Finite Group Databasebeta

← #24993178

Subgroups — #24993178

Order 11008.

564 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 107 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#19145353C211yesmaximal, characteristic
2#19137675C211yesmaximal, characteristic, complemented
3#19135430C211yesmaximal, characteristic
4#19133166C211yesmaximal, characteristic, complemented
5C2×#14582632C211yesmaximal, characteristic
6#19132441C211yesmaximal, characteristic, complemented
7C43×#1294C211yesmaximal, characteristic, complemented
8C2×#13063304C2211yescharacteristic
9C2×#13063299C2211yescharacteristic
10#14583230C412yescomplemented
11#14583218—21no—
12#14583128—22no—
13#14583052C412yescomplemented
14#14583040—21no—
15C2×#13063239—21no—
16C2×#13063239—21no—
17C2×C22⋊(C43⋊C8)C2211yescharacteristic
18#14582803—21no—
19#14582784—21no—
20#14582781—21no—
21#14582772—21no—
22#14582750—21no—
23C4×C22⋊Dic43—21no—
24C4×C22⋊Dic43C2211yescharacteristic
25#14582635—22no—
26#14582632—21no—
27#14582632—21no—
28C2×C22⋊C8×C43C2211yescharacteristic
29C43×#380C2211yescharacteristic
30C2×#95×C43C2211yescharacteristic
31C22×Dic86D411yescharacteristic
32C22×D172C2×C411yescharacteristic
33C22×C22⋊D43—21no—
34C2×#10621873—22no—
35C22×C43⋊C8—21no—
36#13063304—21no—
37#13063304—21no—
38#13063304C2×C412yes—
39#13063304D412yes—
40#13063299—21no—
41#13063299—21no—
42#13063299—21no—
43#13063299—21no—
44C2×C4⋊Dic43C2×C411yescharacteristic
45C2×C4⋊Dic43D411yescharacteristic
46C2×Dic43⋊C4—21no—
47C2×Dic43⋊C4—21no—
48C2×Dic43⋊C4—21no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43D411yescharacteristic
51C2×C22⋊Dic43D411yescharacteristic
52C2×(C2×D43)⋊C4—21no—
53C2×C4×Dic43—21no—
54C2×C4×Dic43—21no—
55C2×C4×Dic43—21no—
56#13063257—22no—
57#13063250—22no—
58#13063247—22no—
59#13063239—42no—
60#13063239—42no—
61C22⋊(C43⋊C8)—21no—
62C22⋊(C43⋊C8)—21no—
63C43⋊#95—21no—
64C43⋊#95—21no—
65C43⋊#95—21no—
66C43⋊#95—21no—
67C43⋊#95—21no—
68C23×C4×C43—21no—
69C23×C4×C43C2311yescharacteristic
70C22×C8×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C22⋊C4×C43—21no—
73C22⋊C8×C43—21no—
74C22⋊C8×C43C2×C412yes—
75#95×C43—21no—
76#95×C43—21no—
77#95×C43D411yescharacteristic
78#95×C43D411yescharacteristic
79C24×C43C2×D411yescharacteristic
80C23×D43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—42no—
84C22×C4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43—81no—
88C22×C4×C43—81no—
89C22×C4×C43C22×C411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43#4111yescharacteristic
94C22×C4×C43#4111yescharacteristic
95C2×C22⋊D43—41no—
96C2×C22⋊D43—41no—
97C2×C22⋊D43—41no—
98C2×C22⋊D43—41no—
99C2×C22⋊D43—41no—
100C2×C22⋊D43—41no—
101C22×Dic43—21no—
102C22×Dic43—21no—
103C22×Dic43—21no—
104C22×Dic43—21no—
105C22×Dic43—21no—
106C2×D172—21no—
107C2×D172—21no—
108C2×D172—81no—
109C2×Dic86—21no—
110C2×Dic86—81no—
111C2×Dic86C22⋊C412yes—
112C2×C8×C43—22no—
113C2×C8×C43—81no—
114C4⋊C4×C43—81no—
115C22⋊C4×C43—41no—
116C22⋊C4×C43—41no—
117C22⋊Dic43—22no—
118C22⋊Dic43—22no—
119C22⋊Dic43—21no—
120C22⋊Dic43—21no—
121C22⋊Dic43—21no—
122C22⋊Dic43SD1612yescomplemented
123(C2×D43)⋊C4—41no—
124(C2×D43)⋊C4—41no—
125C4⋊Dic43—21no—
126C4⋊Dic43—21no—
127C4⋊Dic43—21no—
128C4⋊Dic43C22⋊C412yes—
129Dic43⋊C4—22no—
130Dic43⋊C4—22no—
131Dic43⋊C4—42no—
132Dic43⋊C4—81no—
133C4×Dic43—42no—
134C4×Dic43—81no—
135C4×Dic43—81no—
136C2×C43⋊C8—41no—
137C2×C43⋊C8—81no—
138#10621873—82no—
139C23×C43—41no—
140C23×C43—41no—
