Finite Group Databasebeta

← C2×#21458227 #30558492

Subgroups — C2×#21458227 #30558492

Order 15616.

1918 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840483C211yesmaximal, characteristic, complemented
2C2×#16840476C211yesmaximal, characteristic
3#21458227C2116yesmaximal, direct product factor
4C2×#16840159C211yesmaximal, characteristic, complemented
5C2×#16840102C211yesmaximal, characteristic, complemented
6C2×#16840100C211yesmaximal, characteristic, complemented
7C2×#16840084C211yesmaximal, characteristic, complemented
8C2×#16840083C211yesmaximal, characteristic, complemented
9C2×#16840055C211yesmaximal, characteristic, complemented
10C2×#16840040C211yesmaximal, characteristic, complemented
11C2×#16839988C211yesmaximal, characteristic, complemented
12C2×SD16×Dic61C211yesmaximal, characteristic, complemented
13C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
14C2×#16839800C211yesmaximal, characteristic, complemented
15C2×#16839797C211yesmaximal, characteristic, complemented
16C2×C61×#465C211yesmaximal, characteristic, complemented
17C22×C8×D61C2211yescharacteristic
18#16840483—24no—
19#16840483C2218yescomplemented
20#16840476—24no—
21#16840476C2218yes—
22C2×#14519776C2211yescharacteristic
23C2×#14519776C2211yescharacteristic
24C2×#14519772—21no—
25C2×#14519770—21no—
26C2×#14519764—21no—
27C2×#14519763—21no—
28C2×#14519763—21no—
29C2×#14519753C2211yescharacteristic
30C2×#14519749—21no—
31C2×#14519748C2211yescharacteristic
32C2×Q8×Dic61C2211yescharacteristic
33C2×#14519742—21no—
34C2×D4×Dic61C2211yescharacteristic
35C2×C4×C22⋊D61C2211yescharacteristic
36C2×#14519736C2211yescharacteristic
37C2×#14519736C2211yescharacteristic
38C2×#14519735C2211yescharacteristic
39C2×#14519735C2211yescharacteristic
40C2×#14519733—21no—
41#16840159C2218yescomplemented
42#16840102C2218yescomplemented
43#16840100C2218yescomplemented
44#16840084C2218yescomplemented
45#16840083C2218yescomplemented
46#16840055C2218yescomplemented
47#16840040C2218yescomplemented
48#16839988C2218yescomplemented
49SD16×Dic61C2218yescomplemented
50C8×C22⋊D61C2218yescomplemented
51#16839800C2218yescomplemented
52#16839797C2218yescomplemented
53C2×#14519711C2211yescharacteristic
54C2×#14519711C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519709C2211yescharacteristic
58C2×#14519709C2211yescharacteristic
59C2×#14519708C2211yescharacteristic
60C2×#14519708C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519701C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×C22⋊Q8×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#465C2218yescomplemented
74C2×#106×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122—21no—
79C22×C22⋊D61—21no—
80C22×C22⋊D61D411yescharacteristic
81C23×Dic61—21no—
82C22×C4×D61C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C2×C8×D61—24no—
86C2×C8×D61C2314yes—
87#14519776—22no—
88#14519776—22no—
89#14519776C2314yes—
90#14519776C2314yes—
91#14519772—28no—
92#14519770—28no—
93#14519764—28no—
94#14519763—28no—
95#14519763—28no—
96#14519753—22no—
97#14519753C2314yes—
98#14519749—28no—
99#14519748—22no—
100#14519748C2314yes—
101Q8×Dic61—22no—
102Q8×Dic61C2314yes—
103#14519742—28no—
104D4×Dic61—22no—
105D4×Dic61C2314yes—
