Finite Group Databasebeta

← C2×#21458713 #30560485

Subgroups — C2×#21458713 #30560485

Order 15616.

2082 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×#16840471C211yesmaximal, characteristic, complemented
2C2×#16840427C211yesmaximal, characteristic, complemented
3#21458713C2116yesmaximal, direct product factor
4C2×#16840169C211yesmaximal, characteristic, complemented
5C2×#16840168C211yesmaximal, characteristic, complemented
6C2×#16840159C211yesmaximal, characteristic, complemented
7C2×#16840063C211yesmaximal, characteristic, complemented
8C2×#16840061C211yesmaximal, characteristic, complemented
9C2×#16840051C211yesmaximal, characteristic, complemented
10C2×#16840050C211yesmaximal, characteristic, complemented
11C2×#16840040C211yesmaximal, characteristic, complemented
12C2×#16839891C211yesmaximal, characteristic, complemented
13C2×#16839872C211yesmaximal, characteristic
14C2×#16839871C211yesmaximal, characteristic
15C2×#16839842C211yesmaximal, characteristic
16C2×C61×#476C211yesmaximal, characteristic, complemented
17C22×Q8×D61—21no—
18C22×#11758199C2211yescharacteristic
19#16840471—24no—
20#16840471C2218yescomplemented
21#16840427—24no—
22#16840427C2218yescomplemented
23C2×#14519776C2211yescharacteristic
24C2×#14519776C2211yescharacteristic
25C2×#14519776C2211yescharacteristic
26C2×#14519769C2211yescharacteristic
27C2×#14519768C2211yescharacteristic
28C2×#14519756—21no—
29C2×#14519755—21no—
30C2×#14519755—21no—
31C2×#14519754—21no—
32C2×#14519754—21no—
33C2×#14519753—21no—
34C2×C4×Dic122C2211yescharacteristic
35C2×C4×D244C2211yescharacteristic
36C2×D4×Dic61C2211yescharacteristic
37C2×D4×Dic61C2211yescharacteristic
38C2×#14519739C2211yescharacteristic
39C2×#14519739C2211yescharacteristic
40C22×#11758196—21no—
41#16840169C2218yescomplemented
42#16840168C2218yescomplemented
43#16840159C2218yescomplemented
44#16840063C2218yescomplemented
45#16840061C2218yescomplemented
46#16840051C2218yescomplemented
47#16840050C2218yescomplemented
48#16840040C2218yescomplemented
49#16839891C2218yescomplemented
50#16839872C2218yes—
51#16839871C2218yes—
52#16839842C2218yes—
53C2×#14519711C2211yescharacteristic
54C2×#14519710C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519708C2211yescharacteristic
59C2×#14519708C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519688C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C2×C4⋊Q8×C61C2211yescharacteristic
70C2×C4×D4×C61C2211yescharacteristic
71C61×#476C2218yescomplemented
72C2×#106×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122—21no—
79C22×Dic122—21no—
80C22×Dic122D411yescharacteristic
81C2×Q8×D61—28no—
82C2×Q8×D61—48no—
83C22×D244C2311yescharacteristic
84C23×Dic61—21no—
85C23×Dic61—21no—
86C22×C4×D61—21no—
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C2×#11758199Q818yescomplemented
90C2×#11758199C2314yes—
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93#14519776—22no—
94#14519776—22no—
95#14519776—22no—
96#14519776C2314yes—
97#14519776C2314yes—
98#14519776C2314yes—
99#14519769—22no—
100#14519769C2314yes—
101#14519768—22no—
102#14519768C2314yes—
103#14519756—28no—
104#14519755—28no—
105#14519755—28no—
106#14519754—28no—
107#14519754—28no—
108#14519753—28no—
109C4×Dic122D414yes—
