Finite Group Databasebeta

← #25006881

Subgroups — #25006881

Order 11008.

592 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 83 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#19140401C211yesmaximal, characteristic
2#342×D43C211yesmaximal, characteristic
3#323×D43C211yesmaximal, characteristic
4#19132619C211yesmaximal, characteristic, complemented
5#19132617C211yesmaximal, characteristic, complemented
6#19132615C211yesmaximal, characteristic, complemented
7C43×#1352C211yesmaximal, characteristic, complemented
8C2×#13063305C411yescharacteristic, complemented
9C2×C22⋊C4×D43—21no—
10C2×C22⋊C4×D43C2211yescharacteristic
11C22⋊C8×D43—21no—
12#14582834C411yescharacteristic, complemented
13#14582822—21no—
14#14582821—21no—
15#14582812C411yescharacteristic, complemented
16#14582811C2211yescharacteristic
17#14582770—21no—
18#14582758C411yescharacteristic, complemented
19#14582754—21no—
20#14582666C2211yescharacteristic
21#14582665—21no—
22#14582623C2211yescharacteristic
23#14582622—21no—
24C43×#399C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C24×D43D411yescharacteristic
28C22×Dic86C2×C411yescharacteristic, complemented
29C22×C4×D43—41no—
30C22×C4×D43C2×C411yescharacteristic
31C22×C4×D43D411yescharacteristic
32C2×C8×D43—41no—
33#13063305—41no—
34#13063305—41no—
35C2×C4⋊Dic43—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×C22⋊Dic43—21no—
39C2×C22⋊Dic43—21no—
40C2×C22⋊Dic43D411yescharacteristic
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—41no—
46C2×(C2×D43)⋊C4C2×C411yescharacteristic
47C2×(C2×D43)⋊C4D411yescharacteristic
48C22⋊C4×D43—24no—
49C22⋊C4×D43—41no—
50C22⋊C4×D43—41no—
51C22⋊C4×D43—42no—
52C22⋊(C43⋊C8)—21no—
53(C2×D43)⋊C8—41no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95C2×C411yescharacteristic, complemented
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43—21no—
61C2×C22⋊C4×C43C2311yescharacteristic
62C22⋊C8×C43—21no—
63#95×C43C2×C411yescharacteristic, complemented
64C24×C43C2×D411yescharacteristic
65C23×D43—21no—
66C23×D43—21no—
67C23×D43—22no—
68C23×D43—81no—
69C23×D43—81no—
70C23×D43C22⋊C411yescharacteristic
71C23×D43C22⋊C411yescharacteristic
72C23×D43SD1612yes—
73C23×D43Q1612yes—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—41no—
77C22×C4×C43C22×C411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—41no—
82C22×Dic43C22⋊C411yescharacteristic
83C22×Dic43C22⋊C411yescharacteristic
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86C2×C4×D43—21no—
87C2×C4×D43—21no—
88C2×C4×D43—44no—
89C2×C4×D43—81no—
90C2×C4×D43—82no—
91C2×C4×D43—82no—
92C2×C4×D43—81no—
93C2×Dic86—41no—
94C2×Dic86—81no—
95C2×C8×C43—41no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—81no—
98C22⋊C4×C43—22no—
99C22⋊C4×C43—41no—
100C22⋊C4×C43—41no—
101C22⋊C4×C43—81no—
102C22⋊Dic43—22no—
103C22⋊Dic43—41no—
104C22⋊Dic43—41no—
105C22⋊Dic43—81no—
106(C2×D43)⋊C4—41no—
107(C2×D43)⋊C4—41no—
108(C2×D43)⋊C4—44no—
109(C2×D43)⋊C4—41no—
110(C2×D43)⋊C4—41no—
111(C2×D43)⋊C4—42no—
112(C2×D43)⋊C4—81no—
113(C2×D43)⋊C4—81no—
114C4⋊Dic43—42no—
115Dic43⋊C4—81no—
116Dic43⋊C4—81no—
117C2×C43⋊C8—41no—
118C8×D43—82no—
119C23×C43—21no—
120C23×C43—21no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43C2×C22⋊C411yescharacteristic
124C23×C43C2×SD1611yescharacteristic
