Finite Group Databasebeta

← #24999837

Subgroups — #24999837

Order 11008.

594 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 75 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#19140262C211yesmaximal, characteristic, complemented
2#19134539C211yesmaximal, characteristic
3#19134513C211yesmaximal, characteristic
4#19132504C211yesmaximal, characteristic, complemented
5#19132449C211yesmaximal, characteristic, complemented
6#19132448C211yesmaximal, characteristic, complemented
7C43×#1789C211yesmaximal, characteristic
8C2×#13063252—21no—
9C2×#13063252—21no—
10C2×#13063240—21no—
11C2×#13063240—21no—
12#14582863C2211yescharacteristic
13#14582822—21no—
14#14582822—21no—
15#14582797—21no—
16#14582796—21no—
17#14582786—21no—
18#14582783—21no—
19#14582762C2211yescharacteristic
20#14582762C2211yescharacteristic
21C4×C22⋊Dic43C2211yescharacteristic
22C22×#41×C43C2211yescharacteristic
23C2×#104×C43—21no—
24C2×#104×C43—21no—
25C43×#407C2211yescharacteristic
26C4×C22⋊C4×C43C2211yescharacteristic
27C2×#10621877—21no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×Dic43⋊C4—21no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43D411yescharacteristic
37C2×C22⋊Dic43D411yescharacteristic
38C2×C4×Dic43D411yescharacteristic
39C2×C4×Dic43D411yescharacteristic
40#13063252—42no—
41#13063252—42no—
42#13063240—42no—
43#13063240—42no—
44C22⋊(C43⋊C8)—21no—
45C22⋊(C43⋊C8)—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C2×#41×C43—21no—
54C2×#41×C43—21no—
55C2×#41×C43—21no—
56C2×#41×C43—21no—
57C2×#41×C43—42no—
58C2×#41×C43—42no—
59C22×Q8×C43Q811yescharacteristic
60C22×D4×C43—21no—
61C22×D4×C43Q811yescharacteristic
62C23×C4×C43—21no—
63C23×C4×C43C2311yescharacteristic
64C2×M16×C43—21no—
65C2×C22⋊C4×C43—21no—
66C2×C42×C43D411yescharacteristic
67C2×C42×C43D411yescharacteristic
68#104×C43—42no—
69#104×C43—42no—
70C22⋊C8×C43—21no—
71C22⋊C8×C43—21no—
72#95×C43—21no—
73C24×C43—21no—
74C24×C43C2×D411yescharacteristic
75#41×C43—22no—
76#41×C43—22no—
77#41×C43—22no—
78#41×C43—22no—
79#41×C43—41no—
80#41×C43—41no—
81#41×C43—41no—
82#41×C43—41no—
83#41×C43—42no—
84#41×C43—42no—
85#41×C43—42no—
86#41×C43—42no—
87C2×Q8×C43—21no—
88C2×Q8×C43—21no—
89C2×Q8×C43—42no—
90C2×D4×C43—22no—
91C2×D4×C43—22no—
92C2×D4×C43—21no—
93C2×D4×C43—21no—
94C2×D4×C43—42no—
95C2×D4×C43—41no—
96C2×D4×C43—41no—
97C2×D4×C43—41no—
98C2×D4×C43—41no—
99C22×C4×C43—21no—
100C22×C4×C43—21no—
101C22×C4×C43—21no—
102C22×C4×C43—41no—
103C22×C4×C43—41no—
104C22×C4×C43—42no—
105C22×C4×C43—42no—
106C22×C4×C43—41no—
107C22×C4×C43—41no—
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×Q811yescharacteristic
111C22×C4×C43#4111yescharacteristic
112C22×C4×C43#4111yescharacteristic
113C22×C4×C43#4111yescharacteristic
114C22×Dic43—21no—
115C22×Dic43—21no—
116C22×Dic43—21no—
117C22×Dic43—21no—
118C22×Dic43—41no—
119M16×C43—41no—
120M16×C43—41no—
121C2×C8×C43—41no—
122C22⋊C4×C43—42no—
123C42×C43—41no—
124C42×C43—41no—
125C22⋊Dic43—41no—
126C22⋊Dic43—41no—
127C22⋊Dic43—41no—
128C22⋊Dic43—41no—
129C22⋊Dic43—42no—
130C4⋊Dic43—42no—
131C4⋊Dic43—81no—
132Dic43⋊C4—42no—
133Dic43⋊C4—42no—
134Dic43⋊C4—42no—
135Dic43⋊C4—81no—
136C4×Dic43—41no—
137C4×Dic43—41no—
138#10621877—41no—
139#10621877—41no—