110C4×Dic122C2314yes—
111C4×D244—22no—
112C4×D244C2314yes—
113D4×Dic61—22no—
114D4×Dic61—22no—
115D4×Dic61C2314yes—
116D4×Dic61C2314yes—
117#14519739—22no—
118#14519739—22no—
119#14519739C2314yes—
120#14519739C2314yes—
121C2×C4⋊Dic61—21no—
122C2×C4⋊Dic61D411yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×C4⋊Dic61C2311yescharacteristic
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—28no—
133C2×#11758196D411yescharacteristic
134C2×#11758196D411yescharacteristic
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×C4×Dic61C2311yescharacteristic
141C2×C4×Dic61C2311yescharacteristic
142#14519711C2314yes—
143#14519710C2314yes—
144#14519710C2314yes—
145#14519709C2314yes—
146#14519708C2314yes—
147#14519708C2314yes—
148#14519708C2314yes—
149#14519706C2314yes—
150#14519706C2314yes—
151#14519699C2314yes—
152#14519699C2314yes—
153#14519698C2314yes—
154#14519697C2314yes—
155#14519688C2314yes—
156#14519687C2314yes—
157C8×Dic61C2314yes—
158C22×Q8×C61—21no—
159C22×D4×C61C2311yescharacteristic
160C23×C4×C61—21no—
161C22×C8×C61C2311yescharacteristic
162C22×C8×C61C2311yescharacteristic
163C4⋊Q8×C61—22no—
164C4⋊Q8×C61C2314yes—
165C4×D4×C61—22no—
166C4×D4×C61C2314yes—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61C2311yescharacteristic
169C2×C4⋊C4×C61C2311yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C22⋊C4×C61—21no—
172C2×C42×C61C2311yescharacteristic
173#106×C61C2314yes—
174#106×C61C2314yes—
175C4⋊C8×C61C2314yes—
176#102×C61C2314yes—
177#102×C61C2314yes—
178C24×C61—21no—
179C23×D61—21no—
180C2×Q8×C61—24no—
181C2×Q8×C61—44no—
182C2×D4×C61—21no—
183C2×D4×C61—22no—
184C2×D4×C61C2×Q814yescomplemented
185C2×D4×C61C2412yes—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—24no—
190C22×C4×C61—82no—
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2411yescharacteristic
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—24no—
198C22×Dic61—24no—
199C22×Dic61—44no—
200C22×Dic61—82no—
201C22×Dic61C2×D411yescharacteristic
202C22×Dic61C2×D411yescharacteristic
203C22×Dic61C2×D411yescharacteristic
204C22×Dic61C2×D411yescharacteristic
205Q8×D61—432no—
206C2×D244—21no—
207C2×D244—22no—
208C2×D244C2×Q814yes—
209C2×D244C2412yes—
210C2×C4×D61—24no—
211C2×C4×D61—24no—
212C2×C4×D61—24no—
213C2×C4×D61—44no—
214C2×C4×D61—44no—
215C2×C4×D61—44no—
216C2×Dic122—24no—
217C2×Dic122—24no—
218C2×Dic122—24no—
219C2×Dic122—24no—
220C2×Dic122—44no—
221C2×Dic122—44no—
222C2×Dic122—82no—
223C2×Dic122C2×D414yes—
224C2×C8×C61—22no—
225C2×C8×C61—22no—
226C2×C8×C61C2412yes—
227C2×C8×C61C2412yes—
228C4⋊C4×C61—24no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61C2412yes—
233C4⋊C4×C61C2412yes—
234C4⋊C4×C61C2412yes—
235C22⋊C4×C61—24no—
236C42×C61C2×D412yes—
237C42×C61C2412yes—
238C22⋊Dic61—24no—
239C22⋊Dic61—24no—
240#11758199C2×Q8116yescomplemented
241#11758198—24no—
242#11758198—24no—
243#11758198—24no—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—24no—
248C4⋊Dic61C2×D414yes—
249C4⋊Dic61C2412yes—
250C4⋊Dic61C2412yes—
251C4⋊Dic61C2412yes—
252#11758196—24no—
253#11758196—24no—
254#11758196—24no—
255#11758196—24no—
256#11758196—24no—
257#11758196—24no—
258#11758196C2×D414yes—
259#11758196C2×D414yes—
260C4×Dic61C2×D412yes—
261C4×Dic61C2×D412yes—
