Finite Group Databasebeta

← #29586640

Subgroups — #29586640

Order 15616.

1494 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840269C211yesmaximal, characteristic
2#21454338C211yesmaximal, characteristic, complemented
3C2×#16839725C211yesmaximal, characteristic, complemented
4#21448198C211yesmaximal, characteristic, complemented
5#21445530C211yesmaximal, characteristic, complemented
6C2×#16839518C211yesmaximal, characteristic, complemented
7C2×C61×#421C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10#16840269—22no—
11#16840269—22no—
12#16840269—22no—
13#16840269C414yescomplemented
14C2×#14519758—21no—
15C2×#14519753—21no—
16C2×#14519748—21no—
17C2×#14519745—21no—
18C2×C4×C22⋊D61—22no—
19C2×#14519736C2211yescharacteristic
20C2×#14519736C2211yescharacteristic
21#16839771—21no—
22#16839767—21no—
23#16839763—22no—
24#16839758—22no—
25#16839725—22no—
26#16839725—22no—
27C2×#14519689—22no—
28#16839623—21no—
29#16839619—22no—
30#16839617—21no—
31C4×#11758198—22no—
32#16839523—22no—
33#16839518—22no—
34C22×#41×C61C2211yescharacteristic
35C22×M16×C61C2211yescharacteristic
36C2×#117×C61C2211yescharacteristic
37C61×#421—22no—
38C61×#421—22no—
39C2×#104×C61—22no—
40C24×D61D411yescharacteristic
41C22×C22⋊D61—22no—
42C23×Dic61D411yescharacteristic
43C22×C4×D61—21no—
44C22×C4×D61—21no—
45C22×C4×D61—21no—
46C22×C4×D61—21no—
47C22×C4×D61—21no—
48C22×C4×D61—21no—
49C22×C4×D61—21no—
50C22×C4×D61—21no—
51C22×C4×D61—21no—
52C22×C4×D61—21no—
53C22×C4×D61—21no—
54C22×C4×D61—21no—
55C22×C4×D61C2×C412yes—
56C22×C4×D61D412yes—
57C2×#11758194—21no—
58C2×#11758194—21no—
59C2×#11758194—21no—
60C2×#11758194—21no—
61C2×#11758194—21no—
62C2×#11758194—21no—
63C22×#92418D412yescomplemented
64#14519758—24no—
65#14519758—24no—
66#14519753—24no—
67#14519753—24no—
68#14519748—24no—
69#14519748—24no—
70#14519745—24no—
71#14519745—24no—
72C4×C22⋊D61—28no—
73C4×C22⋊D61—28no—
74#14519736—21no—
75#14519736—21no—
76#14519736—21no—
77#14519736—21no—
78#14519736—21no—
79#14519736—21no—
80#14519736C2×C412yes—
81#14519736D412yes—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61D412yescomplemented
84C2×#11758196—22no—
85C2×C22⋊Dic61—22no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×#11758198—22no—
89C2×#11758198—24no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61D412yes—
92#14519701—24no—
93#14519698—24no—
94#14519689—28no—
95#14519684—24no—
96C2×#41×C61—21no—
97C2×#41×C61—21no—
98C2×#41×C61—21no—
99C2×#41×C61—21no—
100C2×#41×C61—21no—
101C2×#41×C61—21no—
102C2×#41×C61—21no—
103C2×#41×C61—21no—
104C2×#41×C61—21no—
105C2×#41×C61—21no—
106C2×#41×C61C2×C412yes—
107C2×#41×C61D412yes—
108C22×Q8×C61D411yescharacteristic
109C22×D4×C61—21no—
110C22×D4×C61D411yescharacteristic
111C23×C4×C61—21no—
112C23×C4×C61C2311yescharacteristic
113C2×M16×C61—21no—
114C2×M16×C61—21no—
115C2×M16×C61—21no—
116C2×M16×C61—21no—
117C2×M16×C61—21no—
118C2×M16×C61D412yescomplemented
119C22×C8×C61—21no—
