Finite Group Databasebeta

← #24985453

Subgroups — #24985453

Order 11008.

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

normal subgroups only

This group has 542 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#19135841C211yesmaximal, characteristic, complemented
2#19135731C211yesmaximal, characteristic, complemented
3#19135731C211yesmaximal, characteristic, complemented
4#19132418C211yesmaximal, characteristic, complemented
5#19132416C211yesmaximal, characteristic, complemented
6#19132416C211yesmaximal, characteristic, complemented
7C43×#2682C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9C2×#13063248—21no—
10C2×#13063248—21no—
11C2×#13063246—21no—
12C2×#13063246—21no—
13#14582661—21no—
14#14582661—21no—
15#14582654C2211yescharacteristic
16#14582654C2211yescharacteristic
17#14582654C2211yescharacteristic
18C2×#123×C43—21no—
19C2×#121×C43—21no—
20C43×#396—21no—
21C43×#394—21no—
22C43×#392—21no—
23C43×#390C2211yescharacteristic
24C43×#390C2211yescharacteristic
25C43×#389C2211yescharacteristic
26C43×#385—21no—
27C22×Dic86—21no—
28C22×C43⋊C8—21no—
29C22×C43⋊C8—21no—
30C22×C43⋊C8—21no—
31#13063325—42no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43—21no—
34#13063248—42no—
35#13063248—42no—
36#13063246—42no—
37#13063246—42no—
38C22×D4×C43—21no—
39C22×D4×C43—21no—
40C22×D4×C43D411yescharacteristic
41C22×D4×C43D411yescharacteristic
42C23×C4×C43—21no—
43#123×C43—42no—
44#123×C43—42no—
45#121×C43—42no—
46#121×C43—42no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C4⋊C4×C43D411yescharacteristic
51C2×C4⋊C4×C43D411yescharacteristic
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C22⋊C4×C43—21no—
54C2×C22⋊C4×C43—21no—
55C2×C22⋊C4×C43—21no—
56C2×C22⋊C4×C43—21no—
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43—21no—
59C2×C22⋊C4×C43—21no—
60C2×C42×C43C2311yescharacteristic
61#95×C43—21no—
62#95×C43—21no—
63C24×C43—21no—
64C24×C43—21no—
65C2×D4×C43—21no—
66C2×D4×C43—21no—
67C2×D4×C43—21no—
68C2×D4×C43—42no—
69C2×D4×C43—42no—
70C2×D4×C43—42no—
71C2×D4×C43—41no—
72C2×D4×C43—41no—
73C2×D4×C43—41no—
74C2×D4×C43—41no—
75C2×D4×C43—81no—
76C2×D4×C43—81no—
77C2×D4×C43—81no—
78C2×D4×C43SD1612yes—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—42no—
84C22×C4×C43—42no—
85C22×C4×C43—81no—
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×Dic43—41no—
90C2×Dic86—22no—
91C2×Dic86—41no—
92C2×Dic86—41no—
93C2×Dic86—41no—
94C2×Dic86—41no—
95C2×Dic86—41no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—42no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43D812yes—
104C22⋊C4×C43—42no—
105C22⋊C4×C43—42no—
106C22⋊C4×C43—41no—
107C22⋊C4×C43—41no—
108C22⋊C4×C43—41no—
109C22⋊C4×C43—41no—
110C22⋊C4×C43—41no—
111C22⋊C4×C43—41no—
112C22⋊C4×C43—41no—
113C22⋊C4×C43—41no—
114C22⋊C4×C43—81no—
115C42×C43—41no—
116C4⋊Dic43—22no—
117C4⋊Dic43—22no—
118C4⋊Dic43—41no—
119C4⋊Dic43—41no—
120C2×C43⋊C8—41no—
121C2×C43⋊C8—41no—
122C2×C43⋊C8—41no—
123C2×C43⋊C8—41no—
124C2×C43⋊C8—41no—
125C2×C43⋊C8—41no—
126C2×C43⋊C8—41no—
127C2×C43⋊C8—41no—
128C2×C43⋊C8—41no—
129C23×C43—22no—
130C23×C43—41no—
131C23×C43—41no—
132C23×C43—41no—
133C23×C43—41no—
134C23×C43—41no—
135C23×C43—41no—
136C23×C43—41no—
137C23×C43—41no—
138C23×C43—41no—
139C23×C43—41no—
140C23×C43—41no—
141C23×C43—41no—
142C23×C43—41no—
143C23×C43#12011yescharacteristic
144D4×C43—42no—
145D4×C43—42no—
146D4×C43—81no—
147D4×C43—81no—
148D4×C43—84no—
149D4×C43—84no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—22no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
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—84no—
169C2×C4×C43C2×D811yescharacteristic
170C2×C4×C43C2×SD1611yescharacteristic
171C2×C4×C43#13511yescharacteristic
172C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C43#13711yescharacteristic
175C2×Dic43—42no—
176C2×Dic43—81no—
177C2×Dic43—81no—
178Dic86—42no—
179Dic86—42no—
180Dic86—81no—
181Dic86—81no—
182C43⋊C8—81no—
183C43⋊C8—81no—
184C43⋊C8—81no—
185#7762—431nomaximal, Sylow
186C22×C43—42no—
187C22×C43—42no—
188C22×C43—42no—
189C22×C43—81no—
190C22×C43—81no—
191C22×C43—81no—
192C22×C43—81no—
193C22×C43—81no—
194C22×C43—81no—
195C22×C43—81no—
196C22×C43—81no—
197C22×C43—81no—
198C22×C43—81no—
199C22×C43—81no—
200C22×C43#44711yescharacteristic
201C22×C43#45011yescharacteristic
202C22×C43#45211yescharacteristic
203C22×C43#45411yescharacteristic
204C22×C43#45511yescharacteristic
205C22×C43#45511yescharacteristic
206C22×C43B(4,𝔽2)11yescharacteristic
