Finite Group Databasebeta

← #29587259

Subgroups — #29587259

Order 15616.

1230 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519710C211yesmaximal, characteristic, complemented
2C22×#14519689C211yesmaximal, characteristic
3C2×#16839619C211yesmaximal, characteristic
4C2×#16839619C211yesmaximal, characteristic
5C2×#16839525C211yesmaximal, characteristic, complemented
6C2×#16839524C211yesmaximal, characteristic, complemented
7C2×C61×#340C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C23×#92418C2211yescharacteristic
10C22×C4⋊Dic61C2211yescharacteristic
11C22×C4⋊Dic61C2211yescharacteristic
12C22×#11758198—21no—
13C22×#11758198—21no—
14C2×#14519710—22no—
15C2×#14519710—22no—
16C2×#14519710—22no—
17C2×#14519689—22no—
18C2×#14519689—22no—
19C2×#14519689C414yescomplemented
20#16839619—22no—
21#16839619—22no—
22#16839619—22no—
23#16839619—22no—
24C2×#14519684—21no—
25C2×#14519684—21no—
26#16839525—22no—
27#16839524—22no—
28C23×C8×C61C2211yescharacteristic
29C22×C4⋊C4×C61C2211yescharacteristic
30C22×C4⋊C4×C61C2211yescharacteristic
31C61×#340—22no—
32C24×D61D411yescharacteristic
33C23×Dic61—21no—
34C23×Dic61—21no—
35C23×Dic61D411yescharacteristic
36C22×C4×D61—21no—
37C22×C4×D61—21no—
38C22×C4×D61—21no—
39C22×C4×D61—21no—
40C22×C4×D61—21no—
41C22×C4×D61—21no—
42C22×C4×D61—21no—
43C22×C4×D61—21no—
44C22×C4×D61—21no—
45C22×C4×D61—21no—
46C22×C4×D61—21no—
47C22×C4×D61—21no—
48C22×C4×D61C2×C412yes—
49C22×C4×D61Q812yes—
50C22×#92418—21no—
51C22×#92418—21no—
52C22×#92418—21no—
53C22×#92418—21no—
54C22×#92418C2×C412yes—
55C22×#92418D412yes—
56C22×#92418D412yes—
57C2×C4⋊Dic61—21no—
58C2×C4⋊Dic61—21no—
59C2×C4⋊Dic61—21no—
60C2×C4⋊Dic61—21no—
61C2×C4⋊Dic61—21no—
62C2×C4⋊Dic61—21no—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61D412yes—
68C2×C4⋊Dic61D412yes—
69C2×#11758198—24no—
70C2×#11758198—24no—
71C2×#11758198—42no—
72C2×#11758198—42no—
73C2×#11758198—42no—
74C2×#11758198—42no—
75#14519710—28no—
76#14519689—28no—
77#14519684—24no—
78#14519684—24no—
79C23×C4×C61—21no—
80C23×C4×C61—21no—
81C23×C4×C61C2311yescharacteristic
82C22×C8×C61—21no—
83C22×C8×C61—21no—
84C22×C8×C61—21no—
85C22×C8×C61—21no—
86C22×C8×C61—21no—
87C22×C8×C61—21no—
88C22×C8×C61C2×C412yes—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—21no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61D412yes—
100C2×C4⋊C4×C61D412yes—
101C24×C61C2×D411yescharacteristic
102C23×D61—21no—
103C23×D61—21no—
104C23×D61—21no—
105C23×D61—21no—
106C23×D61—21no—
107C23×D61—21no—
108C23×D61—21no—
109C23×D61—21no—
110C23×D61—21no—
111C23×D61—21no—
112C23×D61—21no—
113C23×D61—21no—
114C23×D61C4⋊C412yes—
115C23×D61D812yes—
116C23×D61Q1612yes—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—41no—
120C22×C4×C61—41no—
121C22×C4×C61—41no—
122C22×C4×C61—41no—
123C22×C4×C61—41no—
124C22×C4×C61—41no—
125C22×C4×C61—41no—
126C22×C4×C61—41no—
127C22×C4×C61—41no—
128C22×C4×C61—41no—
129C22×C4×C61—41no—
130C22×C4×C61—41no—
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×Q811yescharacteristic
139C22×C4×C61#4111yescharacteristic
