Finite Group Databasebeta

← C2×#21458258 #30558543

Subgroups — C2×#21458258 #30558543

Order 15616.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840450C211yesmaximal, characteristic, complemented
2C2×#16840415C211yesmaximal, characteristic
3#21458258C2116yesmaximal, direct product factor
4C2×#16840099C211yesmaximal, characteristic, complemented
5C2×#16840088C211yesmaximal, characteristic, complemented
6C2×#16840094C211yesmaximal, characteristic, complemented
7C2×#16840077C211yesmaximal, characteristic, complemented
8C2×#16840054C211yesmaximal, characteristic, complemented
9C2×#16840059C211yesmaximal, characteristic, complemented
10C2×#16840009C211yesmaximal, characteristic, complemented
11C2×#16839992C211yesmaximal, characteristic, complemented
12C2×#16839864C211yesmaximal, characteristic, complemented
13C2×#16839835C211yesmaximal, characteristic, complemented
14C2×#16839801C211yesmaximal, characteristic, complemented
15C2×#107×D61C211yesmaximal, characteristic, complemented
16C2×C61×#501C211yesmaximal, characteristic, complemented
17C22×#11758226—21no—
18C22×#11758190C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21#16840450—24no—
22#16840450C2218yescomplemented
23#16840415—24no—
24#16840415C2218yes—
25C2×#14519772—21no—
26C2×#14519768—21no—
27C2×#14519762—21no—
28C2×#14519762—21no—
29C2×#14519762—21no—
30C2×#14519757C2211yescharacteristic
31C2×#14519757C2211yescharacteristic
32C2×#14519753—21no—
33C2×#14519752C2211yescharacteristic
34C2×#14519752C2211yescharacteristic
35C2×C4×Dic122C2211yescharacteristic
36C2×C4×D244C2211yescharacteristic
37C2×C4×D244C2211yescharacteristic
38C2×#14519735—21no—
39C2×#14519735C2211yescharacteristic
40C2×C4⋊C4×D61C2211yescharacteristic
41C2×C4⋊C4×D61C2211yescharacteristic
42C2×C4⋊C4×D61C2211yescharacteristic
43#16840099C2218yescomplemented
44#16840094C2218yescomplemented
45#16840088C2218yescomplemented
46#16840077C2218yescomplemented
47#16840059C2218yescomplemented
48#16840054C2218yescomplemented
49#16840009C2218yescomplemented
50#16839992C2218yescomplemented
51#16839864C2218yescomplemented
52#16839835C2218yescomplemented
53#16839801C2218yescomplemented
54C2×#14519711C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519710C2211yescharacteristic
58#107×D61C2218yescomplemented
59C2×#14519708C2211yescharacteristic
60C2×C4⋊#92418C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C2×C4⋊Q8×C61C2211yescharacteristic
70C2×#125×C61C2211yescharacteristic
71C61×#501C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#107×C61C2211yescharacteristic
74C2×#106×C61C2211yescharacteristic
75C2×#106×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C2×#11758226—28no—
78C2×#11758226—48no—
79C22×Dic122C2311yescharacteristic
80C22×D244—21no—
81C22×D244—21no—
82C22×D244D411yescharacteristic
83C22×D244C2311yescharacteristic
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C22×C4×D61—21no—
88C22×C4×D61C2311yescharacteristic
89C22×C4×D61C2311yescharacteristic
90C2×#11758190—24no—
91C2×#11758190C2314yes—
92C2×#11758189—24no—
93C2×#11758189C2314yes—
94C22×#92418C2311yescharacteristic
95C22×#92418C2311yescharacteristic
96C2×C8×D61—24no—
97C2×C8×D61C2314yes—
98#14519772—28no—
99#14519768—28no—
100#14519762—28no—
