Finite Group Databasebeta

← #24996926

Subgroups — #24996926

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#19145397C211yesmaximal, characteristic
2#19144535C211yesmaximal, characteristic
3#19135430C211yesmaximal, characteristic
4#19134694C211yesmaximal, characteristic, complemented
5#19133115C211yesmaximal, characteristic, complemented
6#19132501C211yesmaximal, characteristic, complemented
7C43×#2625C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9#14583232—21no—
10#14583223—22no—
11#14583217—21no—
12#14583212—21no—
13#14583212—21no—
14#14583147—22no—
15#14583049—21no—
16#14583038—21no—
17#14582942—21no—
18#14582903—21no—
19C2×#13063239—22no—
20#14582863C2211yescharacteristic
21#14582863C2211yescharacteristic
22C4×C22⋊Dic43C2211yescharacteristic
23#14582658—22no—
24#14582636—22no—
25C2×C22⋊Q8×C43C2211yescharacteristic
26C2×#117×C43C2211yescharacteristic
27C43×#400—21no—
28C43×#398—21no—
29C43×#397—22no—
30C43×#391—21no—
31C43×#389—21no—
32C43×#380C2211yescharacteristic
33C22×D172D411yescharacteristic
34C22×C22⋊D43—21no—
35C2×#10621884—22no—
36C2×#10621877—21no—
37C2×#10621877D412yes—
38#13063299—21no—
39#13063299—21no—
40#13063299—21no—
41#13063299—21no—
42C2×C4⋊Dic43D411yescharacteristic
43C2×C22⋊Dic43—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×C4×Dic43—21no—
46#13063258—22no—
47#13063258—22no—
48#13063256—22no—
49#13063249—22no—
50#13063245—22no—
51#13063245—22no—
52#13063245—22no—
53#13063239—44no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)D412yes—
58C43⋊#95—21no—
59C22×Q8×C43D411yescharacteristic
60C23×C4×C43C2311yescharacteristic
61C22⋊Q8×C43—21no—
62C22⋊Q8×C43—21no—
63C22⋊Q8×C43—21no—
64C22⋊Q8×C43—21no—
65#117×C43—21no—
66#117×C43—21no—
67#117×C43—21no—
68#117×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—22no—
72C2×C4⋊C4×C43D411yescharacteristic
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C4⋊C4×C43D411yescharacteristic
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—21no—
77C2×C22⋊C4×C43D412yes—
78C2×C42×C43—21no—
79#95×C43—22no—
80#95×C43—22no—
81#95×C43—22no—
82#95×C43—21no—
83C24×C43C2×D411yescharacteristic
84C23×D43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43—21no—
87C2×Q8×C43—42no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—22no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—42no—
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43#4111yescharacteristic
100C2×C22⋊D43—42no—
101C2×C22⋊D43—42no—
102C2×C22⋊D43—41no—
103C2×C22⋊D43—41no—
104C22×Dic43—21no—
105C22×Dic43—41no—
106C2×D172—21no—
107C2×D172—21no—
108C2×D172—42no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—42no—
116C4⋊C4×C43—41no—
117C4⋊C4×C43—41no—
118C4⋊C4×C43—82no—
119C22⋊C4×C43—42no—
120C22⋊C4×C43—41no—
121C22⋊C4×C43—41no—
122C22⋊C4×C43—41no—
123C22⋊C4×C43—41no—
124C42×C43—41no—
125C42×C43—41no—
126C22⋊Dic43—22no—
127C22⋊Dic43—41no—
128#10621884—82no—
129(C2×D43)⋊C4—41no—
130(C2×D43)⋊C4—41no—
131C4⋊Dic43—21no—
132C4⋊Dic43—21no—
133C4×Dic43—42no—
134#10621877—42no—
135#10621877—42no—
136C2×C43⋊C8—22no—
137C2×C43⋊C8—22no—
138C23×C43—21no—
139C23×C43—21no—
140C23×C43—41no—
141C23×C43—41no—
142C23×C43#12011yescharacteristic
143C23×C43#12111yescharacteristic
144C23×C43#12711yescharacteristic
145C22×D43—41no—
146C22×D43—42no—
147C22×D43—81no—
148C22×D43—81no—
149Q8×C43—42no—
150Q8×C43—81no—
151C2×C4×C43—22no—
152C2×C4×C43—22no—
153C2×C4×C43—22no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—42no—
158C2×C4×C43—42no—
159C2×C4×C43—42no—
160C2×C4×C43—42no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—42no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43#12011yescharacteristic
171C2×C4×C43#12011yescharacteristic
172C2×C4×C43#12111yescharacteristic
173C2×C4×C43#12111yescharacteristic
174C22⋊D43—82no—
175C22⋊D43—81no—
176C22⋊D43—81no—
177C2×Dic43—42no—
178C2×Dic43—42no—
179C2×Dic43—41no—
180C2×Dic43—81no—
181C2×Dic43—81no—
182D172—42no—
183D172—42no—
184C43⋊C8—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#39211yescharacteristic
198C22×C43#45311yescharacteristic
199C22×C43#45411yescharacteristic
200C2×D43—81no—
201C2×D43—81no—
202C2×D43—81no—
203C2×D43—162no—
204C4×C43—21no—
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—82no—
208C4×C43—81no—
209C4×C43—81no—
210C4×C43—81no—
211C4×C43—81no—
212C4×C43#45812yes—
213Dic43—82no—
214Dic43—81no—
215#3193—431no—
216#3094—431no—
217#2625D4311yescharacteristic, complemented
