Finite Group Databasebeta

← C2×#21458321 #30558610

Subgroups — C2×#21458321 #30558610

Order 15616.

1962 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×#16840477C211yesmaximal, characteristic, complemented
2C2×#16840458C211yesmaximal, characteristic, complemented
3#21458321C2116yesmaximal, direct product factor
4C2×#16840171C211yesmaximal, characteristic, complemented
5C2×#16840087C211yesmaximal, characteristic, complemented
6C2×#16840087C211yesmaximal, characteristic, complemented
7C2×#16840087C211yesmaximal, characteristic, complemented
8C2×#16840076C211yesmaximal, characteristic, complemented
9C2×#16840063C211yesmaximal, characteristic, complemented
10C2×#16840043C211yesmaximal, characteristic, complemented
11C2×#16840015C211yesmaximal, characteristic, complemented
12C2×#16839998C211yesmaximal, characteristic, complemented
13C2×#16839875C211yesmaximal, characteristic, complemented
14C2×#16839804C211yesmaximal, characteristic, complemented
15C2×#16839800C211yesmaximal, characteristic, complemented
16C2×C61×#435C211yesmaximal, characteristic, complemented
17C22×D488C2211yescharacteristic
18#16840477—24no—
19#16840477C2218yescomplemented
20#16840458—24no—
21#16840458C2218yescomplemented
22C2×#14519777C2211yescharacteristic
23C2×#14519772—21no—
24C2×#14519769C2211yescharacteristic
25C2×#14519763—21no—
26C2×#14519763—21no—
27C2×#14519759—21no—
28C2×#14519751C2211yescharacteristic
29C2×#14519751C2211yescharacteristic
30C2×#14519751C2211yescharacteristic
31C2×#14519751C2211yescharacteristic
32C2×#14519749—21no—
33C2×#14519748—21no—
34C2×C4×D244C2211yescharacteristic
35C2×C4×D244C2211yescharacteristic
36C2×#14519737—21no—
37C2×#14519736C2211yescharacteristic
38C2×#14519736C2211yescharacteristic
39C2×#14519736C2211yescharacteristic
40C2×#14519735—21no—
41C22×C4⋊Dic61C2211yescharacteristic
42#16840171C2218yescomplemented
43#16840087C2218yescomplemented
44#16840087C2218yescomplemented
45#16840087C2218yescomplemented
46#16840076C2218yescomplemented
47#16840063C2218yescomplemented
48#16840043C2218yescomplemented
49#16840015C2218yescomplemented
50#16839998C2218yescomplemented
51#16839875C2218yescomplemented
52#16839804C2218yescomplemented
53#16839800C2218yescomplemented
54C2×#14519711C2211yescharacteristic
55C2×#14519711C2211yescharacteristic
56C2×#14519711C2211yescharacteristic
57C2×#14519711C2211yescharacteristic
58C2×#14519711C2211yescharacteristic
59C2×#14519709C2211yescharacteristic
60C2×#14519709C2211yescharacteristic
61C2×#14519709C2211yescharacteristic
62C2×#14519709C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519699C2211yescharacteristic
66C2×#14519699C2211yescharacteristic
67C2×#14519699C2211yescharacteristic
68C2×#14519699C2211yescharacteristic
69C22×M16×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C61×#435C2218yescomplemented
73C2×C4⋊C8×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×C22⋊C8×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×D244C2311yescharacteristic
79C22×D244C2311yescharacteristic
80C22×C22⋊D61—21no—
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C23×Dic61—21no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C2×D488—24no—
88C2×D488C2314yes—
89#14519777—22no—
90#14519777C2314yes—
91#14519772—28no—
92#14519769—22no—
