Finite Group Databasebeta

← C2×#21458549 #30559713

Subgroups — C2×#21458549 #30559713

Order 15616.

2122 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840488C211yesmaximal, characteristic, complemented
2C2×#16840433C211yesmaximal, characteristic
3#21458549C2116yesmaximal, direct product factor
4C2×#16840127C211yesmaximal, characteristic, complemented
5C2×#16840125C211yesmaximal, characteristic, complemented
6C2×#16840107C211yesmaximal, characteristic, complemented
7C2×#16840065C211yesmaximal, characteristic, complemented
8C2×#16840062C211yesmaximal, characteristic, complemented
9C2×#16840041C211yesmaximal, characteristic, complemented
10C2×#16839962C211yesmaximal, characteristic, complemented
11C2×#16839960C211yesmaximal, characteristic, complemented
12C2×#16839960C211yesmaximal, characteristic, complemented
13C2×#16839890C211yesmaximal, characteristic, complemented
14C2×#16839865C211yesmaximal, characteristic, complemented
15C2×#16839847C211yesmaximal, characteristic, complemented
16C2×C61×#440C211yesmaximal, characteristic, complemented
17C22×#11758222—21no—
18C22×#11758201C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20#16840488—24no—
21#16840488C2218yescomplemented
22#16840433—24no—
23#16840433C2218yes—
24C2×#14519776—21no—
25C2×#14519776C2211yescharacteristic
26C2×#14519774C2211yescharacteristic
27C2×#14519773C2211yescharacteristic
28C2×#14519773C2211yescharacteristic
29C2×#14519769—21no—
30C2×#14519769C2211yescharacteristic
31C2×#14519768—21no—
32C2×#14519768C2211yescharacteristic
33C2×#14519751—21no—
34C2×#14519750—21no—
35C2×#14519750—21no—
36C2×Q8×Dic61C2211yescharacteristic
37C2×Q8×Dic61C2211yescharacteristic
38C2×C4×Dic122—21no—
39C2×C4×Dic122C2211yescharacteristic
40C2×#14519739C2211yescharacteristic
41C2×#14519739C2211yescharacteristic
42#16840127C2218yescomplemented
43#16840125C2218yescomplemented
44#16840107C2218yescomplemented
45#16840065C2218yescomplemented
46#16840062C2218yescomplemented
47#16840041C2218yescomplemented
48#16839962C2218yescomplemented
49#16839960C2218yescomplemented
50#16839960C2218yescomplemented
51#16839890C2218yescomplemented
52#16839865C2218yescomplemented
53#16839847C2218yescomplemented
54C2×#14519710C2211yescharacteristic
55C2×#14519708C2211yescharacteristic
56C2×C4⋊#92418C2211yescharacteristic
57C2×#14519706C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519699C2211yescharacteristic
60C2×#14519699C2211yescharacteristic
61C2×#14519699C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C61×#440C2218yescomplemented
73C2×#107×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C2×#11758222—28no—
78C2×#11758222—48no—
79C22×Dic122—21no—
80C22×Dic122D411yescharacteristic
81C22×D244—21no—
82C22×D244—21no—
83C22×D244C2311yescharacteristic
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C22×C22⋊D61—21no—
89C22×C4×D61—21no—
90C22×C4×D61—21no—
91C2×#11758201—24no—
92C2×#11758201—24no—
93C2×#11758201C2314yes—
94C2×#11758201C2314yes—
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97#14519776—28no—
98#14519776—22no—
99#14519776C2314yes—
100#14519774—22no—
101#14519774C2314yes—
102#14519773—22no—
103#14519773—22no—
104#14519773C2314yes—
105#14519773C2314yes—
106#14519769—22no—
107#14519769—28no—
108#14519769C2314yes—
109#14519768—28no—
110#14519768—22no—
111#14519768C2314yes—
112#14519751—28no—
113#14519750—28no—
