Finite Group Databasebeta

← C2×#21457287 #30552986

Subgroups — C2×#21457287 #30552986

Order 15616.

1882 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840384C211yesmaximal, characteristic, complemented
2C2×#16840381C211yesmaximal, characteristic, complemented
3#21457287C2116yesmaximal, direct product factor
4C2×#16840047C211yesmaximal, characteristic, complemented
5C2×#16840045C211yesmaximal, characteristic, complemented
6C2×#16840053C211yesmaximal, characteristic, complemented
7C2×#16840050C211yesmaximal, characteristic, complemented
8C2×#16840017C211yesmaximal, characteristic, complemented
9C2×#16840014C211yesmaximal, characteristic
10C2×#16839994C211yesmaximal, characteristic, complemented
11C2×#16839988C211yesmaximal, characteristic, complemented
12C2×#16839986C211yesmaximal, characteristic, complemented
13C2×#16839979C211yesmaximal, characteristic, complemented
14C2×#16839974C211yesmaximal, characteristic, complemented
15C2×#16839787C211yesmaximal, characteristic, complemented
16C2×C61×#464C211yesmaximal, characteristic, complemented
17C22×#11758201C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21#16840384—24no—
22#16840384C2218yescomplemented
23#16840381—24no—
24#16840381C2218yescomplemented
25C2×#14519777C2211yescharacteristic
26C2×#14519776C2211yescharacteristic
27C2×#14519771—21no—
28C2×#14519770—21no—
29C2×#14519766C2211yescharacteristic
30C2×#14519765—21no—
31C2×#14519763—21no—
32C2×#14519762—21no—
33C2×#14519761—21no—
34C2×#14519755—21no—
35C2×#14519754—21no—
36C2×#14519753C2211yescharacteristic
37C2×#14519753C2211yescharacteristic
38C2×#14519752C2211yescharacteristic
39C2×#14519748C2211yescharacteristic
40C2×Q8×Dic61C2211yescharacteristic
41C2×C4×D244C2211yescharacteristic
42C2×D4×Dic61C2211yescharacteristic
43C2×#14519734C2211yescharacteristic
44#16840053C2218yescomplemented
45#16840050C2218yescomplemented
46#16840047C2218yescomplemented
47#16840045C2218yescomplemented
48#16840017C2218yescomplemented
49#16840014C2218yes—
50#16839994C2218yescomplemented
51#16839988C2218yescomplemented
52#16839986C2218yescomplemented
53#16839979C2218yescomplemented
54#16839974C2218yescomplemented
55C2×#14519709C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519708C2211yescharacteristic
59#16839787C2218yescomplemented
60C2×C4⋊#92418C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519706C2211yescharacteristic
63C2×#14519701C2211yescharacteristic
64C2×#14519701C2211yescharacteristic
65C2×#14519701C2211yescharacteristic
66C2×#14519699C2211yescharacteristic
67C2×#14519699C2211yescharacteristic
68C2×#14519698C2211yescharacteristic
69C22×Q16×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C2×#124×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic
73C61×#464C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122—21no—
79C22×D244—21no—
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C23×Dic61—21no—
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85C2×#11758201—42no—
86C2×#11758201C2314yes—
87C2×#11758199—42no—
88C2×#11758199C2314yes—
89C2×#11758189—42no—
90C2×#11758189C2314yes—
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93C2×C8×D61—42no—
94C2×C8×D61C2314yes—
95#14519777—22no—
96#14519777C2314yes—
97#14519776—22no—
98#14519776C2314yes—
99#14519771—28no—