120#117×C61—21no—
121#117×C61—21no—
122#117×C61—21no—
123#117×C61—21no—
124C2×C4⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C42×C61D412yescomplemented
127#104×C61—28no—
128C24×C61—21no—
129C24×C61C2×D411yescharacteristic
130C23×D61—21no—
131C23×D61—21no—
132C23×D61—21no—
133C23×D61—21no—
134C23×D61—21no—
135C23×D61—21no—
136C23×D61—44no—
137C23×D61C22⋊C412yes—
138#41×C61—22no—
139#41×C61—22no—
140#41×C61—22no—
141#41×C61—22no—
142#41×C61—22no—
143#41×C61—22no—
144#41×C61—22no—
145#41×C61—22no—
146#41×C61—41no—
147#41×C61—41no—
148#41×C61—41no—
149#41×C61—41no—
150#41×C61—41no—
151#41×C61—41no—
152#41×C61—41no—
153#41×C61—41no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61C22⋊C412yescomplemented
160C2×D4×C61—22no—
161C2×D4×C61—22no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—41no—
168C2×D4×C61—41no—
169C2×D4×C61—41no—
170C2×D4×C61—41no—
171C2×D4×C61C22⋊C412yescomplemented
172C22×C4×C61—21no—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—41no—
177C22×C4×C61—41no—
178C22×C4×C61—41no—
179C22×C4×C61—41no—
180C22×C4×C61C22×C411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61#4111yescharacteristic
191C22×C4×C61#4111yescharacteristic
192C22×C4×C61#4111yescharacteristic
193C22×C4×C61#4111yescharacteristic
194C2×C22⋊D61—28no—
195C2×C22⋊D61—48no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—22no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—22no—
204C22×Dic61C22⋊C412yes—
205C2×C4×D61—22no—
206C2×C4×D61—22no—
207C2×C4×D61—22no—
208C2×C4×D61—22no—
209C2×C4×D61—22no—
210C2×C4×D61—22no—
211C2×C4×D61—22no—
212C2×C4×D61—22no—
213C2×C4×D61—22no—
214C2×C4×D61—22no—
215C2×C4×D61—22no—
216C2×C4×D61—22no—
217C2×C4×D61—41no—
218C2×C4×D61—41no—
219C2×C4×D61—41no—
220C2×C4×D61—41no—
221C2×C4×D61—41no—
222C2×C4×D61—41no—
223C2×C4×D61—41no—
224C2×C4×D61—41no—
225C2×C4×D61—41no—
226C2×C4×D61—41no—
227C2×C4×D61—41no—
228C2×C4×D61—41no—
229C2×C4×D61—41no—
230C2×C4×D61—41no—
231C2×C4×D61—41no—
232C2×C4×D61—41no—
233M16×C61—22no—
234M16×C61—22no—
235M16×C61—41no—
236M16×C61—41no—
237C2×C8×C61—22no—
238C2×C8×C61—41no—
239C2×C8×C61—41no—
240C4⋊C4×C61—41no—
241C4⋊C4×C61—41no—
242C22⋊C4×C61—41no—
243C22⋊C4×C61—41no—
244C42×C61—22no—
245C42×C61—22no—
246C22⋊Dic61—28no—
247C22⋊Dic61—22no—
248C22⋊Dic61—22no—
249C22⋊Dic61—41no—
250C22⋊Dic61—41no—
251#11758198—28no—
252#11758198—48no—
253C4⋊Dic61—22no—
254C4⋊Dic61—22no—
255C4⋊Dic61—22no—
256C4⋊Dic61—22no—
257#11758196—28no—
258C4×Dic61—22no—
259C4×Dic61—41no—
260C4×Dic61—41no—
261C4×Dic61C22⋊C414yescomplemented
262#11758194—41no—
263#11758194—41no—
264#11758194—41no—
265#11758194—41no—
266C2×#92418—22no—
267C2×#92418—22no—
268C2×#92418—22no—
269C23×C61—22no—
270C23×C61—42no—
271C23×C61—44no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61C2×C22⋊C411yescharacteristic
275C23×C61#12011yescharacteristic
276C23×C61#12011yescharacteristic
277C23×C61#12011yescharacteristic
278C23×C61#12111yescharacteristic