262C4×Dic61C2412yes—
263C4×Dic61C2412yes—
264C2×#92418—22no—
265C2×#92418C2×Q814yescomplemented
266C2×#92418C2412yes—
267C2×#92418C2412yes—
268C23×C61—24no—
269C23×C61—22no—
270C23×C61—42no—
271C23×C61—42no—
272C23×C61C22×D411yescharacteristic
273C22×D61—24no—
274C22×D61—22no—
275C22×D61—42no—
276C22×D61—42no—
277Q8×C61—48no—
278D4×C61—24no—
279D4×C61—22no—
280D4×C61C22×Q814yescomplemented
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—84no—
290C2×C4×C61C22×D412yes—
291C2×C4×C61C22×D412yes—
292C2×C4×C61C22×D411yescharacteristic
293C2×C4×C61C22×Q812yes—
294C2×C4×C612−1+412yes—
295C2×C4×C61C2511yescharacteristic
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—48no—
306C2×Dic61—84no—
307C2×Dic61AGL(1,ℤ/8)14yes—
308C2×Dic61C22×D412yes—
309C2×Dic61C22×D412yes—
310C2×Dic61C22×D412yes—
311C2×Dic61C22×D412yes—
312D244—24no—
313D244—22no—
314D244C22×Q814yes—
315C4×D61—48no—
316C4×D61—48no—
317C4×D61—48no—
318Dic122—28no—
319Dic122—48no—
320Dic122—48no—
321Dic122—84no—
322C8×C61—22no—
323C8×C61—22no—
324#92418—22no—
325#92418C22×Q814yescomplemented
326C2×#3384—611nomaximal, Sylow
327C22×C61—24no—
328C22×C61—48no—
329C22×C61—42no—
330C22×C61—42no—
331C22×C61D4×Q812yes—
332C22×C61C2×AGL(1,ℤ/8)12yes—
333C22×C61#57712yes—
334C22×C61C23×D411yescharacteristic
335C2×D61—24no—
336C2×D61—48no—
337C2×D61—42no—
338C2×D61—42no—
339C4×C61—22no—
340C4×C61—22no—
341C4×C61—42no—
342C4×C61—42no—
343C4×C61—42no—
344C4×C61D4×Q812yes—
345C4×C61C23×Q811yescharacteristic
346C4×C61C2×2−1+411yescharacteristic
347Dic61—22no—
348Dic61—22no—
349Dic61—22no—
350Dic61—42no—
351Dic61—42no—
352Dic61—42no—
353Dic61C2×AGL(1,ℤ/8)14yes—
354C2×#554—611no—
355C2×D4×Q8—611no—
356#3384—6116no—
357C2×#501—611no—
358C2×#501—611no—
359C2×#498—611no—
360C2×#478—611no—
361C2×#478—611no—
362C2×#476—611no—
363C2×#476—611no—
364C2×#476D6111yescharacteristic, complemented
365C2×#474—611no—
366C2×#446—611no—
367C2×#442—611no—
368C2×#442—611no—
369C2×C4×D8—611no—
370C2×C61—44no—
371C2×C61#338414yescomplemented
372C2×C61C2×D4×Q811yescharacteristic
373C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
374C2×C61C2×#57711yescharacteristic
375D61—44no—
376C23×Q8—1221no—
377C22×D8—611no—
378#554—618no—
379#554—1224no—
380D4×Q8—618no—
381D4×Q8—1224no—
382C2×C4⋊Q8—611no—
383C2×C4⋊Q8—611no—
384C2×C4⋊Q8—611no—
385C2×C4⋊Q8C2×D6111yescharacteristic
386C2×#125—611no—
387C2×#125—611no—
388C2×C22⋊Q8—1221no—
389C2×C22⋊Q8—1221no—
390C2×C22⋊Q8—1221no—
391C2×C22⋊Q8—1221no—
392C2×C22⋊Q8—1221no—
393C2×C22⋊Q8—1221no—
394C2×C4×Q8—611no—
395C2×C4×D4—611no—
396C2×C4×D4—611no—
397C2×C4×D4—611no—
398C2×C4×D4—611no—
399C2×C4×D4—611no—
400C2×C4×D4C2×D6111yescharacteristic
401C22×C4⋊C4—1221no—
402#501—618no—
403#501—618no—
404#498—618no—
405#478—618no—
406#478—618no—
407#476—618no—
408#476—618no—
409#476C2×D6118yescomplemented
410#474—618no—
411#446—618no—
412#442—618no—
413#442—618no—
414C4×D8—618no—
415C2×#107—611no—
416C2×#107—611no—
417C2×#107—611no—
418C2×#106—611no—
419C2×#106—611no—
420C2×#106—611no—
421C2×#106—611no—
422C2×#106C2×D6111yescharacteristic
423C2×#106C2×D6111yescharacteristic
424C2×C4⋊C8—611no—
425C2×C4⋊C8—611no—
426C2×C4⋊C8C2×D6111yescharacteristic
427C2×#102—611no—
428C2×#102—611no—
429C2×#102—611no—