125C23×C43C2×Q1611yescharacteristic
126C22×D43—21no—
127C22×D43—21no—
128C22×D43—22no—
129C22×D43—22no—
130C22×D43—22no—
131C22×D43—22no—
132C22×D43—41no—
133C22×D43—41no—
134C22×D43—42no—
135C22×D43—42no—
136C22×D43—41no—
137C22×D43—41no—
138C22×D43—81no—
139C22×D43—81no—
140C22×D43—82no—
141C22×D43—82no—
142C22×D43—84no—
143C22×D43#9911yescharacteristic
144C22×D43#9911yescharacteristic
145C22×D43#10312yes—
146C22×D43#10312yes—
147C22×D43#10412yes—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—42no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—81no—
160C2×C4×C43—81no—
161C2×Dic43—21no—
162C2×Dic43—21no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—42no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—81no—
173C2×Dic43—81no—
174C4×D43—42no—
175C4×D43—81no—
176C4×D43—81no—
177C4×D43—81no—
178C4×D43—88no—
179Dic86—82no—
180C8×C43—81no—
181C43⋊C8—81no—
182#11716—431nomaximal, Sylow
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—41no—
188C22×C43—41no—
189C22×C43—41no—
190C22×C43—41no—
191C22×C43—81no—
192C22×C43C2×#9911yescharacteristic
193C22×C43C2×#10311yescharacteristic
194C22×C43C2×#10411yescharacteristic
195C2×D43—21no—
196C2×D43—21no—
197C2×D43—21no—
198C2×D43—21no—
199C2×D43—22no—
200C2×D43—42no—
201C2×D43—42no—
202C2×D43—44no—
203C2×D43—44no—
204C2×D43—41no—
205C2×D43—41no—
206C2×D43—42no—
207C2×D43—82no—
208C2×D43—82no—
209C2×D43—81no—
210C2×D43#32812yes—
211C2×D43#32812yes—
212C4×C43—41no—
213C4×C43—41no—
214C4×C43—81no—
215C4×C43—82no—
216C4×C43—81no—
217Dic43—41no—
218Dic43—41no—
219Dic43—81no—
220Dic43—82no—
221Dic43—81no—
222#2626—431no—
223C2×#342—431no—
224C2×#323—431no—
225#1352—431no—
226#1352D4311yescharacteristic, complemented
227#1351—431no—
228#1351—431no—
229C2×C43—21no—
230C2×C43—21no—
231C2×C43—41no—
232C2×C43—41no—
233C2×C43C2×#32811yescharacteristic
234C2×C43#212111yescharacteristic
235C2×C43#212711yescharacteristic
236D43—22no—
237D43—22no—
238D43—42no—
239C2×C22⋊Q8—431no—
240C22×C22⋊C4—431no—
241C22×C22⋊C4—861no—
242C2×C22⋊C8—861no—
243#399—431no—
244#399C2×D4311yescharacteristic
245#396—861no—
246#396—861no—
247#393—431no—
248#393—431no—
249#385—861no—
250#380—431no—
251#379—861no—
252#342—431no—
253#342—861no—
254#342C2×D4311yescharacteristic
255#323—431no—
256#323—861no—
257#323C2×D4311yescharacteristic
258C43#1171611yescharacteristic, complemented, Sylow
259C25—431no—
260C22×Q8—431no—
261C23×C4—431no—
262C23×C4—431no—
263C23×C4—1721no—
264C22×C8—1721no—
265C22⋊Q8—1721no—
266C22⋊Q8—1721no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—861no—
269C2×C4⋊C4—861no—
270C2×C4⋊C4—861no—
271C2×C4⋊C4C4×D4311yescharacteristic, complemented
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—431no—
275C2×C22⋊C4—431no—
276C2×C22⋊C4—431no—
277C2×C22⋊C4—864no—
278C2×C22⋊C4—861no—
279C2×C22⋊C4—861no—
280C2×C22⋊C4—861no—
281C2×C22⋊C4—861no—
282C2×C22⋊C4—861no—
283C2×C22⋊C4—861no—
284C2×C22⋊C4—1721no—
285C2×C22⋊C4—1721no—
286C2×C22⋊C4—1722no—
287C2×C22⋊C4—1721no—
288C2×C22⋊C4C22×D4311yescharacteristic
289C22⋊C8—21no—
290C22⋊C8—861no—
291C22⋊C8—1721no—
292#95—431no—
293#95—861no—
294#95—861no—
295#95C4×D4311yescharacteristic, complemented
296C24—431no—
297C24—432no—
298C24—432no—
299C24—431no—
300C24—862no—
301C24—861no—
