Finite Group Databasebeta

← #25112941

Subgroups — #25112941

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×#14583550C211yesmaximal, characteristic
2C2×#14582970C211yesmaximal, characteristic, complemented
3#19137520C211yesmaximal, characteristic, complemented
4#19135566C211yesmaximal, characteristic, complemented
5#19135541C211yesmaximal, characteristic, complemented
6#19135032C211yesmaximal, characteristic, complemented
7#19135023C211yesmaximal, characteristic, complemented
8#19134916C211yesmaximal, characteristic, complemented
9#19134912C211yesmaximal, characteristic, complemented
10#19134684C211yesmaximal, characteristic, complemented
11#19134681C211yesmaximal, characteristic, complemented
12#19134604C211yesmaximal, characteristic, complemented
13#19134419C211yesmaximal, characteristic, complemented
14#19134313C211yesmaximal, characteristic, complemented
15C2×C43×#340C211yesmaximal, characteristic, complemented
16C22×#10621898—21no—
17C22×#10621872C2211yescharacteristic
18#14583550—24no—
19#14583550C418yescomplemented
20C2×#13063324C2211yescharacteristic
21C2×#13063310—21no—
22C2×#13063308—21no—
23C2×#13063303—21no—
24C2×#13063300C2211yescharacteristic
25C2×#13063299C2211yescharacteristic
26C2×#13063287C2211yescharacteristic
27C2×C4×C22⋊D43C2211yescharacteristic
28C2×#13063283C2211yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic
30#14582970—24no—
31C2×Dic43⋊C8C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×(C2×D43)⋊C8C2211yescharacteristic
38C2×#13063235C2211yescharacteristic
39#14582789—21no—
40#14582780—21no—
41#14582778—21no—
42#14582764C2211yescharacteristic
43#14582759C2211yescharacteristic
44#14582756C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46C4×C22⋊Dic43—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C23×C8×C43C2211yescharacteristic
56C22×C4⋊C4×C43C2211yescharacteristic
57C22×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C2×#10621898—28no—
63C2×#10621898—44no—
64C2×#10621898—44no—
65C22×Dic86—21no—
66C22×D172—21no—
67C22×D172C2311yescharacteristic
68C22×C22⋊D43—21no—
69C22×C22⋊D43D411yescharacteristic
70C22×C4×D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43C2311yescharacteristic
73C2×#10621872—22no—
74C2×#10621872—22no—
75C2×#10621872—41no—
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78#13063324—22no—
79#13063324C2×C414yescomplemented
80#13063310—28no—
81#13063308—28no—
82#13063303—28no—
83#13063300—22no—
84#13063300C2×C414yescomplemented
85#13063299—22no—
86#13063299C2×C414yes—
87#13063287—22no—
88#13063287C2×C414yescomplemented
89C4×C22⋊D43C2×C414yes—
90C4×C22⋊D43D414yes—
91#13063283—22no—
92#13063283—41no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4D411yescharacteristic
99C4⋊C4×D43—22no—
100C4⋊C4×D43C2×C414yescomplemented
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43D411yescharacteristic
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4D411yescharacteristic
109C2×C4×Dic43—21no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43C2311yescharacteristic
112Dic43⋊C8—22no—
113#13063247—22no—
114#13063247—41no—
115#13063245—22no—
116#13063245—41no—
117C22⋊(C43⋊C8)—22no—
118(C2×D43)⋊C8—22no—
119#13063235—22no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C23×C4×C43—21no—
126C23×C4×C43—21no—
127C23×C4×C43C2311yescharacteristic
128C22×C8×C43—22no—
129C22×C8×C43—22no—
130C22×C8×C43—41no—
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—22no—
135C2×C4⋊C4×C43—22no—
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43—41no—
138C2×C4⋊C4×C43C2×C414yes—