430C2×#102—611no—
431C2×#102C2×D6111yescharacteristic
432C2×#102C2×D6111yescharacteristic
433C2×#97—611no—
434C2×#97—611no—
435C2×C4×C8—611no—
436C61C2×#338411yescharacteristic, complemented, Sylow
437C22×Q8—21no—
438C22×Q8—611no—
439C22×Q8—1221no—
440C22×Q8—1221no—
441C22×Q8—1221no—
442C22×Q8—1228no—
443C22×Q8—2448no—
444C22×D4—611no—
445C22×D4C22×D6111yescharacteristic
446C23×C4—21no—
447C23×C4—1221no—
448C23×C4—1221no—
449C23×C4—1221no—
450C23×C4—1221no—
451C23×C4—1221no—
452C2×D8—618no—
453C2×D8—614no—
454C22×C8—611no—
455C22×C8—611no—
456C22×C8C22×D6111yescharacteristic
457C22×C8C22×D6111yescharacteristic
458C4⋊Q8—22no—
459C4⋊Q8—614no—
460C4⋊Q8—614no—
461C4⋊Q8—614no—
462C4⋊Q8—1222no—
463C4⋊Q8—1222no—
464C4⋊Q8—1222no—
465C4⋊Q8C22×D6114yes—
466#125—614no—
467#125—614no—
468#125—1222no—
469#125—1222no—
470C22⋊Q8—1228no—
471C22⋊Q8—1228no—
472C22⋊Q8—1228no—
473C22⋊Q8—1228no—
474C22⋊Q8—1228no—
475C22⋊Q8—1228no—
476C4×Q8—614no—
477C4×Q8—614no—
478C4×D4—22no—
479C4×D4—614no—
480C4×D4—614no—
481C4×D4—614no—
482C4×D4—614no—
483C4×D4—614no—
484C4×D4—1222no—
485C4×D4—1222no—
486C4×D4—1222no—
487C4×D4—1222no—
488C4×D4—1222no—
489C4×D4C22×D6114yes—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—1228no—
498C2×C4⋊C4—1221no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4C22×D6111yescharacteristic
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C4⋊C4C22×D6111yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C42—611no—
515C2×C42—611no—
516C2×C42C22×D6111yescharacteristic
517#107—614no—
518#107—614no—
519#107—614no—
520#106—614no—
521#106—614no—
522#106—614no—
523#106—614no—
524#106C22×D6114yes—
525#106C22×D6114yes—
526C4⋊C8—614no—
527C4⋊C8—614no—
528C4⋊C8C22×D6114yes—
529#102—614no—
530#102—614no—
531#102—614no—
532#102—614no—
533#102C22×D6114yes—
534#102C22×D6114yes—
535#97—614no—
536#97—614no—
537C4×C8—614no—
538C24—21no—
539C24—1221no—
540C2×Q8—24no—
541C2×Q8—44no—
542C2×Q8—614no—
543C2×Q8—1224no—
544C2×Q8—1224no—
545C2×Q8—1224no—
546C2×Q8—1224no—
547C2×Q8—4882no—
548C2×Q8—2444no—
549C2×Q8—2444no—
550C2×Q8—24432no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—614no—
554C2×D4—612no—
555C2×D4—1221no—
556C2×D4—1222no—
557C2×D4Q8×D6114yescomplemented
558C2×D4C23×D6112yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—24no—
563C22×C4—82no—
564C22×C4—611no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—1224no—
569C22×C4—1224no—
570C22×C4—1224no—
571C22×C4—1224no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1224no—
576C22×C4—4882no—
577C22×C4—2444no—
578C22×C4—2444no—
579C22×C4—2444no—
580C22×C4—2444no—
581C22×C4D4×D6111yescharacteristic
582C22×C4D4×D6111yescharacteristic
583C22×C4C23×D6111yescharacteristic
584D8—6116no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—614no—
588C2×C8—612no—
589C2×C8—612no—
590C2×C8—1222no—
591C2×C8C23×D6112yes—
592C2×C8C23×D6112yes—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—614no—
598C4⋊C4—614no—
599C4⋊C4—614no—
600C4⋊C4—612no—
601C4⋊C4—612no—
602C4⋊C4—612no—
603C4⋊C4—1224no—
604C4⋊C4—1224no—
605C4⋊C4—1224no—
606C4⋊C4—1224no—
607C4⋊C4—1224no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1224no—
612C4⋊C4—1224no—
613C4⋊C4C23×D6112yes—
614C4⋊C4C23×D6112yes—
615C4⋊C4C23×D6112yes—
