Finite Group Databasebeta

← C2×#21446318 #29681918

Subgroups — C2×#21446318 #29681918

Order 15616.

1798 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840560C211yesmaximal, characteristic
2C2×#41×Dic61C211yesmaximal, characteristic, complemented
3C22×#14519703C211yesmaximal, characteristic, complemented
4C2×#16839735C211yesmaximal, characteristic, complemented
5#21446318C218yesmaximal, direct product factor
6C2×#16839533C211yesmaximal, characteristic, complemented
7C2×#16839521C211yesmaximal, characteristic, complemented
8C2×C61×#421C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10#16840560—22no—
11#16840560—22no—
12#16840560C414yescomplemented
13#16840560C2214yes—
14C2×#14519808—21no—
15C2×#14519807C412yescomplemented
16C2×#14519803—21no—
17C2×#14519802C412yescomplemented
18C2×#14519797—22no—
19C22×#11758194C2211yescharacteristic
20#41×Dic61—22no—
21#41×Dic61—22no—
22#41×Dic61—22no—
23#41×Dic61C2214yescomplemented
24C2×Q8×Dic61—21no—
25C2×D4×Dic61—22no—
26C2×D4×Dic61—21no—
27C2×#14519736—21no—
28C2×#14519736C2211yescharacteristic
29C22×C4×Dic61—21no—
30C22×C4×Dic61C2211yescharacteristic
31C2×#14519703—21no—
32C2×#14519703—21no—
33C2×#14519703—22no—
34C2×#14519703C2214yescomplemented
35#16839735—22no—
36#16839735C2214yescomplemented
37C2×#14519691—22no—
38#16839533C2214yescomplemented
39#16839521C2214yescomplemented
40C22×#41×C61C2211yescharacteristic
41C22×M16×C61C2211yescharacteristic
42C2×#117×C61C2211yescharacteristic
43C61×#421—22no—
44C61×#421C2214yescomplemented
45C2×#104×C61—22no—
46C2×#11758222—21no—
47C2×#11758222—21no—
48C2×#11758222—21no—
49C2×#11758222—21no—
50C2×#11758222—21no—
51C2×#11758222—21no—
52C2×#11758222—21no—
53C2×#11758222—21no—
54C2×#11758222—21no—
55C2×#11758222—21no—
56C2×#11758222C2×C412yescomplemented
57C2×#11758222C2312yes—
58C22×Dic122C2×C411yescharacteristic, complemented
59C22×D244C2×C411yescharacteristic, complemented
60C22×C22⋊D61—21no—
61C23×Dic61—22no—
62C23×Dic61—21no—
63C22×C4×D61—21no—
64#14519808—24no—
65#14519808—24no—
66#14519807—24no—
67#14519807C2×C418yescomplemented
68#14519803—24no—
69#14519803—24no—
70#14519802—24no—
71#14519802C2×C418yescomplemented
72#14519797—28no—
73#14519797—28no—
74C2×#11758202—22no—
75C2×#11758200—22no—
76C2×#11758201—22no—
77C2×#11758199—22no—
78C2×#11758194—21no—
79C2×#11758194—21no—
80C2×#11758194—21no—
81C2×#11758194C2×C412yescomplemented
82C2×#11758194C2×C412yescomplemented
83C2×#11758194C2312yes—
84C22×#92418—21no—
85Q8×Dic61—24no—
86Q8×Dic61—24no—
87D4×Dic61—28no—
88D4×Dic61—24no—
89D4×Dic61—24no—
90D4×Dic61—28no—
91#14519736—24no—
92#14519736—21no—
93#14519736—21no—
94#14519736—24no—
95#14519736D412yes—
96#14519736C2312yes—
97C2×C4⋊Dic61—22no—
98C2×C4⋊Dic61—21no—
99C2×C22⋊Dic61—22no—
100C2×C22⋊Dic61D412yes—
101C2×C4×Dic61—22no—
102C2×C4×Dic61—24no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61—24no—
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D412yes—
111C2×C4×Dic61C2312yes—
112#14519703—24no—
113#14519703—24no—
114#14519691—28no—
115C2×#41×C61—21no—
116C2×#41×C61—21no—
117C2×#41×C61—21no—
118C2×#41×C61—21no—
119C2×#41×C61—21no—
120C2×#41×C61—21no—
121C2×#41×C61C2×C412yes—
122C2×#41×C61C2×C412yes—
123C2×#41×C61D412yes—
124C2×#41×C61D412yes—
125C2×#41×C61D412yes—
