Finite Group Databasebeta

← #24994520

Subgroups — #24994520

Order 11008.

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

normal subgroups only

This group has 660 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#19138876C211yesmaximal, characteristic
2#19137191C211yesmaximal, characteristic
3#19134667C211yesmaximal, characteristic
4#19134667C211yesmaximal, characteristic
5#19134667C211yesmaximal, characteristic
6C43⋊#1304C211yesmaximal, characteristic
7C43×#1304C211yesmaximal, characteristic
8C22×C22⋊Dic43C2211yescharacteristic
9C22×C22⋊Dic43C2211yescharacteristic
10#14582824—22no—
11#14582793—22no—
12#14582787—22no—
13#14582774—21no—
14#14582774C412yescomplemented
15#14582760—21no—
16#14582760C412yescomplemented
17#14582757—21no—
18#14582755C2211yescharacteristic
19#14582755C2211yescharacteristic
20C22⋊C4×Dic43—21no—
21#14582665—22no—
22#14582665—22no—
23#14582665—22no—
24C43×#379C2211yescharacteristic
25C43×#379C2211yescharacteristic
26C43×#379C2211yescharacteristic
27C23×Dic43C2×C411yescharacteristic
28C23×Dic43C2×C411yescharacteristic
29C23×Dic43D411yescharacteristic
30C23×Dic43D411yescharacteristic
31C2×C4⋊Dic43—22no—
32C2×Dic43⋊C4—22no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37C2×C22⋊Dic43—21no—
38C2×C22⋊Dic43—21no—
39C2×C22⋊Dic43—21no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43—21no—
46C2×C22⋊Dic43—21no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43C2×C412yes—
49C2×C22⋊Dic43D412yes—
50C2×C22⋊Dic43D412yes—
51C2×C4×Dic43—22no—
52C43⋊#95—22no—
53C43⋊#95—22no—
54C43⋊#95—22no—
55C43⋊#95—22no—
56C43⋊#95—22no—
57C25×C43C2311yescharacteristic
58C2×C22⋊C4×C43—21no—
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43—21no—
61C2×C22⋊C4×C43—21no—
62C2×C22⋊C4×C43—21no—
63C2×C22⋊C4×C43—21no—
64C2×C22⋊C4×C43—21no—
65C2×C22⋊C4×C43C2×C412yes—
66C2×C22⋊C4×C43D412yes—
67C24×C43—42no—
68C24×C43—42no—
69C24×C43—81no—
70C24×C43C22×C411yescharacteristic
71C24×C43C2×D411yescharacteristic
72C24×C43C2×D411yescharacteristic
73C24×C43C2×D411yescharacteristic
74C24×C43C2×D411yescharacteristic
75C24×C43#4111yescharacteristic
76C24×C43#4111yescharacteristic
77C22×C4×C43—22no—
78C22×C4×C43—22no—
79C22×C4×C43—41no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C22×Dic43—21no—
83C22×Dic43—21no—
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—22no—
89C22×Dic43—21no—
90C22×Dic43—21no—
91C22×Dic43—42no—
92C22×Dic43—42no—
93C22×Dic43—41no—
94C22×Dic43—81no—
95C22×Dic43—81no—
96C22×Dic43C22⋊C412yes—
97C22×Dic43C22⋊C412yes—
98C22⋊C4×C43—42no—
99C22⋊C4×C43—42no—
100C22⋊C4×C43—42no—
101C22⋊C4×C43—42no—
102C22⋊C4×C43—42no—
103C22⋊C4×C43—42no—
104C22⋊C4×C43—81no—
105C22⋊C4×C43—81no—
106C22⋊C4×C43—81no—
107C22⋊Dic43—22no—
108C22⋊Dic43—22no—
109C22⋊Dic43—22no—
110C22⋊Dic43—22no—
111C22⋊Dic43—42no—
112C22⋊Dic43—42no—
113C22⋊Dic43—42no—
114C22⋊Dic43—42no—
115C22⋊Dic43—41no—
116C22⋊Dic43—41no—
117C22⋊Dic43—41no—
118C22⋊Dic43—41no—
119C22⋊Dic43—81no—
120C22⋊Dic43—81no—
121C4⋊Dic43—82no—
122Dic43⋊C4—82no—
123C4×Dic43—82no—
124C23×C43—22no—
125C23×C43—22no—
