Finite Group Databasebeta

← #29700289

Subgroups — #29700289

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×#16839863C211yesmaximal, characteristic, complemented
2C22×#14519701C211yesmaximal, characteristic, complemented
3#21448839C211yesmaximal, characteristic
4Q8×C22⋊Dic61C211yesmaximal, characteristic, complemented
5#21446702C211yesmaximal, characteristic, complemented
6#21446511C211yesmaximal, characteristic, complemented
7#21446462C211yesmaximal, characteristic, complemented
8#21446248C211yesmaximal, characteristic
9#21446176C211yesmaximal, characteristic, complemented
10#21446155C211yesmaximal, characteristic, complemented
11#21446075C211yesmaximal, characteristic, complemented
12#21446009C211yesmaximal, characteristic, complemented
13#21445651C211yesmaximal, characteristic, complemented
14#21445598C211yesmaximal, characteristic, complemented
15C2×C61×#448C211yesmaximal, characteristic
16C23×#92418C2211yescharacteristic
17C2×Q8×Dic61C2211yescharacteristic
18C2×Q8×Dic61C2211yescharacteristic
19C2×D4×Dic61—21no—
20C2×D4×Dic61C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22#16839863—24no—
23C2×#14519711C2211yescharacteristic
24C2×#14519711C2211yescharacteristic
25C2×#14519701—24no—
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519687C2211yescharacteristic
33C2×#14519687C2211yescharacteristic
34#16839669—21no—
35#16839669—21no—
36#16839669C2211yescharacteristic
37#16839669C2211yescharacteristic
38#16839665C2211yescharacteristic
39#16839661C2211yescharacteristic
40#16839655—21no—
41#16839642—21no—
42#16839637—21no—
43#16839622—21no—
44#16839622C2211yescharacteristic
45C4⋊C4×Dic61C2211yescharacteristic
46C4×C22⋊Dic61—21no—
47C4×C22⋊Dic61C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C23×Q8×C61C2211yescharacteristic
55C22×SD16×C61C2211yescharacteristic
56C22×SD16×C61C2211yescharacteristic
57C2×#121×C61C2211yescharacteristic
58C61×#448C418yescomplemented
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C23×Dic61—21no—
63C23×Dic61—21no—
64C22×#92418—22no—
65C22×#92418—22no—
66C22×#92418—41no—
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69Q8×Dic61—22no—
70Q8×Dic61—22no—
71Q8×Dic61—41no—
72Q8×Dic61—41no—
73D4×Dic61—22no—
74D4×Dic61—41no—
75D4×Dic61—44no—
76C2×C4⋊Dic61—22no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61—41no—
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61D411yescharacteristic
91C2×C22⋊Dic61D411yescharacteristic
92C2×C4×Dic61—21no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61—21no—
95C2×C4×Dic61C2311yescharacteristic
96C2×C4×Dic61C2311yescharacteristic
97#14519711—22no—
98#14519711—41no—
99#14519701—22no—
100#14519701—22no—
101#14519701—22no—
102#14519701D414yescomplemented
103#14519698—22no—
104#14519698—41no—
105#14519687—22no—
106#14519687—41no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684D411yescharacteristic
115#14519684D411yescharacteristic
116C22×Q8×C61—21no—
117C22×Q8×C61—22no—
118C22×Q8×C61—22no—
119C22×Q8×C61—22no—
120C22×Q8×C61—41no—
121C22×Q8×C61—41no—
122C22×Q8×C61C2×C414yescomplemented
123C22×Q8×C61C2311yescharacteristic
124C22×Q8×C61C2311yescharacteristic
125C22×D4×C61—21no—
126C22×D4×C61C2311yescharacteristic
127C23×C4×C61—21no—
128C23×C4×C61C2311yescharacteristic
129C2×SD16×C61—22no—
130C2×SD16×C61—22no—
131C2×SD16×C61—41no—
132C2×SD16×C61—41no—
133C2×SD16×C61C2×C414yescomplemented
134C2×SD16×C61C2×C414yescomplemented
135C22×C8×C61C2311yescharacteristic
136C22×C8×C61C2311yescharacteristic
137#121×C61—22no—
138#121×C61C2×C414yes—
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61—21no—