279C23×C61#12111yescharacteristic
280C23×C61#12311yescharacteristic
281C22×D61—24no—
282C22×D61—24no—
283C22×D61—24no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—44no—
288C22×D61—44no—
289C22×D61—44no—
290C22×D61—44no—
291C22×D61—42no—
292C22×D61—42no—
293C22×D61—42no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298Q8×C61—22no—
299Q8×C61—22no—
300Q8×C61—41no—
301Q8×C61—41no—
302D4×C61—22no—
303D4×C61—22no—
304D4×C61—42no—
305D4×C61—42no—
306D4×C61—42no—
307D4×C61—42no—
308D4×C61—41no—
309D4×C61—41no—
310C2×C4×C61—22no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—44no—
318C2×C4×C61—42no—
319C2×C4×C61C2×C22⋊C411yescharacteristic
320C2×C4×C61C2×C22⋊C411yescharacteristic
321C2×C4×C61C4×D411yescharacteristic
322C2×C4×C61C4×D411yescharacteristic
323C2×C4×C61C4×D411yescharacteristic
324C2×C4×C61C4×D411yescharacteristic
325C2×C4×C61#12011yescharacteristic
326C2×C4×C61#12011yescharacteristic
327C2×C4×C61#12011yescharacteristic
328C2×C4×C61#12011yescharacteristic
329C2×C4×C61#12011yescharacteristic
330C2×C4×C61#12111yescharacteristic
331C2×C4×C61#12111yescharacteristic
332C2×C4×C61#12111yescharacteristic
333C2×C4×C61#12111yescharacteristic
334C2×C4×C61#12111yescharacteristic
335C2×C4×C61#12111yescharacteristic
336C2×C4×C61#12111yescharacteristic
337C2×C4×C61#12111yescharacteristic
338C2×C4×C61#12111yescharacteristic
339C2×C4×C61#12111yescharacteristic
340C2×C4×C61#12311yescharacteristic
341C2×C4×C61#12311yescharacteristic
342C2×C4×C61#12311yescharacteristic
343C2×C4×C61#12411yescharacteristic
344C2×C4×C61#12411yescharacteristic
345C2×C4×C61#12711yescharacteristic
346C2×C4×C61#12711yescharacteristic
347C22⋊D61—416no—
348C2×Dic61—24no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—44no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—44no—
358C2×Dic61—42no—
359C4×D61—42no—
360C4×D61—42no—
361C4×D61—42no—
362C4×D61—42no—
363C4×D61—42no—
364C4×D61—42no—
365C4×D61—42no—
366C4×D61—42no—
367C8×C61—42no—
368#92418—42no—
369#10994—611nomaximal, Sylow
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—22no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—44no—
378C22×C61—42no—
379C22×C61—82no—
380C22×C61—82no—
381C22×C61#37911yescharacteristic
382C22×C61#38611yescharacteristic
383C22×C61#38611yescharacteristic
384C22×C61#39211yescharacteristic
385C22×C61#39211yescharacteristic
386C22×C61#39411yescharacteristic
387C22×C61#39411yescharacteristic
388C2×D61—24no—
389C2×D61—24no—
390C2×D61—24no—
391C2×D61—42no—
392C2×D61—44no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—44no—
396C2×D61—44no—
397C2×D61—42no—
398C2×D61—44no—
399C4×C61—42no—
400C4×C61—82no—
401C4×C61#38611yescharacteristic
402C4×C61#38611yescharacteristic
403C4×C61#39011yescharacteristic
404C4×C61#39011yescharacteristic
405C4×C61#39211yescharacteristic
406C4×C61#39211yescharacteristic
407C4×C61#39411yescharacteristic
408C4×C61#39411yescharacteristic
409Dic61—44no—
