Finite Group Databasebeta

← #29700290

Subgroups — #29700290

Order 15616.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839903C211yesmaximal, characteristic
2C2×#16839864C211yesmaximal, characteristic, complemented
3C22×#14519702C211yesmaximal, characteristic, complemented
4#21448833C211yesmaximal, characteristic
5C22⋊C4×Dic122C211yesmaximal, characteristic, complemented
6#21446700C211yesmaximal, characteristic, complemented
7#21446509C211yesmaximal, characteristic, complemented
8#21446461C211yesmaximal, characteristic, complemented
9#21446247C211yesmaximal, characteristic
10#21446173C211yesmaximal, characteristic, complemented
11#21446152C211yesmaximal, characteristic, complemented
12#21446076C211yesmaximal, characteristic, complemented
13#21446009C211yesmaximal, characteristic, complemented
14#21445650C211yesmaximal, characteristic, complemented
15C61×#1752C211yesmaximal, characteristic, complemented
16C23×Dic122C2211yescharacteristic
17C22×#11758190C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic
21C2×C4×Dic122C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23C2×#14519737—21no—
24C22×C4⋊Dic61C2211yescharacteristic
25#16839903C418yescomplemented
26#16839864—24no—
27C2×#14519711C2211yescharacteristic
28C2×#14519711C2211yescharacteristic
29C2×#14519702—24no—
30C2×#14519702C2211yescharacteristic
31C2×#14519702C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519702C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519699C2211yescharacteristic
38#16839668C2211yescharacteristic
39#16839668C2211yescharacteristic
40#16839666—21no—
41#16839666—21no—
42#16839664C2211yescharacteristic
43#16839660C2211yescharacteristic
44#16839654—21no—
45#16839639—21no—
46#16839636—21no—
47#16839622C2211yescharacteristic
48#16839620—21no—
49C4×C4⋊Dic61C2211yescharacteristic
50C22⋊C4×Dic61—21no—
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55C23×C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×#97×C61C2211yescharacteristic
58C2×#97×C61C2211yescharacteristic
59C4×C22⋊C4×C61C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C22×Dic122—22no—
63C22×Dic122—22no—
64C22×Dic122—21no—
65C22×Dic122—22no—
66C22×Dic122—41no—
67C22×Dic122—41no—
68C22×Dic122C2×C414yescomplemented
69C22×Dic122C2311yescharacteristic
70C22×Dic122C2311yescharacteristic
71C22×D244C2311yescharacteristic
72C22×C22⋊D61—21no—
73C23×Dic61—21no—
74C23×Dic61—21no—
75C22×C4×D61—21no—
76C2×#11758190—22no—
77C2×#11758190—22no—
78C2×#11758190—41no—
79C2×#11758190—41no—
80C2×#11758190C2×C414yescomplemented
81C2×#11758190C2×C414yescomplemented
82#14519751—22no—
83#14519751C2×C414yes—
84C4×Dic122—22no—
85C4×Dic122—22no—
86C4×Dic122—41no—
87C4×Dic122—41no—
88C4×D244—22no—
89C4×D244—41no—
90#14519737—44no—
91C2×C4⋊Dic61—22no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61—41no—
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×C22⋊Dic61—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61—21no—
110#14519711—22no—
111#14519711—41no—
112#14519702—22no—
113#14519702—22no—
114#14519702—22no—
115#14519702C2×C414yescomplemented
116#14519702C2×C414yescomplemented
117#14519702D414yescomplemented
118#14519699—22no—
119#14519699—41no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125#14519684—21no—
126#14519684—21no—
127C23×C4×C61C2311yescharacteristic
128C22×C8×C61—22no—
129C22×C8×C61—22no—
130C22×C8×C61—41no—
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C2×C22⋊C4×C61D411yescharacteristic
136C2×C22⋊C4×C61D411yescharacteristic
137C2×C42×C61C2311yescharacteristic
138C2×C42×C61C2311yescharacteristic
139C22⋊C8×C61C2×C414yescomplemented
140#97×C61—22no—
141#97×C61—41no—
142#95×C61D411yescharacteristic
143#95×C61D411yescharacteristic
144C24×C61C2×D411yescharacteristic
145C23×D61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61C22×C412yes—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61#4112yes—
157C22×C4×C61C2411yescharacteristic
158C2×C22⋊D61—24no—
159C2×C22⋊D61—42no—
160C2×C22⋊D61—42no—
161C22×Dic61—21no—
162C22×Dic61—24no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—42no—
170C22×Dic61—42no—
171C22×Dic61—42no—
172C22×Dic61—42no—
173C22×Dic61—81no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244C22×C412yes—
180C2×C4×D61—42no—
181C2×C4×D61—42no—
182C2×C4×D61—81no—
183C2×Dic122—21no—
184C2×Dic122—21no—
185C2×Dic122—21no—
186C2×Dic122—21no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—28no—
191C2×Dic122—24no—
192C2×Dic122—21no—
193C2×Dic122—44no—
194C2×Dic122—44no—
195C2×Dic122—44no—
196C2×Dic122—42no—
197C2×Dic122—42no—
198C2×Dic122C22×C412yes—
