Finite Group Databasebeta

← C2×#21458389 #30558702

Subgroups — C2×#21458389 #30558702

Order 15616.

1834 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840454C211yesmaximal, characteristic
2C2×#16840446C211yesmaximal, characteristic
3#21458389C2116yesmaximal, direct product factor
4C2×#16840162C211yesmaximal, characteristic, complemented
5C2×#16840096C211yesmaximal, characteristic, complemented
6C2×#16840095C211yesmaximal, characteristic, complemented
7C2×#16840101C211yesmaximal, characteristic, complemented
8C2×#16840100C211yesmaximal, characteristic, complemented
9C2×#16840071C211yesmaximal, characteristic, complemented
10C2×#16840067C211yesmaximal, characteristic, complemented
11C2×#16840017C211yesmaximal, characteristic, complemented
12C2×Q16×Dic61C211yesmaximal, characteristic, complemented
13C2×#16839838C211yesmaximal, characteristic
14C2×#16839804C211yesmaximal, characteristic, complemented
15C2×#16839801C211yesmaximal, characteristic, complemented
16C2×C61×#470C211yesmaximal, characteristic, complemented
17C22×#11758189C2211yescharacteristic
18#16840454—24no—
19#16840454C2218yes—
20#16840446—24no—
21#16840446C2218yes—
22C2×#14519772—21no—
23C2×#14519770—21no—
24C2×#14519768—21no—
25C2×#14519768C2211yescharacteristic
26C2×#14519768C2211yescharacteristic
27C2×#14519767—21no—
28C2×#14519761—21no—
29C2×#14519759—21no—
30C2×#14519753C2211yescharacteristic
31C2×#14519753C2211yescharacteristic
32C2×Q8×Dic61C2211yescharacteristic
33C2×Q8×Dic61C2211yescharacteristic
34C2×C4×C22⋊D61C2211yescharacteristic
35C2×#14519736C2211yescharacteristic
36C2×#14519735—21no—
37C2×#14519735C2211yescharacteristic
38C2×#14519733—21no—
39C22×C4⋊Dic61C2211yescharacteristic
40C2×C4⋊C4×D61C2211yescharacteristic
41#16840162C2218yescomplemented
42#16840101C2218yescomplemented
43#16840100C2218yescomplemented
44#16840096C2218yescomplemented
45#16840095C2218yescomplemented
46#16840071C2218yescomplemented
47#16840067C2218yescomplemented
48#16840017C2218yescomplemented
49Q16×Dic61C2218yescomplemented
50#16839838C2218yes—
51#16839804C2218yescomplemented
52#16839801C2218yescomplemented
53C2×#14519711C2211yescharacteristic
54C2×#14519711C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519710C2211yescharacteristic
58C2×#14519709C2211yescharacteristic
59C2×#14519709C2211yescharacteristic
60C2×#14519708C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519701C2211yescharacteristic
64C2×#14519701C2211yescharacteristic
65C2×#14519701C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×Q16×C61C2211yescharacteristic
70C22×M16×C61C2211yescharacteristic
71C2×C22⋊Q8×C61C2211yescharacteristic
72C2×C22⋊Q8×C61C2211yescharacteristic
73C61×#470C2218yescomplemented
74C2×#106×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#103×C61C2211yescharacteristic
77C22×C22⋊D61D411yescharacteristic
78C23×Dic61—21no—
79C22×C4×D61—21no—
80C22×C4×D61C2311yescharacteristic
81C2×#11758189—24no—
82C2×#11758189C2314yes—
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85#14519772—28no—
86#14519770—28no—
87#14519768—28no—
88#14519768—22no—
89#14519768—22no—
90#14519768C2314yes—
91#14519768C2314yes—