114#14519750—28no—
115Q8×Dic61—22no—
116Q8×Dic61—22no—
117Q8×Dic61C2314yes—
118Q8×Dic61C2314yes—
119C4×Dic122—28no—
120C4×Dic122D414yes—
121C4×Dic122C2314yes—
122#14519739—22no—
123#14519739—22no—
124#14519739C2314yes—
125#14519739C2314yes—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61D411yescharacteristic
130C2×C4⋊Dic61C2311yescharacteristic
131C2×C4⋊Dic61C2311yescharacteristic
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196D411yescharacteristic
137C2×#11758196D411yescharacteristic
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61—21no—
142C2×C4×Dic61C2311yescharacteristic
143C2×C4×Dic61C2311yescharacteristic
144#14519710C2314yes—
145#14519708C2314yes—
146C4⋊#92418C2314yes—
147#14519706C2314yes—
148#14519706C2314yes—
149#14519699C2314yes—
150#14519699C2314yes—
151#14519699C2314yes—
152#14519699C2314yes—
153#14519698C2314yes—
154#14519698C2314yes—
155#14519697C2314yes—
156#14519697C2314yes—
157#14519687C2314yes—
158C8×Dic61C2314yes—
159C22×Q8×C61C2311yescharacteristic
160C22×D4×C61C2311yescharacteristic
161C23×C4×C61—21no—
162C2×SD16×C61—24no—
163C2×SD16×C61C2314yes—
164C22×C8×C61C2311yescharacteristic
165C22×C8×C61C2311yescharacteristic
166C4×Q8×C61—22no—
167C4×Q8×C61C2314yes—
168C4×D4×C61—22no—
169C4×D4×C61C2314yes—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C22⋊C4×C61—21no—
174C2×C42×C61—21no—
175C2×C42×C61C2311yescharacteristic
176#107×C61C2314yes—
177#103×C61C2314yes—
178#102×C61C2314yes—
179#97×C61C2314yes—
180C24×C61—21no—
181C23×D61—21no—
182C23×D61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—22no—
185C2×Q8×C61#4114yescomplemented
186C2×Q8×C61C2412yes—
187C2×D4×C61—21no—
188C2×D4×C61—22no—
189C2×D4×C61—22no—
190C2×D4×C61C2412yes—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—24no—
195C22×C4×C61—44no—
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2411yescharacteristic
199C2×C22⋊D61—24no—
200C2×C22⋊D61—24no—
201C2×C22⋊D61—24no—
202C2×C22⋊D61—24no—
203C2×C22⋊D61—44no—
204C2×C22⋊D61—44no—
205C2×C22⋊D61—82no—
206C2×C22⋊D61—82no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213#11758222—432no—
214C2×D244—22no—
215C2×D244—22no—
216C2×D244—22no—
217C2×D244—22no—
218C2×D244—24no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244—24no—
222C2×D244—44no—
223C2×D244—82no—
224C2×D244C2412yes—
225C2×D244C2412yes—
226C2×C4×D61—24no—
227C2×C4×D61—24no—
228C2×C4×D61—44no—
229C2×C4×D61—44no—
230C2×Dic122—24no—
231C2×Dic122—24no—
232C2×Dic122—44no—
233C2×Dic122C2×D414yes—
234SD16×C61—28no—
235C2×C8×C61—22no—
236C2×C8×C61—22no—
237C2×C8×C61C2412yes—
238C2×C8×C61C2412yes—
239C4⋊C4×C61—24no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61C2412yes—
243C4⋊C4×C61C2412yes—
244C22⋊C4×C61—24no—
245C42×C61—24no—
246C42×C61C2×D412yes—
247C42×C61C2412yes—
248#11758201—28no—
249#11758201—28no—
250#11758198—24no—
251#11758198—24no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—24no—
255C4⋊Dic61—24no—
256C4⋊Dic61—24no—
257C4⋊Dic61C2×D414yes—
258C4⋊Dic61C2412yes—
259C4⋊Dic61C2412yes—
260#11758196—24no—
261#11758196—24no—
262#11758196—24no—
263#11758196—24no—
264#11758196C2×D414yes—
265#11758196C2×D414yes—
266C4×Dic61—24no—
267C4×Dic61—24no—
268C4×Dic61C2×D412yes—
269C4×Dic61C2×D412yes—
270C4×Dic61C2412yes—
271C4×Dic61C2412yes—
272C2×#92418—22no—
273C2×#92418—22no—
274C2×#92418C2412yes—
275C2×#92418C2412yes—
276C23×C61—22no—