199C2×Dic122C22×C412yes—
200C2×Dic122C2×D412yes—
201C2×Dic122#4112yes—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—44no—
212C2×C8×C61C22×C412yes—
213C2×C8×C61C22×C412yes—
214C2×C8×C61C2×D412yes—
215C22⋊C4×C61—22no—
216C22⋊C4×C61—22no—
217C42×C61—21no—
218C42×C61—21no—
219C42×C61—21no—
220C42×C61—21no—
221C22⋊Dic61—42no—
222#11758198—24no—
223#11758198—42no—
224#11758198—42no—
225#11758198—81no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—42no—
235C4⋊Dic61C22×C412yes—
236C4⋊Dic61C2×D412yes—
237#11758196—42no—
238#11758196—42no—
239#11758196—42no—
240C4×Dic61—42no—
241C4×Dic61—42no—
242C4×Dic61—42no—
243#11758190—28no—
244#11758190—44no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61C4×D412yes—
250C23×C61AGL(1,ℤ/8)12yes—
251C23×C61#13712yes—
252C23×C61C22×D411yescharacteristic
253C22×D61—22no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61C4×D412yes—
279C2×C4×C61C23×C411yescharacteristic
280C2×C4×C61C22×D411yescharacteristic
281C2×C4×C61C2×#4111yescharacteristic
282C2×C4×C61C2×#4111yescharacteristic
283C2×C4×C61H(5,𝔽2)11yescharacteristic
284C2×C4×C61H(5,𝔽2)11yescharacteristic
285C22⋊D61—48no—
286C2×Dic61—22no—
287C2×Dic61—22no—
288C2×Dic61—22no—
289C2×Dic61—22no—
290C2×Dic61—22no—
291C2×Dic61—22no—
292C2×Dic61—48no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—84no—
309D244—22no—
310D244—22no—
311D244—41no—
312D244—41no—
313C4×D61—84no—
314Dic122—22no—
315Dic122—22no—
316Dic122—22no—
317Dic122—22no—
318Dic122—22no—
319Dic122—48no—
320Dic122—41no—
321Dic122—41no—
322Dic122C4×D414yescomplemented
323C8×C61—22no—
324C8×C61—22no—
325C8×C61—22no—
326C8×C61—41no—
327#22855—611nomaximal, Sylow
328C22×C61—22no—
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—22no—
334C22×C61#44014yescomplemented
335C22×C61C2×C4×D411yescharacteristic
336C22×C61D4211yescharacteristic
337C22×C61#54611yescharacteristic
338C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C61C2×#13711yescharacteristic
340C22×C61#57711yescharacteristic
341C22×C61#57811yescharacteristic
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—81no—
346C2×D61—81no—
347C2×D61—81no—
348C2×D61—81no—
349C4×C61—22no—
350C4×C61—41no—
351C4×C61—41no—
352C4×C61—41no—
353C4×C61—41no—
354C4×C61C2×C4×D411yescharacteristic
355C4×C61#51811yescharacteristic
356C4×C61#54611yescharacteristic
357C4×C61#55111yescharacteristic
358Dic61—24no—
359Dic61—42no—
360Dic61—42no—
361Dic61—42no—
362Dic61—81no—
363Dic61—81no—
364Dic61—81no—
365C2×#448—611no—
366C2×#440—611no—
367C22×#103—611no—
368#2361—611no—
369Q8×C22⋊C4—611no—
370#1973—611no—
371#1935—611no—
372#1928—611no—
373#1893—611no—
374#1880—611no—
375#1877—611no—
376#1863—611no—
377#1852—611no—
378#1763—611no—
379#1752D6111yescharacteristic, complemented
380C2×C61—24no—
381C2×C61#235811yescharacteristic
382C2×C61C2×#44011yescharacteristic
383C2×C61#294711yescharacteristic
384C2×C61#326511yescharacteristic
385C2×C61#327011yescharacteristic
386C2×C61#330811yescharacteristic
387C2×C61#332011yescharacteristic
388D61—82no—
389C23×Q8—611no—
390C22×SD16—611no—
391C22×SD16—611no—
392C23×C8C2×D6111yescharacteristic
393C2×#121—611no—
394C2×C4×Q8—611no—
395C2×C4×Q8—611no—
396C2×C4×D4—611no—
397C2×C4×D4—1221no—
398C22×C4⋊C4—611no—
399#448—618no—
400#440—1224no—
401C2×#107—611no—
402C2×#107—611no—
403C2×#103—611no—
404C2×#103—611no—
405C2×#103—611no—
406C2×#103—611no—
407C2×#103—611no—
408C2×#103—611no—
409C2×#103—1224no—
410C2×#102—611no—
411C2×#102—611no—
412C2×C22⋊C8C2×D6111yescharacteristic
413C2×#97C2×D6111yescharacteristic
414C2×#97C2×D6111yescharacteristic
415#391—611no—
416#391—611no—
417#391—1221no—
418#391—1221no—
419#390—611no—
420#389—611no—
421#388—1221no—
422#386—1221no—
423#385—1221no—
424#380—611no—
425#380—1221no—
426C4×C4⋊C4—611no—
427C4×C22⋊C4—1221no—
428C4×C22⋊C4C2×D6111yescharacteristic
429#340—611no—
430#340—611no—
431#340—611no—
432#340—611no—
433#336C2×D6111yescharacteristic
434#336C2×D6111yescharacteristic
435C61#2285511yescharacteristic, complemented, Sylow
436C22×Q8—614no—
437C22×Q8—611no—
438C22×Q8—611no—
439C22×Q8—1222no—
440C22×Q8—1222no—
441C22×Q8—1221no—
442C22×Q8—1222no—
443C22×Q8—2441no—
444C22×Q8—2441no—
445C22×D4—611no—
446C22×D4—1221no—
447C23×C4—1221no—
448C23×C4—1221no—
449C23×C4—1221no—
450C23×C4C22×D6111yescharacteristic
451C2×SD16—614no—
452C2×SD16—614no—
453C2×SD16—1222no—
454C2×SD16—1222no—
455C2×SD16—2441no—
456C2×SD16—2441no—
457C22×C8—22no—
458C22×C8—22no—
459C22×C8—41no—
460C22×C8C22×D6111yescharacteristic
461C22×C8C22×D6111yescharacteristic
462C22×C8C22×D6111yescharacteristic
463C22×C8C22×D6111yescharacteristic
464#121—614no—