92#14519767—28no—
93#14519761—28no—
94#14519759—28no—
95#14519753—22no—
96#14519753—22no—
97#14519753C2314yes—
98#14519753C2314yes—
99Q8×Dic61—22no—
100Q8×Dic61—22no—
101Q8×Dic61C2314yes—
102Q8×Dic61C2314yes—
103C4×C22⋊D61D414yes—
104C4×C22⋊D61C2314yes—
105#14519736—22no—
106#14519736C2314yes—
107#14519735—22no—
108#14519735—28no—
109#14519735C2314yes—
110#14519733—28no—
111C2×C4⋊Dic61—22no—
112C2×C4⋊Dic61—21no—
113C2×C4⋊Dic61—21no—
114C2×C4⋊Dic61—21no—
115C2×C4⋊Dic61—21no—
116C2×C4⋊Dic61—21no—
117C2×C4⋊Dic61C2314yes—
118C2×C4⋊Dic61C2311yescharacteristic
119C2×C4⋊Dic61C2311yescharacteristic
120C2×C4⋊Dic61C2311yescharacteristic
121C2×C4⋊Dic61C2311yescharacteristic
122C2×#11758196—21no—
123C2×#11758196—21no—
124C2×#11758196—21no—
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196D411yescharacteristic
128C4⋊C4×D61—22no—
129C4⋊C4×D61C2314yes—
130C2×C22⋊Dic61—21no—
131C2×C22⋊Dic61D411yescharacteristic
132C2×#11758198—21no—
133C2×#11758198—21no—
134C2×#11758198—21no—
135C2×#11758198D411yescharacteristic
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#14519710C2314yes—
146#14519709C2314yes—
147#14519709C2314yes—
148#14519708C2314yes—
149#14519706C2314yes—
150#14519701C2314yes—
151#14519701C2314yes—
152#14519701C2314yes—
153#14519701C2314yes—
154C22⋊#92418C2314yes—
155#14519689C2314yes—
156C8×Dic61C2314yes—
157C22×Q8×C61C2311yescharacteristic
158C22×Q8×C61C2311yescharacteristic
159C23×C4×C61C2311yescharacteristic
160C2×Q16×C61—24no—
161C2×Q16×C61C2314yes—
162C2×M16×C61—24no—
163C2×M16×C61C2314yes—
164C22×C8×C61C2311yescharacteristic
165C22×C8×C61C2311yescharacteristic
166C22⋊Q8×C61—22no—
167C22⋊Q8×C61—22no—
168C22⋊Q8×C61C2314yes—
169C22⋊Q8×C61C2314yes—
170C2×C4⋊C4×C61—21no—
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#103×C61C2314yes—
179C24×C61C2×D411yescharacteristic
180C23×D61C2×D411yescharacteristic
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—22no—
184C2×Q8×C61—22no—
185C2×Q8×C61—22no—
186C2×Q8×C61—22no—
187C2×Q8×C61C2412yes—
188C2×Q8×C61C2412yes—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D412yes—
197C22×C4×C61C2412yes—
198C22×C4×C61C2411yescharacteristic
199C2×C22⋊D61—42no—
200C2×C22⋊D61C2×D414yes—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—24no—
205C22×Dic61—21no—
206C22×Dic61—44no—
207C22×Dic61C2×D411yescharacteristic
208C22×Dic61C2×D411yescharacteristic
209C22×Dic61C2×D411yescharacteristic
210C2×C4×D61—22no—
211C2×C4×D61—22no—
212C2×C4×D61—24no—
213C2×C4×D61—44no—
214C2×C4×D61C2×D412yes—
215C2×C4×D61C2412yes—
216Q16×C61—28no—
217M16×C61—28no—
218C2×C8×C61—22no—
219C2×C8×C61#4114yes—
220C2×C8×C61C2412yes—
221C2×C8×C61C2412yes—
222C4⋊C4×C61—24no—
223C4⋊C4×C61—24no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61C2412yes—
227C4⋊C4×C61C2412yes—
228C22⋊C4×C61—24no—
229C22⋊C4×C61—24no—
230C22⋊Dic61—24no—
231C22⋊Dic61C2×D414yes—
232#11758198—24no—
233#11758198—24no—
234#11758198—24no—
235#11758198C2×D414yes—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—24no—
240C4⋊Dic61—21no—
241C4⋊Dic61—24no—
242C4⋊Dic61—24no—
243C4⋊Dic61—24no—
244C4⋊Dic61—24no—
245C4⋊Dic61C2412yes—
246C4⋊Dic61C2412yes—
