Finite Group Databasebeta

← #24988242

Subgroups — #24988242

Order 11008.

788 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 788 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C2×#14583605C211yesmaximal, characteristic
2C4×#13063243C211yesmaximal, characteristic, complemented
3#19133197C211yesmaximal, characteristic, complemented
4#19133039C211yesmaximal, characteristic
5#19133037C211yesmaximal, characteristic
6#19132938C211yesmaximal, characteristic, complemented
7C43×#1528C211yesmaximal, characteristic, complemented
8#14583605—22no—
9#14583605—22no—
10#14583605—22no—
11#14583605—22no—
12C2×#13063324C411yescharacteristic
13C2×#13063316C411yescharacteristic
14C2×#13063305—21no—
15C2×#13063303—21no—
16C2×#13063303—21no—
17C2×C4×Dic86C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×#13063287C411yescharacteristic
20C2×#13063287C411yescharacteristic
21C2×C4⋊C4×D43—21no—
22#14582956C2211yescharacteristic
23C2×#13063243—21no—
24C4×#10621877C2211yescharacteristic
25#14582667—21no—
26#14582641—22no—
27#14582628—22no—
28#14582626—22no—
29#14582624—21no—
30#14582624—21no—
31C2×#125×C43C2211yescharacteristic
32C43×#432C2211yescharacteristic
33C4×M16×C43C2211yescharacteristic
34C43×#330—22no—
35C22×Dic86—21no—
36C22×Dic86D411yescharacteristic
37C22×D172C2×C411yescharacteristic
38C22×C4×D43—21no—
39C22×C4×D43—21no—
40C22×C4×D43—21no—
41C2×#10621877—21no—
42#13063324—22no—
43#13063324—22no—
44#13063316—22no—
45#13063316—22no—
46#13063305—24no—
47#13063305—24no—
48#13063303—24no—
49#13063303—24no—
50#13063303—24no—
51#13063303—24no—
52C4×Dic86—21no—
53C4×Dic86—21no—
54C4×Dic86—21no—
55C4×Dic86—21no—
56C4×D172—21no—
57C4×D172—21no—
58C4×D172D412yes—
59C4×D172D412yes—
60#13063287—22no—
61#13063287—22no—
62#13063287—22no—
63#13063287—22no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43C2×C411yescharacteristic
66C2×C4⋊Dic43D411yescharacteristic
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4—21no—
69C2×Dic43⋊C4D411yescharacteristic
70C2×Dic43⋊C4D411yescharacteristic
71C4⋊C4×D43—24no—
72C4⋊C4×D43—24no—
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4—21no—
75C2×(C2×D43)⋊C4—21no—
76C2×C4×Dic43C2×C411yescharacteristic
77C2×C4×Dic43C2×C411yescharacteristic
78C4⋊(C43⋊C8)—21no—
79#13063243—24no—
80C22⋊(C43⋊C8)—21no—
81#13063236—21no—
82#13063236—21no—
83C4×C43⋊C8—21no—
84C2×M16×C43—21no—
85#125×C43—21no—
86#125×C43—21no—
87#125×C43D412yes—
88#125×C43D412yes—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43—21no—
91C2×C4⋊C4×C43C2×C411yescharacteristic
92C2×C4⋊C4×C43C2×C411yescharacteristic
93C2×C42×C43C2311yescharacteristic
94C4⋊C8×C43—21no—
95C22⋊C8×C43—21no—
96#97×C43—21no—
97#97×C43—21no—
