Finite Group Databasebeta

← #25101741

Subgroups — #25101741

Order 11008.

1150 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583520C211yesmaximal, characteristic
2C2×#14582960C211yesmaximal, characteristic, complemented
3#19135547C211yesmaximal, characteristic, complemented
4#19135543C211yesmaximal, characteristic, complemented
5#19135527C211yesmaximal, characteristic, complemented
6#19135527C211yesmaximal, characteristic, complemented
7#19134917C211yesmaximal, characteristic
8#19134912C211yesmaximal, characteristic
9#19134907C211yesmaximal, characteristic, complemented
10#19134902C211yesmaximal, characteristic, complemented
11#19134428C211yesmaximal, characteristic, complemented
12#19134423C211yesmaximal, characteristic, complemented
13C4×#13063248C211yesmaximal, characteristic, complemented
14C4×#13063245C211yesmaximal, characteristic, complemented
15C43×#2274C211yesmaximal, characteristic, complemented
16#14583520—24no—
17#14583520C418yescomplemented
18C2×#13063325C2211yescharacteristic
19C2×#13063320—21no—
20C2×#13063313C2211yescharacteristic
21C2×#13063311—21no—
22C2×#13063307—21no—
23C2×#13063304C2211yescharacteristic
24C2×#13063303—21no—
25C2×#13063299C2211yescharacteristic
26C2×C4×Dic86C2211yescharacteristic
27C2×C4×D172C2211yescharacteristic
28#14582960—24no—
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×#13063236C2211yescharacteristic
42C2×C4×C43⋊C8C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51C2×#117×C43C2211yescharacteristic
52C2×#117×C43C2211yescharacteristic
53C22×C4⋊C4×C43C2211yescharacteristic
54C4×C4⋊C4×C43—21no—
55C4×C4⋊C4×C43—21no—
56C4×C4⋊C4×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic
60C4×C22⋊C4×C43—21no—
61C4×C22⋊C4×C43—21no—
62C22×Dic86—21no—
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C22×C4×D43—21no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063325—22no—
72#13063325C2×C414yescomplemented
73#13063320—28no—
74#13063313—22no—
75#13063313C2×C414yescomplemented
76#13063311—28no—
77#13063307—28no—
78#13063304—22no—
79#13063304C2×C414yes—
80#13063303—28no—
81#13063299—22no—
82#13063299C2×C414yes—
83C4×Dic86—22no—
84C4×Dic86C2×C414yescomplemented
85C4×D172—22no—
86C4×D172C2×C414yescomplemented
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×C22⋊Dic43—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×C4×Dic43—21no—
98C4⋊(C43⋊C8)—22no—
99C4⋊(C43⋊C8)—22no—
100#13063248—22no—
101#13063248—22no—
102#13063248—22no—
103#13063248—22no—
104#13063245—22no—
105#13063245—22no—
106#13063245—22no—
107#13063245—22no—
108C22⋊(C43⋊C8)—22no—
109C22⋊(C43⋊C8)—22no—
110#13063236—22no—
111C4×C43⋊C8—22no—
112C23×C4×C43—21no—
113C23×C4×C43C2311yescharacteristic
114#117×C43—22no—
115#117×C43—22no—
116#117×C43C2×C414yes—
117#117×C43D414yes—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43—22no—
120C2×C4⋊C4×C43—22no—
121C2×C4⋊C4×C43D411yescharacteristic
122C2×C4⋊C4×C43D411yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43D411yescharacteristic
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C42×C43—21no—
131C2×C42×C43—21no—
132C2×C42×C43—21no—
133C2×C42×C43—21no—
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C2×C42×C43C2311yescharacteristic
137#95×C43—21no—
138#95×C43—21no—
139#95×C43—21no—
140#95×C43—21no—
141C24×C43C2×D411yescharacteristic
142C23×D43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—24no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—81no—
153C22×C4×C43—81no—
154C22×C4×C43C22×C412yes—
