Finite Group Databasebeta

← #24997003

Subgroups — #24997003

Order 11008.

654 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 85 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#19144543C211yesmaximal, characteristic, complemented
2#19139753C211yesmaximal, characteristic
3#19134694C211yesmaximal, characteristic, complemented
4#19133127C211yesmaximal, characteristic, complemented
5#19132922C211yesmaximal, characteristic
6#19132447C211yesmaximal, characteristic, complemented
7C43×#2482C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9#14583240—22no—
10#14583234—21no—
11#14583229—21no—
12#14582942—21no—
13#14582907—21no—
14#14582863C2211yescharacteristic
15#14582863C2211yescharacteristic
16#14582824—21no—
17#14582811—21no—
18#14582793—22no—
19#14582762—21no—
20#14582755—21no—
21C4×C22⋊Dic43C2211yescharacteristic
22#14582658—22no—
23#14582635—22no—
24#14582623—22no—
25C2×#117×C43C2211yescharacteristic
26C22×C22⋊C4×C43C2211yescharacteristic
27C43×#399—21no—
28C43×#397—21no—
29C43×#388—22no—
30C43×#385—21no—
31C43×#381C2211yescharacteristic
32C43×#379—21no—
33C22×Dic86D411yescharacteristic
34C2×#10621877—21no—
35C2×#10621877—21no—
36#13063304—21no—
37#13063304—21no—
38#13063304—21no—
39#13063304—21no—
40C2×C4⋊Dic43D411yescharacteristic
41C2×Dic43⋊C4—21no—
42C2×C22⋊Dic43—22no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43—22no—
46C2×C4×Dic43D412yes—
47#13063258—22no—
48#13063256—22no—
49#13063248—22no—
50#13063248—22no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)D412yes—
55C43⋊#95—22no—
56C43⋊#95—22no—
57C43⋊#95—21no—
58C25×C43D411yescharacteristic
59C23×C4×C43D411yescharacteristic
60C23×C4×C43C2311yescharacteristic
61#117×C43—21no—
62#117×C43—21no—
63#117×C43—21no—
64#117×C43—21no—
65C2×C4⋊C4×C43—22no—
66C2×C4⋊C4×C43D411yescharacteristic
67C2×C4⋊C4×C43D411yescharacteristic
68C2×C22⋊C4×C43—22no—
69C2×C22⋊C4×C43—21no—
70C2×C22⋊C4×C43—21no—
71C2×C22⋊C4×C43—21no—
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—21no—
77C2×C22⋊C4×C43—22no—
78C2×C42×C43—21no—
79#95×C43—22no—
80#95×C43—21no—
81#95×C43D412yes—
82C24×C43—21no—
83C24×C43—21no—
84C24×C43—21no—
85C24×C43—42no—
86C24×C43—42no—
87C24×C43—42no—
88C24×C43C2×D411yescharacteristic
89C22×C4×C43—22no—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43—21no—
95C22×C4×C43—42no—
96C22×C4×C43—42no—
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43#4111yescharacteristic
103C22×Dic43—22no—
104C22×Dic43—21no—
105C22×Dic43—21no—
106C2×Dic86—21no—
107C2×Dic86—21no—
108C2×Dic86—42no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—82no—
114C22⋊C4×C43—42no—
115C22⋊C4×C43—44no—
116C22⋊C4×C43—41no—
117C22⋊C4×C43—41no—
118C22⋊C4×C43—41no—
119C22⋊C4×C43—41no—
120C22⋊C4×C43—41no—
121C22⋊C4×C43—41no—
122C22⋊C4×C43—82no—
123C42×C43—41no—
124C42×C43—41no—
125C22⋊Dic43—42no—
126C22⋊Dic43—44no—
127C22⋊Dic43—41no—
128C22⋊Dic43—41no—
129C22⋊Dic43—82no—
130C4⋊Dic43—21no—
131C4⋊Dic43—21no—
132Dic43⋊C4—41no—
133Dic43⋊C4—41no—