106C4×C22⋊D61D414yes—
107C4×C22⋊D61C2314yes—
108#14519736—22no—
109#14519736—22no—
110#14519736C2314yes—
111#14519736C2314yes—
112#14519735—22no—
113#14519735—22no—
114#14519735C2314yes—
115#14519735C2314yes—
116#14519733—28no—
117C2×C4⋊Dic61—21no—
118C2×C4⋊Dic61C2311yescharacteristic
119C2×C4⋊Dic61C2311yescharacteristic
120C2×C4⋊Dic61C2311yescharacteristic
121C2×C4⋊Dic61C2311yescharacteristic
122C2×#11758196—21no—
123C2×#11758196—21no—
124C2×#11758196—21no—
125C2×#11758196D411yescharacteristic
126C2×C22⋊Dic61—21no—
127C2×C22⋊Dic61—21no—
128C2×C22⋊Dic61—21no—
129C2×C22⋊Dic61—21no—
130C2×C22⋊Dic61D411yescharacteristic
131C2×#11758198—21no—
132C2×#11758198—21no—
133C2×#11758198—21no—
134C2×#11758198D411yescharacteristic
135C2×C4×Dic61—21no—
136C2×C4×Dic61—21no—
137C2×C4×Dic61—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61C2311yescharacteristic
141#14519711C2314yes—
142#14519711C2314yes—
143#14519710C2314yes—
144#14519710C2314yes—
145#14519709C2314yes—
146#14519709C2314yes—
147#14519708C2314yes—
148#14519708C2314yes—
149#14519706C2314yes—
150#14519701C2314yes—
151#14519701C2314yes—
152#14519698C2314yes—
153#14519698C2314yes—
154C22⋊#92418C2314yes—
155#14519689C2314yes—
156C8×Dic61C2314yes—
157C22×Q8×C61C2311yescharacteristic
158C22×D4×C61—21no—
159C22×D4×C61C2311yescharacteristic
160C23×C4×C61C2311yescharacteristic
161C2×SD16×C61—24no—
162C2×SD16×C61C2314yes—
163C22×C8×C61—24no—
164C22×C8×C61C2311yescharacteristic
165C22×C8×C61C2314yes—
166C22×C8×C61C2311yescharacteristic
167C22⋊Q8×C61—22no—
168C22⋊Q8×C61C2314yes—
169#121×C61—22no—
170#121×C61C2314yes—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176#106×C61C2314yes—
177#103×C61C2314yes—
178#102×C61C2314yes—
179C24×C61—21no—
180C24×C61C2×D411yescharacteristic
181C23×D61C2×D411yescharacteristic
182C2×Q8×C61—21no—
183C2×Q8×C61—22no—
184C2×Q8×C61—22no—
185C2×Q8×C61C2412yes—
186C2×D4×C61—24no—
187C2×D4×C61—21no—
188C2×D4×C61—22no—
189C2×D4×C61—22no—
190C2×D4×C61—82no—
191C2×D4×C61C2412yes—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D412yes—
199C22×C4×C61C2412yes—
200C22×C4×C61C2411yescharacteristic
201C2×C22⋊D61—24no—
202C2×C22⋊D61—24no—
203C2×C22⋊D61—82no—
204C2×C22⋊D61C2×D414yes—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—24no—
210C22×Dic61—44no—
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213C22×Dic61C2×D411yescharacteristic
214C2×C4×D61—22no—
215C2×C4×D61—22no—
216C2×C4×D61C2×D412yes—
217C2×C4×D61C2412yes—
218C2×Dic122—24no—
219C2×Dic122—24no—
220C2×Dic122—44no—
221C2×Dic122—82no—
222SD16×C61—28no—
223C2×C8×C61—22no—
224C2×C8×C61—28no—
225C2×C8×C61#4114yes—
226C2×C8×C61C2412yes—
227C2×C8×C61C2412yes—
228C4⋊C4×C61—24no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61C2412yes—
232C4⋊C4×C61C2412yes—
233C22⋊C4×C61—24no—
234C22⋊C4×C61—24no—
235C22⋊Dic61—24no—
236C22⋊Dic61—24no—
237C22⋊Dic61—24no—
238C22⋊Dic61—24no—
239C22⋊Dic61C2×D414yes—
240#11758198—24no—
241#11758198—24no—
242#11758198—24no—
243#11758198C2×D414yes—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—24no—
249C4⋊Dic61C2412yes—
250C4⋊Dic61C2412yes—
251C4⋊Dic61C2412yes—
252C4⋊Dic61C2412yes—
253#11758196—24no—
254#11758196—24no—
255#11758196—24no—