155C22×C4×C43C2×D412yes—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C2×C22⋊D43—24no—
163C2×C22⋊D43—81no—
164C2×C22⋊D43—81no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172C22×C412yes—
174C2×C4×D43—24no—
175C2×C4×D43—81no—
176C2×C4×D43—81no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—24no—
183C2×Dic86—81no—
184C2×Dic86—81no—
185C2×Dic86C22×C412yes—
186C4⋊C4×C43—24no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43C22⋊C414yes—
192C4⋊C4×C43C22⋊C414yes—
193C4⋊C4×C43#4112yes—
194C4⋊C4×C43#4112yes—
195C4⋊C4×C43#4112yes—
196C4⋊C4×C43#4112yes—
197C22⋊C4×C43—24no—
198C22⋊C4×C43C22⋊C414yes—
199C22⋊C4×C43C22⋊C414yes—
200C42×C43—24no—
201C42×C43—81no—
202C42×C43—81no—
203C42×C43—81no—
204C42×C43—81no—
205C42×C43C22×C412yes—
206C42×C43C22×C412yes—
207C42×C43C2×D412yes—
208C42×C43C2×D412yes—
209C22⋊Dic43—24no—
210(C2×D43)⋊C4—24no—
211(C2×D43)⋊C4—24no—
212(C2×D43)⋊C4—24no—
213(C2×D43)⋊C4—24no—
214C4⋊Dic43—24no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43C22×C412yes—
218C4⋊Dic43C22×C412yes—
219Dic43⋊C4—24no—
220Dic43⋊C4—24no—
221C4×Dic43—24no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43C2×C22⋊C412yes—
241C23×C43C22×D411yescharacteristic
242C22×D43—22no—
243C22×D43—41no—
244C22×D43—41no—
245C22×D43—41no—
246C22×D43—41no—
247C22×D43—41no—
248C22×D43—41no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—84no—
276C2×C4×C43C2×C22⋊C412yes—
277C2×C4×C43C2×C22⋊C412yes—
278C2×C4×C43C2×C22⋊C412yes—
279C2×C4×C43C2×C22⋊C412yes—
280C2×C4×C43C2×C22⋊C412yes—
281C2×C4×C43C23×C411yescharacteristic
282C2×C4×C43C22×D411yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C22⋊D43—84no—
288C2×Dic43—22no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297D172—22no—
298D172—22no—
299D172—41no—
300D172—41no—
301C4×D43—84no—
302Dic86—22no—
303Dic86—22no—
304Dic86—41no—
305Dic86—41no—
306Dic86—84no—
307C43⋊C8—41no—
308C43⋊C8—41no—
309C43⋊C8—41no—
310C43⋊C8—41no—
311#21397—431nomaximal, Sylow
312C22×C43—22no—
313C22×C43—22no—
314C22×C43—22no—
315C22×C43—41no—
316C22×C43—41no—
317C22×C43—41no—
318C22×C43—41no—
319C22×C43C22×C22⋊C411yescharacteristic
320C22×C43#52511yescharacteristic
321C22×C43#52511yescharacteristic
322C22×C43#57611yescharacteristic
323C22×C43#57711yescharacteristic
324C22×C43#57711yescharacteristic
325C22×C43#57811yescharacteristic
326C2×D43—42no—
327C2×D43—42no—
328C2×D43—42no—
329C2×D43—81no—
330C2×D43—81no—
331C2×D43—81no—
332C2×D43—81no—
333C4×C43—22no—
334C4×C43—22no—
335C4×C43—22no—
336C4×C43—22no—
337C4×C43—22no—
338C4×C43—42no—
339C4×C43—42no—
340C4×C43—42no—
341C4×C43—42no—
342C4×C43C4×#4111yescharacteristic
343C4×C43C4×#4111yescharacteristic
344C4×C43#53211yescharacteristic
345C4×C43#53211yescharacteristic
346Dic43—42no—
347Dic43—42no—
348Dic43—42no—
349C2×#542—431no—
350C2×#433—431no—
351#2274D4311yescharacteristic, complemented
352#1988—431no—
353#1987—431no—
354#1983—431no—
355#1983—431no—
356#1875—431no—
357#1874—431no—
358#1873—431no—
359#1872—431no—
360#1763—431no—
361#1762—431no—
362C4×#103—431no—
363C4×#102—431no—
364C2×C43—42no—
365C2×C43#229711yescharacteristic
366C2×C43#289711yescharacteristic
367C2×C43#289811yescharacteristic
368C2×C43#311811yescharacteristic
369C2×C43#312111yescharacteristic
370C2×C43#312411yescharacteristic
371C2×C43#312511yescharacteristic
372D43—82no—
373#542—438no—
374#542—864no—
375C2×C4⋊Q8—431no—
376C2×#126—861no—
377C2×#124—431no—
378C2×#124—861no—
379C2×#123—861no—
380C2×C22⋊Q8—431no—
381C2×C22⋊Q8—861no—
