Finite Group Databasebeta

← #25112947

Subgroups — #25112947

Order 11008.

1390 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583553C211yesmaximal, characteristic
2#19137524C211yesmaximal, characteristic, complemented
3#19135568C211yesmaximal, characteristic, complemented
4#19135542C211yesmaximal, characteristic, complemented
5#19135033C211yesmaximal, characteristic, complemented
6#19135023C211yesmaximal, characteristic, complemented
7#19134915C211yesmaximal, characteristic, complemented
8#19134910C211yesmaximal, characteristic, complemented
9#19134686C211yesmaximal, characteristic, complemented
10#19134682C211yesmaximal, characteristic, complemented
11#19134606C211yesmaximal, characteristic, complemented
12#19134421C211yesmaximal, characteristic, complemented
13#19134315C211yesmaximal, characteristic, complemented
14C2×#14582662C211yesmaximal, characteristic, complemented
15C2×C43×#435C211yesmaximal, characteristic, complemented
16C22×#10621900—21no—
17#14583553—24no—
18#14583553C418yescomplemented
19C2×#13063325C2211yescharacteristic
20C2×#13063309—21no—
21C2×#13063309—21no—
22C2×#13063305—21no—
23C2×#13063299C2211yescharacteristic
24C2×#13063299C2211yescharacteristic
25C2×C4×D172C2211yescharacteristic
26C2×#13063284C2211yescharacteristic
27C22×C4⋊Dic43C2211yescharacteristic
28C22×C4⋊Dic43C2211yescharacteristic
29C22×C4⋊Dic43C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34#14582792—21no—
35#14582785—21no—
36#14582779—21no—
37#14582765C2211yescharacteristic
38#14582759C2211yescharacteristic
39#14582759C2211yescharacteristic
40C4×C4⋊Dic43C2211yescharacteristic
41C22⋊C4×Dic43—21no—
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54C22×M16×C43C2211yescharacteristic
55C23×C8×C43C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C43×#435—24no—
58C2×C4⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C2×#97×C43C2211yescharacteristic
62C2×#10621900—28no—
63C2×#10621900—44no—
64C2×#10621900—44no—
65C22×Dic86—21no—
66C22×D172C2311yescharacteristic
67C22×C22⋊D43—21no—
68C22×C22⋊D43—21no—
69C23×Dic43—21no—
70C23×Dic43—21no—
71C23×Dic43—21no—
72C22×C4×D43—21no—
73#13063325—22no—
74#13063325C2×C414yescomplemented
75#13063309—28no—
76#13063309—28no—
77#13063305—28no—
78#13063299—22no—
79#13063299—22no—
80#13063299C2×C414yes—
81#13063299C2×C414yescomplemented
82C4×D172—22no—
83C4×D172C2×C414yescomplemented
84#13063284—22no—
85#13063284—41no—
86C2×C4⋊Dic43—22no—
87C2×C4⋊Dic43—22no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—41no—
94C2×C4⋊Dic43C2×C414yes—
95C2×C4⋊Dic43C2×C414yescomplemented
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43—21no—
111#13063247—22no—
112#13063247—22no—
113#13063247—41no—
114#13063247—41no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C22×D4×C43D411yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C2×M16×C43—22no—
124C2×M16×C43—22no—
125C2×M16×C43—41no—
126C22×C8×C43—22no—
127C22×C8×C43—22no—
128C22×C8×C43—41no—
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C4×D4×C43C2×C414yes—
134C4×D4×C43D414yes—
135C2×C4⋊C4×C43D411yescharacteristic
136C2×C22⋊C4×C43D411yescharacteristic
137C2×C22⋊C4×C43D411yescharacteristic
138C2×C42×C43C2311yescharacteristic
139C4⋊C8×C43—22no—
140C22⋊C8×C43—22no—
141C22⋊C8×C43—22no—
142#97×C43—22no—
143C24×C43C2×D411yescharacteristic
144C24×C43C2×D411yescharacteristic
145C23×D43—21no—
146C2×D4×C43—22no—
147C2×D4×C43—22no—
148C2×D4×C43C22⋊C414yes—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43C22×C412yes—
158C22×C4×C43C22×C412yes—
159C22×C4×C43C2×D412yes—
160C22×C4×C43C2×D412yes—
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2411yescharacteristic
