Finite Group Databasebeta

← C2×#21458430 #30558747

Subgroups — C2×#21458430 #30558747

Order 15616.

1866 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840480C211yesmaximal, characteristic
2C2×#16840467C211yesmaximal, characteristic
3#21458430C2116yesmaximal, direct product factor
4C2×#16840159C211yesmaximal, characteristic, complemented
5C2×#16840105C211yesmaximal, characteristic, complemented
6C2×#16840103C211yesmaximal, characteristic, complemented
7C2×#16840094C211yesmaximal, characteristic, complemented
8C2×#16840092C211yesmaximal, characteristic, complemented
9C2×#16840056C211yesmaximal, characteristic, complemented
10C2×#16840046C211yesmaximal, characteristic, complemented
11C2×#16840021C211yesmaximal, characteristic, complemented
12C2×#16840020C211yesmaximal, characteristic, complemented
13C2×#16839856C211yesmaximal, characteristic, complemented
14C2×#16839838C211yesmaximal, characteristic
15C2×#16839803C211yesmaximal, characteristic, complemented
16C2×C61×#428C211yesmaximal, characteristic, complemented
17C22×Dic244C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19#16840480—24no—
20#16840480C2218yes—
21#16840467—24no—
22#16840467C2218yes—
23C2×#14519776C2211yescharacteristic
24C2×#14519776C2211yescharacteristic
25C2×#14519771—21no—
26C2×#14519770—21no—
27C2×#14519767—21no—
28C2×#14519763—21no—
29C2×#14519757C2211yescharacteristic
30C2×#14519757C2211yescharacteristic
31C2×#14519756—21no—
32C2×#14519756C2211yescharacteristic
33C2×#14519756C2211yescharacteristic
34C2×#14519755—21no—
35C2×C4×Dic122—21no—
36C2×#14519742C2211yescharacteristic
37C2×#14519742C2211yescharacteristic
38C2×C4×C22⋊D61—21no—
39C2×C4×C22⋊D61C2211yescharacteristic
40C2×#14519735C2211yescharacteristic
41C2×C4⋊C4×D61C2211yescharacteristic
42#16840159C2218yescomplemented
43#16840105C2218yescomplemented
44#16840103C2218yescomplemented
45#16840094C2218yescomplemented
46#16840092C2218yescomplemented
47#16840056C2218yescomplemented
48#16840046C2218yescomplemented
49#16840021C2218yescomplemented
50#16840020C2218yescomplemented
51#16839856C2218yescomplemented
52#16839838C2218yes—
53#16839803C2218yescomplemented
54C2×#14519710C2211yescharacteristic
55C2×#14519709C2211yescharacteristic
56C2×#14519708C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519708C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65C2×#14519700C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×M16×C61C2211yescharacteristic
70C2×#117×C61C2211yescharacteristic
71C22×C4⋊C4×C61C2211yescharacteristic
72C61×#428C2218yescomplemented
73C2×#107×C61C2211yescharacteristic
74C2×#107×C61C2211yescharacteristic
75C2×#106×C61C2211yescharacteristic
76C2×#106×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122—21no—
79C22×Dic122C2311yescharacteristic
80C22×Dic122C2311yescharacteristic
81C22×C22⋊D61D411yescharacteristic
82C22×C4×D61—21no—
83C22×C4×D61C2311yescharacteristic
84C2×Dic244—24no—
85C2×Dic244C2314yes—
86C2×#11758189—24no—
87C2×#11758189C2314yes—
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90#14519776—22no—
91#14519776—22no—
92#14519776C2314yes—
93#14519776C2314yes—
94#14519771—28no—
95#14519770—28no—
96#14519767—28no—
97#14519763—28no—
98#14519757—22no—