126C2×#41×C61C2312yes—
127C22×Q8×C61D411yescharacteristic
128C22×D4×C61—21no—
129C22×D4×C61D411yescharacteristic
130C23×C4×C61—21no—
131C23×C4×C61C2311yescharacteristic
132C2×M16×C61—21no—
133C2×M16×C61—21no—
134C2×M16×C61—21no—
135C2×M16×C61—21no—
136C2×M16×C61—21no—
137C2×M16×C61C2312yes—
138C22×C8×C61—21no—
139#117×C61—21no—
140#117×C61—21no—
141#117×C61—21no—
142#117×C61C2312yes—
143C2×C4⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145C2×C42×C61—21no—
146#104×C61—28no—
147C24×C61—21no—
148C24×C61C2×D411yescharacteristic
149C23×D61—21no—
150#41×C61—22no—
151#41×C61—22no—
152#41×C61—22no—
153#41×C61—22no—
154#41×C61—22no—
155#41×C61—22no—
156#41×C61—22no—
157#41×C61—22no—
158#41×C61—22no—
159#41×C61—22no—
160#41×C61—22no—
161#41×C61—22no—
162#41×C61C22⋊C414yes—
163#41×C61C22⋊C414yes—
164#41×C61C22×C414yes—
165#41×C61C2×D414yes—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61C22⋊C412yes—
170C2×Q8×C61C22⋊C412yes—
171C2×Q8×C61C2×D412yes—
172C2×D4×C61—22no—
173C2×D4×C61—22no—
174C2×D4×C61—22no—
175C2×D4×C61—22no—
176C2×D4×C61—22no—
177C2×D4×C61—22no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61C22⋊C412yes—
182C2×D4×C61C22⋊C412yes—
183C2×D4×C61C2×D412yes—
184C22×C4×C61—21no—
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—41no—
192C22×C4×C61C22×C411yescharacteristic
193C22×C4×C61C22×C411yescharacteristic
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61#4111yescharacteristic
202C22×C4×C61#4111yescharacteristic
203C22×C4×C61#4111yescharacteristic
204C22×C4×C61#4111yescharacteristic
205C22×C4×C61C2411yescharacteristic
206C2×C22⋊D61—22no—
207C2×C22⋊D61—22no—
208C2×C22⋊D61—41no—
209C2×C22⋊D61—41no—
210C2×C22⋊D61—41no—
211C2×C22⋊D61—41no—
212C22×Dic61—21no—
213C22×Dic61—28no—
214C22×Dic61—21no—
215C22×Dic61—22no—
216C22×Dic61—21no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—44no—
220C22×Dic61—48no—
221#11758222—22no—
222#11758222—22no—
223#11758222—22no—
224#11758222—22no—
225#11758222—22no—
226#11758222—22no—
227#11758222—22no—
228#11758222—22no—
229#11758222—41no—
230#11758222—41no—
231#11758222—41no—
232#11758222—41no—
233#11758222—41no—
234#11758222—41no—
235#11758222—41no—
236#11758222—41no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244—21no—
240C2×D244—21no—
241C2×D244—21no—
242C2×D244C22×C412yescomplemented
243C2×C4×D61—22no—
244C2×C4×D61—22no—
245C2×C4×D61—41no—
246C2×C4×D61—41no—
247C2×C4×D61—41no—
248C2×C4×D61—41no—
249C2×Dic122—21no—
250C2×Dic122—21no—
251C2×Dic122—21no—
252C2×Dic122—21no—
253C2×Dic122—21no—
254C2×Dic122C22×C412yescomplemented
255M16×C61—22no—
256M16×C61—22no—
257M16×C61—41no—
258M16×C61—41no—
259C2×C8×C61—22no—
260C2×C8×C61—41no—
261C2×C8×C61—41no—
262C4⋊C4×C61—22no—
263C4⋊C4×C61—41no—
264C22⋊C4×C61—22no—
265C22⋊C4×C61—41no—
266C42×C61—22no—
267C42×C61—41no—
268C22⋊Dic61—28no—
269C22⋊Dic61—22no—
270C22⋊Dic61C2×D414yes—
271#11758202—28no—
272#11758201—28no—
273#11758200—28no—
274#11758199—28no—
275C4⋊Dic61—28no—
276C4⋊Dic61—22no—
277C4⋊Dic61—22no—
278C4×Dic61—28no—
279C4×Dic61—21no—
280C4×Dic61—22no—
281C4×Dic61—21no—
282C4×Dic61—22no—
283C4×Dic61—22no—
284C4×Dic61—22no—
285C4×Dic61C2×D412yes—
286C4×Dic61C2×D412yes—
287#11758194—22no—
288#11758194—22no—
289#11758194—22no—
290#11758194C22×C414yescomplemented
