Finite Group Databasebeta

← #25014908

Subgroups — #25014908

Order 11008.

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

normal subgroups only

This group has 552 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#19139588C211yesmaximal, characteristic
2C2×#14582694C211yesmaximal, characteristic
3C2×#14582693C211yesmaximal, characteristic
4C2×#14582693C211yesmaximal, characteristic
5#19134581C211yesmaximal, characteristic
6#99×Dic43C211yesmaximal, characteristic
7C2×C43×#354C211yesmaximal, characteristic
8C2×#13063323C411yescharacteristic, complemented
9C2×#13063312C2211yescharacteristic
10C2×D4×Dic43C2211yescharacteristic
11C2×#13063240C2211yescharacteristic
12C2×#13063240C2211yescharacteristic
13#14582827—21no—
14#14582827—21no—
15#14582806C411yescharacteristic, complemented
16#14582805C411yescharacteristic, complemented
17#14582757—21no—
18#14582757—21no—
19#14582757—21no—
20C4×Dic43⋊C4C411yescharacteristic, complemented
21C22⋊C4×Dic43—21no—
22#14582694—22no—
23#14582693—22no—
24#14582693—22no—
25#14582665—21no—
26#14582665—21no—
27C2×#124×C43C2211yescharacteristic
28C2×#99×C43C2211yescharacteristic
29C2×#99×C43C2211yescharacteristic
30C43×#354—22no—
31C22×Dic86C2×C411yescharacteristic
32C23×Dic43D411yescharacteristic
33C23×Dic43D411yescharacteristic
34#13063323—41no—
35#13063323—41no—
36#13063312—21no—
37#13063312—21no—
38#13063312—21no—
39#13063312—21no—
40D4×Dic43—41no—
41D4×Dic43—41no—
42C2×C4⋊Dic43C2×C411yescharacteristic
43C2×Dic43⋊C4—21no—
44C2×Dic43⋊C4—21no—
45C2×Dic43⋊C4—21no—
46C2×Dic43⋊C4—41no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43—21no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43—21no—
51C2×C22⋊Dic43D411yescharacteristic
52C2×C22⋊Dic43D411yescharacteristic
53C2×C4×Dic43—41no—
54C2×C4×Dic43C2×C411yescharacteristic
55C2×C4×Dic43C2×C411yescharacteristic
56#13063240—21no—
57#13063240—21no—
58#13063240—21no—
59#13063240D412yes—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C43⋊#95—21no—
65C43⋊#95—41no—
66C43⋊#95—41no—
67C22×Q8×C43C2×C411yescharacteristic
68C22×D4×C43C2311yescharacteristic
69#124×C43—21no—
70#124×C43—21no—
71#124×C43—21no—
72#124×C43—21no—
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—21no—
77C2×C42×C43C2×C411yescharacteristic
78#99×C43—21no—
79#99×C43—21no—
80#99×C43—21no—
81#99×C43D412yes—
82C24×C43C2×D411yescharacteristic
83C24×C43C2×D411yescharacteristic
84C2×Q8×C43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43—41no—
87C2×Q8×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43—41no—
90C2×D4×C43C2×D411yescharacteristic
91C2×D4×C43C2×D411yescharacteristic
92C2×D4×C43#4111yescharacteristic
93C2×D4×C43#4111yescharacteristic
94C22×C4×C43—21no—
95C22×C4×C43—21no—
96C22×C4×C43—41no—
97C22×C4×C43—41no—
98C22×C4×C43C22×C411yescharacteristic
99C22×Dic43—21no—
100C22×Dic43—21no—
101C22×Dic43—21no—
102C22×Dic43—21no—
103C22×Dic43—21no—
104C22×Dic43—21no—
105C22×Dic43—41no—
106C22×Dic43—41no—
107C22×Dic43—42no—
108C22×Dic43—42no—
109C22×Dic43C22⋊C411yescharacteristic
110C22×Dic43C22⋊C411yescharacteristic
111C22×Dic43C22⋊C411yescharacteristic
112C22×Dic43C22⋊C411yescharacteristic
113C2×Dic86—21no—
114C2×Dic86—21no—
115C2×Dic86—41no—
116C2×Dic86—41no—
117C22⋊C4×C43—22no—
118C22⋊C4×C43—41no—
119C22⋊C4×C43—41no—
120C22⋊C4×C43—41no—
121C22⋊C4×C43—41no—
122C22⋊C4×C43—41no—
123C22⋊C4×C43—41no—
124C22⋊C4×C43—41no—
125C42×C43—21no—
126C42×C43—21no—
127C22⋊Dic43—22no—
128C22⋊Dic43—41no—
129C22⋊Dic43—41no—
130C22⋊Dic43—41no—
131C22⋊Dic43—41no—
132C22⋊Dic43—41no—
133C22⋊Dic43—41no—
134C22⋊Dic43—41no—
