Finite Group Databasebeta

← #24997360

Subgroups — #24997360

Order 11008.

568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 101 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#19144599C211yesmaximal, characteristic
2#19139500C211yesmaximal, characteristic
3#19133159C211yesmaximal, characteristic, complemented
4#19133019C211yesmaximal, characteristic
5#19132990C211yesmaximal, characteristic, complemented
6#19132455C211yesmaximal, characteristic, complemented
7C43×#3078C211yesmaximal, characteristic, complemented
8C2×#13063301—21no—
9C2×C4×D172C2211yescharacteristic
10#14583227—21no—
11#14583186—21no—
12#14583101—21no—
13#14583049—21no—
14C4×#10621884—22no—
15#14582952C2211yescharacteristic
16#14582952C2211yescharacteristic
17#14582829—21no—
18#14582816—21no—
19#14582790—22no—
20#14582765C2211yescharacteristic
21#14582756—21no—
22#14582636—22no—
23Q8⋊(C43⋊C8)—22no—
24#14582626—22no—
25C43×#533C2211yescharacteristic
26C2×C4×Q8×C43C2211yescharacteristic
27C43×#479—22no—
28C43×#477—21no—
29C43×#475—21no—
30C43×#428—21no—
31C43×#423C2211yescharacteristic
32C43×#419—21no—
33C22×D172D411yescharacteristic
34C22×C4×D43—21no—
35C2×#10621884—22no—
36#13063301—42no—
37#13063301—42no—
38C4×D172—21no—
39C4×D172—21no—
40C4×D172—21no—
41C4×D172—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43D411yescharacteristic
44C2×Dic43⋊C4—22no—
45C2×(C2×D43)⋊C4—22no—
46C2×(C2×D43)⋊C4—22no—
47C2×(C2×D43)⋊C4—21no—
48#13063256—22no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)—21no—
51#13063249—22no—
52#13063245—22no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)—21no—
55C4×C43⋊C8—21no—
56C4×C43⋊C8D412yes—
57C43⋊#95—22no—
58C43⋊#95—21no—
59C43⋊#95D412yes—
60C22×Q8×C43D411yescharacteristic
61C2×M16×C43—21no—
62C4⋊Q8×C43D411yescharacteristic
63C4⋊Q8×C43D411yescharacteristic
64#125×C43—21no—
65C22⋊Q8×C43—21no—
66C22⋊Q8×C43—21no—
67C4×Q8×C43—21no—
68C4×Q8×C43—21no—
69C4×Q8×C43—21no—
70C4×Q8×C43—21no—
71C4×Q8×C43—21no—
72C4×Q8×C43—21no—
73#117×C43—21no—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43D411yescharacteristic
76C2×C42×C43—21no—
77C2×C42×C43C2311yescharacteristic
78#107×C43—22no—
79#106×C43—22no—
80C4⋊C8×C43—21no—
81C4⋊C8×C43D412yes—
82#103×C43—22no—
83#103×C43—22no—
84C23×D43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43—21no—
87C2×Q8×C43—21no—
88C2×Q8×C43—21no—
89C2×Q8×C43—21no—
90C2×Q8×C43—21no—
91C2×Q8×C43—21no—
92C2×Q8×C43SD1612yescomplemented
93C22×C4×C43—21no—
94C22×C4×C43—21no—
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×Dic43—22no—
99C22×Dic43—21no—
100C2×D172—21no—
101C2×D172—21no—
102C2×D172—42no—
103C2×C4×D43—41no—
104C2×C4×D43—41no—
105C2×C4×D43—41no—
106C2×C4×D43—41no—
107C2×C4×D43—41no—
108C2×C4×D43—41no—
109M16×C43—41no—
110M16×C43—41no—
111C2×C8×C43—22no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—21no—
116C4⋊C4×C43—21no—
117C4⋊C4×C43—21no—
118C4⋊C4×C43—41no—
119C4⋊C4×C43—41no—
120C4⋊C4×C43—41no—
121C4⋊C4×C43—41no—
122C22⋊C4×C43—41no—
123C42×C43—41no—
124C42×C43—41no—
125C42×C43—41no—
126C42×C43C2×D411yescharacteristic
127C42×C43C2×D411yescharacteristic
128C42×C43C2×D411yescharacteristic
129C42×C43#4111yescharacteristic
130#10621884—44no—
131(C2×D43)⋊C4—44no—
132(C2×D43)⋊C4—44no—
133(C2×D43)⋊C4—41no—
134(C2×D43)⋊C4—41no—