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C24×C43C2×D411yescharacteristic
144C23×D43—21no—
145C23×D43C2×D411yescharacteristic
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—24no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—42no—
156C22×C4×C43—42no—
157C22×C4×C43—42no—
158C22×C4×C43—42no—
159C22×C4×C43—81no—
160C22×C4×C43C22×C412yes—
161C22×C4×C43C2×D412yes—
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2411yescharacteristic
164C2×C22⋊D43—24no—
165C2×C22⋊D43—22no—
166C2×C22⋊D43—22no—
167C2×C22⋊D43—42no—
168C2×C22⋊D43—42no—
169C2×C22⋊D43C22⋊C414yes—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175C22×Dic43C2×D411yescharacteristic
176#10621898—432no—
177C2×D172—21no—
178C2×D172—24no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—42no—
184C2×D172—42no—
185C2×D172C22×C412yes—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—24no—
191C2×C4×D43—24no—
192C2×C4×D43—42no—
193C2×C4×D43—42no—
194C2×C4×D43—42no—
195C2×C4×D43—42no—
196C2×C4×D43C22×C412yes—
197C2×C4×D43C2×D412yes—
198C2×Dic86—24no—
199C2×Dic86—42no—
200C2×Dic86—42no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—44no—
207C2×C8×C43#4112yescomplemented
208C4⋊C4×C43—24no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—42no—
215C4⋊C4×C43C22×C412yes—
216C4⋊C4×C43C22×C412yes—
217C4⋊C4×C43#4112yescomplemented
218C22⋊Dic43—42no—
219C22⋊Dic43C22⋊C414yes—
220(C2×D43)⋊C4—24no—
221(C2×D43)⋊C4—24no—
222(C2×D43)⋊C4—24no—
223(C2×D43)⋊C4—42no—
224(C2×D43)⋊C4—81no—
225(C2×D43)⋊C4C22⋊C414yes—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43C22×C412yes—
232Dic43⋊C4—24no—
233Dic43⋊C4—24no—
234Dic43⋊C4C22⋊C414yes—
235C4×Dic43—42no—
236C4×Dic43—81no—
237C4×Dic43C22×C412yes—
238C4×Dic43C2×D412yes—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245#10621872—44no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43C2×C22⋊C412yes—
251C23×C43AGL(1,ℤ/8)12yes—
252C23×C43AGL(1,ℤ/8)12yes—
253C23×C43C22×D411yescharacteristic
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—22no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43C2×C22⋊C412yes—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—48no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—84no—
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—28no—
296C22⋊D43—48no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—22no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43C2×C22⋊C412yes—
313C2×Dic43C2×C22⋊C412yes—
314C2×Dic43C2×C22⋊C412yes—
315D172—22no—
316D172—22no—
317D172—48no—
318D172—41no—
319D172—41no—
320C4×D43—22no—
321C4×D43—22no—
322C4×D43—22no—
323C4×D43—22no—
324C4×D43—48no—
325C4×D43—48no—
326Dic86—48no—
327C8×C43—22no—
328C8×C43—41no—
329C43⋊C8—41no—
330C43⋊C8—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#41814yes—
339C22×C43C22×C22⋊C411yescharacteristic
340C22×C43#54611yescharacteristic
341C22×C43#54711yescharacteristic
342C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
344C22×C43#57711yescharacteristic
345C22×C43#57811yescharacteristic
346C2×D43—22no—
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—41no—
350C2×D43—41no—
351C2×D43—41no—
352C2×D43—41no—
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—42no—
362C4×C43—42no—
363C4×C43—42no—
364C4×C43—81no—
365C4×C43C4×#4111yescharacteristic
366C4×C43#52011yescharacteristic
367C4×C43#54611yescharacteristic
368C4×C43#54711yescharacteristic
369Dic43—22no—
370Dic43—22no—
371Dic43—22no—
372Dic43—42no—
373Dic43—81no—
374Dic43—81no—
375C2×#547—431no—
376C2×#435—431no—
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×#340D4311yescharacteristic, complemented
