Finite Group Databasebeta

← #25000994

Subgroups — #25000994

Order 11008.

490 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 99 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#19145367C211yesmaximal, characteristic
2#19135580C211yesmaximal, characteristic
3#19135019C211yesmaximal, characteristic
4#19135016C211yesmaximal, characteristic
5#19134775C211yesmaximal, characteristic
6#19132462C211yesmaximal, characteristic
7C43×#1996C211yesmaximal, characteristic
8C23×C43⋊C8C2211yescharacteristic
9C2×#13063304C2211yescharacteristic
10#14583234—21no—
11#14583232—21no—
12#14583138—21no—
13#14583138—21no—
14#14583055—21no—
15#14583054—21no—
16C2×C4⋊(C43⋊C8)—21no—
17C2×#13063249—21no—
18C2×#13063248—21no—
19C2×C22⋊(C43⋊C8)C2211yescharacteristic
20#14582759C2211yescharacteristic
21#14582665—21no—
22#14582665—21no—
23#14582661—21no—
24#14582661—21no—
25#14582654—21no—
26C2×C22⋊Q8×C43C2211yescharacteristic
27C43×#380C2211yescharacteristic
28C4×C22⋊C4×C43C2211yescharacteristic
29C43×#342—21no—
30C43×#342—21no—
31C22×Dic86D411yescharacteristic
32C2×#10621885—21no—
33C2×#10621885—21no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36C22×C43⋊C8—21no—
37C22×C43⋊C8—42no—
38C22×C43⋊C8D411yescharacteristic
39C22×C43⋊C8D411yescharacteristic
40#13063304—21no—
41#13063304—21no—
42#13063304—21no—
43#13063304—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43D411yescharacteristic
46C2×Dic43⋊C4—21no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43—21no—
49#13063258—21no—
50#13063258—21no—
51C4⋊(C43⋊C8)—42no—
52#13063249—21no—
53#13063249—21no—
54#13063249—42no—
55#13063248—21no—
56#13063248—21no—
57#13063248—42no—
58C22⋊(C43⋊C8)—21no—
59C22⋊(C43⋊C8)—21no—
60C43⋊#95—21no—
61C22×Q8×C43D411yescharacteristic
62C23×C4×C43C2311yescharacteristic
63C22⋊Q8×C43—21no—
64C22⋊Q8×C43—21no—
65C22⋊Q8×C43—21no—
66C22⋊Q8×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43D411yescharacteristic
70C2×C22⋊C4×C43—21no—
71C2×C22⋊C4×C43—21no—
72C2×C22⋊C4×C43D411yescharacteristic
73C2×C22⋊C4×C43D411yescharacteristic
74C2×C42×C43—21no—
75#95×C43—21no—
76#95×C43—21no—
77C24×C43C2×D411yescharacteristic
78C2×Q8×C43—21no—
79C2×Q8×C43—21no—
80C2×Q8×C43—41no—
81C2×Q8×C43—41no—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43#4111yescharacteristic
93C22×C4×C43#4111yescharacteristic
94C22×C4×C43#4111yescharacteristic
95C22×Dic43—21no—
96C22×Dic43—21no—
97C22×Dic43—41no—
98C2×Dic86—21no—
99C2×Dic86—21no—
100C2×Dic86—41no—
101C2×Dic86—41no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C22⋊C4×C43—21no—
109C22⋊C4×C43—21no—
110C22⋊C4×C43—21no—
111C22⋊C4×C43—41no—
112C22⋊C4×C43—41no—
113C22⋊C4×C43—41no—
114C22⋊C4×C43—41no—
115C22⋊C4×C43Q1612yescomplemented
116C42×C43—41no—
117C42×C43—41no—
118C22⋊Dic43—41no—
119C22⋊Dic43—41no—
120C22⋊Dic43—41no—
121C22⋊Dic43—41no—
122#10621885—81no—
123#10621885—81no—
124C4⋊Dic43—21no—
125C4⋊Dic43—21no—
126C4⋊Dic43—41no—
127C4⋊Dic43—41no—
128Dic43⋊C4—41no—
129Dic43⋊C4—41no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8—22no—
133C2×C43⋊C8—21no—
134C2×C43⋊C8—21no—
135C2×C43⋊C8—41no—
136C2×C43⋊C8—41no—
137C2×C43⋊C8—41no—
138C2×C43⋊C8—41no—
