Finite Group Databasebeta

← #24996996

Subgroups — #24996996

Order 11008.

798 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 798 conjugacy classes of subgroups — too many to draw. Only its 85 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#19143855C211yesmaximal, characteristic
2#19139975C211yesmaximal, characteristic, complemented
3#19134539C211yesmaximal, characteristic
4#19133127C211yesmaximal, characteristic, complemented
5#19132925C211yesmaximal, characteristic, complemented
6#19132447C211yesmaximal, characteristic, complemented
7C43×#2406C211yesmaximal, characteristic
8C2×#13063355—21no—
9C2×#13063304C2211yescharacteristic
10#14583061—22no—
11#14583055—21no—
12#14583050—21no—
13C2×#13063252—22no—
14#14582900—21no—
15#14582863C2211yescharacteristic
16#14582863C2211yescharacteristic
17#14582829—21no—
18#14582819—21no—
19#14582794—22no—
20#14582772—21no—
21#14582772—21no—
22C4×C22⋊Dic43C2211yescharacteristic
23#14582635—22no—
24#14582625—22no—
25C22×#41×C43C2211yescharacteristic
26C2×#123×C43—21no—
27C22×C4⋊C4×C43C2211yescharacteristic
28C43×#395—21no—
29C43×#394—21no—
30C43×#386—21no—
31C43×#385—22no—
32C43×#381C2211yescharacteristic
33C22×Dic86D411yescharacteristic
34#13063355—44no—
35C2×#10621885—22no—
36C2×#10621883—22no—
37C2×#10621877—21no—
38C2×#10621877—21no—
39#13063304—21no—
40#13063304—21no—
41#13063304—21no—
42#13063304—21no—
43C2×C4⋊Dic43D411yescharacteristic
44C2×Dic43⋊C4—22no—
45C2×Dic43⋊C4—21no—
46C2×Dic43⋊C4—22no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43—21no—
49C2×C4×Dic43D412yes—
50#13063252—44no—
51#13063249—22no—
52#13063246—22no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)D412yes—
57C43⋊#95—22no—
58C43⋊#95—22no—
59C43⋊#95—21no—
60C2×#41×C43—21no—
61C2×#41×C43—21no—
62C2×#41×C43—21no—
63C2×#41×C43—21no—
64C2×#41×C43—44no—
65C22×Q8×C43D411yescharacteristic
66C22×D4×C43—21no—
67C22×D4×C43D411yescharacteristic
68C23×C4×C43—21no—
69C23×C4×C43D411yescharacteristic
70C23×C4×C43D411yescharacteristic
71C23×C4×C43C2311yescharacteristic
72#123×C43—44no—
73C2×C4⋊C4×C43—22no—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43—21no—
80C2×C22⋊C4×C43—22no—
81C2×C22⋊C4×C43—22no—
82C2×C22⋊C4×C43—21no—
83#95×C43—22no—
84#95×C43—21no—
85#95×C43D412yes—
86C24×C43—21no—
87C24×C43C2×D411yescharacteristic
88#41×C43—24no—
89#41×C43—24no—
90#41×C43—42no—
91#41×C43—42no—
92#41×C43—42no—
93#41×C43—42no—
94#41×C43—42no—
95#41×C43—42no—
96C2×Q8×C43—21no—
97C2×Q8×C43—21no—
98C2×Q8×C43—42no—
99C2×D4×C43—24no—
100C2×D4×C43—21no—
101C2×D4×C43—21no—
102C2×D4×C43—42no—
103C2×D4×C43—42no—
104C2×D4×C43—41no—
105C2×D4×C43—41no—
106C22×C4×C43—21no—
107C22×C4×C43—21no—
108C22×C4×C43—21no—
109C22×C4×C43—22no—
110C22×C4×C43—21no—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—42no—
115C22×C4×C43—42no—
116C22×C4×C43—42no—
117C22×C4×C43—42no—
118C22×C4×C43—42no—
119C22×C4×C43—41no—
120C22×C4×C43—41no—
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43#4111yescharacteristic
127C22×Dic43—22no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C2×Dic86—21no—
131C2×Dic86—21no—
132C2×Dic86—42no—
133C4⋊C4×C43—44no—
134C4⋊C4×C43—41no—
135C4⋊C4×C43—41no—
136C4⋊C4×C43—41no—
137C4⋊C4×C43—41no—
138C22⋊C4×C43—42no—
139C22⋊C4×C43—44no—
140C22⋊C4×C43—44no—