465#121—1222no—
466C4×Q8—1222no—
467C4×Q8—1222no—
468C4×Q8—2441no—
469C4×Q8—2441no—
470C4×D4—1222no—
471C4×D4—2441no—
472C4×D4—2444no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—1222no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—2441no—
484C2×C22⋊C4—1221no—
485C2×C22⋊C4—1221no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4D24411yescharacteristic
490C2×C22⋊C4D24411yescharacteristic
491C2×C42—1221no—
492C2×C42—1221no—
493C2×C42—1221no—
494C2×C42C22×D6111yescharacteristic
495C2×C42C22×D6111yescharacteristic
496#107—1222no—
497#107—2441no—
498#103—614no—
499#103—614no—
500#103—614no—
501#103—1222no—
502#103—1222no—
503#103—1222no—
504#102—1222no—
505#102—2441no—
506C22⋊C8C4×D6114yescomplemented
507#97—22no—
508#97—41no—
509#95—1221no—
510#95—1221no—
511#95—1221no—
512#95—1221no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516#95D24411yescharacteristic
517#95D24411yescharacteristic
518C24—1221no—
519C24C2×D24411yescharacteristic
520C2×Q8—612no—
521C2×Q8—612no—
522C2×Q8—612no—
523C2×Q8—612no—
524C2×Q8—1228no—
525C2×Q8—1221no—
526C2×Q8—1221no—
527C2×Q8—1221no—
528C2×Q8—1221no—
529C2×Q8—1224no—
530C2×Q8—1221no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×Q8—2442no—
535C2×Q8—2442no—
536C2×Q8—2444no—
537C2×Q8—2444no—
538C2×Q8—2444no—
539C2×D4—612no—
540C2×D4—1224no—
541C2×D4—1221no—
542C2×D4—1221no—
543C2×D4—1221no—
544C2×D4—1221no—
545C2×D4—1221no—
546C2×D4—2442no—
547C2×D4—2442no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1224no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—4881no—
561C22×C4—4881no—
562C22×C4—2442no—
563C22×C4—2442no—
564C22×C4—2442no—
565C22×C4—2442no—
566C22×C4—2442no—
567C22×C4—2442no—
568C22×C4C2×C4×D6112yes—
569C22×C4C2×D24411yescharacteristic
570C22×C4C2×D24411yescharacteristic
571C22×C4C2×D24411yescharacteristic
572C22×C4C2×D24411yescharacteristic
573C22×C4C2×D24411yescharacteristic
574C22×C4#1175822212yes—
575C22×C4C23×D6111yescharacteristic
576SD16—1228no—
577SD16—2444no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—44no—
588C2×C8C2×C4×D6112yes—
589C2×C8C2×C4×D6112yes—
590C2×C8D4×D6112yes—
591C4⋊C4—612no—
592C4⋊C4—612no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—2442no—
602C4⋊C4—2442no—
603C4⋊C4—2442no—
604C4⋊C4—2442no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—1224no—
608C22⋊C4—4881no—
609C22⋊C4—2442no—
610C22⋊C4—2442no—
611C22⋊C4—2442no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—2442no—
617C42—2442no—
618C42—2442no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—1222no—
624C23—2441no—
625C23—2441no—
626C23—2441no—
627C23—2441no—
628C23—2441no—
629C23—2441no—
630C23C4×D24412yes—
631C23#1451980512yes—
632C23#1451981012yes—
633C23C22×D24411yescharacteristic
634Q8—614no—
635Q8—1222no—
636Q8—1222no—
637Q8—1222no—
638Q8—1222no—
639Q8—1222no—
640Q8—2448no—
641Q8—2441no—
642Q8—2441no—
643D4—1222no—
644D4—1222no—
645D4—2448no—
646D4—2441no—
647D4—2441no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—4884no—
673C2×C4—4884no—
674C2×C4—2448no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4C4×D24412yes—
691C2×C4C22×C4×D6111yescharacteristic
692C2×C4C2×D4×D6111yescharacteristic
693C2×C4#41×D6111yescharacteristic
694C2×C4C2×#1175822211yescharacteristic
695C2×C4#1451982211yescharacteristic
696C2×C4#1451982311yescharacteristic
697C8—22no—
698C8—22no—
699C8—22no—
700C8—41no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—4881no—
708C22—4881no—
709C22—4881no—
710C22—4881no—
711C22—2442no—
712C22—2442no—
713C22—2442no—
714C22#1683986414yescomplemented
715C22C2×C4×D24411yescharacteristic
716C22D4×D24411yescharacteristic
717C22#1684040711yescharacteristic
718C22C2×#1451980511yescharacteristic
719C22C2×#1451981011yescharacteristic
720C22#1684057411yescharacteristic
721C22#1684057911yescharacteristic
722C4—22no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—1224no—
728C4—4881no—
729C4—4881no—
730C4—4881no—
731C4—2442no—
732C4—2442no—
733C4—2442no—
734C4C4×D4×D6111yescharacteristic
735C4#1684023411yescharacteristic
736C4#1684040211yescharacteristic
737C4#1684043611yescharacteristic
738C2—24no—
739C2—4882no—
740C2#2144880111yescharacteristic
741C2C2×#1683986411yescharacteristic
742C2#2145466411yescharacteristic
743C2#2145731911yescharacteristic
744C2#2145739411yescharacteristic
745C2#2145781211yescharacteristic
746C2#2145799211yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1752C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
cosocleC22×C4×C61C24
hypercenter#1752D61
hypocenterC61#22855
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1752

