Finite Group Databasebeta

← #29700285

Subgroups — #29700285

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×#16839901C211yesmaximal, characteristic
2C2×#16839865C211yesmaximal, characteristic, complemented
3#21448835C211yesmaximal, characteristic
4Q8×C22⋊Dic61C211yesmaximal, characteristic, complemented
5#21446697C211yesmaximal, characteristic, complemented
6#21446506C211yesmaximal, characteristic, complemented
7#21446463C211yesmaximal, characteristic, complemented
8#21446247C211yesmaximal, characteristic
9#21446172C211yesmaximal, characteristic, complemented
10#21446150C211yesmaximal, characteristic, complemented
11#21446071C211yesmaximal, characteristic, complemented
12#21446007C211yesmaximal, characteristic, complemented
13#21445651C211yesmaximal, characteristic, complemented
14#21445595C211yesmaximal, characteristic, complemented
15C22×#103×C61C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20C2×Q8×Dic61C2211yescharacteristic
21C2×#14519739C2211yescharacteristic
22C2×C4×C22⋊D61—21no—
23#16839901C418yescomplemented
24#16839865—24no—
25C2×#14519710C2211yescharacteristic
26C2×#14519710C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×#14519687C2211yescharacteristic
33C2×#14519687C2211yescharacteristic
34#16839669—21no—
35#16839669—21no—
36#16839669C2211yescharacteristic
37#16839669C2211yescharacteristic
38#16839663C2211yescharacteristic
39#16839658C2211yescharacteristic
40#16839652—21no—
41#16839641—21no—
42#16839633—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
55C23×C8×C61C2211yescharacteristic
56C22×C4⋊C4×C61C2211yescharacteristic
57C2×#103×C61—24no—
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C22×C4×D61—21no—
65C2×#11758201—22no—
66C2×#11758201—22no—
67C2×#11758201—41no—
68C2×#11758201—41no—
69C2×#11758201C2×C414yescomplemented
70C2×#11758201C2×C414yescomplemented
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73#14519751—22no—
74#14519751C2×C414yes—
75Q8×Dic61—22no—
76Q8×Dic61—22no—
77Q8×Dic61—41no—
78Q8×Dic61—41no—
79#14519739—22no—
80#14519739—41no—
81C4×C22⋊D61—44no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×#11758196—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61D411yescharacteristic
90C2×C22⋊Dic61D411yescharacteristic
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61C2311yescharacteristic
99C2×C4×Dic61C2311yescharacteristic
100#14519710—22no—
101#14519710—41no—
102#14519701C2×C414yescomplemented
103#14519701C2×C414yescomplemented
104#14519699—22no—
105#14519699—41no—
106C22⋊#92418C2×C414yescomplemented
107#14519687—22no—
108#14519687—41no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684D411yescharacteristic
117#14519684D411yescharacteristic
118C22×Q8×C61—21no—
119C22×Q8×C61—22no—
120C22×Q8×C61—22no—
121C22×Q8×C61—22no—
122C22×Q8×C61—41no—
123C22×Q8×C61—41no—
124C22×Q8×C61C2×C414yescomplemented
125C22×Q8×C61C2311yescharacteristic
126C22×Q8×C61C2311yescharacteristic
127C23×C4×C61—21no—
128C23×C4×C61—21no—
129C23×C4×C61C2311yescharacteristic
130C22×C8×C61—22no—
131C22×C8×C61—22no—
132C22×C8×C61—41no—
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C2×C4⋊C4×C61—22no—
136C2×C4⋊C4×C61—21no—
137C2×C4⋊C4×C61—41no—
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
140#103×C61—22no—
141#103×C61—22no—
142#103×C61—22no—
143#103×C61D414yescomplemented
144C24×C61C2×D411yescharacteristic
145C23×D61—21no—
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—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—24no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—42no—
175C22×C4×C61—42no—
176C22×C4×C61—42no—
177C22×C4×C61—42no—
178C22×C4×C61—81no—
179C22×C4×C61C22×C412yes—
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61#4112yes—
182C22×C4×C61C2411yescharacteristic
183C2×C22⋊D61—24no—
184C2×C22⋊D61—42no—
185C2×C22⋊D61—42no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61C2×D411yescharacteristic