141C22⋊Dic43—24no—
142C22⋊Dic43—41no—
143C22⋊Dic43—41no—
144#10621885—44no—
145#10621883—44no—
146C4⋊Dic43—21no—
147C4⋊Dic43—21no—
148Dic43⋊C4—44no—
149Dic43⋊C4—41no—
150Dic43⋊C4—41no—
151Dic43⋊C4—82no—
152C4×Dic43—42no—
153#10621877—42no—
154#10621877—42no—
155C2×C43⋊C8—22no—
156C2×C43⋊C8—41no—
157C23×C43—22no—
158C23×C43—22no—
159C23×C43—22no—
160C23×C43—41no—
161C23×C43—42no—
162C23×C43—41no—
163C23×C43—41no—
164C23×C43—42no—
165C23×C43#12011yescharacteristic
166C23×C43#12011yescharacteristic
167C23×C43#12111yescharacteristic
168Q8×C43—22no—
169Q8×C43—22no—
170Q8×C43—41no—
171Q8×C43—41no—
172D4×C43—22no—
173D4×C43—22no—
174D4×C43—41no—
175D4×C43—41no—
176D4×C43—44no—
177D4×C43—44no—
178C2×C4×C43—22no—
179C2×C4×C43—22no—
180C2×C4×C43—22no—
181C2×C4×C43—22no—
182C2×C4×C43—22no—
183C2×C4×C43—22no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43—44no—
189C2×C4×C43—44no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—42no—
197C2×C4×C43—42no—
198C2×C4×C43—42no—
199C2×C4×C43—41no—
200C2×C4×C43—42no—
201C2×C4×C43—42no—
202C2×C4×C43—81no—
203C2×C4×C43#12011yescharacteristic
204C2×C4×C43#12111yescharacteristic
205C2×C4×C43#12111yescharacteristic
206C2×C4×C43#12711yescharacteristic
207C2×Dic43—24no—
208C2×Dic43—42no—
209C2×Dic43—42no—
210C2×Dic43—42no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213C2×Dic43—42no—
214Dic86—42no—
215Dic86—81no—
216C43⋊C8—42no—
217C43⋊C8—81no—
218#9943—431nomaximal, Sylow
219C22×C43—21no—
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—21no—
223C22×C43—21no—
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—44no—
227C22×C43—44no—
228C22×C43—42no—
229C22×C43—82no—
230C22×C43—81no—
231C22×C43—81no—
232C22×C43#39211yescharacteristic
233C22×C43#45612yes—
234C22×C43B(4,𝔽2)12yes—
235C4×C43—21no—
236C4×C43—21no—
237C4×C43—21no—
238C4×C43—21no—
239C4×C43—42no—
240C4×C43—42no—
241C4×C43—82no—
242C4×C43—81no—
243Dic43—44no—
244Dic43—81no—
245Dic43—81no—
246#3007—431no—
247#2583—431no—
248#2406D4311yescharacteristic
249#1789—431no—
250#1511—431no—
251#1463—431no—
252#1284—431no—
253C2×C43—22no—
254C2×C43—22no—
255C2×C43—41no—
256C2×C43—82no—
257C2×C43#200511yescharacteristic
258C2×C43#201011yescharacteristic
259C2×C43#202111yescharacteristic
260C22×#41C2×D4311yescharacteristic
261C2×#137—861no—
262C2×#123—21no—
263C2×C22⋊Q8—431no—
264C22×C4⋊C4C2×D4311yescharacteristic
265#452—862no—
266#451—861no—
267#450—861no—
268C2×#104—862no—
269#417—861no—
270#407—431no—
271#407—431no—
272#398—861no—
273#395—21no—
274#395—861no—
275#394—21no—
276#389—862no—
277#386—21no—
278#385—22no—
279#385—861no—
280#385—861no—
281#381C2×D4311yescharacteristic
282C4×C22⋊C4—431no—
283#328—862no—
284#324—862no—
285C43#994311yescharacteristic, complemented, Sylow
286C2×#41—21no—
287C2×#41—21no—
288C2×#41—21no—
289C2×#41—21no—
290C2×#41—44no—
291C22×Q8—431no—
292C22×Q8C22⋊D4311yescharacteristic
293C22×D4—21no—
294C22×D4C22⋊D4311yescharacteristic
295C23×C4—21no—
296C23×C4C22⋊D4311yescharacteristic
297C23×C4C22⋊D4311yescharacteristic
298C23×C4C22×D4311yescharacteristic
299#137—1724no—
300C2×Q16—862no—
301C2×SD16—862no—
302C2×M16—861no—
303C2×M16—861no—
304#123—44no—
305C22⋊Q8—861no—
306C22⋊Q8—861no—
307C22⋊Q8—861no—
308C22⋊Q8—861no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—431no—
