Finite Group Databasebeta

← #24989101

Subgroups — #24989101

Order 11008.

754 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 107 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×#14583522C211yesmaximal, characteristic
2#19134676C211yesmaximal, characteristic, complemented
3#19134670C211yesmaximal, characteristic, complemented
4#19133128C211yesmaximal, characteristic, complemented
5#19133125C211yesmaximal, characteristic
6#19133123C211yesmaximal, characteristic
7C43×#1511C211yesmaximal, characteristic, complemented
8#14583522—22no—
9#14583522—22no—
10#14583522—22no—
11#14583522—22no—
12C2×#13063324C411yescharacteristic, complemented
13C2×#13063320—21no—
14C2×#13063314C411yescharacteristic, complemented
15C2×#13063311—21no—
16C2×#13063307—21no—
17C2×#13063305—21no—
18C2×#13063299C2211yescharacteristic
19C2×Q8×Dic43C411yescharacteristic, complemented
20C2×#13063287C411yescharacteristic, complemented
21C2×#13063284C2211yescharacteristic
22#14582863C2211yescharacteristic
23#14582762C2211yescharacteristic
24#14582667—21no—
25#14582667—21no—
26#14582665—21no—
27#14582665—21no—
28#14582636—22no—
29#14582634—22no—
30#14582632—22no—
31C2×C22⋊Q8×C43C2211yescharacteristic
32C43×#407C2211yescharacteristic
33C43×#381C2211yescharacteristic
34C43×#328—22no—
35C22×Dic86—21no—
36C22×D172C2×C411yescharacteristic
37C22×C22⋊D43—21no—
38C22×C4×D43—21no—
39C2×#10621877—21no—
40#13063324—22no—
41#13063324—22no—
42#13063320—24no—
43#13063320—24no—
44#13063314—22no—
45#13063314—22no—
46#13063311—24no—
47#13063311—24no—
48#13063307—24no—
49#13063307—24no—
50#13063305—24no—
51#13063305—24no—
52#13063299—21no—
53#13063299—21no—
54#13063299D412yes—
55#13063299D412yes—
56Q8×Dic43—22no—
57Q8×Dic43—22no—
58#13063287—22no—
59#13063287—22no—
60#13063284—21no—
61#13063284—21no—
62#13063284—21no—
63#13063284—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43C2×C411yescharacteristic
66C2×C4⋊Dic43D411yescharacteristic
67C2×C4⋊Dic43D411yescharacteristic
68C2×Dic43⋊C4—21no—
69C2×C22⋊Dic43—21no—
70C2×C22⋊Dic43D411yescharacteristic
71C2×C22⋊Dic43D411yescharacteristic
72C2×(C2×D43)⋊C4—21no—
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4—21no—
75C2×(C2×D43)⋊C4—21no—
76C2×C4×Dic43—21no—
77C2×C4×Dic43C2×C411yescharacteristic
78C2×C4×Dic43C2×C411yescharacteristic
79C22⋊(C43⋊C8)—21no—
80C22⋊(C43⋊C8)—21no—
81C43⋊#95—21no—
82C43⋊#95—21no—
83C22×Q8×C43C2×C411yescharacteristic
84C23×C4×C43C2311yescharacteristic
85C2×M16×C43—21no—
86C22⋊Q8×C43—21no—
87C22⋊Q8×C43—21no—
88C22⋊Q8×C43D412yes—
89C22⋊Q8×C43D412yes—
90C2×C4⋊C4×C43—21no—
91C2×C4⋊C4×C43C2×C411yescharacteristic
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C22⋊C8×C43—21no—
95C22⋊C8×C43—21no—
96#95×C43—21no—
97#95×C43—21no—
98C24×C43C2×D411yescharacteristic
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×C43—42no—
106C22×C4×C43—41no—
107C22×C4×C43C22×C411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43C2×D411yescharacteristic
113C2×C22⋊D43—22no—
114C2×C22⋊D43—22no—
115C2×C22⋊D43—82no—
116C22×Dic43—21no—
117C22×Dic43—41no—
118C22×Dic43C22⋊C411yescharacteristic
119C22×Dic43C22⋊C411yescharacteristic
120C22×Dic43C22⋊C411yescharacteristic
121C22×Dic43C22⋊C411yescharacteristic
122C2×D172—21no—
123C2×D172—42no—
124C2×D172C22⋊C412yes—
125C2×C4×D43—24no—
126C2×C4×D43—82no—
127C2×Dic86—24no—
128C2×Dic86—82no—
129M16×C43—42no—
130C2×C8×C43—41no—
131C4⋊C4×C43—21no—
132C4⋊C4×C43—22no—
133C4⋊C4×C43—22no—
134C4⋊C4×C43C22⋊C412yes—
135C22⋊C4×C43—22no—
136C22⋊C4×C43—22no—
137C22⋊C4×C43—42no—
138C22⋊Dic43—21no—
139C22⋊Dic43—21no—
140C22⋊Dic43—21no—
141C22⋊Dic43—21no—
142C22⋊Dic43—42no—
