Finite Group Databasebeta

← #25014092

Subgroups — #25014092

Order 11008.

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

normal subgroups only

This group has 818 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×#14582883C211yesmaximal, characteristic, complemented
2C2×#14582686C212yesmaximal, complemented
3#19134513C211yesmaximal, characteristic, complemented
4#19132713C212yesmaximal, complemented
5C43×#2404C211yesmaximal, characteristic
6C22×#10621877—21no—
7#14582883—24no—
8C2×#13063244—21no—
9C2×#13063242C2212yes—
10C2×#13063240—21no—
11C2×#13063240C2212yes—
12#14582762—21no—
13#14582686—24no—
14C22×#41×C43C2211yescharacteristic
15C2×#120×C43C411yescharacteristic, complemented
16C2×#120×C43C2211yescharacteristic
17C22×C22⋊C4×C43C411yescharacteristic, complemented
18C43×#393—21no—
19C43×#392—21no—
20C43×#386—21no—
21C43×#386—21no—
22C43×#386C411yescharacteristic, complemented
23C43×#386C2211yescharacteristic
24C43×#381C411yescharacteristic, complemented
25C2×#10621877—24no—
26C2×#10621877—22no—
27C2×#10621877—41no—
28C2×#10621877—42no—
29C22×C43⋊C8—41no—
30C2×C22⋊Dic43—22no—
31#13063244—24no—
32#13063242—22no—
33#13063242D414yescomplemented
34#13063240—22no—
35#13063240—22no—
36#13063240—42no—
37C43⋊#95—41no—
38C43⋊#95—41no—
39C25×C43C2×C411yescharacteristic
40C2×#41×C43—22no—
41C2×#41×C43—22no—
42C2×#41×C43—41no—
43C2×#41×C43—41no—
44C2×#41×C43—42no—
45C22×Q8×C43D411yescharacteristic
46C22×D4×C43—21no—
47C22×D4×C43—21no—
48C22×D4×C43C2×C411yescharacteristic
49C22×D4×C43D411yescharacteristic
50C22×D4×C43C2311yescharacteristic
51C23×C4×C43C2×C411yescharacteristic
52C23×C4×C43C2×C411yescharacteristic
53C23×C4×C43D411yescharacteristic
54C23×C4×C43D411yescharacteristic
55#120×C43—22no—
56#120×C43—22no—
57#120×C43—42no—
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—41no—
65C2×C22⋊C4×C43—41no—
66C2×C22⋊C4×C43C2×C411yescharacteristic
67C2×C22⋊C4×C43C2×C411yescharacteristic
68#95×C43—21no—
69#95×C43—21no—
70#95×C43—21no—
71#95×C43—21no—
72C24×C43—21no—
73C24×C43—22no—
74C24×C43—41no—
75C24×C43—42no—
76C24×C43—41no—
77C24×C43—81no—
78C24×C43C22⋊C411yescharacteristic
79C24×C43C22×C411yescharacteristic
80C24×C43C2×D411yescharacteristic
81#41×C43—44no—
82#41×C43—44no—
83#41×C43—44no—
84#41×C43—44no—
85C2×Q8×C43—21no—
86C2×Q8×C43—21no—
87C2×Q8×C43—41no—
88C2×Q8×C43—41no—
89C2×D4×C43—22no—
90C2×D4×C43—22no—
91C2×D4×C43—22no—
92C2×D4×C43—22no—
93C2×D4×C43—41no—
94C2×D4×C43—41no—
95C2×D4×C43—41no—
96C2×D4×C43—41no—
97C2×D4×C43—42no—
98C2×D4×C43—42no—
99C2×D4×C43—42no—
100C2×D4×C43—42no—
101C2×D4×C43—81no—
102C2×D4×C43—81no—
103C2×D4×C43C2×D412yes—
104C2×D4×C43#4112yes—
105C22×C4×C43—21no—
106C22×C4×C43—21no—
107C22×C4×C43—21no—
108C22×C4×C43—21no—
109C22×C4×C43—21no—
110C22×C4×C43—21no—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—22no—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—41no—
120C22×C4×C43—41no—
121C22×C4×C43—41no—
122C22×C4×C43—81no—
123C22×C4×C43C22⋊C411yescharacteristic
124C22×C4×C43C22⋊C411yescharacteristic
125C22×C4×C43C22⋊C411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×Dic43—42no—
128C22⋊C4×C43—22no—
129C22⋊C4×C43—41no—
130C22⋊C4×C43—42no—
131C22⋊C4×C43—42no—
132C22⋊C4×C43—41no—
133C22⋊C4×C43—41no—
134C22⋊C4×C43—41no—
135C22⋊C4×C43—41no—
136C22⋊C4×C43—81no—
137C22⋊C4×C43—81no—
138C22⋊Dic43—42no—
139C22⋊Dic43—42no—
140#10621877—24no—
141#10621877—44no—
142#10621877—42no—
143C2×C43⋊C8—44no—