317C2×C4⋊C4—862no—
318C2×C4⋊C4—862no—
319C2×C4⋊C4—861no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—861no—
324C2×C22⋊C4—861no—
325C2×C42—432no—
326#104—1724no—
327#103—862no—
328#102—862no—
329C22⋊C8—432no—
330C22⋊C8—861no—
331C22⋊C8—861no—
332C22⋊C8—861no—
333#95—22no—
334#95—21no—
335#95—862no—
336#95—862no—
337#95—861no—
338#95C22⋊D4312yes—
339C24—21no—
340C24C2×C22⋊D4311yescharacteristic
341#41—24no—
342#41—24no—
343#41—42no—
344#41—42no—
345#41—42no—
346#41—42no—
347#41—42no—
348#41—42no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—42no—
352C2×Q8—861no—
353C2×Q8—861no—
354C2×Q8—1722no—
355C2×D4—24no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—42no—
359C2×D4—42no—
360C2×D4—41no—
361C2×D4—41no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—42no—
377C22×C4—862no—
378C22×C4—861no—
379C22×C4—861no—
380C22×C4D4×D4311yescharacteristic
381C22×C4D4×D4311yescharacteristic
382C22×C4D4×D4311yescharacteristic
383C22×C4#1062190011yescharacteristic
384C22×C4C2×C22⋊D4311yescharacteristic
385C22×C4C2×C22⋊D4311yescharacteristic
386Q16—1724no—
387SD16—1724no—
388M16—1722no—
389M16—1722no—
390C2×C8—862no—
391C2×C8—1721no—
392C4⋊C4—44no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—861no—
398C4⋊C4—861no—
399C4⋊C4—3442no—
400C4⋊C4—1724no—
401C4⋊C4—1721no—
402C4⋊C4—1721no—
403C22⋊C4—44no—
404C22⋊C4—42no—
405C22⋊C4—44no—
406C22⋊C4—864no—
407C22⋊C4—1721no—
408C22⋊C4—1721no—
409C42—1722no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—41no—
414C23—42no—
415C23—41no—
416C23—41no—
417C23—42no—
418C23#1306329311yescharacteristic
419C23#1306329411yescharacteristic
420C23#1306329711yescharacteristic
421Q8—22no—
422Q8—22no—
423Q8—41no—
424Q8—41no—
425Q8—3441no—
426Q8—1722no—
427D4—22no—
428D4—22no—
429D4—41no—
430D4—41no—
431D4—44no—
432D4—44no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—81no—
458C2×C4—864no—
459C2×C4—1722no—
460C2×C4—1721no—
461C2×C4—1721no—
462C2×C4—1722no—
463C2×C4—1722no—
464C2×C4—1722no—
465C2×C4#1306329311yescharacteristic
466C2×C4#1306329611yescharacteristic
467C2×C4#1306329711yescharacteristic
468C2×C4#1306332111yescharacteristic
469C8—3441no—
470C8—1722no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—44no—
479C22—44no—
480C22—42no—
481C22—82no—
482C22—81no—
483C22—81no—
484C22#1458280711yescharacteristic
485C22#1458308212yes—
486C22#1458308512yes—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—42no—
492C4—42no—
493C4—82no—
494C4—81no—
495C4—3441no—
496C4—3441no—
497C4—1724no—
498C2—22no—
499C2—22no—
500C2—41no—
501C2—82no—
502C2#1913562911yescharacteristic
503C2#1913566011yescharacteristic
504C2#1913571811yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#2406C2
socleC22×C43#392
prime radicalC22×#41×C43C22
hypercenter#2406D43
hypocenterC43#9943
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2406

Complements

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

NH ≅ G/Ntype
2. #19139975C2semidirect
4. #19133127C2semidirect
5. #19132925C2semidirect
6. #19132447C2semidirect
285. C43#9943semidirect

Maximal subgroups

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

subgroupindex
#191438552
#191399752
#191345392
#191331272
#191329252
#191324472
C43×#24062
#994343