Finite Group Databasebeta

← C2×#21458289 #30558576

Subgroups — C2×#21458289 #30558576

Order 15616.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840458C211yesmaximal, characteristic, complemented
2#21458289C2116yesmaximal, direct product factor
3C2×#16840168C211yesmaximal, characteristic, complemented
4C2×#16840080C211yesmaximal, characteristic, complemented
5C2×#16840078C211yesmaximal, characteristic, complemented
6C2×#16840083C211yesmaximal, characteristic, complemented
7C2×#16840075C211yesmaximal, characteristic, complemented
8C2×#16840062C211yesmaximal, characteristic, complemented
9C2×#16840049C211yesmaximal, characteristic, complemented
10C2×#16840013C211yesmaximal, characteristic, complemented
11C2×#16839996C211yesmaximal, characteristic, complemented
12C2×#16839872C211yesmaximal, characteristic, complemented
13C2×#16839834C211yesmaximal, characteristic, complemented
14C2×#16839802C211yesmaximal, characteristic, complemented
15C22×#14519708C211yesmaximal, characteristic, complemented
16C2×C61×#547C211yesmaximal, characteristic, complemented
17C22×#11758199C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20#16840458—24no—
21#16840458C2218yescomplemented
22C2×#14519772—21no—
23C2×#14519769C2211yescharacteristic
24C2×#14519759—21no—
25C2×#14519751C2211yescharacteristic
26C2×#14519751C2211yescharacteristic
27C2×#14519749—21no—
28C2×C4×D244C2211yescharacteristic
29C2×#14519737—21no—
30C2×#14519736C2211yescharacteristic
31C22×C4⋊Dic61C2211yescharacteristic
32#16840168C2218yescomplemented
33#16840083C2218yescomplemented
34#16840080C2218yescomplemented
35#16840078C2218yescomplemented
36#16840075C2218yescomplemented
37#16840062C2218yescomplemented
38#16840049C2218yescomplemented
39#16840013C2218yescomplemented
40#16839996C2218yescomplemented
41#16839872C2218yescomplemented
42#16839834C2218yescomplemented
43#16839802C2218yescomplemented
44C2×#14519710C2211yescharacteristic
45C2×#14519710C2211yescharacteristic
46C2×#14519710C2211yescharacteristic
47C2×#14519708C2211yescharacteristic
48C2×#14519708C2211yescharacteristic
49C2×#14519708C2211yescharacteristic
50C2×#14519708C2211yescharacteristic
51C2×#14519708C2211yescharacteristic
52C2×#14519708C2211yescharacteristic
53C2×#14519708C2218yescomplemented
54C2×C4⋊#92418C2211yescharacteristic
55C2×#14519698C2211yescharacteristic
56C2×#14519698C2211yescharacteristic
57C2×#14519698C2211yescharacteristic
58C2×#14519697C2211yescharacteristic
59C2×#14519697C2211yescharacteristic
60C2×#14519697C2211yescharacteristic
61C2×C22⋊#92418C2211yescharacteristic
62C2×C22⋊#92418C2211yescharacteristic
63C2×#14519688C2211yescharacteristic
64C22×#41×C61—21no—
65C61×#547—24no—
66C61×#547C2218yescomplemented
67C2×C4⋊Q8×C61C2211yescharacteristic
68C2×#123×C61—21no—
69C2×#123×C61—21no—
70C2×C22⋊Q8×C61—21no—
71C2×#121×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C2×C4×D4×C61C2211yescharacteristic
74C2×C4×D4×C61C2211yescharacteristic
75C22×C4⋊C4×C61C2211yescharacteristic
76C22×C4⋊C4×C61C2211yescharacteristic
77C22×D244C2311yescharacteristic
78C22×C22⋊D61—21no—
79C22×C22⋊D61—21no—
80C23×Dic61—21no—
81C22×C4×D61—21no—
82C2×#11758199—24no—
83C2×#11758199C2314yes—
84C2×#11758194—24no—
85C2×#11758194C2314yes—
86C22×#92418—24no—
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C22×#92418C2314yes—
91C22×#92418C2311yescharacteristic
92#14519772—28no—
93#14519769—22no—
94#14519769C2314yes—
95#14519759—28no—
96#14519751—22no—
97#14519751—22no—
