Finite Group Databasebeta

← C2×#21447104 #29707866

Subgroups — C2×#21447104 #29707866

Order 15616.

1382 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840560C211yesmaximal, characteristic
2C2×#16839785C211yesmaximal, characteristic, complemented
3C22×#14519704C211yesmaximal, characteristic, complemented
4C22×#14519703C211yesmaximal, characteristic, complemented
5C2×#16839744C211yesmaximal, characteristic, complemented
6#21447104C218yesmaximal, direct product factor
7C2×#16839520C211yesmaximal, characteristic, complemented
8C2×C61×#413C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10#16840560—22no—
11#16840560—22no—
12#16840560—22no—
13#16840560C2214yes—
14C2×#14519808—21no—
15C2×#14519807—21no—
16C2×#14519803—21no—
17C2×#14519802—21no—
18C2×#14519797—22no—
19C22×#11758194C2211yescharacteristic
20C22×#11758194C2211yescharacteristic
21C22×C4×Dic61C2211yescharacteristic
22#16839785—22no—
23#16839785C2214yescomplemented
24C2×#14519706—22no—
25C2×#14519704—21no—
26C2×#14519704—21no—
27C2×#14519704—22no—
28C2×#14519704C2214yescomplemented
29C2×#14519703—21no—
30C2×#14519703—21no—
31C2×#14519703—22no—
32C2×#14519703C2214yescomplemented
33#16839744—22no—
34#16839744C2214yescomplemented
35C2×#14519695—21no—
36C2×#14519693—21no—
37#16839520C2214yescomplemented
38C22×#41×C61C2211yescharacteristic
39C22×M16×C61C2211yescharacteristic
40C22×M16×C61C2211yescharacteristic
41C61×#413—22no—
42C61×#413C2214yescomplemented
43C2×#101×C61—21no—
44C2×#100×C61—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×#11758222—21no—
55C2×#11758222D412yes—
56C2×#11758222C2312yes—
57C22×Dic122D411yescharacteristic
58C22×D244D411yescharacteristic
59C22×C22⋊D61—21no—
60C23×Dic61—21no—
61C22×C4×D61—21no—
62#14519808—24no—
63#14519808—24no—
64#14519807—24no—
65#14519807—24no—
66#14519803—24no—
67#14519803—24no—
68#14519802—24no—
69#14519802—24no—
70#14519797—28no—
71#14519797—28no—
72C2×#11758202—22no—
73C2×#11758200—22no—
74C2×#11758201—22no—
75C2×#11758199—22no—
76C2×#11758194—21no—
77C2×#11758194—21no—
78C2×#11758194—21no—
79C2×#11758194—21no—
80C2×#11758194—21no—
81C2×#11758194—21no—
82C2×#11758194—21no—
83C2×#11758194—21no—
84C2×#11758194—21no—
85C2×#11758194D412yes—
86C2×#11758194C2312yes—
87C2×#11758194C2312yes—
88C22×#92418—21no—
89C22×#92418D412yes—
90C2×C4×Dic61—21no—
91C2×C4×Dic61—21no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61D411yescharacteristic
94C2×C4×Dic61D412yes—
95C2×C4×Dic61D411yescharacteristic
96C2×C4×Dic61C2312yes—
97#14519706—28no—
98#14519704—24no—
99#14519704—24no—
100#14519703—24no—
101#14519703—24no—
102#14519695—24no—
103#14519693—24no—
104C2×#41×C61—21no—
105C2×#41×C61—21no—
106C2×#41×C61—21no—
107C2×#41×C61—21no—
108C2×#41×C61—21no—
109C2×#41×C61—21no—
110C2×#41×C61—21no—
111C2×#41×C61—21no—
112C2×#41×C61—21no—
113C2×#41×C61—21no—
114C2×#41×C61D412yes—
115C2×#41×C61C2312yes—
116C22×Q8×C61D411yescharacteristic
117C22×D4×C61—21no—
