Finite Group Databasebeta

← #24997169

Subgroups — #24997169

Order 11008.

658 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C2×#14583234C211yesmaximal, characteristic, complemented
2C2×#14583217C211yesmaximal, characteristic
3#19140523C211yesmaximal, characteristic
4C2×#14582635C211yesmaximal, characteristic, complemented
5C2×#14582632C211yesmaximal, characteristic
6#19132438C211yesmaximal, characteristic, complemented
7C43×#1445C211yesmaximal, characteristic, complemented
8C2×#13063304C2211yescharacteristic
9C2×#13063299C2211yescharacteristic
10#14583234—22no—
11#14583234—22no—
12#14583217—22no—
13#14583217—22no—
14C2×#13063258—21no—
15C2×#13063256—21no—
16C2×#13063248—21no—
17C2×#13063245—21no—
18C2×C22⋊(C43⋊C8)C2211yescharacteristic
19C2×C22⋊(C43⋊C8)C2211yescharacteristic
20#14582839—21no—
21#14582826—21no—
22#14582817—21no—
23#14582812—21no—
24#14582778—22no—
25#14582635—22no—
26#14582632—22no—
27C22×C4⋊C4×C43C2211yescharacteristic
28C2×#95×C43—22no—
29C2×#95×C43C2211yescharacteristic
30C2×#95×C43C2211yescharacteristic
31C22×Dic86D411yescharacteristic
32C22×D172D411yescharacteristic
33C22×C22⋊D43—21no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36#13063304—21no—
37#13063304—21no—
38#13063304—21no—
39#13063304—21no—
40#13063299—21no—
41#13063299—21no—
42#13063299—21no—
43#13063299—21no—
44C2×C4⋊Dic43D411yescharacteristic
45C2×C4⋊Dic43D411yescharacteristic
46C2×Dic43⋊C4—21no—
47C2×C22⋊Dic43—21no—
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—22no—
50C2×(C2×D43)⋊C4—22no—
51#13063258—24no—
52#13063256—24no—
53#13063248—24no—
54#13063245—24no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)D412yes—
58C22⋊(C43⋊C8)D412yes—
59C43⋊#95—22no—
60C43⋊#95—22no—
61C23×C4×C43—21no—
62C23×C4×C43—21no—
63C23×C4×C43D412yes—
64C23×C4×C43C2311yescharacteristic
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43D412yes—
71#95×C43—21no—
72#95×C43—21no—
73#95×C43—21no—
74#95×C43—21no—
75#95×C43—44no—
76C24×C43C2×D411yescharacteristic
77C23×D43—21no—
78C22×C4×C43—22no—
79C22×C4×C43—22no—
80C22×C4×C43—22no—
81C22×C4×C43—22no—
82C22×C4×C43—22no—
83C22×C4×C43—42no—
84C22×C4×C43—42no—
85C22×C4×C43—42no—
86C22×C4×C43—42no—
87C22×C4×C43—41no—
88C22×C4×C43—42no—
89C22×C4×C43—42no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43—42no—
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43#4111yescharacteristic
100C2×C22⋊D43—41no—
101C2×C22⋊D43—41no—
102C2×C22⋊D43—42no—
103C2×C22⋊D43—42no—
104C22×Dic43—21no—
105C22×Dic43—21no—
106C22×Dic43—21no—
107C2×D172—21no—
108C2×D172—21no—
109C2×D172—42no—
110C2×Dic86—21no—
111C2×Dic86—21no—
112C2×Dic86—42no—
113C4⋊C4×C43—22no—
114C4⋊C4×C43—22no—
115C4⋊C4×C43—41no—
116C4⋊C4×C43—41no—
117C22⋊Dic43—41no—
118C22⋊Dic43—41no—
119(C2×D43)⋊C4—41no—
120(C2×D43)⋊C4—41no—
121(C2×D43)⋊C4—82no—
122(C2×D43)⋊C4—82no—
123C4⋊Dic43—21no—
124C4⋊Dic43—21no—
125C4⋊Dic43—21no—
126C4⋊Dic43—21no—
127Dic43⋊C4—41no—
128Dic43⋊C4—41no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—42no—
132C2×C43⋊C8—42no—
133C23×C43—21no—
134C23×C43—21no—
135C23×C43—22no—
136C23×C43#12011yescharacteristic
