Finite Group Databasebeta

← #24988232

Subgroups — #24988232

Order 11008.

808 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 808 conjugacy classes of subgroups — too many to draw. Only its 113 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×#14583631C211yesmaximal, characteristic
2C4×#13063243C211yesmaximal, characteristic, complemented
3#19133193C211yesmaximal, characteristic, complemented
4#19133039C211yesmaximal, characteristic, complemented
5#19133037C211yesmaximal, characteristic, complemented
6#19132938C211yesmaximal, characteristic, complemented
7C43×#1527C211yesmaximal, characteristic, complemented
8#14583631—22no—
9#14583631—22no—
10#14583631—22no—
11#14583631—22no—
12C2×#13063321C411yescharacteristic
13C2×#13063314C411yescharacteristic
14C2×#13063311—21no—
15C2×#13063309—21no—
16C2×#13063307—21no—
17C2×Q8×Dic43C411yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×D4×Dic43C411yescharacteristic
21C2×(C22⋊D43)⋊C4—21no—
22#14582956C2211yescharacteristic
23C2×#13063243—21no—
24C4×#10621877C2211yescharacteristic
25#14582667—21no—
26#14582639—22no—
27#14582628—22no—
28#14582626—22no—
29#14582624—21no—
30#14582624—21no—
31C2×#124×C43C2211yescharacteristic
32C43×#432C2211yescharacteristic
33C4×M16×C43C2211yescharacteristic
34C43×#329—22no—
35C22×Dic86D411yescharacteristic
36C22×D172C2×C411yescharacteristic
37C22×C22⋊D43—21no—
38C22×C22⋊D43—21no—
39C23×Dic43—21no—
40C22×C4×D43—21no—
41C2×#10621877—21no—
42#13063321—22no—
43#13063321—22no—
44#13063314—22no—
45#13063314—22no—
46#13063311—24no—
47#13063311—24no—
48#13063309—24no—
49#13063309—24no—
50#13063307—24no—
51#13063307—24no—
52Q8×Dic43—22no—
53Q8×Dic43—22no—
54C4×Dic86—21no—
55C4×Dic86—21no—
56C4×Dic86—21no—
57C4×Dic86—21no—
58C4×D172—21no—
59C4×D172—21no—
60C4×D172D412yes—
61C4×D172D412yes—
62D4×Dic43—22no—
63D4×Dic43—22no—
64(C22⋊D43)⋊C4—24no—
65(C22⋊D43)⋊C4—24no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43C2×C411yescharacteristic
68C2×C4⋊Dic43D411yescharacteristic
69C2×Dic43⋊C4D411yescharacteristic
70C2×Dic43⋊C4D411yescharacteristic
71C2×C22⋊Dic43—21no—
72C2×(C2×D43)⋊C4—21no—
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4—21no—
75C2×C4×Dic43—21no—
76C2×C4×Dic43C2×C411yescharacteristic
77C2×C4×Dic43C2×C411yescharacteristic
78C4⋊(C43⋊C8)—21no—
79#13063243—24no—
80C22⋊(C43⋊C8)—21no—
81#13063236—21no—
82#13063236—21no—
83C4×C43⋊C8—21no—
84C22×Q8×C43C2×C411yescharacteristic
85C22×D4×C43C2×C411yescharacteristic
86C2×M16×C43—21no—
87#124×C43—21no—
88#124×C43—21no—
89#124×C43D412yes—
90#124×C43D412yes—
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43—21no—
93C2×C42×C43C2311yescharacteristic
94C4⋊C8×C43—21no—
95C22⋊C8×C43—21no—
96#97×C43—21no—
97#97×C43—21no—
98C4×C8×C43—21no—
99C24×C43—21no—
100C23×D43—21no—
101C2×Q8×C43—21no—
102C2×Q8×C43—42no—
