Finite Group Databasebeta

← C2×#21458634 #30559749

Subgroups — C2×#21458634 #30559749

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×#16840495C211yesmaximal, characteristic
2C2×Q8×Dic122C211yesmaximal, characteristic, complemented
3#21458634C2116yesmaximal, direct product factor
4C2×#16840122C211yesmaximal, characteristic, complemented
5C2×#16840120C211yesmaximal, characteristic, complemented
6C2×#16840107C211yesmaximal, characteristic
7C2×#16840056C211yesmaximal, characteristic, complemented
8C2×#16840042C211yesmaximal, characteristic, complemented
9C2×#16840041C211yesmaximal, characteristic, complemented
10C2×#16839984C211yesmaximal, characteristic, complemented
11C2×#16839982C211yesmaximal, characteristic, complemented
12C2×#16839960C211yesmaximal, characteristic
13C2×#16839890C211yesmaximal, characteristic, complemented
14C2×#16839865C211yesmaximal, characteristic, complemented
15C2×#16839854C211yesmaximal, characteristic, complemented
16C2×C61×#440C211yesmaximal, characteristic, complemented
17C22×#11758202C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19#16840495—24no—
20#16840495C2218yes—
21Q8×Dic122—24no—
22Q8×Dic122C2218yescomplemented
23C2×#14519777—21no—
24C2×#14519777C2211yescharacteristic
25C2×#14519776—21no—
26C2×#14519776—21no—
27C2×#14519776C2211yescharacteristic
28C2×#14519776C2211yescharacteristic
29C2×#14519773C2211yescharacteristic
30C2×#14519765C2211yescharacteristic
31C2×#14519764C2211yescharacteristic
32C2×#14519763—21no—
33C2×#14519760—21no—
34C2×#14519759—21no—
35C2×Q8×Dic61C2211yescharacteristic
36C2×Q8×Dic61C2211yescharacteristic
37C2×C4×Dic122—21no—
38C2×C4×Dic122C2211yescharacteristic
39C2×#14519742C2211yescharacteristic
40C2×#14519739C2211yescharacteristic
41C2×C4×C22⋊D61—21no—
42#16840122C2218yescomplemented
43#16840120C2218yescomplemented
44#16840107C2218yes—
45#16840056C2218yescomplemented
46#16840042C2218yescomplemented
47#16840041C2218yescomplemented
48#16839984C2218yescomplemented
49#16839982C2218yescomplemented
50#16839960C2218yes—
51#16839890C2218yescomplemented
52#16839865C2218yescomplemented
53#16839854C2218yescomplemented
54C2×#14519710C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×C4⋊#92418C2211yescharacteristic
57C2×#14519706C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C61×#440C2218yescomplemented
73C2×#107×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122—21no—
79C22×Dic122—21no—
80C22×Dic122D411yescharacteristic
81C22×Dic122C2311yescharacteristic
82C22×D244C2311yescharacteristic
83C22×C22⋊D61—21no—
84C22×C22⋊D61—21no—
85C22×C4×D61—21no—
86C2×#11758202—24no—
87C2×#11758202C2314yes—
88C2×#11758201—24no—
89C2×#11758201C2314yes—
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92#14519777—22no—
93#14519777—28no—
94#14519777C2314yes—
95#14519776—28no—
96#14519776—28no—
97#14519776—22no—
98#14519776—22no—
99#14519776C2314yes—
100#14519776C2314yes—
101#14519773—22no—
102#14519773C2314yes—
103#14519765—22no—
104#14519765C2314yes—
105#14519764—22no—
106#14519764C2314yes—
107#14519763—28no—
108#14519760—28no—
109#14519759—28no—
110Q8×Dic61—22no—
111Q8×Dic61—22no—
112Q8×Dic61C2314yes—
113Q8×Dic61C2314yes—
114C4×Dic122—28no—
115C4×Dic122D414yes—
116C4×Dic122C2314yes—
117#14519742—22no—
118#14519742C2314yes—
119#14519739—22no—
120#14519739C2314yes—
121C4×C22⋊D61—28no—
122C2×C4⋊Dic61—21no—
123C2×C4⋊Dic61—21no—
124C2×C4⋊Dic61—21no—
125C2×C4⋊Dic61D411yescharacteristic
126C2×C4⋊Dic61C2311yescharacteristic
127C2×C4⋊Dic61C2311yescharacteristic
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196D411yescharacteristic
132C2×#11758196D411yescharacteristic
133C2×C22⋊Dic61—21no—
134C2×C22⋊Dic61—21no—
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61C2311yescharacteristic
142C2×C4×Dic61C2311yescharacteristic
143#14519710C2314yes—
144#14519710C2314yes—
145C4⋊#92418C2314yes—
146#14519706C2314yes—
147#14519706C2314yes—
148#14519702C2314yes—
149#14519702C2314yes—
150#14519700C2314yes—