93#14519769C2314yes—
94#14519763—28no—
95#14519763—28no—
96#14519759—28no—
97#14519751—22no—
98#14519751—22no—
99#14519751—22no—
100#14519751—22no—
101#14519751C2314yes—
102#14519751C2314yes—
103#14519751C2314yes—
104#14519751C2314yes—
105#14519749—28no—
106#14519748—28no—
107C4×D244—22no—
108C4×D244—22no—
109C4×D244C2314yes—
110C4×D244C2314yes—
111#14519737—28no—
112#14519736—22no—
113#14519736—22no—
114#14519736—22no—
115#14519736C2314yes—
116#14519736C2314yes—
117#14519736C2314yes—
118#14519735—28no—
119C2×C4⋊Dic61—22no—
120C2×C4⋊Dic61—21no—
121C2×C4⋊Dic61—21no—
122C2×C4⋊Dic61C2314yes—
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×C4⋊Dic61C2311yescharacteristic
126C2×C4⋊Dic61C2311yescharacteristic
127C2×C4⋊Dic61C2311yescharacteristic
128C2×C4⋊Dic61C2311yescharacteristic
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×C22⋊Dic61—21no—
132C2×C22⋊Dic61—21no—
133C2×C22⋊Dic61—21no—
134C2×#11758198—21no—
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61—21no—
142C2×C4×Dic61—21no—
143#14519711C2314yes—
144#14519711C2314yes—
145#14519711C2314yes—
146#14519711C2314yes—
147#14519711C2314yes—
148#14519709C2314yes—
149#14519709C2314yes—
150#14519709C2314yes—
151#14519709C2314yes—
152#14519699C2314yes—
153#14519699C2314yes—
154#14519699C2314yes—
155#14519699C2314yes—
156#14519699C2314yes—
157#14519699C2314yes—
158C22×D4×C61D411yescharacteristic
159C23×C4×C61C2311yescharacteristic
160C23×C4×C61C2311yescharacteristic
161C2×M16×C61—24no—
162C2×M16×C61C2314yes—
163C22×C8×C61—24no—
164C22×C8×C61C2314yes—
165C22×C8×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C4×D4×C61D414yes—
170C4×D4×C61C2314yes—
171C2×C4⋊C4×C61D411yescharacteristic
172C2×C22⋊C4×C61D411yescharacteristic
173C2×C22⋊C4×C61D411yescharacteristic
174C2×C42×C61C2311yescharacteristic
175C4⋊C8×C61C2314yes—
176C22⋊C8×C61C2314yes—
177C22⋊C8×C61C2314yes—
178#97×C61C2314yes—
179C24×C61C2×D411yescharacteristic
180C24×C61C2×D411yescharacteristic
181C23×D61—21no—
182C23×D61—21no—
183C2×D4×C61—42no—
184C2×D4×C61C2×D414yes—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D412yes—
194C22×C4×C61C2×D412yes—
195C22×C4×C61C2412yes—
196C22×C4×C61C2412yes—
197C22×C4×C61C2411yescharacteristic
198C2×C22⋊D61—24no—
199C2×C22⋊D61—24no—
200C2×C22⋊D61—24no—
201C2×C22⋊D61—24no—
202C2×C22⋊D61—44no—
203C2×C22⋊D61—82no—
204C2×C22⋊D61—82no—
205C2×C22⋊D61—82no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—24no—
213C22×Dic61—82no—
214C2×D244—22no—
215C2×D244—22no—
216C2×D244—22no—
217C2×D244—22no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244C2412yes—
221C2×D244C2412yes—
222C2×C4×D61—24no—
223C2×C4×D61—24no—
224C2×C4×D61—44no—
225C2×C4×D61—82no—
226C2×Dic122—24no—
227C2×Dic122—82no—
228M16×C61—28no—
229C2×C8×C61—22no—
230C2×C8×C61—22no—
231C2×C8×C61—22no—
232C2×C8×C61—28no—
233C2×C8×C61#4114yes—
234C2×C8×C61C2412yes—
235C2×C8×C61C2412yes—
236C2×C8×C61C2412yes—
237C2×C8×C61C2412yes—
238C4⋊C4×C61C2×D414yes—
239C22⋊C4×C61C2×D414yes—
240C22⋊C4×C61C2×D414yes—
241C42×C61C2×D412yes—
242C42×C61C2412yes—
243C22⋊Dic61—24no—
244C22⋊Dic61—24no—
245C22⋊Dic61—24no—
246#11758198—24no—
247#11758198—24no—
248#11758198—24no—
249#11758198—24no—
250#11758198—24no—
251#11758198—24no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—24no—
