Finite Group Databasebeta

← #24996873

Subgroups — #24996873

Order 11008.

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

normal subgroups only

This group has 810 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
1C2×#14583057C211yesmaximal, characteristic
2#19140411C211yesmaximal, characteristic
3C2×#14582820C211yesmaximal, characteristic
4#19134529C211yesmaximal, characteristic
5C2×#14582635C211yesmaximal, characteristic
6C2×#14582624C211yesmaximal, characteristic
7C43×#1294C211yesmaximal, characteristic
8C23×Dic86C2211yescharacteristic
9C22×Dic172—21no—
10C2×#13063304C2211yescharacteristic
11C22×C4⋊Dic43—21no—
12C22×Dic43⋊C4C2211yescharacteristic
13#14583057—22no—
14#14583057—22no—
15C2×#13063250—21no—
16C2×#13063248—22no—
17C2×C22⋊(C43⋊C8)C2211yescharacteristic
18#14582839—21no—
19#14582829—22no—
20#14582820—22no—
21#14582820—21no—
22#14582820—22no—
23#14582774—21no—
24#14582760—21no—
25C2×C43⋊#95—21no—
26#14582635—22no—
27#14582624—22no—
28C2×C22⋊C8×C43C2211yescharacteristic
29C43×#380C2211yescharacteristic
30C2×#95×C43C2211yescharacteristic
31C22×Dic86—21no—
32C22×Dic86—21no—
33C22×Dic86—21no—
34C22×Dic86—21no—
35C22×Dic86—21no—
36C22×Dic86—44no—
37C22×Dic86D412yes—
38C22×Dic86D411yescharacteristic
39C23×Dic43—21no—
40C23×Dic43D411yescharacteristic
41C23×Dic43D411yescharacteristic
42C2×Dic172—24no—
43C2×Dic172—44no—
44C22×C43⋊C8—21no—
45#13063304—21no—
46#13063304—21no—
47#13063304—21no—
48#13063304—21no—
49C2×C4⋊Dic43—24no—
50C2×C4⋊Dic43—22no—
51C2×C4⋊Dic43—44no—
52C2×C4⋊Dic43D411yescharacteristic
53C2×Dic43⋊C4—21no—
54C2×Dic43⋊C4—21no—
55C2×Dic43⋊C4—21no—
56C2×Dic43⋊C4—21no—
57C2×Dic43⋊C4—21no—
58C2×Dic43⋊C4—21no—
59C2×Dic43⋊C4—21no—
60C2×C22⋊Dic43—21no—
61#13063250—24no—
62#13063248—44no—
63C22⋊(C43⋊C8)—21no—
64C22⋊(C43⋊C8)—21no—
65C43⋊#95—24no—
66C43⋊#95—22no—
67C43⋊#95—22no—
68C43⋊#95—22no—
69C23×C4×C43—21no—
70C23×C4×C43C2311yescharacteristic
71C22×C8×C43—21no—
72C2×C4⋊C4×C43D412yes—
73C2×C22⋊C4×C43—21no—
74C22⋊C8×C43—21no—
75C22⋊C8×C43D412yes—
76#95×C43—21no—
77#95×C43—21no—
78#95×C43D412yes—
79C24×C43C2×D411yescharacteristic
80C22×C4×C43—24no—
81C22×C4×C43—22no—
82C22×C4×C43—22no—
83C22×C4×C43—42no—
84C22×C4×C43—42no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43#4111yescharacteristic
93C22×Dic43—24no—
94C22×Dic43—21no—
95C22×Dic43—21no—
96C22×Dic43—22no—
97C22×Dic43—21no—
98C22×Dic43—21no—
99C22×Dic43—21no—
100C22×Dic43—21no—
101C22×Dic43—21no—
102C22×Dic43—21no—
103C22×Dic43—21no—
104C22×Dic43—21no—
105C22×Dic43—21no—
106C22×Dic43—42no—
107C22×Dic43—42no—
108C22×Dic43—41no—
109C22×Dic43—41no—
110C22×Dic43Q1612yescomplemented
111C2×Dic86—24no—
112C2×Dic86—24no—
113C2×Dic86—22no—
114C2×Dic86—22no—
115C2×Dic86—21no—
116C2×Dic86—21no—
117C2×Dic86—44no—
118C2×Dic86—44no—
119C2×Dic86—44no—
120C2×Dic86—44no—
121C2×Dic86—42no—
122C2×Dic86—42no—
123C2×Dic86—41no—
124C2×Dic86—41no—
125C2×Dic86—42no—
126C2×C8×C43—22no—
127C2×C8×C43—42no—
128C4⋊C4×C43—42no—
129C22⋊C4×C43—41no—
130C22⋊C4×C43—41no—
131C22⋊Dic43—41no—
132C22⋊Dic43—41no—
133C4⋊Dic43—21no—
134C4⋊Dic43—21no—
135C4⋊Dic43—48no—
136C4⋊Dic43—82no—
137Dic43⋊C4—41no—
138Dic43⋊C4—41no—
139Dic43⋊C4—41no—
140Dic43⋊C4—41no—
141Dic43⋊C4—41no—
142Dic43⋊C4—41no—
143C2×C43⋊C8—42no—
144C2×C43⋊C8—41no—
145Dic172—48no—
146C23×C43—22no—
147C23×C43—22no—
148C23×C43#12011yescharacteristic
149C23×C43#12011yescharacteristic