277C23×C61—42no—
278C23×C61—42no—
279C23×C61—42no—
280C23×C61C22×D411yescharacteristic
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61—42no—
286C22×D61—42no—
287C22×D61—42no—
288C22×D61—42no—
289Q8×C61—24no—
290Q8×C61—22no—
291Q8×C61C2×#4114yescomplemented
292D4×C61—22no—
293D4×C61—22no—
294D4×C61—42no—
295C2×C4×C61—24no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—48no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61C22×D412yes—
305C2×C4×C61C22×D412yes—
306C2×C4×C61C22×D411yescharacteristic
307C2×C4×C61C2×#4112yes—
308C2×C4×C612−1+412yes—
309C2×C4×C61C2511yescharacteristic
310C22⋊D61—48no—
311C22⋊D61—48no—
312C22⋊D61—84no—
313C22⋊D61—84no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61AGL(1,ℤ/8)14yes—
322C2×Dic61C22×D412yes—
323C2×Dic61C22×D412yes—
324C2×Dic61C22×D412yes—
325C2×Dic61C22×D412yes—
326D244—22no—
327D244—22no—
328D244—22no—
329D244—22no—
330D244—48no—
331D244—42no—
332D244—42no—
333D244—84no—
334C4×D61—48no—
335C4×D61—48no—
336Dic122—28no—
337Dic122—48no—
338C8×C61—22no—
339C8×C61—22no—
340#92418—22no—
341#92418—22no—
342C2×#3368—611nomaximal, Sylow
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—84no—
347C22×C61#54812yes—
348C22×C61C2×AGL(1,ℤ/8)12yes—
349C22×C61#57712yes—
350C22×C61C23×D411yescharacteristic
351C2×D61—42no—
352C2×D61—42no—
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—84no—
358C2×D61—84no—
359C4×C61—24no—
360C4×C61—22no—
361C4×C61—22no—
362C4×C61—42no—
363C4×C61—42no—
364C4×C61#54812yes—
365C4×C61C22×#4111yescharacteristic
366C4×C61C2×2−1+411yescharacteristic
367Dic61—22no—
368Dic61—22no—
369Dic61—22no—
370Dic61—42no—
371Dic61—42no—
372Dic61C2×AGL(1,ℤ/8)14yes—
373C2×#557—611no—
374C2×#550—611no—
375#3368—6116no—
376C2×#490—611no—
377C2×#490—611no—
378C2×#486—611no—
379C2×#478—611no—
380C2×#478—611no—
381C2×#474—611no—
382C2×#460—611no—
383C2×#460—611no—
384C2×#460—611no—
385C2×#446—611no—
386C2×#440—611no—
387C2×#440D6111yescharacteristic, complemented
388C2×C4×SD16—611no—
389C2×C61—82no—
390C2×C61#336814yescomplemented
391C2×C61C2×#54811yescharacteristic
392C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
393C2×C61C2×#57711yescharacteristic
394D61—82no—
395D61—82no—
396C22×#41—1221no—
397C22×SD16—611no—
398C22×SD16—611no—
399C22×SD16C2×D6111yescharacteristic
400#557—618no—
401#557—1224no—
402#550—618no—
403#550—1224no—
404C2×C4⋊Q8—611no—
405C2×C4⋊Q8—1221no—
406C2×#127—611no—
407C2×#127—611no—
408C2×#127—611no—
409C2×#125—611no—
410C2×#125—611no—
411C2×#125—1221no—
412C2×#125—1221no—
413C2×#121—1221no—
414C2×#121—1221no—
415C2×#121—1221no—
416C2×C4×Q8—611no—
417C2×C4×Q8—611no—
418C2×C4×Q8—611no—
419C2×C4×Q8—1221no—
420C2×C4×Q8C2×D6111yescharacteristic
421C2×C4×D4—611no—
422C2×C4×D4—611no—
423C2×C4×D4C2×D6111yescharacteristic
424#490—618no—
425#490—618no—
426#486—618no—
427#478—618no—
428#478—618no—
429#474—618no—
430#460—618no—
431#460—618no—
432#460—618no—
433#446—618no—
434#440—618no—
435#440C2×D6118yescomplemented
436C4×SD16—618no—
437C2×#107—611no—
438C2×#107C2×D6111yescharacteristic
439C2×#106—611no—
440C2×C4⋊C8—611no—
441C2×C4⋊C8—611no—
442C2×C4⋊C8—611no—
443C2×#103C2×D6111yescharacteristic
444C2×#102—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102—611no—
449C2×#102—611no—
450C2×#102—611no—
451C2×#102—611no—
452C2×#102C2×D6111yescharacteristic
453C2×#97—611no—
454C2×#97C2×D6111yescharacteristic