410Dic61—42no—
411Dic61—82no—
412C2×#525—611no—
413C2×#421D6111yescharacteristic, complemented
414#2896—611no—
415C2×#407—611no—
416#2280—611no—
417#1733—611no—
418C2×H(3,ℤ/4)—611no—
419C2×C61—21no—
420C2×C61—21no—
421C2×C61—21no—
422C2×C61—21no—
423C2×C61—21no—
424C2×C61—21no—
425C2×C61—82no—
426C2×C61#143811yescharacteristic
427C2×C61#201012yes—
428D61—44no—
429C22×#41C2×D6111yescharacteristic
430C24×C4—611no—
431C22×M16—611no—
432C22×M16C2×D6111yescharacteristic
433#525—614no—
434#525—1222no—
435#525—1222no—
436#525—1222no—
437C2×#123—1221no—
438C2×C22⋊Q8—1221no—
439C2×#121—1221no—
440C2×#120—1221no—
441C2×C4×D4—1222no—
442C2×#117—611no—
443C2×#117—611no—
444C2×#117C2×D6111yescharacteristic
445#421—22no—
446#421—22no—
447C2×#104—22no—
448#419—1221no—
449#418—1221no—
450#417—1222no—
451#416—1222no—
452#407—1222no—
453#407—1222no—
454C2×C22⋊C8—1222no—
455#381—1221no—
456#380—1222no—
457#379—1221no—
458C4×C22⋊C4—1222no—
459#339—1222no—
460H(3,ℤ/4)—1222no—
461C61#1099411yescharacteristic, complemented, Sylow
462C25—611no—
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—21no—
473C2×#41C4×D6112yes—
474C2×#41C22⋊D6112yes—
475C22×Q8D24411yescharacteristic
476C22×D4—21no—
477C22×D4—1222no—
478C22×D4D24411yescharacteristic
479C23×C4—21no—
480C23×C4—611no—
481C23×C4—612no—
482C23×C4—612no—
483C23×C4—1221no—
484C23×C4—1221no—
485C23×C4—1221no—
486C23×C4—1221no—
487C23×C4—1221no—
488C23×C4—1221no—
489C23×C4—1221no—
490C23×C4—1221no—
491C23×C4—1221no—
492C23×C4—1221no—
493C23×C4—1221no—
494C23×C4—1221no—
495C23×C4C22×D6111yescharacteristic
496C2×M16—21no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—1221no—
502C2×M16—1221no—
503C2×M16—1221no—
504C2×M16—1221no—
505C2×M16—1221no—
506C2×M16—1221no—
507C2×M16C22⋊D6112yescomplemented
508C22×C8—21no—
509C22×C8—612no—
510#123—1224no—
511#123—1224no—
512C22⋊Q8—1224no—
513C22⋊Q8—1224no—
514#121—1224no—
515#121—1224no—
516#120—1224no—
517#120—1224no—
518C4×D4—1228no—
519C4×D4—1228no—
520#117—21no—
521#117—21no—
522#117—21no—
523#117—21no—
524#117—612no—
525#117—612no—
526#117—1221no—
527#117—1221no—
528#117—1221no—
529#117—1221no—
530#117—1221no—
531#117—1221no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—612no—
534C2×C4⋊C4—1222no—
535C2×C4⋊C4—1221no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—1222no—
538C2×C22⋊C4—1222no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1224no—
541C2×C22⋊C4—1221no—
542C2×C42—612no—
543C2×C42—1221no—
544C2×C42C22⋊D6112yescomplemented
545#104—28no—
546#103—1224no—
547#102—1224no—
548C22⋊C8—1228no—
549#95—1224no—
550C24—21no—
551C24—612no—
552C24—1221no—
553C24—1221no—
554C24—1221no—
555C24—1221no—
556C24—1221no—
557C24—1221no—
558C24—2444no—
559C24D4×D6111yescharacteristic
560#41—22no—
561#41—22no—
562#41—22no—
563#41—22no—
564#41—22no—
565#41—22no—
566#41—22no—
567#41—22no—
568#41—41no—
569#41—41no—
570#41—41no—
571#41—41no—
572#41—41no—
573#41—41no—
574#41—41no—