255C4⋊Dic61—24no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61C2412yes—
261C4⋊Dic61C2412yes—
262C4⋊Dic61C2412yes—
263C4⋊Dic61C2412yes—
264C4⋊Dic61C2412yes—
265C4⋊Dic61C2412yes—
266#11758196—24no—
267#11758196—24no—
268C4×Dic61—24no—
269C4×Dic61—24no—
270C4×Dic61—24no—
271D488—28no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61C22×D412yes—
279C23×C61C22×D412yes—
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—
289D4×C61—44no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—24no—
295C2×C4×C61—24no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61C22×D412yes—
301C2×C4×C61C22×D412yes—
302C2×C4×C61C22×D412yes—
303C2×C4×C61C22×D412yes—
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C2×#4112yes—
306C2×C4×C612−1+412yes—
307C2×C4×C61C2511yescharacteristic
308C22⋊D61—48no—
309C22⋊D61—84no—
310C22⋊D61—84no—
311C22⋊D61—84no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—84no—
325D244—22no—
326D244—22no—
327D244—22no—
328D244—22no—
329D244—42no—
330D244—42no—
331C4×D61—48no—
332C4×D61—84no—
333Dic122—84no—
334C8×C61—22no—
335C8×C61—22no—
336C8×C61—22no—
337C8×C61C2×#4114yes—
338C2×#3347—611nomaximal, Sylow
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—44no—
346C22×C61—44no—
347C22×C61#54712yes—
348C22×C61#57512yes—
349C22×C61#57612yes—
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—22no—
360C4×C61—22no—
361C4×C61—22no—
362C4×C61—22no—
363C4×C61#54712yes—
364C4×C61C22×#4111yescharacteristic
365C4×C61C2×2−1+411yescharacteristic
366Dic61—42no—
367Dic61—42no—
368Dic61—42no—
369Dic61—42no—
370Dic61—42no—
371Dic61—42no—
372C2×#555—611no—
373C2×#553—611no—
374#3347—6116no—
375C2×#501—611no—
376C2×#482—611no—
377C2×#482—611no—
378C2×#482—611no—
379C2×#480—611no—
380C2×#478—611no—
381C2×#474—611no—
382C2×#469—611no—
383C2×#466—611no—
384C2×#442—611no—
385C2×#435D6111yescharacteristic, complemented
386C2×#428—611no—
387C2×#427—611no—
388C2×C61—42no—
389C2×C61—42no—
390C2×C61#334714yescomplemented
391C2×C61C2×#54711yescharacteristic
392C2×C61C2×#57511yescharacteristic
393C2×C61C2×#57611yescharacteristic
394D61—82no—
395D61—82no—
396C22×D8—611no—
397C22×M16C2×D6111yescharacteristic
398C23×C8C2×D6111yescharacteristic
399#555—618no—
400#555—1224no—
401#553—618no—
402#553—1224no—
403C2×C4⋊Q8—611no—
404C2×#126—1221no—
405C2×#125—611no—
406C2×#124—1221no—
407C2×#124—1221no—
408C2×#123—1221no—
409C2×#121—611no—
410C2×#121—611no—
411C2×#121—611no—
412C2×#121—611no—
413C2×#121—1221no—
414C2×#121—1221no—
415C2×C4×D4—611no—
416C2×C4×D4—611no—
417C2×C4×D4—1221no—
418C2×C4×D4C2×D6111yescharacteristic
419C2×#117—611no—
420C2×#117—611no—
421C2×#117—611no—
422C2×#117—1221no—
423C22×C4⋊C4—611no—
424#501—618no—
425#482—618no—
426#482—618no—
427#482—618no—
428#480—618no—
429#478—618no—
430#474—618no—
431#469—618no—
432#466—618no—
433#442—618no—
434#435C2×D6118yescomplemented
435#428—618no—
436#427—618no—
437C2×#107—611no—
438C2×#107—611no—
439C2×#107—611no—
440C2×#107—611no—
441C2×#107—611no—
442C2×#106—611no—
443C2×#106—611no—
444C2×#106—611no—
445C2×#106—611no—
446C2×C4⋊C8C2×D6111yescharacteristic
447C2×#102—611no—
448C2×#102—611no—
449C2×#102—611no—
450C2×#102—611no—
451C2×#102—611no—
452C2×#102—611no—
453C2×C22⋊C8C2×D6111yescharacteristic
454C2×C22⋊C8C2×D6111yescharacteristic