166C2×C22⋊D43—24no—
167C2×C22⋊D43—24no—
168C2×C22⋊D43—42no—
169C2×C22⋊D43—42no—
170C2×C22⋊D43—42no—
171C2×C22⋊D43—42no—
172C22×Dic43—24no—
173C22×Dic43—24no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—42no—
182C22×Dic43—42no—
183C22×Dic43—42no—
184C22×Dic43—42no—
185C22×Dic43—42no—
186C22×Dic43—42no—
187C22×Dic43—81no—
188#10621900—432no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172—21no—
193C2×D172—21no—
194C2×D172C22×C412yes—
195C2×C4×D43—24no—
196C2×C4×D43—42no—
197C2×C4×D43—42no—
198C2×Dic86—24no—
199C2×Dic86—42no—
200C2×Dic86—42no—
201M16×C43—44no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—44no—
214C2×C8×C43#4112yescomplemented
215C4⋊C4×C43C22⋊C414yes—
216C22⋊C4×C43C22⋊C414yes—
217C22⋊C4×C43C22⋊C414yes—
218C42×C43C22×C412yes—
219C42×C43C2×D412yes—
220C22⋊Dic43—42no—
221C22⋊Dic43—42no—
222C22⋊Dic43—81no—
223(C2×D43)⋊C4—24no—
224(C2×D43)⋊C4—24no—
225(C2×D43)⋊C4—24no—
226C4⋊Dic43—24no—
227C4⋊Dic43—24no—
228C4⋊Dic43—24no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—42no—
240C4⋊Dic43C22×C412yes—
241C4⋊Dic43C22×C412yes—
242C4⋊Dic43C22×C412yes—
243C4⋊Dic43#4112yescomplemented
244C4×Dic43—42no—
245C4×Dic43—81no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43C2×C22⋊C412yes—
257C23×C43C2×C22⋊C412yes—
258C23×C43AGL(1,ℤ/8)12yes—
259C23×C43AGL(1,ℤ/8)12yes—
260C23×C43C22×D411yescharacteristic
261C22×D43—22no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268D4×C43—28no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43C2×C22⋊C412yes—
286C2×C4×C43C2×C22⋊C412yes—
287C2×C4×C43C2×C22⋊C412yes—
288C2×C4×C43C2×C22⋊C412yes—
289C2×C4×C43C23×C411yescharacteristic
290C2×C4×C43C22×D411yescharacteristic
291C2×C4×C43C2×#4111yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43H(5,𝔽2)11yescharacteristic
294C2×C4×C432−1+411yescharacteristic
295C22⋊D43—48no—
296C22⋊D43—48no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—48no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—48no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—84no—
321D172—22no—
322D172—22no—
323D172—41no—
324D172—41no—
325C4×D43—48no—
326Dic86—48no—
327C8×C43—22no—
328C8×C43—41no—
329C8×C43—41no—
330C8×C43—41no—
331#22495—431nomaximal, Sylow
332C22×C43—22no—
333C22×C43—22no—
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—22no—
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43#41814yes—
346C22×C43C22×C22⋊C411yescharacteristic
347C22×C43#54611yescharacteristic
348C22×C43#54711yescharacteristic
349C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
350C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
351C22×C43#57711yescharacteristic
352C22×C43#57811yescharacteristic
353C2×D43—42no—
354C2×D43—42no—
355C2×D43—42no—
356C2×D43—81no—
357C2×D43—81no—
358C2×D43—81no—
359C2×D43—81no—
360C4×C43—22no—
361C4×C43—22no—
362C4×C43—22no—
363C4×C43—22no—
364C4×C43C4×#4111yescharacteristic
365C4×C43#52011yescharacteristic
366C4×C43#54611yescharacteristic
367C4×C43#54711yescharacteristic
368Dic43—42no—
369Dic43—42no—
370Dic43—42no—
371Dic43—42no—
372Dic43—81no—
373Dic43—81no—
374Dic43—81no—
375C2×#547—431no—
376C2×#435D4311yescharacteristic, complemented
377#2352—431no—
378#1993—431no—
379#1987—431no—
380#1895—431no—
381#1893—431no—
382#1875—431no—
383#1874—431no—
384#1824—431no—
385#1823—431no—
386#1804—431no—
387#1762—431no—
388#1736—431no—
389C2×#340—431no—
390C2×C43—24no—
391C2×C43—42no—
392C2×C43#233911yescharacteristic
393C2×C43C2×#41811yescharacteristic
394C2×C43#289811yescharacteristic
395C2×C43#330611yescharacteristic
396C2×C43#330811yescharacteristic
397C2×C43#334311yescharacteristic
398C2×C43#334511yescharacteristic