291C2×#92418—22no—
292C2×#92418—22no—
293C2×#92418—22no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—42no—
298C23×C61—44no—
299C23×C61C4×D411yescharacteristic
300C23×C61C4×D411yescharacteristic
301C23×C61#12011yescharacteristic
302C23×C61#12011yescharacteristic
303C23×C61#12111yescharacteristic
304C23×C61#12111yescharacteristic
305C23×C61C22×D411yescharacteristic
306C22×D61—22no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—82no—
310Q8×C61—22no—
311Q8×C61—22no—
312Q8×C61—22no—
313Q8×C61C2×C22⋊C414yes—
314D4×C61—24no—
315D4×C61—24no—
316D4×C61—24no—
317D4×C61—24no—
318D4×C61—22no—
319D4×C61—22no—
320D4×C61—22no—
321D4×C61C2×C22⋊C414yes—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—24no—
326C2×C4×C61—24no—
327C2×C4×C61—24no—
328C2×C4×C61—24no—
329C2×C4×C61—42no—
330C2×C4×C61—82no—
331C2×C4×C61C2×C22⋊C411yescharacteristic
332C2×C4×C61C2×C22⋊C411yescharacteristic
333C2×C4×C61C2×C22⋊C411yescharacteristic
334C2×C4×C61C2×C22⋊C411yescharacteristic
335C2×C4×C61C4×D411yescharacteristic
336C2×C4×C61C4×D411yescharacteristic
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#12111yescharacteristic
344C2×C4×C61#12111yescharacteristic
345C2×C4×C61#12111yescharacteristic
346C2×C4×C61#12111yescharacteristic
347C2×C4×C61#12111yescharacteristic
348C2×C4×C61#12111yescharacteristic
349C2×C4×C61#12311yescharacteristic
350C2×C4×C61#12311yescharacteristic
351C2×C4×C61#12311yescharacteristic
352C2×C4×C61#12311yescharacteristic
353C2×C4×C61C23×C411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C61C2×#4111yescharacteristic
358C2×C4×C61C2×#4111yescharacteristic
359C22⋊D61—42no—
360C22⋊D61—42no—
361C22⋊D61—42no—
362C22⋊D61—42no—
363C2×Dic61—24no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—24no—
367C2×Dic61—22no—
368C2×Dic61—44no—
369C2×Dic61—44no—
370C2×Dic61—416no—
371C2×Dic61—44no—
372C2×Dic61—42no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375D244—22no—
376D244—22no—
377D244—41no—
378D244—41no—
379C4×D61—42no—
380C4×D61—42no—
381C4×D61—42no—
382C4×D61—42no—
383Dic122—22no—
384Dic122—22no—
385Dic122—41no—
386Dic122—41no—
387C8×C61—42no—
388#92418—24no—
389C2×#1906—611nomaximal, Sylow
390C22×C61—22no—
391C22×C61—22no—
392C22×C61—22no—
393C22×C61—24no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—44no—
399C22×C61—44no—
400C22×C61—44no—
401C22×C61#38611yescharacteristic
402C22×C61#38611yescharacteristic
403C22×C61#38611yescharacteristic
404C22×C61#38611yescharacteristic
405C22×C61C2×C4×D411yescharacteristic
406C22×C61C2×#12011yescharacteristic
407C22×C61C2×#12111yescharacteristic
408C2×D61—42no—
409C2×D61—82no—
410C2×D61—82no—
411C2×D61—82no—
412C4×C61—24no—
413C4×C61—82no—
414C4×C61#38611yescharacteristic
415C4×C61#38611yescharacteristic
416C4×C61#38611yescharacteristic
417C4×C61#38611yescharacteristic
418C4×C61C22×C22⋊C411yescharacteristic
419C4×C61C2×C4×D411yescharacteristic
420C4×C61C2×#12111yescharacteristic
421C4×C61C2×#12311yescharacteristic
422Dic61—24no—
423Dic61—44no—
424Dic61—42no—
425Dic61—42no—
426C2×#575—611no—
427C2×C4×#41—611no—
428C2×#421D6111yescharacteristic, complemented
429C22×#104—611no—
430C2×#410—611no—
431#1906—618no—
432C2×#344—611no—
433C2×#339—611no—
434C2×C61—21no—
435C2×C61—21no—
436C2×C61—21no—
437C2×C61—21no—