99#14519757—22no—
100#14519757C2314yes—
101#14519757C2314yes—
102#14519756—22no—
103#14519756—22no—
104#14519756—28no—
105#14519756C2314yes—
106#14519756C2314yes—
107#14519755—28no—
108C4×Dic122—28no—
109#14519742—22no—
110#14519742—22no—
111#14519742C2314yes—
112#14519742C2314yes—
113C4×C22⋊D61—28no—
114C4×C22⋊D61D414yes—
115C4×C22⋊D61C2314yes—
116#14519735—22no—
117#14519735C2314yes—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61C2311yescharacteristic
121C2×C4⋊Dic61C2311yescharacteristic
122C2×#11758196—21no—
123C2×#11758196—21no—
124C2×#11758196—21no—
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196D411yescharacteristic
130C4⋊C4×D61—22no—
131C4⋊C4×D61C2314yes—
132C2×C22⋊Dic61—21no—
133C2×C22⋊Dic61—21no—
134C2×C22⋊Dic61D411yescharacteristic
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198D411yescharacteristic
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61—21no—
142C2×C4×Dic61C2311yescharacteristic
143#14519710C2314yes—
144#14519709C2314yes—
145#14519708C2314yes—
146#14519708C2314yes—
147#14519708C2314yes—
148#14519706C2314yes—
149#14519702C2314yes—
150#14519702C2314yes—
151#14519700C2314yes—
152#14519700C2314yes—
153#14519700C2314yes—
154#14519700C2314yes—
155C22⋊#92418C2314yes—
156#14519689C2314yes—
157C8×Dic61C2314yes—
158C23×C4×C61—21no—
159C23×C4×C61C2311yescharacteristic
160C2×M16×C61—24no—
161C2×M16×C61C2314yes—
162C22×C8×C61C2311yescharacteristic
163C22×C8×C61C2311yescharacteristic
164#117×C61—22no—
165#117×C61C2314yes—
166C2×C4⋊C4×C61—22no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61C2311yescharacteristic
169C2×C4⋊C4×C61C2314yes—
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C22⋊C4×C61—21no—
174C2×C42×C61—21no—
175#107×C61C2314yes—
176#107×C61C2314yes—
177#106×C61C2314yes—
178#106×C61C2314yes—
179C24×C61C2×D411yescharacteristic
180C23×D61C2×D411yescharacteristic
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—24no—
188C22×C4×C61—82no—
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D412yes—
191C22×C4×C61C2412yes—
192C22×C4×C61C2411yescharacteristic
193C2×C22⋊D61—24no—
194C2×C22⋊D61C2×D414yes—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61C2×D411yescharacteristic
200C22×Dic61C2×D411yescharacteristic
201C22×Dic61C2×D411yescharacteristic
202C2×C4×D61—22no—
203C2×C4×D61—22no—
204C2×C4×D61—24no—
205C2×C4×D61—82no—
206C2×C4×D61C2×D412yes—
207C2×C4×D61C2412yes—
208C2×Dic122—22no—
209C2×Dic122—22no—
210C2×Dic122—22no—
211C2×Dic122—22no—
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122—24no—
215C2×Dic122—24no—
216C2×Dic122—44no—
217C2×Dic122—82no—
218C2×Dic122C2412yes—
219C2×Dic122C2412yes—
220M16×C61—28no—
221C2×C8×C61—22no—
222C2×C8×C61#4114yes—
223C2×C8×C61C2412yes—
224C2×C8×C61C2412yes—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—24no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61C2412yes—
231C4⋊C4×C61C2412yes—
232C4⋊C4×C61C2412yes—
233C4⋊C4×C61C2412yes—
234C22⋊C4×C61—24no—
235C42×C61—24no—
236C22⋊Dic61—24no—
237C22⋊Dic61—24no—
238C22⋊Dic61C2×D414yes—
239#11758198—24no—
240#11758198—24no—
241#11758198—24no—
242#11758198C2×D414yes—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61—24no—
246C4⋊Dic61—24no—
247C4⋊Dic61C2412yes—
