Finite Group Databasebeta

← C2×#21455538 #30547407

Subgroups — C2×#21455538 #30547407

Order 15616.

2650 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840562C211yesmaximal, characteristic, complemented
2C2×#16840560C211yesmaximal, characteristic, complemented
3C22×#14519797C211yesmaximal, characteristic, complemented
4C22×#14519785C211yesmaximal, characteristic, complemented
5#21455538C2116yesmaximal, direct product factor
6C2×#16840036C212yesmaximal, complemented
7C2×#16840031C212yesmaximal, complemented
8C2×#16840028C212yesmaximal, complemented
9C2×#16840024C212yesmaximal, complemented
10C22×#14519712C211yesmaximal, characteristic, complemented
11C2×#16839744C211yesmaximal, characteristic, complemented
12C2×C61×#413C211yesmaximal, characteristic, complemented
13C22×#11758222C2211yescharacteristic
14C22×#11758222C2211yescharacteristic
15#16840562—24no—
16#16840562C2218yescomplemented
17#16840560—24no—
18#16840560C2218yescomplemented
19C2×#14519810—21no—
20C2×#14519810C2212yes—
21C2×#14519808C2212yes—
22C2×#14519807—21no—
23C2×#14519805—21no—
24C2×#14519805C2212yes—
25C2×#14519803C2212yes—
26C2×#14519802—21no—
27C2×#14519799—22no—
28C2×#14519797—21no—
29C2×#14519797—21no—
30C2×#14519797—21no—
31C2×#14519797—21no—
32C2×#14519797—24no—
33C2×#14519797—22no—
34C2×#14519797C2218yescomplemented
35C22×#11758202C2211yescharacteristic, complemented
36C22×#11758200C2211yescharacteristic, complemented
37C22×#11758201C2211yescharacteristic, complemented
38C22×#11758199C2211yescharacteristic, complemented
39C2×#14519785—21no—
40C2×#14519785—21no—
41C2×#14519785—24no—
42C2×#14519785C2212yes—
43C2×#14519785C2212yes—
44C2×#14519785C2218yescomplemented
45C22×#11758194C2211yescharacteristic
46C22×#11758189—21no—
47C23×#92418C2211yescharacteristic
48C22×C8×D61—21no—
49#16840036C22116yescomplemented
50#16840031C22116yescomplemented
51#16840028C22116yescomplemented
52#16840024C22116yescomplemented
53C2×#14519712C2212yescomplemented
54C2×#14519712C2212yescomplemented
55C2×#14519712C2218yescomplemented
56#16839744C2218yescomplemented
57C2×#14519695C2212yescomplemented
58C2×#14519693C2212yescomplemented
59C22×#41×C61C2211yescharacteristic
60C22×M16×C61C2211yescharacteristic
61C22×M16×C61C2211yescharacteristic
62C61×#413C2218yescomplemented
63C2×#101×C61C2212yescomplemented
64C2×#100×C61C2212yescomplemented
65C2×#11758222—21no—
66C2×#11758222—22no—
67C2×#11758222—21no—
68C2×#11758222—22no—
69C2×#11758222—22no—
70C2×#11758222—21no—
71C2×#11758222—21no—
72C2×#11758222—22no—
73C2×#11758222—21no—
74C2×#11758222—21no—
75C2×#11758222—22no—
76C2×#11758222D412yes—
77C2×#11758222D414yes—
78C2×#11758222C2312yes—
79C2×#11758222C2314yes—
80C2×#11758222C2314yes—
81C22×Dic122D411yescharacteristic
82C22×Dic122C2311yescharacteristic
83C22×D244D411yescharacteristic
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89#14519810—24no—
90#14519810—28no—
91#14519810C2318yes—
92#14519808—24no—
93#14519808C2318yes—
94#14519807—28no—
95#14519805—24no—
