Finite Group Databasebeta

← C2×#21458628 #30559743

Subgroups — C2×#21458628 #30559743

Order 15616.

1906 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840494C211yesmaximal, characteristic
2C2×Q8×Dic122C211yesmaximal, characteristic, complemented
3#21458628C2116yesmaximal, direct product factor
4C2×#16840123C211yesmaximal, characteristic, complemented
5C2×#16840121C211yesmaximal, characteristic, complemented
6C2×#16840107C211yesmaximal, characteristic
7C2×#16840055C211yesmaximal, characteristic, complemented
8C2×#16840043C211yesmaximal, characteristic, complemented
9C2×#16840040C211yesmaximal, characteristic, complemented
10C2×#16839986C211yesmaximal, characteristic, complemented
11C2×#16839960C211yesmaximal, characteristic
12C2×#16839891C211yesmaximal, characteristic, complemented
13C2×#16839863C211yesmaximal, characteristic, complemented
14C2×#16839860C211yesmaximal, characteristic, complemented
15C2×Q16×Dic61C211yesmaximal, characteristic, complemented
16C2×C61×#464C211yesmaximal, characteristic, complemented
17C22×#11758201C2211yescharacteristic
18#16840494—24no—
19#16840494C2218yes—
20Q8×Dic122—24no—
21Q8×Dic122C2218yescomplemented
22C2×#14519777—21no—
23C2×#14519777C2211yescharacteristic
24C2×#14519776—21no—
25C2×#14519776—21no—
26C2×#14519776C2211yescharacteristic
27C2×#14519776C2211yescharacteristic
28C2×#14519773C2211yescharacteristic
29C2×#14519766C2211yescharacteristic
30C2×#14519763—21no—
31C2×#14519761—21no—
32C2×#14519759—21no—
33C2×Q8×Dic61C2211yescharacteristic
34C2×Q8×Dic61C2211yescharacteristic
35C2×Q8×Dic61C2211yescharacteristic
36C2×C4×Dic122—21no—
37C2×C4×Dic122C2211yescharacteristic
38C2×C4×D244C2211yescharacteristic
39C2×D4×Dic61C2211yescharacteristic
40C2×#14519737—21no—
41#16840123C2218yescomplemented
42#16840121C2218yescomplemented
43#16840107C2218yes—
44#16840055C2218yescomplemented
45#16840043C2218yescomplemented
46#16840040C2218yescomplemented
47#16839986C2218yescomplemented
48#16839960C2218yes—
49#16839891C2218yescomplemented
50#16839863C2218yescomplemented
51#16839860C2218yescomplemented
52Q16×Dic61C2218yescomplemented
53C2×#14519711C2211yescharacteristic
54C2×#14519711C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×#14519706C2211yescharacteristic
57C2×#14519706C2211yescharacteristic
58C2×#14519701C2211yescharacteristic
59C2×#14519701C2211yescharacteristic
60C2×#14519701C2211yescharacteristic
61C2×#14519699C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519688C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
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×Dic122—21no—
80C22×Dic122D411yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C23×Dic61—21no—
85C22×C4×D61—21no—
86C2×#11758201—24no—
87C2×#11758201C2314yes—
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90#14519777—22no—
91#14519777—28no—
92#14519777C2314yes—
93#14519776—28no—
94#14519776—28no—
95#14519776—22no—
96#14519776—22no—
97#14519776C2314yes—
98#14519776C2314yes—
99#14519773—22no—
100#14519773C2314yes—
101#14519766—22no—
102#14519766C2314yes—
103#14519763—28no—
104#14519761—28no—
105#14519759—28no—
106Q8×Dic61—22no—
107Q8×Dic61—22no—
