Finite Group Databasebeta

← #24992559

Subgroups — #24992559

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#19140515C211yesmaximal, characteristic
3C4×#13063239C211yesmaximal, characteristic
4#19133116C211yesmaximal, characteristic, complemented
5#19133114C211yesmaximal, characteristic, complemented
6#19132447C211yesmaximal, characteristic, complemented
7C43×#1284C211yesmaximal, characteristic, complemented
8C2×#13063304C2211yescharacteristic
9C2×C4×C22⋊D43C2211yescharacteristic
10#14582973—22no—
11#14582968—22no—
12#14582953—21no—
13C2×#13063239—21no—
14#14582863C2211yescharacteristic
15C22⋊C8×D43—21no—
16#14582831C411yescharacteristic, complemented
17#14582826C411yescharacteristic, complemented
18#14582824—21no—
19#14582820C411yescharacteristic, complemented
20#14582815—21no—
21#14582812C411yescharacteristic, complemented
22#14582784—21no—
23#14582773—21no—
24C4×C22⋊Dic43C2211yescharacteristic
25#14582665—21no—
26#14582637—22no—
27#14582635—22no—
28C43×#407C2211yescharacteristic
29C43×#381C2211yescharacteristic
30C4×C22⋊C4×C43C2211yescharacteristic
31C22×Dic86C2×C411yescharacteristic
32C22×C22⋊D43D411yescharacteristic
33C22×C4×D43D411yescharacteristic
34C2×#10621877—21no—
35C2×C8×D43—22no—
36#13063304—21no—
37#13063304—21no—
38#13063304—21no—
39#13063304—21no—
40C4×C22⋊D43—21no—
41C4×C22⋊D43—21no—
42C4×C22⋊D43—21no—
43C4×C22⋊D43—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43—21no—
46C2×C4⋊Dic43C2×C411yescharacteristic
47C2×Dic43⋊C4—21no—
48C2×Dic43⋊C4C2×C411yescharacteristic
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43—21no—
51C2×C22⋊Dic43D411yescharacteristic
52C2×(C2×D43)⋊C4—21no—
53C2×(C2×D43)⋊C4—21no—
54C2×(C2×D43)⋊C4C2×C411yescharacteristic
55C2×C4×Dic43—21no—
56C2×C4×Dic43D411yescharacteristic
57Dic43⋊C8—22no—
58#13063239—24no—
59C22⋊(C43⋊C8)—21no—
60C22⋊(C43⋊C8)D412yes—
61(C2×D43)⋊C8—22no—
62#13063235—22no—
63C43⋊#95—21no—
64C43⋊#95—21no—
65C43⋊#95—21no—
66C43⋊#95—21no—
67C43⋊#95—21no—
68C23×C4×C43C2311yescharacteristic
69C2×M16×C43—21no—
70C2×C22⋊C4×C43—21no—
71C2×C22⋊C4×C43—21no—
72C2×C42×C43—21no—
73C22⋊C8×C43—21no—
74C22⋊C8×C43D412yes—
75#95×C43—21no—
76#95×C43—21no—
77#95×C43C2×C411yescharacteristic
78#95×C43C2×C411yescharacteristic
79C24×C43C2×D411yescharacteristic
80C23×D43C22⋊C411yescharacteristic
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—41no—
84C22×C4×C43—81no—
85C22×C4×C43C22×C411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43#4111yescharacteristic
90C22×C4×C43#4111yescharacteristic
91C2×C22⋊D43—21no—
92C2×C22⋊D43—21no—
93C2×C22⋊D43—22no—
94C2×C22⋊D43—41no—
95C22×Dic43—21no—
96C22×Dic43—21no—
97C22×Dic43—41no—
98C22×Dic43C22⋊C411yescharacteristic
99C22×Dic43C22⋊C411yescharacteristic
100C22×Dic43C22⋊C411yescharacteristic
101C2×C4×D43—21no—
102C2×C4×D43—21no—
103C2×C4×D43—81no—
104C2×Dic86—21no—
105C2×Dic86—21no—
106C2×Dic86—81no—
107M16×C43—81no—
108C2×C8×C43—22no—
109C22⋊C4×C43—22no—
110C22⋊C4×C43—41no—
111C22⋊C4×C43—81no—
112C42×C43—81no—
113C22⋊Dic43—22no—
114C22⋊Dic43—21no—
115C22⋊Dic43—21no—
116C22⋊Dic43—41no—
117C22⋊Dic43—41no—
118C22⋊Dic43—41no—
119(C2×D43)⋊C4—21no—
120(C2×D43)⋊C4—21no—
121(C2×D43)⋊C4—42no—
122(C2×D43)⋊C4—81no—
123C4⋊Dic43—21no—
124C4⋊Dic43—21no—
125C4⋊Dic43—42no—
126C4⋊Dic43—81no—
127Dic43⋊C4—21no—
128Dic43⋊C4—21no—
129Dic43⋊C4—41no—
130Dic43⋊C4—41no—
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—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
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—42no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—81no—
163C2×C4×C43—81no—
164C2×C4×C43C4×D411yescharacteristic
165C2×C4×C43C4×D411yescharacteristic
166C2×C4×C43#12011yescharacteristic
167C2×C4×C43#12311yescharacteristic
168C22⋊D43—42no—
169C22⋊D43—42no—
170C2×Dic43—21no—
