Finite Group Databasebeta

← C2×#21446181 #29681487

Subgroups — C2×#21446181 #29681487

Order 15616.

1682 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840560C211yesmaximal, characteristic
2C2×#16839778C211yesmaximal, characteristic, complemented
3C2×#16839758C211yesmaximal, characteristic, complemented
4C2×#16839730C211yesmaximal, characteristic, complemented
5#21446181C218yesmaximal, direct product factor
6C2×#16839533C211yesmaximal, characteristic, complemented
7C2×#16839526C211yesmaximal, characteristic, complemented
8C2×C61×#568C211yesmaximal, 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
20C23×#92418C2211yescharacteristic
21C2×#14519736C2211yescharacteristic
22#16839778—22no—
23#16839778C2214yescomplemented
24C2×#14519703—22no—
25#16839758—22no—
26#16839758C2214yescomplemented
27C2×#14519701—21no—
28C2×#14519698—21no—
29#16839730—22no—
30#16839730C2214yescomplemented
31C2×#14519689—22no—
32#16839533C2214yescomplemented
33#16839526C2214yescomplemented
34C22×#41×C61C2211yescharacteristic
35C61×#568—22no—
36C61×#568—22no—
37C61×#568—22no—
38C61×#568C2214yescomplemented
39C2×#131×C61—22no—
40C2×#131×C61—22no—
41C22×M16×C61—22no—
42C22×M16×C61C2211yescharacteristic
43C22×M16×C61C2211yescharacteristic
44C2×#11758222—21no—
45C2×#11758222—21no—
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×#11758222C2×C412yes—
55C2×#11758222C2312yes—
56C22×Dic122C2×C411yescharacteristic
57C22×D244C2×C411yescharacteristic
58C22×C22⋊D61—21no—
59C22×C4×D61—21no—
60#14519808—24no—
61#14519808—24no—
62#14519807—24no—
63#14519807C2×C418yescomplemented
64#14519803—24no—
65#14519803—24no—
66#14519802—24no—
67#14519802C2×C418yescomplemented
68#14519797—28no—
69#14519797—28no—
70C2×#11758202—22no—
71C2×#11758200—22no—
72C2×#11758201—22no—
73C2×#11758199—22no—
74C2×#11758194—21no—
75C2×#11758194—21no—
76C2×#11758194—21no—
77C2×#11758194C2×C412yes—
78C2×#11758194C2×C412yes—
79C2×#11758194C2312yes—
80C22×#92418—21no—
81C22×#92418—21no—
82C22×#92418—21no—
83C22×#92418—21no—
84C22×#92418—21no—
85C22×#92418—21no—
86C22×#92418—21no—
87C22×#92418C2312yes—
88#14519736—21no—
89#14519736—21no—
90#14519736—21no—
91#14519736C2312yes—
92C2×C4⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C4×Dic61—21no—
95#14519703—28no—
96#14519701—24no—
97#14519698—24no—
98#14519689—28no—
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×C61C2×C412yes—
106C2×#41×C61C2×C412yes—
107C2×#41×C61D412yes—
108C2×#41×C61D412yes—
109C2×#41×C61D412yes—
110C2×#41×C61C2312yes—
111C22×Q8×C61D411yescharacteristic
112C22×D4×C61—21no—
113C22×D4×C61D411yescharacteristic
114C23×C4×C61—21no—
115C23×C4×C61C2311yescharacteristic
116#131×C61—28no—
117#131×C61—28no—
118#131×C61—28no—
119#131×C61—28no—
120C2×M16×C61—24no—
121C2×M16×C61—28no—
122C2×M16×C61—21no—
123C2×M16×C61—21no—
124C2×M16×C61—21no—
125C2×M16×C61—21no—
126C2×M16×C61—21no—
127C2×M16×C61—21no—
128C2×M16×C61—21no—
129C2×M16×C61—28no—
