Finite Group Databasebeta

← C2×#21458853 #30560984

Subgroups — C2×#21458853 #30560984

Order 15616.

1906 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840490C211yesmaximal, characteristic, complemented
2C2×#16840481C211yesmaximal, characteristic
3#21458853C2116yesmaximal, direct product factor
4C2×#16840157C211yesmaximal, characteristic
5C2×#16840153C211yesmaximal, characteristic
6C2×#16840140C211yesmaximal, characteristic, complemented
7C2×#16839983C211yesmaximal, characteristic
8C2×#16839973C211yesmaximal, characteristic, complemented
9C2×#16839971C211yesmaximal, characteristic, complemented
10C2×#16839970C211yesmaximal, characteristic, complemented
11C2×#16839965C211yesmaximal, characteristic
12C2×#16839891C211yesmaximal, characteristic, complemented
13C2×#16839867C211yesmaximal, characteristic, complemented
14C2×#16839866C211yesmaximal, characteristic, complemented
15C2×#16839853C211yesmaximal, characteristic
16C2×C61×#464C211yesmaximal, characteristic
17C22×Dic244C2211yescharacteristic
18C22×Dic244C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758202C2211yescharacteristic
21C22×#11758202C2211yescharacteristic
22C22×#11758200C2211yescharacteristic
23C22×#11758200C2211yescharacteristic
24#16840490—24no—
25#16840490C2218yescomplemented
26#16840481—24no—
27#16840481C2218yes—
28C2×#14519777C2211yescharacteristic
29C2×#14519775C2211yescharacteristic
30C2×#14519775C2211yescharacteristic
31C2×#14519775C2211yescharacteristic
32C2×#14519770—21no—
33C2×#14519770—21no—
34C2×#14519769—21no—
35C2×#14519767—21no—
36C2×#14519767—21no—
37C2×#14519764C2211yescharacteristic
38C2×#14519754—21no—
39C2×Q8×Dic61C2211yescharacteristic
40C2×C4×Dic122—21no—
41C2×C4×Dic122C2211yescharacteristic
42C2×C4×Dic122C2211yescharacteristic
43C2×#14519742C2211yescharacteristic
44C2×#14519742C2211yescharacteristic
45C2×D4×Dic61C2211yescharacteristic
46C2×#14519733—21no—
47#16840157C2218yes—
48#16840153C2218yes—
49#16840140C2218yescomplemented
50#16839983C2218yes—
51#16839973C2218yescomplemented
52#16839971C2218yescomplemented
53#16839970C2218yescomplemented
54#16839965C2218yes—
55#16839891C2218yescomplemented
56#16839867C2218yescomplemented
57#16839866C2218yescomplemented
58#16839853C2218yes—
59C2×#14519708C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519702C2211yescharacteristic
63C2×#14519702C2211yescharacteristic
64C2×#14519701C2211yescharacteristic
65C2×#14519700C2211yescharacteristic
66C2×#14519688C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×Q16×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C2×#124×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic
73C61×#464C2218yes—
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122D411yescharacteristic
78C22×Dic122C2311yescharacteristic
79C22×Dic122C2311yescharacteristic
80C22×Dic122C2311yescharacteristic
81C23×Dic61—21no—
82C2×Dic244—42no—
83C2×Dic244—42no—
84C2×Dic244C2314yes—
85C2×Dic244C2314yes—
86C2×#11758202—24no—
87C2×#11758202—24no—
88C2×#11758202—42no—
89C2×#11758202C2314yes—
90C2×#11758202C2314yes—
91C2×#11758202C2314yes—
92C2×#11758200—24no—
93C2×#11758200—42no—
94C2×#11758200C2314yes—
