Finite Group Databasebeta

← C2×#21456038 #30548281

Subgroups — C2×#21456038 #30548281

Order 15616.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840375C211yesmaximal, characteristic, complemented
2C2×#16840241C211yesmaximal, characteristic
3#21456038C2116yesmaximal, direct product factor
4C2×#16840099C211yesmaximal, characteristic, complemented
5C2×#16840094C211yesmaximal, characteristic, complemented
6C2×#16840066C211yesmaximal, characteristic, complemented
7C2×#16839973C211yesmaximal, characteristic, complemented
8C2×#16839967C211yesmaximal, characteristic, complemented
9C2×#16839925C211yesmaximal, characteristic
10C2×#16839925C211yesmaximal, characteristic
11C2×#16839868C211yesmaximal, characteristic, complemented
12C2×#16839859C211yesmaximal, characteristic, complemented
13C2×#16839856C211yesmaximal, characteristic, complemented
14C2×#16839853C211yesmaximal, characteristic, complemented
15C2×#16839822C211yesmaximal, characteristic, complemented
16C2×C61×#478C211yesmaximal, characteristic, complemented
17C22×#11758224C2211yescharacteristic
18C22×Dic244C2211yescharacteristic
19C22×Dic244C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758200C2211yescharacteristic
22#16840375—24no—
23#16840375C2218yescomplemented
24C2×#14519777C2211yescharacteristic
25C2×#14519772—21no—
26C2×#14519772—21no—
27C2×#14519768—21no—
28C2×#14519768—21no—
29C2×#14519757C2211yescharacteristic
30C2×#14519757C2211yescharacteristic
31#16840241—24no—
32#16840241C2218yes—
33C2×C4×Dic122C2211yescharacteristic
34C2×#14519742C2211yescharacteristic
35C2×#14519742C2211yescharacteristic
36C2×#14519742C2211yescharacteristic
37C2×D4×Dic61C2211yescharacteristic
38C2×C4×C22⋊D61—21no—
39C2×#14519737—21no—
40C2×#14519734C2211yescharacteristic
41C2×#14519733—21no—
42C22×#11758196—21no—
43C2×C4⋊C4×D61C2211yescharacteristic
44#16840099C2218yescomplemented
45#16840094C2218yescomplemented
46#16840066C2218yescomplemented
47#16839973C2218yescomplemented
48#16839967C2218yescomplemented
49#16839925C2218yes—
50#16839925C2218yes—
51#16839868C2218yescomplemented
52#16839859C2218yescomplemented
53#16839856C2218yescomplemented
54#16839853C2218yescomplemented
55#16839822C2218yescomplemented
56C2×#14519710C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×C4⋊#92418C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65C2×#14519689C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C2×#125×C61C2211yescharacteristic
70C2×C4×D4×C61C2211yescharacteristic
71C61×#478C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758224—24no—
78C2×#11758224—22no—
79C2×#11758224—24no—
80C2×#11758224C2314yes—
81C22×Dic122C2311yescharacteristic
82C22×Dic122C2311yescharacteristic
83C22×Dic122C2311yescharacteristic
84C22×C22⋊D61—21no—
85C23×Dic61—21no—
86C23×Dic61—21no—
87C22×C4×D61—21no—
88C22×C4×D61C2311yescharacteristic
89C2×Dic244—24no—
90C2×Dic244—24no—
91C2×Dic244C2314yes—
92C2×Dic244C2314yes—
93C2×#11758200—24no—
94C2×#11758200—24no—
95C2×#11758200C2314yes—
96C2×#11758200C2314yes—
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99#14519777—22no—
100#14519777C2314yes—
101#14519772—28no—
102#14519772—28no—
103#14519768—28no—
104#14519768—28no—
105#14519757—22no—
106#14519757—22no—
107#14519757C2314yes—