98C4×C8×C43—21no—
99C23×D43—21no—
100C22×C4×C43—21no—
101C22×C4×C43—21no—
102C22×C4×C43C22×C411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×Dic43—21no—
106C22×Dic43C22⋊C411yescharacteristic
107C22×Dic43C22⋊C411yescharacteristic
108C22×Dic43C22⋊C411yescharacteristic
109C22×Dic43C22⋊C411yescharacteristic
110C2×D172—21no—
111C2×D172—24no—
112C2×D172C22⋊C412yes—
113C2×C4×D43—24no—
114C2×C4×D43—24no—
115C2×C4×D43—22no—
116C2×C4×D43—22no—
117C2×C4×D43—42no—
118C2×C4×D43—42no—
119C2×C4×D43—82no—
120C2×C4×D43—82no—
121C2×Dic86—21no—
122C2×Dic86—21no—
123C2×Dic86—22no—
124C2×Dic86—24no—
125C2×Dic86—41no—
126C2×Dic86—82no—
127M16×C43—22no—
128M16×C43—41no—
129C2×C8×C43—41no—
130C2×C8×C43—41no—
131C4⋊C4×C43—21no—
132C4⋊C4×C43—21no—
133C4⋊C4×C43—22no—
134C4⋊C4×C43—22no—
135C4⋊C4×C43—22no—
136C4⋊C4×C43—22no—
137C4⋊C4×C43C22⋊C412yes—
138C4⋊C4×C43C22⋊C412yes—
139C42×C43C2×D411yescharacteristic
140C42×C43C2×D411yescharacteristic
141C42×C43C2×D411yescharacteristic
142C42×C43C2×D411yescharacteristic
143(C2×D43)⋊C4—24no—
144(C2×D43)⋊C4—24no—
145(C2×D43)⋊C4—22no—
146(C2×D43)⋊C4—22no—
147C4⋊Dic43—24no—
148C4⋊Dic43—21no—
149C4⋊Dic43—21no—
150C4⋊Dic43—21no—
151C4⋊Dic43C22⋊C412yes—
152Dic43⋊C4—24no—
153Dic43⋊C4—24no—
154Dic43⋊C4—21no—
155Dic43⋊C4—21no—
156Dic43⋊C4—21no—
157Dic43⋊C4—21no—
158C4×Dic43—21no—
159C4×Dic43—21no—
160C4×Dic43—21no—
161C4×Dic43—21no—
162#10621877—22no—
163#10621877—41no—
164C2×C43⋊C8—41no—
165C2×C43⋊C8—41no—
166C23×C43C2×C22⋊C411yescharacteristic
167C22×D43—24no—
168C22×D43—22no—
169C22×D43—42no—
170C22×D43—41no—
171C22×D43—41no—
172C2×C4×C43—21no—
173C2×C4×C43—21no—
174C2×C4×C43—22no—
175C2×C4×C43—22no—
176C2×C4×C43—22no—
177C2×C4×C43—41no—
178C2×C4×C43—42no—
179C2×C4×C43—41no—
180C2×C4×C43—41no—
181C2×C4×C43C2×C22⋊C411yescharacteristic
182C2×C4×C43C2×C22⋊C411yescharacteristic
183C2×C4×C43#12011yescharacteristic
184C2×C4×C43#12011yescharacteristic
185C2×C4×C43#12011yescharacteristic
186C2×C4×C43#12011yescharacteristic
187C2×Dic43—21no—
188C2×Dic43—21no—
189C2×Dic43—21no—
190C2×Dic43—21no—
191C2×Dic43—21no—
192C2×Dic43—22no—
193C2×Dic43—21no—
194C2×Dic43—21no—
195C2×Dic43—42no—
196C2×Dic43—41no—
197C2×Dic43—41no—
198C2×Dic43#10412yes—
199D172—24no—
200D172—22no—
201D172#10114yescomplemented
202C4×D43—48no—
203C4×D43—82no—
204C4×D43—82no—
205C4×D43—84no—
206Dic86—42no—
207Dic86—42no—
208Dic86—84no—
209C8×C43—42no—
210C8×C43—81no—
211C43⋊C8—42no—
212C43⋊C8—81no—
213#8372—431nomaximal, Sylow
214C22×C43—21no—
215C22×C43—21no—
216C22×C43#37911yescharacteristic
217C22×C43C2×#10411yescharacteristic
218C22×C43#42111yescharacteristic
219C2×D43—24no—
220C2×D43—44no—
221C2×D43—44no—
222C2×D43—42no—