248C4⋊Dic61C2412yes—
249#11758196—24no—
250#11758196—24no—
251#11758196—24no—
252#11758196—24no—
253#11758196—24no—
254#11758196—24no—
255#11758196—24no—
256#11758196C2×D414yes—
257C4×Dic61—24no—
258C4×Dic61—24no—
259C4×Dic61—24no—
260C4×Dic61C2×D412yes—
261C4×Dic61C2412yes—
262C2×#92418—22no—
263C2×#92418—22no—
264C2×#92418C2412yes—
265C2×#92418C2412yes—
266Dic244—28no—
267#11758189—28no—
268C23×C61—22no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61C22×D412yes—
272C23×C61C22×D411yescharacteristic
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61C22×D412yes—
277C2×C4×C61—22no—
278C2×C4×C61—24no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—84no—
290C2×C4×C61C22×D412yes—
291C2×C4×C61C22×D411yescharacteristic
292C2×C4×C61C2×#4112yes—
293C2×C4×C612−1+412yes—
294C2×C4×C61C2511yescharacteristic
295C22⋊D61—28no—
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—42no—
303C2×Dic61—42no—
304C2×Dic61—42no—
305C2×Dic61—42no—
306C2×Dic61#13714yes—
307C2×Dic61C22×D412yes—
308C2×Dic61C22×D412yes—
309C2×Dic61C22×D412yes—
310C4×D61—24no—
311C4×D61—22no—
312C4×D61—22no—
313C4×D61—84no—
314Dic122—22no—
315Dic122—22no—
316Dic122—22no—
317Dic122—22no—
318Dic122—42no—
319Dic122—42no—
320Dic122—48no—
321Dic122—84no—
322C8×C61—22no—
323C8×C61C2×#4114yes—
324#92418—22no—
325#92418—22no—
326C2×#3356—611nomaximal, Sylow
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—22no—
330C22×C61—44no—
331C22×C61#54712yes—
332C22×C61C2×#13712yes—
333C22×C61#57712yes—
334C22×C61C23×D411yescharacteristic
335C2×D61—22no—
336C2×D61—22no—
337C2×D61—22no—
338C2×D61—44no—
339C4×C61—22no—
340C4×C61—42no—
341C4×C61—42no—
342C4×C61—42no—
343C4×C61—42no—
344C4×C61#54712yes—
345C4×C61C22×#4111yescharacteristic
346C4×C61C2×2−1+411yescharacteristic
347Dic61—22no—
348Dic61—22no—
349Dic61—42no—
350Dic61—42no—
351Dic61—42no—
352Dic61—42no—
353Dic61C2×#13714yes—
354C2×#556—611no—
355C2×#554—611no—
356#3356—6116no—
357C2×#498—611no—
358C2×#485—611no—
359C2×#485—611no—
360C2×#483—611no—
361C2×#483—611no—
362C2×#477—611no—
363C2×#475—611no—
364C2×#470—611no—
365C2×#470—611no—
366C2×C4×Q16—611no—
367C2×#436—611no—
368C2×#428—611no—
369C2×#428D6111yescharacteristic, complemented
370C2×C61—42no—
371C2×C61#335614yescomplemented
372C2×C61C2×#54711yescharacteristic
373C2×C61C22×#13711yescharacteristic
374C2×C61C2×#57711yescharacteristic
375D61—42no—
376C22×Q16—611no—
377C22×M16—611no—
378C22×M16C2×D6111yescharacteristic
379#556—618no—
380#556—1224no—
381#554—618no—
382#554—1224no—
383C2×C4⋊Q8—611no—
384C2×C4⋊Q8—611no—
385C2×#126—1221no—
386C2×#126—1221no—
387C2×#125—1221no—
388C2×#124—1221no—
389C2×C22⋊Q8—611no—
390C2×C22⋊Q8—611no—
391C2×C22⋊Q8—611no—
392C2×C22⋊Q8—611no—
393C2×C22⋊Q8—1221no—
394C2×C22⋊Q8—1221no—
395C2×C4×Q8—611no—
396C2×C4×Q8—611no—
397C2×C4×Q8—1221no—
398C2×C4×D4—611no—
399C2×C4×D4—1221no—
400C2×#117—611no—
401C2×#117C2×D6111yescharacteristic
402C22×C4⋊C4—611no—
403C22×C4⋊C4C2×D6111yescharacteristic
404#498—618no—
405#485—618no—
406#485—618no—
407#483—618no—
408#483—618no—
409#477—618no—
410#475—618no—
411#470—618no—
412#470—618no—
413C4×Q16—618no—
414#436—618no—
415#428—618no—
416#428C2×D6118yescomplemented
417C2×#107—611no—
