Finite Group Databasebeta

← C2×#21457241 #30552935

Subgroups — C2×#21457241 #30552935

Order 15616.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840377C211yesmaximal, characteristic
2C2×#16840373C211yesmaximal, characteristic, complemented
3#21457241C2116yesmaximal, direct product factor
4C2×#16840070C211yesmaximal, characteristic, complemented
5C2×#16840055C211yesmaximal, characteristic, complemented
6C2×#16840045C211yesmaximal, characteristic, complemented
7C2×#16840062C211yesmaximal, characteristic, complemented
8C2×#16840019C211yesmaximal, characteristic, complemented
9C2×#16840005C211yesmaximal, characteristic
10C2×#16840002C211yesmaximal, characteristic, complemented
11C2×#16839988C211yesmaximal, characteristic
12C2×#16839982C211yesmaximal, characteristic, complemented
13C2×#16839982C211yesmaximal, characteristic, complemented
14C2×#16839969C211yesmaximal, characteristic, complemented
15C2×#16839787C211yesmaximal, characteristic, complemented
16C2×C61×#461C211yesmaximal, characteristic, complemented
17C22×#11758202C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21#16840377—24no—
22#16840377C2218yes—
23#16840373—24no—
24#16840373C2218yescomplemented
25C2×#14519776C2211yescharacteristic
26C2×#14519772—21no—
27C2×#14519772—21no—
28C2×#14519770—21no—
29C2×#14519769C2211yescharacteristic
30C2×#14519767—21no—
31C2×#14519767—21no—
32C2×#14519764C2211yescharacteristic
33C2×#14519763—21no—
34C2×#14519760—21no—
35C2×#14519757C2211yescharacteristic
36C2×#14519756—21no—
37C2×#14519753C2211yescharacteristic
38C2×#14519753C2211yescharacteristic
39C2×#14519748C2211yescharacteristic
40C2×Q8×Dic61C2211yescharacteristic
41C2×Q8×Dic61C2211yescharacteristic
42C2×C4×Dic122C2211yescharacteristic
43C2×#14519734C2211yescharacteristic
44#16840070C2218yescomplemented
45#16840062C2218yescomplemented
46#16840055C2218yescomplemented
47#16840045C2218yescomplemented
48#16840019C2218yescomplemented
49#16840005C2218yes—
50#16840002C2218yescomplemented
51#16839988C2218yes—
52#16839982C2218yescomplemented
53#16839982C2218yescomplemented
54#16839969C2218yescomplemented
55C2×#14519711C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519709C2211yescharacteristic
58C2×#14519708C2211yescharacteristic
59#16839787C2218yescomplemented
60C2×C4⋊#92418C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519706C2211yescharacteristic
63C2×#14519702C2211yescharacteristic
64C2×#14519702C2211yescharacteristic
65C2×#14519701C2211yescharacteristic
66C2×#14519701C2211yescharacteristic
67C2×#14519698C2211yescharacteristic
68C2×#14519698C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C2×C4⋊Q8×C61C2211yescharacteristic
72C2×C4×D4×C61C2211yescharacteristic
73C61×#461C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#103×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C22×C22⋊D61—21no—
80C22×C4×D61C2311yescharacteristic
81C2×#11758202—42no—
82C2×#11758202—42no—
83C2×#11758202C2314yes—
84C2×#11758202C2314yes—
85C2×#11758189—42no—
86C2×#11758189C2314yes—
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C2×C8×D61—42no—
90C2×C8×D61C2314yes—
91#14519776—22no—
92#14519776C2314yes—
93#14519772—28no—
94#14519772—28no—
95#14519770—28no—
