Finite Group Databasebeta

← #24991710

Subgroups — #24991710

Order 11008.

468 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144508C211yesmaximal, characteristic
2#19143645C211yesmaximal, characteristic
3#19134666C211yesmaximal, characteristic, complemented
4#19133084C211yesmaximal, characteristic
5#19132482C211yesmaximal, characteristic, complemented
6#19132443C211yesmaximal, characteristic, complemented
7C43×#1826C211yesmaximal, characteristic, complemented
8#14583410C2211yescharacteristic
9#14583240—21no—
10#14583234C411yescharacteristic, complemented
11#14583229C411yescharacteristic, complemented
12#14583223—21no—
13#14583217C411yescharacteristic, complemented
14#14583212C411yescharacteristic, complemented
15#14582975—21no—
16#14582968—21no—
17#14582967—21no—
18(C22⋊D43)⋊C8—21no—
19#14582957—21no—
20#14582935—21no—
21#14582893—21no—
22#14582864—21no—
23C2×C22⋊(C43⋊C8)C2211yescharacteristic
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25C2×C22⋊(C43⋊C8)C2211yescharacteristic
26#14582654—21no—
27#14582654—21no—
28#14582635—21no—
29#14582632—21no—
30C2×#117×C43C2211yescharacteristic
31C43×#407C2211yescharacteristic
32C4×C22⋊C4×C43C2211yescharacteristic
33C43×#339—21no—
34C43×#339—21no—
35C2×#10621898D411yescharacteristic
36C2×#10621872—21no—
37C22×C43⋊C8—21no—
38C22×C43⋊C8—21no—
39C22×C43⋊C8D411yescharacteristic
40C22×C43⋊C8D411yescharacteristic
41C2×C8×D43—21no—
42#13063308—21no—
43#13063304C2×C411yescharacteristic
44#13063304D411yescharacteristic
45#13063299C2×C411yescharacteristic
46#13063299D411yescharacteristic
47#13063294—21no—
48C4×C22⋊D43—21no—
49C4×C22⋊D43—21no—
50#13063284D411yescharacteristic
51#13063258—21no—
52#13063258—21no—
53#13063256—21no—
54#13063256—21no—
55Dic43⋊C8—21no—
56Dic43⋊C8—21no—
57#13063248—21no—
58#13063248—21no—
59#13063245—21no—
60#13063245—21no—
61C22⋊(C43⋊C8)—21no—
62C22⋊(C43⋊C8)—21no—
63C22⋊(C43⋊C8)—21no—
64C22⋊(C43⋊C8)—21no—
65C22⋊(C43⋊C8)—21no—
66C22⋊(C43⋊C8)C2×C411yescharacteristic
67C22⋊(C43⋊C8)C2×C411yescharacteristic
68(C2×D43)⋊C8—21no—
69(C2×D43)⋊C8—21no—
70#13063235—21no—
71C8×Dic43—21no—
72C23×C4×C43C2311yescharacteristic
73C2×M16×C43D411yescharacteristic
74C2×M16×C43D411yescharacteristic
75#117×C43—21no—
76#117×C43—21no—
77#117×C43—21no—
78#117×C43—21no—
79C2×C4⋊C4×C43C2×C411yescharacteristic
80C2×C4⋊C4×C43C2×C411yescharacteristic
81C2×C22⋊C4×C43—21no—
82C2×C22⋊C4×C43—21no—
83C2×C42×C43—21no—
84C2×C42×C43—21no—
85C22⋊C8×C43—21no—
86C22⋊C8×C43—21no—
87#95×C43—21no—
88C24×C43#4111yescharacteristic
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43C22×C411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43#4111yescharacteristic
100C2×C22⋊D43—21no—
101C2×C22⋊D43—21no—
102C2×C22⋊D43—21no—
103#10621898—41no—
104#10621898—41no—
105C2×D172C22⋊C411yescharacteristic
106C2×C4×D43—21no—
107C2×Dic86C22⋊C411yescharacteristic
108M16×C43—41no—
109M16×C43—41no—
110C2×C8×C43—21no—
111C2×C8×C43—21no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—21no—
116C22⋊C4×C43—22no—
117C22⋊C4×C43—41no—
118C22⋊C4×C43—41no—
119C22⋊C4×C43—41no—
120C42×C43—41no—