247C4⋊Dic61C2412yes—
248C4⋊Dic61C2412yes—
249#11758196—24no—
250#11758196—24no—
251#11758196—24no—
252#11758196—24no—
253#11758196—24no—
254#11758196C2×D414yes—
255C4×Dic61—24no—
256C4×Dic61—24no—
257C4×Dic61—24no—
258C4×Dic61—24no—
259C4×Dic61C2×D412yes—
260C4×Dic61C2412yes—
261C2×#92418—22no—
262C2×#92418—22no—
263C2×#92418C2412yes—
264C2×#92418C2412yes—
265#11758189—28no—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61—22no—
269C23×C61C22×D412yes—
270C23×C61C22×D411yescharacteristic
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61C22×D412yes—
275Q8×C61—22no—
276Q8×C61—22no—
277Q8×C61—22no—
278Q8×C61—22no—
279Q8×C61—42no—
280Q8×C61—42no—
281C2×C4×C61—22no—
282C2×C4×C61—24no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61C22×D412yes—
294C2×C4×C61C22×D411yescharacteristic
295C2×C4×C61C2×#4112yes—
296C2×C4×C612−1+412yes—
297C2×C4×C61C2511yescharacteristic
298C22⋊D61—44no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—48no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61C22×D412yes—
312C2×Dic61C22×D412yes—
313C2×Dic61C22×D412yes—
314C4×D61—24no—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—48no—
318C8×C61—22no—
319C8×C61C2×#4114yes—
320#92418—22no—
321#92418—22no—
322C2×#3352—611nomaximal, Sylow
323C22×C61—22no—
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—44no—
327C22×C61#54712yes—
328C22×C61#57512yes—
329C22×C61#57812yes—
330C22×C61C23×D411yescharacteristic
331C2×D61—22no—
332C2×D61—22no—
333C2×D61—22no—
334C2×D61—44no—
335C4×C61—22no—
336C4×C61—42no—
337C4×C61—42no—
338C4×C61—42no—
339C4×C61—42no—
340C4×C61#54712yes—
341C4×C61C22×#4111yescharacteristic
342C4×C61C2×2−1+411yescharacteristic
343Dic61—22no—
344Dic61—22no—
345Dic61—22no—
346Dic61—42no—
347Dic61—42no—
348Dic61—42no—
349Dic61—42no—
350C2×#552—611no—
351C2×#552—611no—
352#3352—6116no—
353C2×#499—611no—
354C2×#484—611no—
355C2×#484—611no—
356C2×#485—611no—
357C2×#485—611no—
358C2×#479—611no—
359C2×#479—611no—
360C2×#470—611no—
361C2×#470D6111yescharacteristic, complemented
362C2×C4×Q16—611no—
363C2×#436—611no—
364C2×#428—611no—
365C2×#428—611no—
366C2×C61—42no—
367C2×C61#335214yescomplemented
368C2×C61C2×#54711yescharacteristic
369C2×C61C2×#57511yescharacteristic
370C2×C61C2×#57811yescharacteristic
371D61—42no—
372C22×Q16C2×D6111yescharacteristic
373C22×M16—611no—
374C22×M16C2×D6111yescharacteristic
375#552—618no—
376#552—618no—
377#552—1224no—
378#552—1224no—
379C2×#126—1221no—
380C2×#126—1221no—
381C2×#125—611no—
382C2×#125—611no—
383C2×#125—1221no—
384C2×#125—1221no—
385C2×#123—1221no—
386C2×#123—1221no—
387C2×C22⋊Q8—611no—
388C2×C22⋊Q8—611no—
389C2×C22⋊Q8C2×D6111yescharacteristic
390C2×C22⋊Q8C2×D6111yescharacteristic
391C2×C4×Q8—611no—
392C2×C4×Q8—611no—
393C2×C4×D4—611no—
394C2×#117—611no—
395C2×#117—611no—
396C2×#117—1221no—
397C2×#117—1221no—
398C22×C4⋊C4—611no—
399C22×C4⋊C4—611no—
400#499—618no—
401#485—618no—
402#485—618no—
403#484—618no—
404#484—618no—
405#479—618no—
406#479—618no—
407#470—618no—
408#470C2×D6118yescomplemented
409C4×Q16—618no—
410#436—618no—
411#428—618no—
412#428—618no—
413C2×#107—611no—
414C2×#107—611no—
415C2×#107—611no—
