacteristic
290C2×C22⋊C4—21no—
291C2×C22⋊C4—861no—
292C2×C42—21no—
293C2×C42—861no—
294#107—21no—
295#107—21no—
296#106—21no—
297#106—21no—
298C4⋊C8—861no—
299C4⋊C8—861no—
300#103—21no—
301#103—21no—
302#102—21no—
303#102—21no—
304C22⋊C8—21no—
305C22⋊C8—861no—
306C22⋊C8—861no—
307C22⋊C8—861no—
308C22⋊C8—861no—
309C22⋊C8—861no—
310C22⋊C8—861no—
311C22⋊C8—861no—
312C22⋊C8—861no—
313C22⋊C8C2×Dic4311yescharacteristic
314C22⋊C8C2×Dic4311yescharacteristic
315#97—861no—
316C4×C8—861no—
317#95—861no—
318C24#1062190011yescharacteristic
319#41—41no—
320#41—41no—
321C2×Q8C22⋊Dic4311yescharacteristic
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4C22⋊Dic4311yescharacteristic
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—1721no—
332C22×C4D4×D4311yescharacteristic
333C22×C4D4×D4311yescharacteristic
334C22×C4#1062190011yescharacteristic
335C22×C4C22×Dic4311yescharacteristic
336C22×C4C2×C22⋊D4311yescharacteristic
337C22×C4C2×C22⋊D4311yescharacteristic
338M16—3441no—
339M16—1721no—
340M16—1721no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—861no—
346C2×C8—861no—
347C2×C8—861no—
348C2×C8—861no—
349C2×C8—3441no—
350C2×C8—1721no—
351C2×C8—1721no—
352C2×C8—1721no—
353C2×C8—1721no—
354C2×C8—1721no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4C22⋊Dic4311yescharacteristic
362C4⋊C4C22⋊Dic4311yescharacteristic
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—21no—
366C22⋊C4—21no—
367C22⋊C4—21no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—862no—
371C22⋊C4—1721no—
372C42—21no—
373C42—41no—
374C42—41no—
375C42—1721no—
376C42—1721no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—41no—
381C23—41no—
382C23D4×Dic4311yescharacteristic
383C23#1306329711yescharacteristic
384C23#1306330611yescharacteristic
385Q8—41no—
386D4—41no—
387D4—41no—
388D4—41no—
389D4—81no—
390D4—81no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—3441no—
411C2×C4—3441no—
412C2×C4—1722no—
413C2×C4C2×C22⋊Dic4311yescharacteristic
414C2×C4D4×Dic4311yescharacteristic
415C2×C4#1306329311yescharacteristic
416C2×C4#1306329711yescharacteristic
417C8—41no—
418C8—41no—
419C8—3441no—
420C8—1721no—
421C8—1721no—
422C8—1721no—
423C8—1721no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—81no—
436C22—81no—
437C22#1458277911yescharacteristic
438C22#1458301611yescharacteristic
439C22#1458302111yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—41no—
444C4—41no—
445C4—41no—
446C4—81no—
447C4—81no—
448C4—3442no—
449C4#1458308811yescharacteristic
450C4#1458308811yescharacteristic
451C2—21no—
452C2—21no—
453C2—41no—
454C2—41no—
455C2—81no—
456C2#1913492411yescharacteristic
457C2#1913495911yescharacteristic
458C2#1913500911yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#3091C2
socleC22×C43#386
prime radicalC43×#525C22
cosocleC23×C4×C43C23
hypercenter#3091D43
hypocenterC43#9038
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3091

Complements

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

NH ≅ G/Ntype
2. #19134694C2semidirect
3. #19134666C2semidirect
5. #19132483C2semidirect
6. #19132441C2semidirect
27. C43×#484C4semidirect
28. C43×#483C4semidirect
30. C43×#481C4semidirect
31. C43×#480C4semidirect
240. #484Dic43semidirect
241. #483Dic43semidirect
243. #481Dic43semidirect
244. #480Dic43semidirect
264. C43#9038semidirect

Maximal subgroups

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

subgroupindex
#191436432
#191346942
#191346662
#191330862
#191324832
#191324412
C43×#30912
#903843