130C2×M16×C61D412yes—
131C2×M16×C61D412yes—
132C2×M16×C61D412yes—
133C2×M16×C61C2312yes—
134C2×M16×C61C2312yes—
135C22×C8×C61—24no—
136C22×C8×C61—21no—
137C22×C8×C61D412yes—
138C24×C61—21no—
139C24×C61#4111yescharacteristic
140C23×D61—21no—
141#41×C61—22no—
142#41×C61—22no—
143#41×C61—22no—
144#41×C61—22no—
145#41×C61—22no—
146#41×C61—22no—
147#41×C61—22no—
148#41×C61—22no—
149#41×C61—22no—
150#41×C61—22no—
151#41×C61—22no—
152#41×C61—22no—
153#41×C61C22⋊C414yes—
154#41×C61C22⋊C414yes—
155#41×C61C22×C414yes—
156#41×C61C2×D414yes—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61C22⋊C412yes—
161C2×Q8×C61C22⋊C412yes—
162C2×Q8×C61C2×D412yes—
163C2×D4×C61—22no—
164C2×D4×C61—22no—
165C2×D4×C61—22no—
166C2×D4×C61—22no—
167C2×D4×C61—22no—
168C2×D4×C61—22no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61C22⋊C412yes—
173C2×D4×C61C22⋊C412yes—
174C2×D4×C61C2×D412yes—
175C22×C4×C61—21no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61C22×C411yescharacteristic
183C22×C4×C61C22×C411yescharacteristic
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×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61#4111yescharacteristic
193C22×C4×C61#4111yescharacteristic
194C22×C4×C61#4111yescharacteristic
195C22×C4×C61C2411yescharacteristic
196C2×C22⋊D61—22no—
197C2×C22⋊D61—22no—
198C2×C22⋊D61—41no—
199C2×C22⋊D61—41no—
200C2×C22⋊D61—41no—
201C2×C22⋊D61—41no—
202C22×Dic61—21no—
203C22×Dic61—41no—
204#11758222—22no—
205#11758222—22no—
206#11758222—22no—
207#11758222—22no—
208#11758222—22no—
209#11758222—22no—
210#11758222—22no—
211#11758222—22no—
212#11758222—41no—
213#11758222—41no—
214#11758222—41no—
215#11758222—41no—
216#11758222—41no—
217#11758222—41no—
218#11758222—41no—
219#11758222—41no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244C22×C412yes—
226C2×C4×D61—22no—
227C2×C4×D61—22no—
228C2×C4×D61—41no—
229C2×C4×D61—41no—
230C2×C4×D61—41no—
231C2×C4×D61—41no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122C22×C412yes—
238M16×C61—216no—
239M16×C61—22no—
240M16×C61—22no—
241M16×C61—22no—
242M16×C61—22no—
243M16×C61—22no—
244M16×C61—22no—
245M16×C61—22no—
246M16×C61C2×D414yes—
247C2×C8×C61—216no—
248C2×C8×C61—22no—
249C2×C8×C61—22no—
250C2×C8×C61—22no—
251C2×C8×C61—22no—
252C2×C8×C61—22no—
253C2×C8×C61C2×D414yes—
254C22⋊Dic61—22no—
255C22⋊Dic61—41no—
256#11758202—28no—
257#11758201—28no—
258#11758200—28no—
259#11758199—28no—
260C4⋊Dic61—22no—
261C4⋊Dic61—41no—
262C4×Dic61—22no—
263C4×Dic61—41no—
264#11758194—22no—
265#11758194—22no—
266#11758194—22no—
267#11758194C22×C414yes—
268C2×#92418—22no—
269C2×#92418—22no—
270C2×#92418—22no—
271C2×#92418—22no—
272C2×#92418—22no—
273C2×#92418—22no—
274C2×#92418—41no—
275C2×#92418—41no—
276C2×#92418—41no—
277C2×#92418—41no—
278C23×C61—22no—
279C23×C61—22no—
280C23×C61—22no—
281C23×C61—42no—
282C23×C61—82no—
283C23×C61C4×D411yescharacteristic
284C23×C61C4×D411yescharacteristic
285C23×C61#12111yescharacteristic