121C42×C43—41no—
122C42×C43—41no—
123C42×C43—41no—
124C22⋊Dic43—21no—
125C22⋊Dic43—21no—
126C22⋊Dic43—21no—
127(C2×D43)⋊C4—21no—
128(C2×D43)⋊C4—21no—
129C4⋊Dic43C22⋊C411yescharacteristic
130C4⋊Dic43C22⋊C411yescharacteristic
131Dic43⋊C4—21no—
132Dic43⋊C4—21no—
133C4×Dic43—21no—
134C2×C43⋊C8—21no—
135C2×C43⋊C8—21no—
136C2×C43⋊C8—21no—
137C2×C43⋊C8—21no—
138C2×C43⋊C8—41no—
139C2×C43⋊C8—41no—
140C2×C43⋊C8—41no—
141C2×C43⋊C8—41no—
142C2×C43⋊C8—41no—
143C2×C43⋊C8—41no—
144C2×C43⋊C8—41no—
145#10621872—81no—
146C8×D43—81no—
147C23×C43—21no—
148C23×C43—21no—
149C23×C43—41no—
150C23×C43—41no—
151C23×C43C4×D411yescharacteristic
152C23×C43#12111yescharacteristic
153C23×C43#12311yescharacteristic
154C22×D43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—21no—
158C2×C4×C43—21no—
159C2×C4×C43—21no—
160C2×C4×C43—21no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—42no—
165C2×C4×C43—42no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—81no—
171C2×C4×C43—81no—
172C2×C4×C43C2×C22⋊C411yescharacteristic
173C2×C4×C43C4×D411yescharacteristic
174C2×C4×C43#12011yescharacteristic
175C2×C4×C43#12111yescharacteristic
176C22⋊D43—41no—
177C22⋊D43—41no—
178C22⋊D43—81no—
179C22⋊D43—81no—
180C2×Dic43—21no—
181C2×Dic43—21no—
182C2×Dic43—21no—
183D172—41no—
184C4×D43—41no—
185C4×D43—41no—
186Dic86—41no—
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—81no—
204C22×C43—81no—
205C22×C43#38611yescharacteristic
206C22×C43#44311yescharacteristic
207C22×C43#44411yescharacteristic
208C2×D43—41no—
209C2×D43—41no—
210C2×D43—41no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—21no—
214C4×C43—82no—
215C4×C43—81no—
216C4×C43—81no—
217C4×C43#45811yescharacteristic
218C4×C43#45811yescharacteristic
219Dic43—41no—
220Dic43—41no—
221Dic43—41no—
222#3091—431no—
223#2976—431no—
224#1826D4311yescharacteristic, complemented
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#187611yescharacteristic
234C2×C43#188111yescharacteristic
235C2×C43#189011yescharacteristic
236D43—81no—
237#525—431no—
238C2×#117C2×D4311yescharacteristic
239#485—861no—
240#484—431no—
241#483—431no—
242#482—861no—
243#481—431no—
244#480—431no—
245#436—861no—
246#435—861no—
247#435—861no—
248C8×D4—861no—
249#433—861no—
250#427—861no—
251#416—861no—
252#408—861no—
253#407C2×D4311yescharacteristic
254C2×C22⋊C8—431no—
255C2×C22⋊C8—431no—
256C2×C22⋊C8—431no—
257C4×C22⋊C4C2×D4311yescharacteristic
258#339—21no—
259#339—21no—
260#336—861no—
261#336—861no—
262#328—861no—
263#327—861no—
264C43#903811yescharacteristic, complemented, Sylow
265C2×#41—431no—
266C23×C4C22×D4311yescharacteristic
267C2×M16—861no—
268C2×M16C22⋊D4311yescharacteristic
269C2×M16C22⋊D4311yescharacteristic
270C22×C8—431no—
271C22×C8—431no—
272C22×C8—861no—
273C22×C8—861no—
274C22×C8—861no—
275#123—861no—
276C22⋊Q8—431no—
277C22⋊Q8—431no—
278#121—431no—
279#121—431no—
280#120—861no—
281C4×D4—861no—
282C4×D4—861no—
283#117—21no—
284#117—21no—
285#117—21no—
286#117—21no—
287#117—431no—
288C2×C4⋊C4C4×D4311yescharacteristic
289C2×C4⋊C4C4×D4311yescharacteristic
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C42—21no—