95C2×#11758200C2314yes—
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98#14519777—22no—
99#14519777C2314yes—
100#14519775—22no—
101#14519775—22no—
102#14519775—22no—
103#14519775C2314yes—
104#14519775C2314yes—
105#14519775C2314yes—
106#14519770—28no—
107#14519770—28no—
108#14519769—28no—
109#14519767—28no—
110#14519767—28no—
111#14519764—22no—
112#14519764C2314yes—
113#14519754—28no—
114Q8×Dic61—22no—
115Q8×Dic61C2314yes—
116C4×Dic122—28no—
117C4×Dic122—22no—
118C4×Dic122D414yes—
119C4×Dic122C2314yes—
120C4×Dic122C2314yes—
121#14519742—22no—
122#14519742—22no—
123#14519742C2314yes—
124#14519742C2314yes—
125D4×Dic61—22no—
126D4×Dic61C2314yes—
127#14519733—28no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61—21no—
130C2×C4⋊Dic61—21no—
131C2×C4⋊Dic61D411yescharacteristic
132C2×C4⋊Dic61C2311yescharacteristic
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×#11758196—21no—
141C2×#11758196—21no—
142C2×#11758196D411yescharacteristic
143C2×#11758196D411yescharacteristic
144C2×C22⋊Dic61—21no—
145C2×C22⋊Dic61—21no—
146C2×C22⋊Dic61—21no—
147C2×C4×Dic61—21no—
148C2×C4×Dic61—21no—
149C2×C4×Dic61—21no—
150C2×C4×Dic61—21no—
151C2×C4×Dic61C2311yescharacteristic
152C2×C4×Dic61C2311yescharacteristic
153#14519708C2314yes—
154#14519706C2314yes—
155#14519706C2314yes—
156#14519702C2314yes—
157#14519702C2314yes—
158#14519701C2314yes—
159#14519700C2314yes—
160#14519688C2314yes—
161#14519687C2314yes—
162C8×Dic61C2314yes—
163C22×Q8×C61C2311yescharacteristic
164C22×Q8×C61C2311yescharacteristic
165C22×D4×C61C2311yescharacteristic
166C2×Q16×C61—42no—
167C2×Q16×C61C2314yes—
168C2×SD16×C61—42no—
169C2×SD16×C61C2314yes—
170C22×C8×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172#124×C61—22no—
173#124×C61C2314yes—
174C4×Q8×C61—22no—
175C4×Q8×C61C2314yes—
176C2×C4⋊C4×C61—21no—
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C42×C61—21no—
181C2×C42×C61C2311yescharacteristic
182C4⋊C8×C61C2314yes—
183#103×C61C2314yes—
184#102×C61C2314yes—
185C24×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61—21no—
188C2×Q8×C61—22no—
189C2×Q8×C61—22no—
190C2×Q8×C61—22no—
191C2×Q8×C61—22no—
192C2×Q8×C61C2412yes—
193C2×Q8×C61C2412yes—
194C2×D4×C61—21no—
195C2×D4×C61—22no—
196C2×D4×C61—22no—
197C2×D4×C61C2412yes—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2411yescharacteristic
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—24no—
209C22×Dic61—44no—
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213C22×Dic61C2×D411yescharacteristic
214C2×Dic122—24no—
215C2×Dic122—22no—
216C2×Dic122—22no—
217C2×Dic122—22no—
218C2×Dic122—22no—
219C2×Dic122—22no—
220C2×Dic122—22no—
221C2×Dic122—21no—
222C2×Dic122—21no—
223C2×Dic122—21no—
224C2×Dic122C2×D414yes—
225C2×Dic122C2412yes—
226C2×Dic122C2412yes—
227C2×Dic122C2412yes—
228Q16×C61—44no—
229SD16×C61—44no—
230C2×C8×C61—22no—
231C2×C8×C61—22no—
232C2×C8×C61C2412yes—
233C2×C8×C61C2412yes—
234C4⋊C4×C61—24no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61C2412yes—
237C22⋊C4×C61—24no—
238C22⋊C4×C61—24no—
239C42×C61—24no—
240C42×C61C2×D412yes—
241C42×C61C2412yes—
242C22⋊Dic61—24no—
243C22⋊Dic61—24no—
244C22⋊Dic61—24no—