223C2×D43—42no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—21no—
227C4×C43—21no—
228C4×C43—21no—
229C4×C43—42no—
230C4×C43—42no—
231C4×C43C2×#10112yes—
232Dic43—22no—
233Dic43—41no—
234Dic43—42no—
235Dic43—41no—
236Dic43—41no—
237C2×#554—431no—
238C4×#101—431no—
239#1528—431no—
240#1528D4311yescharacteristic, complemented
241#1490—431no—
242#1490—431no—
243#1467—431no—
244C2×C43—21no—
245C2×C43—21no—
246C2×C43#178411yescharacteristic
247C2×C43#178911yescharacteristic
248C2×C43#179511yescharacteristic
249D43—44no—
250#554—862no—
251#554—862no—
252#554—862no—
253#554—862no—
254C2×C4⋊Q8—431no—
255C2×#125—431no—
256C2×#125C2×D4311yescharacteristic
257C2×C22⋊Q8—861no—
258C2×C22⋊Q8—861no—
259C2×C22⋊Q8—861no—
260C2×C4×Q8—431no—
261C2×C4×D4—431no—
262C2×C4×D4—431no—
263C2×C4×D4—431no—
264C22×C4⋊C4—861no—
265#432—431no—
266#432C2×D4311yescharacteristic
267C2×#101—861no—
268C4×M16—431no—
269C4×M16C2×D4311yescharacteristic
270#343—861no—
271#330—22no—
272#330—862no—
273D4⋊C8—862no—
274D4⋊C8—862no—
275#324—861no—
276#324—861no—
277C43#837211yescharacteristic, complemented, Sylow
278C22×Q8—431no—
279C22×Q8—861no—
280C22×D4—431no—
281C23×C4—861no—
282C23×C4—861no—
283C23×C4—861no—
284C2×M16—21no—
285C2×M16—861no—
286C4⋊Q8—862no—
287C4⋊Q8—862no—
288#125—21no—
289#125—21no—
290#125—862no—
291#125—862no—
292#125D17212yes—
293#125C22⋊D4312yes—
294C22⋊Q8—864no—
295C22⋊Q8—864no—
296C22⋊Q8—864no—
297C22⋊Q8—864no—
298C22⋊Q8—864no—
299C22⋊Q8—864no—
300C4×Q8—861no—
301C4×Q8—861no—
302C4×Q8—861no—
303C4×Q8—861no—
304C4×D4—432no—
305C4×D4—432no—
306C4×D4—862no—
307C4×D4—862no—
308C4×D4—862no—
309C4×D4—862no—
310C4×D4—861no—
311C4×D4—861no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—431no—
315C2×C4⋊C4—431no—
316C2×C4⋊C4—431no—
317C2×C4⋊C4—431no—
318C2×C4⋊C4—864no—
319C2×C4⋊C4—864no—
320C2×C4⋊C4—861no—
321C2×C4⋊C4—861no—
322C2×C4⋊C4—861no—
323C2×C4⋊C4C4×D4311yescharacteristic
324C2×C4⋊C4C4×D4311yescharacteristic
325C2×C22⋊C4—861no—
326C2×C22⋊C4—861no—
327C2×C22⋊C4—861no—
328C2×C42—431no—
329C2×C42—431no—
330C2×C42C22×D4311yescharacteristic
331C4⋊C8—21no—
332C4⋊C8—861no—
333#101—864no—
334C22⋊C8—21no—
335C22⋊C8—861no—
336#97—21no—
337#97—21no—
338#97—861no—
339#97—861no—
340C4×C8—21no—
341C4×C8—861no—
342C24—861no—
343C2×Q8—862no—
344C2×Q8—864no—
345C2×Q8—861no—
346C2×Q8—861no—
347C2×Q8—3442no—
348C2×Q8—1721no—
349C2×D4—432no—
350C2×D4—864no—
351C2×D4—861no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—431no—
355C22×C4—431no—
356C22×C4—431no—
357C22×C4—431no—
358C22×C4—864no—
359C22×C4—864no—
360C22×C4—861no—
361C22×C4—862no—
362C22×C4—862no—
363C22×C4—3442no—
364C22×C4—3442no—
365C22×C4—1722no—
366C22×C4—1722no—
367C22×C4C2×C4×D4311yescharacteristic