438C2×C61—21no—
439C2×C61—21no—
440C2×C61—44no—
441C2×C61#190612yescomplemented
442C2×C61C2×#38611yescharacteristic
443D61—82no—
444C22×#41—611no—
445C22×#41C2×D6111yescharacteristic
446#575—614no—
447#575—614no—
448#575—1222no—
449#575—1222no—
450C2×#137—612no—
451C2×#137—1221no—
452C2×AGL(1,ℤ/8)—612no—
453C2×AGL(1,ℤ/8)—1221no—
454C2×#135—1222no—
455C22×M16—611no—
456C22×M16C2×D6111yescharacteristic
457C4×#41—614no—
458C4×#41—1222no—
459C4×#41—1222no—
460C4×#41—1222no—
461C2×C4×Q8—1221no—
462C2×C4×D4—1222no—
463C2×C4×D4—1221no—
464C2×#117—611no—
465C2×#117—1221no—
466C2×#117C2×D6111yescharacteristic
467C22×C42—611no—
468C22×C42—1221no—
469#421—22no—
470#421C2×D6114yescomplemented
471C2×#104—22no—
472C2×#104—614no—
473C2×#104—1221no—
474C2×#104—1222no—
475C2×#104—1221no—
476#410—614no—
477#410—1222no—
478C2×#99—1222no—
479#344—614no—
480#339—614no—
481C61C2×#190611yescharacteristic, complemented, Sylow
482C2×#41—21no—
483C2×#41—21no—
484C2×#41—21no—
485C2×#41—21no—
486C2×#41—21no—
487C2×#41—21no—
488C2×#41—612no—
489C2×#41—612no—
490C2×#41—1221no—
491C2×#41—1221no—
492C2×#41—1221no—
493C2×#41—1221no—
494C2×#41—1221no—
495C2×#41—1221no—
496C2×#41—1221no—
497C2×#41—1221no—
498C2×#41—1221no—
499C2×#41—1221no—
500C2×#41C4×D6112yes—
501C2×#41C4×D6112yes—
502C2×#41D24412yes—
503C2×#41C22⋊D6112yes—
504C2×#41C22⋊D6112yes—
505C2×#41C22×D6112yes—
506C22×Q8—611no—
507C22×Q8D24411yescharacteristic
508C22×D4—21no—
509C22×D4—611no—
510C22×D4—1221no—
511C22×D4D24411yescharacteristic
512C23×C4—21no—
513C23×C4—1222no—
514C23×C4—1221no—
515C23×C4—1221no—
516C23×C4C22×D6111yescharacteristic
517#137—618no—
518#137—1224no—
519#137—1224no—
520#137—1224no—
521AGL(1,ℤ/8)—618no—
522AGL(1,ℤ/8)—1224no—
523AGL(1,ℤ/8)—1224no—
524AGL(1,ℤ/8)—1224no—
525#135—1228no—
526#135—1228no—
527C2×Q16—1222no—
528C2×SD16—1222no—
529C2×SD16—1222no—
530C2×D8—1222no—
531C2×M16—21no—
532C2×M16—21no—
533C2×M16—21no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—612no—
537C2×M16—612no—
538C2×M16—612no—
539C2×M16—1221no—
540C2×M16—1221no—
541C2×M16—1221no—
542C2×M16C22×D6112yes—
543C22×C8—21no—
544C22×C8—1221no—
545C4×Q8—1224no—
546C4×Q8—1224no—
547C4×D4—1228no—
548C4×D4—1228no—
549C4×D4—1224no—
550C4×D4—1224no—
551#117—21no—
552#117—21no—
553#117—21no—
554#117—612no—
555#117—612no—
556#117—1224no—
557#117—1224no—
558#117—1221no—
559#117—1221no—
560#117C22×D6112yes—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—1222no—
563C2×C4⋊C4—1221no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—612no—
566C2×C22⋊C4—1222no—
567C2×C42—21no—
568C2×C42—611no—
569C2×C42—612no—
570C2×C42—611no—
571C2×C42—612no—
572C2×C42—1224no—
573C2×C42—1222no—
574C2×C42—1224no—
575C2×C42—1221no—
576C2×C42—1221no—
577C2×C42—1221no—
578C2×C42—1221no—
579#104—28no—
580#104—1224no—
581#104—1224no—
582#99—1228no—
583C24—21no—
584C24—1221no—
585C24D4×D6111yescharacteristic
586#41—22no—
587#41—22no—
588#41—22no—
589#41—22no—
590#41—22no—
591#41—22no—
592#41—22no—
593#41—22no—
594#41—22no—
595#41—22no—
596#41—22no—
597#41—22no—
598#41—1222no—
599#41—1222no—
600#41—1222no—
601#41—1222no—
602#41—1222no—
603#41—1222no—
604#41—1222no—
605#41—1222no—
606#41—2441no—
607#41—2441no—
608#41—2441no—
609#41—2441no—
610#41—2441no—
611#41—2441no—
612#41—2441no—