101#14519762—28no—
102#14519762—28no—
103#14519757—22no—
104#14519757—22no—
105#14519757C2314yes—
106#14519757C2314yes—
107#14519753—28no—
108#14519752—22no—
109#14519752—22no—
110#14519752C2314yes—
111#14519752C2314yes—
112C4×Dic122—22no—
113C4×Dic122C2314yes—
114C4×D244—22no—
115C4×D244D414yes—
116C4×D244C2314yes—
117C4×D244C2314yes—
118#14519735—22no—
119#14519735—28no—
120#14519735C2314yes—
121C2×C4⋊Dic61—21no—
122C2×C4⋊Dic61—21no—
123C2×C4⋊Dic61D411yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×C4⋊Dic61C2311yescharacteristic
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C4⋊C4×D61—22no—
131C4⋊C4×D61—22no—
132C4⋊C4×D61—22no—
133C4⋊C4×D61C2314yes—
134C4⋊C4×D61C2314yes—
135C4⋊C4×D61C2314yes—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198D411yescharacteristic
143C2×#11758198D411yescharacteristic
144C2×C4×Dic61—21no—
145C2×C4×Dic61—21no—
146#14519711C2314yes—
147#14519710C2314yes—
148#14519710C2314yes—
149#14519710C2314yes—
150#14519708C2314yes—
151C4⋊#92418C2314yes—
152#14519702C2314yes—
153#14519700C2314yes—
154#14519700C2314yes—
155#14519699C2314yes—
156#14519697C2314yes—
157#14519697C2314yes—
158#14519689C2314yes—
159#14519689C2314yes—
160C22×Q8×C61—21no—
161C22×C8×C61C2311yescharacteristic
162C22×C8×C61C2311yescharacteristic
163C4⋊Q8×C61—22no—
164C4⋊Q8×C61C2314yes—
165#125×C61—22no—
166#125×C61C2314yes—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61—21no—
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C42×C61C2311yescharacteristic
175#107×C61C2314yes—
176#107×C61C2314yes—
177#106×C61C2314yes—
178#106×C61C2314yes—
179#97×C61C2314yes—
180C23×D61—21no—
181C23×D61C2×D411yescharacteristic
182C23×D61C2×D411yescharacteristic
183C2×Q8×C61—24no—
184C2×Q8×C61—44no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2411yescharacteristic
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61C2×D411yescharacteristic
196C22×Dic61C2×D411yescharacteristic
197#11758226—432no—
198C2×D244—24no—
199C2×D244—22no—
200C2×D244—22no—
201C2×D244—24no—
202C2×D244—24no—
203C2×D244—21no—
204C2×D244—44no—
205C2×D244—44no—
206C2×D244C2×D414yes—
207C2×D244C2412yes—
208C2×C4×D61—22no—
209C2×C4×D61—22no—
210C2×C4×D61—22no—
211C2×C4×D61—22no—
212C2×C4×D61—24no—
213C2×C4×D61—24no—
214C2×C4×D61—24no—
215C2×C4×D61—24no—
216C2×C4×D61—44no—
217C2×C4×D61—44no—
218C2×C4×D61—44no—
219C2×C4×D61—44no—
220C2×C4×D61C2×D412yes—
221C2×C4×D61C2×D412yes—
222C2×C4×D61C2412yes—
223C2×C4×D61C2412yes—
224C2×Dic122—22no—
225C2×Dic122—22no—
226C2×Dic122—21no—
227C2×Dic122C2412yes—
228C2×C8×C61—22no—
229C2×C8×C61#4114yescomplemented
230C2×C8×C61C2412yes—
231C2×C8×C61C2412yes—
232C4⋊C4×C61—24no—
233C4⋊C4×C61—24no—
234C4⋊C4×C61—24no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61C2412yes—
240C4⋊C4×C61C2412yes—
241C4⋊C4×C61C2412yes—
242C4⋊C4×C61C2412yes—
243C42×C61C2×D412yes—
244C42×C61C2412yes—
245#11758198—24no—
246#11758198—24no—
247#11758198—24no—
248#11758198—24no—
249#11758198—24no—
250#11758198—24no—
251#11758198C2×D414yes—
252#11758198C2×D414yes—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
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—
264C4×Dic61—24no—
265C4×Dic61—24no—
266C2×#92418—22no—
267C2×#92418—22no—
268C2×#92418C2412yes—
269C2×#92418C2412yes—