108#14519757C2314yes—
109C4×Dic122—22no—
110C4×Dic122C2314yes—
111#14519742—22no—
112#14519742—22no—
113#14519742—22no—
114#14519742C2314yes—
115#14519742C2314yes—
116#14519742C2314yes—
117D4×Dic61—22no—
118D4×Dic61C2314yes—
119C4×C22⋊D61—28no—
120#14519737—28no—
121#14519734D414yes—
122#14519734C2314yes—
123#14519733—28no—
124C2×C4⋊Dic61—21no—
125C2×C4⋊Dic61—21no—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61C2311yescharacteristic
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—28no—
135C2×#11758196D411yescharacteristic
136C2×#11758196D411yescharacteristic
137C4⋊C4×D61—22no—
138C4⋊C4×D61C2314yes—
139C2×C22⋊Dic61—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198D411yescharacteristic
143C2×#11758198D411yescharacteristic
144C2×C4×Dic61—21no—
145C2×C4×Dic61—21no—
146C2×C4×Dic61—21no—
147C2×C4×Dic61—21no—
148C2×C4×Dic61C2311yescharacteristic
149#14519710C2314yes—
150#14519708C2314yes—
151C4⋊#92418C2314yes—
152#14519702C2314yes—
153#14519702C2314yes—
154#14519700C2314yes—
155#14519700C2314yes—
156#14519700C2314yes—
157#14519700C2314yes—
158#14519689C2314yes—
159#14519689C2314yes—
160#14519687C2314yes—
161C8×Dic61C2314yes—
162C22×D4×C61C2311yescharacteristic
163C23×C4×C61—21no—
164C22×C8×C61C2311yescharacteristic
165C22×C8×C61C2311yescharacteristic
166#125×C61—22no—
167#125×C61C2314yes—
168C4×D4×C61—22no—
169C4×D4×C61C2314yes—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C42×C61C2311yescharacteristic
177#107×C61C2314yes—
178#106×C61C2314yes—
179C4⋊C8×C61C2314yes—
180#102×C61C2314yes—
181#102×C61C2314yes—
182C24×C61—21no—
183C23×D61C2×D411yescharacteristic
184C2×D4×C61—21no—
185C2×D4×C61—22no—
186C2×D4×C61#4114yes—
187C2×D4×C61C2412yes—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—24no—
192C22×C4×C61—82no—
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2411yescharacteristic
196C2×C22⋊D61—28no—
197C2×C22⋊D61—24no—
198C22×Dic61—28no—
199C22×Dic61—21no—
200C22×Dic61—24no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—24no—
205C22×Dic61—82no—
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208C22×Dic61C2×D411yescharacteristic
209#11758224—216no—
210#11758224—28no—
211#11758224—28no—
212C2×C4×D61—22no—
213C2×C4×D61—22no—
214C2×C4×D61—24no—
215C2×C4×D61—82no—
216C2×C4×D61C2×D412yes—
217C2×C4×D61C2412yes—
218C2×Dic122—21no—
219C2×Dic122—22no—
220C2×Dic122—22no—
221C2×Dic122—22no—
222C2×Dic122—22no—
223C2×Dic122—22no—
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122#4114yes—
227C2×Dic122C2412yes—
228C2×Dic122C2412yes—
229C2×Dic122C2412yes—
230C2×C8×C61—22no—
231C2×C8×C61—22no—
232C2×C8×C61C2412yes—
233C2×C8×C61C2412yes—
234C4⋊C4×C61—24no—
235C4⋊C4×C61—24no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61C2412yes—
240C4⋊C4×C61C2412yes—
241C4⋊C4×C61C2412yes—
242C22⋊C4×C61—24no—
243C42×C61C2×D412yes—
244C42×C61C2412yes—
245C22⋊Dic61—24no—
246#11758200—28no—
247#11758200—28no—
248#11758198—24no—
249#11758198—24no—
250#11758198C2×D414yes—
251#11758198C2×D414yes—
252C4⋊Dic61—21no—
253C4⋊Dic61—24no—
254C4⋊Dic61—24no—
255C4⋊Dic61—24no—
256C4⋊Dic61—24no—
257C4⋊Dic61C2412yes—
258#11758196—24no—
259#11758196—24no—
260#11758196—24no—
261#11758196—24no—
262#11758196—24no—
263#11758196C2×D414yes—
264#11758196C2×D414yes—