134C4×Dic43—42no—
135#10621877—42no—
136#10621877—42no—
137C2×C43⋊C8—22no—
138C2×C43⋊C8—41no—
139C23×C43—22no—
140C23×C43—22no—
141C23×C43—22no—
142C23×C43—22no—
143C23×C43—22no—
144C23×C43—41no—
145C23×C43—42no—
146C23×C43—41no—
147C23×C43—41no—
148C23×C43—42no—
149C23×C43—41no—
150C23×C43—41no—
151C23×C43—42no—
152C23×C43—42no—
153C23×C43—81no—
154C23×C43—81no—
155C23×C43—88no—
156C23×C43#12011yescharacteristic
157C23×C43#12011yescharacteristic
158C23×C43#12111yescharacteristic
159C2×C4×C43—22no—
160C2×C4×C43—22no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—42no—
166C2×C4×C43—42no—
167C2×C4×C43—42no—
168C2×C4×C43—42no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43—42no—
173C2×C4×C43—42no—
174C2×C4×C43—42no—
175C2×C4×C43—81no—
176C2×C4×C43#12011yescharacteristic
177C2×C4×C43#12111yescharacteristic
178C2×C4×C43#12111yescharacteristic
179C2×C4×C43#12711yescharacteristic
180C2×Dic43—42no—
181C2×Dic43—42no—
182C2×Dic43—42no—
183C2×Dic43—41no—
184C2×Dic43—41no—
185C2×Dic43—42no—
186C2×Dic43—42no—
187Dic86—42no—
188Dic86—81no—
189C43⋊C8—42no—
190C43⋊C8—81no—
191#9944—431nomaximal, Sylow
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—44no—
200C22×C43—44no—
201C22×C43—44no—
202C22×C43—42no—
203C22×C43—82no—
204C22×C43—82no—
205C22×C43—82no—
206C22×C43—82no—
207C22×C43—81no—
208C22×C43—81no—
209C22×C43#39211yescharacteristic
210C22×C43#45512yes—
211C22×C43#45812yes—
212C4×C43—21no—
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—21no—
216C4×C43—82no—
217C4×C43—81no—
218C4×C43—81no—
219C4×C43—81no—
220Dic43—82no—
221Dic43—81no—
222Dic43—81no—
223#3095—431no—
224#2561—431no—
225#2482D4311yescharacteristic
226#1826—431no—
227#1511—431no—
228#1462—431no—
229#1284—431no—
230C2×C43—22no—
231C2×C43—22no—
232C2×C43—41no—
233C2×C43—82no—
234C2×C43#200411yescharacteristic
235C2×C43#201011yescharacteristic
236C2×C43#202211yescharacteristic
237C2×C22⋊Q8—431no—
238C2×#117C2×D4311yescharacteristic
239C22×C22⋊C4C2×D4311yescharacteristic
240#485—862no—
241#484—861no—
242#483—861no—
243#428—861no—
244#419—861no—
245#407—431no—
246#407—431no—
247#399—21no—
248#397—21no—
249#397—861no—
250#393—861no—
251#388—22no—
252#388—862no—
253#385—21no—
254#381—861no—
255#381C2×D4311yescharacteristic
256#379—21no—
257#379—861no—
258C4×C22⋊C4—431no—
259#339—862no—
260#328—862no—
261#323—862no—
262C43#994411yescharacteristic, complemented, Sylow
263C25C22⋊D4311yescharacteristic
264C22×Q8—431no—
265C23×C4C22⋊D4311yescharacteristic
266C23×C4C22×D4311yescharacteristic
267C2×M16—861no—
268C2×M16—861no—
269C22⋊Q8—861no—
270C22⋊Q8—861no—
271C22⋊Q8—861no—
272C22⋊Q8—861no—
273#117—21no—
274#117—21no—
275#117—21no—
276#117—21no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—431no—
279C2×C4⋊C4—861no—
280C2×C4⋊C4C22⋊D4311yescharacteristic
281C2×C4⋊C4C22⋊D4311yescharacteristic
282C2×C22⋊C4—22no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—862no—
293C2×C22⋊C4—862no—
294C2×C22⋊C4—861no—
295C2×C22⋊C4—861no—
