Finite Group Databasebeta

← #29586772

Subgroups — #29586772

Order 15616.

1574 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519802C211yesmaximal, characteristic
2C2×#16839768C211yesmaximal, characteristic, complemented
3#21448411C211yesmaximal, characteristic, complemented
4C2×#16839664C211yesmaximal, characteristic, complemented
5C2×#16839530C211yesmaximal, characteristic, complemented
6C2×#16839522C211yesmaximal, characteristic, complemented
7C22×#104×C61C211yesmaximal, characteristic, complemented
8C23×D244C2211yescharacteristic
9C2×#14519802—22no—
10C2×#14519802—22no—
11C2×#14519802—22no—
12C2×#14519802—22no—
13C2×#14519802—22no—
14C2×#14519802C414yescomplemented
15C22×#11758201—21no—
16C22×#11758199—21no—
17C22×#11758194C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758198—22no—
21#16839768—22no—
22#16839768—22no—
23C2×#14519699—22no—
24#16839669—21no—
25#16839665—21no—
26#16839664—22no—
27#16839664—22no—
28#16839642—22no—
29#16839622—22no—
30#16839530—22no—
31#16839522—22no—
32C22×#41×C61C2211yescharacteristic
33C22×M16×C61C2211yescharacteristic
34C22×C42×C61C2211yescharacteristic
35C2×#104×C61—22no—
36C2×#104×C61—22no—
37C2×#104×C61—22no—
38C24×D61—21no—
39C22×D244—21no—
40C22×D244—21no—
41C22×D244—21no—
42C22×D244—21no—
43C22×D244—21no—
44C22×D244—21no—
45C22×D244—21no—
46C22×D244—21no—
47C22×D244—21no—
48C22×D244—21no—
49C22×D244—21no—
50C22×D244C2×C412yes—
51C22×D244D412yes—
52C22×D244D412yes—
53C23×Dic61D412yes—
54#14519802—28no—
55#14519802—28no—
56#14519802—28no—
57#14519802—28no—
58C2×#11758201—24no—
59C2×#11758201—24no—
60C2×#11758201—24no—
61C2×#11758199—24no—
62C2×#11758199—24no—
63C2×#11758199—24no—
64C2×#11758194—21no—
65C2×#11758194—21no—
66C2×#11758194—21no—
67C2×#11758194C2×C412yes—
68C2×#11758194D412yes—
69C2×#11758194D412yes—
70C22×#92418—21no—
71#14519736—21no—
72#14519736—21no—
73#14519736—21no—
74#14519736—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61D412yes—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—24no—
84C2×#11758198—28no—
85C2×#11758198—48no—
86C2×C4×Dic61—21no—
87#14519699—28no—
88#14519684—24no—
89C2×#41×C61—21no—
90C2×#41×C61—21no—
91C2×#41×C61—21no—
92C2×#41×C61—21no—
93C2×#41×C61—21no—
94C2×#41×C61—21no—
95C2×#41×C61—21no—
96C2×#41×C61—21no—
97C2×#41×C61—21no—
98C2×#41×C61—21no—
99C2×#41×C61C2×C412yes—
100C2×#41×C61D412yes—
101C22×Q8×C61D411yescharacteristic
102C22×D4×C61—21no—
103C22×D4×C61D411yescharacteristic
104C23×C4×C61—21no—
105C23×C4×C61—21no—
106C23×C4×C61C2311yescharacteristic
107C2×M16×C61—21no—
108C2×M16×C61—21no—
109C2×M16×C61—21no—
110C2×M16×C61—21no—
111C2×M16×C61—21no—
112C2×M16×C61D412yes—
113C22×C8×C61—21no—
114C2×C42×C61—21no—
115C2×C42×C61—21no—
116C2×C42×C61—21no—
117C2×C42×C61—21no—
118C2×C42×C61—21no—
119C2×C42×C61D412yes—
120#104×C61—28no—
121C24×C61—21no—
122C24×C61C2×D411yescharacteristic