151#14519699C2314yes—
152#14519699C2314yes—
153#14519698C2314yes—
154#14519698C2314yes—
155#14519697C2314yes—
156#14519687C2314yes—
157C8×Dic61C2314yes—
158C22×Q8×C61C2311yescharacteristic
159C22×D4×C61C2311yescharacteristic
160C23×C4×C61—21no—
161C2×SD16×C61—24no—
162C2×SD16×C61C2314yes—
163C22×C8×C61C2311yescharacteristic
164C22×C8×C61C2311yescharacteristic
165C4×Q8×C61—22no—
166C4×Q8×C61C2314yes—
167C4×D4×C61—22no—
168C4×D4×C61C2314yes—
169C2×C4⋊C4×C61—21no—
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C22⋊C4×C61—21no—
173C2×C42×C61—21no—
174C2×C42×C61C2311yescharacteristic
175#107×C61C2314yes—
176#103×C61C2314yes—
177#102×C61C2314yes—
178#97×C61C2314yes—
179C24×C61—21no—
180C23×D61—21no—
181C2×Q8×C61—21no—
182C2×Q8×C61—22no—
183C2×Q8×C61#4114yes—
184C2×Q8×C61C2412yes—
185C2×D4×C61—21no—
186C2×D4×C61—22no—
187C2×D4×C61—22no—
188C2×D4×C61C2412yes—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—24no—
193C22×C4×C61—82no—
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2411yescharacteristic
197C2×C22⋊D61—24no—
198C2×C22⋊D61—24no—
199C2×C22⋊D61—44no—
200C2×C22⋊D61—82no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61C2×D411yescharacteristic
205C22×Dic61C2×D411yescharacteristic
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208C2×D244—22no—
209C2×D244—22no—
210C2×D244—21no—
211C2×D244C2412yes—
212C2×C4×D61—24no—
213C2×C4×D61—82no—
214C2×Dic122—24no—
215C2×Dic122—22no—
216C2×Dic122—22no—
217C2×Dic122—21no—
218C2×Dic122—24no—
219C2×Dic122—24no—
220C2×Dic122—24no—
221C2×Dic122—82no—
222C2×Dic122—82no—
223C2×Dic122—82no—
224C2×Dic122C2×D414yes—
225C2×Dic122C2412yes—
226SD16×C61—28no—
227C2×C8×C61—22no—
228C2×C8×C61—22no—
229C2×C8×C61C2412yes—
230C2×C8×C61C2412yes—
231C4⋊C4×C61—24no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61C2412yes—
235C4⋊C4×C61C2412yes—
236C22⋊C4×C61—24no—
237C42×C61—24no—
238C42×C61C2×D412yes—
239C42×C61C2412yes—
240C22⋊Dic61—24no—
241C22⋊Dic61—24no—
242#11758202—28no—
243#11758201—28no—
244#11758198—24no—
245#11758198—24no—
246#11758198—24no—
247C4⋊Dic61—24no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—24no—
251C4⋊Dic61—24no—
252C4⋊Dic61C2×D414yes—
253C4⋊Dic61C2412yes—
254C4⋊Dic61C2412yes—
255#11758196—24no—
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×C61C2×#4114yes—
283D4×C61—22no—
284D4×C61—22no—
285D4×C61—42no—
286C2×C4×C61—24no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—84no—
295C2×C4×C61C22×D412yes—
296C2×C4×C61C22×D412yes—
297C2×C4×C61C22×D411yescharacteristic
298C2×C4×C61C2×#4112yes—
299C2×C4×C612−1+412yes—
300C2×C4×C61C2511yescharacteristic
301C22⋊D61—48no—
302C22⋊D61—84no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61—42no—
312C2×Dic61#13714yes—
313C2×Dic61C22×D412yes—
314C2×Dic61C22×D412yes—
315C2×Dic61C22×D412yes—
316C2×Dic61C22×D412yes—
317D244—22no—
318D244—22no—
319D244—42no—
320C4×D61—84no—
321Dic122—28no—
322Dic122—22no—
323Dic122—22no—
324Dic122—42no—
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×#464—611no—
371C2×#460—611no—
372C2×#446—611no—
373C2×#440—611no—
374C2×#440D6111yescharacteristic, complemented
375C2×C4×Q16—611no—
376C2×C61—82no—
377C2×C61#337514yescomplemented
378C2×C61C2×#54811yescharacteristic
379C2×C61C22×#13711yescharacteristic
380C2×C61C2×#57611yescharacteristic
381D61—82no—
382C22×Q16—611no—
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—611no—
398C2×#124—1221no—
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—1221no—
409C2×C4×D4C2×D6111yescharacteristic
410#489—618no—
411#489—618no—
412#486—618no—
413#477—618no—
414#474—618no—
415#474—618no—
416#464—618no—
417#464—618no—
418#460—618no—
419#446—618no—
420#440—618no—
421#440C2×D6118yescomplemented
422C4×Q16—618no—
423C2×#107—611no—
424C2×#107—611no—
425C2×#107C2×D6111yescharacteristic
426C2×C4⋊C8—611no—
427C2×C4⋊C8—611no—
428C2×C4⋊C8—611no—
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×#97C2×D6111yescharacteristic
441C2×C4×C8—611no—
