Finite Group Databasebeta

← #25015256

Subgroups — #25015256

Order 11008.

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

normal subgroups only

This group has 616 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#19137957C211yesmaximal, characteristic
2#19134585C211yesmaximal, characteristic
3#99×Dic43C211yesmaximal, characteristic
4#19132714C211yesmaximal, characteristic
5#19132713C211yesmaximal, characteristic
6#19132712C211yesmaximal, characteristic
7C43×#1390C211yesmaximal, characteristic
8C23×Dic86C411yescharacteristic, complemented
9C2×#13063302—21no—
10C2×D4×Dic43C2211yescharacteristic
11#14582922—21no—
12C2×#13063242C2211yescharacteristic
13C2×#13063240C2211yescharacteristic
14#14582820—21no—
15#14582811—21no—
16#14582803—21no—
17#14582779C2211yescharacteristic
18#14582774C411yescharacteristic, complemented
19#14582772C411yescharacteristic, complemented
20#14582757C411yescharacteristic, complemented
21C22⋊C4×Dic43—21no—
22#14582667—21no—
23#14582665—21no—
24C2×#100×C43C2211yescharacteristic
25C2×#99×C43C2211yescharacteristic
26C43×#386C2211yescharacteristic
27C22×Dic86—21no—
28C22×Dic86—21no—
29C22×Dic86—44no—
30C22×Dic86—41no—
31C22×Dic86—41no—
32C23×Dic43C2×C411yescharacteristic
33C23×Dic43C2×C411yescharacteristic
34C23×Dic43D411yescharacteristic
35C2×#10621877—21no—
36#13063302—44no—
37D4×Dic43—41no—
38D4×Dic43—41no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43D411yescharacteristic
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—21no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43C2×C411yescharacteristic
46C2×C22⋊Dic43C2×C411yescharacteristic
47C2×C22⋊Dic43D411yescharacteristic
48C2×C4×Dic43—41no—
49C2×C4×Dic43D411yescharacteristic
50Dic43⋊C8—41no—
51Dic43⋊C8—41no—
52#13063242—21no—
53#13063242—21no—
54#13063240—21no—
55#13063240Q812yescomplemented
56C43⋊#95—21no—
57C43⋊#95—21no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—41no—
61C22×D4×C43C2311yescharacteristic
62C23×C4×C43C2×C411yescharacteristic
63C2×M16×C43—21no—
64C2×C22⋊C4×C43—21no—
65C2×C22⋊C4×C43—21no—
66C2×C22⋊C4×C43C2×C411yescharacteristic
67#100×C43—21no—
68#100×C43—21no—
69#99×C43—21no—
70#99×C43Q812yescomplemented
71#95×C43—21no—
72C24×C43C22×C411yescharacteristic
73C24×C43C2×D411yescharacteristic
74C2×D4×C43—41no—
75C2×D4×C43—41no—
76C2×D4×C43C2×Q811yescharacteristic
77C2×D4×C43C2×Q811yescharacteristic
78C2×D4×C43#4111yescharacteristic
79C2×D4×C43#4111yescharacteristic
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—41no—
83C22×C4×C43—41no—
84C22×C4×C43—42no—
85C22×C4×C43C2×D411yescharacteristic
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C22×Dic43—21no—
90C22×Dic43—21no—
91C22×Dic43—21no—
92C22×Dic43—41no—
93C22×Dic43—41no—
94C22×Dic43—42no—
95C22×Dic43—42no—
96C22×Dic43—42no—
97C22×Dic43C22⋊C411yescharacteristic
98C22×Dic43C22⋊C411yescharacteristic
99C22×Dic43C22⋊C411yescharacteristic
100C22×Dic43C22⋊C411yescharacteristic
101C2×Dic86—24no—
102C2×Dic86—42no—
103C2×Dic86—42no—
104C2×Dic86—42no—
105C2×Dic86—42no—
106C2×Dic86—44no—
107C2×Dic86—44no—
108C2×Dic86—44no—
109C2×Dic86—41no—
110C2×Dic86—41no—
111C2×Dic86—44no—
112M16×C43—41no—
113M16×C43—41no—
114C2×C8×C43—41no—
115C22⋊C4×C43—22no—
116C22⋊C4×C43—41no—
117C22⋊C4×C43—41no—
118C22⋊C4×C43—42no—
119C22⋊Dic43—22no—
120C22⋊Dic43—41no—
121C22⋊Dic43—41no—
122C22⋊Dic43—41no—
123C22⋊Dic43—41no—
124C22⋊Dic43—42no—
125C4⋊Dic43—41no—
126C4⋊Dic43—42no—
127Dic43⋊C4—42no—
128Dic43⋊C4—42no—
129C4×Dic43—21no—