108Q8×Dic61—22no—
109Q8×Dic61C2314yes—
110Q8×Dic61C2314yes—
111Q8×Dic61C2314yes—
112C4×Dic122—28no—
113C4×Dic122D414yes—
114C4×Dic122C2314yes—
115C4×D244—22no—
116C4×D244C2314yes—
117D4×Dic61—22no—
118D4×Dic61C2314yes—
119#14519737—28no—
120C2×C4⋊Dic61—21no—
121C2×C4⋊Dic61—21no—
122C2×C4⋊Dic61—21no—
123C2×C4⋊Dic61—21no—
124C2×C4⋊Dic61D411yescharacteristic
125C2×C4⋊Dic61C2311yescharacteristic
126C2×C4⋊Dic61C2311yescharacteristic
127C2×C4⋊Dic61C2311yescharacteristic
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196D411yescharacteristic
131C2×#11758196D411yescharacteristic
132C2×C22⋊Dic61—21no—
133C2×#11758198—21no—
134C2×#11758198—21no—
135C2×#11758198—21no—
136C2×C4×Dic61—21no—
137C2×C4×Dic61—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61C2311yescharacteristic
140C2×C4×Dic61C2311yescharacteristic
141#14519711C2314yes—
142#14519711C2314yes—
143#14519710C2314yes—
144#14519706C2314yes—
145#14519706C2314yes—
146#14519701C2314yes—
147#14519701C2314yes—
148#14519701C2314yes—
149#14519699C2314yes—
150#14519699C2314yes—
151#14519698C2314yes—
152#14519698C2314yes—
153#14519697C2314yes—
154#14519688C2314yes—
155#14519687C2314yes—
156C8×Dic61C2314yes—
157C22×Q8×C61C2311yescharacteristic
158C22×Q8×C61C2311yescharacteristic
159C22×D4×C61C2311yescharacteristic
160C2×Q16×C61—24no—
161C2×Q16×C61C2314yes—
162C2×SD16×C61—24no—
163C2×SD16×C61C2314yes—
164C22×C8×C61C2311yescharacteristic
165C22×C8×C61C2311yescharacteristic
166#124×C61—22no—
167#124×C61C2314yes—
168C4×Q8×C61—22no—
169C4×Q8×C61C2314yes—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C22⋊C4×C61—21no—
173C2×C22⋊C4×C61—21no—
174C2×C42×C61—21no—
175C2×C42×C61C2311yescharacteristic
176C4⋊C8×C61C2314yes—
177#103×C61C2314yes—
178#102×C61C2314yes—
179C24×C61—21no—
180C23×D61—21no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—22no—
184C2×Q8×C61—22no—
185C2×Q8×C61—22no—
186C2×Q8×C61#4114yes—
187C2×Q8×C61C2412yes—
188C2×Q8×C61C2412yes—
189C2×D4×C61—21no—
190C2×D4×C61—22no—
191C2×D4×C61—22no—
192C2×D4×C61C2412yes—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2411yescharacteristic
199C2×C22⋊D61—24no—
200C2×C22⋊D61—24no—
201C2×C22⋊D61—44no—
202C2×C22⋊D61—82no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—24no—
207C22×Dic61—82no—
208C22×Dic61C2×D411yescharacteristic
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212C2×D244—22no—
213C2×D244—22no—
214C2×D244—21no—
215C2×D244C2412yes—
216C2×C4×D61—24no—
217C2×C4×D61—82no—
218C2×Dic122—24no—
219C2×Dic122—24no—
220C2×Dic122—24no—
221C2×Dic122—24no—
222C2×Dic122—82no—
223C2×Dic122—82no—
224C2×Dic122—82no—
225C2×Dic122C2×D414yes—
226Q16×C61—28no—
227SD16×C61—28no—
228C2×C8×C61—22no—
229C2×C8×C61—22no—
230C2×C8×C61C2412yes—
231C2×C8×C61C2412yes—
232C4⋊C4×C61—24no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61C2412yes—
235C22⋊C4×C61—24no—
236C22⋊C4×C61—24no—
237C42×C61—24no—
238C42×C61C2×D412yes—
239C42×C61C2412yes—
240C22⋊Dic61—24no—
241#11758201—28no—
242#11758198—24no—
243#11758198—24no—
244#11758198—24no—
245C4⋊Dic61—24no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61—24no—
250C4⋊Dic61—24no—
251C4⋊Dic61—24no—
252C4⋊Dic61C2×D414yes—
253C4⋊Dic61C2412yes—