416C2×#107—611no—
417C2×#107—611no—
418C2×#106—611no—
419C2×#106—611no—
420C2×#106—611no—
421C2×#106C2×D6111yescharacteristic
422C2×C4⋊C8—611no—
423C2×#103—611no—
424C2×#103—611no—
425C2×#103—611no—
426C2×#103—611no—
427C2×#103C2×D6111yescharacteristic
428C2×#103C2×D6111yescharacteristic
429C2×C22⋊C8—611no—
430C2×C22⋊C8—611no—
431C2×C4×C8—611no—
432C61C2×#335211yescharacteristic, complemented, Sylow
433C22×Q8C22×D6111yescharacteristic
434C22×Q8C22×D6111yescharacteristic
435C22×D4—611no—
436C23×C4—611no—
437C23×C4—1221no—
438C23×C4—1221no—
439C23×C4C22×D6111yescharacteristic
440C2×Q16—24no—
441C2×Q16C22×D6114yes—
442C2×M16—24no—
443C2×M16—614no—
444C2×M16—1224no—
445C2×M16C22×D6114yes—
446C22×C8—611no—
447C22×C8—611no—
448C22×C8C22×D6111yescharacteristic
449C22×C8C22×D6111yescharacteristic
450#126—1228no—
451#126—1228no—
452#125—614no—
453#125—614no—
454#125—1222no—
455#125—1222no—
456#125—1228no—
457#125—1228no—
458#123—1228no—
459#123—1228no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—614no—
463C22⋊Q8—614no—
464C22⋊Q8—1222no—
465C22⋊Q8—1222no—
466C22⋊Q8C22×D6114yes—
467C22⋊Q8C22×D6114yes—
468C4×Q8—614no—
469C4×Q8—614no—
470C4×Q8—1222no—
471C4×Q8—1222no—
472C4×D4—614no—
473C4×D4—614no—
474#117—614no—
475#117—614no—
476#117—1228no—
477#117—1228no—
478#117—1222no—
479#117—1222no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—614no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—614no—
489C2×C4⋊C4—1222no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
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—1222no—
501C2×C4⋊C4C22×D6111yescharacteristic
502C2×C4⋊C4C22×D6111yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—611no—
506C2×C22⋊C4—611no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C42—611no—
512C2×C42—1221no—
513C2×C42—1221no—
514C2×C42—1221no—
515C2×C42—1221no—
516#107—614no—
517#107—614no—
518#107—614no—
519#107—614no—
520#107—614no—
521#106—614no—
522#106—614no—
523#106—614no—
524#106C22×D6114yes—
525C4⋊C8—614no—
526#103—614no—
527#103—614no—
528#103—614no—
529#103—614no—
530#103C22×D6114yes—
531#103C22×D6114yes—
532C22⋊C8—614no—
533C22⋊C8—614no—
534C4×C8—614no—
535C24—611no—
536C24D4×D6111yescharacteristic
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8C23×D6112yes—
544C2×Q8C23×D6112yes—
545C2×D4—614no—
546C2×D4—2442no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—612no—
557C22×C4—612no—
558C22×C4—1224no—
559C22×C4—1222no—
560C22×C4—1222no—
561C22×C4—1224no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—2444no—
567C22×C4—2444no—
568C22×C4D4×D6112yes—
569C22×C4D4×D6111yescharacteristic
570C22×C4C23×D6112yes—
571C22×C4C23×D6111yescharacteristic
572Q16—28no—
573M16—28no—
574M16—1228no—
575C2×C8—22no—
576C2×C8—612no—
577C2×C8—612no—
578C2×C8—1222no—
579C2×C8—1222no—
580C2×C8#1175822414yes—
581C2×C8C23×D6112yes—
582C2×C8C23×D6112yes—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—614no—
588C4⋊C4—612no—
589C4⋊C4—612no—
590C4⋊C4—612no—
591C4⋊C4—612no—
592C4⋊C4—1224no—
593C4⋊C4—1224no—
594C4⋊C4—1224no—
595C4⋊C4—1224no—
596C4⋊C4—1224no—
597C4⋊C4—1224no—
598C4⋊C4—1224no—
599C4⋊C4—1224no—
