Finite Group Databasebeta

← #25014077

Subgroups — #25014077

Order 11008.

864 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C22×#13063242C211yesmaximal, characteristic
2C2×#14582689C212yesmaximal, complemented
3#19134510C211yesmaximal, characteristic
4#19132713C212yesmaximal, complemented
5C43×#2405C211yesmaximal, characteristic
6C22×#10621877—21no—
7C2×#13063242—24no—
8C2×#13063242—21no—
9C2×#13063242C2212yes—
10C2×#13063240—21no—
11C2×#13063240C2212yes—
12#14582755—21no—
13#14582689—24no—
14C23×D4×C43C2211yescharacteristic
15C2×#123×C43C411yescharacteristic, complemented
16C2×#123×C43C2211yescharacteristic
17C22×C22⋊C4×C43C411yescharacteristic, complemented
18C43×#394—21no—
19C43×#394—21no—
20C43×#386C411yescharacteristic, complemented
21C43×#386C2211yescharacteristic
22C43×#385—21no—
23C43×#379—21no—
24C43×#379C411yescharacteristic, complemented
25C2×#10621877—24no—
26C2×#10621877—22no—
27C2×#10621877—42no—
28C2×#10621877—41no—
29C22×C43⋊C8—41no—
30C2×C22⋊Dic43—22no—
31C2×C22⋊Dic43—41no—
32C2×C22⋊Dic43—41no—
33#13063242—24no—
34#13063242—22no—
35#13063242D414yes—
36#13063240—22no—
37#13063240—22no—
38#13063240—42no—
39C25×C43C2×C411yescharacteristic
40C25×C43D411yescharacteristic
41C22×D4×C43—22no—
42C22×D4×C43—22no—
43C22×D4×C43—42no—
44C22×D4×C43—41no—
45C22×D4×C43—41no—
46C22×D4×C43C2×C411yescharacteristic
47C22×D4×C43D411yescharacteristic
48C22×D4×C43D411yescharacteristic
49C22×D4×C43C2311yescharacteristic
50C23×C4×C43C2×C411yescharacteristic
51C23×C4×C43C2×C411yescharacteristic
52C23×C4×C43D411yescharacteristic
53#123×C43—22no—
54#123×C43—22no—
55#123×C43—42no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43—21no—
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—21no—
65C2×C22⋊C4×C43—21no—
66C2×C22⋊C4×C43—41no—
67C2×C22⋊C4×C43—41no—
68C2×C22⋊C4×C43C2×C411yescharacteristic
69C2×C22⋊C4×C43C2×C411yescharacteristic
70#95×C43—21no—
71#95×C43—21no—
72C24×C43—21no—
73C24×C43—21no—
74C24×C43—21no—
75C24×C43—21no—
76C24×C43—22no—
77C24×C43—22no—
78C24×C43—41no—
79C24×C43—41no—
80C24×C43—42no—
81C24×C43—42no—
82C24×C43—81no—
83C24×C43—81no—
84C24×C43C22⋊C411yescharacteristic
85C24×C43C22⋊C411yescharacteristic
86C24×C43C22⋊C411yescharacteristic
87C24×C43C22×C411yescharacteristic
88C24×C43C2×D411yescharacteristic
89C2×D4×C43—22no—
90C2×D4×C43—22no—
91C2×D4×C43—21no—
92C2×D4×C43—21no—
93C2×D4×C43—22no—
94C2×D4×C43—22no—
95C2×D4×C43—41no—
96C2×D4×C43—41no—
97C2×D4×C43—41no—
98C2×D4×C43—41no—
99C2×D4×C43—41no—
100C2×D4×C43—41no—
101C2×D4×C43—44no—
102C2×D4×C43—44no—
103C2×D4×C43—44no—
104C2×D4×C43—44no—
105C2×D4×C43C2×D412yes—
106C2×D4×C43#4112yes—
107C22×C4×C43—22no—
108C22×C4×C43—21no—
109C22×C4×C43—21no—
110C22×C4×C43—21no—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43—22no—
117C22×C4×C43—41no—
118C22×C4×C43—41no—
119C22×C4×C43—41no—
120C22×C4×C43—81no—
121C22×C4×C43C22⋊C411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×Dic43—42no—
124C4⋊C4×C43—42no—
125C4⋊C4×C43—41no—
126C4⋊C4×C43—41no—
127C22⋊C4×C43—22no—
128C22⋊C4×C43—41no—
129C22⋊C4×C43—42no—
130C22⋊C4×C43—42no—
131C22⋊C4×C43—42no—
132C22⋊C4×C43—41no—
133C22⋊C4×C43—41no—
134C22⋊C4×C43—42no—
135C22⋊C4×C43—81no—
136C22⋊C4×C43—81no—
137C22⋊C4×C43—81no—
138C22⋊Dic43—42no—
139C22⋊Dic43—42no—
140C22⋊Dic43—82no—
141C22⋊Dic43—82no—
142#10621877—24no—
143#10621877—44no—
144#10621877—42no—
145C2×C43⋊C8—44no—
146C2×C43⋊C8—42no—
147C23×C43—22no—
148C23×C43—21no—
149C23×C43—21no—
150C23×C43—21no—
151C23×C43—21no—
152C23×C43—21no—
153C23×C43—21no—
154C23×C43—21no—
155C23×C43—21no—
156C23×C43—21no—