150C23×C43#12111yescharacteristic
151C23×C43C2×Q1611yescharacteristic
152C23×C43#13511yescharacteristic
153C23×C43#13711yescharacteristic
154C23×C43#13711yescharacteristic
155C2×C4×C43—22no—
156C2×C4×C43—22no—
157C2×C4×C43—24no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—42no—
163C2×C4×C43—44no—
164C2×C4×C43—44no—
165C2×C4×C43—42no—
166C2×C4×C43—42no—
167C2×C4×C43—42no—
168C2×C4×C43—42no—
169C2×C4×C43#12011yescharacteristic
170C2×C4×C43#12111yescharacteristic
171C2×C4×C43#12111yescharacteristic
172C2×C4×C43#12711yescharacteristic
173C2×Dic43—24no—
174C2×Dic43—22no—
175C2×Dic43—22no—
176C2×Dic43—22no—
177C2×Dic43—42no—
178C2×Dic43—44no—
179C2×Dic43—41no—
180C2×Dic43—42no—
181C2×Dic43—41no—
182C2×Dic43—41no—
183C2×Dic43—44no—
184C2×Dic43—41no—
185C2×Dic43—42no—
186C2×Dic43—41no—
187C2×Dic43—41no—
188C2×Dic43—41no—
189C2×Dic43—42no—
190C2×Dic43—42no—
191C2×Dic43—42no—
192C2×Dic43—81no—
193Dic86—24no—
194Dic86—24no—
195Dic86—44no—
196Dic86—42no—
197Dic86—42no—
198Dic86—44no—
199Dic86—42no—
200Dic86—81no—
201C8×C43—42no—
202C43⋊C8—81no—
203#9925—431nomaximal, Sylow
204C22×C43—22no—
205C22×C43—22no—
206C22×C43—22no—
207C22×C43—22no—
208C22×C43—21no—
209C22×C43—21no—
210C22×C43—21no—
211C22×C43—21no—
212C22×C43#39211yescharacteristic
213C22×C43#45111yescharacteristic
214C22×C43#45111yescharacteristic
215C22×C43#45211yescharacteristic
216C22×C43#45211yescharacteristic
217C22×C43#45612yes—
218C22×C43B(4,𝔽2)12yes—
219C22×C43#46711yescharacteristic
220C22×C43#47011yescharacteristic
221C4×C43—21no—
222C4×C43—21no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—44no—
226C4×C43—82no—
227Dic43—42no—
228Dic43—44no—
229Dic43—81no—
230Dic43—81no—
231Dic43—81no—
232C2×#451—431no—
233#2627—431no—
234C2×#395—431no—
235#1787—431no—
236C2×#328—431no—
237C2×#324—431no—
238#1294D4311yescharacteristic
239C2×C43—21no—
240C2×C43—21no—
241C2×C43—21no—
242C2×C43—21no—
243C2×C43#160312yes—
244C2×C43#160512yes—
245C2×C43#200111yescharacteristic
246C2×C43#200511yescharacteristic
247C2×C43#202111yescharacteristic
248C23×Q8—431no—
249C22×Q16—861no—
250C2×C22⋊Q8—431no—
251C22×C4⋊C4—431no—
252C22×C4⋊C4—861no—
253#451—862no—
254#451—862no—
255C2×#103—861no—
256C2×#103—862no—
257C2×C22⋊C8—431no—
258C2×C22⋊C8C2×D4311yescharacteristic
259#400—861no—
260#398—862no—
261#395—861no—
262#395—862no—
263#395—862no—
264#385—861no—
265#381—861no—
266#380C2×D4311yescharacteristic
267C2×#95—861no—
268C2×#95C2×D4311yescharacteristic
269#328—862no—
270#324—862no—
271C43#992511yescharacteristic, complemented, Sylow
272C22×Q8—431no—
273C22×Q8—432no—
274C22×Q8—861no—
275C22×Q8—861no—
276C22×Q8—861no—
277C22×Q8—861no—
278C22×Q8—861no—
279C22×Q8—1724no—
280C23×C4—21no—
281C23×C4—431no—
282C23×C4—431no—
283C23×C4—861no—
284C23×C4C22×D4311yescharacteristic
285C2×Q16—864no—
286C2×Q16—1724no—
287C22×C8—21no—
288C22×C8—861no—
289C22⋊Q8—861no—
290C22⋊Q8—861no—
291C22⋊Q8—861no—
292C22⋊Q8—861no—
293C2×C4⋊C4—431no—
294C2×C4⋊C4—862no—
295C2×C4⋊C4—864no—
296C2×C4⋊C4—861no—
297C2×C4⋊C4—861no—
298C2×C4⋊C4—861no—
299C2×C4⋊C4—861no—
300C2×C4⋊C4—861no—
301C2×C4⋊C4—861no—
302C2×C4⋊C4—861no—
303C2×C4⋊C4—1724no—
304C2×C4⋊C4D17212yes—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—861no—
307#103—864no—
308#103—1724no—
309C22⋊C8—21no—
310C22⋊C8—861no—
311C22⋊C8—861no—
312C22⋊C8D17212yes—
313#95—21no—
314#95—21no—
315#95—864no—
