Finite Group Databasebeta

← C2×#21456185 #30549262

Subgroups — C2×#21456185 #30549262

Order 15616.

2070 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840392C211yesmaximal, characteristic, complemented
2C2×#16840337C211yesmaximal, characteristic
3#21456185C2116yesmaximal, direct product factor
4C2×#16840129C211yesmaximal, characteristic, complemented
5C2×#16840123C211yesmaximal, characteristic, complemented
6C2×#16840122C211yesmaximal, characteristic, complemented
7C2×#16840119C211yesmaximal, characteristic, complemented
8C2×#16840118C211yesmaximal, characteristic, complemented
9C2×#16840112C211yesmaximal, characteristic, complemented
10C2×#16840111C211yesmaximal, characteristic, complemented
11C2×#16839762C211yesmaximal, characteristic
12C2×#16839769C211yesmaximal, characteristic, complemented
13C2×#16839757C211yesmaximal, characteristic
14C2×#103×D61C211yesmaximal, characteristic, complemented
15C2×#16839719C211yesmaximal, characteristic, complemented
16C2×C61×#491C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21#16840392—24no—
22#16840392C2218yescomplemented
23#16840337—24no—
24#16840337C2218yes—
25C2×#14519777C2211yescharacteristic
26C2×#14519776—21no—
27C2×#14519776C2211yescharacteristic
28C2×#14519775C2211yescharacteristic
29C2×#14519768C2211yescharacteristic
30C2×#14519767—21no—
31C2×#14519766C2211yescharacteristic
32C2×#14519765C2211yescharacteristic
33C2×#14519762—21no—
34C2×#14519762—21no—
35C2×#14519757—21no—
36C2×#14519755—21no—
37C2×#14519755—21no—
38C2×#14519755—21no—
39C2×#14519735C2211yescharacteristic
40C2×#14519734C2211yescharacteristic
41C2×C4⋊C4×D61C2211yescharacteristic
42#16840129C2218yescomplemented
43#16840123C2218yescomplemented
44#16840122C2218yescomplemented
45#16840119C2218yescomplemented
46#16840118C2218yescomplemented
47#16840112C2218yescomplemented
48#16840111C2218yescomplemented
49#16839769C2218yescomplemented
50#16839762C2218yes—
51#16839757C2218yes—
52C2×#14519702C2211yescharacteristic
53C2×#14519702C2211yescharacteristic
54C2×#14519701C2211yescharacteristic
55C2×#14519701C2211yescharacteristic
56C2×#14519701C2211yescharacteristic
57C2×#14519701C2211yescharacteristic
58C2×#14519700C2211yescharacteristic
59C2×#14519700C2211yescharacteristic
60#103×D61C2218yescomplemented
61C2×#14519699C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65#16839719C2218yescomplemented
66C2×#14519687C2211yescharacteristic
67C2×C4×#92418C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C2×C4⋊Q8×C61C2211yescharacteristic
70C2×#125×C61C2211yescharacteristic
71C61×#491C2218yescomplemented
72C2×#103×C61C2211yescharacteristic
73C2×#103×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C2×#11758226—22no—
78C2×#11758226—24no—
79C2×#11758226—24no—
80C2×#11758226C2314yes—
81C22×Dic122—21no—
82C22×Dic122—21no—
83C22×Dic122—21no—
84C22×Dic122C2311yescharacteristic
85C2×Q8×D61—22no—
86C2×Q8×D61—24no—
87C2×Q8×D61—24no—
88C2×Q8×D61C2314yes—
89C22×D244—21no—
90C22×D244C2311yescharacteristic
91C22×C4×D61—21no—
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C22×C4×D61C2311yescharacteristic
