Finite Group Databasebeta

← #24992557

Subgroups — #24992557

Order 11008.

532 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 91 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#19143622C211yesmaximal, characteristic
2#19140513C211yesmaximal, characteristic
3C4×#13063239C211yesmaximal, characteristic
4#19133115C211yesmaximal, characteristic, complemented
5#19132449C211yesmaximal, characteristic, complemented
6#19132448C211yesmaximal, characteristic, complemented
7C43×#1508C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D43C2211yescharacteristic
9#14582973—22no—
10#14582968—22no—
11#14582953—21no—
12C2×#13063239—21no—
13#14582863C2211yescharacteristic
14C22⋊C8×D43—21no—
15#14582830C411yescharacteristic, complemented
16#14582827—21no—
17#14582825C411yescharacteristic, complemented
18#14582818C411yescharacteristic, complemented
19#14582814—21no—
20#14582810C411yescharacteristic, complemented
21#14582780—21no—
22#14582770—21no—
23#14582762C2211yescharacteristic
24C4×C22⋊Dic43C2211yescharacteristic
25#14582665—21no—
26#14582636—22no—
27C2×C22⋊Q8×C43C2211yescharacteristic
28C43×#407C2211yescharacteristic
29C4×C22⋊C4×C43C2211yescharacteristic
30C43×#328—22no—
31C22×C22⋊D43D411yescharacteristic
32C22×C4×D43D411yescharacteristic
33C2×#10621877—21no—
34C2×C8×D43—22no—
35C4×C22⋊D43—21no—
36C4×C22⋊D43—21no—
37C4×C22⋊D43—21no—
38C4×C22⋊D43—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4C2×C411yescharacteristic
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43D411yescharacteristic
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4C2×C411yescharacteristic
48C2×C4×Dic43—21no—
49C2×C4×Dic43D411yescharacteristic
50Dic43⋊C8—22no—
51#13063239—24no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)D412yes—
54(C2×D43)⋊C8—22no—
55#13063235—22no—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95C2×C411yescharacteristic
63C43⋊#95C2×C411yescharacteristic
64C22×Q8×C43C2×C411yescharacteristic
65C23×C4×C43C2311yescharacteristic
66C2×M16×C43—21no—
67C22⋊Q8×C43—21no—
68C22⋊Q8×C43—21no—
69C22⋊Q8×C43—21no—
70C22⋊Q8×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43C2×C411yescharacteristic
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—21no—
75C2×C42×C43—21no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43D412yes—
78#95×C43—21no—
79C24×C43C2×D411yescharacteristic
80C23×D43C22⋊C411yescharacteristic
81C2×Q8×C43—21no—
82C2×Q8×C43—21no—
83C2×Q8×C43—81no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—41no—
87C22×C4×C43—81no—
88C22×C4×C43C22×C411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43#4111yescharacteristic
93C22×C4×C43#4111yescharacteristic
94C2×C22⋊D43—21no—
95C2×C22⋊D43—21no—
96C2×C22⋊D43—22no—
97C2×C22⋊D43—41no—
98C22×Dic43—21no—
99C22×Dic43—21no—
100C22×Dic43—41no—
101C22×Dic43C22⋊C411yescharacteristic
102C22×Dic43C22⋊C411yescharacteristic
103C22×Dic43C22⋊C411yescharacteristic
104C2×C4×D43—21no—
105C2×C4×D43—21no—
106C2×C4×D43—81no—
107M16×C43—81no—
108C2×C8×C43—22no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C22⋊C4×C43—22no—
114C22⋊C4×C43—41no—
115C22⋊C4×C43—41no—
116C22⋊C4×C43—41no—
117C42×C43—81no—
118C22⋊Dic43—22no—
119C22⋊Dic43—21no—
120C22⋊Dic43—21no—
121C22⋊Dic43—41no—
122C22⋊Dic43—81no—
123(C2×D43)⋊C4—21no—
124(C2×D43)⋊C4—21no—
125(C2×D43)⋊C4—42no—