123C23×D61—22no—
124C23×D61—22no—
125C23×D61—22no—
126C23×D61—44no—
127C23×D61—44no—
128C23×D61—41no—
129C23×D61—41no—
130C23×D61—41no—
131C23×D61—41no—
132#41×C61—22no—
133#41×C61—22no—
134#41×C61—22no—
135#41×C61—22no—
136#41×C61—22no—
137#41×C61—22no—
138#41×C61—22no—
139#41×C61—22no—
140#41×C61—41no—
141#41×C61—41no—
142#41×C61—41no—
143#41×C61—41no—
144#41×C61—41no—
145#41×C61—41no—
146#41×C61—41no—
147#41×C61—41no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61C22⋊C412yescomplemented
154C2×D4×C61—22no—
155C2×D4×C61—22no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—41no—
162C2×D4×C61—41no—
163C2×D4×C61—41no—
164C2×D4×C61—41no—
165C2×D4×C61C22⋊C412yescomplemented
166C22×C4×C61—24no—
167C22×C4×C61—22no—
168C22×C4×C61—21no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—42no—
172C22×C4×C61—41no—
173C22×C4×C61—41no—
174C22×C4×C61—41no—
175C22×C4×C61—41no—
176C22×C4×C61—41no—
177C22×C4×C61—41no—
178C22×C4×C61C22×C411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
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×C61#4111yescharacteristic
189C22×C4×C61#4111yescharacteristic
190C22×C4×C61#4111yescharacteristic
191C22×C4×C61#4111yescharacteristic
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—44no—
197C2×D244—22no—
198C2×D244—22no—
199C2×D244—22no—
200C2×D244—22no—
201C2×D244—22no—
202C2×D244—22no—
203C2×D244—22no—
204C2×D244—22no—
205C2×D244—22no—
206C2×D244—22no—
207C2×D244—22no—
208C2×D244—22no—
209C2×D244—22no—
210C2×D244—22no—
211C2×D244—22no—
212C2×D244—41no—
213C2×D244—41no—
214C2×D244—41no—
215C2×D244—41no—
216C2×D244—41no—
217C2×D244—41no—
218C2×D244—41no—
219C2×D244—41no—
220C2×D244—41no—
221C2×D244—41no—
222C2×D244—41no—
223C2×D244—41no—
224C2×D244C22⋊C414yescomplemented
225M16×C61—22no—
226M16×C61—22no—
227M16×C61—41no—
228M16×C61—41no—
229C2×C8×C61—22no—
230C2×C8×C61—41no—
231C2×C8×C61—41no—
232C42×C61—22no—
233C42×C61—22no—
234C42×C61—41no—
235C42×C61—41no—
236C22⋊Dic61—41no—
237C22⋊Dic61—41no—
238C22⋊Dic61—84no—
239#11758201—216no—
240#11758199—216no—
241#11758198—416no—
242C4⋊Dic61—22no—
243C4⋊Dic61—22no—
244C4⋊Dic61—41no—
245C4⋊Dic61—41no—
246C4⋊Dic61—41no—
247C4⋊Dic61—41no—
248C4×Dic61—41no—
249C4×Dic61—41no—
250#11758194—22no—
251#11758194—22no—
252#11758194—22no—
253#11758194C22⋊C414yescomplemented
254C2×#92418—22no—
255C2×#92418—22no—
256C2×#92418—22no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—42no—
263C23×C61—42no—
264C23×C61C4×D411yescharacteristic
265C23×C61#12011yescharacteristic
266C23×C61#12011yescharacteristic
267C23×C61#12111yescharacteristic
268C23×C61#12111yescharacteristic
269C23×C61#12111yescharacteristic
270C23×C61#12711yescharacteristic
271C22×D61—24no—
272C22×D61—44no—
273C22×D61—48no—
274C22×D61—44no—
275C22×D61—48no—
276C22×D61—42no—
277C22×D61—42no—