140C22×C4×C61#4111yescharacteristic
141C22×C4×C61#4111yescharacteristic
142C22×C4×C61#4111yescharacteristic
143C22×C4×C61#4111yescharacteristic
144C22×C4×C61#4111yescharacteristic
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—41no—
154C22×Dic61—41no—
155C22×Dic61—41no—
156C22×Dic61—41no—
157C22×Dic61—41no—
158C22×Dic61—41no—
159C22×Dic61—41no—
160C22×Dic61—41no—
161C22×Dic61—41no—
162C22×Dic61—41no—
163C22×Dic61—41no—
164C22×Dic61—41no—
165C22×Dic61C4⋊C412yes—
166C2×C4×D61—22no—
167C2×C4×D61—22no—
168C2×C4×D61—22no—
169C2×C4×D61—22no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—22no—
174C2×C4×D61—22no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—22no—
178C2×C4×D61—41no—
179C2×C4×D61—41no—
180C2×C4×D61—41no—
181C2×C4×D61—41no—
182C2×C4×D61—41no—
183C2×C4×D61—41no—
184C2×C4×D61—41no—
185C2×C4×D61—41no—
186C2×C4×D61—41no—
187C2×C4×D61—41no—
188C2×C4×D61—41no—
189C2×C4×D61—41no—
190C2×C4×D61—41no—
191C2×C4×D61—41no—
192C2×C4×D61—41no—
193C2×C4×D61—41no—
194C2×C8×C61—22no—
195C2×C8×C61—22no—
196C2×C8×C61—22no—
197C2×C8×C61—41no—
198C2×C8×C61—41no—
199C2×C8×C61—41no—
200C2×C8×C61—41no—
201C4⋊C4×C61—22no—
202C4⋊C4×C61—22no—
203C4⋊C4×C61—22no—
204C4⋊C4×C61—22no—
205C4⋊C4×C61—41no—
206C4⋊C4×C61—41no—
207C4⋊C4×C61—41no—
208C4⋊C4×C61—41no—
209#11758198—48no—
210#11758198—48no—
211C4⋊Dic61—22no—
212C4⋊Dic61—22no—
213C4⋊Dic61—22no—
214C4⋊Dic61—22no—
215C4⋊Dic61—41no—
216C4⋊Dic61—41no—
217C4⋊Dic61—41no—
218C4⋊Dic61—41no—
219C2×#92418—22no—
220C2×#92418—22no—
221C2×#92418—22no—
222C2×#92418—22no—
223C2×#92418—22no—
224C2×#92418—22no—
225C2×#92418C22⋊C414yescomplemented
226C23×C61C2×C4⋊C411yescharacteristic
227C23×C61#12011yescharacteristic
228C23×C61#12011yescharacteristic
229C23×C61#12111yescharacteristic
230C23×C61#12111yescharacteristic
231C23×C61#12311yescharacteristic
232C23×C61#12311yescharacteristic
233C23×C61C2×D811yescharacteristic
234C23×C61C2×Q1611yescharacteristic
235C23×C61#13511yescharacteristic
236C23×C61#13511yescharacteristic
237C23×C61AGL(1,ℤ/8)11yescharacteristic
238C23×C61AGL(1,ℤ/8)11yescharacteristic
239C23×C61#13711yescharacteristic
240C23×C61#13711yescharacteristic
241C22×D61—22no—
242C22×D61—22no—
243C22×D61—22no—
244C22×D61—22no—
245C22×D61—22no—
246C22×D61—22no—
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—22no—
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61#10714yescomplemented
276C2×C4×C61—42no—
277C2×C4×C61—42no—
278C2×C4×C61—42no—
279C2×C4×C61—42no—
280C2×C4×C61—42no—
281C2×C4×C61—42no—
282C2×C4×C61—81no—
283C2×C4×C61—81no—
284C2×C4×C61—81no—
285C2×C4×C61—81no—
286C2×C4×C61—81no—
287C2×C4×C61—81no—
288C2×C4×C61—81no—
289C2×C4×C61—81no—
290C2×C4×C61C2×C22⋊C411yescharacteristic
291C2×C4×C61#11711yescharacteristic
292C2×C4×C61C4×D411yescharacteristic
293C2×C4×C61C4×D411yescharacteristic
294C2×C4×C61C4×D411yescharacteristic
295C2×C4×C61C4×D411yescharacteristic
296C2×C4×C61#12011yescharacteristic
297C2×C4×C61#12111yescharacteristic
298C2×C4×C61#12111yescharacteristic
299C2×C4×C61#12111yescharacteristic
300C2×C4×C61#12111yescharacteristic