141C23×C43C4×D411yescharacteristic
142C23×C43#12011yescharacteristic
143C23×C43#12111yescharacteristic
144C23×C43C2×SD1611yescharacteristic
145C23×C43#13511yescharacteristic
146C23×C43AGL(1,ℤ/8)11yescharacteristic
147C23×C43#13711yescharacteristic
148C22×D43—41no—
149C22×D43—41no—
150C22×D43—41no—
151C22×D43—81no—
152C22×D43—81no—
153C2×C4×C43—22no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—82no—
166C2×C4×C43—82no—
167C2×C4×C43—81no—
168C2×C4×C43—81no—
169C2×C4×C43—81no—
170C2×C4×C43C2×C22⋊C411yescharacteristic
171C2×C4×C43C4×D411yescharacteristic
172C2×C4×C43#12111yescharacteristic
173C2×C4×C43#12311yescharacteristic
174C22⋊D43—81no—
175C22⋊D43—81no—
176C22⋊D43—81no—
177C22⋊D43—81no—
178C2×Dic43—22no—
179C2×Dic43—22no—
180C2×Dic43—22no—
181C2×Dic43—41no—
182C2×Dic43—41no—
183C2×Dic43—41no—
184C2×Dic43—41no—
185C2×Dic43—41no—
186C2×Dic43—41no—
187C2×Dic43—41no—
188C2×Dic43—41no—
189C2×Dic43—41no—
190C2×Dic43—41no—
191C2×Dic43—41no—
192C2×Dic43—41no—
193D172—42no—
194D172—81no—
195Dic86—42no—
196Dic86—81no—
197C8×C43—42no—
198C43⋊C8—81no—
199#9278—431nomaximal, Sylow
200C22×C43—21no—
201C22×C43—21no—
202C22×C43—21no—
203C22×C43—21no—
204C22×C43—21no—
205C22×C43—21no—
206C22×C43—41no—
207C22×C43—41no—
208C22×C43—41no—
209C22×C43—41no—
210C22×C43#38611yescharacteristic
211C22×C43C4×SD1611yescharacteristic
212C22×C43#44011yescharacteristic
213C22×C43#44811yescharacteristic
214C22×C43#44911yescharacteristic
215C22×C43#46011yescharacteristic
216C22×C43#46411yescharacteristic
217C2×D43—81no—
218C2×D43—81no—
219C2×D43—81no—
220C2×D43—161no—
221C2×D43—161no—
222C4×C43—21no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—42no—
227C4×C43—81no—
228C4×C43—161no—
229Dic43—42no—
230Dic43—42no—
231Dic43—42no—
232Dic43—81no—
233Dic43—81no—
234#3187—431no—
235#2368—431no—
236#1964—431no—
237#1520—431no—
238C2×#327—431no—
239#1294D4311yescharacteristic, complemented
240#1282—431no—
241C2×C43—21no—
242C2×C43—21no—
243C2×C43—21no—
244C2×C43—21no—
245C2×C43—21no—
246C2×C43—21no—
247C2×C43#188011yescharacteristic
248C2×C43#190611yescharacteristic
249C2×C43#191311yescharacteristic
250D43—161no—
251C2×C22⋊Q8—431no—
252C2×#121—431no—
253#483—432no—
254#481—861no—
255#465—862no—
256#450—432no—
257#448—861no—
258C2×#99—861no—
259C2×#99—861no—
260C2×C22⋊C8—431no—
261C2×C22⋊C8C2×D4311yescharacteristic
262#391—861no—
263#387—861no—
264#387—861no—
265#385—861no—
266#380C2×D4311yescharacteristic
267C4×C4⋊C4—861no—
268C4×C22⋊C4—431no—
269C4×C22⋊C4—861no—
270C2×#95C2×D4311yescharacteristic
271#328—862no—
272#327—861no—
273#327—861no—
274C43#927811yescharacteristic, complemented, Sylow
275C22×Q8—431no—
276C22×D4—431no—
277C22×D4—861no—
278C23×C4—21no—
279C23×C4C22×D4311yescharacteristic
280C2×SD16—862no—
281C22×C8—21no—
282C22×C8—861no—
283C22⋊Q8—432no—
284C22⋊Q8—432no—
285C22⋊Q8—861no—
286C22⋊Q8—861no—
287#121—861no—
288#121—861no—
289#121—861no—
290#121—861no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—431no—
293C2×C4⋊C4—431no—
294C2×C4⋊C4—861no—
295C2×C4⋊C4—861no—
296C2×C4⋊C4—861no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—431no—
299C2×C22⋊C4—431no—
300C2×C22⋊C4—861no—
301C2×C22⋊C4—861no—
302C2×C42—861no—
303C2×C42—861no—
304C2×C42—861no—
305#106—862no—
306#103—862no—
307#102—862no—
308#99—1722no—
309#99—1722no—
310C22⋊C8—21no—
311C22⋊C8—861no—
312C22⋊C8—861no—
313C22⋊C8C4×D4312yes—
314#95—21no—
315#95—21no—
316#95—861no—
317#95—861no—
318#95—861no—
319#95—861no—
320#95—861no—