96#14519805—28no—
97#14519805C2318yes—
98#14519803—24no—
99#14519803C2318yes—
100#14519802—28no—
101#14519799—216no—
102#14519797—216no—
103#14519797—28no—
104#14519797—28no—
105#14519797—28no—
106#14519797—28no—
107C2×Dic244—22no—
108C2×#11758202—22no—
109C2×#11758202—21no—
110C2×#11758202—21no—
111C2×#11758202—22no—
112C2×#11758202C2314yescomplemented
113C2×#11758190—22no—
114C2×#11758190—22no—
115C2×#11758200—22no—
116C2×#11758200—21no—
117C2×#11758200—21no—
118C2×#11758200—22no—
119C2×#11758200C2314yescomplemented
120C2×#11758201—22no—
121C2×#11758201—21no—
122C2×#11758201—21no—
123C2×#11758201—22no—
124C2×#11758201C2314yescomplemented
125C2×D488—22no—
126C2×#11758199—22no—
127C2×#11758199—21no—
128C2×#11758199—21no—
129C2×#11758199—22no—
130C2×#11758199C2314yescomplemented
131#14519785—24no—
132#14519785—24no—
133#14519785—28no—
134#14519785—28no—
135#14519785C2318yes—
136#14519785C2318yes—
137C2×#11758194—21no—
138C2×#11758194—22no—
139C2×#11758194C2312yes—
140C2×#11758194C2314yes—
141C2×#11758189—22no—
142C2×#11758189—22no—
143C2×#11758189—28no—
144C22×#92418—21no—
145C22×#92418D411yescharacteristic
146C22×#92418D411yescharacteristic
147C22×#92418D411yescharacteristic
148C22×#92418D411yescharacteristic
149C22×#92418D414yes—
150C22×#92418C2311yescharacteristic
151C22×#92418C2311yescharacteristic
152C22×#92418C2314yes—
153C2×C8×D61—22no—
154C2×C8×D61—22no—
155C2×C8×D61—28no—
156#14519712C2318yescomplemented
157#14519712C2318yescomplemented
158#14519695C2318yescomplemented
159#14519693C2318yescomplemented
160C2×#41×C61—22no—
161C2×#41×C61—21no—
162C2×#41×C61—21no—
163C2×#41×C61—22no—
164C2×#41×C61—21no—
165C2×#41×C61—21no—
166C2×#41×C61—22no—
167C2×#41×C61C2314yes—
168C22×Q8×C61C2311yescharacteristic
169C22×D4×C61—21no—
170C22×D4×C61C2311yescharacteristic
171C23×C4×C61—21no—
172C23×C4×C61C2311yescharacteristic
173C2×M16×C61—21no—
174C2×M16×C61—22no—
175C2×M16×C61—21no—
176C2×M16×C61—22no—
177C2×M16×C61C2312yes—
178C2×M16×C61C2314yes—
179C2×M16×C61C2312yes—
180C2×M16×C61C2314yes—
181C22×C8×C61—21no—
182C22×C8×C61—21no—
183#101×C61C2318yescomplemented
184#100×C61C2318yescomplemented
185C24×C61—21no—
186C24×C61#4111yescharacteristic
187C23×D61—21no—
188C23×D61—21no—
189#41×C61—24no—
190#41×C61—24no—
191#41×C61—24no—
192#41×C61—24no—
193#41×C61—42no—
194#41×C61—42no—
195#41×C61—42no—
196#41×C61—42no—
197C2×Q8×C61—21no—
198C2×Q8×C61—21no—
199C2×Q8×C61—21no—
200C2×Q8×C61—21no—
201C2×Q8×C61—21no—
202C2×Q8×C61C2412yes—
203C2×D4×C61—24no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61—41no—
210C2×D4×C61—41no—
211C2×D4×C61—42no—
212C2×D4×C61C2412yes—
213C22×C4×C61—21no—
214C22×C4×C61—24no—
215C22×C4×C61—41no—
216C22×C4×C61—42no—
217C22×C4×C61—41no—
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D412yes—
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D412yes—
224C22×C4×C61#4111yescharacteristic
225C22×C4×C61#4112yes—
226C22×C4×C61C2411yescharacteristic
227C22×C4×C61C2412yes—
228C2×C22⋊D61—22no—
229C2×C22⋊D61—24no—