301C2×C4×C61#12111yescharacteristic
302C2×C4×C61#12111yescharacteristic
303C2×C4×C61C22⋊Q811yescharacteristic
304C2×C4×C61C22⋊Q811yescharacteristic
305C2×C4×C61C22⋊Q811yescharacteristic
306C2×C4×C61C22⋊Q811yescharacteristic
307C2×C4×C61C22⋊Q811yescharacteristic
308C2×C4×C61C22⋊Q811yescharacteristic
309C2×C4×C61#12311yescharacteristic
310C2×C4×C61#12311yescharacteristic
311C2×C4×C61#12311yescharacteristic
312C2×C4×C61#12411yescharacteristic
313C2×C4×C61#12411yescharacteristic
314C2×C4×C61#12411yescharacteristic
315C2×C4×C61#12611yescharacteristic
316C2×C4×C61#12611yescharacteristic
317C2×C4×C61#12711yescharacteristic
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61—81no—
332C2×Dic61—81no—
333C2×Dic61—81no—
334C2×Dic61—81no—
335C2×Dic61—81no—
336C2×Dic61—81no—
337C2×Dic61—81no—
338C2×Dic61—81no—
339C4×D61—42no—
340C4×D61—42no—
341C4×D61—42no—
342C4×D61—42no—
343C4×D61—42no—
344C4×D61—42no—
345C4×D61—42no—
346C4×D61—42no—
347C8×C61—42no—
348#92418—24no—
349#11096—611nomaximal, Sylow
350C22×C61#38011yescharacteristic
351C22×C61#38511yescharacteristic
352C22×C61#38511yescharacteristic
353C22×C61#39211yescharacteristic
354C22×C61#39411yescharacteristic
355C22×C61#39411yescharacteristic
356C22×C61#39711yescharacteristic
357C22×C61C2×#10711yescharacteristic
358C22×C61#42711yescharacteristic
359C22×C61#42811yescharacteristic
360C22×C61#42811yescharacteristic
361C22×C61#44711yescharacteristic
362C22×C61#44711yescharacteristic
363C22×C61#44911yescharacteristic
364C22×C61#44911yescharacteristic
365C22×C61#45111yescharacteristic
366C22×C61#45111yescharacteristic
367C22×C61#45211yescharacteristic
368C22×C61#45211yescharacteristic
369C22×C61#46611yescharacteristic
370C22×C61#46611yescharacteristic
371C22×C61#46711yescharacteristic
372C22×C61#46711yescharacteristic
373C22×C61#46811yescharacteristic
374C22×C61#46811yescharacteristic
375C22×C61#46911yescharacteristic
376C22×C61#47011yescharacteristic
377C22×C61#48011yescharacteristic
378C22×C61#48011yescharacteristic
379C22×C61#48211yescharacteristic
380C22×C61#48211yescharacteristic
381C22×C61#48411yescharacteristic
382C22×C61#48411yescharacteristic
383C22×C61#48511yescharacteristic
384C22×C61#48511yescharacteristic
385C2×D61—24no—
386C2×D61—24no—
387C2×D61—24no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—42no—
400C4×C61—82no—
401C4×C61—82no—
402C4×C61#38611yescharacteristic
403C4×C61#38811yescharacteristic
404C4×C61#38811yescharacteristic
405C4×C61#39011yescharacteristic
406C4×C61#39311yescharacteristic
407C4×C61#39611yescharacteristic
408C4×C61#39611yescharacteristic
409C4×C61#39911yescharacteristic
410Dic61—42no—
411Dic61—82no—
412Dic61—82no—
413C22×#107—611no—
414C22×C22⋊C8—611no—
415C2×#380—611no—
416C2×#380—611no—
417C2×#340—611no—
418C2×#340—611no—
419C2×#340D6111yescharacteristic, complemented
420C2×C61#143911yescharacteristic
421C2×C61#180811yescharacteristic
422C2×C61#180911yescharacteristic
423C2×C61#185211yescharacteristic
424C2×C61#185211yescharacteristic
425C2×C61#185411yescharacteristic
426C2×C61#185411yescharacteristic