382C2×#121—431no—
383C2×C4×Q8—431no—
384C2×C4×D4—431no—
385C2×#117C2×D4311yescharacteristic
386C2×#117C2×D4311yescharacteristic
387C22×C4⋊C4C2×D4311yescharacteristic
388#433—864no—
389C2×C4⋊C8—431no—
390C2×C4⋊C8—431no—
391C2×#103—431no—
392C2×#103—431no—
393C2×#103—431no—
394C2×#103—431no—
395C2×#102—431no—
396C2×#102—431no—
397C2×#102—431no—
398C2×#102—431no—
399C2×C22⋊C8—431no—
400C2×C22⋊C8—431no—
401C2×#97—431no—
402C2×C4×C8—431no—
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4C2×D4311yescharacteristic
406C4×C4⋊C4C2×D4311yescharacteristic
407C4×C4⋊C4C2×D4311yescharacteristic
408C4×C4⋊C4C2×D4311yescharacteristic
409C4×C22⋊C4—21no—
410C4×C22⋊C4—21no—
411#340—431no—
412#340—431no—
413#340—431no—
414#340—431no—
415#340—431no—
416#340—431no—
417#340—431no—
418#340—431no—
419C43#2139711yescharacteristic, complemented, Sylow
420C22×Q8—431no—
421C22×Q8—861no—
422C22×D4—431no—
423C22×D4—861no—
424C23×C4—21no—
425C23×C4—861no—
426C23×C4C22×D4311yescharacteristic
427C22×C8—431no—
428C22×C8—431no—
429C22×C8—431no—
430C22×C8—431no—
431C4⋊Q8—434no—
432C4⋊Q8—862no—
433#126—868no—
434#124—434no—
435#124—868no—
436#124—862no—
437#123—868no—
438C22⋊Q8—434no—
439C22⋊Q8—862no—
440C22⋊Q8—868no—
441#121—434no—
442#121—862no—
443C4×Q8—434no—
444C4×Q8—862no—
445C4×D4—434no—
446C4×D4—862no—
447#117—22no—
448#117—22no—
449#117C4×D4314yes—
450#117D17214yes—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—431no—
455C2×C4⋊C4—431no—
456C2×C4⋊C4—861no—
457C2×C4⋊C4—861no—
458C2×C4⋊C4—861no—
459C2×C4⋊C4C22⋊D4311yescharacteristic
460C2×C4⋊C4C22⋊D4311yescharacteristic
461C2×C4⋊C4C22×D4311yescharacteristic
462C2×C4⋊C4C22×D4311yescharacteristic
463C2×C4⋊C4C22×D4311yescharacteristic
464C2×C4⋊C4C22×D4311yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—861no—
467C2×C22⋊C4—861no—
468C2×C22⋊C4—861no—
469C2×C22⋊C4—861no—
470C2×C22⋊C4—861no—
471C2×C22⋊C4C22⋊D4311yescharacteristic
472C2×C22⋊C4C22⋊D4311yescharacteristic
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—21no—
478C2×C42—861no—
479C2×C42C22×D4311yescharacteristic
480C2×C42C22×D4311yescharacteristic
481C4⋊C8—862no—
482C4⋊C8—862no—
483#103—862no—
484#103—862no—
485#103—862no—
486#103—862no—
487#102—862no—
488#102—862no—
489#102—862no—
490#102—862no—
491C22⋊C8—862no—
492C22⋊C8—862no—
493#97—862no—
494C4×C8—862no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499C24—861no—
500C24C2×C22⋊D4311yescharacteristic
501C2×Q8—432no—
502C2×Q8—864no—
503C2×Q8—861no—
504C2×Q8—861no—
505C2×Q8—861no—
506C2×Q8—861no—
507C2×Q8—861no—
508C2×Q8—3441no—
509C2×Q8—3441no—
510C2×D4—432no—
511C2×D4—864no—
512C2×D4—861no—
513C2×D4—861no—
514C2×D4—861no—
515C2×D4—861no—
516C2×D4—861no—
517C2×D4—3441no—
518C2×D4—3441no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—24no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—861no—
531C22×C4—861no—
532C22×C4—861no—
533C22×C4—864no—
534C22×C4—3441no—
535C22×C4—3441no—
536C22×C4C2×C4×D4312yes—
537C22×C4C2×D17212yes—
538C22×C4C2×C22⋊D4311yescharacteristic
539C22×C4C2×C22⋊D4311yescharacteristic
540C22×C4C2×C22⋊D4311yescharacteristic
541C22×C4C2×C22⋊D4311yescharacteristic
542C22×C4C2×C22⋊D4311yescharacteristic
543C22×C4C23×D4311yescharacteristic
544C2×C8—861no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C2×C8—861no—
552C2×C8—861no—
553C2×C8—861no—
554C2×C8—861no—
555C2×C8—861no—
556C4⋊C4—24no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—432no—
562C4⋊C4—432no—
563C4⋊C4—864no—
564C4⋊C4—864no—
565C4⋊C4—864no—