230C2×C22⋊D61—22no—
231C2×C22⋊D61—24no—
232C2×C22⋊D61—24no—
233C2×C22⋊D61—41no—
234C2×C22⋊D61—41no—
235C2×C22⋊D61—42no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238#11758222—24no—
239#11758222—24no—
240#11758222—24no—
241#11758222—22no—
242#11758222—24no—
243#11758222—22no—
244#11758222—24no—
245#11758222—24no—
246#11758222—24no—
247#11758222—24no—
248#11758222—24no—
249#11758222—42no—
250#11758222—42no—
251#11758222—42no—
252#11758222—42no—
253#11758222C2×D414yes—
254#11758222C2×D418yes—
255#11758222C2414yes—
256C2×D244—21no—
257C2×D244—22no—
258C2×D244—21no—
259C2×D244—21no—
260C2×D244—21no—
261C2×D244—21no—
262C2×D244—21no—
263C2×D244C2×D412yes—
264C2×D244C2×D414yes—
265C2×D244C2412yes—
266C2×C4×D61—24no—
267C2×C4×D61—22no—
268C2×C4×D61—22no—
269C2×C4×D61—24no—
270C2×C4×D61—24no—
271C2×C4×D61—41no—
272C2×C4×D61—42no—
273C2×C4×D61—41no—
274C2×Dic122—21no—
275C2×Dic122—22no—
276C2×Dic122—21no—
277C2×Dic122—21no—
278C2×Dic122—21no—
279C2×Dic122—21no—
280C2×Dic122—21no—
281C2×Dic122C2×D414yes—
282C2×Dic122C2×D412yes—
283C2×Dic122C2412yes—
284M16×C61—22no—
285M16×C61—24no—
286M16×C61—22no—
287M16×C61—24no—
288M16×C61C2414yes—
289M16×C61C2414yes—
290C2×C8×C61—22no—
291C2×C8×C61—24no—
292C2×C8×C61—22no—
293C2×C8×C61—24no—
294#11758202—28no—
295#11758202—24no—
296#11758202—24no—
297#11758201—28no—
298#11758201—24no—
299#11758201—24no—
300#11758200—28no—
301#11758200—24no—
302#11758200—24no—
303#11758199—28no—
304#11758199—24no—
305#11758199—24no—
306#11758194—22no—
307#11758194—24no—
308#11758194C2414yes—
309C2×#92418—22no—
310C2×#92418—24no—
311C2×#92418C2×D411yescharacteristic
312C2×#92418C2×D411yescharacteristic
313C2×#92418C2×D414yes—
314C2×#92418C2×D411yescharacteristic
315C2×#92418C2×D411yescharacteristic
316C2×#92418C2×D414yes—
317C2×#92418C2×D412yes—
318C2×#92418C2×D412yes—
319C2×#92418C2×D414yes—
320C2×#92418C2×D414yes—
321C2×#92418C2412yes—
322C2×#92418C2412yes—
323Dic244—28no—
324D488—28no—
325#11758190—28no—
326#11758190—28no—
327#11758189—28no—
328#11758189—28no—
329C8×D61—28no—
330C8×D61—28no—
331C23×C61—22no—
332C23×C61—42no—
333C23×C61—41no—
334C23×C61—41no—
335C23×C61—82no—
336C23×C61#12111yescharacteristic
337C23×C61#12111yescharacteristic
338C23×C61#12112yes—
339C23×C61C2×#4111yescharacteristic
340C23×C61C2×#4112yes—
341C22×D61—24no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—44no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—82no—
348Q8×C61—22no—
349Q8×C61—22no—
350Q8×C61—41no—
351Q8×C61—41no—
352D4×C61—22no—
353D4×C61—22no—
354D4×C61—44no—
355D4×C61—44no—
356D4×C61—41no—
357D4×C61—41no—
358C2×C4×C61—22no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—44no—
362C2×C4×C61—44no—
363C2×C4×C61#12111yescharacteristic
364C2×C4×C61#12112yes—
365C2×C4×C61#12112yes—
366C2×C4×C61#12112yes—
367C2×C4×C61#12112yes—
368C2×C4×C61#12112yes—
369C2×C4×C61#12111yescharacteristic
370C2×C4×C61C22×D411yescharacteristic
371C2×C4×C61C22×D412yes—
372C2×C4×C61C22×D411yescharacteristic