442C61C2×#337511yescharacteristic, complemented, Sylow
443C22×Q8—611no—
444C22×Q8—611no—
445C22×Q8—1221no—
446C22×Q8—1221no—
447C22×Q8—1221no—
448C22×Q8C22×D6111yescharacteristic
449C22×D4—611no—
450C22×D4—1221no—
451C22×D4—1221no—
452C22×D4C22×D6111yescharacteristic
453C23×C4—21no—
454C23×C4—1221no—
455C2×Q16—614no—
456C2×Q16—1224no—
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—614no—
477#124—614no—
478#124—1222no—
479#124—1228no—
480#124—1222no—
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—22no—
495C4×D4—614no—
496C4×D4—1222no—
497C4×D4—1228no—
498C4×D4C22×D6114yes—
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⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4C22×D6111yescharacteristic
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—1221no—
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#107C22×D6114yes—
529C4⋊C8—614no—
530C4⋊C8—614no—
531C4⋊C8—614no—
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#97C22×D6114yes—
544C4×C8—614no—
545C24—21no—
546C24—1221no—
547C2×Q8—21no—
548C2×Q8—22no—
549C2×Q8—614no—
550C2×Q8—612no—
551C2×Q8—1224no—
552C2×Q8—1224no—
553C2×Q8—1224no—
554C2×Q8—1224no—
555C2×Q8—1221no—
556C2×Q8—1222no—
557C2×Q8—1222no—
558C2×Q8—4882no—
559C2×Q8—4882no—
560C2×Q8—4882no—
561C2×Q8#1175822214yes—
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—24no—
579C22×C4—82no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—1224no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—4882no—
589C22×C4D4×D6111yescharacteristic
590C22×C4D4×D6111yescharacteristic
591C22×C4C23×D6111yescharacteristic
592Q16—1228no—
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—21no—
606C4⋊C4—614no—
607C4⋊C4—614no—
608C4⋊C4—614no—
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—1224no—
619C4⋊C4C23×D6112yes—
620C4⋊C4C23×D6112yes—
621C22⋊C4—24no—
622C22⋊C4—1224no—
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—1228no—
649Q8—1222no—
650Q8—1222no—
651Q8—4884no—
652Q8—4884no—
653Q8—4884no—
654Q8—2442no—
655Q8C2×#1175822214yes—
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—84no—
673C2×C4—614no—
674C2×C4—612no—
675C2×C4—612no—
676C2×C4—612no—
677C2×C4—612no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
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×#1175822212yes—
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#1684042112yes—
707C22#137×D6112yes—
708C22#1684056612yes—
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#1684042112yes—
723C4C22×#1175822211yescharacteristic
724C4C2×#1451982411yescharacteristic
725C2—82no—
726C2—4882no—
727C2#2145863414yesdirect product factor
728C2C2×#1684042111yescharacteristic
729C2C2×#137×D6111yescharacteristic
730C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
prime radicalC2×#14519773C22
hypercenterC2×#440D61
hypocenterC61C2×#3375
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic122C2semidirect
3. #21458634C2direct (N × H)
4. C2×#16840122C2semidirect
5. C2×#16840120C2semidirect
7. C2×#16840056C2semidirect
8. C2×#16840042C2semidirect
9. C2×#16840041C2semidirect
10. C2×#16839984C2semidirect
11. C2×#16839982C2semidirect
13. C2×#16839890C2semidirect
14. C2×#16839865C2semidirect
15. C2×#16839854C2semidirect
16. C2×C61×#440C2semidirect
22. Q8×Dic122C22semidirect
42. #16840122C22semidirect
43. #16840120C22semidirect
45. #16840056C22semidirect
46. #16840042C22semidirect
47. #16840041C22semidirect
48. #16839984C22semidirect
49. #16839982C22semidirect
51. #16839890C22semidirect
52. #16839865C22semidirect
53. #16839854C22semidirect
72. C61×#440C22semidirect
374. C2×#440D61semidirect
377. C2×C61#3375semidirect
421. #440C2×D61semidirect
442. C61C2×#3375semidirect
727. C2#21458634direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404952
C2×Q8×Dic1222
#214586342
C2×#168401222
C2×#168401202
C2×#168401072
C2×#168400562
C2×#168400422
C2×#168400412
C2×#168399842
C2×#168399822
C2×#168399602
C2×#168398902
C2×#168398652
C2×#168398542
C2×C61×#4402
C2×#337561