455C2×#97C2×D6111yescharacteristic
456C61C2×#334711yescharacteristic, complemented, Sylow
457C22×Q8—1221no—
458C22×D4—611no—
459C22×D4—611no—
460C22×D4—1221no—
461C22×D4—1221no—
462C22×D4—1221no—
463C22×D4—1221no—
464C22×D4D24411yescharacteristic
465C23×C4—1221no—
466C23×C4—1221no—
467C23×C4—1221no—
468C23×C4C22×D6111yescharacteristic
469C23×C4C22×D6111yescharacteristic
470C2×D8—614no—
471C2×D8—1224no—
472C2×M16—24no—
473C2×M16C22×D6114yes—
474C22×C8—24no—
475C22×C8C22×D6111yescharacteristic
476C22×C8C22×D6114yes—
477C22×C8C22×D6111yescharacteristic
478C22×C8C22×D6111yescharacteristic
479C22×C8C22×D6111yescharacteristic
480C4⋊Q8—614no—
481C4⋊Q8—1222no—
482#126—1228no—
483#125—614no—
484#125—1222no—
485#124—1228no—
486#124—1228no—
487#123—1228no—
488#121—614no—
489#121—614no—
490#121—614no—
491#121—614no—
492#121—1228no—
493#121—1228no—
494#121—1222no—
495#121—1222no—
496#121—1222no—
497#121—1222no—
498C4×D4—614no—
499C4×D4—614no—
500C4×D4—1228no—
501C4×D4—1222no—
502C4×D4—1222no—
503C4×D4D24414yes—
504C4×D4C22×D6114yes—
505#117—614no—
506#117—614no—
507#117—614no—
508#117—1222no—
509#117—1222no—
510#117—1222no—
511#117—1228no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—614no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1222no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4D24411yescharacteristic
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4D24411yescharacteristic
535C2×C22⋊C4D24411yescharacteristic
536C2×C42—1221no—
537C2×C42—1221no—
538C2×C42—1221no—
539C2×C42C22×D6111yescharacteristic
540#107—614no—
541#107—614no—
542#107—614no—
543#107—614no—
544#107—614no—
545#106—614no—
546#106—614no—
547#106—614no—
548#106—614no—
549C4⋊C8C22×D6114yes—
550#102—614no—
551#102—614no—
552#102—614no—
553#102—614no—
554#102—614no—
555#102—614no—
556C22⋊C8C22×D6114yes—
557C22⋊C8C22×D6114yes—
558#97C22×D6114yes—
559C24—1221no—
560C24—1221no—
561C24C2×D24411yescharacteristic
562C24C2×D24411yescharacteristic
563C2×Q8—1224no—
564C2×Q8—4882no—
565C2×D4—42no—
566C2×D4—612no—
567C2×D4—612no—
568C2×D4—1224no—
569C2×D4—1224no—
570C2×D4—1224no—
571C2×D4—1224no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—1222no—
575C2×D4—1222no—
576C2×D4—1222no—
577C2×D4—1222no—
578C2×D4—4882no—
579C2×D4—4882no—
580C2×D4—4882no—
581C2×D4—2444no—
582C2×D4C2×D24414yes—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—1224no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1224no—
595C22×C4—1224no—
596C22×C4—4882no—
597C22×C4—4882no—
598C22×C4—2444no—
599C22×C4C2×D24412yes—
600C22×C4C2×D24412yes—
601C22×C4C2×D24411yescharacteristic
602C22×C4C2×D24411yescharacteristic
603C22×C4C2×D24411yescharacteristic
604C22×C4C2×D24411yescharacteristic
605C22×C4C23×D6112yes—
606C22×C4C23×D6112yes—
607C22×C4C23×D6111yescharacteristic
608D8—1228no—
609M16—28no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—28no—
614C2×C8#1175822414yes—
615C2×C8C23×D6112yes—
616C2×C8C23×D6112yes—
617C2×C8C23×D6112yes—
618C2×C8C23×D6112yes—
619C4⋊C4—612no—
620C4⋊C4—612no—
621C4⋊C4—612no—
622C4⋊C4—612no—
623C4⋊C4—612no—
624C4⋊C4—612no—
625C4⋊C4—1221no—
626C4⋊C4—1221no—
627C4⋊C4—1224no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4—1224no—
633C4⋊C4—1224no—
634C4⋊C4—1224no—
635C4⋊C4C2×D24414yes—