135C4⋊Dic43—21no—
136C4⋊Dic43—21no—
137C4⋊Dic43—41no—
138C4⋊Dic43—41no—
139Dic43⋊C4—44no—
140C2×C43⋊C8—22no—
141C2×C43⋊C8—41no—
142C23×C43#12011yescharacteristic
143C22×D43—22no—
144C22×D43—41no—
145C22×D43—41no—
146C22×D43—41no—
147C22×D43—41no—
148C22×D43—41no—
149C22×D43—41no—
150Q8×C43—22no—
151Q8×C43—22no—
152Q8×C43—42no—
153Q8×C43—41no—
154Q8×C43—41no—
155Q8×C43—81no—
156C2×C4×C43—22no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—42no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43#12011yescharacteristic
166C2×C4×C43#12011yescharacteristic
167C2×C4×C43#12111yescharacteristic
168C2×C4×C43#12111yescharacteristic
169C2×C4×C43#12111yescharacteristic
170C2×C4×C43#12711yescharacteristic
171C2×C4×C43C2×SD1611yescharacteristic
172C2×C4×C43#13511yescharacteristic
173C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C43#13711yescharacteristic
175C2×Dic43—42no—
176C2×Dic43—42no—
177C2×Dic43—41no—
178C2×Dic43—41no—
179C2×Dic43—42no—
180C2×Dic43—41no—
181D172—22no—
182D172—22no—
183D172—41no—
184D172—41no—
185C4×D43—81no—
186C4×D43—81no—
187C4×D43—81no—
188C4×D43—81no—
189C8×C43—42no—
190C43⋊C8—42no—
191C43⋊C8—81no—
192#10001—431nomaximal, Sylow
193C22×C43—21no—
194C22×C43—21no—
195C22×C43#39211yescharacteristic
196C22×C43#45011yescharacteristic
197C22×C43#45211yescharacteristic
198C2×D43—42no—
199C2×D43—42no—
200C2×D43—42no—
201C2×D43—81no—
202C2×D43—81no—
203C2×D43—81no—
204C2×D43—81no—
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—42no—
210C4×C43—81no—
211C4×C43—81no—
212C4×C43—81no—
213C4×C43#44811yescharacteristic
214C4×C43#44911yescharacteristic
215C4×C43#46511yescharacteristic
216C4×C43#46811yescharacteristic
217Dic43—82no—
218Dic43—81no—
219#3101—431no—
220#3078D4311yescharacteristic, complemented
221#2536—431no—
222#1518—431no—
223#1486—431no—
224#1479—431no—
225#1286—431no—
226C2×C43—21no—
227C2×C43—21no—
228C2×C43#200011yescharacteristic
229C2×C43#200911yescharacteristic
230C2×C43#201011yescharacteristic
231D43—82no—
232#533C2×D4311yescharacteristic
233C2×C22⋊Q8—861no—
234C2×C4×Q8C2×D4311yescharacteristic
235C2×C4×D4—431no—
236#483—861no—
237#479—22no—
238#477—21no—
239#476—861no—
240#475—21no—
241#461—861no—
242#450—861no—
243C4×SD16—862no—
244#431—431no—
245#431—431no—
246#428—21no—
247#423C2×D4311yescharacteristic
248#419—21no—
249#398—861no—
250#394—861no—
251#388—862no—
252#382—431no—
253#380—861no—
254#328—862no—
255Q8⋊C8—862no—
256D4⋊C8—862no—
257C43#1000111yescharacteristic, complemented, Sylow
258C22×Q8C22⋊D4311yescharacteristic
259C22×D4—431no—
260C23×C4—861no—
261C2×SD16—862no—
262C2×M16—21no—
263C4⋊Q8C22⋊D4311yescharacteristic
264C4⋊Q8C22⋊D4311yescharacteristic
265#125—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268C22⋊Q8—1722no—
269C22⋊Q8—1722no—
270C4×Q8—21no—
271C4×Q8—21no—
272C4×Q8—21no—
273C4×Q8—21no—
274C4×Q8—21no—
275C4×Q8—21no—
276C4×D4—861no—
277C4×D4—861no—
278C4×D4—861no—
279C4×D4—861no—
280#117—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—431no—
283C2×C4⋊C4—862no—
284C2×C4⋊C4—861no—
285C2×C4⋊C4C22⋊D4311yescharacteristic
286C2×C22⋊C4—862no—
287C2×C22⋊C4—862no—
288C2×C22⋊C4—861no—
289C2×C42—21no—
290C2×C42C22×D4311yescharacteristic
291#107—22no—
292#106—22no—
293#106—862no—
294C4⋊C8—21no—