254C4⋊Dic61C2412yes—
255C4⋊Dic61C2412yes—
256#11758196—24no—
257#11758196—24no—
258#11758196C2×D414yes—
259#11758196C2×D414yes—
260C4×Dic61—24no—
261C4×Dic61—24no—
262C4×Dic61—24no—
263C4×Dic61C2×D412yes—
264C4×Dic61C2×D412yes—
265C4×Dic61C2412yes—
266C4×Dic61C2412yes—
267C2×#92418—22no—
268C2×#92418—22no—
269C2×#92418C2412yes—
270C2×#92418C2412yes—
271C23×C61—22no—
272C23×C61—42no—
273C23×C61—42no—
274C23×C61—42no—
275C23×C61C22×D411yescharacteristic
276C22×D61—22no—
277C22×D61—42no—
278C22×D61—42no—
279C22×D61—42no—
280Q8×C61—24no—
281Q8×C61—22no—
282Q8×C61—22no—
283Q8×C61—22no—
284Q8×C61—42no—
285Q8×C61C2×#4114yes—
286D4×C61—22no—
287D4×C61—22no—
288D4×C61—42no—
289C2×C4×C61—24no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
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
303C22⋊D61—48no—
304C22⋊D61—84no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—84no—
315C2×Dic61#13714yes—
316C2×Dic61C22×D412yes—
317C2×Dic61C22×D412yes—
318C2×Dic61C22×D412yes—
319C2×Dic61C22×D412yes—
320D244—22no—
321D244—22no—
322D244—42no—
323C4×D61—84no—
324Dic122—28no—
325Dic122—84no—
326Dic122—84no—
327Dic122—84no—
328C8×C61—22no—
329C8×C61—22no—
330#92418—22no—
331#92418—22no—
332C2×#3375—611nomaximal, Sylow
333C22×C61—42no—
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—84no—
337C22×C61#54812yes—
338C22×C61C2×#13712yes—
339C22×C61#57612yes—
340C22×C61C23×D411yescharacteristic
341C2×D61—42no—
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—84no—
345C4×C61—24no—
346C4×C61—22no—
347C4×C61—22no—
348C4×C61—42no—
349C4×C61—42no—
350C4×C61#54812yes—
351C4×C61C22×#4111yescharacteristic
352C4×C61C2×2−1+411yescharacteristic
353Dic61—22no—
354Dic61—22no—
355Dic61—22no—
356Dic61—42no—
357Dic61—42no—
358Dic61—42no—
359Dic61C2×#13714yes—
360C2×#559—611no—
361C2×Q82—611no—
362#3375—6116no—
363C2×#489—611no—
364C2×#489—611no—
365C2×#486—611no—
366C2×#477—611no—
367C2×#474—611no—
368C2×#474—611no—
369C2×#464—611no—
370C2×#464D6111yescharacteristic, complemented
371C2×#460—611no—
372C2×#446—611no—
373C2×#440—611no—
374C2×#440—611no—
375C2×C4×Q16—611no—
376C2×C61—82no—
377C2×C61#337514yescomplemented
378C2×C61C2×#54811yescharacteristic
379C2×C61C22×#13711yescharacteristic
380C2×C61C2×#57611yescharacteristic
381D61—82no—
382C22×Q16C2×D6111yescharacteristic
383C22×SD16—611no—
384C22×SD16C2×D6111yescharacteristic
385#559—618no—
386#559—1224no—
387Q82—618no—
388Q82—1224no—
389C2×C4⋊Q8—611no—
390C2×C4⋊Q8—611no—
391C2×C4⋊Q8—611no—
392C2×C4⋊Q8—1221no—
393C2×C4⋊Q8—1221no—
394C2×C4⋊Q8—1221no—
395C2×#127—611no—
396C2×#124—611no—
397C2×#124—1221no—
398C2×#124C2×D6111yescharacteristic
399C2×#123—1221no—
400C2×#123—1221no—
401C2×C4×Q8—611no—
402C2×C4×Q8—611no—
403C2×C4×Q8—611no—
404C2×C4×Q8—611no—
405C2×C4×Q8—1221no—
406C2×C4×Q8C2×D6111yescharacteristic
407C2×C4×D4—611no—
408C2×C4×D4—611no—
409C2×C4×D4—1221no—
410#489—618no—
411#489—618no—
412#486—618no—
413#477—618no—
414#474—618no—
415#474—618no—
416#464—618no—
417#464C2×D6118yescomplemented
418#460—618no—
419#446—618no—
420#440—618no—
421#440—618no—
422C4×Q16—618no—
423C2×#107—611no—
424C2×#107—611no—
425C2×#107—611no—
426C2×C4⋊C8—611no—