139C2×C43⋊C8—41no—
140C2×C43⋊C8—41no—
141C23×C43—41no—
142C23×C43—41no—
143C23×C43#12111yescharacteristic
144C23×C43#12111yescharacteristic
145C23×C43#12111yescharacteristic
146C23×C43C2×Q1611yescharacteristic
147C23×C43#13511yescharacteristic
148C23×C43#13711yescharacteristic
149C23×C43#13711yescharacteristic
150Q8×C43—42no—
151Q8×C43—41no—
152Q8×C43—41no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—21no—
158C2×C4×C43—21no—
159C2×C4×C43—22no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—81no—
171C2×C4×C43—81no—
172C2×C4×C43—81no—
173C2×C4×C43—81no—
174C2×C4×C43—81no—
175C2×C4×C43#12011yescharacteristic
176C2×C4×C43#12311yescharacteristic
177C2×C4×C43#12311yescharacteristic
178C2×C4×C43#12411yescharacteristic
179C2×Dic43—41no—
180C2×Dic43—41no—
181C2×Dic43—81no—
182C2×Dic43—81no—
183C2×Dic43—81no—
184C2×Dic43—81no—
185C2×Dic43—81no—
186Dic86—42no—
187Dic86—41no—
188Dic86—41no—
189C43⋊C8—42no—
190C43⋊C8—41no—
191C43⋊C8—41no—
192#10566—431nomaximal, Sylow
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—41no—
200C22×C43—41no—
201C22×C43—41no—
202C22×C43—41no—
203C22×C43#39411yescharacteristic
204C22×C43#46211yescharacteristic
205C22×C43#46211yescharacteristic
206C22×C43#46411yescharacteristic
207C22×C43#46411yescharacteristic
208C22×C43#46711yescharacteristic
209C22×C43#47011yescharacteristic
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—42no—
214C4×C43—81no—
215C4×C43—81no—
216C4×C43—81no—
217C4×C43—161no—
218C4×C43B(4,𝔽2)11yescharacteristic
219C4×C43#45811yescharacteristic
220Dic43—81no—
221Dic43—81no—
222Dic43—161no—
223#3189—431no—
224#1996—431no—
225#1996D4311yescharacteristic
226#1892—431no—
227#1892—431no—
228#1850—431no—
229#1289—431no—
230C2×C43—21no—
231C2×C43—21no—
232C2×C43—21no—
233C2×C43—21no—
234C2×C43—21no—
235C2×C43—21no—
236C2×C43#204411yescharacteristic
237C2×C43#205311yescharacteristic
238C2×C43#205611yescharacteristic
239C23×C8—431no—
240C2×C22⋊Q8—431no—
241C2×C22⋊Q8C2×D4311yescharacteristic
242#484—861no—
243#484—861no—
244#467—861no—
245#467—861no—
246#451—861no—
247#451—861no—
248C2×C4⋊C8—861no—
249C2×#103—861no—
250C2×#103—861no—
251C2×C22⋊C8—431no—
252#380—431no—
253#380C2×D4311yescharacteristic
254C4×C22⋊C4C2×D4311yescharacteristic
255#342—21no—
256#342—21no—
257#342—861no—
258#342—861no—
259#340—861no—
260#340—861no—
261#336—861no—
262C43#1056611yescharacteristic, complemented, Sylow
263C22×Q8—431no—
264C22×Q8D17211yescharacteristic
265C23×C4C22×D4311yescharacteristic
266C2×Q16—861no—
267C2×Q16—861no—
268C22×C8—431no—
269C22×C8—431no—
270C22×C8—861no—
271C22×C8—861no—
272C22×C8—861no—
273C22×C8—1722no—
274C22⋊Q8—21no—
275C22⋊Q8—21no—
276C22⋊Q8—21no—
277C22⋊Q8—21no—
278C22⋊Q8—861no—
279C22⋊Q8—861no—
280C22⋊Q8—861no—
281C22⋊Q8—861no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—431no—
285C2×C4⋊C4—861no—
286C2×C4⋊C4—861no—
287C2×C4⋊C4D17211yescharacteristic
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—861no—
291C2×C22⋊C4—861no—
292C2×C22⋊C4C22⋊D4311yescharacteristic
293C2×C22⋊C4C22⋊D4311yescharacteristic
294C2×C42—21no—
295#107—861no—
296#107—861no—
297C4⋊C8—1722no—
298#103—861no—
299#103—861no—