245#11758202—28no—
246#11758202—28no—
247#11758202—44no—
248#11758200—28no—
249#11758200—44no—
250C4⋊Dic61—24no—
251C4⋊Dic61—24no—
252C4⋊Dic61—21no—
253C4⋊Dic61—24no—
254C4⋊Dic61C2×D414yes—
255C4⋊Dic61C2412yes—
256#11758196—24no—
257#11758196—24no—
258#11758196—24no—
259#11758196—24no—
260#11758196—24no—
261#11758196—24no—
262#11758196—24no—
263#11758196—24no—
264#11758196—24no—
265#11758196C2×D414yes—
266#11758196C2×D414yes—
267C4×Dic61—24no—
268C4×Dic61—24no—
269C4×Dic61—24no—
270C4×Dic61—24no—
271C4×Dic61C2×D412yes—
272C4×Dic61C2×D412yes—
273C4×Dic61C2412yes—
274C4×Dic61C2412yes—
275C2×#92418—22no—
276C2×#92418#4114yes—
277C2×#92418C2412yes—
278C2×#92418C2412yes—
279Dic244—44no—
280Dic244—44no—
281C23×C61—22no—
282C23×C61—42no—
283C23×C61—42no—
284C23×C61—42no—
285C23×C61C22×D411yescharacteristic
286Q8×C61—22no—
287Q8×C61—22no—
288Q8×C61—22no—
289Q8×C61—22no—
290Q8×C61—42no—
291Q8×C61—42no—
292D4×C61—22no—
293D4×C61—22no—
294D4×C61—42no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61C22×D412yes—
304C2×C4×C61C22×D412yes—
305C2×C4×C61C22×D411yescharacteristic
306C2×C4×C61C2×#4112yes—
307C2×C4×C61H(5,𝔽2)12yes—
308C2×C4×C61C2511yescharacteristic
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—48no—
321C2×Dic61#13714yes—
322C2×Dic61C22×D412yes—
323C2×Dic61C22×D412yes—
324C2×Dic61C22×D412yes—
325C2×Dic61C22×D412yes—
326Dic122—28no—
327Dic122—22no—
328Dic122—22no—
329Dic122—22no—
330Dic122—22no—
331Dic122—22no—
332Dic122—22no—
333Dic122—42no—
334Dic122—42no—
335Dic122—42no—
336C8×C61—22no—
337C8×C61—22no—
338#92418—22no—
339#92418C2×#4114yes—
340C2×#3398—611nomaximal, Sylow
341C22×C61—42no—
342C22×C61—42no—
343C22×C61—42no—
344C22×C61—84no—
345C22×C61#55012yes—
346C22×C61C2×#13712yes—
347C22×C61#57812yes—
348C22×C61C23×D411yescharacteristic
349C4×C61—22no—
350C4×C61—22no—
351C4×C61—42no—
352C4×C61—42no—
353C4×C61—42no—
354C4×C61#55012yes—
355C4×C61C22×#4111yescharacteristic
356C4×C61C2×H(5,𝔽2)11yescharacteristic
357Dic61—22no—
358Dic61—22no—
359Dic61—22no—
360Dic61—42no—
361Dic61—42no—
362Dic61—42no—
363Dic61—42no—
364Dic61C2×#13714yes—
365C2×#557—611no—
366C2×#556—611no—
367#3398—6116no—
368C2×#497—611no—
369C2×#497—611no—
370C2×#494—611no—
371C2×#464—611no—
372C2×#464D6111yescharacteristic
373C2×#462—611no—
374C2×#462—611no—
375C2×#462—611no—
376C2×#461—611no—
377C2×#446—611no—
378C2×#441—611no—
379C2×#441—611no—
380C2×C4×SD16—611no—
381C2×C61—82no—
382C2×C61#339814yescomplemented
383C2×C61C2×#55011yescharacteristic
384C2×C61C22×#13711yescharacteristic
385C2×C61C2×#57811yescharacteristic
386C22×Q16—611no—
387C22×Q16—611no—
388C22×Q16—611no—
389C22×Q16—611no—
390C22×Q16—611no—
391C22×Q16C2×D6111yescharacteristic
392C22×SD16—611no—
393C22×SD16—611no—
394C22×SD16C2×D6111yescharacteristic
395#557—618no—
396#557—1224no—
397#556—618no—
398#556—1224no—
399C2×C4⋊Q8—611no—
400C2×C4⋊Q8—611no—
401C2×C4⋊Q8—611no—
402C2×C4⋊Q8—611no—
403C2×#126—1221no—
404C2×#126—1221no—
405C2×#125—1221no—
406C2×#125—1221no—
407C2×#125—1221no—
408C2×#124—611no—
409C2×#124C2×D6111yescharacteristic
410C2×C22⋊Q8—1221no—
411C2×C4×Q8—611no—
412C2×C4×Q8—611no—
413C2×C4×Q8—611no—