157C23×C43—21no—
158C23×C43—21no—
159C23×C43—21no—
160C23×C43—41no—
161C23×C43—42no—
162C23×C43—42no—
163C23×C43—42no—
164C23×C43—42no—
165C23×C43—41no—
166C23×C43—41no—
167C23×C43—41no—
168C23×C43—41no—
169C23×C43—41no—
170C23×C43—41no—
171C23×C43—42no—
172C23×C43—42no—
173C23×C43—41no—
174C23×C43—41no—
175C23×C43—42no—
176C23×C43—42no—
177C23×C43—81no—
178C23×C43—81no—
179C23×C43—81no—
180C23×C43—81no—
181C23×C43—84no—
182C23×C43—84no—
183C23×C43—84no—
184C23×C43—84no—
185C23×C43#9911yescharacteristic
186C23×C43#9911yescharacteristic
187C23×C43C2×C22⋊C411yescharacteristic
188C23×C43C4×D412yes—
189C23×C43#12112yes—
190D4×C43—42no—
191D4×C43—42no—
192D4×C43—44no—
193D4×C43—44no—
194D4×C43—42no—
195D4×C43—42no—
196C2×C4×C43—22no—
197C2×C4×C43—22no—
198C2×C4×C43—22no—
199C2×C4×C43—22no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—82no—
217C2×C4×C43—82no—
218C2×C4×C43#9912yes—
219C2×C4×C43#12011yescharacteristic
220C2×C4×C43#12311yescharacteristic
221C2×Dic43—82no—
222C2×Dic43—82no—
223C2×Dic43—82no—
224C43⋊C8—44no—
225#13080—431nomaximal, Sylow
226C22×C43—21no—
227C22×C43—21no—
228C22×C43—21no—
229C22×C43—21no—
230C22×C43—21no—
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—22no—
234C22×C43—22no—
235C22×C43—42no—
236C22×C43—42no—
237C22×C43—42no—
238C22×C43—42no—
239C22×C43—42no—
240C22×C43—42no—
241C22×C43—41no—
242C22×C43—41no—
243C22×C43—41no—
244C22×C43—41no—
245C22×C43—41no—
246C22×C43—41no—
247C22×C43—41no—
248C22×C43—41no—
249C22×C43—41no—
250C22×C43—41no—
251C22×C43—81no—
252C22×C43—84no—
253C22×C43—84no—
254C22×C43—81no—
255C22×C43—81no—
256C22×C43—81no—
257C22×C43—84no—
258C22×C43—84no—
259C22×C43#35212yescomplemented
260C22×C43#38611yescharacteristic
261C22×C43C2×#9911yescharacteristic
262C22×C43C2×#9911yescharacteristic
263C4×C43—21no—
264C4×C43—22no—
265C4×C43—21no—
266C4×C43—81no—
267C4×C43—81no—
268C4×C43—81no—
269C4×C43—81no—
270Dic43—162no—
271C22×#100—431no—
272#2405D4311yescharacteristic
273C2×#352—432no—
274#1781—431no—
275#1390—432no—
276C2×C43—21no—
277C2×C43—21no—
278C2×C43—22no—
279C2×C43—42no—
280C2×C43—41no—
281C2×C43—42no—
282C2×C43—81no—
283C2×C43—81no—
284C2×C43#189811yescharacteristic
285C2×C43C2×#35211yescharacteristic
286C2×C43#212111yescharacteristic
287C23×D4C2×D4311yescharacteristic
288C22×M16—861no—
289C2×#123Dic4311yescharacteristic, complemented
290C2×#123C2×D4311yescharacteristic
291C22×C22⋊C4Dic4311yescharacteristic, complemented
292C2×#100—432no—
293C2×#100—864no—
294C2×#100—861no—
295C2×#99—432no—
296C2×#99—861no—
297#394—21no—
298#394—21no—
299#386Dic4311yescharacteristic, complemented
300#386C2×D4311yescharacteristic
301#385—21no—
302#379—21no—
303#379—861no—
304#379Dic4311yescharacteristic, complemented
305#352—864no—
306C43#1308011yescharacteristic, complemented, Sylow
307C25C2×Dic4311yescharacteristic
308C25C22⋊D4311yescharacteristic
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—42no—
312C22×D4—41no—
313C22×D4—41no—
314C22×D4C2×Dic4311yescharacteristic
315C22×D4C22⋊D4311yescharacteristic
316C22×D4C22⋊D4311yescharacteristic
317C22×D4C22×D4311yescharacteristic
318C23×C4C2×Dic4311yescharacteristic
319C23×C4C2×Dic4311yescharacteristic
320C23×C4C22⋊D4311yescharacteristic
321C2×M16—864no—
322C2×M16—862no—
323C2×M16—1721no—
324C2×M16—1722no—
325C22×C8—1721no—
326#123—22no—
327#123—22no—
328#123—42no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—41no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—862no—
342C2×C22⋊C4—1721no—
343C2×C22⋊C4—1721no—
344C2×C22⋊C4C2×Dic4311yescharacteristic