103C2×Q8×C43C22⋊C412yes—
104C2×D4×C43—21no—
105C2×D4×C43—42no—
106C2×D4×C43C22⋊C412yes—
107C22×C4×C43—21no—
108C22×C4×C43C22×C411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C2×C22⋊D43—24no—
112C2×C22⋊D43—24no—
113C2×C22⋊D43—42no—
114C2×C22⋊D43—42no—
115C2×C22⋊D43—82no—
116C22×Dic43—24no—
117C22×Dic43—21no—
118C22×Dic43—82no—
119C22×Dic43C22⋊C411yescharacteristic
120C22×Dic43C22⋊C411yescharacteristic
121C22×Dic43C22⋊C411yescharacteristic
122C22×Dic43C22⋊C411yescharacteristic
123C2×D172—21no—
124C2×D172—42no—
125C2×D172C22⋊C412yes—
126C2×C4×D43—22no—
127C2×C4×D43—22no—
128C2×C4×D43—82no—
129C2×Dic86—21no—
130C2×Dic86—21no—
131C2×Dic86—22no—
132C2×Dic86—41no—
133M16×C43—22no—
134M16×C43—41no—
135C2×C8×C43—41no—
136C2×C8×C43—41no—
137C22⋊C4×C43—22no—
138C22⋊C4×C43—22no—
139C22⋊C4×C43—22no—
140C22⋊C4×C43—22no—
141C42×C43C2×D411yescharacteristic
142C42×C43C2×D411yescharacteristic
143C42×C43C2×D411yescharacteristic
144C42×C43C2×D411yescharacteristic
145C22⋊Dic43—24no—
146(C2×D43)⋊C4—24no—
147(C2×D43)⋊C4—24no—
148(C2×D43)⋊C4—22no—
149(C2×D43)⋊C4—22no—
150C4⋊Dic43—24no—
151C4⋊Dic43—21no—
152C4⋊Dic43—21no—
153C4⋊Dic43—21no—
154C4⋊Dic43C22⋊C412yes—
155Dic43⋊C4—21no—
156Dic43⋊C4—21no—
157Dic43⋊C4—21no—
158Dic43⋊C4—21no—
159C4×Dic43—24no—
160C4×Dic43—21no—
161C4×Dic43—21no—
162C4×Dic43—21no—
163C4×Dic43—21no—
164#10621877—22no—
165#10621877—41no—
166C2×C43⋊C8—41no—
167C2×C43⋊C8—41no—
168C23×C43—22no—
169C23×C43—42no—
170C23×C43—42no—
171C23×C43—41no—
172C23×C43—41no—
173C23×C43C2×C22⋊C411yescharacteristic
174C22×D43—22no—
175C22×D43—42no—
176C22×D43—42no—
177C22×D43—41no—
178C22×D43—41no—
179Q8×C43—42no—
180Q8×C43—42no—
181D4×C43—42no—
182D4×C43—42no—
183C2×C4×C43—21no—
184C2×C4×C43—21no—
185C2×C4×C43—22no—
186C2×C4×C43—22no—
187C2×C4×C43—41no—
188C2×C4×C43—42no—
189C2×C4×C43C2×C22⋊C411yescharacteristic
190C2×C4×C43C2×C22⋊C411yescharacteristic
191C2×C4×C43#12011yescharacteristic
192C2×C4×C43#12011yescharacteristic
193C2×C4×C43#12011yescharacteristic
194C2×C4×C43#12011yescharacteristic
195C22⋊D43—48no—
196C22⋊D43—84no—
197C2×Dic43—21no—
198C2×Dic43—21no—
199C2×Dic43—21no—
200C2×Dic43—21no—
201C2×Dic43—21no—
202C2×Dic43—22no—
203C2×Dic43—21no—
204C2×Dic43—21no—
205C2×Dic43—42no—
206C2×Dic43—41no—
207C2×Dic43—41no—
208C2×Dic43—84no—
209C2×Dic43#10412yes—
210D172—24no—
211D172—42no—
212C4×D43—82no—
213C4×D43—82no—
214Dic86—42no—
215Dic86—42no—
216C8×C43—42no—
217C8×C43—81no—
218C43⋊C8—42no—
219C43⋊C8—81no—
220#8370—431nomaximal, Sylow
221C22×C43—21no—
222C22×C43—21no—
223C22×C43—42no—
224C22×C43—42no—
225C22×C43—42no—
226C22×C43—82no—
227C22×C43—82no—
228C22×C43#37911yescharacteristic
229C22×C43C2×#10411yescharacteristic
230C22×C43#42111yescharacteristic
231C2×D43—42no—
232C2×D43—42no—
233C2×D43—42no—
234C2×D43—82no—
235C2×D43—82no—