300#103—861no—
301#103—861no—
302#103—1722no—
303#103—1722no—
304C22⋊C8—861no—
305C22⋊C8—861no—
306#95—21no—
307#95—21no—
308#95—861no—
309C24C2×C22⋊D4311yescharacteristic
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×Q8—861no—
315C2×Q8—861no—
316C2×Q8—1721no—
317C2×Q8—1721no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—861no—
326C22×C4—861no—
327C22×C4—1721no—
328C22×C4C2×D17211yescharacteristic
329C22×C4#1062189811yescharacteristic
330C22×C4D4×D4311yescharacteristic
331C22×C4D4×D4311yescharacteristic
332C22×C4#1062190011yescharacteristic
333C22×C4#1062190011yescharacteristic
334Q16—3441no—
335Q16—3441no—
336C2×C8—862no—
337C2×C8—862no—
338C2×C8—862no—
339C2×C8—861no—
340C2×C8—861no—
341C2×C8—1721no—
342C2×C8—1721no—
343C2×C8—1721no—
344C2×C8—1721no—
345C2×C8—1721no—
346C2×C8—1721no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—861no—
354C4⋊C4—861no—
355C4⋊C4—1721no—
356C4⋊C4—1721no—
357C4⋊C4—1721no—
358C4⋊C4—1721no—
359C22⋊C4—21no—
360C22⋊C4—21no—
361C22⋊C4—21no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—1721no—
367C22⋊C4—1721no—
368C22⋊C4—1721no—
369C22⋊C4—1721no—
370C22⋊C4#1062188512yescomplemented
371C42—41no—
372C42—41no—
373C23—41no—
374C23—41no—
375C23#1306329611yescharacteristic
376C23#1306329711yescharacteristic
377C23#1306329911yescharacteristic
378C23C2×#1062188511yescharacteristic
379C23#1306334511yescharacteristic
380C23#1306335511yescharacteristic
381C23#1306335611yescharacteristic
382Q8—42no—
383Q8—41no—
384Q8—41no—
385Q8—1722no—
386Q8—1721no—
387Q8—1721no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—22no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4—3441no—
411C2×C4—3441no—
412C2×C4—3441no—
413C2×C4—3441no—
414C2×C4—3441no—
415C2×C4—1721no—
416C2×C4—1721no—
417C2×C4#1306329511yescharacteristic
418C2×C4#1306330711yescharacteristic
419C2×C4#1306330911yescharacteristic
420C2×C4#1306331111yescharacteristic
421C8—1722no—
422C8—1721no—
423C8—1721no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22#1458281511yescharacteristic
435C22#1458310611yescharacteristic
436C22#1458310911yescharacteristic
437C22#1458311811yescharacteristic
438C22#1458312111yescharacteristic
439C22#1458313811yescharacteristic
440C22#1458315511yescharacteristic
441C4—21no—
442C4—21no—
443C4—21no—
444C4—42no—
445C4—81no—
446C4—81no—
447C4—81no—
448C4—161no—
449C4—3441no—
450C4—3441no—
451C4—6881no—
452C4#1458308711yescharacteristic
453C4#1458309011yescharacteristic
454C2—21no—
455C2—21no—
456C2—21no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2#1913584511yescharacteristic
461C2#1913590011yescharacteristic
462C2#1913591711yescharacteristic
subgroupG/H
centerC22#14582815
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1996C2
socleC22×C43#394
prime radicalC24×C43C2×D4
hypercenter#1996D43
hypocenterC43#10566
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
115. C22⋊C4×C43Q16semidirect
262. C43#10566semidirect
370. C22⋊C4#10621885semidirect

Maximal subgroups

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

subgroupindex
#191453672
#191355802
#191350192
#191350162
#191347752
#191324622
C43×#19962
#1056643