Finite Group Databasebeta

← #29586639

Subgroups — #29586639

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×#16839779C211yesmaximal, characteristic, complemented
2#21454338C211yesmaximal, characteristic, complemented
3C2×#16839726C211yesmaximal, characteristic, complemented
4#21448202C211yesmaximal, characteristic, complemented
5#21445529C211yesmaximal, characteristic, complemented
6C2×#16839518C211yesmaximal, characteristic, complemented
7C2×C61×#525C211yesmaximal, characteristic
8C22×#11758194C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C2×#14519736C2211yescharacteristic
11C2×#14519736C2211yescharacteristic
12#16839779—22no—
13#16839779—22no—
14C2×#14519704—22no—
15#16839771—21no—
16#16839767—21no—
17#16839763—22no—
18#16839758—22no—
19#16839726—22no—
20#16839726—22no—
21C2×C22⋊#92418—22no—
22#16839625—21no—
23#16839622—22no—
24#16839618—21no—
25C4×C22⋊Dic61—22no—
26#16839522—22no—
27#16839518—22no—
28C22×#41×C61C2211yescharacteristic
29C24×C4×C61C2211yescharacteristic
30C61×#525—22no—
31C61×#525—22no—
32C61×#525—22no—
33C61×#525C414yescomplemented
34C2×#123×C61—21no—
35C2×C22⋊Q8×C61—21no—
36C2×#121×C61—21no—
37C2×#120×C61—21no—
38C2×C4×D4×C61—22no—
39C2×#117×C61C2211yescharacteristic
40C2×#11758194—21no—
41C2×#11758194—21no—
42C2×#11758194—21no—
43C2×#11758194—21no—
44C2×#11758194—21no—
45C2×#11758194—21no—
46C2×#11758194—21no—
47C2×#11758194—21no—
48C2×#11758194—21no—
49C2×#11758194—21no—
50C2×#11758194—21no—
51C2×#11758194D412yescomplemented
52C22×#92418—21no—
53C22×#92418D412yescomplemented
54#14519736—21no—
55#14519736—21no—
56#14519736—21no—
57#14519736—21no—
58#14519736—21no—
59#14519736—21no—
60#14519736—21no—
61#14519736—21no—
62C2×C4⋊Dic61—21no—
63C2×C4⋊Dic61D412yescomplemented
64C2×C22⋊Dic61—24no—
65C2×C22⋊Dic61—21no—
66C2×C22⋊Dic61—21no—
67C2×C4×Dic61—21no—
68C2×C4×Dic61D412yescomplemented
69#14519704—28no—
70#14519701—24no—
71#14519698—24no—
72C22⋊#92418—28no—
73#14519684—24no—
74C25×C61D411yescharacteristic
75C2×#41×C61—21no—
76C2×#41×C61—21no—
77C2×#41×C61—21no—
78C2×#41×C61—21no—
79C2×#41×C61—21no—
80C2×#41×C61—21no—
81C2×#41×C61—21no—
82C2×#41×C61—21no—
83C2×#41×C61—21no—
84C2×#41×C61—21no—
85C2×#41×C61C2×C412yes—
86C2×#41×C61D412yes—
87C22×Q8×C61D411yescharacteristic
88C22×D4×C61—22no—
89C22×D4×C61—21no—
90C22×D4×C61D411yescharacteristic
91C23×C4×C61—21no—
92C23×C4×C61—21no—
93C23×C4×C61—21no—
94C23×C4×C61—21no—
95C23×C4×C61—21no—
96C23×C4×C61—21no—
97C23×C4×C61—21no—
98C23×C4×C61—21no—
99C23×C4×C61—21no—
100C23×C4×C61—21no—
101C23×C4×C61—21no—
102C23×C4×C61—21no—
103C23×C4×C61—21no—
104C23×C4×C61C2×C412yes—
105C23×C4×C61D411yescharacteristic
106C23×C4×C61D412yes—
107C23×C4×C61C2311yescharacteristic
108#123×C61—24no—
109#123×C61—24no—
110C22⋊Q8×C61—24no—
111C22⋊Q8×C61—24no—
112#121×C61—24no—
113#121×C61—24no—
114#120×C61—24no—
115#120×C61—24no—
116C4×D4×C61—28no—
117C4×D4×C61—28no—
118#117×C61—21no—
119#117×C61—21no—
120#117×C61C2×C412yes—
121#117×C61D412yes—
122C2×C4⋊C4×C61—22no—
123C2×C4⋊C4×C61—21no—
124C2×C22⋊C4×C61—22no—
125C2×C22⋊C4×C61—22no—
126C2×C22⋊C4×C61—21no—
127C2×C42×C61D412yes—