96#14519769—22no—
97#14519769C2314yes—
98#14519767—28no—
99#14519767—28no—
100#14519764—22no—
101#14519764C2314yes—
102#14519763—28no—
103#14519760—28no—
104#14519757—22no—
105#14519757C2314yes—
106#14519756—28no—
107#14519753—22no—
108#14519753—22no—
109#14519753C2314yes—
110#14519753C2314yes—
111#14519748—22no—
112#14519748C2314yes—
113Q8×Dic61—22no—
114Q8×Dic61—22no—
115Q8×Dic61C2314yes—
116Q8×Dic61C2314yes—
117C4×Dic122—22no—
118C4×Dic122C2314yes—
119#14519734D414yes—
120#14519734C2314yes—
121C2×C4⋊Dic61—21no—
122C2×C4⋊Dic61—21no—
123C2×C4⋊Dic61—21no—
124C2×C4⋊Dic61C2311yescharacteristic
125C2×C4⋊Dic61C2311yescharacteristic
126C2×C4⋊Dic61C2311yescharacteristic
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196D411yescharacteristic
134C2×#11758196D411yescharacteristic
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198D411yescharacteristic
142C2×#11758198D411yescharacteristic
143C2×C4×Dic61—21no—
144C2×C4×Dic61—21no—
145C2×C4×Dic61—21no—
146C2×C4×Dic61C2311yescharacteristic
147#14519711C2314yes—
148#14519710C2314yes—
149#14519709C2314yes—
150#14519708C2314yes—
151C4⋊#92418C2314yes—
152#14519706C2314yes—
153#14519706C2314yes—
154#14519702C2314yes—
155#14519702C2314yes—
156#14519701C2314yes—
157#14519701C2314yes—
158#14519698C2314yes—
159#14519698C2314yes—
160C22×Q8×C61C2311yescharacteristic
161C22×Q8×C61C2311yescharacteristic
162C22×D4×C61C2311yescharacteristic
163C23×C4×C61—21no—
164C2×SD16×C61—42no—
165C2×SD16×C61—42no—
166C2×SD16×C61C2314yes—
167C2×SD16×C61C2314yes—
168C22×C8×C61C2311yescharacteristic
169C22×C8×C61C2311yescharacteristic
170C4⋊Q8×C61—22no—
171C4⋊Q8×C61C2314yes—
172C4×D4×C61—22no—
173C4×D4×C61C2314yes—
174C2×C4⋊C4×C61—21no—
175C2×C4⋊C4×C61—21no—
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C22⋊C4×C61—21no—
178C2×C42×C61C2311yescharacteristic
179C4⋊C8×C61C2314yes—
180#103×C61C2314yes—
181#103×C61C2314yes—
182C24×C61—21no—
183C23×D61C2×D411yescharacteristic
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—22no—
187C2×Q8×C61—22no—
188C2×Q8×C61—22no—
189C2×Q8×C61—22no—
190C2×Q8×C61C2412yes—
191C2×Q8×C61C2412yes—
192C2×D4×C61—21no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61C2412yes—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—24no—
200C22×C4×C61—82no—
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2411yescharacteristic
204C2×C22⋊D61—24no—
205C2×C22⋊D61—82no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213C2×C4×D61—22no—
214C2×C4×D61—22no—
215C2×C4×D61C2×D412yes—
216C2×C4×D61C2412yes—
217C2×Dic122—22no—
218C2×Dic122—22no—
219C2×Dic122—21no—
220C2×Dic122—24no—
221C2×Dic122—82no—
222C2×Dic122C2412yes—
223SD16×C61—44no—
224SD16×C61—44no—
225C2×C8×C61—22no—
226C2×C8×C61—22no—
227C2×C8×C61C2412yes—
228C2×C8×C61C2412yes—
229C4⋊C4×C61—24no—
230C4⋊C4×C61—24no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61C2412yes—
233C22⋊C4×C61—24no—
234C42×C61C2×D412yes—
235C42×C61C2412yes—
236C22⋊Dic61—24no—
237C22⋊Dic61—24no—
238C22⋊Dic61—24no—
239#11758202—44no—
240#11758202—44no—
241#11758198—24no—
242#11758198—24no—
243#11758198—24no—
244#11758198C2×D414yes—
245#11758198C2×D414yes—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61—24no—