171C2×Dic43—21no—
172C2×Dic43—21no—
173C2×Dic43—21no—
174C2×Dic43—21no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43—41no—
178C2×Dic43—41no—
179C2×Dic43—42no—
180C2×Dic43—41no—
181C2×Dic43—41no—
182C2×Dic43—41no—
183C2×Dic43—41no—
184C2×Dic43—81no—
185C2×Dic43—81no—
186C4×D43—42no—
187C4×D43—81no—
188Dic86—81no—
189Dic86—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—81no—
216C4×C43—81no—
217C4×C43—82no—
218Dic43—41no—
219Dic43—41no—
220Dic43—41no—
221Dic43—82no—
222Dic43—81no—
223Dic43—81no—
224#2973—431no—
225#2638—431no—
226C4×#99—431no—
227#1508—431no—
228#1508—431no—
229#1284—431no—
230#1284D4311yescharacteristic, complemented
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⋊Q8—431no—
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#381C2×D4311yescharacteristic
257C4×C22⋊C4—431no—
258C4×C22⋊C4C2×D4311yescharacteristic
259#342—861no—
260#328—862no—
261#328—862no—
262C43#918311yescharacteristic, complemented, Sylow
263C22×Q8—431no—
264C22×D4—431no—
265C23×C4—431no—
266C23×C4C22×D4311yescharacteristic
267C2×M16—21no—
268C2×M16—861no—
269C22×C8—862no—
270C22⋊Q8—861no—
271C22⋊Q8—861no—
272C22⋊Q8—861no—
273C22⋊Q8—861no—
274C4×D4—861no—
275C4×D4—861no—
276C4×D4—861no—
277C4×D4—861no—
278C2×C4⋊C4—431no—
279C2×C4⋊C4—431no—
280C2×C4⋊C4—861no—
281C2×C4⋊C4—861no—
282C2×C4⋊C4—861no—
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⋊C8D17212yes—
301#97—862no—
302#95—21no—
303#95—21no—
304#95—861no—
305#95—861no—
306#95—861no—
307#95—861no—
308#95—861no—
309#95C4×D4311yescharacteristic
310#95C4×D4311yescharacteristic
311C24—431no—
312C24D4×D4311yescharacteristic
313C2×Q8—861no—
314C2×Q8—861no—
315C2×Q8—3441no—
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×C4C2×D17211yescharacteristic
335C22×C4#1062189811yescharacteristic
336C22×C4D4×D4311yescharacteristic
337C22×C4D4×D4311yescharacteristic
338C22×C4#1062190211yescharacteristic
339M16—81no—
340M16—3441no—
341C2×C8—22no—
342C2×C8—862no—
343C2×C8—3442no—
344C4⋊C4—861no—
345C4⋊C4—861no—
346C4⋊C4—861no—
347C4⋊C4—861no—
348C4⋊C4—3441no—
349C4⋊C4—1722no—
350C4⋊C4—1721no—
351C4⋊C4—1721no—
352C22⋊C4—22no—
353C22⋊C4—41no—
354C22⋊C4—81no—
355C22⋊C4—861no—
356C22⋊C4—861no—
357C22⋊C4—861no—
358C22⋊C4—861no—
359C22⋊C4—862no—
360C22⋊C4—3441no—
361C22⋊C4—1722no—
362C22⋊C4—1721no—
363C22⋊C4—1721no—
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#1306329811yescharacteristic
380C23#1306330011yescharacteristic
381Q8—3441no—
382Q8—3441no—
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#1306328711yescharacteristic
419C2×C4C4×D17211yescharacteristic
420C2×C4#1306329511yescharacteristic
421C2×C4#1306331011yescharacteristic
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#1458277711yescharacteristic
440C22#104×D4311yescharacteristic
441C22#1458291411yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—81no—
447C4—81no—
448C4—82no—
449C4—3442no—
450C4—3441no—
451C4—3441no—
452C4—1721no—
453C4—1721no—
454C4—1721no—
455C2—21no—
456C2—21no—
457C2—41no—
458C2—41no—
459C2—1722no—
460C2#1913489611yescharacteristic
461C2#1913511611yescharacteristic
462C2#1913513611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1284C2
socleC22×C43#386
prime radicalC22×C22⋊D43D4
cosocleC23×C4×C43C23
hypercenter#1284D43
hypocenterC43#9183
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
4. #19133116C2semidirect
5. #19133114C2semidirect
6. #19132447C2semidirect
7. C43×#1284C2semidirect
16. #14582831C4semidirect
17. #14582826C4semidirect
19. #14582820C4semidirect
21. #14582812C4semidirect
230. #1284D43semidirect
262. C43#9183semidirect

Maximal subgroups

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

subgroupindex
#191436222
#191405152
C4×#130632392
#191331162
#191331142
#191324472
C43×#12842
#918343