256#11758196C2×D414yes—
257C4×Dic61—24no—
258C4×Dic61—24no—
259C4×Dic61—24no—
260C4×Dic61—24no—
261C4×Dic61—24no—
262C4×Dic61C2×D412yes—
263C4×Dic61C2412yes—
264C2×#92418—22no—
265C2×#92418—22no—
266C2×#92418C2412yes—
267C2×#92418C2412yes—
268C8×D61—28no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—42no—
274C23×C61—42no—
275C23×C61—42no—
276C23×C61C22×D412yes—
277C23×C61C22×D411yescharacteristic
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61C22×D412yes—
282Q8×C61—22no—
283Q8×C61—22no—
284Q8×C61—42no—
285D4×C61—22no—
286D4×C61—22no—
287D4×C61—42no—
288D4×C61—84no—
289C2×C4×C61—22no—
290C2×C4×C61—24no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61C22×D412yes—
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C2×#4112yes—
302C2×C4×C612−1+412yes—
303C2×C4×C61C2511yescharacteristic
304C22⋊D61—28no—
305C22⋊D61—84no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—48no—
317C2×Dic61#13514yes—
318C2×Dic61C22×D412yes—
319C2×Dic61C22×D412yes—
320C2×Dic61C22×D412yes—
321C4×D61—24no—
322C4×D61—22no—
323C4×D61—22no—
324Dic122—48no—
325Dic122—84no—
326C8×C61—22no—
327C8×C61C2×#4114yes—
328#92418—22no—
329#92418—22no—
330C2×#3340—611nomaximal, Sylow
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—44no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—42no—
338C22×C61—84no—
339C22×C61#54712yes—
340C22×C61C2×#13512yes—
341C22×C61#57712yes—
342C22×C61C23×D411yescharacteristic
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—44no—
347C4×C61—22no—
348C4×C61—42no—
349C4×C61—42no—
350C4×C61—42no—
351C4×C61#54712yes—
352C4×C61C22×#4111yescharacteristic
353C4×C61C2×2−1+411yescharacteristic
354Dic61—22no—
355Dic61—22no—
356Dic61—42no—
357Dic61—42no—
358Dic61—42no—
359Dic61—42no—
360Dic61C2×#13514yes—
361C2×#556—611no—
362C2×#555—611no—
363#3340—6116no—
364C2×#498—611no—
365C2×#485—611no—
366C2×#485—611no—
367C2×#482—611no—
368C2×#482—611no—
369C2×#477—611no—
370C2×#474—611no—
371C2×#465—611no—
372C2×#465D6111yescharacteristic, complemented
373C2×C4×SD16—611no—
374C2×C8×D4—611no—
375C2×#427—611no—
376C2×#427—611no—
377C2×C61—42no—
378C2×C61—82no—
379C2×C61#334014yescomplemented
380C2×C61C2×#54711yescharacteristic
381C2×C61C22×#13511yescharacteristic
382C2×C61C2×#57711yescharacteristic
383D61—42no—
384C22×SD16C2×D6111yescharacteristic
385C23×C8—611no—
386C23×C8C2×D6111yescharacteristic
387#556—618no—
388#556—1224no—
389#555—618no—
390#555—1224no—
391C2×C4⋊Q8—611no—
392C2×C4⋊Q8—611no—
393C2×#126—1221no—
394C2×#126—1221no—
395C2×#124—1221no—
396C2×#124—1221no—
397C2×#124—1221no—
398C2×C22⋊Q8—611no—
399C2×C22⋊Q8C2×D6111yescharacteristic
400C2×#121—611no—
401C2×#121—1221no—
402C2×#121C2×D6111yescharacteristic
403C2×C4×Q8—611no—
404C2×C4×Q8—1221no—
405C2×C4×D4—611no—
406C2×C4×D4—611no—
407C2×#117—611no—
408C2×#117—611no—
409C2×#117—611no—
410C2×#117—611no—
411C2×#117—1221no—
412#498—618no—
413#485—618no—
414#485—618no—
415#482—618no—
416#482—618no—
417#477—618no—
418#474—618no—
419#465—618no—
420#465C2×D6118yescomplemented
421C4×SD16—618no—
422C8×D4—618no—
423#427—618no—
424#427—618no—
425C2×#107—611no—
426C2×#107—611no—
427C2×#107—611no—
428C2×#107—611no—
429C2×#106—611no—
430C2×#106—611no—
431C2×#106—611no—