126C23×C43—22no—
127C23×C43—22no—
128C23×C43—22no—
129C23×C43—22no—
130C23×C43—41no—
131C23×C43—41no—
132C23×C43—41no—
133C23×C43—41no—
134C23×C43—41no—
135C23×C43—41no—
136C23×C43—41no—
137C23×C43—41no—
138C23×C43—41no—
139C23×C43—41no—
140C23×C43—41no—
141C23×C43—41no—
142C23×C43—41no—
143C23×C43—41no—
144C23×C43—41no—
145C23×C43—88no—
146C23×C43C2×C22⋊C411yescharacteristic
147C23×C43C4×D411yescharacteristic
148C23×C43C4×D411yescharacteristic
149C23×C43#12011yescharacteristic
150C23×C43#12111yescharacteristic
151C23×C43#12111yescharacteristic
152C23×C43#12311yescharacteristic
153C2×C4×C43—42no—
154C2×C4×C43—42no—
155C2×C4×C43—42no—
156C2×C4×C43—42no—
157C2×C4×C43—42no—
158C2×C4×C43—42no—
159C2×C4×C43—81no—
160C2×C4×C43—81no—
161C2×C4×C43—81no—
162C2×Dic43—22no—
163C2×Dic43—22no—
164C2×Dic43—42no—
165C2×Dic43—42no—
166C2×Dic43—42no—
167C2×Dic43—42no—
168C2×Dic43—42no—
169C2×Dic43—42no—
170C2×Dic43—42no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—42no—
174C2×Dic43—42no—
175C2×Dic43—81no—
176C2×Dic43—81no—
177C2×Dic43—81no—
178C2×Dic43—81no—
179C2×Dic43—81no—
180C2×Dic43—81no—
181C2×Dic43—81no—
182C2×Dic43—81no—
183C2×Dic43—81no—
184#9500—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—21no—
193C22×C43—21no—
194C22×C43—21no—
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—21no—
204C22×C43—44no—
205C22×C43—44no—
206C22×C43—82no—
207C22×C43—82no—
208C22×C43—82no—
209C22×C43—82no—
210C22×C43—82no—
211C22×C43#38611yescharacteristic
212C22×C43#41012yes—
213C22×C43#45812yes—
214C4×C43—82no—
215C4×C43—82no—
216C4×C43—161no—
217Dic43—42no—
218Dic43—42no—
219Dic43—82no—
220Dic43—81no—
221Dic43—81no—
222Dic43—161no—
223#2483—431no—
224#2312—431no—
225#1819—431no—
226#1819—431no—
227#1819—431no—
228#1304—431no—
229#1304D4311yescharacteristic
230C2×C43—22no—
231C2×C43—22no—
232C2×C43—41no—
233C2×C43—41no—
234C2×C43—41no—
235C2×C43—41no—
236C2×C43—41no—
237C2×C43#189011yescharacteristic
238C2×C43#189911yescharacteristic
239C2×C43#191311yescharacteristic
240C22×C22⋊C4—431no—
241C22×C22⋊C4—431no—
242#397—862no—
243#388—862no—
244#388—862no—
245#385—432no—
246#385—861no—
247#381—432no—
248#381—861no—
249#380—861no—
250#379—431no—
251#379—431no—
252#379C2×D4311yescharacteristic
253#379C2×D4311yescharacteristic
254#379C2×D4311yescharacteristic
255C4×C22⋊C4—861no—
256#342—862no—
257#342—862no—
258#342—862no—
259C43#950011yescharacteristic, complemented, Sylow
260C25C22×D4311yescharacteristic
261C23×C4—431no—
262C23×C4—431no—
263C23×C4—431no—
264C23×C4—431no—
265C2×C4⋊C4—862no—
266C2×C4⋊C4—862no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—432no—
275C2×C22⋊C4—432no—
276C2×C22⋊C4—432no—
277C2×C22⋊C4—861no—
278C2×C22⋊C4—861no—
279C2×C22⋊C4—861no—
280C2×C22⋊C4—861no—
281C2×C22⋊C4—861no—
282C2×C22⋊C4—861no—
283C2×C22⋊C4—861no—
284C2×C22⋊C4—861no—
285C2×C22⋊C4—861no—
286C2×C22⋊C4—861no—
287C2×C22⋊C4—861no—
288C2×C22⋊C4—861no—
289C2×C22⋊C4—861no—
290C2×C22⋊C4—861no—
291C2×C22⋊C4—861no—
292C2×C22⋊C4C4×D4312yes—
293C2×C22⋊C4D17212yes—
294C2×C42—862no—
295#95—862no—