118C22×D4×C61D411yescharacteristic
119C23×C4×C61—21no—
120C23×C4×C61C2311yescharacteristic
121C2×M16×C61—21no—
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—21no—
130C2×M16×C61—21no—
131C2×M16×C61C2312yes—
132C2×M16×C61C2312yes—
133C22×C8×C61—21no—
134C22×C8×C61—21no—
135#101×C61—24no—
136#100×C61—24no—
137C24×C61—21no—
138C24×C61#4111yescharacteristic
139C23×D61—21no—
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—22no—
147#41×C61—22no—
148#41×C61—41no—
149#41×C61—41no—
150#41×C61—41no—
151#41×C61—41no—
152#41×C61—41no—
153#41×C61—41no—
154#41×C61—41no—
155#41×C61—41no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61C2×D412yes—
162C2×D4×C61—22no—
163C2×D4×C61—22no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—41no—
170C2×D4×C61—41no—
171C2×D4×C61—41no—
172C2×D4×C61—41no—
173C2×D4×C61C2×D412yes—
174C22×C4×C61—21no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—41no—
178C22×C4×C61—41no—
179C22×C4×C61—41no—
180C22×C4×C61—41no—
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×C61#4111yescharacteristic
190C22×C4×C61#4111yescharacteristic
191C22×C4×C61#4111yescharacteristic
192C22×C4×C61#4111yescharacteristic
193C22×C4×C61#4111yescharacteristic
194C22×C4×C61C2411yescharacteristic
195C2×C22⋊D61—22no—
196C2×C22⋊D61—22no—
197C2×C22⋊D61—41no—
198C2×C22⋊D61—41no—
199C2×C22⋊D61—41no—
200C2×C22⋊D61—41no—
201C22×Dic61—21no—
202C22×Dic61—22no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—22no—
206C22×Dic61—44no—
207#11758222—22no—
208#11758222—22no—
209#11758222—22no—
210#11758222—22no—
211#11758222—22no—
212#11758222—22no—
213#11758222—22no—
214#11758222—22no—
215#11758222—41no—
216#11758222—41no—
217#11758222—41no—
218#11758222—41no—
219#11758222—41no—
220#11758222—41no—
221#11758222—41no—
222#11758222—41no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244C2×D412yes—
229C2×C4×D61—22no—
230C2×C4×D61—22no—
231C2×C4×D61—41no—
232C2×C4×D61—41no—
233C2×C4×D61—41no—
234C2×C4×D61—41no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122C2×D412yes—
241M16×C61—22no—
242M16×C61—22no—
243M16×C61—22no—
244M16×C61—22no—
245M16×C61—41no—
246M16×C61—41no—
247M16×C61—41no—
248M16×C61—41no—
249C2×C8×C61—22no—
250C2×C8×C61—22no—
251C2×C8×C61—41no—
252C2×C8×C61—41no—
253C2×C8×C61—41no—
254C2×C8×C61—41no—
255#11758202—28no—
256#11758201—28no—
257#11758200—28no—
258#11758199—28no—
259C4×Dic61—21no—
260C4×Dic61—22no—
261C4×Dic61—21no—
262C4×Dic61—22no—
263C4×Dic61C2×D412yes—
264C4×Dic61C2×D412yes—
265#11758194—22no—
266#11758194—22no—
267#11758194—22no—
268#11758194—22no—
269#11758194—22no—
270#11758194—22no—
271#11758194—41no—
272#11758194—41no—
273C2×#92418—22no—
274C2×#92418—22no—
275C2×#92418—22no—
276C2×#92418—41no—
277C2×#92418—41no—
278C2×#92418C2×D414yes—
279C23×C61—22no—
280C23×C61—42no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—82no—
284C23×C61#12111yescharacteristic
285C23×C61#12111yescharacteristic
286C23×C61#12311yescharacteristic