141#103×C61C2×C414yescomplemented
142#103×C61C2×C414yescomplemented
143C22⋊C8×C61C2×C414yescomplemented
144C24×C61—21no—
145C24×C61C2×D411yescharacteristic
146C2×Q8×C61—24no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—28no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—42no—
157C2×Q8×C61—42no—
158C2×Q8×C61—44no—
159C2×Q8×C61—44no—
160C2×Q8×C61—44no—
161C2×Q8×C61C22×C412yes—
162C2×Q8×C61C22×C412yes—
163C2×Q8×C61C2×D412yes—
164C2×Q8×C61#4112yes—
165C2×D4×C61—24no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—42no—
172C2×D4×C61—42no—
173C2×D4×C61C22×C412yes—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—24no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—42no—
183C22×C4×C61—42no—
184C22×C4×C61C22×C412yes—
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61#4112yes—
187C22×C4×C61C2411yescharacteristic
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—42no—
193C22×Dic61—42no—
194C22×Dic61—42no—
195C22×Dic61—42no—
196C22×Dic61—81no—
197C22×Dic61—81no—
198C22×Dic61C2×D411yescharacteristic
199C22×Dic61C2×D411yescharacteristic
200C22×Dic61C2×D411yescharacteristic
201C22×Dic61C2×D411yescharacteristic
202SD16×C61—28no—
203SD16×C61—44no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61C22×C412yes—
209C2×C8×C61C22×C412yes—
210C4⋊C4×C61—21no—
211C4⋊C4×C61C22×C412yes—
212C22⋊C4×C61—24no—
213C22⋊Dic61—22no—
214C22⋊Dic61—22no—
215C22⋊Dic61—42no—
216C22⋊Dic61—42no—
217C22⋊Dic61—42no—
218C22⋊Dic61—81no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—42no—
227C4⋊Dic61—42no—
228C4⋊Dic61—42no—
229C4⋊Dic61—42no—
230C4⋊Dic61C2×D412yes—
231C4×Dic61—21no—
232C4×Dic61—21no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C4×Dic61—42no—
236C4×Dic61—42no—
237C4×Dic61—42no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—44no—
244C2×#92418C2×D412yes—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—22no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61C4×D412yes—
257C23×C61AGL(1,ℤ/8)12yes—
258C23×C61#13712yes—
259C23×C61C22×D411yescharacteristic
260Q8×C61—22no—
261Q8×C61—22no—
262Q8×C61—22no—
263Q8×C61—22no—
264Q8×C61—22no—
265Q8×C61—48no—
266Q8×C61—41no—
267Q8×C61—41no—
268Q8×C61C4×D414yescomplemented
269D4×C61—22no—
270D4×C61—22no—
271D4×C61—48no—
272D4×C61—41no—
273D4×C61—41no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—21no—
277C2×C4×C61—22no—
278C2×C4×C61—21no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—48no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61C4×D412yes—
291C2×C4×C61C23×C411yescharacteristic
292C2×C4×C61C22×D411yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61H(5,𝔽2)11yescharacteristic
296C2×C4×C61H(5,𝔽2)11yescharacteristic
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—22no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—84no—
322C2×Dic61—84no—
323C8×C61—22no—
324C8×C61—22no—
325#92418—22no—
326#92418—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—42no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61—81no—
340C22×C61—81no—
341C22×C61#44014yescomplemented
342C22×C61C2×C4×D411yescharacteristic
343C22×C61D4211yescharacteristic
344C22×C61#54611yescharacteristic
345C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C61C2×#13711yescharacteristic
347C22×C61#57711yescharacteristic
348C22×C61#57811yescharacteristic
349C4×C61—22no—
350C4×C61—24no—
351C4×C61—42no—
352C4×C61—42no—
353C4×C61C2×C4×D411yescharacteristic
354C4×C61#51811yescharacteristic
355C4×C61#54611yescharacteristic
356C4×C61#55111yescharacteristic
357Dic61—41no—
358Dic61—42no—
359Dic61—41no—
360Dic61—41no—
361Dic61—41no—
362Dic61—81no—
363Dic61—81no—