95C2×#11758189—24no—
96C2×#11758189C2314yes—
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99C2×C8×D61—24no—
100C2×C8×D61C2314yes—
101#14519777—22no—
102#14519777C2314yes—
103#14519776—28no—
104#14519776—22no—
105#14519776C2314yes—
106#14519775—22no—
107#14519775C2314yes—
108#14519768—22no—
109#14519768C2314yes—
110#14519767—28no—
111#14519766—22no—
112#14519766C2314yes—
113#14519765—22no—
114#14519765C2314yes—
115#14519762—28no—
116#14519762—28no—
117#14519757—28no—
118#14519755—28no—
119#14519755—28no—
120#14519755—28no—
121#14519735—22no—
122#14519735C2314yes—
123#14519734D414yes—
124#14519734C2314yes—
125C2×C4⋊Dic61—21no—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61C2311yescharacteristic
128C2×C4⋊Dic61C2311yescharacteristic
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196D411yescharacteristic
135C2×#11758196D411yescharacteristic
136C4⋊C4×D61—22no—
137C4⋊C4×D61C2314yes—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198D411yescharacteristic
144C2×#11758198D411yescharacteristic
145C2×C4×Dic61—21no—
146C2×C4×Dic61C2311yescharacteristic
147#14519702C2314yes—
148#14519702C2314yes—
149#14519701C2314yes—
150#14519701C2314yes—
151#14519701C2314yes—
152#14519701C2314yes—
153#14519700C2314yes—
154#14519700C2314yes—
155#14519699C2314yes—
156#14519699C2314yes—
157#14519697C2314yes—
158#14519697C2314yes—
159#14519687C2314yes—
160C4×#92418C2314yes—
161C8×Dic61C2314yes—
162C22×Q8×C61C2311yescharacteristic
163C22×Q8×C61C2311yescharacteristic
164C22×C8×C61C2311yescharacteristic
165C22×C8×C61C2311yescharacteristic
166C4⋊Q8×C61—22no—
167C4⋊Q8×C61C2314yes—
168#125×C61—22no—
169#125×C61C2314yes—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61—21no—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C42×C61C2311yescharacteristic
177#103×C61C2314yes—
178#103×C61C2314yes—
179#103×C61C2314yes—
180#103×C61C2314yes—
181#97×C61C2314yes—
182C23×D61—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—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2411yescharacteristic
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61C2×D411yescharacteristic
203C22×Dic61C2×D411yescharacteristic
204C22×Dic61C2×D411yescharacteristic
205#11758226—28no—
206#11758226—28no—
207#11758226—48no—
208Q8×D61—28no—
209Q8×D61—28no—
210Q8×D61—48no—
211C2×D244—22no—
212C2×D244—22no—
213C2×D244—24no—
214C2×D244—21no—
215C2×D244—44no—
216C2×D244C2412yes—
217C2×C4×D61—24no—
218C2×C4×D61—24no—
219C2×C4×D61—24no—
220C2×C4×D61—44no—
221C2×C4×D61—44no—
222C2×C4×D61—82no—
223C2×C4×D61C2×D412yes—
224C2×C4×D61#4114yes—
225C2×C4×D61#4114yes—
226C2×C4×D61C2412yes—
227C2×Dic122—22no—
228C2×Dic122—22no—
229C2×Dic122—21no—
230C2×Dic122—24no—
231C2×Dic122—24no—
232C2×Dic122—24no—
233C2×Dic122—44no—
234C2×Dic122—82no—
235C2×Dic122—82no—
236C2×Dic122C2412yes—
237C2×C8×C61—22no—
238C2×C8×C61—22no—
239C2×C8×C61C2412yes—
240C2×C8×C61C2412yes—
241C4⋊C4×C61—24no—
242C4⋊C4×C61—24no—
243C4⋊C4×C61—24no—
244C4⋊C4×C61—24no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61C2412yes—
248C4⋊C4×C61C2412yes—