414C2×C4×Q8—611no—
415C2×C4×Q8—611no—
416C2×C4×Q8—1221no—
417C2×C4×Q8C2×D6111yescharacteristic
418C2×C4×D4—611no—
419C2×#117—1221no—
420#497—618no—
421#497—618no—
422#494—618no—
423#464—618no—
424#464C2×D6118yes—
425#462—618no—
426#462—618no—
427#462—618no—
428#461—618no—
429#446—618no—
430#441—618no—
431#441—618no—
432C4×SD16—618no—
433C2×#106—611no—
434C2×C4⋊C8—611no—
435C2×C4⋊C8—611no—
436C2×C4⋊C8C2×D6111yescharacteristic
437C2×#103—611no—
438C2×#103—611no—
439C2×#103—611no—
440C2×#103—611no—
441C2×#103C2×D6111yescharacteristic
442C2×#102C2×D6111yescharacteristic
443C2×#97—611no—
444C2×#97—611no—
445C2×C4×C8—611no—
446C61C2×#339811yescharacteristic, complemented, Sylow
447C22×Q8—611no—
448C22×Q8—611no—
449C22×Q8—611no—
450C22×Q8—611no—
451C22×Q8C22×D6111yescharacteristic
452C22×Q8C22×D6111yescharacteristic
453C22×D4C22×D6111yescharacteristic
454C23×C4—1221no—
455C2×Q16—42no—
456C2×Q16—614no—
457C2×Q16—614no—
458C2×Q16—614no—
459C2×Q16—614no—
460C2×Q16—614no—
461C2×Q16—1224no—
462C2×Q16—1224no—
463C2×Q16—2442no—
464C2×Q16—2442no—
465C2×Q16—2442no—
466C2×Q16C22×D6114yes—
467C2×SD16—42no—
468C2×SD16—614no—
469C2×SD16—614no—
470C2×SD16—1224no—
471C2×SD16—2442no—
472C2×SD16C22×D6114yes—
473C22×C8—611no—
474C22×C8—611no—
475C22×C8C22×D6111yescharacteristic
476C22×C8C22×D6111yescharacteristic
477C4⋊Q8—614no—
478C4⋊Q8—614no—
479C4⋊Q8—614no—
480C4⋊Q8—614no—
481C4⋊Q8—1222no—
482C4⋊Q8—1222no—
483C4⋊Q8—1222no—
484C4⋊Q8—1222no—
485#126—1228no—
486#126—1228no—
487#125—1228no—
488#125—1228no—
489#125—1228no—
490#124—22no—
491#124—614no—
492#124—1222no—
493#124C22×D6114yes—
494C22⋊Q8—1228no—
495C4×Q8—22no—
496C4×Q8—614no—
497C4×Q8—614no—
498C4×Q8—614no—
499C4×Q8—614no—
500C4×Q8—614no—
501C4×Q8—614no—
502C4×Q8—1228no—
503C4×Q8—1222no—
504C4×Q8—1222no—
505C4×Q8—1222no—
506C4×Q8—1222no—
507C4×Q8C22×D6114yes—
508C4×D4—614no—
509C4×D4—1222no—
510#117—1228no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4C22×D6111yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C42—21no—
535C2×C42—611no—
536C2×C42—611no—
537C2×C42—1221no—
538C2×C42—1221no—
539C2×C42—1221no—
540C2×C42—1221no—
541C2×C42C22×D6111yescharacteristic
542#106—614no—
543C4⋊C8—614no—
544C4⋊C8—614no—
545C4⋊C8C22×D6114yes—
546#103—614no—
547#103—614no—
548#103—614no—
549#103—614no—
550#103C22×D6114yes—
551#102C22×D6114yes—
552#97—614no—
553#97—614no—
554C4×C8—614no—
555C24—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—614no—
563C2×Q8—612no—
564C2×Q8—612no—
565C2×Q8—612no—
566C2×Q8—1224no—
567C2×Q8—1221no—
568C2×Q8—1221no—
569C2×Q8—1221no—
570C2×Q8—1222no—
571C2×Q8—1222no—
572C2×Q8—1222no—
573C2×Q8—1222no—
574C2×Q8—1222no—
575C2×Q8—1222no—
576C2×Q8C23×D6112yes—
577C2×Q8C23×D6112yes—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4C23×D6112yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—1224no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—2444no—
595C22×C4D4×D6111yescharacteristic
596C22×C4D4×D6111yescharacteristic
597C22×C4C23×D6111yescharacteristic
598Q16—44no—
599Q16—1228no—
600Q16—1228no—
601Q16—2444no—
602Q16—2444no—
603Q16—2444no—
604SD16—44no—
605SD16—1228no—