250C4⋊Dic61—24no—
251C4⋊Dic61—24no—
252C4⋊Dic61C2412yes—
253C4⋊Dic61C2412yes—
254C4⋊Dic61C2412yes—
255#11758196—24no—
256#11758196—24no—
257#11758196—24no—
258#11758196—24no—
259#11758196—24no—
260#11758196—24no—
261#11758196C2×D414yes—
262#11758196C2×D414yes—
263C4×Dic61—24no—
264C4×Dic61—24no—
265C4×Dic61—24no—
266C4×Dic61C2×D412yes—
267C4×Dic61C2412yes—
268C2×#92418—22no—
269C2×#92418—22no—
270C2×#92418C2412yes—
271C2×#92418C2412yes—
272#11758189—44no—
273C8×D61—44no—
274C23×C61—22no—
275C23×C61—42no—
276C23×C61—42no—
277C23×C61—42no—
278C23×C61C22×D411yescharacteristic
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61C22×D412yes—
283Q8×C61—22no—
284Q8×C61—22no—
285Q8×C61—22no—
286Q8×C61—22no—
287Q8×C61—42no—
288Q8×C61—42no—
289D4×C61—22no—
290D4×C61—22no—
291D4×C61—42no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61—42no—
300C2×C4×C61—84no—
301C2×C4×C61C22×D412yes—
302C2×C4×C61C22×D412yes—
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61H(5,𝔽2)12yes—
305C2×C4×C612−1+412yes—
306C2×C4×C61C2511yescharacteristic
307C22⋊D61—84no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61C22×D412yes—
320C2×Dic61C22×D412yes—
321C2×Dic61C22×D412yes—
322C4×D61—24no—
323C4×D61—22no—
324C4×D61—22no—
325Dic122—22no—
326Dic122—22no—
327Dic122—42no—
328Dic122—84no—
329C8×C61—22no—
330C8×C61—22no—
331#92418—22no—
332#92418—22no—
333C2×#3258—611nomaximal, Sylow
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—84no—
338C22×C61#53712yes—
339C22×C61#57712yes—
340C22×C61#57812yes—
341C22×C61C23×D411yescharacteristic
342C2×D61—22no—
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—44no—
346C4×C61—22no—
347C4×C61—22no—
348C4×C61—42no—
349C4×C61—42no—
350C4×C61—42no—
351C4×C61#53712yes—
352C4×C61C2×H(5,𝔽2)11yescharacteristic
353C4×C61C2×2−1+411yescharacteristic
354Dic61—22no—
355Dic61—22no—
356Dic61—22no—
357Dic61—42no—
358Dic61—42no—
359Dic61—42no—
360Dic61—42no—
361C2×#542—611no—
362C2×#541—611no—
363#3258—6116no—
364C2×#479—611no—
365C2×#477—611no—
366C2×#475—611no—
367C2×#478—611no—
368C2×#470—611no—
369C2×#468—611no—
370C2×#467—611no—
371C2×#465—611no—
372C2×#464—611no—
373C2×#464—611no—
374C2×#462—611no—
375C2×#461D6111yescharacteristic, complemented
376C2×#424—611no—
377C2×C61—82no—
378C2×C61#325814yescomplemented
379C2×C61C2×#53711yescharacteristic
380C2×C61C2×#57711yescharacteristic
381C2×C61C2×#57811yescharacteristic
382D61—42no—
383C22×Q16—611no—
384C22×Q16—611no—
385C22×SD16C2×D6111yescharacteristic
386C22×SD16C2×D6111yescharacteristic
387C22×M16—611no—
388C23×C8—611no—
389#542—618no—
390#542—1224no—
391#541—618no—
392#541—1224no—
393C2×C4⋊Q8—611no—
394C2×C4⋊Q8C2×D6111yescharacteristic
395C2×#126—1221no—
396C2×#126—1221no—
397C2×#126—1221no—
398C2×#125—611no—
399C2×#125—1221no—
400C2×#125—1221no—
401C2×#124—611no—
402C2×#124—1221no—
403C2×#123—1221no—
404C2×C22⋊Q8—611no—
405C2×C22⋊Q8—611no—
406C2×C22⋊Q8—611no—
407C2×C22⋊Q8—1221no—
408C2×#121—611no—
409C2×C4×Q8—611no—
410C2×C4×Q8—611no—
411C2×C4×Q8—611no—
412C2×C4×D4C2×D6111yescharacteristic
413C2×#117—611no—
414#479—618no—
415#478—618no—
416#477—618no—
417#475—618no—
418#470—618no—
419#468—618no—
420#467—618no—
421#465—618no—
422#464—618no—