249C42×C61C2×D412yes—
250C42×C61C2412yes—
251#11758198—24no—
252#11758198—24no—
253#11758198—24no—
254#11758198—24no—
255#11758198—24no—
256#11758198C2×D414yes—
257#11758198C2×D414yes—
258C4⋊Dic61—21no—
259C4⋊Dic61—24no—
260C4⋊Dic61—21no—
261C4⋊Dic61—24no—
262C4⋊Dic61C2412yes—
263C4⋊Dic61C2412yes—
264#11758196—24no—
265#11758196—24no—
266#11758196—24no—
267#11758196—24no—
268#11758196—24no—
269#11758196C2×D414yes—
270#11758196C2×D414yes—
271C4×Dic61—24no—
272C4×Dic61C2×D412yes—
273C4×Dic61C2412yes—
274C2×#92418—22no—
275C2×#92418—22no—
276C2×#92418C2412yes—
277C2×#92418C2412yes—
278#11758189—28no—
279C8×D61—28no—
280C23×C61C22×D411yescharacteristic
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—42no—
285C22×D61—42no—
286C22×D61—42no—
287C22×D61#12414yes—
288C22×D61C22×D412yes—
289Q8×C61—22no—
290Q8×C61—22no—
291Q8×C61—22no—
292Q8×C61—22no—
293Q8×C61—42no—
294Q8×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—22no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61C22×D412yes—
306C2×C4×C61C22×D412yes—
307C2×C4×C61C22×D411yescharacteristic
308C2×C4×C61C2×#4112yes—
309C2×C4×C61C2×#4112yes—
310C2×C4×C61C2511yescharacteristic
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#12414yes—
320C2×Dic61C22×D412yes—
321C2×Dic61C22×D412yes—
322C2×Dic61C22×D412yes—
323D244—22no—
324D244—22no—
325D244—48no—
326D244—42no—
327C4×D61—48no—
328C4×D61—48no—
329C4×D61—84no—
330C4×D61#12418yes—
331C4×D61C2×#4114yes—
332C4×D61C2×#4114yes—
333Dic122—22no—
334Dic122—22no—
335Dic122—42no—
336Dic122—48no—
337Dic122—84no—
338Dic122—84no—
339C8×C61—22no—
340C8×C61—22no—
341#92418—22no—
342#92418—22no—
343C2×#3137—611nomaximal, Sylow
344C22×C61C2×#12412yes—
345C22×C61#57712yes—
346C22×C61#57812yes—
347C22×C61C23×D411yescharacteristic
348C2×D61—28no—
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—42no—
352C2×D61—42no—
353C2×D61—42no—
354C2×D61—84no—
355C2×D61C2×#12414yes—
356C4×C61—22no—
357C4×C61—22no—
358C4×C61—42no—
359C4×C61—42no—
360C4×C61—42no—
361C4×C61—42no—
362C4×C61C2×#12412yes—
363C4×C61C22×#4111yescharacteristic
364C4×C61C22×#4111yescharacteristic
365Dic61—22no—
366Dic61—22no—
367Dic61—42no—
368Dic61—42no—
369Dic61—42no—
370Dic61C2×#12414yes—
371C2×#544—611no—
372C2×#536—611no—
373#3137—6116no—
374C2×#491—611no—
375C2×#491D6111yescharacteristic, complemented
376C2×#489—611no—
377C2×#489—611no—
378C2×#488—611no—
379C2×#488—611no—
380C2×#487—611no—
381C2×#487—611no—
382C2×#417—611no—
383C2×#419—611no—
384C2×#416—611no—
385C22×#103—611no—
386C2×#405—611no—
387C2×C61#313714yescomplemented
388C2×C61C22×#12411yescharacteristic
389C2×C61C2×#57711yescharacteristic
390C2×C61C2×#57811yescharacteristic
391D61—24no—
392D61—82no—
393C22×#41—611no—
394C23×Q8—611no—
395C22×M16—611no—
396C23×C8—611no—
397#544—618no—
398#544—1224no—
399#536—618no—
400#536—1224no—
401C2×C4⋊Q8—611no—
402C2×C4⋊Q8—611no—
403C2×C4⋊Q8—611no—
404C2×C4⋊Q8—1221no—
405C2×C4⋊Q8C2×D6111yescharacteristic
406C2×#125—611no—
407C2×#125—1221no—
408C2×#125C2×D6111yescharacteristic
409C2×#124—611no—
410C2×#124—611no—
411C2×#123—1221no—