278C22×D61—42no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61—42no—
282C22×D61—84no—
283C22×D61—82no—
284C22×D61—82no—
285C22×D61—84no—
286C22×D61—82no—
287C22×D61—82no—
288Q8×C61—22no—
289Q8×C61—22no—
290Q8×C61—41no—
291Q8×C61—41no—
292D4×C61—22no—
293D4×C61—22no—
294D4×C61—42no—
295D4×C61—42no—
296D4×C61—42no—
297D4×C61—42no—
298D4×C61—41no—
299D4×C61—41no—
300C2×C4×C61—24no—
301C2×C4×C61—22no—
302C2×C4×C61—44no—
303C2×C4×C61—42no—
304C2×C4×C61—44no—
305C2×C4×C61—42no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61—42no—
312C2×C4×C61C2×C22⋊C411yescharacteristic
313C2×C4×C61C2×C22⋊C411yescharacteristic
314C2×C4×C61C2×C22⋊C411yescharacteristic
315C2×C4×C61C4×D411yescharacteristic
316C2×C4×C61C4×D411yescharacteristic
317C2×C4×C61C4×D411yescharacteristic
318C2×C4×C61#12011yescharacteristic
319C2×C4×C61#12011yescharacteristic
320C2×C4×C61#12011yescharacteristic
321C2×C4×C61#12011yescharacteristic
322C2×C4×C61#12011yescharacteristic
323C2×C4×C61#12011yescharacteristic
324C2×C4×C61#12111yescharacteristic
325C2×C4×C61#12111yescharacteristic
326C2×C4×C61#12111yescharacteristic
327C2×C4×C61#12111yescharacteristic
328C2×C4×C61#12111yescharacteristic
329C2×C4×C61#12111yescharacteristic
330C2×C4×C61#12111yescharacteristic
331C2×C4×C61#12111yescharacteristic
332C2×C4×C61#12111yescharacteristic
333C2×C4×C61#12311yescharacteristic
334C2×C4×C61#12311yescharacteristic
335C2×C4×C61#12311yescharacteristic
336C2×C4×C61#12311yescharacteristic
337C2×C4×C61#12411yescharacteristic
338C2×C4×C61#12411yescharacteristic
339C2×C4×C61#12711yescharacteristic
340C2×Dic61—44no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61—44no—
345C2×Dic61—42no—
346C2×Dic61—82no—
347D244—24no—
348D244—24no—
349D244—42no—
350D244—42no—
351D244—42no—
352D244—42no—
353D244—42no—
354D244—42no—
355C8×C61—42no—
356#92418—24no—
357#11016—611nomaximal, Sylow
358C22×C61—22no—
359C22×C61—22no—
360C22×C61—21no—
361C22×C61—21no—
362C22×C61—21no—
363C22×C61—21no—
364C22×C61—22no—
365C22×C61—22no—
366C22×C61—44no—
367C22×C61—42no—
368C22×C61—81no—
369C22×C61—81no—
370C22×C61—82no—
371C22×C61#38611yescharacteristic
372C22×C61#38611yescharacteristic
373C22×C61#39011yescharacteristic
374C22×C61#39211yescharacteristic
375C22×C61#39211yescharacteristic
376C22×C61#39211yescharacteristic
377C22×C61#39411yescharacteristic
378C22×C61#45312yes—
379C22×C61#45412yes—
380C2×D61—48no—
381C2×D61—44no—
382C2×D61—84no—
383C2×D61—84no—
384C2×D61—84no—
385C2×D61—84no—
386C2×D61—82no—
387C2×D61—82no—
388C2×D61—84no—
389C4×C61—44no—
390C4×C61—42no—
391C4×C61#37911yescharacteristic
392C4×C61#38611yescharacteristic
393C4×C61#38611yescharacteristic
394C4×C61#39011yescharacteristic
395C4×C61#39211yescharacteristic
396C4×C61#39411yescharacteristic
397C4×C61#39411yescharacteristic
398C4×C61#39411yescharacteristic
399Dic61—82no—
400Dic61—82no—
401C22×AGL(1,ℤ/8)—611no—