126(C2×D43)⋊C4—81no—
127Dic43⋊C4—21no—
128Dic43⋊C4—21no—
129Dic43⋊C4—42no—
130Dic43⋊C4—81no—
131C4×Dic43—21no—
132C4×Dic43—21no—
133C4×Dic43—81no—
134#10621877—81no—
135C2×C43⋊C8—22no—
136C8×D43—82no—
137C23×C43—21no—
138C23×C43—21no—
139C23×C43—41no—
140C23×C43—41no—
141C23×C43C2×C22⋊C411yescharacteristic
142C23×C43#12111yescharacteristic
143C23×C43#12111yescharacteristic
144C22×D43—21no—
145C22×D43—21no—
146C22×D43—41no—
147C22×D43—41no—
148C22×D43#10412yes—
149Q8×C43—81no—
150Q8×C43—81no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—42no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—81no—
165C2×C4×C43—81no—
166C2×C4×C43C4×D411yescharacteristic
167C2×C4×C43C4×D411yescharacteristic
168C2×C4×C43#12011yescharacteristic
169C2×C4×C43#12311yescharacteristic
170C22⋊D43—42no—
171C22⋊D43—42no—
172C2×Dic43—21no—
173C2×Dic43—21no—
174C2×Dic43—21no—
175C2×Dic43—21no—
176C2×Dic43—21no—
177C2×Dic43—41no—
178C2×Dic43—41no—
179C2×Dic43—41no—
180C2×Dic43—41no—
181C2×Dic43—42no—
182C2×Dic43—41no—
183C2×Dic43—41no—
184C2×Dic43—41no—
185C2×Dic43—41no—
186C2×Dic43—81no—
187C2×Dic43—81no—
188C4×D43—42no—
189C4×D43—81no—
190C8×C43—42no—
191C43⋊C8—42no—
192#9183—431nomaximal, Sylow
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—21no—
200C22×C43—21no—
201C22×C43—81no—
202C22×C43—81no—
203C22×C43#38611yescharacteristic
204C22×C43C2×#10411yescharacteristic
205C22×C43#42111yescharacteristic
206C2×D43—22no—
207C2×D43—41no—
208C2×D43—41no—
209C2×D43—42no—
210C2×D43—81no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—82no—
216C4×C43—81no—
217C4×C43—81no—
218Dic43—41no—
219Dic43—41no—
220Dic43—41no—
221Dic43—81no—
222Dic43—81no—
223Dic43—82no—
224#2973—431no—
225#2638—431no—
226C4×#99—431no—
227#1508—431no—
228#1508D4311yescharacteristic, complemented
229#1284—431no—
230#1284—431no—
231C2×C43—21no—
232C2×C43—21no—
233C2×C43—41no—
234C2×C43—41no—
235C2×C43#187111yescharacteristic
236C2×C43#190911yescharacteristic
237C2×C43#191311yescharacteristic
238D43—42no—
239C2×C22⋊Q8C2×D4311yescharacteristic
240C2×C4×D4—431no—
241#435—862no—
242#435—862no—
243#432—861no—
244C2×#99—861no—
245#407—431no—
246#407C2×D4311yescharacteristic
247C2×C22⋊C8—861no—
248#398—431no—
249#397—431no—
250#397—861no—
251#395—431no—
252#394—861no—
253#393—431no—
254#387—861no—
255#385—861no—
256#381—431no—
257C4×C22⋊C4—431no—
258C4×C22⋊C4C2×D4311yescharacteristic
259#342—861no—
260#328—22no—
261#328—862no—
262C43#918311yescharacteristic, complemented, Sylow
263C22×Q8C4×D4311yescharacteristic
264C22×D4—431no—
265C23×C4—431no—
266C23×C4C22×D4311yescharacteristic
267C2×M16—21no—
268C2×M16—861no—
269C22×C8—862no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272C22⋊Q8—21no—
273C22⋊Q8—21no—
274C4×D4—861no—
275C4×D4—861no—
276C4×D4—861no—
277C4×D4—861no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—431no—
280C2×C4⋊C4—861no—
281C2×C4⋊C4—861no—
282C2×C4⋊C4C4×D4311yescharacteristic
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—431no—
286C2×C22⋊C4—431no—
287C2×C22⋊C4—861no—
288C2×C22⋊C4—861no—
289C2×C22⋊C4—861no—
290C2×C22⋊C4—861no—
291C2×C42—21no—
292C2×C42—431no—
293C2×C42—861no—
294C4⋊C8—862no—
295#99—864no—
296C22⋊C8—21no—
297C22⋊C8—432no—
298C22⋊C8—862no—
299C22⋊C8—861no—
300C22⋊C8C22⋊D4312yes—
301#97—862no—
302#95—21no—