423#464—618no—
424#462—618no—
425#461C2×D6118yescomplemented
426C2×#107—611no—
427C2×#107—611no—
428C2×#106—611no—
429C2×#106—611no—
430#424—618no—
431C2×C4⋊C8—611no—
432C2×C4⋊C8—611no—
433C2×C4⋊C8—611no—
434C2×C4⋊C8C2×D6111yescharacteristic
435C2×#103—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#103—611no—
439C2×#103C2×D6111yescharacteristic
440C2×#103C2×D6111yescharacteristic
441C2×#102—611no—
442C2×#102—611no—
443C61C2×#325811yescharacteristic, complemented, Sylow
444C22×Q8—611no—
445C22×Q8—1221no—
446C22×Q8C22×D6111yescharacteristic
447C22×Q8C22×D6111yescharacteristic
448C22×D4—1221no—
449C22×D4C22×D6111yescharacteristic
450C23×C4—21no—
451C23×C4—611no—
452C2×Q16—614no—
453C2×Q16—614no—
454C2×Q16—2442no—
455C2×Q16—2442no—
456C2×SD16—42no—
457C2×SD16—42no—
458C2×SD16C22×D6114yes—
459C2×SD16C22×D6114yes—
460C2×M16—614no—
461C2×M16—2442no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8—614no—
465C22×C8—2442no—
466C22×C8C22×D6111yescharacteristic
467C22×C8C22×D6111yescharacteristic
468C4⋊Q8—22no—
469C4⋊Q8—614no—
470C4⋊Q8—1222no—
471C4⋊Q8C22×D6114yes—
472#126—1228no—
473#126—1228no—
474#126—1228no—
475#125—614no—
476#125—1228no—
477#125—1228no—
478#125—1222no—
479#124—614no—
480#124—1222no—
481#124—1228no—
482#123—1228no—
483C22⋊Q8—614no—
484C22⋊Q8—614no—
485C22⋊Q8—614no—
486C22⋊Q8—1222no—
487C22⋊Q8—1228no—
488C22⋊Q8—1222no—
489C22⋊Q8—1222no—
490#121—614no—
491#121—1222no—
492C4×Q8—614no—
493C4×Q8—614no—
494C4×Q8—614no—
495C4×Q8—1222no—
496C4×Q8—1222no—
497C4×Q8—1222no—
498C4×D4—22no—
499C4×D4C22×D6114yes—
500#117—614no—
501#117—614no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4C22×D6111yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—611no—
521C2×C22⋊C4—611no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C42—611no—
529C2×C42—1221no—
530C2×C42—1221no—
531C2×C42—1221no—
532C2×C42C22×D6111yescharacteristic
533#107—614no—
534#107—614no—
535#106—614no—
536#106—614no—
537C4⋊C8—614no—
538C4⋊C8—614no—
539C4⋊C8—614no—
540C4⋊C8C22×D6114yes—
541#103—614no—
542#103—614no—
543#103—614no—
544#103—614no—
545#103C22×D6114yes—
546#103C22×D6114yes—
547#102—614no—
548#102—614no—
549C24—21no—
550C24—611no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—612no—
558C2×Q8—1224no—
559C2×Q8—1221no—
560C2×Q8—1222no—
561C2×Q8—1222no—
562C2×Q8—4882no—
563C2×Q8C23×D6112yes—
564C2×Q8C23×D6112yes—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—1224no—
569C2×D4—4882no—
570C2×D4C23×D6112yes—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—24no—
575C22×C4—82no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—612no—
580C22×C4—612no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4D4×D6111yescharacteristic
588C22×C4D4×D6111yescharacteristic
589C22×C4C23×D6111yescharacteristic
590Q16—2444no—
591Q16—2444no—
592SD16—44no—
593SD16—44no—
594M16—2444no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—612no—
598C2×C8—612no—
599C2×C8—1222no—
600C2×C8—1222no—
601C2×C8—2444no—
602C2×C8C23×D6112yes—
603C2×C8C23×D6112yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—614no—
608C4⋊C4—614no—
609C4⋊C4—612no—
610C4⋊C4—612no—
611C4⋊C4—612no—
612C4⋊C4—1224no—
613C4⋊C4—1224no—
614C4⋊C4—1224no—