636C22⋊C4—1224no—
637C22⋊C4—1224no—
638C22⋊C4—1224no—
639C22⋊C4—1224no—
640C22⋊C4—1224no—
641C22⋊C4—1224no—
642C22⋊C4—1224no—
643C22⋊C4—1224no—
644C22⋊C4—1224no—
645C22⋊C4C2×D24414yes—
646C22⋊C4C2×D24414yes—
647C42—1224no—
648C42—1224no—
649C42—1224no—
650C42C2×D24412yes—
651C42C23×D6112yes—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—1222no—
659C23—1222no—
660C23—2442no—
661C23—2442no—
662C23—2442no—
663C23—2442no—
664C23—2442no—
665C23—2442no—
666C23C22×D24412yes—
667C23C22×D24412yes—
668C23C22×D24411yescharacteristic
669Q8—4884no—
670D4—44no—
671D4—1222no—
672D4—1222no—
673D4—1222no—
674D4—1222no—
675D4—4884no—
676D4—4884no—
677D4—4884no—
678D4—2448no—
679D4—2442no—
680D4—2442no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—4884no—
698C2×C4—4884no—
699C2×C4—2448no—
700C2×C4—2442no—
701C2×C4—2442no—
702C2×C4—2442no—
703C2×C4—2442no—
704C2×C4—2442no—
705C2×C4—2442no—
706C2×C4C22×D24412yes—
707C2×C4C22×D24412yes—
708C2×C4C22×D24412yes—
709C2×C4C22×D24412yes—
710C2×C4C22×D24411yescharacteristic
711C2×C4C2×#1175822412yes—
712C2×C4#1451982412yes—
713C2×C4C24×D6111yescharacteristic
714C8—22no—
715C8—22no—
716C8—22no—
717C8C2×#1175822414yes—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—4884no—
727C22—4884no—
728C22—2442no—
729C22—2442no—
730C22—2442no—
731C22—2442no—
732C22—2442no—
733C22—2442no—
734C22#1684041612yes—
735C22#1684056212yes—
736C22#1684056712yes—
737C22C23×D24411yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—2442no—
743C4—2442no—
744C4—2442no—
745C4—2442no—
746C4—2442no—
747C4—2442no—
748C4#1684041612yes—
749C4C22×#1175822411yescharacteristic
750C4C2×#1451982411yescharacteristic
751C2—42no—
752C2—42no—
753C2—4882no—
754C2—4882no—
755C2#2145832114yesdirect product factor
756C2C2×#1684041611yescharacteristic
757C2C2×#1684056211yescharacteristic
758C2C2×#1684056711yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#435C2
socleC23×C61C22×D4
hypercenterC2×#435D61
hypocenterC61C2×#3347
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16840477C2semidirect
2. C2×#16840458C2semidirect
3. #21458321C2direct (N × H)
4. C2×#16840171C2semidirect
5. C2×#16840087C2semidirect
6. C2×#16840087C2semidirect
7. C2×#16840087C2semidirect
8. C2×#16840076C2semidirect
9. C2×#16840063C2semidirect
10. C2×#16840043C2semidirect
11. C2×#16840015C2semidirect
12. C2×#16839998C2semidirect
13. C2×#16839875C2semidirect
14. C2×#16839804C2semidirect
15. C2×#16839800C2semidirect
16. C2×C61×#435C2semidirect
19. #16840477C22semidirect
21. #16840458C22semidirect
42. #16840171C22semidirect
43. #16840087C22semidirect
44. #16840087C22semidirect
45. #16840087C22semidirect
46. #16840076C22semidirect
47. #16840063C22semidirect
48. #16840043C22semidirect
49. #16840015C22semidirect
50. #16839998C22semidirect
51. #16839875C22semidirect
52. #16839804C22semidirect
53. #16839800C22semidirect
72. C61×#435C22semidirect
385. C2×#435D61semidirect
390. C2×C61#3347semidirect
434. #435C2×D61semidirect
456. C61C2×#3347semidirect
755. C2#21458321direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404772
C2×#168404582
#214583212
C2×#168401712
C2×#168400872
C2×#168400762
C2×#168400632
C2×#168400432
C2×#168400152
C2×#168399982
C2×#168398752
C2×#168398042
C2×#168398002
C2×C61×#4352
C2×#334761