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192C22×Dic61C2×D411yescharacteristic
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244C22×C412yes—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61—81no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—44no—
208C2×C8×C61C2×D412yes—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—42no—
213C4⋊C4×C61C2×D412yes—
214C22⋊Dic61—22no—
215C22⋊Dic61—22no—
216C22⋊Dic61—42no—
217#11758201—28no—
218#11758201—44no—
219#11758198—24no—
220#11758198—42no—
221#11758198—42no—
222#11758198—81no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—42no—
229C4⋊Dic61—42no—
230C4⋊Dic61C22×C412yes—
231#11758196—42no—
232C4×Dic61—21no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C4×Dic61—21no—
236C4×Dic61—42no—
237C4×Dic61—42no—
238C4×Dic61—42no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418C22×C412yes—
244C2×#92418C22×C412yes—
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—
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
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—21no—
272C2×C4×C61—22no—
273C2×C4×C61—21no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—48no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—84no—
289C2×C4×C61C4×D412yes—
290C2×C4×C61C23×C411yescharacteristic
291C2×C4×C61C22×D411yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61H(5,𝔽2)11yescharacteristic
295C2×C4×C61H(5,𝔽2)11yescharacteristic
296C22⋊D61—48no—
297C2×Dic61—22no—
298C2×Dic61—21no—
299C2×Dic61—21no—
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—
318D244—22no—
319D244—22no—
320D244—41no—
321D244—41no—
322C4×D61—84no—
323C8×C61—22no—
324C8×C61—41no—
325#92418—22no—
326#92418—22no—
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—24no—
351C4×C61—42no—
352C4×C61—42no—
353C4×C61—81no—
354C4×C61C2×C4×D411yescharacteristic
355C4×C61#51811yescharacteristic
356C4×C61#54611yescharacteristic
357C4×C61#55111yescharacteristic
358Dic61—42no—
359Dic61—41no—
360Dic61—41no—
361Dic61—41no—
362Dic61—41no—
363Dic61—81no—
364Dic61—81no—
365C2×#448—611no—
366C2×#440—611no—
367C22×#103D6111yescharacteristic, complemented
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#235811yescharacteristic
382C2×C61C2×#44011yescharacteristic
383C2×C61#294711yescharacteristic
384C2×C61#326511yescharacteristic
385C2×C61#327011yescharacteristic
386C2×C61#330811yescharacteristic
387C2×C61#332011yescharacteristic
388D61—82no—
389C23×Q8C2×D6111yescharacteristic
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⋊C4C2×D6111yescharacteristic
399#448—618no—
400#440—1224no—
401C2×#107—611no—
402C2×#107—611no—
403C2×#103—24no—
404C2×#103—611no—
405C2×#103—611no—
406C2×#103C2×D6111yescharacteristic
407C2×#103C2×D6111yescharacteristic
408C2×#103C2×D6111yescharacteristic
409C2×#103C2×D6111yescharacteristic
410C2×#102—611no—
411C2×#102—611no—
412C2×C22⋊C8—611no—
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×Q8C4×D6114yescomplemented
443C22×Q8C22×D6111yescharacteristic
444C22×Q8C22×D6111yescharacteristic
445C22×D4—611no—
446C22×D4—1221no—
447C23×C4—21no—
448C23×C4—21no—
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×C8—611no—
461C22×C8—611no—
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—22no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—41no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4C22×D6111yescharacteristic
483C2×C4⋊C4C22×D6111yescharacteristic
484C2×C22⋊C4—611no—
485C2×C22⋊C4—611no—
486C2×C22⋊C4—1221no—
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—22no—
499#103—22no—
500#103—22no—
501#103—614no—
502#103—614no—
503#103C22⋊D6114yescomplemented
504#102—1222no—
505#102—2441no—
506C22⋊C8—614no—
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—1221no—
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×Q8C2×C4×D6112yes—
536C2×Q8C2×C4×D6112yes—
537C2×Q8#1175822212yes—
538C2×Q8C2×C22⋊D6112yes—
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—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—24no—