615C4⋊C4—1224no—
616C4⋊C4—1224no—
617C4⋊C4—1224no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1224no—
622C4⋊C4—1224no—
623C4⋊C4—1224no—
624C4⋊C4C23×D6112yes—
625C22⋊C4—24no—
626C22⋊C4—614no—
627C22⋊C4—614no—
628C22⋊C4—1224no—
629C22⋊C4—1224no—
630C22⋊C4—1224no—
631C22⋊C4—1224no—
632C22⋊C4—1224no—
633C22⋊C4—1224no—
634C42—612no—
635C42—612no—
636C42—1224no—
637C42—1224no—
638C42—1224no—
639C42D4×D6112yes—
640C42C23×D6112yes—
641C23—22no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—612no—
646C23—1222no—
647C23—1222no—
648C23—1222no—
649C23C2×D4×D6111yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—42no—
655Q8—42no—
656Q8—1222no—
657Q8—1222no—
658Q8—4884no—
659Q8—2442no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—4884no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—84no—
673C2×C4—612no—
674C2×C4—612no—
675C2×C4—612no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1224no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—2442no—
687C2×C4—2442no—
688C2×C4—2442no—
689C2×C4—2442no—
690C2×C4C2×D4×D6112yes—
691C2×C4C2×D4×D6112yes—
692C2×C4C2×D4×D6111yescharacteristic
693C2×C4#1451982212yes—
694C2×C4#1451982412yes—
695C2×C4C24×D6111yescharacteristic
696C8—22no—
697C8—22no—
698C8—1222no—
699C8—1222no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—84no—
704C22—1222no—
705C22—1222no—
706C22—1222no—
707C22—2444no—
708C22#1684034112yes—
709C22#1684056812yes—
710C22#1684057812yes—
711C22C22×D4×D6111yescharacteristic
712C4—22no—
713C4—22no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—1222no—
718C4—1222no—
719C4—1222no—
720C4—2442no—
721C4—2442no—
722C4—2442no—
723C4—2442no—
724C4#1684034112yes—
725C4C2×#1451982211yescharacteristic
726C4C2×#1451982411yescharacteristic
727C2—82no—
728C2—2442no—
729C2#2145724114yesdirect product factor
730C2C2×#1684034111yescharacteristic
731C2C2×#1684056811yescharacteristic
732C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#461C2
socleC23×C61C22×D4
prime radicalC2×#14519748C22
hypercenterC2×#461D61
hypocenterC61C2×#3258
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
2. C2×#16840373C2semidirect
3. #21457241C2direct (N × H)
4. C2×#16840070C2semidirect
5. C2×#16840055C2semidirect
6. C2×#16840045C2semidirect
7. C2×#16840062C2semidirect
8. C2×#16840019C2semidirect
10. C2×#16840002C2semidirect
12. C2×#16839982C2semidirect
13. C2×#16839982C2semidirect
14. C2×#16839969C2semidirect
15. C2×#16839787C2semidirect
16. C2×C61×#461C2semidirect
24. #16840373C22semidirect
44. #16840070C22semidirect
45. #16840062C22semidirect
46. #16840055C22semidirect
47. #16840045C22semidirect
48. #16840019C22semidirect
50. #16840002C22semidirect
52. #16839982C22semidirect
53. #16839982C22semidirect
54. #16839969C22semidirect
59. #16839787C22semidirect
73. C61×#461C22semidirect
375. C2×#461D61semidirect
378. C2×C61#3258semidirect
425. #461C2×D61semidirect
443. C61C2×#3258semidirect
729. C2#21457241direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403772
C2×#168403732
#214572412
C2×#168400702
C2×#168400552
C2×#168400452
C2×#168400622
C2×#168400192
C2×#168400052
C2×#168400022
C2×#168399882
C2×#168399822
C2×#168399692
C2×#168397872
C2×C61×#4612
C2×#325861