427C2×C61#199911yescharacteristic
428C2×C61#200111yescharacteristic
429C2×C61#203311yescharacteristic
430C2×C61#203311yescharacteristic
431C2×C61#203611yescharacteristic
432C2×C61#203611yescharacteristic
433C2×C61#207511yescharacteristic
434C2×C61#207611yescharacteristic
435D61—44no—
436C24×C4—611no—
437C23×C8—611no—
438C23×C8C2×D6111yescharacteristic
439C22×C4⋊C4—611no—
440C22×C4⋊C4—611no—
441C22×C4⋊C4C2×D6111yescharacteristic
442C22×C4⋊C4C2×D6111yescharacteristic
443C22×C22⋊C4—1221no—
444C22×C22⋊C4—1221no—
445C2×#107—1222no—
446C2×#107—1222no—
447C2×#107—1222no—
448C2×C22⋊C8—614no—
449C2×C22⋊C8—1222no—
450C2×C22⋊C8—1222no—
451#380—1222no—
452#380—1222no—
453#380—1222no—
454#380—1222no—
455C2×#95—1221no—
456C2×#95—1221no—
457#340—22no—
458#340—1222no—
459#340—1222no—
460C61#1109611yescharacteristic, complemented, Sylow
461C25—611no—
462C23×C4—21no—
463C23×C4—21no—
464C23×C4—611no—
465C23×C4—612no—
466C23×C4—612no—
467C23×C4—1221no—
468C23×C4—1221no—
469C23×C4—1221no—
470C23×C4—1221no—
471C23×C4—1221no—
472C23×C4—1221no—
473C23×C4—1221no—
474C23×C4—1221no—
475C23×C4—1221no—
476C23×C4—1221no—
477C23×C4—1221no—
478C23×C4—1221no—
479C23×C4—1221no—
480C23×C4—1221no—
481C23×C4C22×D6111yescharacteristic
482C22×C8—21no—
483C22×C8—21no—
484C22×C8—21no—
485C22×C8—21no—
486C22×C8—21no—
487C22×C8—21no—
488C22×C8—612no—
489C22×C8—612no—
490C22×C8—612no—
491C22×C8—1221no—
492C22×C8—1221no—
493C22×C8—1221no—
494C22×C8—1221no—
495C22×C8C4×D6112yes—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—612no—
507C2×C4⋊C4—612no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4D24412yes—
519C2×C4⋊C4C22⋊D6112yes—
520C2×C22⋊C4—1224no—
521C2×C22⋊C4—1224no—
522C2×C22⋊C4—2442no—
523C2×C22⋊C4—2442no—
524C2×C22⋊C4—2442no—
525C2×C22⋊C4—2442no—
526#107—1228no—
527C22⋊C8—1228no—
528#95—1224no—
529#95—1224no—
530C24—612no—
531C24—612no—
532C24—612no—
533C24—1221no—
534C24—1221no—
535C24—1221no—
536C24—1221no—
537C24—1221no—
538C24—1221no—
539C24—1221no—
540C24—1221no—
541C24—1221no—
542C24—1221no—
543C24—1221no—
544C24—1221no—
545C24D4×D6111yescharacteristic
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—612no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—2441no—
582C22×C4—2441no—
583C22×C4—2441no—
584C22×C4—2441no—
585C22×C4—2441no—
586C22×C4—2441no—
587C22×C4—2441no—
588C22×C4—2441no—
589C22×C4—2441no—
590C22×C4—2441no—
591C22×C4—2441no—
592C22×C4—2441no—
593C22×C4—2441no—
594C22×C4—2441no—
595C22×C4—2441no—
596C22×C4—2441no—
597C22×C4—2441no—
598C22×C4—2441no—
599C22×C4—2441no—
600C22×C4—2441no—
601C22×C4—2441no—
602C22×C4—2441no—
603C22×C4—2441no—
604C22×C4—2441no—
605C22×C4—2441no—
606C22×C4—2441no—
607C22×C4—2441no—
608C22×C4—2441no—
609C22×C4C2×C4×D6111yescharacteristic
610C22×C4C2×D24411yescharacteristic
611C22×C4#1175822211yescharacteristic
612C22×C4#1175822211yescharacteristic
613C22×C4#1175822211yescharacteristic
614C22×C4#1175822211yescharacteristic
615C22×C4D4×D6111yescharacteristic
616C22×C4D4×D6111yescharacteristic
617C22×C4D4×D6111yescharacteristic
618C22×C4D4×D6111yescharacteristic
