Finite Group Databasebeta

← #24996924

Subgroups — #24996924

Order 11008.

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

normal subgroups only

This group has 568 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#19144531C211yesmaximal, characteristic
2#19140393C211yesmaximal, characteristic, complemented
3#19135432C211yesmaximal, characteristic
4#19134692C211yesmaximal, characteristic, complemented
5#19133115C211yesmaximal, characteristic, complemented
6#19132500C211yesmaximal, characteristic, complemented
7C43×#3193C211yesmaximal, characteristic
8C2×#13063284C2211yescharacteristic
9#14583220—22no—
10#14583215—21no—
11#14583210—21no—
12#14582939—21no—
13#14582904—21no—
14C2×#13063240—22no—
15#14582863C2211yescharacteristic
16#14582838—21no—
17#14582829—21no—
18#14582827—22no—
19#14582806—21no—
20#14582795—21no—
21#14582759C2211yescharacteristic
22C4×C22⋊Dic43C2211yescharacteristic
23#14582660—22no—
24#14582636—22no—
25C2×C22⋊Q8×C43C2211yescharacteristic
26C2×#121×C43C2211yescharacteristic
27C43×#484—21no—
28C43×#480—21no—
29C43×#468—22no—
30C43×#450—21no—
31C43×#448—21no—
32C43×#407C2211yescharacteristic
33C2×#10621877—21no—
34#13063284—21no—
35#13063284—21no—
36#13063284—21no—
37#13063284—21no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43D411yescharacteristic
40C2×C4⋊Dic43D411yescharacteristic
41C2×Dic43⋊C4—22no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43D412yes—
45C2×C4×Dic43—21no—
46C2×C4×Dic43—21no—
47#13063258—22no—
48#13063256—22no—
49#13063246—22no—
50#13063246—22no—
51#13063240—44no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)D412yes—
54C43⋊#95—22no—
55C43⋊#95—22no—
56C43⋊#95—22no—
57C43⋊#95—21no—
58C43⋊#95—21no—
59C22×Q8×C43D411yescharacteristic
60C22×D4×C43—21no—
61C22×D4×C43D411yescharacteristic
62C23×C4×C43C2311yescharacteristic
63C2×SD16×C43—22no—
64C2×M16×C43D412yes—
65C22⋊Q8×C43—21no—
66C22⋊Q8×C43—21no—
67C22⋊Q8×C43—21no—
68C22⋊Q8×C43—21no—
69#121×C43—21no—
70#121×C43—21no—
71#121×C43—21no—
72#121×C43—21no—
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43D411yescharacteristic
75C2×C4⋊C4×C43D411yescharacteristic
76C2×C22⋊C4×C43—21no—
77C2×C22⋊C4×C43—21no—
78#107×C43—22no—
79#103×C43—22no—
80#102×C43—22no—
81C22⋊C8×C43—21no—
82C22⋊C8×C43—21no—
83C24×C43—21no—
84C24×C43C2×D411yescharacteristic
85C2×Q8×C43—21no—
86C2×Q8×C43—21no—
87C2×Q8×C43—42no—
88C2×D4×C43—21no—
89C2×D4×C43—21no—
90C2×D4×C43—42no—
91C2×D4×C43—42no—
92C2×D4×C43—41no—
93C2×D4×C43—41no—
94C2×D4×C43—42no—
95C22×C4×C43—21no—
96C22×C4×C43—21no—
97C22×C4×C43—21no—
98C22×C4×C43—42no—
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43#4111yescharacteristic
105C22×Dic43—21no—
106C22×Dic43—22no—
107C22×Dic43—21no—
108C22×Dic43—41no—
109SD16×C43—82no—
110M16×C43—42no—
111C2×C8×C43—22no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—21no—
116C4⋊C4×C43—41no—
117C4⋊C4×C43—41no—
118C22⋊C4×C43—41no—
119C22⋊C4×C43—41no—
120C22⋊C4×C43—41no—
121C22⋊C4×C43—41no—
122C22⋊Dic43—22no—
123C22⋊Dic43—42no—
124C22⋊Dic43—41no—
125C22⋊Dic43—41no—