265C4×Dic61—24no—
266C4×Dic61—24no—
267C4×Dic61—24no—
268C4×Dic61—24no—
269C4×Dic61C2×D412yes—
270C4×Dic61C2412yes—
271C2×#92418—22no—
272C2×#92418—22no—
273C2×#92418C2412yes—
274C2×#92418C2412yes—
275Dic244—28no—
276Dic244—28no—
277C23×C61—24no—
278C23×C61—22no—
279C23×C61—42no—
280C23×C61—42no—
281C23×C61C22×D411yescharacteristic
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61C22×D412yes—
286D4×C61—24no—
287D4×C61—22no—
288D4×C61C2×#4114yes—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—42no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—84no—
298C2×C4×C61C22×D412yes—
299C2×C4×C61C22×D412yes—
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C2×#4112yes—
302C2×C4×C61C2×#4112yes—
303C2×C4×C61C2511yescharacteristic
304C22⋊D61—216no—
305C2×Dic61—216no—
306C2×Dic61—24no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—84no—
318C2×Dic61C22×D412yes—
319C2×Dic61C22×D412yes—
320C2×Dic61C22×D412yes—
321C4×D61—24no—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—84no—
325Dic122—24no—
326Dic122—22no—
327Dic122—22no—
328Dic122—22no—
329Dic122—22no—
330Dic122—22no—
331Dic122—42no—
332Dic122—42no—
333Dic122C2×#4114yes—
334C8×C61—22no—
335C8×C61—22no—
336#92418—22no—
337#92418—22no—
338C2×#3120—611nomaximal, Sylow
339C22×C61—24no—
340C22×C61—48no—
341C22×C61—42no—
342C22×C61—42no—
343C22×C61#52512yes—
344C22×C61#57712yes—
345C22×C61#57812yes—
346C22×C61C23×D411yescharacteristic
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—44no—
351C4×C61—22no—
352C4×C61—22no—
353C4×C61—42no—
354C4×C61—42no—
355C4×C61—42no—
356C4×C61#52512yes—
357C4×C61C22×#4111yescharacteristic
358C4×C61C22×#4111yescharacteristic
359Dic61—24no—
360Dic61—22no—
361Dic61—22no—
362Dic61—22no—
363Dic61—42no—
364Dic61—42no—
365Dic61—42no—
366C2×#541—611no—
367C2×#520—611no—
368#3120—6116no—
369C2×#484—611no—
370C2×#483—611no—
371C2×#479—611no—
372C2×#478D6111yescharacteristic, complemented
373C2×#462—611no—
374C2×#461—611no—
375C2×#452—611no—
376C2×#452—611no—
377C2×#441—611no—
378C2×#440—611no—
379C2×C4×Q16—611no—
380C2×C4×SD16—611no—
381C2×#433—611no—
382C2×C61—44no—
383C2×C61#312014yescomplemented
384C2×C61C2×#52511yescharacteristic
385C2×C61C2×#57711yescharacteristic
386C2×C61C2×#57811yescharacteristic
387D61—42no—
388C22×#41—611no—
389C22×Q16—611no—
390C22×Q16—611no—
391C22×SD16—611no—
392C22×SD16—611no—
393#541—618no—
394#541—1224no—
395C2×C4⋊Q8—611no—
396C2×#126—1221no—
397C2×#126—1221no—
398C2×#125—1221no—
399C2×#125—1221no—
400C2×#125C2×D6111yescharacteristic
401C2×C22⋊Q8—611no—
402C2×C22⋊Q8—611no—
403#520—618no—
404#520—1224no—
405C2×C4×Q8—611no—
406C2×C4×Q8—611no—
407C2×C4×Q8—611no—
408C2×C4×Q8—611no—
409C2×C4×D4—611no—
410C2×C4×D4—1221no—
411C2×C4×D4—1221no—
412C2×C4×D4C2×D6111yescharacteristic
413C2×#117—611no—
414C2×#117—1221no—
415C22×C4⋊C4—611no—
416C22×C4⋊C4—1221no—
417#484—618no—
418#483—618no—
419#479—618no—
420#478C2×D6118yescomplemented
421#462—618no—
422#461—618no—
423#452—618no—
424#452—618no—
425#441—618no—
426#440—618no—
427C4×Q16—618no—
428C4×SD16—618no—
429#433—618no—
430C2×#107—611no—
431C2×#107C2×D6111yescharacteristic
432C2×#106—611no—
433C2×#106C2×D6111yescharacteristic
434C2×C4⋊C8—611no—
435C2×C4⋊C8C2×D6111yescharacteristic