Complements

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

NH ≅ G/Ntype
2. C2×#16839864C2semidirect
3. C22×#14519702C2semidirect
5. C22⋊C4×Dic122C2semidirect
6. #21446700C2semidirect
7. #21446509C2semidirect
8. #21446461C2semidirect
10. #21446173C2semidirect
11. #21446152C2semidirect
12. #21446076C2semidirect
13. #21446009C2semidirect
14. #21445650C2semidirect
15. C61×#1752C2semidirect
25. #16839903C4semidirect
68. C22×Dic122C2×C4semidirect
80. C2×#11758190C2×C4semidirect
81. C2×#11758190C2×C4semidirect
115. #14519702C2×C4semidirect
116. #14519702C2×C4semidirect
117. #14519702D4semidirect
139. C22⋊C8×C61C2×C4semidirect
322. Dic122C4×D4semidirect
334. C22×C61#440semidirect
379. #1752D61semidirect
435. C61#22855semidirect
506. C22⋊C8C4×D61semidirect
714. C22#16839864semidirect

Maximal subgroups

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

subgroupindex
C2×#168399032
C2×#168398642
C22×#145197022
#214488332
C22⋊C4×Dic1222
#214467002
#214465092
#214464612
#214462472
#214461732
#214461522
#214460762
#214460092
#214456502
C61×#17522
#2285561