Finite Group Databasebeta

← #24989103

Subgroups — #24989103

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×#14583516C211yesmaximal, characteristic
2#19134676C211yesmaximal, characteristic, complemented
3#19134670C211yesmaximal, characteristic, complemented
4#19133129C211yesmaximal, characteristic, complemented
5#19133127C211yesmaximal, characteristic, complemented
6#19133124C211yesmaximal, characteristic
7C43×#1510C211yesmaximal, characteristic
8#14583516—22no—
9#14583516—22no—
10#14583516—22no—
11#14583516—22no—
12C2×#13063324C411yescharacteristic, complemented
13C2×#13063318—21no—
14C2×#13063312—21no—
15C2×#13063312C411yescharacteristic, complemented
16C2×#13063306—21no—
17C2×#13063304C2211yescharacteristic
18C2×#13063302—21no—
19C2×#13063290C411yescharacteristic, complemented
20C2×D4×Dic43C411yescharacteristic, complemented
21C2×#13063284C2211yescharacteristic
22#14582863C2211yescharacteristic
23#14582762C2211yescharacteristic
24#14582667—21no—
25#14582667—21no—
26#14582665—21no—
27#14582665—21no—
28#14582637—22no—
29#14582635—22no—
30#14582633—22no—
31C2×#121×C43C2211yescharacteristic
32C43×#407C2211yescharacteristic
33C43×#381C2211yescharacteristic
34C43×#327—22no—
35C22×Dic86—21no—
36C22×Dic86C2×C411yescharacteristic
37C23×Dic43—21no—
38C2×#10621877—21no—
39#13063324—22no—
40#13063324—22no—
41#13063318—24no—
42#13063318—24no—
43#13063312—24no—
44#13063312—24no—
45#13063312—22no—
46#13063312—22no—
47#13063306—24no—
48#13063306—24no—
49#13063304—21no—
50#13063304—21no—
51#13063304D412yes—
52#13063304D412yes—
53#13063302—24no—
54#13063302—24no—
55#13063290—22no—
56#13063290—22no—
57D4×Dic43—22no—
58D4×Dic43—22no—
59#13063284—21no—
60#13063284—21no—
61#13063284—21no—
62#13063284—21no—
63C2×C4⋊Dic43C2×C411yescharacteristic
64C2×C4⋊Dic43D411yescharacteristic
65C2×C4⋊Dic43D411yescharacteristic
66C2×Dic43⋊C4—21no—
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4—21no—
69C2×C22⋊Dic43—21no—
70C2×C22⋊Dic43—21no—
71C2×C22⋊Dic43—21no—
72C2×C22⋊Dic43—21no—
73C2×C22⋊Dic43—21no—
74C2×C22⋊Dic43D411yescharacteristic
75C2×C22⋊Dic43D411yescharacteristic
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×D4×C43—21no—
84C22×D4×C43C2×C411yescharacteristic
85C23×C4×C43C2311yescharacteristic
86C2×M16×C43—21no—
87#121×C43—21no—
88#121×C43—21no—
89#121×C43D412yes—
90#121×C43D412yes—
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×C43—21no—
99C24×C43C2×D411yescharacteristic
100C2×D4×C43—21no—
101C2×D4×C43—22no—
102C2×D4×C43—22no—
103C2×D4×C43—42no—
104C2×D4×C43—82no—
105C2×D4×C43C22⋊C412yes—
106C22×C4×C43—21no—
107C22×C4×C43—42no—
108C22×C4×C43—41no—
109C22×C4×C43C22×C411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43C2×D411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×Dic43—24no—
116C22×Dic43—21no—
117C22×Dic43—21no—
118C22×Dic43—41no—
119C22×Dic43—82no—
120C22×Dic43C22⋊C411yescharacteristic
121C22×Dic43C22⋊C411yescharacteristic
122C22×Dic43C22⋊C411yescharacteristic
123C22×Dic43C22⋊C411yescharacteristic
124C2×Dic86—21no—
125C2×Dic86—24no—
126C2×Dic86—42no—
127C2×Dic86—82no—
128C2×Dic86C22⋊C412yes—
129M16×C43—42no—
130C2×C8×C43—41no—
131C4⋊C4×C43—21no—
132C4⋊C4×C43C22⋊C412yes—
133C22⋊C4×C43—22no—
134C22⋊C4×C43—22no—
135C22⋊C4×C43—42no—
136C22⋊Dic43—24no—
137C22⋊Dic43—24no—
138C22⋊Dic43—24no—
139C22⋊Dic43—22no—
140C22⋊Dic43—22no—
141C22⋊Dic43—21no—
142C22⋊Dic43—21no—
143C22⋊Dic43—21no—
144C22⋊Dic43—21no—
145C22⋊Dic43—42no—
146C4⋊Dic43—21no—
147C4⋊Dic43—21no—
148C4⋊Dic43—21no—
149C4⋊Dic43—21no—
150C4⋊Dic43—21no—
151C4⋊Dic43C22⋊C412yes—
152Dic43⋊C4—24no—
153Dic43⋊C4—24no—
154Dic43⋊C4—22no—
155Dic43⋊C4—22no—
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—22no—
165C23×C43—41no—
166C23×C43—41no—
167C23×C43—42no—
168C23×C43—42no—
169C23×C43—42no—
170C23×C43C2×C22⋊C411yescharacteristic
171C23×C43#12011yescharacteristic
172C23×C43#12011yescharacteristic
173D4×C43—42no—
174D4×C43—42no—
175D4×C43—82no—
176D4×C43—82no—
177C2×C4×C43—22no—
178C2×C4×C43—22no—
179C2×C4×C43—22no—
180C2×C4×C43—41no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
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
192C2×Dic43—21no—
193C2×Dic43—21no—
194C2×Dic43—21no—
195C2×Dic43—22no—
196C2×Dic43—21no—
197C2×Dic43—22no—
198C2×Dic43—42no—