140C2×C43⋊C8—41no—
141C23×C43—21no—
142C23×C43—21no—
143C23×C43—22no—
144C23×C43—41no—
145C23×C43—41no—
146C23×C43—41no—
147C23×C43—41no—
148C23×C43—81no—
149C23×C43—81no—
150C23×C43#12011yescharacteristic
151C23×C43C22⋊Q811yescharacteristic
152C23×C43#12411yescharacteristic
153Q8×C43—22no—
154Q8×C43—22no—
155Q8×C43—41no—
156Q8×C43—41no—
157D4×C43—22no—
158D4×C43—22no—
159D4×C43—41no—
160D4×C43—41no—
161D4×C43—42no—
162D4×C43—42no—
163D4×C43—42no—
164D4×C43—42no—
165C2×C4×C43—21no—
166C2×C4×C43—21no—
167C2×C4×C43—21no—
168C2×C4×C43—21no—
169C2×C4×C43—22no—
170C2×C4×C43—22no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—42no—
176C2×C4×C43—42no—
177C2×C4×C43—42no—
178C2×C4×C43—42no—
179C2×C4×C43—41no—
180C2×C4×C43—41no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43C22⋊Q811yescharacteristic
187C2×C4×C43C22⋊Q811yescharacteristic
188C2×C4×C43#12411yescharacteristic
189C2×C4×C43#12411yescharacteristic
190C2×Dic43—22no—
191C2×Dic43—41no—
192C2×Dic43—41no—
193C2×Dic43—41no—
194C2×Dic43—41no—
195C2×Dic43—41no—
196C2×Dic43—41no—
197C2×Dic43—41no—
198C2×Dic43—41no—
199C2×Dic43—41no—
200C2×Dic43—41no—
201C2×Dic43—41no—
202C2×Dic43—81no—
203C2×Dic43—81no—
204C2×Dic43—81no—
205C8×C43—81no—
206C43⋊C8—81no—
207#10388—431nomaximal, Sylow
208C22×C43—21no—
209C22×C43—21no—
210C22×C43—21no—
211C22×C43—21no—
212C22×C43—21no—
213C22×C43—21no—
214C22×C43—21no—
215C22×C43—21no—
216C22×C43—42no—
217C22×C43—81no—
218C22×C43—81no—
219C22×C43—82no—
220C22×C43—82no—
221C22×C43—81no—
222C22×C43—81no—
223C22×C43#39311yescharacteristic
224C22×C43B(4,𝔽2)11yescharacteristic
225C22×C43B(4,𝔽2)11yescharacteristic
226C4×C43—21no—
227C4×C43—21no—
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—42no—
231C4×C43—42no—
232C4×C43—81no—
233Dic43—42no—
234Dic43—81no—
235Dic43—81no—
236Dic43—81no—
237Dic43—161no—
238#2608—431no—
239#1789—431no—
240#1789D4311yescharacteristic
241#1782—431no—
242#1306—431no—
243#1284—431no—
244#1284—431no—
245C2×C43—21no—
246C2×C43—21no—
247C2×C43—41no—
248C2×C43—41no—
249C2×C43—82no—
250C2×C43#202911yescharacteristic
251C2×C43#203111yescharacteristic
252C2×C43#203111yescharacteristic
253C22×#41C2×D4311yescharacteristic
254C2×#104—21no—
255C2×#104—21no—
256C2×#104—861no—
257C2×#104—861no—
258C2×#99—861no—
259C2×#99—861no—
260#407—431no—
261#407C2×D4311yescharacteristic
262#396—861no—
263#396—861no—
264#389—861no—
265#389—861no—
266#387—861no—
267#387—861no—
268#381—431no—
269#381—431no—
270C4×C22⋊C4—431no—
271C4×C22⋊C4C2×D4311yescharacteristic
272C43#1038811yescharacteristic, complemented, Sylow
273C2×#41—21no—
274C2×#41—21no—
275C2×#41—21no—
276C2×#41—21no—
277C2×#41—42no—
278C2×#41—42no—
279C22×Q8Dic8611yescharacteristic
280C22×D4—21no—
281C22×D4Dic8611yescharacteristic
282C23×C4—21no—
283C23×C4C22×D4311yescharacteristic
284C2×M16—21no—
285C2×M16—861no—
286C2×C4⋊C4—861no—
287C2×C4⋊C4—861no—
288C2×C4⋊C4—861no—
289C2×C4⋊C4—861no—
290C2×C4⋊C4—861no—
291C2×C4⋊C4—861no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—431no—
294C2×C22⋊C4—431no—
295C2×C22⋊C4—861no—
296C2×C22⋊C4—861no—
297C2×C42—431no—
298C2×C42—431no—
299C2×C42C22⋊D4311yescharacteristic
300C2×C42C22⋊D4311yescharacteristic
301#104—42no—
302#104—42no—