399D43—82no—
400C22×#41—861no—
401C22×M16C2×D4311yescharacteristic
402C23×C8C2×D4311yescharacteristic
403#547—438no—
404#547—864no—
405C2×C4⋊Q8—431no—
406C2×#123—861no—
407C2×#123—861no—
408C2×C22⋊Q8—861no—
409C2×#121—431no—
410C2×#121—431no—
411C2×C4×D4—431no—
412C2×C4×D4C2×D4311yescharacteristic
413C2×#117—431no—
414C22×C4⋊C4—431no—
415C22×C4⋊C4—431no—
416C22×C4⋊C4—431no—
417#435—24no—
418C2×C4⋊C8C2×D4311yescharacteristic
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422C2×#102—431no—
423C2×C22⋊C8C2×D4311yescharacteristic
424C2×C22⋊C8C2×D4311yescharacteristic
425C2×#97C2×D4311yescharacteristic
426#388—861no—
427#387—861no—
428#386—861no—
429#382—431no—
430#380—431no—
431#380—431no—
432C4×C4⋊C4—431no—
433C4×C22⋊C4—861no—
434#340—431no—
435#340—431no—
436#340—431no—
437#340—431no—
438#340—431no—
439#340—431no—
440#340—431no—
441#340—431no—
442#340—431no—
443#340—431no—
444#340—431no—
445#340—431no—
446C43#2249511yescharacteristic, complemented, Sylow
447C2×#41—868no—
448C2×#41—1724no—
449C2×#41—1724no—
450C22×Q8—861no—
451C22×D4—431no—
452C22×D4—861no—
453C22×D4—861no—
454C22×D4D17211yescharacteristic
455C23×C4—861no—
456C23×C4—861no—
457C23×C4—861no—
458C23×C4—861no—
459C23×C4C22×D4311yescharacteristic
460C23×C4C22×D4311yescharacteristic
461C2×M16—22no—
462C2×M16—22no—
463C2×M16—41no—
464C22×C8—22no—
465C22×C8—22no—
466C22×C8—41no—
467C22×C8C22×D4311yescharacteristic
468C22×C8C22×D4311yescharacteristic
469C22×C8C22×D4311yescharacteristic
470C22×C8C22×D4311yescharacteristic
471C4⋊Q8—434no—
472C4⋊Q8—862no—
473#123—868no—
474#123—868no—
475C22⋊Q8—868no—
476#121—434no—
477#121—434no—
478#121—862no—
479#121—862no—
480C4×D4—434no—
481C4×D4—862no—
482C4×D4C4×D4314yes—
483C4×D4C22⋊D4314yes—
484#117—862no—
485#117—1721no—
486C2×C4⋊C4—434no—
487C2×C4⋊C4—434no—
488C2×C4⋊C4—431no—
489C2×C4⋊C4—431no—
490C2×C4⋊C4—431no—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—862no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—862no—
500C2×C4⋊C4—862no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—1721no—
503C2×C4⋊C4D17211yescharacteristic
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4D17211yescharacteristic
511C2×C22⋊C4D17211yescharacteristic
512C2×C42—861no—
513C2×C42—861no—
514C2×C42C22×D4311yescharacteristic
515C4⋊C8—22no—
516#102—862no—
517#102—862no—
518#102—1721no—
519#102—1721no—
520C22⋊C8—22no—
521C22⋊C8—22no—
522#97—22no—
523#95—861no—
524#95—861no—
525#95—861no—
526#95—861no—
527#95—861no—
528C24—861no—
529C24C2×D17211yescharacteristic
530C24C2×D17211yescharacteristic
531#41—17232no—
532C2×Q8—864no—
533C2×Q8—1722no—
534C2×Q8—1722no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—432no—
538C2×D4—864no—
539C2×D4—864no—
540C2×D4—861no—
541C2×D4—861no—
542C2×D4—861no—
543C2×D4—861no—
544C2×D4—861no—
545C2×D4—1722no—
546C2×D4—1722no—
547C2×D4—1722no—
548C2×D4—1722no—
549C2×D4(C2×D43)⋊C414yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—864no—
559C22×C4—864no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—864no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—3441no—
569C22×C4—1722no—
570C22×C4—1722no—
571C22×C4—1722no—
572C22×C4—1722no—
573C22×C4—1722no—
574C22×C4—1722no—
575C22×C4—1722no—
576C22×C4—1722no—
577C22×C4C2×C4×D4312yes—
578C22×C4C2×C4×D4312yes—
579C22×C4C2×D17211yescharacteristic
580C22×C4C2×D17211yescharacteristic
581C22×C4C2×D17211yescharacteristic
582C22×C4C2×D17211yescharacteristic
583C22×C4C2×C22⋊D4312yes—
584C22×C4C2×C22⋊D4312yes—
585C22×C4C23×D4311yescharacteristic
586M16—44no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—44no—
599C2×C8#1062190012yescomplemented
600C4⋊C4—432no—