130C4×Dic43—21no—
131C4×Dic43—82no—
132#10621877—41no—
133#10621877—41no—
134C2×C43⋊C8—41no—
135C23×C43—21no—
136C23×C43—21no—
137C23×C43—21no—
138C23×C43—21no—
139C23×C43—41no—
140C23×C43—41no—
141C23×C43—41no—
142C23×C43—41no—
143C23×C43C2×C22⋊C411yescharacteristic
144C23×C43C4×Q811yescharacteristic
145C23×C43C4×Q811yescharacteristic
146C23×C43C22⋊Q811yescharacteristic
147C23×C43C22⋊Q811yescharacteristic
148D4×C43—41no—
149D4×C43—41no—
150D4×C43—41no—
151D4×C43—41no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—22no—
155C2×C4×C43—41no—
156C2×C4×C43—42no—
157C2×C4×C43—41no—
158C2×C4×C43—42no—
159C2×C4×C43—41no—
160C2×C4×C43—42no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—81no—
164C2×C4×C43—81no—
165C2×C4×C43#12411yescharacteristic
166C2×C4×C43C4⋊Q811yescharacteristic
167C2×Dic43—22no—
168C2×Dic43—22no—
169C2×Dic43—21no—
170C2×Dic43—21no—
171C2×Dic43—21no—
172C2×Dic43—42no—
173C2×Dic43—41no—
174C2×Dic43—42no—
175C2×Dic43—41no—
176C2×Dic43—42no—
177C2×Dic43—42no—
178C2×Dic43—41no—
179C2×Dic43—41no—
180C2×Dic43—41no—
181C2×Dic43—42no—
182C2×Dic43—41no—
183C2×Dic43—42no—
184C2×Dic43—41no—
185C2×Dic43—41no—
186C2×Dic43—81no—
187C2×Dic43—81no—
188C2×Dic43—81no—
189C2×Dic43#9911yescharacteristic
190C2×Dic43#9911yescharacteristic
191Dic86—44no—
192Dic86—48no—
193Dic86—44no—
194C8×C43—81no—
195C43⋊C8—81no—
196#13296—431nomaximal, Sylow
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—21no—
200C22×C43—21no—
201C22×C43—21no—
202C22×C43—21no—
203C22×C43—41no—
204C22×C43—41no—
205C22×C43—41no—
206C22×C43—41no—
207C22×C43—42no—
208C22×C43—41no—
209C22×C43—41no—
210C22×C43—41no—
211C22×C43—41no—
212C22×C43—81no—
213C22×C43#39111yescharacteristic
214C22×C43C2×#9911yescharacteristic
215C22×C43#41011yescharacteristic
216C4×C43—21no—
217C4×C43—21no—
218C4×C43—42no—
219C4×C43—81no—
220C4×C43—82no—
221Dic43—21no—
222Dic43—42no—
223Dic43—41no—
224Dic43—41no—
225Dic43—41no—
226Dic43—81no—
227Dic43—82no—
228Dic43AΣL(1,𝔽16)12yes—
229#2409—431no—
230#1800—431no—
231C4×#99—431no—
232#1390—431no—
233#1390—431no—
234#1390—431no—
235#1390D4311yescharacteristic
236C2×C43—21no—
237C2×C43—21no—
238C2×C43—41no—
239C2×C43—41no—
240C2×C43—41no—
241C2×C43—41no—
242C2×C43#199611yescharacteristic
243C2×C43C2×AΣL(1,𝔽16)11yescharacteristic
244C2×C43#212311yescharacteristic
245C23×Q8—431no—
246C2×C22⋊Q8—861no—
247C2×C4×D4—431no—
248#423—861no—
249C2×#100—431no—
250C2×#100C2×D4311yescharacteristic
251C2×#99—431no—
252C2×#99C2×D4311yescharacteristic
253#395—861no—
254#393—861no—
255#391—861no—
256#386—431no—
257#386C2×D4311yescharacteristic
258#385—431no—
259#385—431no—
260#380—431no—
261C4×C22⋊C4—861no—
262#343—861no—
263#342—861no—
264C43#1329611yescharacteristic, complemented, Sylow
265C22×Q8—861no—
266C22×Q8—861no—
267C22×Q8—1721no—
268C22×Q8—1721no—
269C22×Q8—1724no—
270C22×D4C22×D4311yescharacteristic
271C23×C4—431no—
272C23×C4—431no—
273C23×C4—431no—
274C23×C4C4×D4311yescharacteristic
275C2×M16—21no—
276C2×M16—861no—
277C22⋊Q8—1724no—
278C4×D4—1721no—
279C4×D4—1721no—
280C2×C4⋊C4—431no—
281C2×C4⋊C4—861no—
282C2×C4⋊C4—861no—
283C2×C4⋊C4—861no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—431no—
287C2×C22⋊C4—431no—
288C2×C22⋊C4—431no—
289C2×C22⋊C4—861no—
290C2×C22⋊C4—861no—
291C2×C22⋊C4C4×D4311yescharacteristic
292C2×C42—431no—
293C2×C42—1721no—
294C4⋊C8—1721no—
295C4⋊C8—1721no—
296#100—21no—
297#100—21no—
298#100—861no—
299#100—861no—
300#99—21no—
301#99—432no—
302#99—861no—