270#11758190—28no—
271#11758189—28no—
272C8×D61—28no—
273C23×C61C22×D411yescharacteristic
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—42no—
281C22×D61—42no—
282C22×D61—42no—
283C22×D61AGL(1,ℤ/8)14yes—
284C22×D61C22×D412yes—
285C22×D61C22×D412yes—
286Q8×C61—48no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61C22×D412yes—
298C2×C4×C61C22×D412yes—
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C2×#4112yes—
301C2×C4×C612−1+412yes—
302C2×C4×C61C2511yescharacteristic
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61C22×D412yes—
312C2×Dic61C22×D412yes—
313D244—28no—
314D244—22no—
315D244—22no—
316D244—48no—
317D244—48no—
318D244—42no—
319C4×D61—24no—
320C4×D61—24no—
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—48no—
326C4×D61—48no—
327C4×D61—48no—
328C4×D61—48no—
329Dic122—22no—
330Dic122—22no—
331Dic122—42no—
332C8×C61—22no—
333C8×C61C2×#4114yescomplemented
334#92418—22no—
335#92418—22no—
336C2×#3343—611nomaximal, Sylow
337C22×C61#54712yes—
338C22×C61C2×AGL(1,ℤ/8)12yes—
339C22×C61#57812yes—
340C22×C61C23×D411yescharacteristic
341C2×D61—28no—
342C2×D61—22no—
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—22no—
347C2×D61—44no—
348C2×D61—42no—
349C2×D61—42no—
350C2×D61—42no—
351C2×D61—84no—
352C2×D61C2×AGL(1,ℤ/8)14yes—
353C4×C61—22no—
354C4×C61—22no—
355C4×C61—42no—
356C4×C61—42no—
357C4×C61—42no—
358C4×C61—42no—
359C4×C61#54712yes—
360C4×C61C22×#4111yescharacteristic
361C4×C61C2×2−1+411yescharacteristic
362Dic61—22no—
363Dic61—22no—
364Dic61—42no—
365Dic61—42no—
366Dic61—42no—
367C2×#552—611no—
368C2×#547—611no—
369#3343—6116no—
370C2×#501D6111yescharacteristic, complemented
371C2×#484—611no—
372C2×#482—611no—
373C2×#483—611no—
374C2×#480—611no—
375C2×#477—611no—
376C2×#478—611no—
377C2×#468—611no—
378C2×#465—611no—
379C2×#440—611no—
380C2×#435—611no—
381C2×#428—611no—
382C22×#107—611no—
383C2×C61#334314yescomplemented
384C2×C61C2×#54711yescharacteristic
385C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
386C2×C61C2×#57811yescharacteristic
387D61—24no—
388D61—42no—
389D61—82no—
390C22×#41—1221no—
391C22×SD16—611no—
392C22×M16—611no—
393C23×C8—611no—
394#552—618no—
395#552—1224no—
396#547—618no—
397#547—1224no—
398C2×C4⋊Q8C2×D6111yescharacteristic
399C2×#126—1221no—
400C2×#125—1221no—
401C2×#125C2×D6111yescharacteristic
402C2×#123—1221no—
403C2×#123—1221no—
404C2×#123—1221no—
405C2×C22⋊Q8—611no—
406C2×C22⋊Q8—611no—
407C2×C22⋊Q8—1221no—
408C2×#121—611no—
409C2×#121—611no—
410C2×C4×Q8—611no—
411C2×C4×D4—611no—
412C2×C4×D4—611no—
413C2×#117—611no—
414C2×#117—1221no—
415C22×C4⋊C4—611no—
416C22×C4⋊C4—611no—
417C22×C4⋊C4—611no—
418#501C2×D6118yescomplemented
419#484—618no—
420#483—618no—
421#482—618no—
422#480—618no—
423#478—618no—
424#477—618no—
425#468—618no—
426#465—618no—
427#440—618no—
428#435—618no—
429#428—618no—
430C2×#107—611no—
431C2×#107—611no—
432C2×#107—611no—
433C2×#107—611no—
434C2×#107—618no—
435C2×#107C2×D6111yescharacteristic
436C2×#107C2×D6111yescharacteristic
437C2×#106—611no—
438C2×#106C2×D6111yescharacteristic
439C2×#106C2×D6111yescharacteristic
440C2×C4⋊C8—611no—
441C2×#103—611no—
442C2×#103—611no—
443C2×#103—611no—
444C2×#102—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×C22⋊C8—611no—