373C2×C4×C61C22×D412yes—
374C2×C4×C61C22×D411yescharacteristic
375C2×C4×C61C22×D412yes—
376C2×C4×C61C22×D411yescharacteristic
377C2×C4×C61C22×D412yes—
378C2×C4×C61C2×#4111yescharacteristic
379C2×C4×C61C2×#4112yes—
380C2×C4×C61C2511yescharacteristic
381C22⋊D61—24no—
382C22⋊D61—28no—
383C22⋊D61—24no—
384C22⋊D61—44no—
385C22⋊D61—44no—
386C2×Dic61—24no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391D244—22no—
392D244—24no—
393D244—22no—
394D244—22no—
395D244—41no—
396D244—41no—
397D244C22×D414yes—
398C4×D61—24no—
399C4×D61—28no—
400C4×D61—24no—
401C4×D61—44no—
402C4×D61—44no—
403Dic122—22no—
404Dic122—24no—
405Dic122—22no—
406Dic122—22no—
407Dic122—41no—
408Dic122—41no—
409Dic122C22×D414yes—
410C8×C61—24no—
411C8×C61—24no—
412#92418—24no—
413#92418C22×D412yes—
414#92418C22×D412yes—
415#92418C22×D412yes—
416#92418C22×D412yes—
417C2×#3067—611nomaximal, Sylow
418C22×C61—22no—
419C22×C61—22no—
420C22×C61—22no—
421C22×C61—42no—
422C22×C61—42no—
423C22×C61—42no—
424C22×C61—82no—
425C22×C61—82no—
426C22×C61—82no—
427C22×C61C2×#12112yes—
428C22×C61C2×#12111yescharacteristic
429C22×C61C2×#12112yes—
430C22×C61C2×#12111yescharacteristic
431C22×C61C22×#4111yescharacteristic
432C2×D61—24no—
433C2×D61—48no—
434C2×D61—44no—
435C2×D61—42no—
436C2×D61—82no—
437C2×D61—82no—
438C2×D61—82no—
439C4×C61—42no—
440C4×C61C2×#12111yescharacteristic
441C4×C61C2×#12112yes—
442C4×C61C2×#12111yescharacteristic
443C4×C61C2×#12112yes—
444C4×C61C23×D411yescharacteristic
445C4×C61C23×D411yescharacteristic
446Dic61—24no—
447Dic61—42no—
448C2×#575—611no—
449C2×#575—611no—
450C22×#135—611no—
451C22×#131—611no—
452#3067—6116no—
453C2×#473—612no—
454C2×#472—612no—
455C2×#471—612no—
456C2×#471—612no—
457C22×#108—611no—
458C2×#413—611no—
459C2×#413D6111yescharacteristic, complemented
460C2×C61—22no—
461C2×C61—21no—
462C2×C61—21no—
463C2×C61—22no—
464C2×C61—82no—
465C2×C61#306712yescomplemented
466C2×C61C22×#12111yescharacteristic
467D61—44no—
468D61—82no—
469C22×#41—611no—
470C22×#41—611no—
471C22×#41C2×D6111yescharacteristic
472#575—618no—
473#575—618no—
474#575—1224no—
475#575—1224no—
476C2×#137—612no—
477C2×#137—612no—
478C2×#137—1221no—
479C2×#137—1221no—
480C2×AGL(1,ℤ/8)—612no—
481C2×AGL(1,ℤ/8)—612no—
482C2×AGL(1,ℤ/8)—1221no—
483C2×AGL(1,ℤ/8)—1221no—
484C2×#135—618no—
485C2×#135—1222no—
486C2×#135—1221no—
487C2×#135—1221no—
488C2×#135—1221no—
489C2×#135—1221no—
490C2×#135—1224no—
491C2×#135—1222no—
492C22×Q16—611no—
493C22×SD16—611no—
494C22×SD16—611no—
495C22×D8—611no—
496C2×#131—612no—
497C2×#131—612no—
498C2×#131—618no—
499C2×#131—1221no—
500C2×#131—1221no—
501C2×#131—1224no—
502C22×M16—611no—
503C22×M16—1221no—
504C22×M16C2×D6111yescharacteristic
505C22×M16C2×D6111yescharacteristic
506C23×C8—611no—
507C23×C8—1221no—
508#473—6116no—
509#472—6116no—
510#471—6116no—
511#471—6116no—
512C2×#108—612no—
513C2×#108—612no—
514C2×#108—618no—
515#413—618no—
516#413C2×D6118yescomplemented
517C2×#101—612no—
518C2×#101C2×D6112yescomplemented
519C2×#100—612no—