100#14519770—28no—
101#14519766—22no—
102#14519766C2314yes—
103#14519765—28no—
104#14519763—28no—
105#14519762—28no—
106#14519761—28no—
107#14519755—28no—
108#14519754—28no—
109#14519753—22no—
110#14519753—22no—
111#14519753C2314yes—
112#14519753C2314yes—
113#14519752—22no—
114#14519752C2314yes—
115#14519748—22no—
116#14519748C2314yes—
117Q8×Dic61—22no—
118Q8×Dic61C2314yes—
119C4×D244—22no—
120C4×D244C2314yes—
121D4×Dic61—22no—
122D4×Dic61C2314yes—
123#14519734D414yes—
124#14519734C2314yes—
125C2×C4⋊Dic61—21no—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61C2311yescharacteristic
128C2×C4⋊Dic61C2311yescharacteristic
129C2×C4⋊Dic61C2311yescharacteristic
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196D411yescharacteristic
134C2×#11758196D411yescharacteristic
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198D411yescharacteristic
144C2×#11758198D411yescharacteristic
145C2×C4×Dic61—21no—
146C2×C4×Dic61C2311yescharacteristic
147#14519709C2314yes—
148#14519709C2314yes—
149#14519708C2314yes—
150#14519708C2314yes—
151C4⋊#92418C2314yes—
152#14519706C2314yes—
153#14519706C2314yes—
154#14519701C2314yes—
155#14519701C2314yes—
156#14519701C2314yes—
157#14519699C2314yes—
158#14519699C2314yes—
159#14519698C2314yes—
160C22×Q8×C61C2311yescharacteristic
161C22×Q8×C61C2311yescharacteristic
162C22×D4×C61C2311yescharacteristic
163C2×Q16×C61—42no—
164C2×Q16×C61C2314yes—
165C2×SD16×C61—42no—
166C2×SD16×C61C2314yes—
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169#124×C61—22no—
170#124×C61C2314yes—
171C4×Q8×C61—22no—
172C4×Q8×C61C2314yes—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177C2×C42×C61—21no—
178C2×C42×C61C2311yescharacteristic
179C4⋊C8×C61C2314yes—
180#103×C61C2314yes—
181#102×C61C2314yes—
182C24×C61—21no—
183C23×D61—21no—
184C23×D61C2×D411yescharacteristic
185C2×Q8×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61—22no—
188C2×Q8×C61—22no—
189C2×Q8×C61—22no—
190C2×Q8×C61—22no—
191C2×Q8×C61C2412yes—
192C2×Q8×C61C2412yes—
193C2×D4×C61—21no—
194C2×D4×C61—22no—
195C2×D4×C61—22no—
196C2×D4×C61C2412yes—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2411yescharacteristic
203C2×C22⋊D61—24no—
204C2×C22⋊D61—82no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—24no—
209C22×Dic61—82no—
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213C2×D244—22no—
214C2×D244—22no—
215C2×D244—21no—
216C2×D244—24no—
217C2×D244—82no—
218C2×D244C2412yes—
219C2×C4×D61—22no—
220C2×C4×D61—22no—
221C2×C4×D61—24no—
222C2×C4×D61—82no—
223C2×C4×D61C2×D412yes—
224C2×C4×D61C2412yes—
225C2×Dic122—24no—
226C2×Dic122—24no—
227C2×Dic122—82no—
228C2×Dic122—82no—
229Q16×C61—44no—
230SD16×C61—44no—
231C2×C8×C61—22no—
232C2×C8×C61—22no—
233C2×C8×C61C2412yes—
234C2×C8×C61C2412yes—
235C4⋊C4×C61—24no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61C2412yes—
238C22⋊C4×C61—24no—
239C22⋊C4×C61—24no—
240C42×C61—24no—
241C42×C61C2×D412yes—
242C42×C61C2412yes—
243C22⋊Dic61—24no—
244C22⋊Dic61—24no—
245#11758201—44no—
246#11758199—44no—
247#11758198—24no—
248#11758198—24no—
249#11758198—24no—
250#11758198—24no—
251#11758198—24no—
252#11758198—24no—
253#11758198C2×D414yes—
254#11758198C2×D414yes—
255C4⋊Dic61—24no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—24no—
260C4⋊Dic61C2412yes—
261C4⋊Dic61C2412yes—