302C24—861no—
303C24—3441no—
304C24—3441no—
305C24D4×D4311yescharacteristic
306C2×Q8—3441no—
307C2×Q8—1721no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—41no—
311C22×C4—431no—
312C22×C4—431no—
313C22×C4—861no—
314C22×C4—861no—
315C22×C4—861no—
316C22×C4—861no—
317C22×C4—861no—
318C22×C4—861no—
319C22×C4—3441no—
320C22×C4—3441no—
321C22×C4—3442no—
322C22×C4—3442no—
323C22×C4—1724no—
324C22×C4—1721no—
325C22×C4C2×C4×D4311yescharacteristic
326C22×C4D4×D4311yescharacteristic
327C2×C8—41no—
328C2×C8—3442no—
329C2×C8—1721no—
330C4⋊C4—41no—
331C4⋊C4—81no—
332C4⋊C4—3441no—
333C4⋊C4—3441no—
334C4⋊C4—1722no—
335C22⋊C4—22no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—81no—
339C22⋊C4—862no—
340C22⋊C4—3441no—
341C22⋊C4—3441no—
342C22⋊C4—3441no—
343C22⋊C4—1721no—
344C22⋊C4—1721no—
345C22⋊C4—1721no—
346C22⋊C4—1721no—
347C22⋊C4—1722no—
348C22⋊C4—1724no—
349C22⋊C4—1721no—
350C22⋊C4—1721no—
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23—431no—
356C23—431no—
357C23—432no—
358C23—432no—
359C23—432no—
360C23—862no—
361C23—862no—
362C23—862no—
363C23—862no—
364C23—861no—
365C23—861no—
366C23—3441no—
367C23—3441no—
368C23—3442no—
369C23—3442no—
370C23—3444no—
371C23—1721no—
372C23—1721no—
373C23—1721no—
374C23—1721no—
375C23—1722no—
376C23—1722no—
377C23C22⋊C4×D4311yescharacteristic
378C23SD16×D4311yescharacteristic
379C23Q16×D4311yescharacteristic
380Q8—3442no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—861no—
395C2×C4—861no—
396C2×C4—3441no—
397C2×C4—3441no—
398C2×C4—3441no—
399C2×C4—3448no—
400C2×C4—3441no—
401C2×C4—3441no—
402C2×C4—1722no—
403C2×C4—1722no—
404C2×C4—1721no—
405C2×C4—1721no—
406C2×C4—1721no—
407C2×C4—1721no—
408C2×C4—1721no—
409C2×C4—1721no—
410C2×C4—1721no—
411C2×C4—1721no—
412C8—81no—
413C8—3441no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—81no—
423C22—432no—
424C22—432no—
425C22—861no—
426C22—861no—
427C22—861no—
428C22—861no—
429C22—862no—
430C22—3441no—
431C22—3442no—
432C22—3442no—
433C22—1722no—
434C22—1722no—
435C22—1722no—
436C22—1724no—
437C22—1724no—
438C22—1721no—
439C22—1721no—
440C22#99×D4311yescharacteristic
441C22#103×D4311yescharacteristic
442C22#104×D4311yescharacteristic
443C4—41no—
444C4—41no—
445C4—81no—
446C4—82no—
447C4—81no—
448C4—3441no—
449C4—3442no—
450C4—3441no—
451C4—1721no—
452C4—1721no—
453C2—21no—
454C2—21no—
455C2—41no—
456C2—41no—
457C2—862no—
458C2—862no—
459C2—1722no—
460C2#328×D4311yescharacteristic
461C2#1913624011yescharacteristic
462C2#1913626111yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1352C2
socleC22×C43C2×#99
prime radicalC24×D43D4
cosocleC2×C22⋊C4×C43C23
hypercenter#1352D43
hypocenterC43#11716
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
4. #19132619C2semidirect
5. #19132617C2semidirect
6. #19132615C2semidirect
7. C43×#1352C2semidirect
8. C2×#13063305C4semidirect
12. #14582834C4semidirect
15. #14582812C4semidirect
18. #14582758C4semidirect
28. C22×Dic86C2×C4semidirect
56. C43⋊#95C2×C4semidirect
58. C2×C4⋊C4×C43C2×C4semidirect
63. #95×C43C2×C4semidirect
226. #1352D43semidirect
258. C43#11716semidirect
271. C2×C4⋊C4C4×D43semidirect
295. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191404012
#342×D432
#323×D432
#191326192
#191326172
#191326152
C43×#13522
#1171643