613#41—2441no—
614#41#1175819814yes—
615#41#1175819814yes—
616#41C2×C4×D6114yes—
617#41C2×C22⋊D6114yes—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—612no—
622C2×Q8—1221no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×Q8—1221no—
626C2×Q8—1221no—
627C2×Q8#1175819812yes—
628C2×Q8#1175819812yes—
629C2×Q8C2×D24412yes—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—612no—
640C2×D4—1222no—
641C2×D4—1222no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—2441no—
648C2×D4—2441no—
649C2×D4—2441no—
650C2×D4—2441no—
651C2×D4#1175819812yes—
652C2×D4#1175819812yes—
653C2×D4C2×D24412yes—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—41no—
662C22×C4—1221no—
663C22×C4—1228no—
664C22×C4—1222no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1222no—
668C22×C4—1222no—
669C22×C4—1222no—
670C22×C4—1222no—
671C22×C4—2444no—
672C22×C4—2448no—
673C22×C4—2441no—
674C22×C4—2441no—
675C22×C4—2441no—
676C22×C4—2441no—
677C22×C4C2×C4×D6111yescharacteristic
678C22×C4C2×C4×D6111yescharacteristic
679C22×C4C2×D24411yescharacteristic
680C22×C4C2×D24411yescharacteristic
681C22×C4D4×D6111yescharacteristic
682C22×C4D4×D6111yescharacteristic
683C22×C4D4×D6111yescharacteristic
684C22×C4#1175822411yescharacteristic
685C22×C4#1175822411yescharacteristic
686C22×C4#1175822411yescharacteristic
687C22×C4#1175822411yescharacteristic
688C22×C4C2×C22⋊D6111yescharacteristic
689C22×C4C2×C22⋊D6111yescharacteristic
690C22×C4C23×D6111yescharacteristic
691Q16—1228no—
692SD16—1228no—
693SD16—1228no—
694D8—1228no—
695M16—22no—
696M16—22no—
697M16—41no—
698M16—41no—
699M16—614no—
700M16—1222no—
701M16—1222no—
702M16—1222no—
703C2×C8—22no—
704C2×C8—41no—
705C2×C8—41no—
706C2×C8—1222no—
707C2×C8—1222no—
708C2×C8—1222no—
709C4⋊C4—22no—
710C4⋊C4—41no—
711C4⋊C4—1228no—
712C4⋊C4—1222no—
713C4⋊C4—1222no—
714C22⋊C4—22no—
715C22⋊C4—41no—
716C22⋊C4—614no—
717C22⋊C4—1228no—
718C22⋊C4—1222no—
719C42—22no—
720C42—41no—
721C42—612no—
722C42—612no—
723C42—1228no—
724C42—1222no—
725C42—1222no—
726C42—1221no—
727C42—1221no—
728C42—1222no—
729C42—1222no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—42no—
734C23—44no—
735C23—1222no—
736C23—4882no—
737C23—2441no—
738C23—2441no—
739C23#1451973711yescharacteristic
740C23#1451973711yescharacteristic
741C23#1451974711yescharacteristic
742C23#1451974711yescharacteristic
743C23#1451974911yescharacteristic
744C23#1451974911yescharacteristic
745C23C2×D4×D6111yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—22no—
749Q8—1222no—
750Q8—1222no—
751Q8—2441no—
752Q8—2441no—
753Q8C2×#1175819814yes—
754D4—24no—
755D4—24no—
756D4—24no—
757D4—24no—
758D4—22no—
759D4—22no—
760D4—22no—
761D4—1222no—
762D4—1222no—
763D4—2442no—
764D4—2442no—
765D4—2442no—
766D4—2442no—
767D4—2441no—
768D4—2441no—
769D4C2×#1175819814yes—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—42no—
778C2×C4—82no—
779C2×C4—1224no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1224no—
784C2×C4—2444no—
785C2×C4—2444no—
786C2×C4—24416no—
787C2×C4—2442no—
788C2×C4—2444no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4—2442no—
792C2×C4—2442no—
793C2×C4—2442no—
794C2×C4—2442no—
795C2×C4C2×#1175819811yescharacteristic
796C2×C4C2×#1175819811yescharacteristic
797C2×C4C2×#1175819811yescharacteristic