436C2×#103—611no—
437C2×#103—611no—
438C2×#103—611no—
439C2×#103—611no—
440C2×#103—611no—
441C2×#103—611no—
442C2×#102C2×D6111yescharacteristic
443C2×#102C2×D6111yescharacteristic
444C2×C22⋊C8—611no—
445C2×C22⋊C8—611no—
446C2×#97—611no—
447C2×C4×C8—611no—
448C61C2×#312011yescharacteristic, complemented, Sylow
449C2×#41—614no—
450C2×#41—1222no—
451C2×#41—1224no—
452C2×#41—1224no—
453C22×Q8—611no—
454C22×Q8—611no—
455C22×Q8—611no—
456C22×D4—1221no—
457C22×D4C22×D6111yescharacteristic
458C23×C4—21no—
459C23×C4—611no—
460C23×C4—1221no—
461C23×C4—1221no—
462C23×C4—1221no—
463C2×Q16—614no—
464C2×Q16—614no—
465C2×Q16—1224no—
466C2×Q16—1224no—
467C2×SD16—614no—
468C2×SD16—614no—
469C2×SD16—1224no—
470C2×SD16—1224no—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8C22×D6111yescharacteristic
474C22×C8C22×D6111yescharacteristic
475C4⋊Q8—614no—
476C4⋊Q8—1222no—
477#126—1228no—
478#126—1228no—
479#125—22no—
480#125—1228no—
481#125—1228no—
482#125C22×D6114yes—
483C22⋊Q8—614no—
484C22⋊Q8—614no—
485C22⋊Q8—1222no—
486C22⋊Q8—1222no—
487C4×Q8—614no—
488C4×Q8—614no—
489C4×Q8—614no—
490C4×Q8—614no—
491C4×Q8—1222no—
492C4×Q8—1222no—
493C4×Q8—1222no—
494C4×Q8—1222no—
495C4×D4—22no—
496C4×D4—614no—
497C4×D4—1222no—
498C4×D4—1228no—
499C4×D4—1228no—
500C4×D4C22×D6114yes—
501#117—614no—
502#117—614no—
503#117—1228no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—614no—
510C2×C4⋊C4—1222no—
511C2×C4⋊C4—1228no—
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⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4C22×D6111yescharacteristic
522C2×C4⋊C4C22×D6111yescharacteristic
523C2×C4⋊C4C22×D6111yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4—611no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C42—611no—
531C2×C42—1221no—
532C2×C42—1221no—
533C2×C42—1221no—
534C2×C42—1221no—
535C2×C42C22×D6111yescharacteristic
536#107—614no—
537#107C22×D6114yes—
538#106—614no—
539#106C22×D6114yes—
540C4⋊C8—614no—
541C4⋊C8C22×D6114yes—
542#103—614no—
543#103—614no—
544#103—614no—
545#103—614no—
546#103—614no—
547#103—614no—
548#102C22×D6114yes—
549#102C22×D6114yes—
550C22⋊C8—614no—
551C22⋊C8—614no—
552#97—614no—
553C4×C8—614no—
554C24—21no—
555C24—611no—
556#41—1228no—
557#41—12216no—
558#41—1228no—
559C2×Q8—614no—
560C2×Q8—612no—
561C2×Q8—612no—
562C2×Q8—612no—
563C2×Q8—1221no—
564C2×Q8—1221no—
565C2×Q8—1221no—
566C2×Q8—1222no—
567C2×Q8—1222no—
568C2×Q8—1222no—
569C2×Q8—1222no—
570C2×Q8—1222no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—1224no—
574C2×D4—1228no—
575C2×D4#1175822614yes—
576C2×D4C23×D6112yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—24no—
581C22×C4—82no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—612no—
586C22×C4—612no—
587C22×C4—1224no—
588C22×C4—1224no—
589C22×C4—1224no—
590C22×C4—1228no—
591C22×C4—1221no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—4882no—
598C22×C4—4882no—
599C22×C4D4×D6111yescharacteristic
600C22×C4D4×D6111yescharacteristic
601C22×C4C23×D6111yescharacteristic
602Q16—1228no—
603Q16—1228no—
604SD16—1228no—
605SD16—1228no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—612no—
609C2×C8—612no—
610C2×C8—1222no—
611C2×C8—1222no—
612C2×C8C23×D6112yes—
613C2×C8C23×D6112yes—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—614no—