316#95—862no—
317#95—862no—
318#95—862no—
319#95D17212yes—
320C24D4×D4311yescharacteristic
321C2×Q8—864no—
322C2×Q8—864no—
323C2×Q8—862no—
324C2×Q8—861no—
325C2×Q8—862no—
326C2×Q8—861no—
327C2×Q8—1722no—
328C2×Q8—1722no—
329C2×Q8—1722no—
330C2×Q8—1724no—
331C2×Q8—1724no—
332C2×Q8—1724no—
333C2×Q8—1724no—
334C2×Q8—1721no—
335C2×Q8—1721no—
336C22×C4—24no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—432no—
344C22×C4—864no—
345C22×C4—861no—
346C22×C4—862no—
347C22×C4—861no—
348C22×C4—861no—
349C22×C4—861no—
350C22×C4—861no—
351C22×C4—861no—
352C22×C4—861no—
353C22×C4—861no—
354C22×C4—861no—
355C22×C4—861no—
356C22×C4—861no—
357C22×C4—1722no—
358C22×C4—1722no—
359C22×C4—1721no—
360C22×C4—1721no—
361C22×C4C2×D17211yescharacteristic
362C22×C4C2×D17211yescharacteristic
363C22×C4C2×D17211yescharacteristic
364C22×C4D4×D4311yescharacteristic
365C22×C4D4×D4311yescharacteristic
366C22×C4#1062190211yescharacteristic
367Q16—1728no—
368C2×C8—22no—
369C2×C8—42no—
370C2×C8—1722no—
371C2×C8—1721no—
372C4⋊C4—42no—
373C4⋊C4—861no—
374C4⋊C4—861no—
375C4⋊C4—3442no—
376C4⋊C4—1728no—
377C4⋊C4—1721no—
378C4⋊C4—1721no—
379C4⋊C4—1721no—
380C4⋊C4—1721no—
381C4⋊C4—1721no—
382C4⋊C4—1721no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—1721no—
386C22⋊C4—1721no—
387C23—22no—
388C23—22no—
389C23#1306329511yescharacteristic
390C23#1306329511yescharacteristic
391C23#1306330011yescharacteristic
392C23Q16×D4311yescharacteristic
393C23#1306334411yescharacteristic
394C23#1306335411yescharacteristic
395C23#1306335411yescharacteristic
396Q8—864no—
397Q8—864no—
398Q8—3441no—
399Q8—1722no—
400Q8—1722no—
401Q8—1724no—
402Q8—1722no—
403Q8—1724no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—24no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—864no—
419C2×C4—862no—
420C2×C4—862no—
421C2×C4—862no—
422C2×C4—3441no—
423C2×C4—1722no—
424C2×C4—1721no—
425C2×C4—1721no—
426C2×C4—1721no—
427C2×C4—1722no—
428C2×C4—1722no—
429C2×C4—1722no—
430C2×C4—1722no—
431C2×C4—1724no—
432C2×C4—1721no—
433C2×C4—1721no—
434C2×C4—1721no—
435C2×C4—1722no—
436C2×C4—1724no—
437C2×C4—1721no—
438C2×C4#1306329511yescharacteristic
439C2×C4#1306330011yescharacteristic
440C2×C4#1306330011yescharacteristic
441C2×C4#1306332211yescharacteristic
442C8—42no—
443C8—3441no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22#1458280911yescharacteristic
453C22#1458305611yescharacteristic
454C22#1458305611yescharacteristic
455C22#1458306211yescharacteristic
456C22#1458306211yescharacteristic
457C22#1458308312yes—
458C22#1458308712yes—
459C22#1458314111yescharacteristic
460C22#1458315811yescharacteristic
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—44no—
466C4—82no—
467C4—3441no—
468C4—3441no—
469C4—3441no—
470C4—1722no—
471C4—1724no—
472C2—21no—
473C2—21no—
474C2—21no—
475C2—21no—
476C2#1913355912yes—
477C2#1913357012yes—
478C2#1913560611yescharacteristic
479C2#1913563411yescharacteristic
480C2#1913572211yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1294C2
socleC23×C43#120
prime radicalC24×C43C2×D4
hypercenter#1294D43
hypocenterC43#9925
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
110. C22×Dic43Q16semidirect
271. C43#9925semidirect

Maximal subgroups

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

subgroupindex
C2×#145830572
#191404112
C2×#145828202
#191345292
C2×#145826352
C2×#145826242
C43×#12942
#992543