98#14519751C2314yes—
99#14519751C2314yes—
100#14519749—28no—
101C4×D244—22no—
102C4×D244C2314yes—
103#14519737—28no—
104#14519736—22no—
105#14519736C2314yes—
106C2×C4⋊Dic61—22no—
107C2×C4⋊Dic61—21no—
108C2×C4⋊Dic61C2314yes—
109C2×C4⋊Dic61C2311yescharacteristic
110C2×C4⋊Dic61C2311yescharacteristic
111C2×C4⋊Dic61C2311yescharacteristic
112C2×#11758196—21no—
113C2×#11758196—21no—
114C2×C22⋊Dic61—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×C4×Dic61—21no—
119#14519710C2314yes—
120#14519710C2314yes—
121#14519710C2314yes—
122#14519708C2314yes—
123#14519708C2314yes—
124#14519708C2314yes—
125#14519708C2314yes—
126#14519708C2314yes—
127#14519708C2314yes—
128C4⋊#92418C2314yes—
129#14519698C2314yes—
130#14519698C2314yes—
131#14519698C2314yes—
132#14519697C2314yes—
133#14519697C2314yes—
134#14519697C2314yes—
135C22⋊#92418C2314yes—
136C22⋊#92418C2314yes—
137#14519688C2314yes—
138C2×#41×C61—28no—
139C2×#41×C61—48no—
140C22×Q8×C61—21no—
141C22×D4×C61—21no—
142C22×D4×C61—21no—
143C22×D4×C61D411yescharacteristic
144C22×D4×C61C2311yescharacteristic
145C23×C4×C61—21no—
146C23×C4×C61—21no—
147C23×C4×C61—21no—
148C23×C4×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C4⋊Q8×C61—22no—
151C4⋊Q8×C61C2314yes—
152#123×C61—28no—
153#123×C61—28no—
154C22⋊Q8×C61—28no—
155#121×C61—22no—
156#121×C61—22no—
157#121×C61C2314yes—
158#121×C61C2314yes—
159C4×D4×C61—22no—
160C4×D4×C61D414yes—
161C4×D4×C61C2314yes—
162C4×D4×C61C2314yes—
163C2×C4⋊C4×C61—21no—
164C2×C4⋊C4×C61—22no—
165C2×C4⋊C4×C61—22no—
166C2×C4⋊C4×C61—21no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61D411yescharacteristic
169C2×C4⋊C4×C61C2311yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2314yes—
172C2×C4⋊C4×C61C2314yes—
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177C2×C22⋊C4×C61D411yescharacteristic
178C2×C22⋊C4×C61D411yescharacteristic
179C2×C42×C61C2311yescharacteristic
180C24×C61—21no—
181C24×C61C2×D411yescharacteristic
182C24×C61C2×D411yescharacteristic
183C23×D61—21no—
184#41×C61—432no—
185C2×Q8×C61—24no—
186C2×Q8×C61—44no—
187C2×D4×C61—24no—
188C2×D4×C61—24no—
189C2×D4×C61—24no—
190C2×D4×C61—21no—
191C2×D4×C61—22no—
192C2×D4×C61—22no—
193C2×D4×C61—44no—
194C2×D4×C61—44no—
195C2×D4×C61C2×D414yes—
196C2×D4×C61C2412yes—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—22no—
200C22×C4×C61—22no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—24no—
205C22×C4×C61—24no—
206C22×C4×C61—24no—
207C22×C4×C61—44no—
208C22×C4×C61—44no—
209C22×C4×C61—44no—
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D412yes—
215C22×C4×C61C2×D412yes—
216C22×C4×C61C2412yes—
217C22×C4×C61C2412yes—
218C22×C4×C61C2411yescharacteristic
219C2×C22⋊D61—24no—
220C2×C22⋊D61—24no—
221C2×C22⋊D61—44no—
222C2×C22⋊D61—82no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—24no—
227C22×Dic61—82no—
228C2×D244—22no—
229C2×D244—22no—
230C2×D244—21no—
231C2×D244C2412yes—
232C2×C4×D61—24no—
233C2×C4×D61—82no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—24no—
238C4⋊C4×C61—24no—
239C4⋊C4×C61—24no—
240C4⋊C4×C61C2×D414yes—
241C4⋊C4×C61C2412yes—
242C4⋊C4×C61C2412yes—
243C4⋊C4×C61C2412yes—
244C22⋊C4×C61—24no—
245C22⋊C4×C61—24no—
246C22⋊C4×C61—24no—
247C22⋊C4×C61C2×D414yes—
248C22⋊C4×C61C2×D414yes—
249C42×C61C2×D412yes—
250C42×C61C2412yes—
251C22⋊Dic61—24no—
252#11758199—28no—
253#11758198—24no—
254#11758198—24no—
255#11758198—24no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—24no—
259C4⋊Dic61—21no—
260C4⋊Dic61C2412yes—