128C24×C61—21no—
129C24×C61—21no—
130C24×C61—21no—
131C24×C61—21no—
132C24×C61—21no—
133C24×C61—21no—
134C24×C61—21no—
135C24×C61—44no—
136C24×C61C22⋊C412yes—
137C24×C61C2×D411yescharacteristic
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—28no—
161C2×D4×C61—22no—
162C2×D4×C61—22no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—48no—
169C2×D4×C61—41no—
170C2×D4×C61—41no—
171C2×D4×C61—41no—
172C2×D4×C61—41no—
173C2×D4×C61C22⋊C412yescomplemented
174C22×C4×C61—22no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61—22no—
196C22×C4×C61—41no—
197C22×C4×C61—41no—
198C22×C4×C61—41no—
199C22×C4×C61—41no—
200C22×C4×C61—41no—
201C22×C4×C61—41no—
202C22×C4×C61—41no—
203C22×C4×C61—41no—
204C22×C4×C61—41no—
205C22×C4×C61—41no—
206C22×C4×C61—41no—
207C22×C4×C61—41no—
208C22×C4×C61—41no—
209C22×C4×C61—41no—
210C22×C4×C61—41no—
211C22×C4×C61—41no—
212C22×C4×C61—41no—
213C22×C4×C61—41no—
214C22×C4×C61—41no—
215C22×C4×C61—41no—
216C22×C4×C61C22⋊C412yes—
217C22×C4×C61C22×C411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61#4111yescharacteristic
228C22×C4×C61#4111yescharacteristic
229C22×C4×C61#4111yescharacteristic
230C22×C4×C61#4111yescharacteristic
231C22×Dic61—22no—
232C22×Dic61—22no—
233C4⋊C4×C61—28no—
234C4⋊C4×C61—22no—
235C4⋊C4×C61—22no—
236C22⋊C4×C61—28no—
237C22⋊C4×C61—28no—
238C22⋊C4×C61—22no—
239C22⋊C4×C61—22no—
240C42×C61—22no—
241C42×C61C22⋊C414yescomplemented
242C22⋊Dic61—48no—
243C22⋊Dic61—41no—
244C22⋊Dic61—41no—
245C22⋊Dic61—41no—
246C22⋊Dic61—41no—
247C4⋊Dic61—22no—
248C4⋊Dic61—22no—
249C4⋊Dic61—41no—
250C4⋊Dic61—41no—
251C4×Dic61—22no—
252C4×Dic61—22no—
253C4×Dic61—41no—
254C4×Dic61—41no—
255#11758194—22no—
256#11758194—22no—
257#11758194—41no—
258#11758194—41no—
259#11758194—41no—
260#11758194—41no—
261#11758194—41no—
262#11758194—41no—
263C2×#92418—22no—
264C2×#92418—22no—
265C2×#92418—22no—
266C2×#92418—22no—
267C2×#92418—41no—
268C2×#92418—41no—
269C23×C61—24no—
270C23×C61—24no—
271C23×C61—24no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—44no—
277C23×C61—42no—
278C23×C61—42no—
279C23×C61—42no—
280C23×C61—42no—
281C23×C61—44no—
282C23×C61—44no—
283C23×C61—44no—
284C23×C61—44no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61C2×C22⋊C411yescharacteristic
292C23×C61#12011yescharacteristic
293C23×C61#12011yescharacteristic
294C23×C61#12011yescharacteristic
295C23×C61#12111yescharacteristic
296C23×C61#12111yescharacteristic
297C23×C61#12311yescharacteristic
298Q8×C61—22no—
299Q8×C61—22no—
300Q8×C61—41no—
301Q8×C61—41no—
302D4×C61—22no—
303D4×C61—22no—
304D4×C61—416no—
305D4×C61—42no—
306D4×C61—42no—
307D4×C61—42no—
308D4×C61—42no—
309D4×C61—41no—
310D4×C61—41no—
311C2×C4×C61—24no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—44no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—42no—
324C2×C4×C61—42no—
325C2×C4×C61—42no—
326C2×C4×C61—42no—
327C2×C4×C61—42no—
328C2×C4×C61—42no—
329C2×C4×C61—42no—
330C2×C4×C61—42no—
331C2×C4×C61—42no—
332C2×C4×C61—42no—
333C2×C4×C61—42no—
334C2×C4×C61—42no—
335C2×C4×C61C2×C22⋊C411yescharacteristic
336C2×C4×C61C2×C22⋊C411yescharacteristic