566C4⋊C4—861no—
567C4⋊C4—861no—
568C4⋊C4(C2×D43)⋊C414yes—
569C4⋊C4(C2×D43)⋊C414yes—
570C4⋊C4#1062189812yes—
571C4⋊C4#1062189812yes—
572C4⋊C4#1062189812yes—
573C4⋊C4#1062189812yes—
574C22⋊C4—24no—
575C22⋊C4—864no—
576C22⋊C4—864no—
577C22⋊C4—864no—
578C22⋊C4—864no—
579C22⋊C4—864no—
580C22⋊C4(C2×D43)⋊C414yes—
581C22⋊C4(C2×D43)⋊C414yes—
582C42—24no—
583C42—81no—
584C42—81no—
585C42—81no—
586C42—81no—
587C42—864no—
588C42C2×C4×D4312yes—
589C42C2×C4×D4312yes—
590C42C2×D17212yes—
591C42C2×D17212yes—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—862no—
599C23—1721no—
600C23—1721no—
601C23—1721no—
602C23—1721no—
603C23—1721no—
604C23—1721no—
605C23C2×(C2×D43)⋊C412yes—
606C23C22×C22⋊D4311yescharacteristic
607Q8—862no—
608Q8—862no—
609Q8—3444no—
610Q8—1721no—
611Q8—1721no—
612D4—862no—
613D4—862no—
614D4—3444no—
615D4—1721no—
616D4—1721no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—84no—
644C2×C4—862no—
645C2×C4—862no—
646C2×C4—862no—
647C2×C4—3444no—
648C2×C4—1721no—
649C2×C4—1721no—
650C2×C4—1721no—
651C2×C4—1721no—
652C2×C4—1721no—
653C2×C4—1721no—
654C2×C4C2×(C2×D43)⋊C412yes—
655C2×C4C2×(C2×D43)⋊C412yes—
656C2×C4C2×(C2×D43)⋊C412yes—
657C2×C4C2×(C2×D43)⋊C412yes—
658C2×C4C2×(C2×D43)⋊C412yes—
659C2×C4C22×C4×D4311yescharacteristic
660C2×C4C22×D17211yescharacteristic
661C2×C4C2×#1062189811yescharacteristic
662C2×C4C2×#1062189811yescharacteristic
663C2×C4C2×#1062189811yescharacteristic
664C2×C4C2×#1062189811yescharacteristic
665C8—1721no—
666C8—1721no—
667C8—1721no—
668C8—1721no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—3441no—
677C22—3441no—
678C22—3441no—
679C22—3441no—
680C22—1722no—
681C22—1722no—
682C22—1722no—
683C22C22×(C2×D43)⋊C411yescharacteristic
684C22#1458341011yescharacteristic
685C22#1458341011yescharacteristic
686C22#1458370211yescharacteristic
687C22#1458370711yescharacteristic
688C22#1458371011yescharacteristic
689C22#1458371411yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—1722no—
700C4—1722no—
701C4—1722no—
702C4C4×#1062189811yescharacteristic
703C4C4×#1062189811yescharacteristic
704C4#1458344911yescharacteristic
705C4#1458344911yescharacteristic
706C2—42no—
707C2—3442no—
708C2#1913708511yescharacteristic
709C2#1914311811yescharacteristic
710C2#1914312511yescharacteristic
711C2#1914477911yescharacteristic
712C2#1914482411yescharacteristic
713C2#1914485711yescharacteristic
714C2#1914487211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2274C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
cosocleC22×C4×C43C24
hypercenter#2274D43
hypocenterC43#21397
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2274

Complements

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

NH ≅ G/Ntype
2. C2×#14582960C2semidirect
3. #19135547C2semidirect
4. #19135543C2semidirect
5. #19135527C2semidirect
6. #19135527C2semidirect
9. #19134907C2semidirect
10. #19134902C2semidirect
11. #19134428C2semidirect
12. #19134423C2semidirect
13. C4×#13063248C2semidirect
14. C4×#13063245C2semidirect
15. C43×#2274C2semidirect
17. #14583520C4semidirect
72. #13063325C2×C4semidirect
75. #13063313C2×C4semidirect
84. C4×Dic86C2×C4semidirect
86. C4×D172C2×C4semidirect
351. #2274D43semidirect
419. C43#21397semidirect

Maximal subgroups

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

subgroupindex
C2×#145835202
C2×#145829602
#191355472
#191355432
#191355272
#191349172
#191349122
#191349072
#191349022
#191344282
#191344232
C4×#130632482
C4×#130632452
C43×#22742
#2139743