418C2×#107C2×D6111yescharacteristic
419C2×#107C2×D6111yescharacteristic
420C2×#106—611no—
421C2×#106—611no—
422C2×#106—611no—
423C2×#106—611no—
424C2×#106C2×D6111yescharacteristic
425C2×#106C2×D6111yescharacteristic
426C2×C4⋊C8—611no—
427C2×#103—611no—
428C2×#103—611no—
429C2×#103—611no—
430C2×#103—611no—
431C2×#103—611no—
432C2×#103—611no—
433C2×C22⋊C8—611no—
434C2×C22⋊C8—611no—
435C2×C4×C8—611no—
436C61C2×#335611yescharacteristic, complemented, Sylow
437C22×Q8—611no—
438C22×Q8—611no—
439C22×Q8—1221no—
440C22×Q8—1221no—
441C22×D4—611no—
442C23×C4—21no—
443C23×C4—611no—
444C23×C4—1221no—
445C23×C4C22×D6111yescharacteristic
446C2×Q16—614no—
447C2×Q16—1224no—
448C2×M16—24no—
449C2×M16—614no—
450C2×M16—1224no—
451C2×M16C22×D6114yes—
452C22×C8—611no—
453C22×C8—611no—
454C22×C8C22×D6111yescharacteristic
455C22×C8C22×D6111yescharacteristic
456C4⋊Q8—614no—
457C4⋊Q8—614no—
458C4⋊Q8—1222no—
459C4⋊Q8—1222no—
460#126—1228no—
461#126—1228no—
462#125—1228no—
463#124—1228no—
464C22⋊Q8—614no—
465C22⋊Q8—614no—
466C22⋊Q8—614no—
467C22⋊Q8—614no—
468C22⋊Q8—1228no—
469C22⋊Q8—1228no—
470C22⋊Q8—1222no—
471C22⋊Q8—1222no—
472C22⋊Q8—1222no—
473C22⋊Q8—1222no—
474C4×Q8—614no—
475C4×Q8—614no—
476C4×Q8—1228no—
477C4×Q8—1222no—
478C4×Q8—1222no—
479C4×D4—614no—
480C4×D4—614no—
481C4×D4—1228no—
482#117—22no—
483#117—614no—
484#117—1222no—
485#117C22×D6114yes—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—614no—
492C2×C4⋊C4—1222no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4—1221no—
497C2×C4⋊C4—1221no—
498C2×C4⋊C4—1221no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4C22×D6111yescharacteristic
503C2×C4⋊C4C22×D6111yescharacteristic
504C2×C4⋊C4C22×D6114yes—
505C2×C4⋊C4C22×D6111yescharacteristic
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—611no—
509C2×C22⋊C4—611no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1221no—
515C2×C42—21no—
516C2×C42—611no—
517C2×C42—1221no—
518C2×C42—1221no—
519C2×C42—1221no—
520#107—614no—
521#107C22×D6114yes—
522#107C22×D6114yes—
523#106—614no—
524#106—614no—
525#106—614no—
526#106—614no—
527#106C22×D6114yes—
528#106C22×D6114yes—
529C4⋊C8—614no—
530#103—614no—
531#103—614no—
532#103—614no—
533#103—614no—
534#103—614no—
535#103—614no—
536C22⋊C8—614no—
537C22⋊C8—614no—
538C4×C8—614no—
539C24—611no—
540C24D4×D6111yescharacteristic
541C2×Q8—612no—
542C2×Q8—612no—
543C2×Q8—1224no—
544C2×Q8—1224no—
545C2×Q8—1221no—
546C2×Q8—1221no—
547C2×Q8—1222no—
548C2×Q8—1222no—
549C2×Q8—1222no—
550C2×Q8—1222no—
551C2×Q8—4882no—
552C2×Q8—2444no—
553C2×D4—614no—
554C2×D4—1224no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—82no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—611no—
566C22×C4—612no—
567C22×C4—612no—
568C22×C4—1224no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—4882no—
576C22×C4D4×D6112yes—
577C22×C4D4×D6111yescharacteristic
578C22×C4C23×D6112yes—
579C22×C4C23×D6111yescharacteristic
580Q16—1228no—
581M16—28no—
582M16—1228no—
583C2×C8—22no—
584C2×C8—612no—
585C2×C8—612no—
586C2×C8—1222no—
587C2×C8—1222no—
588C2×C8#1175822214yes—
589C2×C8C23×D6112yes—
590C2×C8C23×D6112yes—
591C4⋊C4—21no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—614no—
597C4⋊C4—612no—
598C4⋊C4—612no—
599C4⋊C4—1224no—