455C2×C4×C8—611no—
456C61C2×#336811yescharacteristic, complemented, Sylow
457C2×#41—1228no—
458C2×#41—2448no—
459C22×Q8—611no—
460C22×Q8—1221no—
461C22×Q8C22×D6111yescharacteristic
462C22×D4—611no—
463C22×D4—611no—
464C22×D4—1221no—
465C22×D4—1221no—
466C22×D4—1221no—
467C22×D4—1221no—
468C22×D4—1221no—
469C22×D4—1221no—
470C22×D4C22×D6111yescharacteristic
471C23×C4—21no—
472C23×C4—1221no—
473C23×C4—1221no—
474C2×SD16—24no—
475C2×SD16—614no—
476C2×SD16—614no—
477C2×SD16—1224no—
478C2×SD16—1224no—
479C2×SD16C22×D6114yes—
480C22×C8—611no—
481C22×C8—611no—
482C22×C8C22×D6111yescharacteristic
483C22×C8C22×D6111yescharacteristic
484C4⋊Q8—614no—
485C4⋊Q8—1222no—
486C4⋊Q8—1228no—
487#127—614no—
488#127—614no—
489#127—614no—
490#127—1222no—
491#127—1222no—
492#127—1222no—
493#125—614no—
494#125—614no—
495#125—1228no—
496#125—1222no—
497#125—1228no—
498#125—1222no—
499#121—1228no—
500#121—1228no—
501#121—1228no—
502C4×Q8—22no—
503C4×Q8—614no—
504C4×Q8—614no—
505C4×Q8—614no—
506C4×Q8—614no—
507C4×Q8—1228no—
508C4×Q8—1222no—
509C4×Q8—1222no—
510C4×Q8C22×D6114yes—
511C4×D4—22no—
512C4×D4—614no—
513C4×D4—614no—
514C4×D4—1222no—
515C4×D4—1222no—
516C4×D4C22×D6114yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4C22×D6111yescharacteristic
531C2×C4⋊C4C22×D6111yescharacteristic
532C2×C22⋊C4—21no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C42—21no—
536C2×C42—611no—
537C2×C42—611no—
538C2×C42—1221no—
539C2×C42—1221no—
540C2×C42C22×D6111yescharacteristic
541#107—614no—
542#107C22×D6114yes—
543#106—614no—
544C4⋊C8—614no—
545C4⋊C8—614no—
546C4⋊C8—614no—
547#103C22×D6114yes—
548#102—614no—
549#102—614no—
550#102—614no—
551#102—614no—
552#102—614no—
553#102—614no—
554#102—614no—
555#102—614no—
556#102C22×D6114yes—
557#97—614no—
558#97C22×D6114yes—
559C4×C8—614no—
560C24—21no—
561C24—1221no—
562C24—1221no—
563#41—24432no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—614no—
567C2×Q8—1224no—
568C2×Q8—1224no—
569C2×Q8—2444no—
570C2×Q8#1175822214yescomplemented
571C2×Q8C23×D6112yes—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—612no—
576C2×D4—612no—
577C2×D4—1224no—
578C2×D4—1224no—
579C2×D4—1224no—
580C2×D4—1224no—
581C2×D4—1224no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—1224no—
585C2×D4—1222no—
586C2×D4—1222no—
587C2×D4—1222no—
588C2×D4—1222no—
589C2×D4—4882no—
590C2×D4—4882no—
591C2×D4—4882no—
592C2×D4—2444no—
593C2×D4—2444no—
594C2×D4—2444no—
595C2×D4C23×D6112yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—44no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—1224no—
606C22×C4—1224no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—2444no—
610C22×C4—2444no—
611C22×C4D4×D6111yescharacteristic
612C22×C4D4×D6111yescharacteristic
613C22×C4C23×D6111yescharacteristic
614SD16—28no—
615SD16—1228no—
616SD16—1228no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—612no—
620C2×C8—612no—
621C2×C8—1222no—
622C2×C8—1222no—
623C2×C8C23×D6112yes—
624C2×C8C23×D6112yes—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—614no—
629C4⋊C4—614no—
630C4⋊C4—614no—
631C4⋊C4—612no—
632C4⋊C4—612no—
633C4⋊C4—1224no—
634C4⋊C4—1224no—
635C4⋊C4—1224no—
636C4⋊C4—1224no—
637C4⋊C4—1224no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—1224no—
641C4⋊C4—1224no—
642C4⋊C4C23×D6112yes—
643C4⋊C4C23×D6112yes—
644C22⋊C4—24no—
645C22⋊C4—1224no—
646C22⋊C4—1224no—