303#95—431no—
304#95—431no—
305#95—861no—
306#95—861no—
307#95—861no—
308#95—861no—
309#95—861no—
310#95—861no—
311C24—431no—
312C24D4×D4311yescharacteristic
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—81no—
316C2×D4—862no—
317C2×D4—861no—
318C2×D4—861no—
319C2×D4—1721no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—41no—
323C22×C4—81no—
324C22×C4—431no—
325C22×C4—431no—
326C22×C4—431no—
327C22×C4—861no—
328C22×C4—861no—
329C22×C4—861no—
330C22×C4—861no—
331C22×C4—3441no—
332C22×C4—1721no—
333C22×C4C2×C4×D4311yescharacteristic
334C22×C4#1062189811yescharacteristic
335C22×C4D4×D4311yescharacteristic
336C22×C4D4×D4311yescharacteristic
337C22×C4#1062190011yescharacteristic
338C22×C4C2×C22⋊D4311yescharacteristic
339M16—81no—
340M16—3441no—
341C2×C8—22no—
342C2×C8—862no—
343C2×C8—3442no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—861no—
349C4⋊C4—861no—
350C4⋊C4—3441no—
351C4⋊C4—1722no—
352C22⋊C4—22no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—861no—
357C22⋊C4—861no—
358C22⋊C4—861no—
359C22⋊C4—861no—
360C22⋊C4—862no—
361C22⋊C4—3441no—
362C22⋊C4—3441no—
363C22⋊C4—1722no—
364C22⋊C4—1721no—
365C42—81no—
366C42—861no—
367C42—861no—
368C42—3441no—
369C23—21no—
370C23—21no—
371C23—41no—
372C23—41no—
373C23—432no—
374C23—861no—
375C23—861no—
376C23—1721no—
377C23—1721no—
378C23C22⋊C4×D4311yescharacteristic
379C23#1306329611yescharacteristic
380C23#1306329811yescharacteristic
381Q8—81no—
382Q8—81no—
383D4—1722no—
384D4—1722no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—861no—
401C2×C4—861no—
402C2×C4—861no—
403C2×C4—861no—
404C2×C4—861no—
405C2×C4—3441no—
406C2×C4—3441no—
407C2×C4—3441no—
408C2×C4—1722no—
409C2×C4—1722no—
410C2×C4—1721no—
411C2×C4—1721no—
412C2×C4—1721no—
413C2×C4—1721no—
414C2×C4—1721no—
415C2×C4—1721no—
416C2×C4—1721no—
417C2×C4—1721no—
418C2×C4(C22⋊D43)⋊C411yescharacteristic
419C2×C4C4×C22⋊D4311yescharacteristic
420C2×C4#1306329311yescharacteristic
421C2×C4#1306330711yescharacteristic
422C8—42no—
423C8—1722no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—81no—
433C22—81no—
434C22—862no—
435C22—3441no—
436C22—1722no—
437C22—1721no—
438C22—1721no—
439C22#1458277511yescharacteristic
440C22#104×D4311yescharacteristic
441C22#1458291411yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—82no—
447C4—81no—
448C4—81no—
449C4—3441no—
450C4—3441no—
451C4—3442no—
452C4—1721no—
453C4—1721no—
454C4—1721no—
455C2—21no—
456C2—21no—
457C2—41no—
458C2—41no—
459C2—1722no—
460C2#1913489411yescharacteristic
461C2#1913511411yescharacteristic
462C2#1913513411yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1508C2
socleC22×C43#386
prime radicalC22×C22⋊D43D4
cosocleC23×C4×C43C23
hypercenter#1508D43
hypocenterC43#9183
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1508

Complements

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

NH ≅ G/Ntype
4. #19133115C2semidirect
5. #19132449C2semidirect
6. #19132448C2semidirect
7. C43×#1508C2semidirect
15. #14582830C4semidirect
17. #14582825C4semidirect
18. #14582818C4semidirect
20. #14582810C4semidirect
228. #1508D43semidirect
262. C43#9183semidirect

Maximal subgroups

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

subgroupindex
#191436222
#191405132
C4×#130632392
#191331152
#191324492
#191324482
C43×#15082
#918343