575#41—41no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8#1175819812yescomplemented
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—1228no—
594C2×D4—2448no—
595C2×D4#1175819812yescomplemented
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—612no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1222no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4—2441no—
626C22×C4—2441no—
627C22×C4—2441no—
628C22×C4—2441no—
629C22×C4—2441no—
630C22×C4—2441no—
631C22×C4—2441no—
632C22×C4—2441no—
633C22×C4—2441no—
634C22×C4—2441no—
635C22×C4—2441no—
636C22×C4—2441no—
637C22×C4—2441no—
638C22×C4—2441no—
639C22×C4—2441no—
640C22×C4—2441no—
641C22×C4C2×C4×D6111yescharacteristic
642C22×C4C2×D24411yescharacteristic
643C22×C4#1175822211yescharacteristic
644C22×C4#1175822211yescharacteristic
645C22×C4D4×D6111yescharacteristic
646C22×C4D4×D6111yescharacteristic
647C22×C4D4×D6111yescharacteristic
648C22×C4D4×D6111yescharacteristic
649C22×C4D4×D6111yescharacteristic
650C22×C4#1175822411yescharacteristic
651C22×C4#1175822411yescharacteristic
652C22×C4C2×C22⋊D6111yescharacteristic
653C22×C4C2×C22⋊D6111yescharacteristic
654C22×C4C2×C22⋊D6111yescharacteristic
655M16—22no—
656M16—22no—
657M16—41no—
658M16—41no—
659M16—2441no—
660M16—2441no—
661M16—2441no—
662M16—2441no—
663C2×C8—22no—
664C2×C8—41no—
665C2×C8—41no—
666C2×C8—1222no—
667C2×C8—1222no—
668C2×C8—1222no—
669C4⋊C4—41no—
670C4⋊C4—41no—
671C4⋊C4—1228no—
672C4⋊C4—1222no—
673C4⋊C4—1222no—
674C4⋊C4—1222no—
675C4⋊C4—1222no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—1228no—
679C22⋊C4—1228no—
680C22⋊C4—1222no—
681C22⋊C4—1222no—
682C22⋊C4—2448no—
683C22⋊C4—2441no—
684C22⋊C4—2441no—
685C42—22no—
686C42—22no—
687C42—614no—
688C42—1222no—
689C42—2441no—
690C42—2441no—
691C23—22no—
692C23—42no—
693C23—44no—
694C23—41no—
695C23—41no—
696C23—1224no—
697C23—1224no—
698C23—1224no—
699C23—1222no—
700C23—1222no—
701C23—1222no—
702C23—2442no—
703C23—2442no—
704C23—2442no—
705C23—2444no—
706C23—2444no—
707C23—2444no—
708C23—2444no—
709C23—2441no—
710C23—2441no—
711C23—2441no—
712C23—2441no—
713C23C22⋊C4×D6111yescharacteristic
714C23#1451974511yescharacteristic
715C23#1451974511yescharacteristic
716C23#1451974711yescharacteristic
717C23#1451974811yescharacteristic
718C23#1451975011yescharacteristic
719C23#1451975911yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724D4—22no—
725D4—22no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—42no—
730D4—41no—
731D4—41no—
732D4—24416no—
733C2×C4—22no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—1224no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—2444no—
747C2×C4—2442no—
748C2×C4—2444no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4—2442no—
756C2×C4—2442no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4C22⋊C4×D6111yescharacteristic
762C2×C4C2×#1175819811yescharacteristic
763C2×C4#1451973711yescharacteristic
764C2×C4#1451973711yescharacteristic