432C2×#106—611no—
433C2×#106C2×D6111yescharacteristic
434C2×C4⋊C8—611no—
435C2×#103—611no—
436C2×#103—611no—
437C2×#103C2×D6111yescharacteristic
438C2×#102—611no—
439C2×#102—611no—
440C2×#102C2×D6111yescharacteristic
441C2×C22⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×C4×C8—611no—
444C61C2×#334011yescharacteristic, complemented, Sylow
445C22×Q8—1221no—
446C22×Q8—1221no—
447C22×Q8C22×D6111yescharacteristic
448C22×D4—21no—
449C22×D4—611no—
450C22×D4—1221no—
451C22×D4C22×D6111yescharacteristic
452C23×C4—611no—
453C23×C4—1221no—
454C23×C4C22×D6111yescharacteristic
455C2×SD16—24no—
456C2×SD16C22×D6114yes—
457C22×C8—24no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—614no—
461C22×C8—1224no—
462C22×C8C22×D6111yescharacteristic
463C22×C8C22×D6114yes—
464C22×C8C22×D6111yescharacteristic
465C4⋊Q8—614no—
466C4⋊Q8—614no—
467C4⋊Q8—1222no—
468C4⋊Q8—1222no—
469#126—1228no—
470#126—1228no—
471#124—1228no—
472#124—1228no—
473#124—1228no—
474C22⋊Q8—22no—
475C22⋊Q8—614no—
476C22⋊Q8—1222no—
477C22⋊Q8C22×D6114yes—
478#121—22no—
479#121—614no—
480#121—1222no—
481#121—1228no—
482#121C22×D6114yes—
483C4×Q8—614no—
484C4×Q8—1222no—
485C4×Q8—1228no—
486C4×D4—614no—
487C4×D4—614no—
488C4×D4—614no—
489C4×D4—1222no—
490#117—614no—
491#117—614no—
492#117—614no—
493#117—614no—
494#117—1228no—
495#117—1222no—
496#117—1222no—
497#117—1222no—
498#117—1222no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4C22×D6111yescharacteristic
510C2×C4⋊C4C22×D6111yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—611no—
514C2×C22⋊C4—611no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C42—611no—
523C2×C42—1221no—
524C2×C42—1221no—
525C2×C42—1221no—
526C2×C42—1221no—
527C2×C42—1221no—
528#107—614no—
529#107—614no—
530#107—614no—
531#107—614no—
532#106—614no—
533#106—614no—
534#106—614no—
535#106—614no—
536#106C22×D6114yes—
537C4⋊C8—614no—
538#103—614no—
539#103—614no—
540#103C22×D6114yes—
541#102—614no—
542#102—614no—
543#102C22×D6114yes—
544C22⋊C8—614no—
545C22⋊C8—614no—
546C4×C8—614no—
547C24—21no—
548C24—611no—
549C24D4×D6111yescharacteristic
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—1224no—
554C2×Q8—1224no—
555C2×Q8—4882no—
556C2×Q8—2444no—
557C2×Q8C23×D6112yes—
558C2×D4—24no—
559C2×D4—21no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—82no—
563C2×D4—614no—
564C2×D4—1224no—
565C2×D4—1224no—
566C2×D4—4882no—
567C2×D4C23×D6112yes—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—611no—
574C22×C4—611no—
575C22×C4—611no—
576C22×C4—612no—
577C22×C4—612no—
578C22×C4—1224no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—2444no—
586C22×C4D4×D6112yes—
587C22×C4D4×D6111yescharacteristic
588C22×C4C23×D6112yes—
589C22×C4C23×D6111yescharacteristic
590SD16—28no—
591C2×C8—22no—
592C2×C8—28no—
593C2×C8—612no—
594C2×C8—612no—
595C2×C8—1222no—
596C2×C8—1222no—
597C2×C8—1228no—
598C2×C8#1175822414yes—
599C2×C8C23×D6112yes—
600C2×C8C23×D6112yes—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—614no—
605C4⋊C4—612no—
606C4⋊C4—612no—
607C4⋊C4—612no—
608C4⋊C4—612no—
609C4⋊C4—1224no—
610C4⋊C4—1224no—
611C4⋊C4—1224no—
612C4⋊C4—1224no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4C23×D6112yes—
618C4⋊C4C23×D6112yes—