619C22×C4#1175822411yescharacteristic
620C22×C4Q8×D6111yescharacteristic
621C22×C4#1175822611yescharacteristic
622C22×C4C2×C22⋊D6111yescharacteristic
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—614no—
631C2×C8—1222no—
632C2×C8—1222no—
633C2×C8—1222no—
634C2×C8—1222no—
635C2×C8—1222no—
636C2×C8—1222no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—41no—
642C4⋊C4—41no—
643C4⋊C4—41no—
644C4⋊C4—41no—
645C4⋊C4—1222no—
646C4⋊C4—1222no—
647C4⋊C4—1222no—
648C4⋊C4—1222no—
649C4⋊C4—2441no—
650C4⋊C4—2441no—
651C4⋊C4—2441no—
652C4⋊C4—2441no—
653C22⋊C4—2448no—
654C22⋊C4—2448no—
655C23—614no—
656C23—1222no—
657C23—1222no—
658C23—1222no—
659C23—1222no—
660C23—1222no—
661C23—1222no—
662C23—1222no—
663C23—1222no—
664C23—1222no—
665C23—1222no—
666C23—1222no—
667C23—1222no—
668C23—1222no—
669C23—1222no—
670C23—1222no—
671C23—1222no—
672C23—1222no—
673C23—1222no—
674C23—2441no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23—2441no—
682C23—2441no—
683C23—2441no—
684C23—2441no—
685C23—2441no—
686C23—2441no—
687C23—2441no—
688C23—2441no—
689C23—2441no—
690C23C4⋊C4×D6111yescharacteristic
691C23#1451974511yescharacteristic
692C23#1451974711yescharacteristic
693C23#1451975011yescharacteristic
694C23#1451975011yescharacteristic
695C23#1451975911yescharacteristic
696C23#1451976211yescharacteristic
697C23D8×D6111yescharacteristic
698C23Q16×D6111yescharacteristic
699C23#1451979811yescharacteristic
700C23#1451979811yescharacteristic
701C23#1451980111yescharacteristic
702C23#1451980411yescharacteristic
703C23#1451980611yescharacteristic
704C23#1451980911yescharacteristic
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—4881no—
723C2×C4—4881no—
724C2×C4—4881no—
725C2×C4—4881no—
726C2×C4—4881no—
727C2×C4—4881no—
728C2×C4—4881no—
729C2×C4—4881no—
730C2×C4—2442no—
731C2×C4—2442no—
732C2×C4—2442no—
733C2×C4—2442no—
734C2×C4—2442no—
735C2×C4—2442no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4—2442no—
743C2×C4—2442no—
744C2×C4—2442no—
745C2×C4—2442no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4C22⋊C4×D6111yescharacteristic
749C2×C4#1451973411yescharacteristic
750C2×C4#1451973711yescharacteristic
751C2×C4C4×C22⋊D6111yescharacteristic
752C2×C4#1451973911yescharacteristic
753C2×C4C4×D24411yescharacteristic
754C2×C4#1451974711yescharacteristic
755C2×C4#1451974911yescharacteristic
756C2×C4#1451975011yescharacteristic
757C2×C4#1451975011yescharacteristic
758C2×C4#1451975011yescharacteristic
759C2×C4#1451975111yescharacteristic
760C2×C4#1451975211yescharacteristic
761C2×C4#1451975311yescharacteristic
762C2×C4#1451975511yescharacteristic
763C2×C4#1451975511yescharacteristic
764C2×C4#1451975511yescharacteristic
765C2×C4#1451975511yescharacteristic
766C2×C4#1451975711yescharacteristic
767C2×C4#1451976011yescharacteristic
768C2×C4#1451976211yescharacteristic
769C2×C4#1451976211yescharacteristic
770C2×C4#1451976311yescharacteristic
771C2×C4#1451976311yescharacteristic
772C2×C4#1451976511yescharacteristic
773C2×C4#1451977111yescharacteristic
774C2×C4#1451977211yescharacteristic