261C4⋊Dic61C2412yes—
262C4⋊Dic61C2412yes—
263#11758196—24no—
264#11758196—24no—
265C4×Dic61—24no—
266#11758194—28no—
267C2×#92418—22no—
268C2×#92418—22no—
269C2×#92418—22no—
270C2×#92418—28no—
271C2×#92418#4114yescomplemented
272C2×#92418C2412yes—
273C2×#92418C2412yes—
274C2×#92418C2412yes—
275C2×#92418C2412yes—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61—22no—
279C23×C61—22no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—42no—
283C23×C61—42no—
284C23×C61—42no—
285C23×C61AGL(1,ℤ/8)14yes—
286C23×C61C22×D412yes—
287C23×C61C22×D412yes—
288C23×C61C22×D411yescharacteristic
289C22×D61—22no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61—42no—
293Q8×C61—48no—
294D4×C61—28no—
295D4×C61—22no—
296D4×C61—22no—
297D4×C61—48no—
298D4×C61—48no—
299D4×C61—42no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—24no—
305C2×C4×C61—24no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—48no—
314C2×C4×C61—48no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61—48no—
319C2×C4×C61C22×D412yes—
320C2×C4×C61C22×D412yes—
321C2×C4×C61C22×D412yes—
322C2×C4×C61C22×D412yes—
323C2×C4×C61C22×D411yescharacteristic
324C2×C4×C61C2×#4112yes—
325C2×C4×C612−1+412yes—
326C2×C4×C61C2511yescharacteristic
327C22⋊D61—48no—
328C22⋊D61—84no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61—84no—
336D244—22no—
337D244—22no—
338D244—42no—
339C4×D61—84no—
340#92418—22no—
341#92418—22no—
342#92418—22no—
343#92418C2×#4114yescomplemented
344C2×#3345—611nomaximal, Sylow
345C22×C61—28no—
346C22×C61—22no—
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—44no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—84no—
356C22×C61#54712yes—
357C22×C61C2×AGL(1,ℤ/8)14yes—
358C22×C61C2×AGL(1,ℤ/8)12yes—
359C22×C61#57712yes—
360C22×C61C23×D411yescharacteristic
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—84no—
365C4×C61—22no—
366C4×C61—22no—
367C4×C61—22no—
368C4×C61—22no—
369C4×C61—42no—
370C4×C61—42no—
371C4×C61—42no—
372C4×C61#54712yes—
373C4×C61C22×#4111yescharacteristic
374C4×C61C2×2−1+411yescharacteristic
375Dic61—42no—
376Dic61—42no—
377Dic61—42no—
378C2×#553—611no—
379C2×#547D6111yescharacteristic, complemented
380#3345—6116no—
381C2×#501—611no—
382C2×#481—611no—
383C2×#481—611no—
384C2×#482—611no—
385C2×#480—611no—
386C2×#478—611no—
387C2×#476—611no—
388C2×#469—611no—
389C2×#466—611no—
390C2×#442—611no—
391C2×#435—611no—
392C2×#428—611no—
393C22×#106—611no—
394C2×C61—24no—
395C2×C61—42no—
396C2×C61—82no—
397C2×C61#334514yescomplemented
398C2×C61C2×#54711yescharacteristic
399C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
400C2×C61C2×#57711yescharacteristic
401D61—82no—
402C22×#41—21no—
403C22×D8—611no—
404C22×M16—611no—
405C23×C8—611no—
406#553—618no—
407#553—1224no—
408#547—24no—
409#547C2×D6118yescomplemented
410C2×C4⋊Q8C2×D6111yescharacteristic
411C2×#126—1221no—
412C2×#125—611no—
413C2×#123—21no—
414C2×#123—21no—
415C2×#123—1221no—
416C2×C22⋊Q8—21no—
417C2×#121—611no—
418C2×#121—611no—
419C2×#121—1221no—
420C2×#121C2×D6111yescharacteristic
421C2×#121C2×D6111yescharacteristic
422C2×C4×D4—611no—
423C2×C4×D4—1221no—
424C2×C4×D4C2×D6111yescharacteristic
425C2×C4×D4C2×D6111yescharacteristic
426C2×#117—611no—
427C22×C4⋊C4—611no—
428C22×C4⋊C4C2×D6111yescharacteristic
429C22×C4⋊C4C2×D6111yescharacteristic
430#501—618no—
431#482—618no—
432#481—618no—
433#481—618no—
434#480—618no—
435#478—618no—
436#476—618no—
437#469—618no—
438#466—618no—
439#442—618no—
440#435—618no—