520C2×#100C2×D6112yescomplemented
521C61C2×#306711yescharacteristic, complemented, Sylow
522C2×#41—22no—
523C2×#41—21no—
524C2×#41—22no—
525C2×#41—21no—
526C2×#41—21no—
527C2×#41—21no—
528C2×#41—22no—
529C2×#41—612no—
530C2×#41—614no—
531C2×#41—612no—
532C2×#41—614no—
533C2×#41—614no—
534C2×#41—1222no—
535C2×#41—1221no—
536C2×#41—1222no—
537C2×#41—1221no—
538C2×#41—1222no—
539C2×#41—1221no—
540C2×#41—1222no—
541C2×#41—1221no—
542C2×#41—1221no—
543C2×#41—1221no—
544C2×#41—1222no—
545C2×#41C22×D6114yes—
546C22×Q8—611no—
547C22×Q8—611no—
548C22×Q8C22×D6111yescharacteristic
549C22×D4—21no—
550C22×D4—611no—
551C22×D4—611no—
552C22×D4—1221no—
553C22×D4—1221no—
554C22×D4C22×D6111yescharacteristic
555C23×C4—21no—
556C23×C4—1221no—
557C23×C4—1221no—
558C23×C4C22×D6111yescharacteristic
559#137—618no—
560#137—618no—
561#137—1228no—
562#137—1224no—
563#137—1224no—
564#137—1228no—
565AGL(1,ℤ/8)—618no—
566AGL(1,ℤ/8)—618no—
567AGL(1,ℤ/8)—1228no—
568AGL(1,ℤ/8)—1224no—
569AGL(1,ℤ/8)—1224no—
570AGL(1,ℤ/8)—1228no—
571#135—12216no—
572#135—1228no—
573#135—1228no—
574#135—1228no—
575#135—1228no—
576#135—12216no—
577C2×Q16—614no—
578C2×Q16—1222no—
579C2×Q16—1221no—
580C2×Q16—1221no—
581C2×Q16—1222no—
582C2×Q16—1222no—
583C2×SD16—614no—
584C2×SD16—614no—
585C2×SD16—1222no—
586C2×SD16—1222no—
587C2×SD16—1221no—
588C2×SD16—1221no—
589C2×SD16—1222no—
590C2×SD16—1221no—
591C2×SD16—1221no—
592C2×SD16—1222no—
593C2×SD16—1222no—
594C2×SD16—1222no—
595C2×D8—614no—
596C2×D8—1222no—
597C2×D8—1221no—
598C2×D8—1221no—
599C2×D8—1222no—
600C2×D8—1222no—
601#131—618no—
602#131—618no—
603#131—1224no—
604#131—1224no—
605#131—1228no—
606#131—1228no—
607C2×M16—21no—
608C2×M16—22no—
609C2×M16—21no—
610C2×M16—22no—
611C2×M16—612no—
612C2×M16—614no—
613C2×M16—1222no—
614C2×M16—1222no—
615C2×M16—1228no—
616C2×M16—1221no—
617C2×M16—1222no—
618C2×M16C22×D6112yes—
619C2×M16C22×D6114yes—
620C2×M16C22×D6112yes—
621C2×M16C22×D6114yes—
622C22×C8—21no—
623C22×C8—21no—
624C22×C8—611no—
625C22×C8—611no—
626C22×C8—611no—
627C22×C8—611no—
628C22×C8—614no—
629C22×C8—611no—
630C22×C8—611no—
631C22×C8—614no—
632C22×C8—1222no—
633C22×C8—1222no—
634C22×C8—1228no—
635C22×C8—1221no—
636#108—618no—
637#108—618no—
638#101—618no—
639#101C22×D6118yescomplemented
640#100—618no—
641#100C22×D6118yescomplemented
642C24—21no—
643C24—1221no—
644C24—1221no—
645C24#1175822211yescharacteristic
646#41—24no—
647#41—24no—
648#41—24no—
649#41—24no—
650#41—42no—
651#41—42no—
652#41—42no—
653#41—42no—
654#41—618no—
655#41—614no—
656#41—614no—
657#41—1222no—
658#41—1224no—
659#41—1224no—
660#41—1222no—
661#41—1224no—
662#41—1224no—
663#41—1224no—
664#41—1224no—
665#41—1224no—
666#41—1224no—
667#41—1224no—
668#41—2442no—
669#41—2442no—
670#41—2442no—
671#41—2442no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—612no—
678C2×Q8—614no—
679C2×Q8—612no—
680C2×Q8—1221no—
681C2×Q8—1221no—
682C2×Q8—1222no—
683C2×Q8—1221no—
684C2×Q8—1221no—
685C2×Q8—1221no—
686C2×Q8—1221no—
687C2×Q8C23×D6112yes—