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#200611yescharacteristic
227C2×C43#200911yescharacteristic
228C2×C43#202211yescharacteristic
229D43—161no—
230C2×C22⋊Q8C2×D4311yescharacteristic
231C2×#121—431no—
232C2×#117C2×D4311yescharacteristic
233#484—861no—
234#482—862no—
235#481—861no—
236#480—861no—
237#480—861no—
238#468—862no—
239#450—861no—
240#448—861no—
241#428—861no—
242#418—861no—
243C2×#99—862no—
244#407—431no—
245#407—431no—
246#400—21no—
247#398—21no—
248#397—22no—
249#391—21no—
250#389—21no—
251#380C2×D4311yescharacteristic
252C4×C22⋊C4—431no—
253#339—862no—
254#328—862no—
255C43#993311yescharacteristic, complemented, Sylow
256C22×Q8C22⋊D4311yescharacteristic
257C22×D4—431no—
258C22×D4—861no—
259C23×C4C22×D4311yescharacteristic
260C2×SD16—862no—
261C2×M16—432no—
262C2×M16—861no—
263C22⋊Q8—21no—
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267#121—861no—
268#121—861no—
269#121—861no—
270#121—861no—
271#117—21no—
272#117—21no—
273#117—21no—
274#117—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—431no—
279C2×C4⋊C4C22⋊D4311yescharacteristic
280C2×C4⋊C4C22⋊D4311yescharacteristic
281C2×C4⋊C4C22⋊D4311yescharacteristic
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—861no—
285C2×C22⋊C4—861no—
286C2×C22⋊C4C22⋊D4312yes—
287C2×C42—21no—
288C2×C42—861no—
289#107—862no—
290#107—862no—
291#106—862no—
292#103—862no—
293#102—862no—
294#102—862no—
295#102—862no—
296#99—1724no—
297C22⋊C8—432no—
298C22⋊C8—861no—
299C22⋊C8—861no—
300C22⋊C8—861no—
301#95—22no—
302#95—22no—
303#95—22no—
304#95—21no—
305#95—861no—
306C24—861no—
307C24C2×C22⋊D4311yescharacteristic
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—42no—
311C2×D4—861no—
312C2×D4—861no—
313C2×D4—1722no—
314C2×D4—1722no—
315C2×D4—1722no—
316C2×D4—1721no—
317C2×D4—1721no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—22no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—42no—
324C22×C4—861no—
325C22×C4—1721no—
326C22×C4D4×D4311yescharacteristic
327C22×C4D4×D4311yescharacteristic
328C22×C4D4×D4311yescharacteristic
329C22×C4#1062190011yescharacteristic
330C22×C4C2×C22⋊D4311yescharacteristic
331C22×C4C2×C22⋊D4311yescharacteristic
332SD16—3442no—
333M16—1722no—
334M16—1722no—
335C2×C8—862no—
336C2×C8—862no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—42no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—82no—
347C4⋊C4—861no—
348C4⋊C4—861no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—42no—
354C22⋊C4—862no—
355C22⋊C4—1721no—
356C22⋊C4—1721no—
357C22⋊C4—1721no—
358C42—41no—
359C42—41no—
360C42—1722no—
361C23—21no—
362C23—21no—
363C23—41no—
364C23—41no—
365C23—3441no—
366C23—3441no—
367C23—1722no—
368C23—1721no—
369C23#1306329411yescharacteristic
370C23#1306329611yescharacteristic
371C23#1306332111yescharacteristic
372Q8—42no—
373Q8—81no—
374D4—3442no—
375D4—3441no—
376D4—3441no—
377D4—1722no—
378D4—1722no—
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—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—3441no—
399C2×C4—3441no—
400C2×C4—1722no—
401C2×C4—1722no—
402C2×C4—1721no—
403C2×C4#1306329311yescharacteristic
404C2×C4#1306329311yescharacteristic
405C2×C4#1306329711yescharacteristic
406C2×C4#1306329711yescharacteristic
407C8—1722no—
408C8—1722no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—81no—
418C22—81no—
419C22—3441no—
420C22—3441no—
421C22—3441no—
422C22—6882no—
423C22#1458280711yescharacteristic
424C22#1458306711yescharacteristic
425C22#1458307211yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—82no—
430C4—81no—
431C4—81no—
432C4—81no—
433C4—81no—
434C4—3442no—
435C4—3441no—
436C4#1458308812yes—
437C2—21no—
438C2—21no—
439C2—41no—
440C2—41no—
441C2—6881no—
442C2#1913563711yescharacteristic
443C2#1913565511yescharacteristic
444C2#1913572311yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#2625C2
socleC22×C43#392
prime radicalC2×#13063299C22
hypercenter#2625D43
hypocenterC43#9933
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2625

Complements

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

NH ≅ G/Ntype
4. #19134694C2semidirect
5. #19133115C2semidirect
6. #19132501C2semidirect
7. C43×#2625C2semidirect
217. #2625D43semidirect
255. C43#9933semidirect

Maximal subgroups

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

subgroupindex
#191453972
#191445352
#191354302
#191346942
#191331152
#191325012
C43×#26252
#993343