303#99Dic8612yescomplemented
304#95—21no—
305#95—861no—
306#95—861no—
307#95—861no—
308#95—861no—
309#95—1721no—
310C24C2×C4×D4311yescharacteristic
311C24D4×D4311yescharacteristic
312C2×Q8—864no—
313C2×Q8—1722no—
314C2×Q8—1721no—
315C2×Q8—1721no—
316C2×Q8—1722no—
317C2×Q8—1722no—
318C2×Q8—1722no—
319C2×Q8—1724no—
320C2×Q8—1724no—
321C2×Q8—1724no—
322C2×Q8—1724no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4C2×Dic8611yescharacteristic
326C2×D4#1062189811yescharacteristic
327C2×D4#1062190011yescharacteristic
328C2×D4Q8×D4311yescharacteristic
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—42no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—431no—
335C22×C4—431no—
336C22×C4—431no—
337C22×C4—431no—
338C22×C4—861no—
339C22×C4—861no—
340C22×C4—861no—
341C22×C4—861no—
342C22×C4—861no—
343C22×C4—861no—
344C22×C4—1722no—
345C22×C4—1722no—
346C22×C4—1722no—
347C22×C4—1721no—
348C22×C4—1721no—
349C22×C4D4×D4311yescharacteristic
350M16—41no—
351M16—41no—
352M16—1721no—
353M16—1721no—
354C2×C8—41no—
355C2×C8—1721no—
356C4⋊C4—1721no—
357C4⋊C4—1722no—
358C4⋊C4—1722no—
359C4⋊C4—1722no—
360C22⋊C4—22no—
361C22⋊C4—42no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—862no—
365C22⋊C4—1721no—
366C22⋊C4—1721no—
367C22⋊C4—1722no—
368C22⋊C4—1721no—
369C22⋊C4—1721no—
370C42—861no—
371C42—861no—
372C42—3442no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23C22⋊C4×D4311yescharacteristic
382C23#1306329011yescharacteristic
383C23C4×Dic8611yescharacteristic
384C23#1306330211yescharacteristic
385C23#1306330311yescharacteristic
386Q8—1724no—
387Q8—1724no—
388Q8—1728no—
389D4—41no—
390D4—41no—
391D4—41no—
392D4—41no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—431no—
407C2×C4—431no—
408C2×C4—862no—
409C2×C4—862no—
410C2×C4—861no—
411C2×C4—861no—
412C2×C4—861no—
413C2×C4—3441no—
414C2×C4—3441no—
415C2×C4—3441no—
416C2×C4—1722no—
417C2×C4—1722no—
418C2×C4—1722no—
419C2×C4—1722no—
420C2×C4—1721no—
421C2×C4—1721no—
422C2×C4—1721no—
423C2×C4—1721no—
424C2×C4—1722no—
425C2×C4—1721no—
426C2×C4—1721no—
427C2×C4—1721no—
428C2×C4—1721no—
429C2×C4—1722no—
430C2×C4#1306331111yescharacteristic
431C2×C4#1306332411yescharacteristic
432C8—81no—
433C8—3441no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—42no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—81no—
450C22#1458280311yescharacteristic
451C22#99×D4311yescharacteristic
452C22#1458287111yescharacteristic
453C4—21no—
454C4—21no—
455C4—42no—
456C4—81no—
457C4—82no—
458C4—432no—
459C4—861no—
460C4—3441no—
461C4—3442no—
462C4—1721no—
463C4—1722no—
464C4—1721no—
465C4—1721no—
466C2—21no—
467C2—21no—
468C2—41no—
469C2—41no—
470C2—41no—
471C2—41no—
472C2#1913557811yescharacteristic
473C2AΣL(1,𝔽16)×D4311yescharacteristic
474C2#1913624711yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC24×C43C22×C4
FrattiniC22×D4C22×D43
FittingC43×#1390C2
socleC22×C43C2×#99
prime radical, cosocleC22×D4×C43C23
hypercenter#1390D43
hypocenterC43#13296
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1390

Complements

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

NH ≅ G/Ntype
8. C23×Dic86C4semidirect
18. #14582774C4semidirect
19. #14582772C4semidirect
20. #14582757C4semidirect
55. #13063240Q8semidirect
70. #99×C43Q8semidirect
264. C43#13296semidirect
303. #99Dic86semidirect

Maximal subgroups

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

subgroupindex
#191379572
#191345852
#99×Dic432
#191327142
#191327132
#191327122
C43×#13902
#1329643