337C2×C4×C61C4×D411yescharacteristic
338C2×C4×C61C4×D411yescharacteristic
339C2×C4×C61C4×D411yescharacteristic
340C2×C4×C61C4×D411yescharacteristic
341C2×C4×C61#12011yescharacteristic
342C2×C4×C61#12011yescharacteristic
343C2×C4×C61#12011yescharacteristic
344C2×C4×C61#12011yescharacteristic
345C2×C4×C61#12011yescharacteristic
346C2×C4×C61#12111yescharacteristic
347C2×C4×C61#12111yescharacteristic
348C2×C4×C61#12111yescharacteristic
349C2×C4×C61#12111yescharacteristic
350C2×C4×C61#12111yescharacteristic
351C2×C4×C61#12111yescharacteristic
352C2×C4×C61#12111yescharacteristic
353C2×C4×C61#12111yescharacteristic
354C2×C4×C61#12111yescharacteristic
355C2×C4×C61#12111yescharacteristic
356C2×C4×C61#12311yescharacteristic
357C2×C4×C61#12311yescharacteristic
358C2×C4×C61#12311yescharacteristic
359C2×C4×C61#12411yescharacteristic
360C2×C4×C61#12411yescharacteristic
361C2×C4×C61#12711yescharacteristic
362C2×C4×C61#12711yescharacteristic
363C2×Dic61—44no—
364C2×Dic61—44no—
365C2×Dic61—42no—
366C2×Dic61—42no—
367#92418—42no—
368#92418—42no—
369#10994—611nomaximal, Sylow
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—22no—
373C22×C61—24no—
374C22×C61—24no—
375C22×C61—24no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61—44no—
381C22×C61—42no—
382C22×C61—42no—
383C22×C61—42no—
384C22×C61—44no—
385C22×C61—44no—
386C22×C61—44no—
387C22×C61—42no—
388C22×C61—44no—
389C22×C61—42no—
390C22×C61—82no—
391C22×C61—82no—
392C22×C61#37911yescharacteristic
393C22×C61#38611yescharacteristic
394C22×C61#38611yescharacteristic
395C22×C61#39211yescharacteristic
396C22×C61#39211yescharacteristic
397C22×C61#39411yescharacteristic
398C22×C61#39411yescharacteristic
399C4×C61—44no—
400C4×C61—42no—
401C4×C61—42no—
402C4×C61#38611yescharacteristic
403C4×C61#38611yescharacteristic
404C4×C61#39011yescharacteristic
405C4×C61#39011yescharacteristic
406C4×C61#39211yescharacteristic
407C4×C61#39211yescharacteristic
408C4×C61#39411yescharacteristic
409C4×C61#39411yescharacteristic
410Dic61—82no—
411Dic61—82no—
412C2×#525D6111yescharacteristic
413C2×#421—611no—
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—44no—
426C2×C61—82no—
427C2×C61#143811yescharacteristic
428C2×C61#201012yes—
429C22×#41C2×D6111yescharacteristic
430C24×C4C2×D6111yescharacteristic
431C22×M16—611no—
432C22×M16—611no—
433#525—22no—
434#525—22no—
435#525—22no—
436#525Dic6114yescomplemented
437C2×#123—21no—
438C2×C22⋊Q8—21no—
439C2×#121—21no—
440C2×#120—21no—
441C2×C4×D4—22no—
442C2×#117—611no—
443C2×#117—611no—
444C2×#117C2×D6111yescharacteristic
445#421—1222no—
446#421—1222no—
447C2×#104—1222no—
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
462C25C22⋊D6111yescharacteristic
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×#41C2×Dic6112yes—
474C2×#41C22⋊D6112yes—
475C22×Q8C22⋊D6111yescharacteristic
476C22×D4—22no—
477C22×D4—21no—
478C22×D4C22⋊D6111yescharacteristic
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—21no—
485C23×C4—21no—
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—21no—
492C23×C4C2×Dic6112yes—
493C23×C4C22⋊D6111yescharacteristic
494C23×C4C22⋊D6112yes—