287C23×C61#12311yescharacteristic
288C23×C61#12311yescharacteristic
289C23×C61#12311yescharacteristic
290C23×C61C2×#4111yescharacteristic
291C22×D61—22no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—82no—
295Q8×C61—22no—
296Q8×C61—22no—
297Q8×C61—41no—
298Q8×C61—41no—
299D4×C61—22no—
300D4×C61—22no—
301D4×C61—42no—
302D4×C61—42no—
303D4×C61—42no—
304D4×C61—42no—
305D4×C61—41no—
306D4×C61—41no—
307C2×C4×C61—22no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—42no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61#12011yescharacteristic
315C2×C4×C61#12011yescharacteristic
316C2×C4×C61#12011yescharacteristic
317C2×C4×C61#12011yescharacteristic
318C2×C4×C61#12111yescharacteristic
319C2×C4×C61#12111yescharacteristic
320C2×C4×C61#12111yescharacteristic
321C2×C4×C61#12111yescharacteristic
322C2×C4×C61#12111yescharacteristic
323C2×C4×C61#12111yescharacteristic
324C2×C4×C61#12111yescharacteristic
325C2×C4×C61#12111yescharacteristic
326C2×C4×C61#12111yescharacteristic
327C2×C4×C61#12111yescharacteristic
328C2×C4×C61#12311yescharacteristic
329C2×C4×C61#12311yescharacteristic
330C2×C4×C61#12311yescharacteristic
331C2×C4×C61#12311yescharacteristic
332C2×C4×C61#12411yescharacteristic
333C2×C4×C61#12411yescharacteristic
334C2×C4×C61#12411yescharacteristic
335C2×C4×C61#12411yescharacteristic
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C2×#4111yescharacteristic
341C2×C4×C61C2×#4111yescharacteristic
342C22⋊D61—42no—
343C22⋊D61—42no—
344C22⋊D61—42no—
345C22⋊D61—42no—
346C2×Dic61—24no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—44no—
351C2×Dic61—44no—
352C2×Dic61—42no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355D244—22no—
356D244—22no—
357D244—41no—
358D244—41no—
359C4×D61—42no—
360C4×D61—42no—
361C4×D61—42no—
362C4×D61—42no—
363Dic122—22no—
364Dic122—22no—
365Dic122—41no—
366Dic122—41no—
367C8×C61—42no—
368C8×C61—42no—
369#92418—24no—
370#92418—42no—
371C2×#2050—611nomaximal, Sylow
372C22×C61—22no—
373C22×C61—22no—
374C22×C61—22no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—42no—
380C22×C61—82no—
381C22×C61—82no—
382C22×C61—82no—
383C22×C61#39411yescharacteristic
384C22×C61#39411yescharacteristic
385C22×C61#39411yescharacteristic
386C22×C61#39411yescharacteristic
387C22×C61C2×#12111yescharacteristic
388C22×C61C2×#12311yescharacteristic
389C22×C61C2×#12311yescharacteristic
390C2×D61—42no—
391C2×D61—82no—
392C2×D61—82no—
393C2×D61—82no—
394C4×C61—42no—
395C4×C61#39411yescharacteristic
396C4×C61#39411yescharacteristic
397C4×C61#39411yescharacteristic
398C4×C61#39411yescharacteristic
399C4×C61C2×#12011yescharacteristic
400C4×C61C2×#12111yescharacteristic
401C4×C61C2×#12111yescharacteristic
402C4×C61C2×#12411yescharacteristic
403Dic61—24no—
404Dic61—42no—
405Dic61—42no—
406C2×#575—611no—
407C2×#423—611no—
408C22×#104—611no—
409C22×#104—611no—
410C2×#413—611no—
411C2×#413D6111yescharacteristic, complemented
412#2050—618no—