296#95—862no—
297#95—862no—
298#95—862no—
299#95—862no—
300C24—42no—
301C24—42no—
302C24—81no—
303C24C2×C4×D4311yescharacteristic
304C24C2×D17211yescharacteristic
305C24#1062189811yescharacteristic
306C24D4×D4311yescharacteristic
307C24D4×D4311yescharacteristic
308C24D4×D4311yescharacteristic
309C24#1062190211yescharacteristic
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—41no—
313C22×C4—432no—
314C22×C4—432no—
315C22×C4—861no—
316C22×C4—861no—
317C22×C4—861no—
318C22×C4—861no—
319C22×C4—861no—
320C22×C4—861no—
321C22×C4—861no—
322C22×C4—861no—
323C22×C4—861no—
324C22×C4—861no—
325C22×C4—862no—
326C22×C4—3441no—
327C22×C4—3441no—
328C22×C4—1721no—
329C22×C4—1722no—
330C22×C4—1722no—
331C4⋊C4—3442no—
332C4⋊C4—3442no—
333C22⋊C4—42no—
334C22⋊C4—42no—
335C22⋊C4—42no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—42no—
339C22⋊C4—81no—
340C22⋊C4—81no—
341C22⋊C4—81no—
342C22⋊C4—862no—
343C22⋊C4—862no—
344C22⋊C4—862no—
345C22⋊C4—862no—
346C22⋊C4—3441no—
347C22⋊C4—3441no—
348C22⋊C4—1722no—
349C22⋊C4—1722no—
350C22⋊C4—1722no—
351C22⋊C4—1721no—
352C22⋊C4—1721no—
353C22⋊C4—1721no—
354C22⋊C4—1721no—
355C22⋊C4—1722no—
356C42—3442no—
357C23—22no—
358C23—22no—
359C23—22no—
360C23—22no—
361C23—22no—
362C23—22no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—88no—
379C23C22⋊C4×D4311yescharacteristic
380C23#1306328711yescharacteristic
381C23C4×D17211yescharacteristic
382C23#1306329511yescharacteristic
383C23#1306329811yescharacteristic
384C23#1306330011yescharacteristic
385C23#1306331011yescharacteristic
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—862no—
396C2×C4—862no—
397C2×C4—3441no—
398C2×C4—3441no—
399C2×C4—3441no—
400C2×C4—3441no—
401C2×C4—3441no—
402C2×C4—3441no—
403C2×C4—3441no—
404C2×C4—3441no—
405C2×C4—3441no—
406C2×C4—1722no—
407C2×C4—1722no—
408C2×C4—1722no—
409C2×C4—1722no—
410C2×C4—1722no—
411C2×C4—1721no—
412C2×C4—1721no—
413C2×C4—1722no—
414C2×C4—1722no—
415C2×C4—1722no—
416C2×C4—1722no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—44no—
437C22—44no—
438C22—82no—
439C22—82no—
440C22—82no—
441C22—82no—
442C22—82no—
443C22#1458277711yescharacteristic
444C22#1458287112yes—
445C22#1458309012yes—
446C4—82no—
447C4—82no—
448C4—161no—
449C4—3442no—
450C4—3441no—
451C4—3441no—
452C4—1722no—
453C4—1722no—
454C4—6881no—
455C2—22no—
456C2—22no—
457C2—41no—
458C2—41no—
459C2—41no—
460C2—41no—
461C2—41no—
462C2#1913500711yescharacteristic
463C2#1913505211yescharacteristic
464C2#1913513611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC24×C43C22×C4
FrattiniC25C22×D43
FittingC43×#1304C2
socleC22×C43#386
prime radical, cosocleC25×C43C23
hypercenter#1304D43
hypocenterC43#9500
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ #1304

Complements

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

NH ≅ G/Ntype
14. #14582774C4semidirect
16. #14582760C4semidirect
259. C43#9500semidirect

Maximal subgroups

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

subgroupindex
#191388762
#191371912
#191346672
C43⋊#13042
C43×#13042
#950043