495C23×C4C22×D6111yescharacteristic
496C2×M16—612no—
497C2×M16—1221no—
498C2×M16—1221no—
499C2×M16—1221no—
500C2×M16—1221no—
501C2×M16—1221no—
502C2×M16—1221no—
503C2×M16—1221no—
504C2×M16—1221no—
505C2×M16—1221no—
506C2×M16—1221no—
507C2×M16—1221no—
508C22×C8—612no—
509C22×C8—1221no—
510#123—24no—
511#123—24no—
512C22⋊Q8—24no—
513C22⋊Q8—24no—
514#121—24no—
515#121—24no—
516#120—24no—
517#120—24no—
518C4×D4—28no—
519C4×D4—28no—
520#117—21no—
521#117—21no—
522#117—1221no—
523#117—1221no—
524#117—1221no—
525#117—1221no—
526#117—1221no—
527#117—1221no—
528#117—1221no—
529#117—1221no—
530#117C2×Dic6112yes—
531#117C22⋊D6112yes—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—612no—
535C2×C4⋊C4—1221no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—1224no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C42—612no—
543C2×C42—1221no—
544C2×C42C22⋊D6112yes—
545#104—1228no—
546#103—1224no—
547#102—1224no—
548C22⋊C8—1228no—
549#95—1224no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24—21no—
555C24—21no—
556C24—21no—
557C24—44no—
558C24C22⋊Dic6112yes—
559C24C2×C22⋊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×Q8C22⋊Dic6112yescomplemented
582C2×D4—28no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—48no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4C22⋊Dic6112yescomplemented
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—1222no—
639C22×C4—1222no—
640C22×C4C22⋊Dic6112yes—
641C22×C4D4×D6111yescharacteristic
642C22×C4D4×D6111yescharacteristic
643C22×C4D4×D6111yescharacteristic
644C22×C4D4×D6111yescharacteristic
645C22×C4#1175822411yescharacteristic
646C22×C4#1175822411yescharacteristic
647C22×C4#1175822411yescharacteristic
648C22×C4#1175822411yescharacteristic
649C22×C4C22×Dic6111yescharacteristic
650C22×C4C2×C22⋊D6111yescharacteristic
651C22×C4C2×C22⋊D6111yescharacteristic
652C22×C4C2×C22⋊D6111yescharacteristic
653C22×C4C2×C22⋊D6111yescharacteristic
654C22×C4C2×C22⋊D6111yescharacteristic
655M16—1222no—
656M16—1222no—
657M16—2441no—
658M16—2441no—
659M16—2441no—
660M16—2441no—
661M16—2441no—
662M16—2441no—
663C2×C8—1222no—
664C2×C8—1222no—
665C2×C8—1222no—
666C2×C8—1222no—
667C2×C8—2441no—
668C2×C8—2441no—
669C4⋊C4—28no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—1222no—
673C4⋊C4—1222no—
674C4⋊C4—2441no—
675C4⋊C4—2441no—
676C22⋊C4—28no—
677C22⋊C4—28no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—2448no—
681C22⋊C4—2441no—
682C22⋊C4—2441no—
683C22⋊C4—2441no—
684C22⋊C4—2441no—
685C42—22no—
686C42—1222no—
687C42—1222no—
688C42—2441no—
689C42—2441no—
690C42C22⋊Dic6114yescomplemented
691C23—24no—
692C23—24no—
693C23—24no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—44no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23C2×C22⋊Dic6111yescharacteristic
714C23#1451974511yescharacteristic
715C23#1451974611yescharacteristic
716C23#1451974611yescharacteristic
717C23#1451974911yescharacteristic
718C23#1451974911yescharacteristic
719C23#1451975811yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724D4—22no—
725D4—22no—
726D4—416no—
727D4—42no—
728D4—42no—
729D4—42no—
730D4—42no—
731D4—41no—