262C4⋊Dic61C2412yes—
263#11758196—24no—
264#11758196—24no—
265#11758196—24no—
266#11758196C2×D414yes—
267#11758196C2×D414yes—
268C4×Dic61—24no—
269C4×Dic61C2×D412yes—
270C4×Dic61C2412yes—
271C2×#92418—22no—
272C2×#92418—22no—
273C2×#92418C2412yes—
274C2×#92418C2412yes—
275#11758189—44no—
276C8×D61—44no—
277C23×C61—22no—
278C23×C61—42no—
279C23×C61—42no—
280C23×C61—42no—
281C23×C61C22×D411yescharacteristic
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—42no—
287C22×D61—42no—
288C22×D61—42no—
289C22×D61C22×D412yes—
290Q8×C61—22no—
291Q8×C61—22no—
292Q8×C61—22no—
293Q8×C61—22no—
294Q8×C61—42no—
295Q8×C61—42no—
296D4×C61—22no—
297D4×C61—22no—
298D4×C61—42no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61C22×D412yes—
308C2×C4×C61C22×D412yes—
309C2×C4×C61C22×D411yescharacteristic
310C2×C4×C61H(5,𝔽2)12yes—
311C2×C4×C612−1+412yes—
312C2×C4×C61C2511yescharacteristic
313C22⋊D61—84no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—84no—
324C2×Dic61C22×D412yes—
325C2×Dic61C22×D412yes—
326C2×Dic61C22×D412yes—
327D244—22no—
328D244—22no—
329D244—42no—
330D244—84no—
331C4×D61—24no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—84no—
335Dic122—84no—
336Dic122—84no—
337C8×C61—22no—
338C8×C61—22no—
339#92418—22no—
340#92418—22no—
341C2×#3263—611nomaximal, Sylow
342C22×C61—42no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—84no—
346C22×C61#53712yes—
347C22×C61#57712yes—
348C22×C61#57712yes—
349C22×C61C23×D411yescharacteristic
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—44no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—84no—
358C4×C61—22no—
359C4×C61—22no—
360C4×C61—42no—
361C4×C61—42no—
362C4×C61—42no—
363C4×C61#53712yes—
364C4×C61C2×H(5,𝔽2)11yescharacteristic
365C4×C61C2×2−1+411yescharacteristic
366Dic61—22no—
367Dic61—22no—
368Dic61—22no—
369Dic61—42no—
370Dic61—42no—
371Dic61—42no—
372C2×#542—611no—
373C2×#542—611no—
374#3263—6116no—
375C2×#475—611no—
376C2×#475—611no—
377C2×#476—611no—
378C2×#476—611no—
379C2×#470—611no—
380C2×#469—611no—
381C2×#465—611no—
382C2×#465—611no—
383C2×#464—611no—
384C2×#464D6111yescharacteristic, complemented
385C2×#463—611no—
386C2×#463—611no—
387C2×#424—611no—
388C2×C61—82no—
389C2×C61#326314yescomplemented
390C2×C61C2×#53711yescharacteristic
391C2×C61C2×#57711yescharacteristic
392C2×C61C2×#57711yescharacteristic
393D61—42no—
394D61—82no—
395C22×Q16C2×D6111yescharacteristic
396C22×SD16—611no—
397C22×SD16C2×D6111yescharacteristic
398C22×D8—611no—
399C22×M16—611no—
400C23×C8—611no—
401#542—618no—
402#542—618no—
403#542—1224no—
404#542—1224no—
405C2×C4⋊Q8—611no—
406C2×C4⋊Q8—611no—
407C2×#126—1221no—
408C2×#126—1221no—
409C2×#124—611no—
410C2×#124—1221no—
411C2×#124—1221no—
412C2×#124C2×D6111yescharacteristic
413C2×#123—1221no—
414C2×#123—1221no—
415C2×C22⋊Q8—611no—
416C2×C22⋊Q8—611no—
417C2×C22⋊Q8—1221no—
418C2×C22⋊Q8—1221no—
419C2×#121—611no—
420C2×#121—611no—
421C2×C4×Q8—611no—
422C2×C4×Q8C2×D6111yescharacteristic
423C2×C4×D4—611no—
424C2×C4×D4—611no—
425C2×#117—611no—
426#476—618no—
427#476—618no—
428#475—618no—
429#475—618no—
430#470—618no—
431#469—618no—
432#465—618no—
433#465—618no—
434#464—618no—
435#464C2×D6118yescomplemented
436#463—618no—
437#463—618no—
438C2×#106—611no—
439C2×#106—611no—
440C2×#106—611no—
441C2×#106—611no—