364Dic61—81no—
365C2×#448D6111yescharacteristic
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#1752—611no—
380C2×C61—24no—
381C2×C61—82no—
382C2×C61#235811yescharacteristic
383C2×C61C2×#44011yescharacteristic
384C2×C61#294711yescharacteristic
385C2×C61#326511yescharacteristic
386C2×C61#327011yescharacteristic
387C2×C61#330811yescharacteristic
388C2×C61#332011yescharacteristic
389C23×Q8C2×D6111yescharacteristic
390C22×SD16C2×D6111yescharacteristic
391C22×SD16C2×D6111yescharacteristic
392C23×C8—611no—
393C2×#121C2×D6111yescharacteristic
394C2×C4×Q8—611no—
395C2×C4×Q8—611no—
396C2×C4×D4—611no—
397C2×C4×D4—1221no—
398C22×C4⋊C4—611no—
399#448Dic6118yescomplemented
400#440—1224no—
401C2×#107—611no—
402C2×#107—611no—
403C2×#103—611no—
404C2×#103—611no—
405C2×#103—611no—
406C2×#103—611no—
407C2×#103—1224no—
408C2×#103C2×D6111yescharacteristic
409C2×#103C2×D6111yescharacteristic
410C2×#102—611no—
411C2×#102—611no—
412C2×C22⋊C8C2×D6111yescharacteristic
413C2×#97—611no—
414C2×#97—611no—
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—611no—
428C4×C22⋊C4—1221no—
429#340—611no—
430#340—611no—
431#340—611no—
432#340—611no—
433#336—611no—
434#336—611no—
435C61#2285511yescharacteristic, complemented, Sylow
436C22×Q8—21no—
437C22×Q8—22no—
438C22×Q8—22no—
439C22×Q8—22no—
440C22×Q8—41no—
441C22×Q8—41no—
442C22×Q8C2×Dic6114yescomplemented
443C22×Q8C22×D6111yescharacteristic
444C22×Q8C22×D6111yescharacteristic
445C22×D4—21no—
446C22×D4C22×D6111yescharacteristic
447C23×C4—21no—
448C23×C4—1221no—
449C23×C4—1221no—
450C23×C4C22×D6111yescharacteristic
451C2×SD16—22no—
452C2×SD16—22no—
453C2×SD16—41no—
454C2×SD16—41no—
455C2×SD16C2×Dic6114yescomplemented
456C2×SD16C2×Dic6114yescomplemented
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—1222no—
460C22×C8—1222no—
461C22×C8—2441no—
462C22×C8C22×D6111yescharacteristic
463C22×C8C22×D6111yescharacteristic
464#121—22no—
465#121C2×Dic6114yes—
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—1222no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—2441no—
483C2×C4⋊C4C22×D6111yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—611no—
486C2×C22⋊C4—611no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C42—611no—
492C2×C42—611no—
493C2×C42—1221no—
494C2×C42—1221no—
495C2×C42—1221no—
496#107—1222no—
497#107—2441no—
498#103—614no—
499#103—1222no—
500#103—1222no—
501#103—1222no—
502#103C2×Dic6114yescomplemented
503#103C2×Dic6114yescomplemented
504#102—1222no—
505#102—2441no—
506C22⋊C8C2×Dic6114yescomplemented
507#97—1222no—
508#97—2441no—
509#95—611no—
510#95—611no—
511#95—1221no—
512#95—1221no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516#95—1221no—
517#95—1221no—
518C24—21no—
519C24D4×D6111yescharacteristic
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—24no—
525C2×Q8—28no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—42no—
531C2×Q8—42no—
532C2×Q8—44no—
533C2×Q8—44no—
534C2×Q8—44no—
535C2×Q8D4×D6112yes—
536C2×Q8#1175822412yes—
537C2×Q8C22×Dic6112yes—
538C2×Q8C22×Dic6112yes—
539C2×D4—24no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4C22×Dic6112yes—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—24no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—4881no—
567C22×C4—4881no—
568C22×C4—2442no—
569C22×C4—2442no—
570C22×C4—2442no—
571C22×C4—2442no—
572C22×C4D4×D6111yescharacteristic
573C22×C4#1175822412yes—
574C22×C4C22×Dic6112yes—
575C22×C4C23×D6111yescharacteristic
576SD16—28no—
577SD16—44no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—612no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—2444no—
589C2×C8C22×Dic6112yes—