427C2×C4⋊C8—611no—
428C2×C4⋊C8C2×D6111yescharacteristic
429C2×#103—611no—
430C2×#103—611no—
431C2×#103—611no—
432C2×#103C2×D6111yescharacteristic
433C2×#102—611no—
434C2×#102—611no—
435C2×#102—611no—
436C2×#102—611no—
437C2×#102—611no—
438C2×#102C2×D6111yescharacteristic
439C2×#97—611no—
440C2×#97—611no—
441C2×C4×C8—611no—
442C61C2×#337511yescharacteristic, complemented, Sylow
443C22×Q8—611no—
444C22×Q8—1221no—
445C22×Q8—1221no—
446C22×Q8—1221no—
447C22×Q8C22×D6111yescharacteristic
448C22×Q8C22×D6111yescharacteristic
449C22×D4—611no—
450C22×D4—1221no—
451C22×D4—1221no—
452C22×D4C22×D6111yescharacteristic
453C23×C4—1221no—
454C23×C4—1221no—
455C2×Q16—24no—
456C2×Q16C22×D6114yes—
457C2×SD16—24no—
458C2×SD16—614no—
459C2×SD16—1224no—
460C2×SD16C22×D6114yes—
461C22×C8—611no—
462C22×C8—611no—
463C22×C8C22×D6111yescharacteristic
464C22×C8C22×D6111yescharacteristic
465C4⋊Q8—614no—
466C4⋊Q8—614no—
467C4⋊Q8—614no—
468C4⋊Q8—1228no—
469C4⋊Q8—1222no—
470C4⋊Q8—1222no—
471C4⋊Q8—1228no—
472C4⋊Q8—1228no—
473C4⋊Q8—1222no—
474#127—614no—
475#127—1222no—
476#124—22no—
477#124—614no—
478#124—1222no—
479#124—1228no—
480#124C22×D6114yes—
481#123—1228no—
482#123—1228no—
483C4×Q8—22no—
484C4×Q8—614no—
485C4×Q8—614no—
486C4×Q8—614no—
487C4×Q8—614no—
488C4×Q8—614no—
489C4×Q8—1228no—
490C4×Q8—1222no—
491C4×Q8—1222no—
492C4×Q8—1222no—
493C4×Q8C22×D6114yes—
494C4×D4—614no—
495C4×D4—614no—
496C4×D4—1222no—
497C4×D4—1228no—
498C4×D4—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—611no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C42—21no—
520C2×C42—611no—
521C2×C42—611no—
522C2×C42—1221no—
523C2×C42—1221no—
524C2×C42—1221no—
525C2×C42C22×D6111yescharacteristic
526#107—614no—
527#107—614no—
528#107—614no—
529C4⋊C8—614no—
530C4⋊C8—614no—
531C4⋊C8C22×D6114yes—
532#103—614no—
533#103—614no—
534#103—614no—
535#103C22×D6114yes—
536#102—614no—
537#102—614no—
538#102—614no—
539#102—614no—
540#102—614no—
541#102C22×D6114yes—
542#97—614no—
543#97—614no—
544C4×C8—614no—
545C24—21no—
546C24—1221no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—614no—
553C2×Q8—1224no—
554C2×Q8—1224no—
555C2×Q8—1224no—
556C2×Q8—1224no—
557C2×Q8—4882no—
558C2×Q8—4882no—
559C2×Q8—4882no—
560C2×Q8#1175822414yes—
561C2×Q8C23×D6112yes—
562C2×Q8C23×D6112yes—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—612no—
567C2×D4—1224no—
568C2×D4—1224no—
569C2×D4—1221no—
570C2×D4—1222no—
571C2×D4—1222no—
572C2×D4—4882no—
573C2×D4—2444no—
574C2×D4C23×D6112yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—1224no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1224no—
587C22×C4—4882no—
588C22×C4—4882no—
589C22×C4D4×D6111yescharacteristic
590C22×C4D4×D6111yescharacteristic
591C22×C4C23×D6111yescharacteristic
592Q16—28no—
593SD16—28no—
594SD16—1228no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—612no—
598C2×C8—612no—
599C2×C8—1222no—
600C2×C8—1222no—
601C2×C8C23×D6112yes—
602C2×C8C23×D6112yes—
603C4⋊C4—24no—
604C4⋊C4—21no—
605C4⋊C4—614no—
606C4⋊C4—614no—
607C4⋊C4—614no—
608C4⋊C4—612no—
609C4⋊C4—612no—
610C4⋊C4—612no—
611C4⋊C4—1224no—
612C4⋊C4—1224no—
613C4⋊C4—1224no—
614C4⋊C4—1224no—