442#424—618no—
443C2×C4⋊C8—611no—
444C2×C4⋊C8—611no—
445C2×C4⋊C8—611no—
446C2×C4⋊C8C2×D6111yescharacteristic
447C2×#103—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#103C2×D6111yescharacteristic
451C2×#102—611no—
452C2×#102—611no—
453C2×#102—611no—
454C2×#102C2×D6111yescharacteristic
455C61C2×#326311yescharacteristic, complemented, Sylow
456C22×Q8—1221no—
457C22×Q8—1221no—
458C22×Q8C22×D6111yescharacteristic
459C22×Q8C22×D6111yescharacteristic
460C22×D4—611no—
461C22×D4—1221no—
462C22×D4—1221no—
463C22×D4C22×D6111yescharacteristic
464C23×C4—611no—
465C23×C4—1221no—
466C23×C4—1221no—
467C2×Q16—42no—
468C2×Q16C22×D6114yes—
469C2×SD16—42no—
470C2×SD16—614no—
471C2×SD16—2442no—
472C2×SD16C22×D6114yes—
473C2×D8—614no—
474C2×D8—2442no—
475C2×M16—614no—
476C2×M16—2442no—
477C22×C8—611no—
478C22×C8—611no—
479C22×C8—614no—
480C22×C8—2442no—
481C22×C8C22×D6111yescharacteristic
482C22×C8C22×D6111yescharacteristic
483C4⋊Q8—614no—
484C4⋊Q8—614no—
485C4⋊Q8—1222no—
486C4⋊Q8—1222no—
487#126—1228no—
488#126—1228no—
489#124—22no—
490#124—614no—
491#124—1228no—
492#124—1222no—
493#124—1228no—
494#124C22×D6114yes—
495#123—1228no—
496#123—1228no—
497C22⋊Q8—614no—
498C22⋊Q8—614no—
499C22⋊Q8—1228no—
500C22⋊Q8—1228no—
501C22⋊Q8—1222no—
502C22⋊Q8—1222no—
503#121—614no—
504#121—614no—
505#121—1222no—
506#121—1222no—
507C4×Q8—22no—
508C4×Q8—614no—
509C4×Q8—1222no—
510C4×Q8C22×D6114yes—
511C4×D4—614no—
512C4×D4—614no—
513C4×D4—1222no—
514C4×D4—1222no—
515#117—614no—
516#117—614no—
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⋊C4C22×D6111yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—611no—
532C2×C22⋊C4—611no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C42—21no—
542C2×C42—611no—
543C2×C42—1221no—
544C2×C42C22×D6111yescharacteristic
545#106—614no—
546#106—614no—
547#106—614no—
548#106—614no—
549C4⋊C8—614no—
550C4⋊C8—614no—
551C4⋊C8—614no—
552C4⋊C8C22×D6114yes—
553#103—614no—
554#103—614no—
555#103—614no—
556#103C22×D6114yes—
557#102—614no—
558#102—614no—
559#102—614no—
560#102C22×D6114yes—
561C24—21no—
562C24—611no—
563C24—1221no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—1224no—
571C2×Q8—1224no—
572C2×Q8—4882no—
573C2×Q8—4882no—
574C2×Q8C23×D6112yes—
575C2×Q8C23×D6112yes—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—612no—
580C2×D4—1224no—
581C2×D4—1224no—
582C2×D4—1221no—
583C2×D4—1222no—
584C2×D4—1222no—
585C2×D4—4882no—
586C2×D4—4882no—
587C2×D4C23×D6112yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—612no—
595C22×C4—612no—
596C22×C4—1224no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1224no—
603C22×C4—4882no—
604C22×C4—4882no—
605C22×C4D4×D6111yescharacteristic
606C22×C4D4×D6111yescharacteristic
607C22×C4C23×D6111yescharacteristic
608Q16—44no—
609SD16—44no—
610SD16—2444no—
611D8—2444no—
612M16—2444no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—612no—
616C2×C8—612no—
617C2×C8—1222no—
618C2×C8—1222no—
619C2×C8—2444no—
620C2×C8C23×D6112yes—
621C2×C8C23×D6112yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—614no—
625C4⋊C4—614no—
626C4⋊C4—612no—
627C4⋊C4—612no—
628C4⋊C4—612no—
629C4⋊C4—1224no—
630C4⋊C4—1224no—
631C4⋊C4—1224no—
632C4⋊C4—1224no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—1224no—