798C2×C4C2×#1175819811yescharacteristic
799C2×C4#1451973711yescharacteristic
800C2×C4#1451973711yescharacteristic
801C2×C4#1451973711yescharacteristic
802C2×C4#1451973711yescharacteristic
803C2×C4#1451973711yescharacteristic
804C2×C4#1451973711yescharacteristic
805C2×C4#1451974711yescharacteristic
806C2×C4#1451974711yescharacteristic
807C2×C4#1451974911yescharacteristic
808C2×C4#1451974911yescharacteristic
809C2×C4#1451974911yescharacteristic
810C2×C4#1451974911yescharacteristic
811C2×C4#1451974911yescharacteristic
812C2×C4#1451974911yescharacteristic
813C2×C4#1451976111yescharacteristic
814C2×C4#1451976111yescharacteristic
815C2×C4#1451976111yescharacteristic
816C2×C4#1451976111yescharacteristic
817C2×C4C22×C4×D6111yescharacteristic
818C2×C4C2×D4×D6111yescharacteristic
819C2×C4C22×C22⋊D6111yescharacteristic
820C2×C4C22×D24411yescharacteristic
821C2×C4C2×#1175822411yescharacteristic
822C2×C4C2×#1175822411yescharacteristic
823C8—42no—
824C8—1224no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—24no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—4882no—
837C22—4882no—
838C22—4882no—
839C22—2442no—
840C22#1683963911yescharacteristic
841C22#1683963911yescharacteristic
842C22#1683963911yescharacteristic
843C22#1683963911yescharacteristic
844C22C2×#1451973711yescharacteristic
845C22C2×#1451974711yescharacteristic
846C22C2×#1451974911yescharacteristic
847C4—24no—
848C4—82no—
849C4—1224no—
850C4—2442no—
851C4—2444no—
852C4—2442no—
853C4#1683963911yescharacteristic
854C4#1683963911yescharacteristic
855C4#1683963911yescharacteristic
856C4#1683963911yescharacteristic
857C4C22×#1175819811yescharacteristic
858C4C2×#1451973711yescharacteristic
859C4C2×#1451974911yescharacteristic
860C4C2×#1451976111yescharacteristic
861C2—21no—
862C2—21no—
863C2—21no—
864C2—21no—
865C2—21no—
866C2—21no—
867C2—44no—
868C2—4882no—
869C2#2144631812yesdirect product factor
870C2C2×#1683963911yescharacteristic
subgroupG/H
centerC2×C4#14519749
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#421C2
socleC22×C61#386
prime radicalC2×#16840560C2
cosocleC22×C4×C61C24
hypercenterC2×#421D61
hypocenterC61C2×#1906
LCSG ▷ C2×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. C2×#41×Dic61C2semidirect
3. C22×#14519703C2semidirect
4. C2×#16839735C2semidirect
5. #21446318C2direct (N × H)
6. C2×#16839533C2semidirect
7. C2×#16839521C2semidirect
8. C2×C61×#421C2semidirect
12. #16840560C4semidirect
15. C2×#14519807C4semidirect
17. C2×#14519802C4semidirect
23. #41×Dic61C22semidirect
34. C2×#14519703C22semidirect
36. #16839735C22semidirect
38. #16839533C22semidirect
39. #16839521C22semidirect
44. C61×#421C22semidirect
56. C2×#11758222C2×C4semidirect
58. C22×Dic122C2×C4semidirect
59. C22×D244C2×C4semidirect
67. #14519807C2×C4semidirect
71. #14519802C2×C4semidirect
81. C2×#11758194C2×C4semidirect
82. C2×#11758194C2×C4semidirect
242. C2×D244C22×C4semidirect
254. C2×Dic122C22×C4semidirect
290. #11758194C22×C4semidirect
428. C2×#421D61semidirect
441. C2×C61#1906semidirect
470. #421C2×D61semidirect
481. C61C2×#1906semidirect
869. C2#21446318direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405602
C2×#41×Dic612
C22×#145197032
C2×#168397352
#214463182
C2×#168395332
C2×#168395212
C2×C61×#4212
C2×#190661