413C2×#338—611no—
414C2×C61—21no—
415C2×C61—21no—
416C2×C61—21no—
417C2×C61—21no—
418C2×C61—21no—
419C2×C61—21no—
420C2×C61—82no—
421C2×C61#205012yescomplemented
422C2×C61C2×#39411yescharacteristic
423D61—82no—
424C22×#41—611no—
425C22×#41C2×D6111yescharacteristic
426#575—614no—
427#575—1222no—
428#575—1222no—
429#575—1222no—
430C2×#137—1221no—
431C2×#137—1221no—
432C2×AGL(1,ℤ/8)—1221no—
433C2×AGL(1,ℤ/8)—1221no—
434C2×#135—1222no—
435C22×M16—611no—
436C22×M16—611no—
437C22×M16C2×D6111yescharacteristic
438C22×M16C2×D6111yescharacteristic
439C22×C42—611no—
440#423—614no—
441#423—1222no—
442C2×C4⋊C8—1222no—
443C2×#104—614no—
444C2×#104—614no—
445C2×#104—1221no—
446C2×#104—1222no—
447C2×#104—1221no—
448C2×#104—1221no—
449C2×#104—1222no—
450C2×#104—1221no—
451#413—22no—
452#413—614no—
453#413—1222no—
454#413C2×D6114yescomplemented
455C2×#101—21no—
456C2×#101—1221no—
457C2×#100—21no—
458C2×#100—1221no—
459#338—614no—
460C61C2×#205011yescharacteristic, complemented, Sylow
461C2×#41—21no—
462C2×#41—21no—
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—612no—
472C2×#41—612no—
473C2×#41—1221no—
474C2×#41—1221no—
475C2×#41—1221no—
476C2×#41—1221no—
477C2×#41—1221no—
478C2×#41—1221no—
479C2×#41—1221no—
480C2×#41—1221no—
481C2×#41—1221no—
482C2×#41—1221no—
483C2×#41C22⋊D6112yes—
484C2×#41C22×D6112yes—
485C22×Q8—611no—
486C22×Q8C22⋊D6111yescharacteristic
487C22×D4—21no—
488C22×D4—611no—
489C22×D4—1221no—
490C22×D4C22⋊D6111yescharacteristic
491C23×C4—21no—
492C23×C4—1221no—
493C23×C4—1221no—
494C23×C4C22×D6111yescharacteristic
495#137—1224no—
496#137—1224no—
497#137—1224no—
498#137—1224no—
499AGL(1,ℤ/8)—1224no—
500AGL(1,ℤ/8)—1224no—
501AGL(1,ℤ/8)—1224no—
502AGL(1,ℤ/8)—1224no—
503#135—1228no—
504#135—1228no—
505C2×Q16—1222no—
506C2×SD16—1222no—
507C2×SD16—1222no—
508C2×D8—1222no—
509C2×M16—21no—
510C2×M16—21no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16—21no—
514C2×M16—21no—
515C2×M16—21no—
516C2×M16—21no—
517C2×M16—21no—
518C2×M16—21no—
519C2×M16—612no—
520C2×M16—612no—
521C2×M16—612no—
522C2×M16—1221no—
523C2×M16—1221no—
524C2×M16—1221no—
525C2×M16—1221no—
526C2×M16—1221no—
527C2×M16—1221no—
528C2×M16—1221no—
529C2×M16—1221no—
530C2×M16—1221no—
531C2×M16C22×D6112yes—
532C2×M16C22×D6112yes—
533C22×C8—21no—
534C22×C8—21no—
535C22×C8—612no—
536C22×C8—1221no—
537C2×C42—611no—
538C2×C42—612no—
539C2×C42—611no—
540C2×C42—612no—
541C2×C42—1221no—
542C2×C42—1221no—
543C2×C42—1221no—
544C4⋊C8—1228no—
545#104—1224no—
546#104—1224no—
547#104—1224no—
548#104—1224no—
549#101—24no—
550#101—1224no—
551#100—24no—
552#100—1224no—
553C24—21no—
554C24—1221no—
555C24#1175822211yescharacteristic
556#41—22no—
557#41—22no—
558#41—22no—
559#41—22no—
560#41—22no—
561#41—22no—
562#41—22no—
563#41—22no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—41no—
568#41—41no—
569#41—41no—
570#41—41no—
571#41—41no—
572#41—1222no—
573#41—1222no—
574#41—1222no—
575#41—1222no—
576#41—1222no—
577#41—1222no—