637C4⋊C4C23×D6112yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—614no—
641C22⋊C4—614no—
642C22⋊C4—1224no—
643C22⋊C4—1224no—
644C22⋊C4—1224no—
645C22⋊C4—1224no—
646C22⋊C4—1224no—
647C22⋊C4—1224no—
648C22⋊C4—1224no—
649C22⋊C4—1224no—
650C42—24no—
651C42—612no—
652C42—612no—
653C42—1224no—
654C42D4×D6112yes—
655C42C23×D6112yes—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—612no—
661C23—1222no—
662C23—1222no—
663C23—1222no—
664C23—1222no—
665C23—2442no—
666C23—2442no—
667C23—2442no—
668C23C2×D4×D6111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—42no—
674Q8—42no—
675Q8—4884no—
676Q8—4884no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—1222no—
681D4—1222no—
682D4—4884no—
683D4—4884no—
684D4—2442no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—612no—
694C2×C4—612no—
695C2×C4—612no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1224no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—4884no—
706C2×C4—4884no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4—2442no—
710C2×C4C2×D4×D6112yes—
711C2×C4C2×D4×D6112yes—
712C2×C4C2×D4×D6111yescharacteristic
713C2×C4#1451982212yes—
714C2×C4#1451982412yes—
715C2×C4C24×D6111yescharacteristic
716C8—22no—
717C8—22no—
718C8—1222no—
719C8—1222no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—84no—
724C22—1222no—
725C22—1222no—
726C22—1222no—
727C22—4884no—
728C22—2442no—
729C22—2442no—
730C22—2442no—
731C22—2444no—
732C22#1684034112yes—
733C22#1684056912yes—
734C22#1684057112yes—
735C22C22×D4×D6111yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—1222no—
742C4—1222no—
743C4—1222no—
744C4—2442no—
745C4—2442no—
746C4—2442no—
747C4#1684034112yes—
748C4C2×#1451982211yescharacteristic
749C4C2×#1451982411yescharacteristic
750C2—82no—
751C2—4882no—
752C2—2442no—
753C2#2145728714yesdirect product factor
754C2C2×#1684034111yescharacteristic
755C2C2×#1684056911yescharacteristic
756C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#464C2
socleC23×C61C22×D4
prime radicalC2×#16840014C2
hypercenterC2×#464D61
hypocenterC61C2×#3263
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#16840384C2semidirect
2. C2×#16840381C2semidirect
3. #21457287C2direct (N × H)
4. C2×#16840047C2semidirect
5. C2×#16840045C2semidirect
6. C2×#16840053C2semidirect
7. C2×#16840050C2semidirect
8. C2×#16840017C2semidirect
10. C2×#16839994C2semidirect
11. C2×#16839988C2semidirect
12. C2×#16839986C2semidirect
13. C2×#16839979C2semidirect
14. C2×#16839974C2semidirect
15. C2×#16839787C2semidirect
16. C2×C61×#464C2semidirect
22. #16840384C22semidirect
24. #16840381C22semidirect
44. #16840053C22semidirect
45. #16840050C22semidirect
46. #16840047C22semidirect
47. #16840045C22semidirect
48. #16840017C22semidirect
50. #16839994C22semidirect
51. #16839988C22semidirect
52. #16839986C22semidirect
53. #16839979C22semidirect
54. #16839974C22semidirect
59. #16839787C22semidirect
73. C61×#464C22semidirect
384. C2×#464D61semidirect
389. C2×C61#3263semidirect
435. #464C2×D61semidirect
455. C61C2×#3263semidirect
753. C2#21457287direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403842
C2×#168403812
#214572872
C2×#168400472
C2×#168400452
C2×#168400532
C2×#168400502
C2×#168400172
C2×#168400142
C2×#168399942
C2×#168399882
C2×#168399862
C2×#168399792
C2×#168399742
C2×#168397872
C2×C61×#4642
C2×#326361