144C2×C43⋊C8—42no—
145C23×C43—21no—
146C23×C43—21no—
147C23×C43—21no—
148C23×C43—21no—
149C23×C43—21no—
150C23×C43—21no—
151C23×C43—22no—
152C23×C43—41no—
153C23×C43—41no—
154C23×C43—41no—
155C23×C43—41no—
156C23×C43—41no—
157C23×C43—41no—
158C23×C43—41no—
159C23×C43—41no—
160C23×C43—41no—
161C23×C43—42no—
162C23×C43—42no—
163C23×C43—41no—
164C23×C43—41no—
165C23×C43—41no—
166C23×C43—82no—
167C23×C43—84no—
168C23×C43—84no—
169C23×C43—82no—
170C23×C43#9912yes—
171C23×C43C2×C22⋊C411yescharacteristic
172C23×C43C4×D412yes—
173C23×C43#12112yes—
174Q8×C43—42no—
175Q8×C43—42no—
176D4×C43—42no—
177D4×C43—42no—
178D4×C43—44no—
179D4×C43—44no—
180D4×C43—84no—
181D4×C43—84no—
182C2×C4×C43—22no—
183C2×C4×C43—22no—
184C2×C4×C43—22no—
185C2×C4×C43—22no—
186C2×C4×C43—21no—
187C2×C4×C43—21no—
188C2×C4×C43—21no—
189C2×C4×C43—21no—
190C2×C4×C43—21no—
191C2×C4×C43—21no—
192C2×C4×C43—21no—
193C2×C4×C43—21no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—42no—
197C2×C4×C43—42no—
198C2×C4×C43—42no—
199C2×C4×C43—42no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—82no—
210C2×C4×C43#9911yescharacteristic
211C2×C4×C43#9911yescharacteristic
212C2×C4×C43#12011yescharacteristic
213C2×C4×C43#12311yescharacteristic
214C2×Dic43—82no—
215C2×Dic43—82no—
216C2×Dic43—82no—
217C43⋊C8—44no—
218#13083—431nomaximal, Sylow
219C22×C43—21no—
220C22×C43—21no—
221C22×C43—22no—
222C22×C43—22no—
223C22×C43—22no—
224C22×C43—42no—
225C22×C43—42no—
226C22×C43—42no—
227C22×C43—42no—
228C22×C43—42no—
229C22×C43—42no—
230C22×C43—41no—
231C22×C43—41no—
232C22×C43—41no—
233C22×C43—41no—
234C22×C43—41no—
235C22×C43—41no—
236C22×C43—42no—
237C22×C43—81no—
238C22×C43—81no—
239C22×C43—81no—
240C22×C43—81no—
241C22×C43—84no—
242C22×C43—84no—
243C22×C43—81no—
244C22×C43—81no—
245C22×C43#38611yescharacteristic
246C22×C43C2×#9911yescharacteristic
247C22×C43C2×#9911yescharacteristic
248C4×C43—21no—
249C4×C43—21no—
250C4×C43—21no—
251C4×C43—21no—
252C4×C43—41no—
253C4×C43—41no—
254C4×C43—81no—
255C4×C43—81no—
256C4×C43—81no—
257Dic43—162no—
258C2×#413—431no—
259#2404D4311yescharacteristic
260C2×AΣL(1,𝔽16)—432no—
261#1782—431no—
262#1390—432no—
263C2×C43—21no—
264C2×C43—21no—
265C2×C43—42no—
266C2×C43—42no—
267C2×C43—42no—
268C2×C43—82no—
269C2×C43#189811yescharacteristic
270C2×C43#212011yescharacteristic
271C2×C43#212211yescharacteristic
272C22×#41C2×D4311yescharacteristic
273C22×M16—861no—
274C2×#120Dic4311yescharacteristic, complemented
275C2×#120C2×D4311yescharacteristic
276C22×C22⋊C4Dic4311yescharacteristic, complemented
277#413—864no—
278C2×#101—861no—
279C2×#100—432no—
280C2×#99—432no—
281C2×#99—861no—
282#393—21no—
283#392—21no—
284#386—21no—
285#386—21no—
286#386Dic4311yescharacteristic, complemented
287#386C2×D4311yescharacteristic
288#381—861no—
289#381Dic4311yescharacteristic, complemented
290AΣL(1,𝔽16)—864no—
291C43#1308311yescharacteristic, complemented, Sylow
292C25C2×Dic4311yescharacteristic
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—41no—
296C2×#41—41no—
297C2×#41—42no—
298C22×Q8C22⋊D4311yescharacteristic
299C22×D4—21no—
300C22×D4—21no—
301C22×D4C2×Dic4311yescharacteristic
302C22×D4C22⋊D4311yescharacteristic
303C22×D4C22×D4311yescharacteristic
304C23×C4C2×Dic4311yescharacteristic
305C23×C4C2×Dic4311yescharacteristic
306C23×C4C22⋊D4311yescharacteristic
307C23×C4C22⋊D4311yescharacteristic
308C2×M16—864no—
309C2×M16—862no—
310C2×M16—1722no—
311C2×M16—1721no—
312C22×C8—1721no—
313#120—22no—