556C22×C4—21no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—81no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—611no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—4881no—
570C22×C4—2442no—
571C22×C4—2442no—
572C22×C4C2×C4×D6112yes—
573C22×C4D4×D6111yescharacteristic
574C22×C4#1175822412yes—
575C22×C4C23×D6111yescharacteristic
576SD16—1228no—
577SD16—2444no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—44no—
584C2×C8—612no—
585C2×C8—612no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8C2×C22⋊D6112yes—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—42no—
595C4⋊C4—612no—
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⋊C4C2×C22⋊D6112yes—
605C22⋊C4—1222no—
606C22⋊C4—1222no—
607C22⋊C4—1224no—
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—1222no—
624C23—2441no—
625C23—2441no—
626C23—2441no—
627C23—2441no—
628C23—2441no—
629C23—2441no—
630C23#1451973712yes—
631C23#1451980412yes—
632C23#1451980912yes—
633C23C2×D4×D6111yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—48no—
640Q8—41no—
641Q8—41no—
642Q8C4×C22⋊D6114yescomplemented
643D4—1222no—
644D4—1222no—
645D4—2448no—
646D4—2441no—
647D4—2441no—
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—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4—1222no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—4884no—
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×C4#1451973712yes—
691C2×C4C22×C4×D6111yescharacteristic
692C2×C4C22×C22⋊D6111yescharacteristic
693C2×C4C2×#1175822411yescharacteristic
694C2×C4C2×#1175822211yescharacteristic
695C2×C4#1451982211yescharacteristic
696C2×C4#1451982211yescharacteristic
697C8—22no—
698C8—41no—
699C8—1222no—
700C8—1222no—
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#1683986514yescomplemented
715C22C2×#1451973711yescharacteristic
716C22D4×C22⋊D6111yescharacteristic
717C22#1684040211yescharacteristic
718C22C2×#1451980411yescharacteristic
719C22C2×#1451980911yescharacteristic
720C22#1684056811yescharacteristic
721C22#1684057511yescharacteristic
722C4—22no—
723C4—24no—
724C4—42no—
725C4—42no—
726C4—81no—
727C4—4881no—
728C4—4881no—
729C4—2442no—
730C4—2441no—
731C4—2441no—
732C4—2441no—
733C4—2441no—
734C4C2×C4×C22⋊D6111yescharacteristic
735C4#1684023511yescharacteristic
736C4#1684040611yescharacteristic
737C4#1684043811yescharacteristic
738C2—24no—
739C2—4882no—
740C2#2144879811yescharacteristic
741C2C2×#1683986511yescharacteristic
742C2#2145465611yescharacteristic
743C2#2145731411yescharacteristic
744C2#2145738911yescharacteristic
745C2#2145780611yescharacteristic
746C2#2145798611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC22×#103×C61C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
cosocleC22×C4×C61C24
hypercenterC22×#103D61
hypocenterC61#22855
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
2. C2×#16839865C2semidirect
4. Q8×C22⋊Dic61C2semidirect
5. #21446697C2semidirect
6. #21446506C2semidirect
7. #21446463C2semidirect
9. #21446172C2semidirect
10. #21446150C2semidirect
11. #21446071C2semidirect
12. #21446007C2semidirect
13. #21445651C2semidirect
14. #21445595C2semidirect
15. C22×#103×C61C2semidirect
23. #16839901C4semidirect
69. C2×#11758201C2×C4semidirect
70. C2×#11758201C2×C4semidirect
102. #14519701C2×C4semidirect
103. #14519701C2×C4semidirect
106. C22⋊#92418C2×C4semidirect
124. C22×Q8×C61C2×C4semidirect
143. #103×C61D4semidirect
268. Q8×C61C4×D4semidirect
334. C22×C61#440semidirect
367. C22×#103D61semidirect
435. C61#22855semidirect
442. C22×Q8C4×D61semidirect
503. #103C22⋊D61semidirect
642. Q8C4×C22⋊D61semidirect
714. C22#16839865semidirect

Maximal subgroups

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

subgroupindex
C2×#168399012
C2×#168398652
#214488352
Q8×C22⋊Dic612
#214466972
#214465062
#214464632
#214462472
#214461722
#214461502
#214460712
#214460072
#214456512
#214455952
C22×#103×C612
#2285561