137C23×C43#12111yescharacteristic
138C23×C43#12711yescharacteristic
139C23×C43#13512yes—
140C23×C43#13712yes—
141C22×D43—41no—
142C22×D43—42no—
143C22×D43—41no—
144C22×D43—41no—
145C22×D43—42no—
146C2×C4×C43—22no—
147C2×C4×C43—22no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—44no—
153C2×C4×C43—42no—
154C2×C4×C43—44no—
155C2×C4×C43—44no—
156C2×C4×C43—42no—
157C2×C4×C43—42no—
158C2×C4×C43—42no—
159C2×C4×C43—42no—
160C2×C4×C43—82no—
161C2×C4×C43—81no—
162C2×C4×C43—82no—
163C2×C4×C43—81no—
164C2×C4×C43—81no—
165C2×C4×C43—81no—
166C2×C4×C43—82no—
167C2×C4×C43#12011yescharacteristic
168C2×C4×C43#12011yescharacteristic
169C2×C4×C43#12111yescharacteristic
170C2×C4×C43#12111yescharacteristic
171C22⋊D43—82no—
172C22⋊D43—81no—
173C22⋊D43—81no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43—42no—
178C2×Dic43—41no—
179C2×Dic43—41no—
180C2×Dic43—42no—
181D172—42no—
182D172—81no—
183Dic86—42no—
184Dic86—81no—
185C43⋊C8—42no—
186C43⋊C8—42no—
187#9969—431nomaximal, Sylow
188C22×C43—22no—
189C22×C43—22no—
190C22×C43—22no—
191C22×C43—22no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43#39211yescharacteristic
197C22×C43#45212yes—
198C22×C43#45311yescharacteristic
199C22×C43#45411yescharacteristic
200C22×C43#45812yes—
201C22×C43#46412yes—
202C22×C43#49511yescharacteristic
203C22×C43#49711yescharacteristic
204C2×D43—82no—
205C2×D43—82no—
206C2×D43—81no—
207C2×D43—81no—
208C2×D43—81no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—82no—
214C4×C43—82no—
215C4×C43—82no—
216Dic43—81no—
217Dic43—81no—
218Dic43—81no—
219C2×#484—431no—
220C2×#481—431no—
221#2639—431no—
222C2×#328—431no—
223C2×#327—431no—
224#1445D4311yescharacteristic, complemented
225#1280—431no—
226C2×C43—21no—
227C2×C43—22no—
228C2×C43—21no—
229C2×C43#161512yes—
230C2×C43#161812yes—
231C2×C43#200611yescharacteristic
232C2×C43#201511yescharacteristic
233C2×C43#202211yescharacteristic
234D43—161no—
235C2×C22⋊Q8—431no—
236C2×#121—431no—
237C22×C4⋊C4C2×D4311yescharacteristic
238#484—862no—
239#484—862no—
240#481—862no—
241#481—862no—
242C2×#107—861no—
243C2×#106—861no—
244C2×#103—861no—
245C2×#102—861no—
246C2×C22⋊C8—431no—
247C2×C22⋊C8—431no—
248#400—861no—
249#397—861no—
250#394—861no—
251#393—861no—
252#386—862no—
253C2×#95—22no—
254C2×#95C2×D4311yescharacteristic
255C2×#95C2×D4311yescharacteristic
256#328—862no—
257#327—862no—
258C43#996911yescharacteristic, complemented, Sylow
259C22×Q8—431no—
260C22×D4—431no—
261C22×D4—861no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4C22⋊D4312yes—
265C23×C4C22×D4311yescharacteristic
266C22×C8—861no—
267C22×C8—861no—
268C22⋊Q8—861no—
269C22⋊Q8—861no—
270C22⋊Q8—861no—
271C22⋊Q8—861no—
272#121—861no—
273#121—861no—
274#121—861no—
275#121—861no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—431no—
282C2×C4⋊C4—431no—
283C2×C4⋊C4—861no—
284C2×C4⋊C4D17212yes—
285C2×C22⋊C4—862no—
286C2×C22⋊C4—862no—
287C2×C22⋊C4—861no—
288C2×C22⋊C4—861no—
289#107—864no—
290#106—864no—
291#103—864no—
292#102—864no—
293C22⋊C8—432no—
294C22⋊C8—432no—
295C22⋊C8—861no—
296C22⋊C8—861no—
297#95—21no—
298#95—21no—
299#95—21no—
300#95—21no—