199C2×Dic43—42no—
200C2×Dic43—41no—
201C2×Dic43—41no—
202C2×Dic43—41no—
203C2×Dic43—41no—
204C2×Dic43—84no—
205C2×Dic43—81no—
206C2×Dic43—81no—
207C2×Dic43—81no—
208Dic86—42no—
209Dic86—42no—
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—42no—
223C22×C43—42no—
224C22×C43—42no—
225C22×C43—82no—
226C22×C43—84no—
227C22×C43#37911yescharacteristic
228C22×C43#41012yes—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—42no—
234C4×C43—161no—
235Dic43—41no—
236Dic43—42no—
237Dic43—41no—
238Dic43—41no—
239Dic43—41no—
240Dic43—42no—
241Dic43—161no—
242C2×#542—431no—
243#1822—431no—
244#1820—431no—
245#1511—431no—
246#1511—431no—
247#1510—431no—
248#1510D4311yescharacteristic
249C2×C43—22no—
250C2×C43—41no—
251C2×C43—41no—
252C2×C43—82no—
253C2×C43#178211yescharacteristic
254C2×C43#179511yescharacteristic
255C2×C43#179611yescharacteristic
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—431no—
266C2×C22⋊Q8—861no—
267C2×#121C2×D4311yescharacteristic
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—862no—
280#328—862no—
281#327—22no—
282#327—862no—
283C43#851911yescharacteristic, complemented, Sylow
284C22×Q8—431no—
285C22×Q8—861no—
286C22×D4—21no—
287C22×D4C4×D4311yescharacteristic
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—862no—
297#124—864no—
298#124—864no—
299#124—862no—
300#123—864no—
301#123—864no—
302C22⋊Q8—432no—
303C22⋊Q8—432no—
304C22⋊Q8—864no—
305C22⋊Q8—864no—
306C22⋊Q8—861no—
307C22⋊Q8—861no—
308#121—21no—
309#121—21no—
310#121D17212yes—
311#121C22⋊D4312yes—
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—431no—
321C2×C4⋊C4—431no—
322C2×C4⋊C4—431no—
323C2×C4⋊C4—861no—
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—21no—
348C24D4×D4311yescharacteristic
349C2×Q8—432no—
350C2×Q8—864no—
351C2×Q8—861no—
352C2×Q8—3442no—
353C2×Q8—1722no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—21no—
357C2×D4—42no—
358C2×D4—82no—
359C2×D4(C2×D43)⋊C412yes—
360C22×C4—21no—
361C22×C4—42no—
362C22×C4—41no—
363C22×C4—431no—
364C22×C4—431no—
365C22×C4—431no—
366C22×C4—431no—
367C22×C4—864no—
368C22×C4—861no—
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—432no—
384C4⋊C4—864no—
385C4⋊C4—864no—
386C4⋊C4—861no—
387C4⋊C4—861no—
388C4⋊C4—861no—
389C4⋊C4—862no—
390C4⋊C4—861no—
391C4⋊C4—861no—
392C4⋊C4—862no—
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—862no—
403C22⋊C4—861no—
404C22⋊C4—861no—
405C22⋊C4—862no—
406C22⋊C4—1722no—
407C42—864no—
408C42—861no—
409C42—861no—
410C42—861no—
411C42—861no—
412C23—22no—
413C23—22no—
414C23—41no—
415C23—41no—
416C23—42no—
417C23—42no—
418C23—42no—
419C23C22⋊C4×D4311yescharacteristic
420C23#1306329311yescharacteristic
421C23#1306329511yescharacteristic
422Q8—3444no—
423Q8—1722no—
424Q8—1722no—
425D4—42no—
426D4—42no—
427D4—82no—
428D4—82no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—81no—
438C2×C4—81no—
439C2×C4—81no—
440C2×C4—861no—
441C2×C4—861no—
442C2×C4—862no—
443C2×C4—861no—
444C2×C4—861no—
445C2×C4—862no—
446C2×C4—3444no—
447C2×C4—3441no—
448C2×C4—3441no—
449C2×C4—3441no—
450C2×C4—1722no—
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—42no—
471C22—42no—
472C22—42no—
473C22—82no—
474C22—84no—
475C22#1458275411yescharacteristic
476C22#1458287112yes—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—42no—
482C4—161no—
483C4—1722no—
484C4—1721no—
485C4—1722no—
486C4—1721no—
487C4—1721no—
488C4—1721no—
489C4—6881no—
490C2—22no—
491C2—41no—
492C2—41no—
493C2—82no—
494C2#1913451111yescharacteristic
495C2#1913456211yescharacteristic
496C2#1913456911yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1510C2
socleC22×C43#379
prime radicalC2×#121×C43C22
cosocleC23×C4×C43C23
hypercenter#1510D43
hypocenterC43#8519
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1510

Complements

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

NH ≅ G/Ntype
2. #19134676C2semidirect
3. #19134670C2semidirect
4. #19133129C2semidirect
5. #19133127C2semidirect
12. C2×#13063324C4semidirect
15. C2×#13063312C4semidirect
19. C2×#13063290C4semidirect
20. C2×D4×Dic43C4semidirect
283. C43#8519semidirect

Maximal subgroups

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

subgroupindex
C2×#145835162
#191346762
#191346702
#191331292
#191331272
#191331242
C43×#15102
#851943