615C4⋊C4—1224no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—1224no—
620C4⋊C4C23×D6112yes—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—1224no—
624C22⋊C4—1224no—
625C22⋊C4—1224no—
626C22⋊C4—1224no—
627C42—24no—
628C42—612no—
629C42—612no—
630C42—612no—
631C42—612no—
632C42—1224no—
633C42—1224no—
634C42—1224no—
635C42D4×D6112yes—
636C42C23×D6112yes—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—1222no—
642C23—2442no—
643C23—2442no—
644C23—2442no—
645C23C2×D4×D6111yescharacteristic
646Q8—22no—
647Q8—24no—
648Q8—22no—
649Q8—22no—
650Q8—42no—
651Q8—1228no—
652Q8—4884no—
653Q8—4884no—
654Q8—4884no—
655Q8C2×#1175822414yes—
656D4—22no—
657D4—22no—
658D4—42no—
659D4—1222no—
660D4—1222no—
661D4—4884no—
662D4—2448no—
663D4—2442no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—614no—
673C2×C4—612no—
674C2×C4—612no—
675C2×C4—612no—
676C2×C4—612no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—4884no—
684C2×C4—4884no—
685C2×C4—2442no—
686C2×C4—2442no—
687C2×C4—2442no—
688C2×C4C2×D4×D6112yes—
689C2×C4C2×D4×D6112yes—
690C2×C4C2×D4×D6111yescharacteristic
691C2×C4C2×#1175822412yes—
692C2×C4#1451982412yes—
693C2×C4C24×D6111yescharacteristic
694C8—22no—
695C8—22no—
696C8—1222no—
697C8—1222no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—84no—
702C22—4884no—
703C22—2442no—
704C22—2442no—
705C22—2442no—
706C22#1684041812yes—
707C22#137×D6112yes—
708C22#1684056412yes—
709C22C22×D4×D6111yescharacteristic
710C4—22no—
711C4—24no—
712C4—22no—
713C4—42no—
714C4—42no—
715C4—614no—
716C4—1222no—
717C4—1222no—
718C4—1222no—
719C4—2442no—
720C4—2442no—
721C4—2442no—
722C4#1684041812yes—
723C4C22×#1175822411yescharacteristic
724C4C2×#1451982411yescharacteristic
725C2—82no—
726C2—4882no—
727C2#2145862814yesdirect product factor
728C2C2×#1684041811yescharacteristic
729C2C2×#137×D6111yescharacteristic
730C2C2×#1684056411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#464C2
socleC23×C61C22×D4
prime radicalC2×#14519773C22
hypercenterC2×#464D61
hypocenterC61C2×#3375
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
2. C2×Q8×Dic122C2semidirect
3. #21458628C2direct (N × H)
4. C2×#16840123C2semidirect
5. C2×#16840121C2semidirect
7. C2×#16840055C2semidirect
8. C2×#16840043C2semidirect
9. C2×#16840040C2semidirect
10. C2×#16839986C2semidirect
12. C2×#16839891C2semidirect
13. C2×#16839863C2semidirect
14. C2×#16839860C2semidirect
15. C2×Q16×Dic61C2semidirect
16. C2×C61×#464C2semidirect
21. Q8×Dic122C22semidirect
41. #16840123C22semidirect
42. #16840121C22semidirect
44. #16840055C22semidirect
45. #16840043C22semidirect
46. #16840040C22semidirect
47. #16839986C22semidirect
49. #16839891C22semidirect
50. #16839863C22semidirect
51. #16839860C22semidirect
52. Q16×Dic61C22semidirect
73. C61×#464C22semidirect
370. C2×#464D61semidirect
377. C2×C61#3375semidirect
417. #464C2×D61semidirect
442. C61C2×#3375semidirect
727. C2#21458628direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404942
C2×Q8×Dic1222
#214586282
C2×#168401232
C2×#168401212
C2×#168401072
C2×#168400552
C2×#168400432
C2×#168400402
C2×#168399862
C2×#168399602
C2×#168398912
C2×#168398632
C2×#168398602
C2×Q16×Dic612
C2×C61×#4642
C2×#337561