236C4×C43—21no—
237C4×C43—21no—
238C4×C43—21no—
239C4×C43—21no—
240C4×C43—21no—
241C4×C43—42no—
242C4×C43#41312yes—
243Dic43—22no—
244Dic43—42no—
245Dic43—41no—
246Dic43—41no—
247Dic43—41no—
248C2×#559—431no—
249C4×#101—431no—
250#1527—431no—
251#1527D4311yescharacteristic, complemented
252#1490—431no—
253#1490—431no—
254#1467—431no—
255C2×C43—21no—
256C2×C43—21no—
257C2×C43—82no—
258C2×C43#178511yescharacteristic
259C2×C43#178911yescharacteristic
260C2×C43#179511yescharacteristic
261D43—82no—
262#559—862no—
263#559—862no—
264#559—862no—
265#559—862no—
266C2×#127—431no—
267C2×#124—431no—
268C2×#124—861no—
269C2×#124C2×D4311yescharacteristic
270C2×#123—861no—
271C2×#123—861no—
272C2×C4×Q8—431no—
273C2×C4×Q8—431no—
274C2×C4×D4—431no—
275C2×C4×D4—431no—
276C2×C4×D4—861no—
277#432—431no—
278#432C2×D4311yescharacteristic
279C2×#101—861no—
280C4×M16—431no—
281C4×M16C2×D4311yescharacteristic
282#343—861no—
283#329—22no—
284#329—862no—
285D4⋊C8—862no—
286D4⋊C8—862no—
287#324—861no—
288#324—861no—
289C43#837011yescharacteristic, complemented, Sylow
290C22×Q8—431no—
291C22×Q8C4×D4311yescharacteristic
292C22×D4—431no—
293C22×D4—861no—
294C22×D4—861no—
295C22×D4C4×D4311yescharacteristic
296C23×C4—861no—
297C23×C4—861no—
298C2×M16—21no—
299C2×M16—861no—
300#127—862no—
301#127—862no—
302#124—21no—
303#124—21no—
304#124—864no—
305#124—864no—
306#124—862no—
307#124—862no—
308#124D17212yes—
309#124C22⋊D4312yes—
310#123—864no—
311#123—864no—
312#123—864no—
313#123—864no—
314C4×Q8—862no—
315C4×Q8—862no—
316C4×Q8—861no—
317C4×Q8—861no—
318C4×Q8—861no—
319C4×Q8—861no—
320C4×D4—432no—
321C4×D4—432no—
322C4×D4—864no—
323C4×D4—864no—
324C4×D4—862no—
325C4×D4—862no—
326C4×D4—861no—
327C4×D4—861no—
328C2×C4⋊C4—431no—
329C2×C4⋊C4—431no—
330C2×C4⋊C4—431no—
331C2×C4⋊C4—431no—
332C2×C4⋊C4—861no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—861no—
336C2×C22⋊C4—861no—
337C2×C22⋊C4—861no—
338C2×C22⋊C4—861no—
339C2×C42—431no—
340C2×C42—431no—
341C2×C42—861no—
342C2×C42C22×D4311yescharacteristic
343C4⋊C8—21no—
344C4⋊C8—861no—
345#101—864no—
346C22⋊C8—21no—
347C22⋊C8—861no—
348#97—21no—
349#97—21no—
350#97—861no—
351#97—861no—
352C4×C8—21no—
353C4×C8—861no—
354C24—21no—
355C24—861no—
356C2×Q8—21no—
357C2×Q8—42no—
358C2×Q8—862no—
359C2×Q8—861no—
360C2×Q8—861no—
361C2×Q8—1721no—
362C2×Q8(C2×D43)⋊C412yes—
363C2×D4—21no—
364C2×D4—42no—
365C2×D4—432no—
366C2×D4—864no—
367C2×D4—864no—
368C2×D4—861no—
369C2×D4—3442no—
370C2×D4—1722no—
371C2×D4—1722no—
372C2×D4—1722no—
373C2×D4(C2×D43)⋊C412yes—
374C22×C4—21no—
375C22×C4—431no—
376C22×C4—431no—
377C22×C4—431no—
378C22×C4—431no—
379C22×C4—864no—
380C22×C4—861no—
381C22×C4—862no—
382C22×C4—862no—
383C22×C4—3442no—
384C22×C4—3442no—
385C22×C4C2×C4×D4311yescharacteristic
386C22×C4D4×D4311yescharacteristic
387C22×C4D4×D4311yescharacteristic