775C2×C4#1451977311yescharacteristic
776C8—42no—
777C8—1224no—
778C22—1224no—
779C22—1224no—
780C22—1224no—
781C22—2442no—
782C22—2442no—
783C22—2442no—
784C22—2442no—
785C22—2442no—
786C22—2442no—
787C22—2442no—
788C22—2442no—
789C22—2442no—
790C22—2442no—
791C22—2442no—
792C22—2442no—
793C22#1683962111yescharacteristic
794C22#1683963311yescharacteristic
795C22#1683963611yescharacteristic
796C22#1683967111yescharacteristic
797C22#1683967711yescharacteristic
798C22#1683968011yescharacteristic
799C22#1683969111yescharacteristic
800C22#107×D6111yescharacteristic
801C22#1683979711yescharacteristic
802C22#1683980111yescharacteristic
803C22#1683980311yescharacteristic
804C22#1683989411yescharacteristic
805C22#1683989711yescharacteristic
806C22#1683990611yescharacteristic
807C22#1683990811yescharacteristic
808C22#1683991611yescharacteristic
809C22#1683991911yescharacteristic
810C22#1683992111yescharacteristic
811C22#1683992711yescharacteristic
812C22#1683999711yescharacteristic
813C22#1683999711yescharacteristic
814C22#1684000211yescharacteristic
815C22#1684000211yescharacteristic
816C22#1684000711yescharacteristic
817C22#1684001111yescharacteristic
818C22#1684001411yescharacteristic
819C22#1684001911yescharacteristic
820C22#1684007411yescharacteristic
821C22#1684007711yescharacteristic
822C22#1684008511yescharacteristic
823C22#1684008811yescharacteristic
824C22#1684009611yescharacteristic
825C22#1684009911yescharacteristic
826C22#1684010111yescharacteristic
827C22#1684010611yescharacteristic
828C4—82no—
829C4—82no—
830C4—4882no—
831C4—4882no—
832C4—2442no—
833C4#1683964011yescharacteristic
834C4#1683965111yescharacteristic
835C4#1683965311yescharacteristic
836C4#1683966211yescharacteristic
837C4#1683967511yescharacteristic
838C4#1683968411yescharacteristic
839C4#1683968611yescharacteristic
840C4#1683969711yescharacteristic
841C2—2444no—
842C2#2144406311yescharacteristic
843C2#2144584711yescharacteristic
844C2#2144585111yescharacteristic
845C2#2144600511yescharacteristic
846C2#2144600811yescharacteristic
847C2#2144601711yescharacteristic
848C2#2144601911yescharacteristic
849C2#2144681611yescharacteristic
850C2#2144682811yescharacteristic
851C2#2144699911yescharacteristic
852C2#2144700411yescharacteristic
853C2#2144702011yescharacteristic
854C2#2144702511yescharacteristic
855C2#2144724611yescharacteristic
856C2#2144725111yescharacteristic
subgroupG/H
centerC24D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#340C2
socleC24×C61C2×D4
prime radicalC24×D61D4
cosocleC23×C4×C61C23
hypercenterC2×#340D61
hypocenterC61#11096
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
1. C22×#14519710C2semidirect
5. C2×#16839525C2semidirect
6. C2×#16839524C2semidirect
7. C2×C61×#340C2semidirect
19. C2×#14519689C4semidirect
225. C2×#92418C22⋊C4semidirect
275. C22×D61#107semidirect
419. C2×#340D61semidirect
460. C61#11096semidirect

Maximal subgroups

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

subgroupindex
C22×#145197102
C22×#145196892
C2×#168396192
C2×#168395252
C2×#168395242
C2×C61×#3402
#1109661