Finite Group Databasebeta

← #24988224

Subgroups — #24988224

Order 11008.

744 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 744 conjugacy classes of subgroups — too many to draw. Only its 113 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×#14583621C211yesmaximal, characteristic
2C4×#13063243C211yesmaximal, characteristic, complemented
3#19133194C211yesmaximal, characteristic
4#19133192C211yesmaximal, characteristic
5#19133042C211yesmaximal, characteristic, complemented
6#19132938C211yesmaximal, characteristic, complemented
7C43×#1491C211yesmaximal, characteristic, complemented
8#14583621—22no—
9#14583621—22no—
10#14583621—22no—
11#14583621—22no—
12C2×#13063323C411yescharacteristic
13C2×#13063320—21no—
14C2×#13063319—21no—
15C2×#13063314C411yescharacteristic
16C2×#13063313C2211yescharacteristic
17C2×#13063303—21no—
18C2×C4×Dic86C2211yescharacteristic
19C2×#13063290C411yescharacteristic
20C2×#13063287C411yescharacteristic
21C2×#13063282—21no—
22#14582956C2211yescharacteristic
23C2×#13063243—21no—
24C4×#10621877C2211yescharacteristic
25#14582667—21no—
26#14582638—22no—
27#14582638—22no—
28Q8⋊(C43⋊C8)—22no—
29#14582624—21no—
30#14582624—21no—
31C2×C4×Q8×C43C2211yescharacteristic
32C43×#432C2211yescharacteristic
33C4×M16×C43C2211yescharacteristic
34C43×Q8⋊C8—22no—
35C22×Dic86C2×C411yescharacteristic
36C22×Dic86D411yescharacteristic
37C22×D172C2×C411yescharacteristic
38C22×C4×D43—21no—
39C2×#10621877—21no—
40#13063323—22no—
41#13063323—22no—
42#13063320—24no—
43#13063320—24no—
44#13063319—24no—
45#13063319—24no—
46#13063314—22no—
47#13063314—22no—
48#13063313—21no—
49#13063313—21no—
50#13063313D412yes—
51#13063313D412yes—
52#13063303—24no—
53#13063303—24no—
54C4×Dic86—21no—
55C4×Dic86—21no—
56C4×Dic86—21no—
57C4×Dic86—21no—
58#13063290—22no—
59#13063290—22no—
60#13063287—22no—
61#13063287—22no—
62#13063282—24no—
63#13063282—24no—
64C2×C4⋊Dic43D411yescharacteristic
65C2×Dic43⋊C4—21no—
66C2×Dic43⋊C4—21no—
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4D411yescharacteristic
69C2×Dic43⋊C4D411yescharacteristic
70C2×(C2×D43)⋊C4—21no—
71C2×(C2×D43)⋊C4—21no—
72C2×(C2×D43)⋊C4—21no—
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4—21no—
75C2×C4×Dic43—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—
84C22×Q8×C43C2×C411yescharacteristic
85C2×M16×C43—21no—
86C4×Q8×C43—21no—
87C4×Q8×C43—21no—
88C4×Q8×C43D412yes—
89C4×Q8×C43D412yes—
90C2×C4⋊C4×C43—21no—
91C2×C4⋊C4×C43C2×C411yescharacteristic
92C2×C42×C43—21no—
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—
100C2×Q8×C43—21no—
101C2×Q8×C43—42no—
102C2×Q8×C43C22⋊C412yes—
103C22×C4×C43—21no—
104C22×C4×C43—21no—
105C22×C4×C43C22×C411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×Dic43—21no—
109C22×Dic43C22⋊C411yescharacteristic
110C22×Dic43C22⋊C411yescharacteristic
111C22×Dic43C22⋊C411yescharacteristic
112C22×Dic43C22⋊C411yescharacteristic
113C2×D172—21no—
114C2×D172—42no—
115C2×D172C22⋊C412yes—
116C2×C4×D43—24no—
117C2×C4×D43—42no—
118C2×C4×D43—42no—
119C2×Dic86—21no—
120C2×Dic86—21no—
121C2×Dic86—21no—
122C2×Dic86—22no—
123C2×Dic86—41no—
124C2×Dic86—42no—
125C2×Dic86C22⋊C412yes—
126M16×C43—22no—
127M16×C43—41no—
128C2×C8×C43—41no—
129C2×C8×C43—41no—
130C4⋊C4×C43—21no—
131C4⋊C4×C43—22no—
132C4⋊C4×C43—22no—
133C4⋊C4×C43C22⋊C412yes—
134C42×C43—22no—
135C42×C43—22no—
136C42×C43C2×D411yescharacteristic
137C42×C43C2×D411yescharacteristic
138C42×C43C2×D411yescharacteristic
139C42×C43C2×D411yescharacteristic