286C23×C61#12111yescharacteristic
287C23×C61#12311yescharacteristic
288C23×C61#12311yescharacteristic
289C23×C61C2×#4111yescharacteristic
290C22×D61—22no—
291C22×D61—44no—
292C22×D61—41no—
293C22×D61—41no—
294Q8×C61—22no—
295Q8×C61—22no—
296Q8×C61—22no—
297Q8×C61C2×C22⋊C414yes—
298D4×C61—24no—
299D4×C61—24no—
300D4×C61—24no—
301D4×C61—24no—
302D4×C61—22no—
303D4×C61—22no—
304D4×C61—22no—
305D4×C61C2×C22⋊C414yes—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—24no—
310C2×C4×C61—24no—
311C2×C4×C61—24no—
312C2×C4×C61—24no—
313C2×C4×C61C2×C22⋊C411yescharacteristic
314C2×C4×C61C2×C22⋊C411yescharacteristic
315C2×C4×C61C2×C22⋊C411yescharacteristic
316C2×C4×C61C2×C22⋊C411yescharacteristic
317C2×C4×C61C4×D411yescharacteristic
318C2×C4×C61C4×D411yescharacteristic
319C2×C4×C61C4×D411yescharacteristic
320C2×C4×C61C4×D411yescharacteristic
321C2×C4×C61C4×D411yescharacteristic
322C2×C4×C61C4×D411yescharacteristic
323C2×C4×C61#12011yescharacteristic
324C2×C4×C61#12011yescharacteristic
325C2×C4×C61#12011yescharacteristic
326C2×C4×C61#12011yescharacteristic
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×C61C23×C411yescharacteristic
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C2×#4111yescharacteristic
341C22⋊D61—42no—
342C22⋊D61—42no—
343C22⋊D61—42no—
344C22⋊D61—42no—
345C2×Dic61—22no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—42no—
349C2×Dic61—82no—
350D244—22no—
351D244—22no—
352D244—41no—
353D244—41no—
354C4×D61—42no—
355C4×D61—42no—
356C4×D61—42no—
357C4×D61—42no—
358Dic122—22no—
359Dic122—22no—
360Dic122—41no—
361Dic122—41no—
362C8×C61—24no—
363C8×C61—24no—
364#92418—24no—
365#92418—42no—
366C2×#1881—611nomaximal, Sylow
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—24no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—44no—
376C22×C61—82no—
377C22×C61—82no—
378C22×C61#38611yescharacteristic
379C22×C61#38611yescharacteristic
380C22×C61#38611yescharacteristic
381C22×C61#38611yescharacteristic
382C22×C61C2×C4×D411yescharacteristic
383C22×C61C2×#12111yescharacteristic
384C22×C61C2×#12311yescharacteristic
385C2×D61—44no—
386C2×D61—42no—
387C2×D61—82no—
388C2×D61—82no—
389C4×C61—24no—
390C4×C61#38611yescharacteristic
391C4×C61#38611yescharacteristic
392C4×C61#38611yescharacteristic
393C4×C61#38611yescharacteristic
394C4×C61C22×C22⋊C411yescharacteristic
395C4×C61C2×C4×D411yescharacteristic
396C4×C61C2×#12011yescharacteristic
397C4×C61C2×#12111yescharacteristic
398Dic61—42no—
399Dic61—82no—
400C2×#575—611no—
401C2×#568D6111yescharacteristic, complemented
402C2×#421—611no—
403C2×#416—611no—
404C2×#408—611no—
405#1881—618no—
406C2×#344—611no—
407C2×#341—611no—
408C2×C61—21no—
409C2×C61—21no—
410C2×C61—21no—
411C2×C61—21no—
412C2×C61—21no—
413C2×C61—21no—
414C2×C61—44no—
415C2×C61#188112yescomplemented
416C2×C61C2×#38611yescharacteristic
417D61—82no—
418C22×#41—611no—
419C22×#41C2×D6111yescharacteristic
420#575—614no—
421#575—614no—