126C22⋊Dic43—41no—
127C4⋊Dic43—21no—
128C4⋊Dic43—21no—
129C4⋊Dic43—21no—
130C4⋊Dic43—21no—
131C4⋊Dic43—42no—
132Dic43⋊C4—82no—
133C4×Dic43—41no—
134C4×Dic43—41no—
135C4×Dic43—42no—
136#10621877—42no—
137C2×C43⋊C8—22no—
138C23×C43—21no—
139C23×C43—21no—
140C23×C43—41no—
141C23×C43—41no—
142C23×C43—42no—
143C23×C43—41no—
144C23×C43—81no—
145C23×C43—81no—
146C23×C43#12011yescharacteristic
147C23×C43#12111yescharacteristic
148C23×C43#12711yescharacteristic
149Q8×C43—42no—
150Q8×C43—81no—
151D4×C43—42no—
152D4×C43—42no—
153D4×C43—82no—
154D4×C43—81no—
155D4×C43—81no—
156C2×C4×C43—22no—
157C2×C4×C43—22no—
158C2×C4×C43—22no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—42no—
163C2×C4×C43—42no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43#12011yescharacteristic
170C2×C4×C43#12011yescharacteristic
171C2×C4×C43#12111yescharacteristic
172C2×C4×C43#12111yescharacteristic
173C2×Dic43—42no—
174C2×Dic43—42no—
175C2×Dic43—42no—
176C2×Dic43—42no—
177C2×Dic43—41no—
178C2×Dic43—41no—
179C2×Dic43—41no—
180C2×Dic43—42no—
181C2×Dic43—41no—
182C2×Dic43—81no—
183C2×Dic43—81no—
184C8×C43—42no—
185C43⋊C8—42no—
186#9933—431nomaximal, Sylow
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—81no—
196C22×C43—81no—
197C22×C43—81no—
198C22×C43—81no—
199C22×C43—81no—
200C22×C43—162no—
201C22×C43#39211yescharacteristic
202C22×C43#45311yescharacteristic
203C22×C43#45411yescharacteristic
204C4×C43—21no—
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—81no—
208C4×C43—81no—
209C4×C43—81no—
210C4×C43#45812yes—
211Dic43—82no—
212Dic43—82no—
213Dic43—81no—
214Dic43—81no—
215#3193D4311yescharacteristic
216#3094—431no—
217#2625—431no—
218#1964—431no—
219#1826—431no—
220#1508—431no—
221#1305—431no—
222C2×C43—21no—
223C2×C43—21no—
224C2×C43—41no—
225C2×C43—41no—
226C2×C43—161no—
227C2×C43#200611yescharacteristic
228C2×C43#200911yescharacteristic
229C2×C43#202211yescharacteristic
230C2×C22⋊Q8C2×D4311yescharacteristic
231C2×#121C2×D4311yescharacteristic
232C2×#117—431no—
233#484—21no—
234#482—862no—
235#481—861no—
236#480—21no—
237#480—861no—
238#468—22no—
239#450—21no—
240#448—21no—
241#428—861no—
242#418—861no—
243C2×#99—862no—
244#407—431no—
245#407C2×D4311yescharacteristic
246#400—861no—
247#398—861no—
248#397—862no—
249#391—861no—
250#389—861no—
251#380—431no—
252C4×C22⋊C4—431no—
253#339—862no—
254#328—862no—
255C43#993311yescharacteristic, complemented, Sylow
256C22×Q8C22⋊D4311yescharacteristic
257C22×D4—21no—
258C22×D4C22⋊D4311yescharacteristic
259C23×C4C22×D4311yescharacteristic
260C2×SD16—22no—
261C2×M16—861no—
262C2×M16C22⋊D4312yes—
263C22⋊Q8—21no—
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267#121—21no—
268#121—21no—
269#121—21no—
270#121—21no—
271#117—861no—
272#117—861no—
273#117—861no—
274#117—861no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—431no—
277C2×C4⋊C4—431no—
278C2×C4⋊C4—862no—
279C2×C4⋊C4—861no—
280C2×C4⋊C4C22⋊D4311yescharacteristic
281C2×C4⋊C4C22⋊D4311yescharacteristic
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—432no—
285C2×C22⋊C4—861no—