345C2×C22⋊C4C2×Dic4311yescharacteristic
346#100—434no—
347#100—864no—
348#100—862no—
349#99—862no—
350#99—862no—
351#99—1722no—
352#95—21no—
353#95—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—22no—
359C24—22no—
360C24—41no—
361C24—41no—
362C24—42no—
363C24—42no—
364C24—81no—
365C24—81no—
366C24C22⋊Dic4311yescharacteristic
367C24C22⋊Dic4311yescharacteristic
368C24C22⋊Dic4311yescharacteristic
369C24C22×Dic4311yescharacteristic
370C24C2×C22⋊D4311yescharacteristic
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—44no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4—44no—
387C2×D4D4×D4312yes—
388C2×D4#1062190012yes—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—81no—
403C22×C4—1722no—
404C22×C4C22⋊Dic4311yescharacteristic
405C22×C4C2×C22⋊D4311yescharacteristic
406M16—864no—
407M16—1724no—
408M16—1722no—
409C2×C8—1724no—
410C2×C8—1722no—
411C4⋊C4—42no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C22⋊C4—22no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C22⋊C4—42no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—42no—
421C22⋊C4—41no—
422C22⋊C4—81no—
423C22⋊C4—81no—
424C22⋊C4—81no—
425C22⋊C4—3442no—
426C22⋊C4—3442no—
427C22⋊C4—1722no—
428C22⋊C4—1722no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—22no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—41no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—42no—
454C23—42no—
455C23—41no—
456C23—41no—
457C23—42no—
458C23—42no—
459C23—81no—
460C23—81no—
461C23—81no—
462C23—81no—
463C23—84no—
464C23—84no—
465C23—84no—
466C23—84no—
467C23#1306324011yescharacteristic
468C23#1306324011yescharacteristic
469C23C2×C22⋊Dic4311yescharacteristic
470C23D4×Dic4312yes—
471C23#1306329712yes—
472D4—42no—
473D4—42no—
474D4—44no—
475D4—44no—
476D4—42no—
477D4—42no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—82no—
499C2×C4—82no—
500C2×C4—3442no—
501C2×C4—3442no—
502C2×C4—3442no—
503C2×C4#1306324012yes—
504C2×C4#1306329311yescharacteristic
505C2×C4#1306330611yescharacteristic
506C8—1724no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—22no—
513C22—22no—
514C22—21no—
515C22—21no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—84no—
534C22—84no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—84no—
539C22—84no—
540C22#1458268912yescomplemented
541C22#1458277911yescharacteristic
542C22C2×#1306324011yescharacteristic
543C22C2×#1306324011yescharacteristic
544C4—21no—
545C4—22no—
546C4—21no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—6882no—
552C2—21no—
553C2—21no—
554C2—22no—
555C2—42no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—81no—
560C2#1913504911yescharacteristic
561C2C2×#1458268911yescharacteristic
562C2#1913624111yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC24×C43C22×C4
FrattiniC22×D4C22×D43
FittingC43×#2405C2
socleC22×C43C2×#99
prime radicalC23×D4×C43C22
cosocleC22×D4×C43C23
hypercenter#2405D43
hypocenterC43#13080
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ #2405

Complements

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

NH ≅ G/Ntype
2. C2×#14582689C2semidirect
4. #19132713C2semidirect
15. C2×#123×C43C4semidirect
17. C22×C22⋊C4×C43C4semidirect
20. C43×#386C4semidirect
24. C43×#379C4semidirect
259. C22×C43#352semidirect
289. C2×#123Dic43semidirect
291. C22×C22⋊C4Dic43semidirect
299. #386Dic43semidirect
304. #379Dic43semidirect
306. C43#13080semidirect
540. C22#14582689semidirect

Maximal subgroups

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

subgroupindex
C22×#130632422
C2×#145826892
#191345102
#191327132
C43×#24052
#1308043