388M16—22no—
389M16—41no—
390M16—862no—
391M16—1721no—
392C2×C8—41no—
393C2×C8—41no—
394C2×C8—1721no—
395C2×C8—1721no—
396C4⋊C4—432no—
397C4⋊C4—864no—
398C4⋊C4—861no—
399C4⋊C4—861no—
400C4⋊C4—861no—
401C4⋊C4—861no—
402C4⋊C4—861no—
403C4⋊C4—861no—
404C4⋊C4—861no—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C22⋊C4—22no—
408C22⋊C4—22no—
409C22⋊C4—864no—
410C22⋊C4—864no—
411C22⋊C4—864no—
412C22⋊C4—862no—
413C22⋊C4—862no—
414C42—864no—
415C42—861no—
416C42—861no—
417C42—861no—
418C42—861no—
419C42C2×D17211yescharacteristic
420C42D4×D4311yescharacteristic
421C42D4×D4311yescharacteristic
422C42C2×C22⋊D4311yescharacteristic
423C23—22no—
424C23—42no—
425C23—42no—
426C23—41no—
427C23—41no—
428C23—862no—
429C23—1722no—
430C23—1722no—
431C23—1721no—
432C23—1721no—
433C23C22⋊C4×D4311yescharacteristic
434Q8—42no—
435Q8—42no—
436Q8—1722no—
437Q8—1722no—
438D4—42no—
439D4—42no—
440D4—864no—
441D4—3444no—
442D4—1722no—
443D4—1728no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—432no—
451C2×C4—861no—
452C2×C4—861no—
453C2×C4—861no—
454C2×C4—861no—
455C2×C4—861no—
456C2×C4—862no—
457C2×C4—861no—
458C2×C4—861no—
459C2×C4—3442no—
460C2×C4—3442no—
461C2×C4—3444no—
462C2×C4—1722no—
463C2×C4—1721no—
464C2×C4—1721no—
465C2×C4C22⋊C4×D4311yescharacteristic
466C2×C4C2×(C2×D43)⋊C411yescharacteristic
467C2×C4#1306329311yescharacteristic
468C2×C4#1306329311yescharacteristic
469C2×C4#1306329511yescharacteristic
470C2×C4#1306329511yescharacteristic
471C8—42no—
472C8—81no—
473C8—3441no—
474C8—1722no—
475C22—21no—
476C22—21no—
477C22—42no—
478C22—42no—
479C22—42no—
480C22—82no—
481C22—82no—
482C22—3442no—
483C22—3442no—
484C22—1722no—
485C22—1722no—
486C22—1722no—
487C22#1458275411yescharacteristic
488C22#104×D4311yescharacteristic
489C22#1458291411yescharacteristic
490C4—21no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—21no—
495C4—42no—
496C4—862no—
497C4—1721no—
498C4—1722no—
499C4—1721no—
500C4—1721no—
501C4#1458288012yes—
502C2—21no—
503C2—21no—
504C2—82no—
505C2—3442no—
506C2#1913452011yescharacteristic
507C2#1913453711yescharacteristic
508C2#1913456411yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1527C2
socleC22×C43#379
prime radicalC2×#13063321C4
cosocleC2×C42×C43C23
hypercenter#1527D43
hypocenterC43#8370
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1527

Complements

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

NH ≅ G/Ntype
2. C4×#13063243C2semidirect
3. #19133193C2semidirect
4. #19133039C2semidirect
5. #19133037C2semidirect
6. #19132938C2semidirect
7. C43×#1527C2semidirect
251. #1527D43semidirect
289. C43#8370semidirect

Maximal subgroups

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

subgroupindex
C2×#145836312
C4×#130632432
#191331932
#191330392
#191330372
#191329382
C43×#15272
#837043