140(C2×D43)⋊C4—24no—
141(C2×D43)⋊C4—24no—
142(C2×D43)⋊C4—24no—
143(C2×D43)⋊C4—22no—
144(C2×D43)⋊C4—22no—
145(C2×D43)⋊C4—22no—
146(C2×D43)⋊C4—22no—
147C4⋊Dic43—21no—
148C4⋊Dic43—21no—
149Dic43⋊C4—24no—
150Dic43⋊C4—24no—
151Dic43⋊C4—24no—
152Dic43⋊C4—21no—
153Dic43⋊C4—21no—
154Dic43⋊C4—21no—
155Dic43⋊C4—21no—
156C4×Dic43—24no—
157C4×Dic43—21no—
158C4×Dic43—21no—
159C4×Dic43—21no—
160C4×Dic43—21no—
161#10621877—22no—
162#10621877—41no—
163C2×C43⋊C8—41no—
164C2×C43⋊C8—41no—
165C23×C43C2×C22⋊C411yescharacteristic
166C22×D43—22no—
167C22×D43—42no—
168C22×D43—42no—
169C22×D43—41no—
170C22×D43—41no—
171Q8×C43—24no—
172Q8×C43—42no—
173C2×C4×C43—21no—
174C2×C4×C43—21no—
175C2×C4×C43—22no—
176C2×C4×C43—22no—
177C2×C4×C43—22no—
178C2×C4×C43—41no—
179C2×C4×C43—42no—
180C2×C4×C43—41no—
181C2×C4×C43—41no—
182C2×C4×C43C2×C22⋊C411yescharacteristic
183C2×C4×C43C2×C22⋊C411yescharacteristic
184C2×C4×C43#12011yescharacteristic
185C2×C4×C43#12011yescharacteristic
186C2×C4×C43#12011yescharacteristic
187C2×C4×C43#12011yescharacteristic
188C2×Dic43—21no—
189C2×Dic43—21no—
190C2×Dic43—21no—
191C2×Dic43—21no—
192C2×Dic43—21no—
193C2×Dic43—22no—
194C2×Dic43—21no—
195C2×Dic43—21no—
196C2×Dic43—42no—
197C2×Dic43—41no—
198C2×Dic43—41no—
199C2×Dic43#10412yes—
200D172—42no—
201D172—42no—
202C4×D43—48no—
203Dic86—42no—
204Dic86—42no—
205Dic86—42no—
206Dic86—42no—
207C8×C43—42no—
208C8×C43—81no—
209C43⋊C8—42no—
210C43⋊C8—81no—
211#8368—431nomaximal, Sylow
212C22×C43—21no—
213C22×C43—21no—
214C22×C43#37911yescharacteristic
215C22×C43C2×#10411yescharacteristic
216C22×C43#42111yescharacteristic
217C2×D43—42no—
218C2×D43—42no—
219C2×D43—42no—
220C2×D43—82no—
221C2×D43—82no—
222C4×C43—21no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—21no—
227C4×C43—42no—
228C4×C43—42no—
229C4×C43#41312yes—
230Dic43—22no—
231Dic43—41no—
232Dic43—41no—
233Dic43—42no—
234Dic43—41no—
235C2×#556—431no—
236C4×#101—431no—
237#1527—431no—
238#1527—431no—
239#1491—431no—
240#1491D4311yescharacteristic, complemented
241#1467—431no—
242C2×C43—21no—
243C2×C43—21no—
244C2×C43#178511yescharacteristic
245C2×C43#178911yescharacteristic
246C2×C43#179611yescharacteristic
247D43—82no—
248#556—862no—
249#556—862no—
250#556—862no—
251#556—862no—
252C2×C4⋊Q8—431no—
253C2×#126—861no—
254C2×#126—861no—
255C2×#124—431no—
256C2×#124—431no—
257C2×C22⋊Q8—861no—
258C2×C4×Q8—431no—
259C2×C4×Q8—431no—
260C2×C4×Q8C2×D4311yescharacteristic
261C2×C4×D4—431no—
262C2×#117—861no—
263#432—431no—
264#432C2×D4311yescharacteristic
265C2×#101—861no—
266C4×M16—431no—
267C4×M16C2×D4311yescharacteristic
268#343—861no—
269#329—862no—
270#329—862no—
271Q8⋊C8—22no—
272Q8⋊C8—862no—
273#324—861no—
274#324—861no—
275C43#836811yescharacteristic, complemented, Sylow
276C22×Q8—431no—
277C22×Q8—431no—
278C22×Q8C4×D4311yescharacteristic
279C22×D4—431no—
280C23×C4—861no—
281C2×M16—21no—
282C2×M16—861no—
283C4⋊Q8—862no—
284C4⋊Q8—862no—
285#126—864no—
286#126—864no—
287#126—864no—
288#126—864no—
289#124—432no—
290#124—432no—
291#124—862no—
292#124—862no—
293#124—861no—
294#124—861no—
295C22⋊Q8—864no—
296C22⋊Q8—864no—
297C4×Q8—21no—
298C4×Q8—21no—
299C4×Q8—862no—
300C4×Q8—862no—
301C4×Q8—861no—
302C4×Q8—861no—
303C4×Q8—861no—
304C4×Q8—861no—
305C4×Q8D17212yes—
306C4×Q8C22⋊D4312yes—
307C4×D4—862no—
308C4×D4—862no—
309#117—864no—
310#117—864no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—431no—
313C2×C4⋊C4—431no—
314C2×C4⋊C4—431no—
315C2×C4⋊C4—861no—