590C2×C8C22×Dic6112yes—
591C4⋊C4—21no—
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—2442no—
601C4⋊C4—2442no—
602C4⋊C4—2442no—
603C4⋊C4—2442no—
604C4⋊C4C22×Dic6112yes—
605C22⋊C4—24no—
606C22⋊C4—1222no—
607C22⋊C4—1222no—
608C22⋊C4—4881no—
609C22⋊C4—2442no—
610C22⋊C4—2442no—
611C22⋊C4—2442no—
612C42—1221no—
613C42—1221no—
614C42—1221no—
615C42—1221no—
616C42—2442no—
617C42—2442no—
618C42—2442no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—22no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23D4×Dic6112yes—
631C23#1451980412yes—
632C23#1451980612yes—
633C23C2×D4×D6111yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—48no—
640Q8—41no—
641Q8—41no—
642Q8D4×Dic6114yescomplemented
643D4—22no—
644D4—22no—
645D4—48no—
646D4—41no—
647D4—41no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—48no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1222no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—4884no—
678C2×C4—4884no—
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×C4D4×Dic6112yes—
691C2×C4C23×Dic6111yescharacteristic
692C2×C4C2×D4×D6111yescharacteristic
693C2×C4C2×#1175822411yescharacteristic
694C2×C4C2×#1175822411yescharacteristic
695C2×C4#1451982211yescharacteristic
696C2×C4#1451982211yescharacteristic
697C8—22no—
698C8—22no—
699C8—1222no—
700C8—2441no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22#1683986314yescomplemented
715C22C2×D4×Dic6111yescharacteristic
716C22#1684039411yescharacteristic
717C22#1684039911yescharacteristic
718C22C2×#1451980411yescharacteristic
719C22C2×#1451980611yescharacteristic
720C22#1684057111yescharacteristic
721C22#1684057811yescharacteristic
722C4—22no—
723C4—24no—
724C4—42no—
725C4—42no—
726C4—4881no—
727C4—4881no—
728C4—4881no—
729C4—2441no—
730C4—2441no—
731C4—2441no—
732C4—2442no—
733C4—2441no—
734C4C2×D4×Dic6111yescharacteristic
735C4#1684023711yescharacteristic
736C4#1684039911yescharacteristic
737C4#1684044311yescharacteristic
738C2—24no—
739C2—82no—
740C2#2144880311yescharacteristic
741C2C2×#1683986311yescharacteristic
742C2#2145466311yescharacteristic
743C2#2145730711yescharacteristic
744C2#2145738211yescharacteristic
745C2#2145781411yescharacteristic
746C2#2145799411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#448C2
socleC23×C61C22×D4
prime radicalC2×#121×C61C22
cosocleC22×C4×C61C24
hypercenterC2×#448D61
hypocenterC61#22855
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×#16839863C2semidirect
2. C22×#14519701C2semidirect
4. Q8×C22⋊Dic61C2semidirect
5. #21446702C2semidirect
6. #21446511C2semidirect
7. #21446462C2semidirect
9. #21446176C2semidirect
10. #21446155C2semidirect
11. #21446075C2semidirect
12. #21446009C2semidirect
13. #21445651C2semidirect
14. #21445598C2semidirect
58. C61×#448C4semidirect
102. #14519701D4semidirect
122. C22×Q8×C61C2×C4semidirect
133. C2×SD16×C61C2×C4semidirect
134. C2×SD16×C61C2×C4semidirect
141. #103×C61C2×C4semidirect
142. #103×C61C2×C4semidirect
143. C22⋊C8×C61C2×C4semidirect
268. Q8×C61C4×D4semidirect
341. C22×C61#440semidirect
399. #448Dic61semidirect
435. C61#22855semidirect
442. C22×Q8C2×Dic61semidirect
455. C2×SD16C2×Dic61semidirect
456. C2×SD16C2×Dic61semidirect
502. #103C2×Dic61semidirect
503. #103C2×Dic61semidirect
506. C22⋊C8C2×Dic61semidirect
642. Q8D4×Dic61semidirect
714. C22#16839863semidirect

Maximal subgroups

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

subgroupindex
C2×#168398632
C22×#145197012
#214488392
Q8×C22⋊Dic612
#214467022
#214465112
#214464622
#214462482
#214461762
#214461552
#214460752
#214460092
#214456512
#214455982
C2×C61×#4482
#2285561