441#428—618no—
442C2×#107—611no—
443C2×#107—611no—
444C2×#107—611no—
445C2×#106—611no—
446C2×#106—611no—
447C2×#106—611no—
448C2×#106—611no—
449C2×#106—618no—
450C2×#106—611no—
451C2×#106—611no—
452C2×C4⋊C8—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#102—611no—
456C2×#102—611no—
457C2×#102—611no—
458C2×#102—611no—
459C2×C22⋊C8—611no—
460C2×C22⋊C8—611no—
461C2×#97—611no—
462C61C2×#334511yescharacteristic, complemented, Sylow
463C2×#41—28no—
464C2×#41—48no—
465C22×Q8—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—611no—
469C22×D4—1221no—
470C22×D4—1221no—
471C22×D4C22⋊D6111yescharacteristic
472C22×D4C22×D6111yescharacteristic
473C23×C4—21no—
474C23×C4—21no—
475C23×C4—21no—
476C23×C4—1221no—
477C23×C4—1221no—
478C23×C4C22×D6111yescharacteristic
479C23×C4C22×D6111yescharacteristic
480C2×D8—614no—
481C2×D8—1224no—
482C2×M16—614no—
483C2×M16—1224no—
484C22×C8—611no—
485C22×C8—611no—
486C22×C8—614no—
487C22×C8—611no—
488C22×C8—611no—
489C22×C8—1224no—
490C4⋊Q8—22no—
491C4⋊Q8C22×D6114yes—
492#126—1228no—
493#125—614no—
494#125—1222no—
495#123—28no—
496#123—28no—
497#123—1228no—
498C22⋊Q8—28no—
499#121—22no—
500#121—22no—
501#121—614no—
502#121—614no—
503#121—1228no—
504#121—1222no—
505#121—1222no—
506#121C22×D6114yes—
507#121C22×D6114yes—
508C4×D4—22no—
509C4×D4—614no—
510C4×D4—1228no—
511C4×D4—1222no—
512C4×D4C22⋊D6114yes—
513C4×D4C22×D6114yes—
514C4×D4C22×D6114yes—
515#117—614no—
516#117—1222no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—614no—
525C2×C4⋊C4—611no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1222no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4C22⋊D6111yescharacteristic
531C2×C4⋊C4C22×D6111yescharacteristic
532C2×C4⋊C4C22×D6111yescharacteristic
533C2×C4⋊C4C22×D6111yescharacteristic
534C2×C4⋊C4C22×D6114yes—
535C2×C4⋊C4C22×D6114yes—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4C22⋊D6111yescharacteristic
544C2×C22⋊C4C22⋊D6111yescharacteristic
545C2×C42—1221no—
546C2×C42C22×D6111yescharacteristic
547#107—614no—
548#107—614no—
549#107—614no—
550#106—614no—
551#106—614no—
552#106—614no—
553#106—614no—
554#106—614no—
555#106—614no—
556C4⋊C8—614no—
557#102—614no—
558#102—614no—
559#102—614no—
560#102—614no—
561#102—614no—
562#102—614no—
563C22⋊C8—614no—
564C22⋊C8—614no—
565#97—614no—
566C24—21no—
567C24—1221no—
568C24C2×C22⋊D6111yescharacteristic
569C24C2×C22⋊D6111yescharacteristic
570#41—432no—
571C2×Q8—24no—
572C2×Q8—44no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—44no—
580C2×D4—44no—
581C2×D4—612no—
582C2×D4—1224no—
583C2×D4—1224no—
584C2×D4—1221no—
585C2×D4—1222no—
586C2×D4—1222no—
587C2×D4—4882no—
588C2×D4—2444no—
589C2×D4C2×C22⋊D6114yes—
590C2×D4C23×D6112yes—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—1224no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1224no—
609C22×C4—4882no—
610C22×C4—4882no—
611C22×C4C2×C22⋊D6112yes—
612C22×C4C2×C22⋊D6112yes—
613C22×C4C2×C22⋊D6111yescharacteristic
614C22×C4C2×C22⋊D6111yescharacteristic
615C22×C4C2×C22⋊D6111yescharacteristic
616C22×C4C2×C22⋊D6111yescharacteristic
617C22×C4C23×D6112yes—
618C22×C4C23×D6112yes—
619C22×C4C23×D6111yescharacteristic
620D8—1228no—
621M16—1228no—
622C2×C8—614no—
623C2×C8—612no—
624C2×C8—612no—
625C2×C8—612no—
626C2×C8—612no—
627C2×C8—1228no—
628C2×C8—1222no—
629C2×C8—1222no—
630C2×C8—1222no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—612no—
638C4⋊C4—612no—
639C4⋊C4—612no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4—1224no—