422#575—1222no—
423#575—1222no—
424C2×#137—612no—
425C2×#137—1221no—
426C2×AGL(1,ℤ/8)—612no—
427C2×AGL(1,ℤ/8)—1221no—
428C2×#135—1222no—
429#568—22no—
430#568—22no—
431#568—22no—
432#568C2×D6114yescomplemented
433C2×#131—22no—
434C2×#131—22no—
435C22×M16—22no—
436C22×M16—611no—
437C22×M16C2×D6111yescharacteristic
438C22×M16C2×D6111yescharacteristic
439C23×C8—611no—
440C2×#117—611no—
441#421—614no—
442#421—1222no—
443C2×#104—1222no—
444#416—614no—
445#416—1222no—
446C2×#103—1221no—
447C2×#102—1221no—
448#408—614no—
449#408—1222no—
450C2×C22⋊C8—1222no—
451#344—614no—
452#341—614no—
453C61C2×#188111yescharacteristic, complemented, Sylow
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—612no—
461C2×#41—612no—
462C2×#41—1221no—
463C2×#41—1221no—
464C2×#41—1221no—
465C2×#41—1221no—
466C2×#41—1221no—
467C2×#41—1221no—
468C2×#41—1221no—
469C2×#41—1221no—
470C2×#41—1221no—
471C2×#41—1221no—
472C2×#41C4×D6112yes—
473C2×#41C4×D6112yes—
474C2×#41D24412yes—
475C2×#41C22⋊D6112yes—
476C2×#41C22⋊D6112yes—
477C2×#41C22×D6112yes—
478C22×Q8—611no—
479C22×Q8D24411yescharacteristic
480C22×D4—21no—
481C22×D4—611no—
482C22×D4—1221no—
483C22×D4D24411yescharacteristic
484C23×C4—21no—
485C23×C4—1221no—
486C23×C4C22×D6111yescharacteristic
487#137—618no—
488#137—1224no—
489#137—1224no—
490#137—1224no—
491AGL(1,ℤ/8)—618no—
492AGL(1,ℤ/8)—1224no—
493AGL(1,ℤ/8)—1224no—
494AGL(1,ℤ/8)—1224no—
495#135—1228no—
496#135—1228no—
497C2×Q16—1222no—
498C2×SD16—1222no—
499C2×SD16—1222no—
500C2×D8—1222no—
501#131—28no—
502#131—28no—
503#131—28no—
504#131—28no—
505C2×M16—24no—
506C2×M16—28no—
507C2×M16—21no—
508C2×M16—21no—
509C2×M16—21no—
510C2×M16—21no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16—21no—
514C2×M16—28no—
515C2×M16—612no—
516C2×M16—612no—
517C2×M16—612no—
518C2×M16—1221no—
519C2×M16—1221no—
520C2×M16—1221no—
521C2×M16C22⋊D6112yes—
522C2×M16C22⋊D6112yes—
523C2×M16C22⋊D6112yes—
524C2×M16C22×D6112yes—
525C2×M16C22×D6112yes—
526C22×C8—24no—
527C22×C8—21no—
528C22×C8—612no—
529C22×C8—1221no—
530C22×C8—1221no—
531C22×C8—1221no—
532C22×C8—1221no—
533C22×C8—1221no—
534C22×C8—1221no—
535C22×C8—1221no—
536C22×C8C22⋊D6112yes—
537#117—612no—
538#117—1221no—
539#117—1221no—
540#117—1221no—
541C2×C4⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C42—1221no—
544#104—1228no—
545#103—1224no—
546#102—1224no—
547C22⋊C8—1228no—
548C24—21no—
549C24—1221no—
550C24#1175822211yescharacteristic
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—22no—
560#41—22no—
561#41—22no—
562#41—22no—
563#41—1222no—
564#41—1222no—
565#41—1222no—
566#41—1222no—
567#41—1222no—
568#41—1222no—
569#41—1222no—
570#41—1222no—
571#41—2441no—
572#41—2441no—
573#41—2441no—
574#41—2441no—
575#41—2441no—
576#41—2441no—
577#41—2441no—
578#41—2441no—
579#41#1175819814yes—
580#41#1175819814yes—
581#41C2×C4×D6114yes—
582#41C2×C22⋊D6114yes—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—612no—
587C2×Q8—1221no—