606SD16—2444no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—614no—
610C2×C8—612no—
611C2×C8—612no—
612C2×C8—1222no—
613C2×C8C23×D6112yes—
614C2×C8C23×D6112yes—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—614no—
618C4⋊C4—614no—
619C4⋊C4—614no—
620C4⋊C4—612no—
621C4⋊C4—1224no—
622C4⋊C4—1224no—
623C4⋊C4—1224no—
624C4⋊C4—1224no—
625C4⋊C4—1224no—
626C4⋊C4—1224no—
627C4⋊C4—1224no—
628C4⋊C4—1224no—
629C4⋊C4—1224no—
630C4⋊C4—1221no—
631C4⋊C4—1224no—
632C4⋊C4—1224no—
633C4⋊C4—1224no—
634C4⋊C4C23×D6112yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—1224no—
638C22⋊C4—1224no—
639C22⋊C4—1224no—
640C42—24no—
641C42—612no—
642C42—612no—
643C42—612no—
644C42—612no—
645C42—1224no—
646C42—1224no—
647C42—1224no—
648C42—1224no—
649C42D4×D6112yes—
650C42C23×D6112yes—
651C23—22no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23C2×D4×D6111yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—1228no—
663Q8—1222no—
664Q8—1222no—
665Q8—1222no—
666Q8—1222no—
667Q8—1222no—
668Q8—1222no—
669Q8—2442no—
670Q8—2442no—
671Q8—2442no—
672D4—22no—
673D4—22no—
674D4—42no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—614no—
684C2×C4—612no—
685C2×C4—612no—
686C2×C4—612no—
687C2×C4—612no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—2448no—
696C2×C4—2442no—
697C2×C4—2442no—
698C2×C4—2442no—
699C2×C4—2442no—
700C2×C4C2×D4×D6112yes—
701C2×C4C2×D4×D6112yes—
702C2×C4C2×D4×D6111yescharacteristic
703C2×C4#41×D6112yes—
704C2×C4#1451982212yes—
705C2×C4C24×D6111yescharacteristic
706C8—22no—
707C8—22no—
708C8—614no—
709C8—1222no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22#1684043012yes—
715C22#137×D6112yes—
716C22#1684057612yes—
717C22C22×D4×D6111yescharacteristic
718C4—22no—
719C4—22no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—614no—
724C4—1222no—
725C4—1222no—
726C4—1222no—
727C4—2442no—
728C4—2442no—
729C4—2442no—
730C4—2442no—
731C4#1684043012yes—
732C4C2×#41×D6111yescharacteristic
733C4C2×#1451982211yescharacteristic
734C2—82no—
735C2#2145885314yesdirect product factor
736C2C2×#1684043011yescharacteristic
737C2C2×#137×D6111yescharacteristic
738C2C2×#1684057611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#464C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
hypercenterC2×#464D61
hypocenterC61C2×#3398
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#16840490C2semidirect
3. #21458853C2direct (N × H)
6. C2×#16840140C2semidirect
8. C2×#16839973C2semidirect
9. C2×#16839971C2semidirect
10. C2×#16839970C2semidirect
12. C2×#16839891C2semidirect
13. C2×#16839867C2semidirect
14. C2×#16839866C2semidirect
25. #16840490C22semidirect
49. #16840140C22semidirect
51. #16839973C22semidirect
52. #16839971C22semidirect
53. #16839970C22semidirect
55. #16839891C22semidirect
56. #16839867C22semidirect
57. #16839866C22semidirect
382. C2×C61#3398semidirect
446. C61C2×#3398semidirect
735. C2#21458853direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404902
C2×#168404812
#214588532
C2×#168401572
C2×#168401532
C2×#168401402
C2×#168399832
C2×#168399732
C2×#168399712
C2×#168399702
C2×#168399652
C2×#168398912
C2×#168398672
C2×#168398662
C2×#168398532
C2×C61×#4642
C2×#339861