143(C2×D43)⋊C4—24no—
144(C2×D43)⋊C4—24no—
145(C2×D43)⋊C4—24no—
146(C2×D43)⋊C4—22no—
147(C2×D43)⋊C4—22no—
148C4⋊Dic43—24no—
149C4⋊Dic43—21no—
150C4⋊Dic43—21no—
151C4⋊Dic43—21no—
152C4⋊Dic43—21no—
153C4⋊Dic43—21no—
154C4⋊Dic43C22⋊C412yes—
155Dic43⋊C4—24no—
156C4×Dic43—24no—
157C4×Dic43—21no—
158C4×Dic43—21no—
159C4×Dic43—21no—
160C4×Dic43—21no—
161#10621877—42no—
162C2×C43⋊C8—41no—
163C23×C43—22no—
164C23×C43—41no—
165C23×C43—41no—
166C23×C43C2×C22⋊C411yescharacteristic
167C23×C43#12011yescharacteristic
168C23×C43#12011yescharacteristic
169C22×D43—22no—
170C22×D43—42no—
171C22×D43—42no—
172C22×D43—42no—
173Q8×C43—42no—
174Q8×C43—42no—
175C2×C4×C43—22no—
176C2×C4×C43—22no—
177C2×C4×C43—22no—
178C2×C4×C43—22no—
179C2×C4×C43—41no—
180C2×C4×C43—41no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—42no—
184C2×C4×C43—42no—
185C2×C4×C43—81no—
186C2×C4×C43—81no—
187C2×C4×C43—81no—
188C2×C4×C43C2×C22⋊C411yescharacteristic
189C2×C4×C43C2×C22⋊C411yescharacteristic
190C2×C4×C43#12011yescharacteristic
191C2×C4×C43#12011yescharacteristic
192C22⋊D43—82no—
193C22⋊D43—82no—
194C2×Dic43—21no—
195C2×Dic43—21no—
196C2×Dic43—22no—
197C2×Dic43—21no—
198C2×Dic43—21no—
199C2×Dic43—42no—
200C2×Dic43—41no—
201C2×Dic43—41no—
202C2×Dic43—41no—
203C2×Dic43—41no—
204C2×Dic43—81no—
205C2×Dic43—81no—
206C2×Dic43—81no—
207D172—42no—
208D172—42no—
209C4×D43—84no—
210Dic86—84no—
211C8×C43—81no—
212C43⋊C8—81no—
213#8519—431nomaximal, Sylow
214C22×C43—21no—
215C22×C43—21no—
216C22×C43—21no—
217C22×C43—21no—
218C22×C43—21no—
219C22×C43—21no—
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—82no—
223C22×C43#37911yescharacteristic
224C22×C43#41012yes—
225C2×D43—42no—
226C2×D43—42no—
227C2×D43—42no—
228C2×D43—84no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—42no—
234C4×C43—42no—
235C4×C43—161no—
236Dic43—41no—
237Dic43—42no—
238Dic43—41no—
239Dic43—41no—
240Dic43—41no—
241Dic43—161no—
242C2×#542—431no—
243#1822—431no—
244#1820—431no—
245#1511—431no—
246#1511D4311yescharacteristic, complemented
247#1510—431no—
248#1510—431no—
249C2×C43—22no—
250C2×C43—41no—
251C2×C43—41no—
252C2×C43#178211yescharacteristic
253C2×C43#179511yescharacteristic
254C2×C43#179611yescharacteristic
255D43—82no—
256#542—862no—
257#542—862no—
258#542—862no—
259#542—862no—
260C2×C4⋊Q8—431no—
261C2×#126—861no—
262C2×#124—431no—
263C2×#124—861no—
264C2×#123—861no—
265C2×C22⋊Q8—861no—
266C2×C22⋊Q8C2×D4311yescharacteristic
267C2×#121—431no—
268C2×C4×Q8—431no—
269C2×C4×D4—431no—
270C2×#117—431no—
271#407—431no—
272#407C2×D4311yescharacteristic
273#381—431no—
274#381C2×D4311yescharacteristic
275#343—861no—
276#343—861no—
277#342—861no—
278#342—861no—
279#328—22no—
280#328—862no—
281#327—862no—
282#327—862no—
283C43#851911yescharacteristic, complemented, Sylow
284C22×Q8—861no—
285C22×Q8C4×D4311yescharacteristic
286C22×D4—431no—
287C22×D4—861no—
288C23×C4—861no—
289C23×C4C22×D4311yescharacteristic
290C2×M16—21no—
291C2×M16—861no—
292C4⋊Q8—862no—
293C4⋊Q8—862no—
294#126—864no—
295#126—864no—
296#124—864no—
297#124—864no—
298#124—862no—
299#124—862no—
300#123—864no—
301#123—864no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—864no—
305C22⋊Q8—864no—
306C22⋊Q8D17212yes—
307C22⋊Q8C22⋊D4312yes—
308#121—432no—
309#121—432no—
310#121—861no—
311#121—861no—
312C4×Q8—862no—
313C4×Q8—862no—
314C4×D4—862no—
315C4×D4—862no—
316#117—861no—
317#117—861no—
318#117—861no—
319#117—861no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—431no—
322C2×C4⋊C4—431no—
323C2×C4⋊C4—431no—
324C2×C4⋊C4—861no—
325C2×C4⋊C4—861no—
326C2×C4⋊C4C4×D4311yescharacteristic