293C2×C42—21no—
294#107—861no—
295#107—861no—
296#106—861no—
297#106—861no—
298C4⋊C8—861no—
299C4⋊C8—861no—
300#103—861no—
301#103—861no—
302#102—861no—
303#102—861no—
304C22⋊C8—21no—
305C22⋊C8—21no—
306C22⋊C8—431no—
307C22⋊C8—431no—
308C22⋊C8—861no—
309C22⋊C8—861no—
310C22⋊C8—861no—
311C22⋊C8—861no—
312C22⋊C8—861no—
313C22⋊C8—861no—
314C22⋊C8—861no—
315#97—861no—
316C4×C8—861no—
317#95—21no—
318C24#1062190011yescharacteristic
319#41—1721no—
320#41—1721no—
321C2×Q8—431no—
322C2×D4—431no—
323C2×D4—861no—
324C2×D4—861no—
325C2×D4—861no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—861no—
332C22×C4C2×C4×D4311yescharacteristic
333C22×C4#1062189811yescharacteristic
334C22×C4D4×D4311yescharacteristic
335C22×C4D4×D4311yescharacteristic
336C22×C4D4×D4311yescharacteristic
337C22×C4C2×C22⋊D4311yescharacteristic
338M16—41no—
339M16—41no—
340M16—3441no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—861no—
344C2×C8—861no—
345C2×C8—861no—
346C2×C8—861no—
347C2×C8—3441no—
348C2×C8—1721no—
349C2×C8—1721no—
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—431no—
360C4⋊C4—431no—
361C4⋊C4—861no—
362C4⋊C4—861no—
363C22⋊C4—22no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—861no—
368C22⋊C4—861no—
369C22⋊C4—861no—
370C22⋊C4—861no—
371C22⋊C4—861no—
372C42—41no—
373C42—41no—
374C42—41no—
375C42—41no—
376C42—861no—
377C23—21no—
378C23—21no—
379C23—41no—
380C23—41no—
381C23—861no—
382C23(C22⋊D43)⋊C411yescharacteristic
383C23#1306329611yescharacteristic
384C23#1306330711yescharacteristic
385Q8—1721no—
386D4—3441no—
387D4—3441no—
388D4—1721no—
389D4—1721no—
390D4—1721no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—861no—
409C2×C4—861no—
410C2×C4—861no—
411C2×C4—1721no—
412C2×C4—1721no—
413C2×C4C22⋊C4×D4311yescharacteristic
414C2×C4C4×C22⋊D4311yescharacteristic
415C2×C4#1306329311yescharacteristic
416C2×C4#1306329811yescharacteristic
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—81no—
433C22—81no—
434C22—1721no—
435C22—1721no—
436C22—1721no—
437C22#1458277511yescharacteristic
438C22#1458301311yescharacteristic
439C22#1458301811yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—82no—
444C4—81no—
445C4—81no—
446C4—1721no—
447C4—1721no—
448C4—1721no—
449C4#1458308811yescharacteristic
450C4#1458308811yescharacteristic
451C2—21no—
452C2—21no—
453C2—41no—
454C2—41no—
455C2—3441no—
456C2#1913491911yescharacteristic
457C2#1913495411yescharacteristic
458C2#1913500511yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1826C2
socleC22×C43#386
prime radical#14583410C22
cosocleC23×C4×C43C23
hypercenter#1826D43
hypocenterC43#9038
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
3. #19134666C2semidirect
5. #19132482C2semidirect
6. #19132443C2semidirect
7. C43×#1826C2semidirect
10. #14583234C4semidirect
11. #14583229C4semidirect
13. #14583217C4semidirect
14. #14583212C4semidirect
224. #1826D43semidirect
264. C43#9038semidirect

Maximal subgroups

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

subgroupindex
#191445082
#191436452
#191346662
#191330842
#191324822
#191324432
C43×#18262
#903843