600C4⋊C4—1224no—
601C4⋊C4—1224no—
602C4⋊C4—1224no—
603C4⋊C4—1224no—
604C4⋊C4—1224no—
605C4⋊C4—1224no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—1224no—
609C4⋊C4—1224no—
610C4⋊C4C23×D6112yes—
611C4⋊C4C23×D6112yes—
612C4⋊C4C23×D6112yes—
613C4⋊C4C23×D6112yes—
614C22⋊C4—24no—
615C22⋊C4—614no—
616C22⋊C4—614no—
617C22⋊C4—1224no—
618C22⋊C4—1224no—
619C22⋊C4—1224no—
620C22⋊C4—1224no—
621C22⋊C4—1224no—
622C42—24no—
623C42—612no—
624C42—612no—
625C42—1224no—
626C42—1224no—
627C42—1224no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—612no—
632C23—1222no—
633C23—1222no—
634C23—1222no—
635C23C2×D4×D6112yes—
636C23C2×D4×D6111yescharacteristic
637Q8—1222no—
638Q8—1222no—
639Q8—1222no—
640Q8—1222no—
641Q8—4884no—
642Q8—2448no—
643Q8—2442no—
644Q8—2442no—
645D4—1228no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—84no—
659C2×C4—614no—
660C2×C4—612no—
661C2×C4—612no—
662C2×C4—612no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1224no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—4884no—
673C2×C4—2442no—
674C2×C4—2442no—
675C2×C4—2442no—
676C2×C4—2442no—
677C2×C4C2×D4×D6112yes—
678C2×C4C2×D4×D6111yescharacteristic
679C2×C4C2×#1175822212yes—
680C2×C4#1451982512yes—
681C2×C4C24×D6111yescharacteristic
682C8—22no—
683C8—1222no—
684C8—1222no—
685C8C2×#1175822214yes—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—44no—
690C22—1222no—
691C22—1222no—
692C22—1222no—
693C22—2444no—
694C22#1684041312yes—
695C22#137×D6112yes—
696C22#1684057212yes—
697C22C22×D4×D6111yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—614no—
704C4—1222no—
705C4—1222no—
706C4—2442no—
707C4—2442no—
708C4—2442no—
709C4—2442no—
710C4#1684041312yes—
711C4C22×#1175822211yescharacteristic
712C4C2×#1451982511yescharacteristic
713C2—42no—
714C2—2442no—
715C2#2145843014yesdirect product factor
716C2C2×#1684041311yescharacteristic
717C2C2×#137×D6111yescharacteristic
718C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#428C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenterC2×#428D61
hypocenterC61C2×#3356
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
3. #21458430C2direct (N × H)
4. C2×#16840159C2semidirect
5. C2×#16840105C2semidirect
6. C2×#16840103C2semidirect
7. C2×#16840094C2semidirect
8. C2×#16840092C2semidirect
9. C2×#16840056C2semidirect
10. C2×#16840046C2semidirect
11. C2×#16840021C2semidirect
12. C2×#16840020C2semidirect
13. C2×#16839856C2semidirect
15. C2×#16839803C2semidirect
16. C2×C61×#428C2semidirect
42. #16840159C22semidirect
43. #16840105C22semidirect
44. #16840103C22semidirect
45. #16840094C22semidirect
46. #16840092C22semidirect
47. #16840056C22semidirect
48. #16840046C22semidirect
49. #16840021C22semidirect
50. #16840020C22semidirect
51. #16839856C22semidirect
53. #16839803C22semidirect
72. C61×#428C22semidirect
369. C2×#428D61semidirect
371. C2×C61#3356semidirect
416. #428C2×D61semidirect
436. C61C2×#3356semidirect
715. C2#21458430direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404802
C2×#168404672
#214584302
C2×#168401592
C2×#168401052
C2×#168401032
C2×#168400942
C2×#168400922
C2×#168400562
C2×#168400462
C2×#168400212
C2×#168400202
C2×#168398562
C2×#168398382
C2×#168398032
C2×C61×#4282
C2×#335661