588C2×Q8—1221no—
589C2×Q8—1221no—
590C2×Q8—1221no—
591C2×Q8—1221no—
592C2×Q8#1175819812yes—
593C2×Q8#1175819812yes—
594C2×Q8C2×D24412yes—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—612no—
605C2×D4—1222no—
606C2×D4—1222no—
607C2×D4—1221no—
608C2×D4—1221no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—2441no—
613C2×D4—2441no—
614C2×D4—2441no—
615C2×D4—2441no—
616C2×D4#1175819812yes—
617C2×D4#1175819812yes—
618C2×D4C2×D24412yes—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—1221no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—2441no—
630C22×C4—2441no—
631C22×C4—2441no—
632C22×C4—2441no—
633C22×C4—2441no—
634C22×C4C2×C4×D6111yescharacteristic
635C22×C4C2×C4×D6111yescharacteristic
636C22×C4C2×D24411yescharacteristic
637C22×C4C2×D24411yescharacteristic
638C22×C4#1175822211yescharacteristic
639C22×C4#1175822211yescharacteristic
640C22×C4#1175822211yescharacteristic
641C22×C4C2×C22⋊D6111yescharacteristic
642C22×C4C2×C22⋊D6111yescharacteristic
643C22×C4C2×C22⋊D6111yescharacteristic
644C22×C4C2×C22⋊D6111yescharacteristic
645C22×C4C2×C22⋊D6111yescharacteristic
646C22×C4C2×C22⋊D6111yescharacteristic
647C22×C4C23×D6111yescharacteristic
648Q16—1228no—
649SD16—1228no—
650SD16—1228no—
651D8—1228no—
652M16—216no—
653M16—22no—
654M16—22no—
655M16—22no—
656M16—22no—
657M16—22no—
658M16—22no—
659M16—22no—
660M16—614no—
661M16—1222no—
662M16—1222no—
663M16—1222no—
664M16C2×C22⋊D6114yes—
665C2×C8—216no—
666C2×C8—22no—
667C2×C8—22no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—1222no—
672C2×C8—1222no—
673C2×C8—1222no—
674C2×C8—1222no—
675C2×C8—1222no—
676C2×C8—1222no—
677C2×C8—2441no—
678C2×C8—2441no—
679C2×C8—2441no—
680C2×C8—2441no—
681C2×C8C2×C22⋊D6114yes—
682C4⋊C4—1222no—
683C4⋊C4—2441no—
684C22⋊C4—1222no—
685C22⋊C4—2441no—
686C42—1222no—
687C42—2441no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—42no—
692C23—82no—
693C23—1222no—
694C23—2444no—
695C23—2441no—
696C23—2441no—
697C23C4×C22⋊D6111yescharacteristic
698C23C4×C22⋊D6111yescharacteristic
699C23#1451975111yescharacteristic
700C23#1451975111yescharacteristic
701C23#1451976011yescharacteristic
702C23#1451976011yescharacteristic
703C23C2×#1175822211yescharacteristic
704Q8—22no—
705Q8—22no—
706Q8—22no—
707Q8—1222no—
708Q8—1222no—
709Q8—2441no—
710Q8—2441no—
711Q8C2×#1175819814yes—
712D4—24no—
713D4—24no—
714D4—24no—
715D4—24no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—1222no—
720D4—1222no—
721D4—2442no—
722D4—2442no—
723D4—2442no—
724D4—2442no—
725D4—2441no—
726D4—2441no—
727D4C2×#1175819814yes—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—1222no—
736C2×C4—4882no—
737C2×C4—2442no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4—2442no—
743C2×C4—2442no—
744C2×C4C2×#1175819811yescharacteristic
745C2×C4C2×#1175819811yescharacteristic
746C2×C4C2×#1175819811yescharacteristic
747C2×C4C2×#1175819811yescharacteristic
748C2×C4C4×C22⋊D6111yescharacteristic