448C2×C22⋊C8—611no—
449C2×#97C2×D6111yescharacteristic
450C61C2×#334311yescharacteristic, complemented, Sylow
451C2×#41—1228no—
452C2×#41—2448no—
453C22×Q8—21no—
454C22×Q8—611no—
455C22×D4—611no—
456C22×D4—611no—
457C22×D4—1221no—
458C22×D4—1221no—
459C23×C4—611no—
460C23×C4—611no—
461C23×C4—1221no—
462C23×C4—1221no—
463C23×C4—1221no—
464C23×C4—1221no—
465C2×SD16—614no—
466C2×SD16—1224no—
467C2×M16—614no—
468C2×M16—1224no—
469C22×C8—611no—
470C22×C8—611no—
471C22×C8—614no—
472C22×C8—1224no—
473C22×C8C22×D6111yescharacteristic
474C22×C8C22×D6111yescharacteristic
475C4⋊Q8—22no—
476C4⋊Q8C22×D6114yes—
477#126—1228no—
478#125—22no—
479#125—1228no—
480#125C22×D6114yes—
481#123—1228no—
482#123—1228no—
483#123—1228no—
484C22⋊Q8—614no—
485C22⋊Q8—614no—
486C22⋊Q8—1222no—
487C22⋊Q8—1222no—
488C22⋊Q8—1228no—
489#121—614no—
490#121—614no—
491#121—1222no—
492#121—1222no—
493C4×Q8—614no—
494C4×Q8—1222no—
495C4×D4—614no—
496C4×D4—614no—
497C4×D4—614no—
498C4×D4—1222no—
499#117—614no—
500#117—1228no—
501#117—1222no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—614no—
509C2×C4⋊C4—614no—
510C2×C4⋊C4—614no—
511C2×C4⋊C4—1222no—
512C2×C4⋊C4—1222no—
513C2×C4⋊C4—1222no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4C22×D6111yescharacteristic
521C2×C4⋊C4C22×D6111yescharacteristic
522C2×C4⋊C4C22×D6111yescharacteristic
523C2×C4⋊C4C22×D6111yescharacteristic
524C2×C22⋊C4—611no—
525C2×C22⋊C4—611no—
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×C42—1221no—
533C2×C42—1221no—
534C2×C42C22×D6111yescharacteristic
535#107—614no—
536#107—614no—
537#107—614no—
538#107—614no—
539#107C22×D6114yes—
540#107C22×D6114yes—
541#106—614no—
542#106C22×D6114yes—
543#106C22×D6114yes—
544C4⋊C8—614no—
545#103—614no—
546#103—614no—
547#103—614no—
548#102—614no—
549#102—614no—
550#102—614no—
551C22⋊C8—614no—
552C22⋊C8—614no—
553#97C22×D6114yes—
554C24—611no—
555C24—611no—
556C24—1221no—
557#41—24432no—
558C2×Q8—24no—
559C2×Q8—44no—
560C2×Q8—612no—
561C2×Q8—1221no—
562C2×Q8—1222no—
563C2×Q8—1222no—
564C2×D4—614no—
565C2×D4—612no—
566C2×D4—1224no—
567C2×D4—1224no—
568C2×D4—1224no—
569C2×D4—1221no—
570C2×D4—1222no—
571C2×D4—1222no—
572C2×D4—2444no—
573C2×D4—2444no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—612no—
581C22×C4—612no—
582C22×C4—612no—
583C22×C4—612no—
584C22×C4—1224no—
585C22×C4—1224no—
586C22×C4—1224no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1224no—
595C22×C4—2444no—
596C22×C4—2444no—
597C22×C4—2444no—
598C22×C4—2444no—
599C22×C4D4×D6111yescharacteristic
600C22×C4D4×D6111yescharacteristic
601C22×C4C23×D6111yescharacteristic
602SD16—1228no—
603M16—1228no—
604C2×C8—22no—
605C2×C8—612no—
606C2×C8—612no—
607C2×C8—1222no—
608C2×C8—1222no—
609C2×C8—1228no—
610C2×C8#1175822614yescomplemented
611C2×C8C23×D6112yes—
612C2×C8C23×D6112yes—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—614no—
621C4⋊C4—612no—
622C4⋊C4—612no—
623C4⋊C4—1224no—
624C4⋊C4—1224no—
625C4⋊C4—1224no—
626C4⋊C4—1224no—
627C4⋊C4—1224no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—1224no—
631C4⋊C4C23×D6112yes—
632C4⋊C4C23×D6112yes—
633C4⋊C4C23×D6112yes—
634C4⋊C4C23×D6112yes—
635C22⋊C4—614no—
636C22⋊C4—614no—
637C22⋊C4—1224no—
638C22⋊C4—1224no—
639C22⋊C4—1224no—
640C22⋊C4—1224no—