578#41—1222no—
579#41—1222no—
580#41—2441no—
581#41—2441no—
582#41—2441no—
583#41—2441no—
584#41—2441no—
585#41—2441no—
586#41—2441no—
587#41—2441no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—612no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×Q8—1221no—
597C2×Q8—1221no—
598C2×Q8—1221no—
599C2×Q8C2×C22⋊D6112yes—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—41no—
608C2×D4—41no—
609C2×D4—41no—
610C2×D4—41no—
611C2×D4—612no—
612C2×D4—1222no—
613C2×D4—1222no—
614C2×D4—1221no—
615C2×D4—1221no—
616C2×D4—1221no—
617C2×D4—1221no—
618C2×D4—1221no—
619C2×D4—2441no—
620C2×D4—2441no—
621C2×D4—2441no—
622C2×D4—2441no—
623C2×D4C2×C22⋊D6112yes—
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—1221no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—1222no—
637C22×C4—1222no—
638C22×C4—2444no—
639C22×C4—2441no—
640C22×C4—2441no—
641C22×C4—2441no—
642C22×C4—2441no—
643C22×C4#1175822211yescharacteristic
644C22×C4#1175822211yescharacteristic
645C22×C4#1175822211yescharacteristic
646C22×C4D4×D6111yescharacteristic
647C22×C4D4×D6111yescharacteristic
648C22×C4D4×D6111yescharacteristic
649C22×C4D4×D6111yescharacteristic
650C22×C4D4×D6111yescharacteristic
651C22×C4D4×D6111yescharacteristic
652C22×C4#1175822411yescharacteristic
653C22×C4#1175822411yescharacteristic
654C22×C4C2×C22⋊D6111yescharacteristic
655C22×C4C2×C22⋊D6111yescharacteristic
656C22×C4C23×D6111yescharacteristic
657Q16—1228no—
658SD16—1228no—
659SD16—1228no—
660D8—1228no—
661M16—22no—
662M16—22no—
663M16—22no—
664M16—22no—
665M16—41no—
666M16—41no—
667M16—41no—
668M16—41no—
669M16—1222no—
670M16—1222no—
671M16—1222no—
672M16—1222no—
673M16—1222no—
674M16—1222no—
675M16—2441no—
676M16—2441no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—41no—
680C2×C8—41no—
681C2×C8—41no—
682C2×C8—41no—
683C2×C8—614no—
684C2×C8—1222no—
685C2×C8—1222no—
686C2×C8—1222no—
687C2×C8—2441no—
688C2×C8—2441no—
689C42—612no—
690C42—612no—
691C42—1222no—
692C42—1221no—
693C42—1222no—
694C42—1221no—
695C23—22no—
696C23—42no—
697C23—41no—
698C23—41no—
699C23—82no—
700C23—1222no—
701C23—4882no—
702C23—2441no—
703C23—2441no—
704C23#1451975011yescharacteristic
705C23#1451975011yescharacteristic
706C23#1451975911yescharacteristic
707C23#1451975911yescharacteristic
708C23#1451976011yescharacteristic
709C23#1451976011yescharacteristic
710C23C2×#1175822211yescharacteristic
711Q8—22no—
712Q8—22no—
713Q8—41no—
714Q8—41no—
715Q8—1222no—
716Q8—1222no—
717Q8—2441no—
718Q8—2441no—
719D4—22no—
720D4—22no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—42no—
725D4—41no—
726D4—41no—
727D4—1222no—
728D4—1222no—
729D4—2442no—
730D4—2442no—
731D4—2442no—
732D4—2442no—
733D4—2441no—
734D4—2441no—
735C2×C4—22no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—1224no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—2444no—
747C2×C4—2444no—
748C2×C4—2442no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2442no—