688C2×D4—24no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—41no—
695C2×D4—41no—
696C2×D4—42no—
697C2×D4—612no—
698C2×D4—614no—
699C2×D4—612no—
700C2×D4—1222no—
701C2×D4—1224no—
702C2×D4—1222no—
703C2×D4—1224no—
704C2×D4—1224no—
705C2×D4—1221no—
706C2×D4—1221no—
707C2×D4—1221no—
708C2×D4—1221no—
709C2×D4—1221no—
710C2×D4—1221no—
711C2×D4—1222no—
712C2×D4—2441no—
713C2×D4—2441no—
714C2×D4—2442no—
715C2×D4C23×D6112yes—
716C22×C4—21no—
717C22×C4—24no—
718C22×C4—41no—
719C22×C4—42no—
720C22×C4—41no—
721C22×C4—1221no—
722C22×C4—1222no—
723C22×C4—1224no—
724C22×C4—1224no—
725C22×C4—1222no—
726C22×C4—1221no—
727C22×C4—1224no—
728C22×C4—2441no—
729C22×C4—2442no—
730C22×C4—2441no—
731C22×C4#1175822212yes—
732C22×C4#1175822211yescharacteristic
733C22×C4D4×D6111yescharacteristic
734C22×C4D4×D6112yes—
735C22×C4D4×D6111yescharacteristic
736C22×C4D4×D6112yes—
737C22×C4D4×D6111yescharacteristic
738C22×C4D4×D6111yescharacteristic
739C22×C4C23×D6111yescharacteristic
740C22×C4C23×D6112yes—
741Q16—1228no—
742Q16—1224no—
743Q16—1224no—
744Q16—1228no—
745SD16—1228no—
746SD16—1228no—
747SD16—1224no—
748SD16—1224no—
749SD16—1224no—
750SD16—1224no—
751SD16—1228no—
752SD16—1228no—
753D8—1228no—
754D8—1224no—
755D8—1224no—
756D8—1228no—
757M16—22no—
758M16—24no—
759M16—22no—
760M16—24no—
761M16—614no—
762M16—1228no—
763M16—1228no—
764M16—1222no—
765M16—1224no—
766M16C23×D6114yes—
767M16C23×D6114yes—
768C2×C8—22no—
769C2×C8—24no—
770C2×C8—22no—
771C2×C8—24no—
772C2×C8—611no—
773C2×C8—611no—
774C2×C8—614no—
775C2×C8—611no—
776C2×C8—611no—
777C2×C8—614no—
778C2×C8—612no—
779C2×C8—612no—
780C2×C8—614no—
781C2×C8—614no—
782C2×C8—612no—
783C2×C8—612no—
784C2×C8—1228no—
785C2×C8—1228no—
786C2×C8—1222no—
787C2×C8—1224no—
788C23—22no—
789C23—42no—
790C23—41no—
791C23—41no—
792C23—82no—
793C23—1224no—
794C23—1222no—
795C23—1222no—
796C23—4882no—
797C23—2444no—
798C23—2441no—
799C23—2441no—
800C23#1451975011yescharacteristic
801C23#1451975011yescharacteristic
802C23#1451975012yes—
803C23C2×#1175822211yescharacteristic
804C23C2×#1175822212yes—
805Q8—22no—
806Q8—22no—
807Q8—41no—
808Q8—41no—
809Q8—614no—
810Q8—1224no—
811Q8—1222no—
812Q8—1222no—
813Q8—1222no—
814Q8—2441no—
815Q8—2441no—
816D4—22no—
817D4—22no—
818D4—44no—
819D4—44no—
820D4—41no—
821D4—41no—
822D4—614no—
823D4—1224no—
824D4—1228no—
825D4—1224no—
826D4—1224no—
827D4—1222no—
828D4—1222no—
829D4—1222no—
830D4—2444no—
831D4—2444no—
832D4—2441no—
833D4—2441no—
834C2×C4—22no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—1224no—
840C2×C4—1222no—
841C2×C4—1228no—
842C2×C4—1224no—
843C2×C4—1224no—
844C2×C4—1222no—
845C2×C4—2441no—
846C2×C4—2441no—
847C2×C4—2444no—
848C2×C4—2444no—
849C2×C4#1451975011yescharacteristic
850C2×C4#1451975012yes—
851C2×C4#1451975012yes—
852C2×C4#1451975012yes—
853C2×C4#1451975012yes—
854C2×C4#1451975012yes—
855C2×C4#1451975011yescharacteristic
856C2×C4C2×D4×D6111yescharacteristic
857C2×C4C2×D4×D6112yes—
858C2×C4C2×D4×D6111yescharacteristic
859C2×C4C2×D4×D6112yes—