641C22⋊C4—1224no—
642C22⋊C4—1224no—
643C42—1224no—
644C42—1224no—
645C42D4×D6112yes—
646C42C23×D6112yes—
647C23—614no—
648C23—612no—
649C23—612no—
650C23—1222no—
651C23—1222no—
652C23—1222no—
653C23—1222no—
654C23—1222no—
655C23—1222no—
656C23—2442no—
657C23—2442no—
658C23—2442no—
659C23C2×D4×D6111yescharacteristic
660Q8—48no—
661Q8—1222no—
662Q8—1222no—
663Q8—2442no—
664D4—1228no—
665D4—1222no—
666D4—1222no—
667D4—2448no—
668D4—2448no—
669D4—2442no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—612no—
681C2×C4—612no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1224no—
689C2×C4—1224no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—2448no—
694C2×C4—2448no—
695C2×C4—2448no—
696C2×C4—2448no—
697C2×C4—2442no—
698C2×C4—2442no—
699C2×C4—2442no—
700C2×C4C2×D4×D6112yes—
701C2×C4C2×D4×D6112yes—
702C2×C4C2×D4×D6111yescharacteristic
703C2×C4C2×#1175822612yes—
704C2×C4#1451982512yes—
705C2×C4C24×D6111yescharacteristic
706C8—22no—
707C8—1222no—
708C8—1222no—
709C8C2×#1175822614yescomplemented
710C22—614no—
711C22—1222no—
712C22—1228no—
713C22—1222no—
714C22—1222no—
715C22—1222no—
716C22—1222no—
717C22—4884no—
718C22—2442no—
719C22—2442no—
720C22—2442no—
721C22—2444no—
722C22#1684041512yes—
723C22AGL(1,ℤ/8)×D6112yes—
724C22#1684057812yes—
725C22C22×D4×D6111yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—42no—
732C4—1222no—
733C4—1222no—
734C4—2442no—
735C4—2442no—
736C4—2442no—
737C4#1684041512yes—
738C4C22×#1175822611yescharacteristic
739C4C2×#1451982511yescharacteristic
740C2—1224no—
741C2—4882no—
742C2—2442no—
743C2#2145825814yesdirect product factor
744C2C2×#1684041511yescharacteristic
745C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
746C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#501C2
socleC23×C61C22×D4
prime radicalC2×#16840415C2
hypercenterC2×#501D61
hypocenterC61C2×#3343
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#16840450C2semidirect
3. #21458258C2direct (N × H)
4. C2×#16840099C2semidirect
5. C2×#16840088C2semidirect
6. C2×#16840094C2semidirect
7. C2×#16840077C2semidirect
8. C2×#16840054C2semidirect
9. C2×#16840059C2semidirect
10. C2×#16840009C2semidirect
11. C2×#16839992C2semidirect
12. C2×#16839864C2semidirect
13. C2×#16839835C2semidirect
14. C2×#16839801C2semidirect
15. C2×#107×D61C2semidirect
16. C2×C61×#501C2semidirect
22. #16840450C22semidirect
43. #16840099C22semidirect
44. #16840094C22semidirect
45. #16840088C22semidirect
46. #16840077C22semidirect
47. #16840059C22semidirect
48. #16840054C22semidirect
49. #16840009C22semidirect
50. #16839992C22semidirect
51. #16839864C22semidirect
52. #16839835C22semidirect
53. #16839801C22semidirect
58. #107×D61C22semidirect
71. C61×#501C22semidirect
229. C2×C8×C61#41semidirect
333. C8×C61C2×#41semidirect
370. C2×#501D61semidirect
383. C2×C61#3343semidirect
418. #501C2×D61semidirect
450. C61C2×#3343semidirect
610. C2×C8#11758226semidirect
709. C8C2×#11758226semidirect
743. C2#21458258direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404502
C2×#168404152
#214582582
C2×#168400992
C2×#168400882
C2×#168400942
C2×#168400772
C2×#168400542
C2×#168400592
C2×#168400092
C2×#168399922
C2×#168398642
C2×#168398352
C2×#168398012
C2×#107×D612
C2×C61×#5012
C2×#334361