620C4⋊C4—614no—
621C4⋊C4—612no—
622C4⋊C4—1224no—
623C4⋊C4—1224no—
624C4⋊C4—1224no—
625C4⋊C4—1224no—
626C4⋊C4—1224no—
627C4⋊C4—1224no—
628C4⋊C4—1221no—
629C4⋊C4—1224no—
630C4⋊C4—1224no—
631C4⋊C4—1224no—
632C4⋊C4C23×D6112yes—
633C4⋊C4C23×D6112yes—
634C4⋊C4C23×D6112yes—
635C22⋊C4—24no—
636C22⋊C4—614no—
637C22⋊C4—614no—
638C22⋊C4—1224no—
639C22⋊C4—1224no—
640C22⋊C4—1224no—
641C42—612no—
642C42—612no—
643C42—1224no—
644C42—1224no—
645C42—1224no—
646C42—1224no—
647C42D4×D6112yes—
648C42C23×D6112yes—
649C23—24no—
650C23—22no—
651C23—42no—
652C23—42no—
653C23—612no—
654C23—1222no—
655C23—1222no—
656C23—1222no—
657C23C2×D4×D6111yescharacteristic
658Q8—614no—
659Q8—1224no—
660Q8—1222no—
661Q8—1222no—
662Q8—1222no—
663Q8—1222no—
664Q8—1222no—
665Q8—2442no—
666Q8—2442no—
667D4—24no—
668D4—22no—
669D4—12216no—
670D4C2×#1175822614yes—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—84no—
680C2×C4—612no—
681C2×C4—612no—
682C2×C4—612no—
683C2×C4—12216no—
684C2×C4—1222no—
685C2×C4—1224no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1224no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—4884no—
696C2×C4—4884no—
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×C4C2×#1175822612yes—
705C2×C4C24×D6111yescharacteristic
706C8—22no—
707C8—22no—
708C8—1222no—
709C8—1222no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—48no—
714C22—1222no—
715C22—1222no—
716C22—1222no—
717C22—2444no—
718C22#1684027512yes—
719C22#1684057212yes—
720C22#1684057612yes—
721C22C22×D4×D6111yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—1222no—
728C4—1222no—
729C4—1222no—
730C4—1224no—
731C4—2442no—
732C4—2442no—
733C4—2442no—
734C4#1684027512yes—
735C4C2×#41×D6111yescharacteristic
736C4C22×#1175822611yescharacteristic
737C2—44no—
738C2—2442no—
739C2#2145603814yesdirect product factor
740C2C2×#1684027511yescharacteristic
741C2C2×#1684057211yescharacteristic
742C2C2×#1684057611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#478C2
socleC23×C61C22×D4
prime radicalC22×#11758224C22
hypercenterC2×#478D61
hypocenterC61C2×#3120
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#16840375C2semidirect
3. #21456038C2direct (N × H)
4. C2×#16840099C2semidirect
5. C2×#16840094C2semidirect
6. C2×#16840066C2semidirect
7. C2×#16839973C2semidirect
8. C2×#16839967C2semidirect
11. C2×#16839868C2semidirect
12. C2×#16839859C2semidirect
13. C2×#16839856C2semidirect
14. C2×#16839853C2semidirect
15. C2×#16839822C2semidirect
16. C2×C61×#478C2semidirect
23. #16840375C22semidirect
44. #16840099C22semidirect
45. #16840094C22semidirect
46. #16840066C22semidirect
47. #16839973C22semidirect
48. #16839967C22semidirect
51. #16839868C22semidirect
52. #16839859C22semidirect
53. #16839856C22semidirect
54. #16839853C22semidirect
55. #16839822C22semidirect
71. C61×#478C22semidirect
372. C2×#478D61semidirect
383. C2×C61#3120semidirect
420. #478C2×D61semidirect
448. C61C2×#3120semidirect
739. C2#21456038direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403752
C2×#168402412
#214560382
C2×#168400992
C2×#168400942
C2×#168400662
C2×#168399732
C2×#168399672
C2×#168399252
C2×#168398682
C2×#168398592
C2×#168398562
C2×#168398532
C2×#168398222
C2×C61×#4782
C2×#312061