135C22⋊Dic43—41no—
136C22⋊Dic43—41no—
137C4⋊Dic43—41no—
138Dic43⋊C4—42no—
139Dic43⋊C4—42no—
140Dic43⋊C4—41no—
141Dic43⋊C4—41no—
142Dic43⋊C4—82no—
143C4×Dic43—21no—
144C4×Dic43—21no—
145C4×Dic43—21no—
146C4×Dic43—21no—
147C4×Dic43—82no—
148C23×C43—21no—
149C23×C43—21no—
150C23×C43—21no—
151C23×C43—21no—
152C23×C43—41no—
153C23×C43—41no—
154C23×C43—41no—
155C23×C43—41no—
156C23×C43C2×C22⋊C411yescharacteristic
157C23×C43#12111yescharacteristic
158C23×C43#12111yescharacteristic
159C23×C43#12411yescharacteristic
160C23×C43#12711yescharacteristic
161Q8×C43—81no—
162Q8×C43—81no—
163D4×C43—41no—
164D4×C43—41no—
165D4×C43—41no—
166D4×C43—41no—
167C2×C4×C43—21no—
168C2×C4×C43—21no—
169C2×C4×C43—41no—
170C2×C4×C43—42no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—81no—
177C2×C4×C43—81no—
178C2×C4×C43—81no—
179C2×C4×C43—81no—
180C2×C4×C43—81no—
181C2×C4×C43C4×D411yescharacteristic
182C2×C4×C43C4×D411yescharacteristic
183C2×Dic43—22no—
184C2×Dic43—21no—
185C2×Dic43—21no—
186C2×Dic43—21no—
187C2×Dic43—42no—
188C2×Dic43—42no—
189C2×Dic43—41no—
190C2×Dic43—41no—
191C2×Dic43—41no—
192C2×Dic43—41no—
193C2×Dic43—42no—
194C2×Dic43—41no—
195C2×Dic43—41no—
196C2×Dic43—41no—
197C2×Dic43—41no—
198C2×Dic43—41no—
199C2×Dic43—81no—
200C2×Dic43—81no—
201C2×Dic43—81no—
202C2×Dic43—81no—
203C2×Dic43—81no—
204C2×Dic43—81no—
205C2×Dic43—81no—
206C2×Dic43#9911yescharacteristic
207C2×Dic43#9911yescharacteristic
208Dic86—81no—
209Dic86—81no—
210#13224—431nomaximal, Sylow
211C22×C43—21no—
212C22×C43—21no—
213C22×C43—21no—
214C22×C43—21no—
215C22×C43—21no—
216C22×C43—21no—
217C22×C43—41no—
218C22×C43—41no—
219C22×C43—41no—
220C22×C43—41no—
221C22×C43—41no—
222C22×C43—41no—
223C22×C43—41no—
224C22×C43—41no—
225C22×C43—81no—
226C22×C43—81no—
227C22×C43#39011yescharacteristic
228C22×C43C2×#9911yescharacteristic
229C22×C43#41011yescharacteristic
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—81no—
233C4×C43—82no—
234C4×C43—81no—
235C4×C43—161no—
236Dic43—21no—
237Dic43—41no—
238Dic43—41no—
239Dic43—41no—
240Dic43—81no—
241Dic43—82no—
242Dic43—81no—
243Dic43—161no—
244Dic43#35412yescomplemented
245#2547—431no—
246C2×#354—431no—
247C2×#354—431no—
248C2×#354—431no—
249C2×#354D4311yescharacteristic
250#1799—431no—
251C4×#99—431no—
252C2×C43—21no—
253C2×C43—21no—
254C2×C43—41no—
255C2×C43—41no—
256C2×C43—41no—
257C2×C43—41no—
258C2×C43#196411yescharacteristic
259C2×C43C2×#35411yescharacteristic
260C2×C43#212911yescharacteristic
261C2×C4⋊Q8—431no—
262C2×#124—431no—
263C2×#124C2×D4311yescharacteristic
264C2×C4×D4—431no—
265C2×#99—431no—
266C2×#99—431no—
267C2×#99C2×D4311yescharacteristic
268C2×#99C2×D4311yescharacteristic
269#397—861no—
270#397—861no—
271#391—431no—
272#391—431no—
273#380—861no—
274#380—861no—
275#380—861no—
276C4×C4⋊C4—431no—
277C4×C22⋊C4—861no—
278#354—22no—
279#354—862no—
280#354—862no—
281#354—862no—
282#342—861no—
283#342—861no—
284C43#1322411yescharacteristic, complemented, Sylow
285C22×Q8—431no—
286C22×Q8C4×D4311yescharacteristic
287C22×D4C22×D4311yescharacteristic
288C23×C4—431no—
289C23×C4—431no—
290C4⋊Q8—1721no—
291C4⋊Q8—1721no—
292#124—21no—
293#124—21no—
294#124—21no—
295#124—21no—
296#124—861no—
297#124—861no—
298#124—861no—
299#124—861no—
300C4×D4—1721no—
301C4×D4—1721no—
302C2×C4⋊C4—431no—
303C2×C4⋊C4—861no—
304C2×C4⋊C4—861no—
305C2×C4⋊C4—861no—
306C2×C4⋊C4—1721no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—431no—
312C2×C22⋊C4—431no—
313C2×C22⋊C4—861no—
314C2×C22⋊C4—861no—
315C2×C22⋊C4—861no—
316C2×C22⋊C4—861no—
317C2×C42—431no—
318C2×C42—431no—
319C2×C42—1721no—