402C22×#104D6111yescharacteristic, complemented
403C2×#418—611no—
404#2311—611no—
405C2×#390—611no—
406C2×#343—611no—
407C2×#339—611no—
408C2×C61—21no—
409C2×C61—21no—
410C2×C61—21no—
411C2×C61—21no—
412C2×C61—82no—
413C2×C61#143811yescharacteristic
414C2×C61#188312yes—
415C2×C61#200211yescharacteristic
416C2×C61#200311yescharacteristic
417C2×C61#200612yes—
418D61—84no—
419C22×#41C2×D6111yescharacteristic
420C23×D4—611no—
421C2×AGL(1,ℤ/8)—614no—
422C2×AGL(1,ℤ/8)—1222no—
423C2×AGL(1,ℤ/8)—1222no—
424C2×AGL(1,ℤ/8)—1222no—
425C2×AGL(1,ℤ/8)—1222no—
426C2×AGL(1,ℤ/8)—1222no—
427C22×SD16—1221no—
428C22×D8—1221no—
429C22×M16—611no—
430C22×M16C2×D6111yescharacteristic
431C2×#117—611no—
432C22×C4⋊C4—611no—
433C22×C22⋊C4—1222no—
434C22×C42C2×D6111yescharacteristic
435C2×#104—22no—
436C2×#104—22no—
437C2×#104—22no—
438#418—1222no—
439#418—1222no—
440C2×#102—1222no—
441#391—1221no—
442#390—1222no—
443#390—1221no—
444#390—1222no—
445#386—1222no—
446#380—1222no—
447#343—1222no—
448#339—1222no—
449C61#1101611yescharacteristic, complemented, Sylow
450C25—1221no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41C4×D6112yes—
462C2×#41C22⋊D6112yes—
463C22×Q8D24411yescharacteristic
464C22×D4—21no—
465C22×D4—612no—
466C22×D4—612no—
467C22×D4—612no—
468C22×D4—1221no—
469C22×D4—1221no—
470C22×D4—1221no—
471C22×D4—1221no—
472C22×D4—1221no—
473C22×D4—1221no—
474C22×D4—1221no—
475C22×D4—1221no—
476C22×D4—1221no—
477C22×D4—1221no—
478C22×D4—1221no—
479C22×D4D24411yescharacteristic
480C23×C4—21no—
481C23×C4—21no—
482C23×C4—612no—
483C23×C4C22×D6111yescharacteristic
484AGL(1,ℤ/8)—1228no—
485AGL(1,ℤ/8)—1228no—
486AGL(1,ℤ/8)—1228no—
487AGL(1,ℤ/8)—1228no—
488C2×SD16—1224no—
489C2×SD16—1224no—
490C2×SD16—1224no—
491C2×D8—1224no—
492C2×D8—1224no—
493C2×D8—1224no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—21no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—612no—
500C2×M16—612no—
501C2×M16—612no—
502C2×M16—1221no—
503C2×M16—1221no—
504C2×M16—1221no—
505C2×M16C22⋊D6112yes—
506C22×C8—21no—
507C22×C8—1221no—
508#117—1221no—
509#117—1221no—
510#117—1221no—
511#117—1221no—
512C2×C4⋊C4—612no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C22⋊C4—1224no—
520C2×C22⋊C4—1228no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—2448no—
523C2×C42—21no—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42—21no—
527C2×C42—21no—
528C2×C42—1221no—
529C2×C42C22⋊D6112yes—
530#104—28no—
531#102—1228no—
532#95—1224no—
533C24—21no—
534C24—1222no—
535C24—1222no—
536C24—1222no—
537C24—2444no—
538C24—2444no—
539C24—2441no—
540C24—2441no—
541C24—2441no—
542C24—2441no—
543C24D4×D6111yescharacteristic
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—22no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8#1175819812yescomplemented
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—614no—
578C2×D4—1222no—
579C2×D4—1222no—