301#95—44no—
302#95—862no—
303#95—862no—
304C24—861no—
305C24C2×C22⋊D4311yescharacteristic
306C2×Q8—861no—
307C2×Q8—861no—
308C2×Q8—1722no—
309C2×D4—861no—
310C2×D4—861no—
311C2×D4—1722no—
312C2×D4—1721no—
313C2×D4—1721no—
314C2×D4—1722no—
315C2×D4—1722no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—41no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—42no—
332C22×C4—861no—
333C22×C4—861no—
334C22×C4—861no—
335C22×C4C2×D17211yescharacteristic
336C22×C4#1062189811yescharacteristic
337C22×C4D4×D4311yescharacteristic
338C22×C4D4×D4311yescharacteristic
339C22×C4D4×D4311yescharacteristic
340C22×C4D4×D4311yescharacteristic
341C2×C8—862no—
342C2×C8—862no—
343C2×C8—1722no—
344C2×C8—1722no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—861no—
350C4⋊C4—861no—
351C4⋊C4—861no—
352C4⋊C4—861no—
353C4⋊C4—1721no—
354C4⋊C4—1721no—
355C22⋊C4—3442no—
356C22⋊C4—3442no—
357C22⋊C4—1721no—
358C22⋊C4—1721no—
359C22⋊C4—1721no—
360C22⋊C4—1721no—
361C23—21no—
362C23—21no—
363C23—22no—
364C23—1722no—
365C23—1721no—
366C23—1721no—
367C23—1721no—
368C23—1722no—
369C23#1306329311yescharacteristic
370C23#1306329911yescharacteristic
371C23#1306332111yescharacteristic
372C23#1306334512yes—
373C23#1306335612yes—
374Q8—3441no—
375Q8—1722no—
376D4—3441no—
377D4—3442no—
378D4—3441no—
379D4—3441no—
380D4—1722no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—82no—
396C2×C4—81no—
397C2×C4—82no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—82no—
402C2×C4—1722no—
403C2×C4—1721no—
404C2×C4—1721no—
405C2×C4—1721no—
406C2×C4—1721no—
407C2×C4—1721no—
408C2×C4—1722no—
409C2×C4#1306329511yescharacteristic
410C2×C4#1306329511yescharacteristic
411C2×C4#1306329811yescharacteristic
412C2×C4#1306329811yescharacteristic
413C8—1722no—
414C8—1722no—
415C22—21no—
416C22—21no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—21no—
422C22—21no—
423C22—3441no—
424C22—3442no—
425C22—3441no—
426C22—3442no—
427C22—3441no—
428C22#1458280811yescharacteristic
429C22#1458305912yes—
430C22#1458306611yescharacteristic
431C22#1458307111yescharacteristic
432C22#1458308812yes—
433C22#1458312112yes—
434C22#1458328111yescharacteristic
435C22#1458329111yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—82no—
441C4—82no—
442C4—82no—
443C4—3441no—
444C4—3441no—
445C4—3441no—
446C2—21no—
447C2—22no—
448C2—21no—
449C2—6881no—
450C2#1913362412yes—
451C2#1913364112yes—
452C2#1913563611yescharacteristic
453C2#1913568811yescharacteristic
454C2#1913572611yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1445C2
socleC23×C43#120
prime radicalC2×#13063299C22
hypercenter#1445D43
hypocenterC43#9969
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1445

Complements

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

NH ≅ G/Ntype
1. C2×#14583234C2semidirect
4. C2×#14582635C2semidirect
6. #19132438C2semidirect
7. C43×#1445C2semidirect
224. #1445D43semidirect
258. C43#9969semidirect

Maximal subgroups

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

subgroupindex
C2×#145832342
C2×#145832172
#191405232
C2×#145826352
C2×#145826322
#191324382
C43×#14452
#996943