320C2×C42C4×D4311yescharacteristic
321#99—21no—
322#99—21no—
323#99—21no—
324#99—432no—
325#99—861no—
326#99—861no—
327#99—861no—
328#99C22⋊D4312yes—
329#95—861no—
330#95—861no—
331#95—861no—
332#95—861no—
333#95—861no—
334#95—1721no—
335#95—1721no—
336C24D4×D4311yescharacteristic
337C24D4×D4311yescharacteristic
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—41no—
341C2×Q8—41no—
342C2×Q8—861no—
343C2×Q8—861no—
344C2×Q8—1721no—
345C2×Q8—1721no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4#1062189811yescharacteristic
349C2×D4D4×D4311yescharacteristic
350C2×D4#1062190011yescharacteristic
351C2×D4C2×C22⋊D4311yescharacteristic
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—431no—
357C22×C4—431no—
358C22×C4—431no—
359C22×C4—431no—
360C22×C4—861no—
361C22×C4—861no—
362C22×C4—861no—
363C22×C4—861no—
364C22×C4—861no—
365C22×C4—861no—
366C22×C4—1722no—
367C22×C4—1722no—
368C22×C4—1721no—
369C22×C4—1721no—
370C22×C4C2×C4×D4311yescharacteristic
371C4⋊C4—3442no—
372C4⋊C4—1721no—
373C4⋊C4—1721no—
374C4⋊C4—1721no—
375C4⋊C4—1722no—
376C4⋊C4—1722no—
377C22⋊C4—22no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—862no—
386C22⋊C4—1721no—
387C22⋊C4—1721no—
388C22⋊C4—1721no—
389C22⋊C4—1721no—
390C22⋊C4—1721no—
391C22⋊C4—1721no—
392C22⋊C4—1721no—
393C22⋊C4—1721no—
394C22⋊C4—1721no—
395C42—21no—
396C42—21no—
397C42—861no—
398C42—861no—
399C42—861no—
400C42—861no—
401C42—3442no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23C22⋊C4×D4311yescharacteristic
411C23#1306329711yescharacteristic
412C23#1306329811yescharacteristic
413C23#1306331111yescharacteristic
414C23#1306332111yescharacteristic
415Q8—81no—
416Q8—81no—
417Q8—3441no—
418Q8—3441no—
419D4—41no—
420D4—41no—
421D4—41no—
422D4—41no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—81no—
433C2×C4—81no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—81no—
437C2×C4—431no—
438C2×C4—431no—
439C2×C4—862no—
440C2×C4—861no—
441C2×C4—861no—
442C2×C4—861no—
443C2×C4—3441no—
444C2×C4—3441no—
445C2×C4—3441no—
446C2×C4—3441no—
447C2×C4—3441no—
448C2×C4—3441no—
449C2×C4—3441no—
450C2×C4—1722no—
451C2×C4—1722no—
452C2×C4—1722no—
453C2×C4—1721no—
454C2×C4—1721no—
455C2×C4—1721no—
456C2×C4—1721no—
457C2×C4—1721no—
458C2×C4—1721no—
459C2×C4—1721no—
460C2×C4—1721no—
461C2×C4—1721no—
462C2×C4(C22⋊D43)⋊C411yescharacteristic
463C2×C4C4×C22⋊D4311yescharacteristic
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—81no—
479C22—81no—
480C22#1458279911yescharacteristic
481C22#99×D4311yescharacteristic
482C22#1458287111yescharacteristic
483C4—21no—
484C4—21no—
485C4—81no—
486C4—82no—
487C4—81no—
488C4—161no—
489C4—432no—
490C4—861no—
491C4—3441no—
492C4—3442no—
493C4—3441no—
494C4—1721no—
495C4—1721no—
496C4—1721no—
497C4—6881no—
498C2—21no—
499C2—21no—
500C2—41no—
501C2—41no—
502C2—41no—
503C2—41no—
504C2#1913542911yescharacteristic
505C2#354×D4311yescharacteristic
506C2#1913626811yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC22×D4C22×D43
FittingC2×C43×#354C2
socleC22×C43C2×#99
prime radical, cosocleC22×D4×C43C23
hypercenterC2×#354D43
hypocenterC43#13224
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#354

Complements

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

NH ≅ G/Ntype
8. C2×#13063323C4semidirect
15. #14582806C4semidirect
16. #14582805C4semidirect
20. C4×Dic43⋊C4C4semidirect
244. Dic43#354semidirect
284. C43#13224semidirect

Maximal subgroups

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

subgroupindex
#191395882
C2×#145826942
C2×#145826932
#191345812
#99×Dic432
C2×C43×#3542
#1322443