643C4⋊C4—1221no—
644C4⋊C4—1224no—
645C4⋊C4—1224no—
646C4⋊C4C2×C22⋊D6114yes—
647C4⋊C4C23×D6112yes—
648C4⋊C4C23×D6112yes—
649C4⋊C4C23×D6112yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—1224no—
654C22⋊C4—1224no—
655C22⋊C4—1224no—
656C22⋊C4—1224no—
657C22⋊C4C2×C22⋊D6114yes—
658C22⋊C4C2×C22⋊D6114yes—
659C42—1224no—
660C42C2×C22⋊D6112yes—
661C42C23×D6112yes—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—1222no—
672C23—2442no—
673C23—2442no—
674C23—2442no—
675C23#1451980314yes—
676C23C22×C22⋊D6112yes—
677C23C22×C22⋊D6112yes—
678C23C22×C22⋊D6111yescharacteristic
679Q8—48no—
680D4—28no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—48no—
685D4—42no—
686D4—1222no—
687D4—1222no—
688D4—4884no—
689D4—2448no—
690D4—2442no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—48no—
705C2×C4—48no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—48no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—4884no—
714C2×C4—4884no—
715C2×C4—2442no—
716C2×C4—2442no—
717C2×C4—2442no—
718C2×C4C22×C22⋊D6112yes—
719C2×C4C22×C22⋊D6112yes—
720C2×C4C22×C22⋊D6112yes—
721C2×C4C22×C22⋊D6112yes—
722C2×C4C22×C22⋊D6111yescharacteristic
723C2×C4#41×D6112yes—
724C2×C4#1451982412yes—
725C2×C4C24×D6111yescharacteristic
726C8—614no—
727C8—1222no—
728C8—1222no—
729C8—1222no—
730C22—22no—
731C22—22no—
732C22—28no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—84no—
741C22—4884no—
742C22—2442no—
743C22—2442no—
744C22—2442no—
745C22#1684041112yes—
746C22C2×#1451980314yes—
747C22C2×#1451980312yes—
748C22#1684057012yes—
749C22C23×C22⋊D6111yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—2442no—
758C4—2442no—
759C4—2442no—
760C4#1684041112yes—
761C4C2×#41×D6111yescharacteristic
762C4C2×#1451982411yescharacteristic
763C2—24no—
764C2—42no—
765C2—82no—
766C2—4882no—
767C2#2145828914yesdirect product factor
768C2C2×#1684041111yescharacteristic
769C2C22×#1451980311yescharacteristic
770C2C2×#1684057011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#547C2
socleC23×C61C22×D4
hypercenterC2×#547D61
hypocenterC61C2×#3345
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#16840458C2semidirect
2. #21458289C2direct (N × H)
3. C2×#16840168C2semidirect
4. C2×#16840080C2semidirect
5. C2×#16840078C2semidirect
6. C2×#16840083C2semidirect
7. C2×#16840075C2semidirect
8. C2×#16840062C2semidirect
9. C2×#16840049C2semidirect
10. C2×#16840013C2semidirect
11. C2×#16839996C2semidirect
12. C2×#16839872C2semidirect
13. C2×#16839834C2semidirect
14. C2×#16839802C2semidirect
15. C22×#14519708C2semidirect
16. C2×C61×#547C2semidirect
21. #16840458C22semidirect
32. #16840168C22semidirect
33. #16840083C22semidirect
34. #16840080C22semidirect
35. #16840078C22semidirect
36. #16840075C22semidirect
37. #16840062C22semidirect
38. #16840049C22semidirect
39. #16840013C22semidirect
40. #16839996C22semidirect
41. #16839872C22semidirect
42. #16839834C22semidirect
43. #16839802C22semidirect
53. C2×#14519708C22semidirect
66. C61×#547C22semidirect
271. C2×#92418#41semidirect
343. #92418C2×#41semidirect
379. C2×#547D61semidirect
397. C2×C61#3345semidirect
409. #547C2×D61semidirect
462. C61C2×#3345semidirect
767. C2#21458289direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404582
#214582892
C2×#168401682
C2×#168400802
C2×#168400782
C2×#168400832
C2×#168400752
C2×#168400622
C2×#168400492
C2×#168400132
C2×#168399962
C2×#168398722
C2×#168398342
C2×#168398022
C22×#145197082
C2×C61×#5472
C2×#334561