647C42—24no—
648C42—612no—
649C42—612no—
650C42—612no—
651C42—612no—
652C42—1224no—
653C42—1224no—
654C42D4×D6112yes—
655C42C23×D6112yes—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—1222no—
661C23—1222no—
662C23—2442no—
663C23—2442no—
664C23—2442no—
665C23—2442no—
666C23—2442no—
667C23—2442no—
668C23C2×D4×D6111yescharacteristic
669Q8—22no—
670Q8—24no—
671Q8—1228no—
672Q8—2448no—
673Q8C2×#1175822214yescomplemented
674D4—22no—
675D4—22no—
676D4—42no—
677D4—1222no—
678D4—1222no—
679D4—1222no—
680D4—1222no—
681D4—4884no—
682D4—4884no—
683D4—4884no—
684D4—2448no—
685D4—2448no—
686D4—2448no—
687D4—2442no—
688D4—2442no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—48no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—614no—
699C2×C4—612no—
700C2×C4—612no—
701C2×C4—612no—
702C2×C4—612no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—2448no—
709C2×C4—2448no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4C2×D4×D6112yes—
713C2×C4C2×D4×D6112yes—
714C2×C4C2×D4×D6111yescharacteristic
715C2×C4C2×#1175822212yes—
716C2×C4#1451982412yes—
717C2×C4C24×D6111yescharacteristic
718C8—22no—
719C8—22no—
720C8—1222no—
721C8—1222no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—4884no—
727C22—4884no—
728C22—2442no—
729C22—2442no—
730C22—2442no—
731C22—2442no—
732C22—2442no—
733C22—2442no—
734C22#1684042112yes—
735C22AGL(1,ℤ/8)×D6112yes—
736C22#1684057112yes—
737C22C22×D4×D6111yescharacteristic
738C4—22no—
739C4—24no—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—614no—
744C4—1222no—
745C4—1222no—
746C4—1222no—
747C4—2442no—
748C4—2442no—
749C4#1684042112yes—
750C4C22×#1175822211yescharacteristic
751C4C2×#1451982411yescharacteristic
752C2—82no—
753C2—4882no—
754C2—4882no—
755C2#2145854914yesdirect product factor
756C2C2×#1684042111yescharacteristic
757C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
758C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
prime radicalC2×#16840433C2
hypercenterC2×#440D61
hypocenterC61C2×#3368
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#16840488C2semidirect
3. #21458549C2direct (N × H)
4. C2×#16840127C2semidirect
5. C2×#16840125C2semidirect
6. C2×#16840107C2semidirect
7. C2×#16840065C2semidirect
8. C2×#16840062C2semidirect
9. C2×#16840041C2semidirect
10. C2×#16839962C2semidirect
11. C2×#16839960C2semidirect
12. C2×#16839960C2semidirect
13. C2×#16839890C2semidirect
14. C2×#16839865C2semidirect
15. C2×#16839847C2semidirect
16. C2×C61×#440C2semidirect
21. #16840488C22semidirect
42. #16840127C22semidirect
43. #16840125C22semidirect
44. #16840107C22semidirect
45. #16840065C22semidirect
46. #16840062C22semidirect
47. #16840041C22semidirect
48. #16839962C22semidirect
49. #16839960C22semidirect
50. #16839960C22semidirect
51. #16839890C22semidirect
52. #16839865C22semidirect
53. #16839847C22semidirect
72. C61×#440C22semidirect
185. C2×Q8×C61#41semidirect
291. Q8×C61C2×#41semidirect
387. C2×#440D61semidirect
390. C2×C61#3368semidirect
435. #440C2×D61semidirect
456. C61C2×#3368semidirect
570. C2×Q8#11758222semidirect
673. Q8C2×#11758222semidirect
755. C2#21458549direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404882
C2×#168404332
#214585492
C2×#168401272
C2×#168401252
C2×#168401072
C2×#168400652
C2×#168400622
C2×#168400412
C2×#168399622
C2×#168399602
C2×#168398902
C2×#168398652
C2×#168398472
C2×C61×#4402
C2×#336861