601C4⋊C4—432no—
602C4⋊C4—432no—
603C4⋊C4—432no—
604C4⋊C4—864no—
605C4⋊C4—864no—
606C4⋊C4—864no—
607C4⋊C4—861no—
608C4⋊C4—861no—
609C4⋊C4—861no—
610C4⋊C4—861no—
611C4⋊C4—861no—
612C4⋊C4—861no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—1722no—
618C4⋊C4(C2×D43)⋊C414yes—
619C22⋊C4—864no—
620C22⋊C4—864no—
621C22⋊C4—864no—
622C22⋊C4—3441no—
623C22⋊C4—1722no—
624C22⋊C4—1722no—
625C22⋊C4(C2×D43)⋊C414yes—
626C22⋊C4(C2×D43)⋊C414yes—
627C42—3441no—
628C42—1722no—
629C42C2×C4×D4312yes—
630C42C2×C22⋊D4312yes—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—862no—
642C23—1721no—
643C23—1721no—
644C23—1721no—
645C23—1721no—
646C23—1721no—
647C23—1721no—
648C23C2×(C2×D43)⋊C412yes—
649C23C2×(C2×D43)⋊C412yes—
650C23#1306335312yes—
651C23#1306335312yes—
652C23C22×D17211yescharacteristic
653Q8—1728no—
654D4—28no—
655D4—862no—
656D4—862no—
657D4—1728no—
658D4—1728no—
659D4—1721no—
660D4—1721no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—862no—
678C2×C4—862no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—3444no—
682C2×C4—1728no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1728no—
693C2×C4—1728no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4C2×(C2×D43)⋊C412yes—
703C2×C4C2×(C2×D43)⋊C412yes—
704C2×C4C2×(C2×D43)⋊C412yes—
705C2×C4C2×(C2×D43)⋊C412yes—
706C2×C4C22×C4×D4311yescharacteristic
707C2×C4C22×C22⋊D4311yescharacteristic
708C2×C4#41×D4311yescharacteristic
709C2×C4C2×#1062190011yescharacteristic
710C2×C4#1306337011yescharacteristic
711C2×C4#1306337211yescharacteristic
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—3441no—
730C22—3441no—
731C22—3441no—
732C22—3441no—
733C22—1722no—
734C22—1722no—
735C22—1722no—
736C22#1458290514yes—
737C22C22×(C2×D43)⋊C411yescharacteristic
738C22#1458354411yescharacteristic
739C22#1458355311yescharacteristic
740C22C2×#1306335311yescharacteristic
741C22C2×#1306335311yescharacteristic
742C22#1458371111yescharacteristic
743C22#1458371611yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—22no—
748C4—3441no—
749C4—3441no—
750C4—3441no—
751C4—1722no—
752C4—1722no—
753C4—1722no—
754C4—1722no—
755C4C4×#1062190011yescharacteristic
756C4#1458337811yescharacteristic
757C4#1458354311yescharacteristic
758C4#1458354811yescharacteristic
759C2—24no—
760C2—42no—
761C2—3442no—
762C2#1913742011yescharacteristic
763C2C2×#1458290511yescharacteristic
764C2#1914312911yescharacteristic
765C2#1914655811yescharacteristic
766C2#1914658811yescharacteristic
767C2#1914703711yescharacteristic
768C2#1914706711yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#435C2
socleC23×C43C22×D4
prime radicalC2×#14583553C2
cosocleC22×C4×C43C24
hypercenterC2×#435D43
hypocenterC43#22495
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #19137524C2semidirect
3. #19135568C2semidirect
4. #19135542C2semidirect
5. #19135033C2semidirect
6. #19135023C2semidirect
7. #19134915C2semidirect
8. #19134910C2semidirect
9. #19134686C2semidirect
10. #19134682C2semidirect
11. #19134606C2semidirect
12. #19134421C2semidirect
13. #19134315C2semidirect
14. C2×#14582662C2semidirect
15. C2×C43×#435C2semidirect
18. #14583553C4semidirect
74. #13063325C2×C4semidirect
81. #13063299C2×C4semidirect
83. C4×D172C2×C4semidirect
95. C2×C4⋊Dic43C2×C4semidirect
214. C2×C8×C43#41semidirect
243. C4⋊Dic43#41semidirect
376. C2×#435D43semidirect
446. C43#22495semidirect
599. C2×C8#10621900semidirect

Maximal subgroups

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

subgroupindex
C2×#145835532
#191375242
#191355682
#191355422
#191350332
#191350232
#191349152
#191349102
#191346862
#191346822
#191346062
#191344212
#191343152
C2×#145826622
C2×C43×#4352
#2249543