580C2×D4—1222no—
581C2×D4—1222no—
582C2×D4—1222no—
583C2×D4—1222no—
584C2×D4—1222no—
585C2×D4—1222no—
586C2×D4—1222no—
587C2×D4—1222no—
588C2×D4—1222no—
589C2×D4—1222no—
590C2×D4—1222no—
591C2×D4—1222no—
592C2×D4—1222no—
593C2×D4—2441no—
594C2×D4—2441no—
595C2×D4—2441no—
596C2×D4—2441no—
597C2×D4—2441no—
598C2×D4—2441no—
599C2×D4—2441no—
600C2×D4—2441no—
601C2×D4—2441no—
602C2×D4—2441no—
603C2×D4—2441no—
604C2×D4—2441no—
605C2×D4#1175819812yescomplemented
606C22×C4—24no—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—42no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—2444no—
623C22×C4C2×C4×D6111yescharacteristic
624C22×C4C2×D24411yescharacteristic
625C22×C4#1175822211yescharacteristic
626C22×C4#1175822211yescharacteristic
627C22×C4D4×D6111yescharacteristic
628C22×C4D4×D6111yescharacteristic
629C22×C4D4×D6111yescharacteristic
630C22×C4D4×D6111yescharacteristic
631C22×C4D4×D6111yescharacteristic
632C22×C4#1175822411yescharacteristic
633C22×C4#1175822411yescharacteristic
634C22×C4C2×C22⋊D6111yescharacteristic
635C22×C4C2×C22⋊D6111yescharacteristic
636C22×C4C2×C22⋊D6111yescharacteristic
637SD16—12216no—
638D8—12216no—
639M16—22no—
640M16—22no—
641M16—41no—
642M16—41no—
643M16—614no—
644M16—1222no—
645M16—1222no—
646M16—1222no—
647C2×C8—22no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8—1222no—
651C2×C8—1222no—
652C2×C8—1222no—
653C4⋊C4—1222no—
654C4⋊C4—1222no—
655C4⋊C4—2441no—
656C4⋊C4—2441no—
657C4⋊C4—2441no—
658C4⋊C4—2441no—
659C22⋊C4—4884no—
660C22⋊C4—24416no—
661C22⋊C4—2441no—
662C22⋊C4—2441no—
663C42—22no—
664C42—22no—
665C42—41no—
666C42—41no—
667C42—2441no—
668C42—2441no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—42no—
673C23—41no—
674C23—41no—
675C23—42no—
676C23—1224no—
677C23—4884no—
678C23—4882no—
679C23—4882no—
680C23—4884no—
681C23—4882no—
682C23—4882no—
683C23—2444no—
684C23—2448no—
685C23—2444no—
686C23—2448no—
687C23—2442no—
688C23—2442no—
689C23—2442no—
690C23—2442no—
691C23—2442no—
692C23—2442no—
693C23#1451973711yescharacteristic
694C23#1451974511yescharacteristic
695C23#1451974711yescharacteristic
696C23#1451974911yescharacteristic
697C23#1451975011yescharacteristic
698C23#1451975011yescharacteristic
699C23#1451977311yescharacteristic
700Q8—22no—
701Q8—22no—
702Q8—41no—
703Q8—41no—
704D4—22no—
705D4—22no—
706D4—42no—
707D4—42no—
708D4—42no—
709D4—42no—
710D4—41no—
711D4—41no—
712D4—1224no—
713D4—1224no—
714D4—2442no—
715D4—2442no—
716D4—2442no—
717D4—2442no—
718D4—2442no—
719D4—2442no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—4882no—
733C2×C4—2444no—
734C2×C4—2442no—
735C2×C4—2442no—
736C2×C4—2442no—
737C2×C4—2442no—
738C2×C4—2444no—
739C2×C4C22⋊C4×D6111yescharacteristic
740C2×C4C22⋊C4×D6111yescharacteristic
741C2×C4C2×#1175819811yescharacteristic
742C2×C4#1451973711yescharacteristic
743C2×C4C4×C22⋊D6111yescharacteristic