390C2×C43—24no—
391C2×C43#233911yescharacteristic
392C2×C43C2×#41811yescharacteristic
393C2×C43#289811yescharacteristic
394C2×C43#330611yescharacteristic
395C2×C43#330811yescharacteristic
396C2×C43#334311yescharacteristic
397C2×C43#334511yescharacteristic
398D43—42no—
399D43—82no—
400C22×#41—861no—
401C22×M16—431no—
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×D4—431no—
413C2×#117—431no—
414C22×C4⋊C4—431no—
415C22×C4⋊C4C2×D4311yescharacteristic
416C22×C4⋊C4C2×D4311yescharacteristic
417#435—864no—
418C2×C4⋊C8—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422C2×#102—431no—
423C2×C22⋊C8—431no—
424C2×C22⋊C8—431no—
425C2×#97—431no—
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#340C2×D4311yescharacteristic
443#340C2×D4311yescharacteristic
444#340C2×D4311yescharacteristic
445#340C2×D4311yescharacteristic
446C43#2249511yescharacteristic, complemented, Sylow
447C2×#41—868no—
448C2×#41—1724no—
449C2×#41—1724no—
450C22×Q8—861no—
451C22×D4—431no—
452C22×D4—431no—
453C22×D4—861no—
454C22×D4—861no—
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—431no—
458C23×C4—861no—
459C23×C4—861no—
460C23×C4C22×D4311yescharacteristic
461C2×M16—862no—
462C2×M16—862no—
463C2×M16—1721no—
464C22×C8—22no—
465C22×C8—22no—
466C22×C8—41no—
467C22×C8—431no—
468C22×C8—431no—
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—434no—
482C4×D4—434no—
483C4×D4—862no—
484#117—862no—
485#117—1721no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—41no—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—434no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—862no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4C4×D4314yes—
500C2×C4⋊C4C22×D4311yescharacteristic
501C2×C4⋊C4C22×D4311yescharacteristic
502C2×C4⋊C4C22×D4311yescharacteristic
503C2×C4⋊C4C22×D4311yescharacteristic
504C2×C22⋊C4—431no—
505C2×C22⋊C4—431no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C42—431no—
513C2×C42—861no—
514C2×C42—861no—
515C4⋊C8—862no—
516#102—862no—
517#102—862no—
518#102—1721no—
519#102—1721no—
520C22⋊C8—862no—
521C22⋊C8—862no—
522#97—862no—
523#95—861no—
524#95—861no—
525#95—861no—
526#95—861no—
527#95—861no—
528C24—431no—
529C24—861no—
530C24D4×D4311yescharacteristic
531#41—17232no—
532C2×Q8—864no—
533C2×Q8—1722no—
534C2×Q8—1722no—
535C2×D4—434no—
536C2×D4—432no—
537C2×D4—864no—
538C2×D4—862no—
539C2×D4—862no—
540C2×D4—864no—
541C2×D4—861no—
542C2×D4—861no—
543C2×D4—861no—
544C2×D4—861no—
545C2×D4—861no—
546C2×D4—1722no—
547C2×D4—1722no—
548C2×D4—1722no—
549C2×D4—1722no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—24no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—81no—
564C22×C4—431no—
565C22×C4—431no—
566C22×C4—431no—
567C22×C4—432no—
568C22×C4—432no—
569C22×C4—864no—
570C22×C4—864no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—1722no—
579C22×C4—1722no—
580C22×C4—1722no—
581C22×C4—1722no—
582C22×C4C2×C4×D4312yes—
583C22×C4D4×D4311yescharacteristic
584C22×C4D4×D4312yes—
585C22×C4C23×D4311yescharacteristic
586M16—1724no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—44no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8—861no—
596C2×C8—861no—
597C2×C8—861no—
598C2×C8—861no—
599C2×C8#1062189812yescomplemented
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—42no—
607C4⋊C4—434no—
608C4⋊C4—432no—
609C4⋊C4—864no—
610C4⋊C4—864no—
611C4⋊C4—861no—
612C4⋊C4—861no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4C2×C4×D4312yes—
617C4⋊C4C2×C4×D4312yes—
618C4⋊C4#1062189812yescomplemented
619C22⋊C4—434no—
620C22⋊C4—434no—
621C22⋊C4—864no—