765C2×C4C4×C22⋊D6111yescharacteristic
766C2×C4C4×C22⋊D6111yescharacteristic
767C2×C4#1451974511yescharacteristic
768C2×C4#1451974511yescharacteristic
769C2×C4#1451974611yescharacteristic
770C2×C4#1451974711yescharacteristic
771C2×C4#1451974711yescharacteristic
772C2×C4#1451974811yescharacteristic
773C2×C4#1451974911yescharacteristic
774C2×C4#1451974911yescharacteristic
775C2×C4#1451974911yescharacteristic
776C2×C4#1451974911yescharacteristic
777C2×C4#1451975011yescharacteristic
778C2×C4#1451975011yescharacteristic
779C2×C4#1451975011yescharacteristic
780C2×C4#1451975111yescharacteristic
781C2×C4#1451975111yescharacteristic
782C2×C4#1451975911yescharacteristic
783C2×C4#1451976011yescharacteristic
784C2×C4#1451976111yescharacteristic
785C2×C4#1451976311yescharacteristic
786C2×C4#1451976311yescharacteristic
787C2×C4#1451977311yescharacteristic
788C2×C4#1451977311yescharacteristic
789C8—42no—
790C8—2442no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—44no—
799C22—42no—
800C22—82no—
801C22—82no—
802C22—1224no—
803C22—1224no—
804C22—1224no—
805C22—2444no—
806C22—2442no—
807C22—2444no—
808C22—2442no—
809C22—2442no—
810C22—2444no—
811C22—2442no—
812C22—2444no—
813C22#1683961711yescharacteristic
814C22#1683963811yescharacteristic
815C22#1683963811yescharacteristic
816C22#1683967011yescharacteristic
817C22#1683967111yescharacteristic
818C22#1683967711yescharacteristic
819C22#1683967811yescharacteristic
820C4—42no—
821C4—82no—
822C4—4882no—
823C4—2444no—
824C4—2442no—
825C4#1683963911yescharacteristic
826C4#1683964111yescharacteristic
827C4#1683966211yescharacteristic
828C4#1683966211yescharacteristic
829C4#1683967011yescharacteristic
830C4#1683967111yescharacteristic
831C4#1683967711yescharacteristic
832C4#1683967811yescharacteristic
833C2—21no—
834C2—21no—
835C2—21no—
836C2—21no—
837C2—21no—
838C2—21no—
839C2—82no—
840C2—2444no—
841C2#2144405811yescharacteristic
842C2#2144688512yes—
subgroupG/H
centerC2×C4#14519773
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#421C2
socleC22×C61#392
prime radicalC2×#16840269C2
cosocleC23×C4×C61C23
hypercenterC2×#421D61
hypocenterC61#10994
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. #21454338C2semidirect
3. C2×#16839725C2semidirect
4. #21448198C2semidirect
5. #21445530C2semidirect
6. C2×#16839518C2semidirect
7. C2×C61×#421C2semidirect
13. #16840269C4semidirect
63. C22×#92418D4semidirect
83. C2×C4⋊Dic61D4semidirect
118. C2×M16×C61D4semidirect
126. C2×C42×C61D4semidirect
159. C2×Q8×C61C22⋊C4semidirect
171. C2×D4×C61C22⋊C4semidirect
261. C4×Dic61C22⋊C4semidirect
413. C2×#421D61semidirect
461. C61#10994semidirect
507. C2×M16C22⋊D61semidirect
544. C2×C42C22⋊D61semidirect
581. C2×Q8#11758198semidirect
595. C2×D4#11758198semidirect

Maximal subgroups

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

subgroupindex
C2×#168402692
#214543382
C2×#168397252
#214481982
#214455302
C2×#168395182
C2×C61×#4212
#1099461