303#104—1722no—
304#104—1722no—
305#99—1722no—
306#99—1722no—
307C22⋊C8—21no—
308C22⋊C8—21no—
309C22⋊C8—861no—
310C22⋊C8—861no—
311#95—21no—
312#95—861no—
313#95—861no—
314#95—861no—
315#95—861no—
316#95—861no—
317#95—861no—
318#95—861no—
319C24—21no—
320C24D4×D4311yescharacteristic
321#41—22no—
322#41—22no—
323#41—22no—
324#41—22no—
325#41—41no—
326#41—41no—
327#41—41no—
328#41—41no—
329#41—42no—
330#41—42no—
331#41—42no—
332#41—42no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—42no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—42no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—861no—
355C22×C4—861no—
356C22×C4—861no—
357C22×C4—861no—
358C22×C4—1721no—
359C22×C4C2×Dic8611yescharacteristic
360C22×C4#1062189811yescharacteristic
361C22×C4D4×D4311yescharacteristic
362C22×C4#1062190011yescharacteristic
363C22×C4#1062190011yescharacteristic
364C22×C4C2×C22⋊D4311yescharacteristic
365M16—41no—
366M16—41no—
367M16—1721no—
368M16—1721no—
369C2×C8—41no—
370C2×C8—1721no—
371C4⋊C4—3441no—
372C4⋊C4—3441no—
373C4⋊C4—1722no—
374C4⋊C4—1722no—
375C4⋊C4—1722no—
376C4⋊C4—1722no—
377C22⋊C4—42no—
378C22⋊C4—1722no—
379C22⋊C4—1721no—
380C22⋊C4—1721no—
381C22⋊C4—1721no—
382C22⋊C4—1721no—
383C42—41no—
384C42—41no—
385C42—1721no—
386C42—1721no—
387C23—21no—
388C23—21no—
389C23—22no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—81no—
395C23—81no—
396C23#1306329311yescharacteristic
397C23#1306330211yescharacteristic
398C23#1306331111yescharacteristic
399Q8—22no—
400Q8—22no—
401Q8—41no—
402Q8—41no—
403D4—22no—
404D4—22no—
405D4—41no—
406D4—41no—
407D4—42no—
408D4—42no—
409D4—42no—
410D4—42no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—862no—
433C2×C4—3441no—
434C2×C4—3441no—
435C2×C4—3441no—
436C2×C4—1721no—
437C2×C4—1721no—
438C2×C4—1721no—
439C2×C4—1721no—
440C2×C4—1721no—
441C2×C4—1721no—
442C2×C4—1721no—
443C2×C4—1721no—
444C2×C4—1721no—
445C2×C4—1721no—
446C2×C4—1721no—
447C2×C4#1306330211yescharacteristic
448C2×C4#1306330411yescharacteristic
449C2×C4#1306331111yescharacteristic
450C2×C4#1306331211yescharacteristic
451C8—81no—
452C8—3441no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—42no—
462C22—81no—
463C22—81no—
464C22—82no—
465C22—82no—
466C22—81no—
467C22—81no—
468C22#1458281111yescharacteristic
469C22#1458308511yescharacteristic
470C22#1458308511yescharacteristic
471C4—21no—
472C4—21no—
473C4—21no—
474C4—21no—
475C4—42no—
476C4—42no—
477C4—81no—
478C4—3441no—
479C4—3441no—
480C4—3441no—
481C4—1722no—
482C4—6881no—
483C2—21no—
484C2—21no—
485C2—41no—
486C2—41no—
487C2—82no—
488C2#1913575911yescharacteristic
489C2#1913576511yescharacteristic
490C2#1913576711yescharacteristic
subgroupG/H
centerC22#14582811
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1789C2
socleC22×C43#393
prime radicalC22×#41×C43C22
hypercenter#1789D43
hypocenterC43#10388
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
1. #19140262C2semidirect
4. #19132504C2semidirect
5. #19132449C2semidirect
6. #19132448C2semidirect
272. C43#10388semidirect

Maximal subgroups

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

subgroupindex
#191402622
#191345392
#191345132
#191325042
#191324492
#191324482
C43×#17892
#1038843