752C2×C4—2442no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4#1451974511yescharacteristic
756C2×C4#1451974511yescharacteristic
757C2×C4#1451974511yescharacteristic
758C2×C4#1451974511yescharacteristic
759C2×C4#1451974911yescharacteristic
760C2×C4#1451974911yescharacteristic
761C2×C4#1451974911yescharacteristic
762C2×C4#1451974911yescharacteristic
763C2×C4#1451975011yescharacteristic
764C2×C4#1451975011yescharacteristic
765C2×C4#1451975011yescharacteristic
766C2×C4#1451975011yescharacteristic
767C2×C4#1451975011yescharacteristic
768C2×C4#1451975011yescharacteristic
769C2×C4#1451975911yescharacteristic
770C2×C4#1451975911yescharacteristic
771C2×C4#1451976011yescharacteristic
772C2×C4#1451976011yescharacteristic
773C2×C4#1451976311yescharacteristic
774C2×C4#1451976311yescharacteristic
775C2×C4#1451976311yescharacteristic
776C2×C4#1451976311yescharacteristic
777C2×C4C2×D4×D6111yescharacteristic
778C2×C4C2×D4×D6111yescharacteristic
779C2×C4C2×D4×D6111yescharacteristic
780C2×C4C22×C22⋊D6111yescharacteristic
781C2×C4C2×#1175822411yescharacteristic
782C2×C4C2×#1175822211yescharacteristic
783C8—42no—
784C8—42no—
785C8—1224no—
786C8—2442no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—4882no—
799C22—4882no—
800C22—4882no—
801C22—2442no—
802C22#1683967711yescharacteristic
803C22#1683967711yescharacteristic
804C22#1683967711yescharacteristic
805C22#1683967711yescharacteristic
806C22C2×#1451975011yescharacteristic
807C22C2×#1451975911yescharacteristic
808C22C2×#1451976011yescharacteristic
809C4—42no—
810C4—1224no—
811C4—2442no—
812C4—2442no—
813C4#1683967711yescharacteristic
814C4#1683967711yescharacteristic
815C4#1683967711yescharacteristic
816C4#1683967711yescharacteristic
817C4C2×#1451974511yescharacteristic
818C4C2×#1451974911yescharacteristic
819C4C2×#1451975011yescharacteristic
820C4C2×#1451976311yescharacteristic
821C2—21no—
822C2—21no—
823C2—21no—
824C2—21no—
825C2—21no—
826C2—21no—
827C2—82no—
828C2—4882no—
829C2#2144710412yesdirect product factor
830C2C2×#1683967711yescharacteristic
subgroupG/H
centerC2×C4#14519763
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#413C2
socleC22×C61#394
prime radicalC2×#16840560C2
hypercenterC2×#413D61
hypocenterC61C2×#2050
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
2. C2×#16839785C2semidirect
3. C22×#14519704C2semidirect
4. C22×#14519703C2semidirect
5. C2×#16839744C2semidirect
6. #21447104C2direct (N × H)
7. C2×#16839520C2semidirect
8. C2×C61×#413C2semidirect
23. #16839785C22semidirect
28. C2×#14519704C22semidirect
32. C2×#14519703C22semidirect
34. #16839744C22semidirect
37. #16839520C22semidirect
42. C61×#413C22semidirect
411. C2×#413D61semidirect
421. C2×C61#2050semidirect
454. #413C2×D61semidirect
460. C61C2×#2050semidirect
829. C2#21447104direct (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×#168397852
C22×#145197042
C22×#145197032
C2×#168397442
#214471042
C2×#168395202
C2×C61×#4132
C2×#205061