368C22×C4D4×D4311yescharacteristic
369C22×C4D4×D4311yescharacteristic
370M16—22no—
371M16—41no—
372M16—862no—
373M16—1721no—
374C2×C8—41no—
375C2×C8—41no—
376C2×C8—1721no—
377C2×C8—1721no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—432no—
385C4⋊C4—864no—
386C4⋊C4—864no—
387C4⋊C4—864no—
388C4⋊C4—861no—
389C4⋊C4—861no—
390C4⋊C4—861no—
391C4⋊C4—861no—
392C4⋊C4—861no—
393C4⋊C4—861no—
394C4⋊C4—861no—
395C4⋊C4(C2×D43)⋊C412yes—
396C4⋊C4(C2×D43)⋊C412yes—
397C22⋊C4—864no—
398C22⋊C4—864no—
399C22⋊C4—862no—
400C22⋊C4—862no—
401C42—861no—
402C42—861no—
403C42—861no—
404C42—861no—
405C42C2×D17211yescharacteristic
406C42D4×D4311yescharacteristic
407C42D4×D4311yescharacteristic
408C42C2×C22⋊D4311yescharacteristic
409C23—864no—
410C23—862no—
411C23—1722no—
412C23—1721no—
413C23—1721no—
414C23C22⋊C4×D4311yescharacteristic
415Q8—3444no—
416Q8—1722no—
417Q8—1722no—
418D4—434no—
419D4—864no—
420D4—862no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—432no—
431C2×C4—861no—
432C2×C4—861no—
433C2×C4—861no—
434C2×C4—861no—
435C2×C4—861no—
436C2×C4—861no—
437C2×C4—861no—
438C2×C4—862no—
439C2×C4—3442no—
440C2×C4—3442no—
441C2×C4—3444no—
442C2×C4—1728no—
443C2×C4—1722no—
444C2×C4—1721no—
445C2×C4—1721no—
446C2×C4C22⋊C4×D4311yescharacteristic
447C2×C4C2×(C2×D43)⋊C411yescharacteristic
448C2×C4#1306329311yescharacteristic
449C2×C4#1306329311yescharacteristic
450C2×C4#1306329511yescharacteristic
451C2×C4#1306329511yescharacteristic
452C8—42no—
453C8—81no—
454C8—3441no—
455C8—1722no—
456C22—21no—
457C22—21no—
458C22—864no—
459C22—1724no—
460C22—1724no—
461C22—1722no—
462C22—1722no—
463C22#1458275411yescharacteristic
464C22#104×D4311yescharacteristic
465C22#1458291411yescharacteristic
466C4—21no—
467C4—21no—
468C4—21no—
469C4—21no—
470C4—21no—
471C4—42no—
472C4—42no—
473C4—862no—
474C4—1721no—
475C4—1721no—
476C4—1722no—
477C4—1721no—
478C4#101×D4312yes—
479C2—21no—
480C2—21no—
481C2—1724no—
482C2#1913451711yescharacteristic
483C2#1913453711yescharacteristic
484C2#1913456411yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1528C2
socleC22×C43#379
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#1528D43
hypocenterC43#8372
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1528

Complements

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

NH ≅ G/Ntype
2. C4×#13063243C2semidirect
3. #19133197C2semidirect
6. #19132938C2semidirect
7. C43×#1528C2semidirect
201. D172#101semidirect
240. #1528D43semidirect
277. C43#8372semidirect

Maximal subgroups

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

subgroupindex
C2×#145836052
C4×#130632432
#191331972
#191330392
#191330372
#191329382
C43×#15282
#837243