616C22⋊C4—24no—
617C22⋊C4—1224no—
618C22⋊C4—1224no—
619C22⋊C4—1224no—
620C22⋊C4—1224no—
621C22⋊C4—1224no—
622C42—612no—
623C42—612no—
624C42—612no—
625C42—612no—
626C42D4×D6112yes—
627C42C23×D6112yes—
628C23—22no—
629C23—24no—
630C23—42no—
631C23—42no—
632C23—1222no—
633C23—1224no—
634C23—2442no—
635C23—2442no—
636C23C2×D4×D6111yescharacteristic
637Q8—48no—
638Q8—1228no—
639Q8—4884no—
640Q8—2448no—
641Q8—2448no—
642D4—22no—
643D4—24no—
644D4—614no—
645D4—1222no—
646D4—1224no—
647D4C2×Q8×D6114yescomplemented
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—84no—
657C2×C4—614no—
658C2×C4—612no—
659C2×C4—612no—
660C2×C4—612no—
661C2×C4—612no—
662C2×C4—1222no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—4884no—
669C2×C4—2448no—
670C2×C4—2448no—
671C2×C4—2448no—
672C2×C4—2448no—
673C2×C4—2442no—
674C2×C4—2442no—
675C2×C4—2442no—
676C2×C4C2×D4×D6112yes—
677C2×C4C2×D4×D6112yes—
678C2×C4C2×D4×D6111yescharacteristic
679C2×C4C2×Q8×D6112yes—
680C2×C4#1451982412yes—
681C2×C4C24×D6111yescharacteristic
682C8—22no—
683C8—22no—
684C8—614no—
685C8—1222no—
686C22—24no—
687C22—48no—
688C22—42no—
689C22—42no—
690C22—1224no—
691C22—2448no—
692C22—2442no—
693C22—2442no—
694C22#1684042512yes—
695C22AGL(1,ℤ/8)×D6112yes—
696C22#1684056812yes—
697C22C22×D4×D6111yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—614no—
704C4—1222no—
705C4—1222no—
706C4—1222no—
707C4—2442no—
708C4—2442no—
709C4—2442no—
710C4#1684042512yes—
711C4C22×Q8×D6111yescharacteristic
712C4C2×#1451982411yescharacteristic
713C2—44no—
714C2—2444no—
715C2#2145871314yesdirect product factor
716C2C2×#1684042511yescharacteristic
717C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
718C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#476C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
hypercenterC2×#476D61
hypocenterC61C2×#3384
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#16840471C2semidirect
2. C2×#16840427C2semidirect
3. #21458713C2direct (N × H)
4. C2×#16840169C2semidirect
5. C2×#16840168C2semidirect
6. C2×#16840159C2semidirect
7. C2×#16840063C2semidirect
8. C2×#16840061C2semidirect
9. C2×#16840051C2semidirect
10. C2×#16840050C2semidirect
11. C2×#16840040C2semidirect
12. C2×#16839891C2semidirect
16. C2×C61×#476C2semidirect
20. #16840471C22semidirect
22. #16840427C22semidirect
41. #16840169C22semidirect
42. #16840168C22semidirect
43. #16840159C22semidirect
44. #16840063C22semidirect
45. #16840061C22semidirect
46. #16840051C22semidirect
47. #16840050C22semidirect
48. #16840040C22semidirect
49. #16839891C22semidirect
71. C61×#476C22semidirect
89. C2×#11758199Q8semidirect
184. C2×D4×C61C2×Q8semidirect
240. #11758199C2×Q8semidirect
265. C2×#92418C2×Q8semidirect
280. D4×C61C22×Q8semidirect
325. #92418C22×Q8semidirect
364. C2×#476D61semidirect
371. C2×C61#3384semidirect
409. #476C2×D61semidirect
436. C61C2×#3384semidirect
557. C2×D4Q8×D61semidirect
647. D4C2×Q8×D61semidirect
715. C2#21458713direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404712
C2×#168404272
#214587132
C2×#168401692
C2×#168401682
C2×#168401592
C2×#168400632
C2×#168400612
C2×#168400512
C2×#168400502
C2×#168400402
C2×#168398912
C2×#168398722
C2×#168398712
C2×#168398422
C2×C61×#4762
C2×#338461