744C2×C4C4×C22⋊D6111yescharacteristic
745C2×C4#1451974511yescharacteristic
746C2×C4#1451974511yescharacteristic
747C2×C4#1451974511yescharacteristic
748C2×C4#1451974611yescharacteristic
749C2×C4#1451974711yescharacteristic
750C2×C4#1451974711yescharacteristic
751C2×C4#1451974811yescharacteristic
752C2×C4#1451974811yescharacteristic
753C2×C4#1451974911yescharacteristic
754C2×C4#1451974911yescharacteristic
755C2×C4#1451974911yescharacteristic
756C2×C4#1451975011yescharacteristic
757C2×C4#1451975011yescharacteristic
758C2×C4#1451975111yescharacteristic
759C2×C4#1451975111yescharacteristic
760C2×C4#1451975911yescharacteristic
761C2×C4#1451975911yescharacteristic
762C2×C4#1451976011yescharacteristic
763C2×C4#1451976111yescharacteristic
764C2×C4#1451976311yescharacteristic
765C2×C4#1451976311yescharacteristic
766C2×C4#1451977311yescharacteristic
767C8—42no—
768C8—1224no—
769C22—22no—
770C22—22no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—22no—
776C22—22no—
777C22—44no—
778C22—42no—
779C22—81no—
780C22—81no—
781C22—82no—
782C22—4884no—
783C22—4884no—
784C22—4884no—
785C22—4884no—
786C22—4882no—
787C22—4882no—
788C22—4884no—
789C22—2448no—
790C22—2444no—
791C22#1683963811yescharacteristic
792C22#1683963911yescharacteristic
793C22#1683966211yescharacteristic
794C22#1683967011yescharacteristic
795C22#1683967111yescharacteristic
796C22#1683967111yescharacteristic
797C22#1683967711yescharacteristic
798C22#1683993112yes—
799C22#1683993612yes—
800C4—44no—
801C4—42no—
802C4—4882no—
803C4—4882no—
804C4#1683961711yescharacteristic
805C4#1683963811yescharacteristic
806C4#1683964111yescharacteristic
807C4#1683966211yescharacteristic
808C4#1683967011yescharacteristic
809C4#1683967711yescharacteristic
810C4#1683967811yescharacteristic
811C4#1683967811yescharacteristic
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—82no—
817C2—4884no—
818C2#2144405811yescharacteristic
819C2#2144619312yes—
820C2#2144683311yescharacteristic
821C2#2144684011yescharacteristic
822C2#2144686212yes—
subgroupG/H
centerC23#14519747
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC22×#104×C61C2
socleC23×C61#120
prime radicalC22×#14519802C2
cosocleC23×C4×C61C23
hypercenterC22×#104D61
hypocenterC61#11016
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C2×#16839768C2semidirect
3. #21448411C2semidirect
4. C2×#16839664C2semidirect
5. C2×#16839530C2semidirect
6. C2×#16839522C2semidirect
7. C22×#104×C61C2semidirect
14. C2×#14519802C4semidirect
153. C2×Q8×C61C22⋊C4semidirect
165. C2×D4×C61C22⋊C4semidirect
224. C2×D244C22⋊C4semidirect
253. #11758194C22⋊C4semidirect
402. C22×#104D61semidirect
449. C61#11016semidirect
565. C2×Q8#11758198semidirect
605. C2×D4#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×#145198022
C2×#168397682
#214484112
C2×#168396642
C2×#168395302
C2×#168395222
C22×#104×C612
#1101661