296C2×C42—21no—
297C2×C42—432no—
298#107—862no—
299#106—862no—
300#103—862no—
301#103—862no—
302C22⋊C8—432no—
303C22⋊C8—861no—
304C22⋊C8—861no—
305C22⋊C8—861no—
306#95—22no—
307#95—21no—
308#95—862no—
309#95—862no—
310#95—861no—
311#95C22⋊D4312yes—
312C24—21no—
313C24—21no—
314C24—21no—
315C24—42no—
316C24—42no—
317C24—42no—
318C24C2×C22⋊D4311yescharacteristic
319C2×Q8—861no—
320C2×Q8—861no—
321C2×Q8—1722no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—862no—
331C22×C4—861no—
332C22×C4—861no—
333C22×C4D4×D4311yescharacteristic
334C22×C4D4×D4311yescharacteristic
335C22×C4D4×D4311yescharacteristic
336C22×C4#1062190011yescharacteristic
337C22×C4C2×C22⋊D4311yescharacteristic
338C22×C4C2×C22⋊D4311yescharacteristic
339M16—1722no—
340M16—1722no—
341C2×C8—862no—
342C2×C8—1721no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—82no—
348C4⋊C4—861no—
349C4⋊C4—861no—
350C4⋊C4—1721no—
351C4⋊C4—1721no—
352C22⋊C4—42no—
353C22⋊C4—44no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—82no—
361C22⋊C4—3442no—
362C22⋊C4—1722no—
363C22⋊C4—1724no—
364C22⋊C4—1721no—
365C22⋊C4—1721no—
366C42—41no—
367C42—41no—
368C42—1722no—
369C23—22no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—22no—
374C23—41no—
375C23—42no—
376C23—41no—
377C23—41no—
378C23—42no—
379C23—41no—
380C23—41no—
381C23—42no—
382C23—42no—
383C23—81no—
384C23—81no—
385C23—88no—
386C23#1306329311yescharacteristic
387C23#1306329411yescharacteristic
388C23#1306329711yescharacteristic
389Q8—3441no—
390Q8—1722no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—81no—
408C2×C4—1722no—
409C2×C4—1722no—
410C2×C4—1722no—
411C2×C4—1721no—
412C2×C4—1721no—
413C2×C4—1722no—
414C2×C4—1722no—
415C2×C4#1306329311yescharacteristic
416C2×C4#1306329611yescharacteristic
417C2×C4#1306329711yescharacteristic
418C2×C4#1306332111yescharacteristic
419C8—3441no—
420C8—1722no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—44no—
429C22—44no—
430C22—44no—
431C22—42no—
432C22—82no—
433C22—82no—
434C22—82no—
435C22—82no—
436C22—81no—
437C22—81no—
438C22#1458280711yescharacteristic
439C22#1458307712yes—
440C22#1458308812yes—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—82no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—3442no—
450C4—3441no—
451C4—3441no—
452C2—22no—
453C2—22no—
454C2—41no—
455C2—82no—
456C2#1913562211yescharacteristic
457C2#1913566011yescharacteristic
458C2#1913572311yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#2482C2
socleC22×C43#392
prime radicalC25×C43D4
hypercenter#2482D43
hypocenterC43#9944
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2482

Complements

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

NH ≅ G/Ntype
1. #19144543C2semidirect
3. #19134694C2semidirect
4. #19133127C2semidirect
6. #19132447C2semidirect
262. C43#9944semidirect

Maximal subgroups

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

subgroupindex
#191445432
#191397532
#191346942
#191331272
#191329222
#191324472
C43×#24822
#994443