732D4—41no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—44no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—2444no—
758C2×C4—2444no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4C2×C22⋊Dic6111yescharacteristic
762C2×C4C2×C22⋊Dic6111yescharacteristic
763C2×C4D4×Dic6111yescharacteristic
764C2×C4D4×Dic6111yescharacteristic
765C2×C4D4×Dic6111yescharacteristic
766C2×C4D4×Dic6111yescharacteristic
767C2×C4#1451974511yescharacteristic
768C2×C4#1451974511yescharacteristic
769C2×C4#1451974511yescharacteristic
770C2×C4#1451974611yescharacteristic
771C2×C4#1451974611yescharacteristic
772C2×C4#1451974811yescharacteristic
773C2×C4#1451974811yescharacteristic
774C2×C4#1451974811yescharacteristic
775C2×C4#1451974811yescharacteristic
776C2×C4#1451974911yescharacteristic
777C2×C4#1451974911yescharacteristic
778C2×C4#1451974911yescharacteristic
779C2×C4#1451974911yescharacteristic
780C2×C4#1451974911yescharacteristic
781C2×C4#1451974911yescharacteristic
782C2×C4#1451975811yescharacteristic
783C2×C4#1451975811yescharacteristic
784C2×C4#1451975811yescharacteristic
785C2×C4#1451976411yescharacteristic
786C2×C4#1451976411yescharacteristic
787C2×C4#1451977311yescharacteristic
788C2×C4#1451977311yescharacteristic
789C8—2442no—
790C8—2442no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—42no—
802C22—44no—
803C22—42no—
804C22—42no—
805C22—44no—
806C22—44no—
807C22—44no—
808C22—42no—
809C22—44no—
810C22—42no—
811C22—82no—
812C22—82no—
813C22#1683961811yescharacteristic
814C22#1683964211yescharacteristic
815C22#1683964211yescharacteristic
816C22#1683967011yescharacteristic
817C22#1683967011yescharacteristic
818C22#1683967611yescharacteristic
819C22#1683967611yescharacteristic
820C4—44no—
821C4—42no—
822C4—42no—
823C4—4882no—
824C4—4882no—
825C4#1683964211yescharacteristic
826C4#1683964211yescharacteristic
827C4#1683966511yescharacteristic
828C4#1683966511yescharacteristic
829C4#1683967011yescharacteristic
830C4#1683967011yescharacteristic
831C4#1683967611yescharacteristic
832C4#1683967611yescharacteristic
833C2—21no—
834C2—21no—
835C2—21no—
836C2—21no—
837C2—21no—
838C2—21no—
839C2—44no—
840C2—82no—
841C2#2144406011yescharacteristic
842C2#2144688412yes—
subgroupG/H
centerC2×C4#14519773
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
Fitting, prime radicalC2×C61×#525C2
socleC22×C61#392
cosocleC23×C4×C61C23
hypercenterC2×#525D61
hypocenterC61#10994
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#16839779C2semidirect
2. #21454338C2semidirect
3. C2×#16839726C2semidirect
4. #21448202C2semidirect
5. #21445529C2semidirect
6. C2×#16839518C2semidirect
33. C61×#525C4semidirect
51. C2×#11758194D4semidirect
53. C22×#92418D4semidirect
63. C2×C4⋊Dic61D4semidirect
68. C2×C4×Dic61D4semidirect
159. C2×Q8×C61C22⋊C4semidirect
173. C2×D4×C61C22⋊C4semidirect
241. C42×C61C22⋊C4semidirect
436. #525Dic61semidirect
461. C61#10994semidirect
581. C2×Q8C22⋊Dic61semidirect
595. C2×D4C22⋊Dic61semidirect
690. C42C22⋊Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168397792
#214543382
C2×#168397262
#214482022
#214455292
C2×#168395182
C2×C61×#5252
#1099461