316C2×C4⋊C4—861no—
317C2×C4⋊C4—861no—
318C2×C4⋊C4C4×D4311yescharacteristic
319C2×C22⋊C4—861no—
320C2×C22⋊C4—861no—
321C2×C22⋊C4—861no—
322C2×C22⋊C4—861no—
323C2×C22⋊C4—861no—
324C2×C42—21no—
325C2×C42—431no—
326C2×C42—431no—
327C2×C42—861no—
328C2×C42C22×D4311yescharacteristic
329C4⋊C8—21no—
330C4⋊C8—861no—
331#101—864no—
332C22⋊C8—21no—
333C22⋊C8—861no—
334#97—21no—
335#97—21no—
336#97—861no—
337#97—861no—
338C4×C8—21no—
339C4×C8—861no—
340C24—861no—
341C2×Q8—21no—
342C2×Q8—42no—
343C2×Q8—432no—
344C2×Q8—862no—
345C2×Q8—861no—
346C2×Q8—861no—
347C2×Q8—861no—
348C2×Q8—1721no—
349C2×Q8—1722no—
350C2×Q8(C2×D43)⋊C412yes—
351C2×D4—432no—
352C2×D4—861no—
353C2×D4—1722no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—431no—
357C22×C4—431no—
358C22×C4—431no—
359C22×C4—431no—
360C22×C4—864no—
361C22×C4—861no—
362C22×C4—1722no—
363C22×C4—1722no—
364C22×C4C2×C4×D4311yescharacteristic
365C22×C4D4×D4311yescharacteristic
366C22×C4D4×D4311yescharacteristic
367M16—22no—
368M16—41no—
369M16—862no—
370M16—1721no—
371C2×C8—41no—
372C2×C8—41no—
373C2×C8—1721no—
374C2×C8—1721no—
375C4⋊C4—21no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—864no—
379C4⋊C4—864no—
380C4⋊C4—864no—
381C4⋊C4—861no—
382C4⋊C4—861no—
383C4⋊C4—861no—
384C4⋊C4—861no—
385C4⋊C4—861no—
386C4⋊C4—861no—
387C4⋊C4(C2×D43)⋊C412yes—
388C22⋊C4—864no—
389C22⋊C4—864no—
390C22⋊C4—864no—
391C22⋊C4—862no—
392C22⋊C4—862no—
393C22⋊C4—862no—
394C22⋊C4—862no—
395C42—22no—
396C42—22no—
397C42—864no—
398C42—861no—
399C42—861no—
400C42—861no—
401C42—861no—
402C42C2×D17211yescharacteristic
403C42D4×D4311yescharacteristic
404C42D4×D4311yescharacteristic
405C42C2×C22⋊D4311yescharacteristic
406C23—862no—
407C23—1722no—
408C23—1722no—
409C23—1721no—
410C23—1721no—
411C23C22⋊C4×D4311yescharacteristic
412Q8—24no—
413Q8—42no—
414Q8—1722no—
415Q8—1722no—
416Q8—1722no—
417Q8—1722no—
418D4—1722no—
419D4—1722no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—432no—
430C2×C4—861no—
431C2×C4—861no—
432C2×C4—861no—
433C2×C4—861no—
434C2×C4—861no—
435C2×C4—861no—
436C2×C4—861no—
437C2×C4—862no—
438C2×C4—1728no—
439C2×C4—1722no—
440C2×C4—1721no—
441C2×C4—1721no—
442C2×C4C22⋊C4×D4311yescharacteristic
443C2×C4C2×(C2×D43)⋊C411yescharacteristic
444C2×C4#1306329311yescharacteristic
445C2×C4#1306329311yescharacteristic
446C2×C4#1306329511yescharacteristic
447C2×C4#1306329511yescharacteristic
448C8—42no—
449C8—81no—
450C8—3441no—
451C8—1722no—
452C22—21no—
453C22—21no—
454C22—3442no—
455C22—3442no—
456C22—1722no—
457C22—1722no—
458C22—1722no—
459C22#1458275411yescharacteristic
460C22#104×D4311yescharacteristic
461C22#1458291411yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—21no—
467C4—42no—
468C4—42no—
469C4—862no—
470C4—1722no—
471C4—1721no—
472C4—1721no—
473C4—1721no—
474C4#1458288112yes—
475C2—21no—
476C2—21no—
477C2—3442no—
478C2#1913452111yescharacteristic
479C2#1913453711yescharacteristic
480C2#1913456711yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1491C2
socleC22×C43#379
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#1491D43
hypocenterC43#8368
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
2. C4×#13063243C2semidirect
5. #19133042C2semidirect
6. #19132938C2semidirect
7. C43×#1491C2semidirect
240. #1491D43semidirect
275. C43#8368semidirect

Maximal subgroups

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

subgroupindex
C2×#145836212
C4×#130632432
#191331942
#191331922
#191330422
#191329382
C43×#14912
#836843