286C2×C22⋊C4—861no—
287C2×C42—861no—
288C2×C42—861no—
289#107—22no—
290#107—862no—
291#106—862no—
292#103—22no—
293#102—22no—
294#102—862no—
295#102—862no—
296#99—1724no—
297C22⋊C8—21no—
298C22⋊C8—21no—
299C22⋊C8—432no—
300C22⋊C8—861no—
301#95—862no—
302#95—862no—
303#95—862no—
304#95—861no—
305#95—861no—
306C24—21no—
307C24D4×D4311yescharacteristic
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—42no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—42no—
314C2×D4—42no—
315C2×D4—42no—
316C2×D4—41no—
317C2×D4—41no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—42no—
322C22×C4—861no—
323C22×C4—862no—
324C22×C4—861no—
325C22×C4—1721no—
326C22×C4D4×D4311yescharacteristic
327C22×C4D4×D4311yescharacteristic
328C22×C4#1062190011yescharacteristic
329C22×C4C2×C22⋊D4311yescharacteristic
330C22×C4C2×C22⋊D4311yescharacteristic
331C22×C4C2×C22⋊D4311yescharacteristic
332SD16—82no—
333M16—42no—
334M16—1722no—
335C2×C8—22no—
336C2×C8—862no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—861no—
344C4⋊C4—861no—
345C4⋊C4—861no—
346C4⋊C4—861no—
347C4⋊C4—3442no—
348C4⋊C4—1722no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—862no—
354C22⋊C4—1721no—
355C22⋊C4—1721no—
356C22⋊C4—1721no—
357C22⋊C4—1722no—
358C42—1722no—
359C42—1721no—
360C42—1721no—
361C23—21no—
362C23—21no—
363C23—41no—
364C23—41no—
365C23—42no—
366C23—41no—
367C23—81no—
368C23—81no—
369C23#1306329311yescharacteristic
370C23#1306329711yescharacteristic
371C23#1306332111yescharacteristic
372Q8—42no—
373Q8—81no—
374D4—42no—
375D4—42no—
376D4—82no—
377D4—81no—
378D4—81no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—3441no—
393C2×C4—3441no—
394C2×C4—1722no—
395C2×C4—1722no—
396C2×C4—1722no—
397C2×C4—1722no—
398C2×C4—1721no—
399C2×C4—1721no—
400C2×C4—1722no—
401C2×C4—1721no—
402C2×C4—1721no—
403C2×C4#1306329311yescharacteristic
404C2×C4#1306329411yescharacteristic
405C2×C4#1306329611yescharacteristic
406C2×C4#1306329711yescharacteristic
407C8—42no—
408C8—1722no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—162no—
423C22#1458280711yescharacteristic
424C22#1458306511yescharacteristic
425C22#1458307011yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—81no—
430C4—81no—
431C4—81no—
432C4—3442no—
433C4—3442no—
434C4—3441no—
435C4—3441no—
436C4#1458308912yes—
437C2—21no—
438C2—21no—
439C2—41no—
440C2—41no—
441C2—161no—
442C2#1913563511yescharacteristic
443C2#1913565311yescharacteristic
444C2#1913572411yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#3193C2
socleC22×C43#392
prime radicalC2×#121×C43C22
hypercenter#3193D43
hypocenterC43#9933
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3193

Complements

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

NH ≅ G/Ntype
2. #19140393C2semidirect
4. #19134692C2semidirect
5. #19133115C2semidirect
6. #19132500C2semidirect
255. C43#9933semidirect

Maximal subgroups

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

subgroupindex
#191445312
#191403932
#191354322
#191346922
#191331152
#191325002
C43×#31932
#993343