749C2×C4C4×C22⋊D6111yescharacteristic
750C2×C4C4×C22⋊D6111yescharacteristic
751C2×C4C4×C22⋊D6111yescharacteristic
752C2×C4C4×C22⋊D6111yescharacteristic
753C2×C4C4×C22⋊D6111yescharacteristic
754C2×C4#1451974611yescharacteristic
755C2×C4#1451974611yescharacteristic
756C2×C4#1451974611yescharacteristic
757C2×C4#1451974611yescharacteristic
758C2×C4#1451975111yescharacteristic
759C2×C4#1451975111yescharacteristic
760C2×C4#1451975111yescharacteristic
761C2×C4#1451975111yescharacteristic
762C2×C4#1451975111yescharacteristic
763C2×C4#1451975111yescharacteristic
764C2×C4#1451976011yescharacteristic
765C2×C4#1451976011yescharacteristic
766C2×C4C22×C4×D6111yescharacteristic
767C2×C4C22×C22⋊D6111yescharacteristic
768C2×C4C22×C22⋊D6111yescharacteristic
769C2×C4C22×C22⋊D6111yescharacteristic
770C2×C4C22×D24411yescharacteristic
771C2×C4C2×#1175822211yescharacteristic
772C8—24no—
773C8—24no—
774C8—1224no—
775C8—2442no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—24no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—44no—
785C22—82no—
786C22—82no—
787C22—4882no—
788C22—4882no—
789C22—2444no—
790C22—2442no—
791C22#1683964111yescharacteristic
792C22#1683964111yescharacteristic
793C22#1683964111yescharacteristic
794C22#1683964111yescharacteristic
795C22C2×C4×C22⋊D6111yescharacteristic
796C22C2×#1451975111yescharacteristic
797C22C2×#1451976011yescharacteristic
798C4—24no—
799C4—4882no—
800C4—2442no—
801C4#1683964111yescharacteristic
802C4#1683964111yescharacteristic
803C4#1683964111yescharacteristic
804C4#1683964111yescharacteristic
805C4C22×#1175819811yescharacteristic
806C4C2×C4×C22⋊D6111yescharacteristic
807C4C2×#1451974611yescharacteristic
808C4C2×#1451975111yescharacteristic
809C2—21no—
810C2—21no—
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—44no—
816C2—4882no—
817C2#2144618112yesdirect product factor
818C2C2×#1683964111yescharacteristic
subgroupG/H
centerC2×C4#14519746
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#568C2
socleC22×C61#386
prime radicalC2×#16840560C2
cosocleC22×C4×C61C24
hypercenterC2×#568D61
hypocenterC61C2×#1881
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
2. C2×#16839778C2semidirect
3. C2×#16839758C2semidirect
4. C2×#16839730C2semidirect
5. #21446181C2direct (N × H)
6. C2×#16839533C2semidirect
7. C2×#16839526C2semidirect
8. C2×C61×#568C2semidirect
12. #16840560C4semidirect
15. C2×#14519807C4semidirect
17. C2×#14519802C4semidirect
23. #16839778C22semidirect
26. #16839758C22semidirect
30. #16839730C22semidirect
32. #16839533C22semidirect
33. #16839526C22semidirect
38. C61×#568C22semidirect
63. #14519807C2×C4semidirect
67. #14519802C2×C4semidirect
401. C2×#568D61semidirect
415. C2×C61#1881semidirect
432. #568C2×D61semidirect
453. C61C2×#1881semidirect
817. C2#21446181direct (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×#168397782
C2×#168397582
C2×#168397302
#214461812
C2×#168395332
C2×#168395262
C2×C61×#5682
C2×#188161