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—42no—
214C4×C43—81no—
215C4×C43—81no—
216C4×C43—81no—
217Dic43—82no—
218#2682D4311yescharacteristic
219#2043—431no—
220#2023—431no—
221#2023—431no—
222#1271—431no—
223#1270—431no—
224#1270—431no—
225C2×C43—82no—
226C2×C43—161no—
227C2×C43#159811yescharacteristic
228C2×C43#160111yescharacteristic
229C2×C43#160611yescharacteristic
230C2×C43#163511yescharacteristic
231C2×C43#163911yescharacteristic
232C2×C43#164111yescharacteristic
233C2×C43#166211yescharacteristic
234C2×C4⋊Q8—431no—
235C2×#123—21no—
236C2×#121—21no—
237C2×#103—861no—
238C2×#103—861no—
239C2×#102—861no—
240C2×#102—861no—
241#396—21no—
242#394—21no—
243#392—21no—
244#390C2×D4311yescharacteristic
245#390C2×D4311yescharacteristic
246#389C2×D4311yescharacteristic
247#385—21no—
248#340—861no—
249#340—861no—
250#336—431no—
251#336—431no—
252#336—431no—
253C43#776211yescharacteristic, complemented, Sylow
254C22×Q8—861no—
255C22×D4—21no—
256C22×D4—21no—
257C22×D4C22⋊D4311yescharacteristic
258C22×D4C22⋊D4311yescharacteristic
259C23×C4—21no—
260C22×C8—861no—
261C22×C8—861no—
262C22×C8—861no—
263C4⋊Q8—1722no—
264#123—42no—
265#123—42no—
266#121—42no—
267#121—42no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—861no—
271C2×C4⋊C4—861no—
272C2×C4⋊C4C22⋊D4311yescharacteristic
273C2×C4⋊C4C22⋊D4311yescharacteristic
274C2×C4⋊C4C22⋊D4311yescharacteristic
275C2×C4⋊C4C22⋊D4311yescharacteristic
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C42C22×D4311yescharacteristic
284#103—1722no—
285#103—1722no—
286#102—1722no—
287#102—1722no—
288#95—21no—
289#95—21no—
290C24—21no—
291C24—21no—
292C2×Q8—862no—
293C2×Q8—1721no—
294C2×Q8—1721no—
295C2×Q8—1721no—
296C2×Q8—1721no—
297C2×Q8—1721no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—42no—
306C2×D4—42no—
307C2×D4—42no—
308C2×D4—81no—
309C2×D4—81no—
310C2×D4—81no—
311C2×D4#1062188312yes—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—81no—
319C22×C4—1721no—
320C22×C4C2×C22⋊D4311yescharacteristic
321C22×C4C2×C22⋊D4311yescharacteristic
322C22×C4C2×C22⋊D4311yescharacteristic
323C2×C8—1721no—
324C2×C8—1721no—
325C2×C8—1721no—
326C2×C8—1721no—
327C2×C8—1721no—
328C2×C8—1721no—
329C2×C8—1721no—
330C2×C8—1721no—
331C2×C8—1721no—
332C4⋊C4—21no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—42no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—862no—
340C4⋊C4—862no—
341C4⋊C4—1721no—
342C4⋊C4—1721no—
343C4⋊C4#1062188212yes—
344C22⋊C4—42no—
345C22⋊C4—42no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—81no—
355C42—41no—
356C23—22no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23#1306329411yescharacteristic
371Q8—3441no—
372Q8—3441no—
373Q8—1722no—
374Q8—1722no—
375D4—42no—
376D4—42no—
377D4—81no—
378D4—81no—
379D4—84no—
380D4—84no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—84no—
400C2×C4—3441no—
401C2×C4—3441no—
402C2×C4—1722no—
403C2×C4C2×#1062188211yescharacteristic
404C2×C4C2×#1062188311yescharacteristic
405C2×C4#1306334511yescharacteristic
406C2×C4#1306335111yescharacteristic
407C2×C4#1306335111yescharacteristic
408C2×C4#1306335511yescharacteristic
409C8—3441no—
410C8—3441no—
411C8—3441no—
412C22—42no—
413C22—42no—
414C22—42no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22#1458303311yescharacteristic
427C22#1458305011yescharacteristic
428C22#1458306111yescharacteristic
429C22#1458307211yescharacteristic
430C22#1458307711yescharacteristic
431C22#1458307711yescharacteristic
432C22#1458308611yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—42no—
440C4—81no—
441C4—81no—
442C4—81no—
443C4—3442no—
444C2—82no—
445C2—161no—
446C2#1913353011yescharacteristic
447C2#1913354711yescharacteristic
448C2#1913357511yescharacteristic
449C2#1913374611yescharacteristic
450C2#1913377411yescharacteristic
451C2#1913378811yescharacteristic
452C2#1913391811yescharacteristic
subgroupG/H
centerC23#13063294
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#2682C2
socleC23×C43#120
hypercenter#2682D43
hypocenterC43#7762
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2682

Complements

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

NH ≅ G/Ntype
1. #19135841C2semidirect
2. #19135731C2semidirect
3. #19135731C2semidirect
4. #19132418C2semidirect
5. #19132416C2semidirect
6. #19132416C2semidirect
253. C43#7762semidirect

Maximal subgroups

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

subgroupindex
#191358412
#191357312
#191324182
#191324162
C43×#26822
#776243