619C22⋊C4—24no—
620C22⋊C4—24no—
621C22⋊C4—614no—
622C22⋊C4—614no—
623C22⋊C4—1224no—
624C22⋊C4—1224no—
625C22⋊C4—1224no—
626C22⋊C4—1224no—
627C22⋊C4—1224no—
628C22⋊C4—1224no—
629C22⋊C4—1224no—
630C42—612no—
631C42—612no—
632C42—1224no—
633C42—1224no—
634C42—1224no—
635C42—1224no—
636C42—1224no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—612no—
645C23—1222no—
646C23—1222no—
647C23—1222no—
648C23C2×D4×D6112yes—
649C23C2×D4×D6111yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—4884no—
654Q8—2448no—
655D4—22no—
656D4—22no—
657D4—42no—
658D4—84no—
659D4—1228no—
660D4—4884no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—614no—
672C2×C4—612no—
673C2×C4—612no—
674C2×C4—612no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1224no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—2448no—
685C2×C4—2442no—
686C2×C4—2442no—
687C2×C4—2442no—
688C2×C4—2442no—
689C2×C4C2×D4×D6112yes—
690C2×C4C2×D4×D6111yescharacteristic
691C2×C4C2×#1175822412yes—
692C2×C4#1451982412yes—
693C2×C4C24×D6111yescharacteristic
694C8—22no—
695C8—1222no—
696C8—1222no—
697C8C2×#1175822414yes—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—44no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—84no—
706C22—1222no—
707C22—1222no—
708C22—1222no—
709C22—2444no—
710C22#1684041212yes—
711C22#135×D6112yes—
712C22#1684056812yes—
713C22C22×D4×D6111yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—614no—
719C4—1222no—
720C4—1222no—
721C4—2442no—
722C4—2442no—
723C4—2442no—
724C4—2442no—
725C4#1684041212yes—
726C4C22×#1175822411yescharacteristic
727C4C2×#1451982411yescharacteristic
728C2—42no—
729C2—82no—
730C2—2442no—
731C2#2145822714yesdirect product factor
732C2C2×#1684041211yescharacteristic
733C2C2×#135×D6111yescharacteristic
734C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#465C2
socleC23×C61C22×D4
prime radicalC2×#16840476C2
hypercenterC2×#465D61
hypocenterC61C2×#3340
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#16840483C2semidirect
3. #21458227C2direct (N × H)
4. C2×#16840159C2semidirect
5. C2×#16840102C2semidirect
6. C2×#16840100C2semidirect
7. C2×#16840084C2semidirect
8. C2×#16840083C2semidirect
9. C2×#16840055C2semidirect
10. C2×#16840040C2semidirect
11. C2×#16839988C2semidirect
12. C2×SD16×Dic61C2semidirect
13. C2×C8×C22⋊D61C2semidirect
14. C2×#16839800C2semidirect
15. C2×#16839797C2semidirect
16. C2×C61×#465C2semidirect
19. #16840483C22semidirect
41. #16840159C22semidirect
42. #16840102C22semidirect
43. #16840100C22semidirect
44. #16840084C22semidirect
45. #16840083C22semidirect
46. #16840055C22semidirect
47. #16840040C22semidirect
48. #16839988C22semidirect
49. SD16×Dic61C22semidirect
50. C8×C22⋊D61C22semidirect
51. #16839800C22semidirect
52. #16839797C22semidirect
73. C61×#465C22semidirect
372. C2×#465D61semidirect
379. C2×C61#3340semidirect
420. #465C2×D61semidirect
444. C61C2×#3340semidirect
731. C2#21458227direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404832
C2×#168404762
#214582272
C2×#168401592
C2×#168401022
C2×#168401002
C2×#168400842
C2×#168400832
C2×#168400552
C2×#168400402
C2×#168399882
C2×SD16×Dic612
C2×C8×C22⋊D612
C2×#168398002
C2×#168397972
C2×C61×#4652
C2×#334061