860C2×C4C2×D4×D6111yescharacteristic
861C2×C4C2×D4×D6112yes—
862C2×C4C2×D4×D6111yescharacteristic
863C2×C4C2×D4×D6112yes—
864C2×C4C2×#1175822212yes—
865C2×C4C2×#1175822211yescharacteristic
866C2×C4C24×D6111yescharacteristic
867C8—24no—
868C8—24no—
869C8—612no—
870C8—612no—
871C8—612no—
872C8—612no—
873C8—1224no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—82no—
881C22—82no—
882C22—82no—
883C22—1224no—
884C22—4882no—
885C22—4882no—
886C22—4882no—
887C22—2448no—
888C22—2442no—
889C22—2444no—
890C22C2×#1451975011yescharacteristic
891C22C2×#1451975012yes—
892C22C2×#1451975012yes—
893C22C2×#1451975011yescharacteristic
894C22C22×#1175822211yescharacteristic
895C4—42no—
896C4—1224no—
897C4—2442no—
898C4C2×#1451975012yes—
899C4C2×#1451975012yes—
900C4C2×#1451975011yescharacteristic
901C4C2×#1451975011yescharacteristic
902C4C22×D4×D6111yescharacteristic
903C4C22×D4×D6111yescharacteristic
904C2—21no—
905C2—21no—
906C2—22no—
907C2—22no—
908C2—82no—
909C2—4882no—
910C2—2444no—
911C2#2145553812yesdirect product factor
912C2C22×#1451975011yescharacteristic
subgroupG/H
centerC2×C4#14519750
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#413C2
socleC22×C61C2×#121
hypercenterC2×#413D61
hypocenterC61C2×#3067
LCSG ▷ C2×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
1. C2×#16840562C2semidirect
2. C2×#16840560C2semidirect
3. C22×#14519797C2semidirect
4. C22×#14519785C2semidirect
5. #21455538C2direct (N × H)
6. C2×#16840036C2semidirect
7. C2×#16840031C2semidirect
8. C2×#16840028C2semidirect
9. C2×#16840024C2semidirect
10. C22×#14519712C2semidirect
11. C2×#16839744C2semidirect
12. C2×C61×#413C2semidirect
16. #16840562C22semidirect
18. #16840560C22semidirect
34. C2×#14519797C22semidirect
35. C22×#11758202C22semidirect
36. C22×#11758200C22semidirect
37. C22×#11758201C22semidirect
38. C22×#11758199C22semidirect
44. C2×#14519785C22semidirect
49. #16840036C22semidirect
50. #16840031C22semidirect
51. #16840028C22semidirect
52. #16840024C22semidirect
53. C2×#14519712C22semidirect
54. C2×#14519712C22semidirect
55. C2×#14519712C22semidirect
56. #16839744C22semidirect
57. C2×#14519695C22semidirect
58. C2×#14519693C22semidirect
62. C61×#413C22semidirect
63. C2×#101×C61C22semidirect
64. C2×#100×C61C22semidirect
112. C2×#11758202C23semidirect
119. C2×#11758200C23semidirect
124. C2×#11758201C23semidirect
130. C2×#11758199C23semidirect
156. #14519712C23semidirect
157. #14519712C23semidirect
158. #14519695C23semidirect
159. #14519693C23semidirect
183. #101×C61C23semidirect
184. #100×C61C23semidirect
459. C2×#413D61semidirect
465. C2×C61#3067semidirect
516. #413C2×D61semidirect
518. C2×#101C2×D61semidirect
520. C2×#100C2×D61semidirect
521. C61C2×#3067semidirect
639. #101C22×D61semidirect
641. #100C22×D61semidirect
911. C2#21455538direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405622
C2×#168405602
C22×#145197972
C22×#145197852
#214555382
C2×#168400362
C2×#168400312
C2×#168400282
C2×#168400242
C22×#145197122
C2×#168397442
C2×C61×#4132
C2×#306761