321#95D17211yescharacteristic
322#95D17211yescharacteristic
323C24—861no—
324C24D4×D4311yescharacteristic
325C2×Q8—432no—
326C2×Q8—861no—
327C2×Q8—3441no—
328C2×D4—861no—
329C2×D4—861no—
330C2×D4—3441no—
331C2×D4—1721no—
332C2×D4—1721no—
333C2×D4—1721no—
334C2×D4—1721no—
335C2×D4—1721no—
336C2×D4—1721no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—42no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—81no—
344C22×C4—81no—
345C22×C4—861no—
346C22×C4—861no—
347C22×C4—861no—
348C22×C4—861no—
349C22×C4—861no—
350C22×C4C2×C4×D4311yescharacteristic
351C22×C4C2×D17211yescharacteristic
352C22×C4#1062189811yescharacteristic
353C22×C4D4×D4311yescharacteristic
354C22×C4D4×D4311yescharacteristic
355C22×C4#1062190211yescharacteristic
356SD16—3442no—
357C2×C8—22no—
358C2×C8—81no—
359C2×C8—3441no—
360C2×C8—1721no—
361C4⋊C4—81no—
362C4⋊C4—432no—
363C4⋊C4—862no—
364C4⋊C4—862no—
365C4⋊C4—861no—
366C4⋊C4—861no—
367C4⋊C4—861no—
368C4⋊C4—3441no—
369C4⋊C4—1722no—
370C22⋊C4—41no—
371C22⋊C4—41no—
372C22⋊C4—432no—
373C22⋊C4—862no—
374C22⋊C4—862no—
375C22⋊C4—861no—
376C22⋊C4—861no—
377C22⋊C4—861no—
378C22⋊C4—1721no—
379C22⋊C4—1721no—
380C42—3441no—
381C42—3441no—
382C42—1722no—
383C23—41no—
384C23—41no—
385C23—3441no—
386C23—3441no—
387C23—1721no—
388C23—1721no—
389C23—1721no—
390C23#1306328711yescharacteristic
391C23#1306329511yescharacteristic
392C23#1306329811yescharacteristic
393C23SD16×D4311yescharacteristic
394C23#1306334611yescharacteristic
395C23#1306334911yescharacteristic
396C23#1306335711yescharacteristic
397Q8—3441no—
398Q8—1722no—
399D4—3441no—
400D4—3441no—
401D4—3441no—
402D4—3441no—
403D4—3441no—
404D4—1722no—
405C2×C4—22no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—862no—
423C2×C4—862no—
424C2×C4—862no—
425C2×C4—1721no—
426C2×C4—1721no—
427C2×C4—1721no—
428C2×C4—1721no—
429C2×C4—1721no—
430C2×C4—1721no—
431C2×C4—1721no—
432C2×C4—1721no—
433C2×C4—1721no—
434C2×C4—1721no—
435C2×C4—1721no—
436C2×C4—1721no—
437C2×C4C22⋊C4×D4311yescharacteristic
438C2×C4C4×D17211yescharacteristic
439C2×C4#1306330011yescharacteristic
440C2×C4#1306331011yescharacteristic
441C8—42no—
442C8—3441no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—3441no—
454C22—3441no—
455C22—3441no—
456C22—6881no—
457C22—6881no—
458C22#1458277711yescharacteristic
459C22#1458298611yescharacteristic
460C22#1458299811yescharacteristic
461C22#1458303911yescharacteristic
462C22#1458304511yescharacteristic
463C22#1458309811yescharacteristic
464C22#1458312411yescharacteristic
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—42no—
470C4—81no—
471C4—161no—
472C4—3441no—
473C4—3441no—
474C4—1722no—
475C4—1722no—
476C4—1722no—
477C2—21no—
478C2—21no—
479C2—21no—
480C2—21no—
481C2—21no—
482C2—21no—
483C2—6881no—
484C2#1913495111yescharacteristic
485C2#1913509511yescharacteristic
486C2#1913513611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1294C2
socleC22×C43#386
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1294D43
hypocenterC43#9278
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
2. #19137675C2semidirect
4. #19133166C2semidirect
6. #19132441C2semidirect
7. C43×#1294C2semidirect
10. #14583230C4semidirect
13. #14583052C4semidirect
122. C22⋊Dic43SD16semidirect
239. #1294D43semidirect
274. C43#9278semidirect

Maximal subgroups

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

subgroupindex
#191453532
#191376752
#191354302
#191331662
C2×#145826322
#191324412
C43×#12942
#927843