314#120—22no—
315#120—42no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—41no—
323C2×C22⋊C4—41no—
324C2×C22⋊C4—862no—
325C2×C22⋊C4C2×Dic4311yescharacteristic
326C2×C22⋊C4C2×Dic4311yescharacteristic
327#101—864no—
328#100—434no—
329#100—862no—
330#99—862no—
331#99—862no—
332#99—1722no—
333#95—21no—
334#95—21no—
335#95—21no—
336#95—21no—
337#95—1721no—
338#95—1721no—
339C24—21no—
340C24—22no—
341C24—41no—
342C24—42no—
343C24—41no—
344C24—81no—
345C24C22⋊Dic4311yescharacteristic
346C24C22×Dic4311yescharacteristic
347C24C2×C22⋊D4311yescharacteristic
348#41—44no—
349#41—44no—
350#41—44no—
351#41—44no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—41no—
355C2×Q8—41no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—42no—
368C2×D4—81no—
369C2×D4—81no—
370C2×D4D4×D4312yes—
371C2×D4#1062190012yes—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—81no—
390C22×C4—1722no—
391C22×C4C22⋊Dic4311yescharacteristic
392C22×C4C22⋊Dic4311yescharacteristic
393C22×C4C22⋊Dic4311yescharacteristic
394C22×C4C2×C22⋊D4311yescharacteristic
395M16—864no—
396M16—1724no—
397M16—1722no—
398C2×C8—1724no—
399C2×C8—1722no—
400C22⋊C4—22no—
401C22⋊C4—42no—
402C22⋊C4—42no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—81no—
409C22⋊C4—81no—
410C22⋊C4—1722no—
411C22⋊C4—1722no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—22no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—42no—
429C23—42no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—82no—
434C23—84no—
435C23—84no—
436C23—82no—
437C23#1306324012yes—
438C23C2×C22⋊Dic4311yescharacteristic
439C23D4×Dic4312yes—
440C23#1306329712yes—
441Q8—42no—
442Q8—42no—
443D4—42no—
444D4—42no—
445D4—44no—
446D4—44no—
447D4—84no—
448D4—84no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—82no—
477C2×C4—3442no—
478C2×C4—3442no—
479C2×C4—3442no—
480C2×C4#1306324011yescharacteristic
481C2×C4#1306324011yescharacteristic
482C2×C4#1306329311yescharacteristic
483C2×C4#1306330611yescharacteristic
484C8—1724no—
485C22—21no—
486C22—21no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—42no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—84no—
508C22—84no—
509C22—81no—
510C22—81no—
511C22#1458277911yescharacteristic
512C22C2×#1306324011yescharacteristic
513C22C2×#1306324011yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—41no—
519C4—41no—
520C4—81no—
521C4—81no—
522C4—81no—
523C4—6882no—
524C2—21no—
525C2—21no—
526C2—42no—
527C2—42no—
528C2—42no—
529C2—82no—
530C2#1913504911yescharacteristic
531C2#1913623611yescharacteristic
532C2#1913624511yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC24×C43C22×C4
FrattiniC22×D4C22×D43
Fitting, prime radicalC43×#2404C2
socleC22×C43C2×#99
cosocleC22×D4×C43C23
hypercenter#2404D43
hypocenterC43#13083
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #2404

Complements

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

NH ≅ G/Ntype
1. C2×#14582883C2semidirect
2. C2×#14582686C2semidirect
3. #19134513C2semidirect
4. #19132713C2semidirect
15. C2×#120×C43C4semidirect
17. C22×C22⋊C4×C43C4semidirect
22. C43×#386C4semidirect
24. C43×#381C4semidirect
33. #13063242D4semidirect
274. C2×#120Dic43semidirect
276. C22×C22⋊C4Dic43semidirect
286. #386Dic43semidirect
289. #381Dic43semidirect
291. C43#13083semidirect

Maximal subgroups

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

subgroupindex
C2×#145828832
C2×#145826862
#191345132
#191327132
C43×#24042
#1308343