600C4⋊C4—1224no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1224no—
605C4⋊C4—1221no—
606C4⋊C4C23×D6112yes—
607C4⋊C4C23×D6112yes—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—614no—
611C22⋊C4—614no—
612C22⋊C4—1224no—
613C22⋊C4—1224no—
614C22⋊C4—1224no—
615C22⋊C4—1224no—
616C42—612no—
617C42—612no—
618C42—1224no—
619C42—1224no—
620C42—1224no—
621C42—1224no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—612no—
626C23—1222no—
627C23—1222no—
628C23—1222no—
629C23C2×D4×D6112yes—
630C23C2×D4×D6111yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—22no—
634Q8—22no—
635Q8—42no—
636Q8—42no—
637D4—2444no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—612no—
651C2×C4—612no—
652C2×C4—612no—
653C2×C4—1222no—
654C2×C4—1222no—
655C2×C4—1222no—
656C2×C4—1222no—
657C2×C4—1222no—
658C2×C4—1224no—
659C2×C4—1222no—
660C2×C4—1222no—
661C2×C4—1222no—
662C2×C4—1222no—
663C2×C4—2448no—
664C2×C4—2448no—
665C2×C4—2442no—
666C2×C4—2442no—
667C2×C4—2442no—
668C2×C4—2442no—
669C2×C4C2×D4×D6112yes—
670C2×C4C2×D4×D6111yescharacteristic
671C2×C4C2×#1175822412yes—
672C2×C4#1451982412yes—
673C2×C4C24×D6111yescharacteristic
674C8—22no—
675C8—1222no—
676C8—1222no—
677C8C2×#1175822414yes—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—44no—
682C22—1222no—
683C22—1222no—
684C22—1222no—
685C22—2444no—
686C22#1684041212yes—
687C22#1684056112yes—
688C22#1684057812yes—
689C22C22×D4×D6111yescharacteristic
690C4—22no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—1222no—
696C4—1222no—
697C4—1222no—
698C4—2442no—
699C4—2442no—
700C4—2442no—
701C4—2442no—
702C4#1684041212yes—
703C4C22×#1175822411yescharacteristic
704C4C2×#1451982411yescharacteristic
705C2—42no—
706C2—2442no—
707C2#2145838914yesdirect product factor
708C2C2×#1684041211yescharacteristic
709C2C2×#1684056111yescharacteristic
710C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#470C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenterC2×#470D61
hypocenterC61C2×#3352
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
3. #21458389C2direct (N × H)
4. C2×#16840162C2semidirect
5. C2×#16840096C2semidirect
6. C2×#16840095C2semidirect
7. C2×#16840101C2semidirect
8. C2×#16840100C2semidirect
9. C2×#16840071C2semidirect
10. C2×#16840067C2semidirect
11. C2×#16840017C2semidirect
12. C2×Q16×Dic61C2semidirect
14. C2×#16839804C2semidirect
15. C2×#16839801C2semidirect
16. C2×C61×#470C2semidirect
41. #16840162C22semidirect
42. #16840101C22semidirect
43. #16840100C22semidirect
44. #16840096C22semidirect
45. #16840095C22semidirect
46. #16840071C22semidirect
47. #16840067C22semidirect
48. #16840017C22semidirect
49. Q16×Dic61C22semidirect
51. #16839804C22semidirect
52. #16839801C22semidirect
73. C61×#470C22semidirect
361. C2×#470D61semidirect
367. C2×C61#3352semidirect
408. #470C2×D61semidirect
432. C61C2×#3352semidirect
707. C2#21458389direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404542
C2×#168404462
#214583892
C2×#168401622
C2×#168400962
C2×#168400952
C2×#168401012
C2×#168401002
C2×#168400712
C2×#168400672
C2×#168400172
C2×Q16×Dic612
C2×#168398382
C2×#168398042
C2×#168398012
C2×C61×#4702
C2×#335261