295C4⋊C8—861no—
296C4⋊C8—861no—
297C4⋊C8C22⋊D4312yes—
298#103—22no—
299#103—22no—
300#103—862no—
301#102—862no—
302C22⋊C8—861no—
303C22⋊C8—861no—
304C4×C8—432no—
305C4×C8—861no—
306#95—432no—
307#95—862no—
308#95—861no—
309C24—861no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8#1062188412yescomplemented
318C2×D4—861no—
319C2×D4—861no—
320C2×D4—1722no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—862no—
324C22×C4—861no—
325C22×C4—1721no—
326C22×C4—1721no—
327C22×C4—1721no—
328C22×C4—1721no—
329C22×C4—1721no—
330C22×C4—1721no—
331C22×C4D4×D4311yescharacteristic
332C22×C4D4×D4311yescharacteristic
333C22×C4C2×C22⋊D4311yescharacteristic
334SD16—1724no—
335M16—41no—
336M16—41no—
337C2×C8—22no—
338C2×C8—862no—
339C2×C8—1721no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—861no—
351C4⋊C4—861no—
352C4⋊C4—1724no—
353C4⋊C4—1721no—
354C4⋊C4—1721no—
355C22⋊C4—41no—
356C22⋊C4—1724no—
357C22⋊C4—1724no—
358C22⋊C4—1721no—
359C22⋊C4—1721no—
360C42—41no—
361C42—41no—
362C42—41no—
363C42D4×D4311yescharacteristic
364C42#1062190011yescharacteristic
365C42C2×C22⋊D4311yescharacteristic
366C42C2×C22⋊D4311yescharacteristic
367C23—862no—
368C23—1721no—
369C23—1721no—
370C23—1721no—
371C23—1721no—
372C23—1721no—
373C23—1721no—
374C23#1306329311yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—42no—
378Q8—41no—
379Q8—41no—
380Q8—81no—
381D4—862no—
382D4—862no—
383D4—1721no—
384D4—1721no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—3441no—
395C2×C4—3441no—
396C2×C4—3441no—
397C2×C4—3441no—
398C2×C4—1722no—
399C2×C4—1722no—
400C2×C4—1722no—
401C2×C4—1721no—
402C2×C4—1721no—
403C2×C4—1721no—
404C2×C4#1306329311yescharacteristic
405C2×C4#1306329411yescharacteristic
406C2×C4#1306329611yescharacteristic
407C2×C4#1306329711yescharacteristic
408C2×C4#1306329711yescharacteristic
409C2×C4#1306332111yescharacteristic
410C2×C4C2×#1062188411yescharacteristic
411C2×C4#1306334511yescharacteristic
412C2×C4#1306335011yescharacteristic
413C2×C4#1306335611yescharacteristic
414C8—42no—
415C8—3441no—
416C8—1722no—
417C22—21no—
418C22—21no—
419C22—3441no—
420C22—3441no—
421C22—3441no—
422C22—3441no—
423C22—1722no—
424C22—1722no—
425C22—1722no—
426C22#1458280711yescharacteristic
427C22#1458304911yescharacteristic
428C22#1458305911yescharacteristic
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—42no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4—3442no—
438C4—3441no—
439C4#1458303811yescharacteristic
440C4#1458304411yescharacteristic
441C4#1458313011yescharacteristic
442C4#1458314711yescharacteristic
443C2—21no—
444C2—21no—
445C2—3442no—
446C2#1913559611yescharacteristic
447C2#1913565311yescharacteristic
448C2#1913565911yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3078C2
socleC22×C43#392
prime radicalC22×D172D4
hypercenter#3078D43
hypocenterC43#10001
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
3. #19133159C2semidirect
5. #19132990C2semidirect
6. #19132455C2semidirect
7. C43×#3078C2semidirect
92. C2×Q8×C43SD16semidirect
220. #3078D43semidirect
257. C43#10001semidirect
317. C2×Q8#10621884semidirect

Maximal subgroups

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

subgroupindex
#191445992
#191395002
#191331592
#191330192
#191329902
#191324552
C43×#30782
#1000143