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—431no—
330C2×C22⋊C4—431no—
331C2×C22⋊C4—861no—
332C2×C22⋊C4—861no—
333C2×C22⋊C4—861no—
334C2×C22⋊C4—861no—
335C2×C22⋊C4—861no—
336C2×C42—431no—
337C2×C42—431no—
338C2×C42—861no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C22⋊C8—861no—
342C22⋊C8—861no—
343#95—21no—
344#95—21no—
345#95—861no—
346#95—861no—
347C24—861no—
348C24D4×D4311yescharacteristic
349C2×Q8—21no—
350C2×Q8—42no—
351C2×Q8—864no—
352C2×Q8—3442no—
353C2×Q8(C2×D43)⋊C412yes—
354C2×D4—432no—
355C2×D4—862no—
356C2×D4—862no—
357C2×D4—861no—
358C2×D4—3442no—
359C2×D4—1722no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—42no—
363C22×C4—41no—
364C22×C4—431no—
365C22×C4—431no—
366C22×C4—431no—
367C22×C4—431no—
368C22×C4—864no—
369C22×C4—861no—
370C22×C4—3442no—
371C22×C4—1721no—
372C22×C4C2×C4×D4311yescharacteristic
373C22×C4C2×D17211yescharacteristic
374C22×C4D4×D4311yescharacteristic
375C22×C4D4×D4311yescharacteristic
376C22×C4D4×D4311yescharacteristic
377C22×C4C2×C22⋊D4311yescharacteristic
378M16—42no—
379M16—1722no—
380C2×C8—41no—
381C2×C8—1721no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—432no—
386C4⋊C4—864no—
387C4⋊C4—864no—
388C4⋊C4—861no—
389C4⋊C4—861no—
390C4⋊C4—861no—
391C4⋊C4—861no—
392C4⋊C4—861no—
393C4⋊C4(C2×D43)⋊C412yes—
394C22⋊C4—22no—
395C22⋊C4—22no—
396C22⋊C4—42no—
397C22⋊C4—864no—
398C22⋊C4—864no—
399C22⋊C4—864no—
400C22⋊C4—861no—
401C22⋊C4—861no—
402C22⋊C4—861no—
403C22⋊C4—861no—
404C22⋊C4—862no—
405C22⋊C4—862no—
406C22⋊C4—1722no—
407C42—864no—
408C42—861no—
409C42—861no—
410C42—861no—
411C42—861no—
412C23—22no—
413C23—41no—
414C23—41no—
415C23—862no—
416C23—1722no—
417C23—1722no—
418C23—1722no—
419C23C22⋊C4×D4311yescharacteristic
420C23#1306329311yescharacteristic
421C23#1306329511yescharacteristic
422Q8—42no—
423Q8—42no—
424Q8—3444no—
425D4—3442no—
426D4—3442no—
427D4—1722no—
428D4—1722no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—81no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—861no—
443C2×C4—861no—
444C2×C4—861no—
445C2×C4—862no—
446C2×C4—861no—
447C2×C4—3444no—
448C2×C4—3441no—
449C2×C4—3441no—
450C2×C4—3441no—
451C2×C4—1722no—
452C2×C4—1721no—
453C2×C4—1721no—
454C2×C4—1721no—
455C2×C4—1721no—
456C2×C4C22⋊C4×D4311yescharacteristic
457C2×C4C2×(C2×D43)⋊C411yescharacteristic
458C2×C4#1306329311yescharacteristic
459C2×C4#1306329511yescharacteristic
460C8—81no—
461C8—3441no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—82no—
471C22—3444no—
472C22—1722no—
473C22—1722no—
474C22—1722no—
475C22#1458275411yescharacteristic
476C22#1458287112yes—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—42no—
482C4—42no—
483C4—161no—
484C4—1721no—
485C4—1722no—
486C4—1721no—
487C4—1721no—
488C4—1721no—
489C4—6881no—
490C2—22no—
491C2—41no—
492C2—41no—
493C2—3442no—
494C2#1913451111yescharacteristic
495C2#1913456411yescharacteristic
496C2#1913456711yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1511C2
socleC22×C43#379
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1511D43
hypocenterC43#8519
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1511

Complements

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

NH ≅ G/Ntype
2. #19134676C2semidirect
3. #19134670C2semidirect
4. #19133128C2semidirect
7. C43×#1511C2semidirect
12. C2×#13063324C4semidirect
14. C2×#13063314C4semidirect
19. C2×Q8×Dic43C4semidirect
20. C2×#13063287C4semidirect
246. #1511D43semidirect
283. C43#8519semidirect

Maximal subgroups

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

subgroupindex
C2×#145835222
#191346762
#191346702
#191331282
#191331252
#191331232
C43×#15112
#851943