622C22⋊C4—864no—
623C22⋊C4—864no—
624C22⋊C4—3441no—
625C22⋊C4—1722no—
626C22⋊C4—1722no—
627C42—432no—
628C42—432no—
629C42—3441no—
630C42—1722no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—432no—
636C23—861no—
637C23—861no—
638C23—861no—
639C23—861no—
640C23—861no—
641C23—861no—
642C23—862no—
643C23—1721no—
644C23—1721no—
645C23—1721no—
646C23—1721no—
647C23—1721no—
648C23—1721no—
649C23C22⋊C4×D4312yes—
650C23#1306334912yes—
651C23#1306335212yes—
652C23C2×D4×D4311yescharacteristic
653Q8—1728no—
654D4—868no—
655D4—862no—
656D4—862no—
657D4—1728no—
658D4—1728no—
659D4—1721no—
660D4—1721no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—48no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—84no—
681C2×C4—432no—
682C2×C4—432no—
683C2×C4—432no—
684C2×C4—861no—
685C2×C4—861no—
686C2×C4—861no—
687C2×C4—861no—
688C2×C4—861no—
689C2×C4—861no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—1728no—
696C2×C4—1728no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4C22⋊C4×D4312yes—
706C2×C4C22×C4×D4311yescharacteristic
707C2×C4C2×D4×D4311yescharacteristic
708C2×C4C2×#1062189811yescharacteristic
709C2×C4C2×#1062189811yescharacteristic
710C2×C4#1306337011yescharacteristic
711C2×C4#1306337311yescharacteristic
712C8—22no—
713C8—41no—
714C8—1721no—
715C8—1721no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—862no—
723C22—862no—
724C22—862no—
725C22—3441no—
726C22—3441no—
727C22—3441no—
728C22—3441no—
729C22—1722no—
730C22—1722no—
731C22—1722no—
732C22—1721no—
733C22—1721no—
734C22—1721no—
735C22—1721no—
736C22#1458290214yes—
737C22C2×C22⋊C4×D4311yescharacteristic
738C22#1458353911yescharacteristic
739C22#1458355011yescharacteristic
740C22C2×#1306334911yescharacteristic
741C22C2×#1306335211yescharacteristic
742C22#1458370511yescharacteristic
743C22#1458371211yescharacteristic
744C4—22no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4—81no—
749C4—862no—
750C4—862no—
751C4—862no—
752C4—3441no—
753C4—3441no—
754C4—1722no—
755C4C4×#1062189811yescharacteristic
756C4#1458338011yescharacteristic
757C4#1458353911yescharacteristic
758C4#1458355011yescharacteristic
759C2—24no—
760C2—3442no—
761C2—1722no—
762C2#1913742211yescharacteristic
763C2C2×#1458290211yescharacteristic
764C2#1914312311yescharacteristic
765C2#1914655211yescharacteristic
766C2#1914658211yescharacteristic
767C2#1914703111yescharacteristic
768C2#1914706111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#340C2
socleC23×C43C22×D4
prime radicalC2×#14583550C2
cosocleC22×C4×C43C24
hypercenterC2×#340D43
hypocenterC43#22495
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C2×#14582970C2semidirect
3. #19137520C2semidirect
4. #19135566C2semidirect
5. #19135541C2semidirect
6. #19135032C2semidirect
7. #19135023C2semidirect
8. #19134916C2semidirect
9. #19134912C2semidirect
10. #19134684C2semidirect
11. #19134681C2semidirect
12. #19134604C2semidirect
13. #19134419C2semidirect
14. #19134313C2semidirect
15. C2×C43×#340C2semidirect
19. #14583550C4semidirect
79. #13063324C2×C4semidirect
84. #13063300C2×C4semidirect
88. #13063287C2×C4semidirect
100. C4⋊C4×D43C2×C4semidirect
207. C2×C8×C43#41semidirect
217. C4⋊C4×C43#41semidirect
389. C2×#340D43semidirect
446. C43#22495semidirect
599. C2×C8#10621898semidirect
618. C4⋊C4#10621898semidirect

Maximal subgroups

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

subgroupindex
C2×#145835502
C2×#145829702
#191375202
#191355662
#191355412
#191350322
#191350232
#191349162
#191349122
#191346842
#191346812
#191346042
#191344192
#191343132
C2×C43×#3402
#2249543