412C2×#123—1221no—
413C2×C22⋊Q8—1221no—
414C2×C22⋊Q8—1221no—
415C2×C22⋊Q8—1221no—
416C2×C22⋊Q8—1221no—
417C2×#117—611no—
418C2×#117—611no—
419C22×C4⋊C4—611no—
420#491—618no—
421#491C2×D6118yescomplemented
422#489—618no—
423#489—618no—
424#488—618no—
425#488—618no—
426#487—618no—
427#487—618no—
428#419—618no—
429#417—618no—
430#416—618no—
431C2×#103—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#103—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#103—611no—
439C2×#103—618no—
440C2×#103C2×D6111yescharacteristic
441C2×#103C2×D6111yescharacteristic
442C2×#103C2×D6111yescharacteristic
443C2×#103C2×D6111yescharacteristic
444C2×#102—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×#102—611no—
448#405—618no—
449C2×#97—611no—
450C2×#97C2×D6111yescharacteristic
451C2×C4×C8—611no—
452C2×C4×C8—611no—
453C61C2×#313711yescharacteristic, complemented, Sylow
454C2×#41—614no—
455C2×#41—1222no—
456C2×#41—1224no—
457C2×#41—1224no—
458C22×Q8—614no—
459C22×Q8—611no—
460C22×Q8—1221no—
461C22×Q8—1221no—
462C22×Q8—1222no—
463C22×Q8—1224no—
464C22×Q8—1224no—
465C22×Q8—1221no—
466C22×Q8C22×D6111yescharacteristic
467C22×Q8C22×D6111yescharacteristic
468C22×D4—611no—
469C22×D4—1221no—
470C23×C4—611no—
471C23×C4—1221no—
472C23×C4—1221no—
473C23×C4—1221no—
474C2×M16—614no—
475C2×M16—1224no—
476C22×C8—611no—
477C22×C8—611no—
478C22×C8—614no—
479C22×C8—1224no—
480C22×C8C22×D6111yescharacteristic
481C22×C8C22×D6111yescharacteristic
482C4⋊Q8—22no—
483C4⋊Q8—614no—
484C4⋊Q8—614no—
485C4⋊Q8—614no—
486C4⋊Q8—1222no—
487C4⋊Q8—1222no—
488C4⋊Q8—1228no—
489C4⋊Q8—1222no—
490C4⋊Q8C22×D6114yes—
491#125—22no—
492#125—614no—
493#125—1222no—
494#125—1228no—
495#125C22×D6114yes—
496#124—614no—
497#124—614no—
498#124—1222no—
499#124—1222no—
500#123—1228no—
501#123—1228no—
502C22⋊Q8—1228no—
503C22⋊Q8—1228no—
504C22⋊Q8—1228no—
505C22⋊Q8—1228no—
506#117—614no—
507#117—614no—
508#117—614no—
509#117—1222no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—614no—
519C2×C4⋊C4—1222no—
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⋊C4C22×D6111yescharacteristic
528C2×C4⋊C4C22×D6111yescharacteristic
529C2×C22⋊C4—611no—
530C2×C22⋊C4—611no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C42—611no—
537C2×C42—1221no—
538C2×C42C22×D6111yescharacteristic
539#103—614no—
540#103—614no—
541#103—614no—
542#103—614no—
543#103—614no—
544#103—614no—
545#103—614no—
546#103—614no—
547#103C22×D6114yes—
548#103C22×D6114yes—
549#103C22×D6114yes—
550#103C22×D6114yes—
551#102—614no—
552#102—614no—
553#102—614no—
554#102—614no—
555#97—614no—
556#97C22×D6114yes—
557C4×C8—614no—
558C4×C8—614no—
559C24—611no—
560C24—1221no—
561#41—1228no—
562#41—1228no—
563#41—2448no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—612no—
571C2×Q8—1224no—
572C2×Q8—1224no—
573C2×Q8—1228no—
574C2×Q8—1228no—
575C2×Q8—1224no—
576C2×Q8—1221no—
577C2×Q8—1222no—
578C2×Q8—1222no—
579C2×Q8—4882no—
580C2×Q8—4882no—
581C2×Q8—2444no—
582C2×Q8—2448no—
583C2×Q8C23×D6112yes—
584C2×Q8C23×D6112yes—
585C2×D4—612no—
586C2×D4—1224no—
587C2×D4—1221no—
588C2×D4—1222no—
589C2×D4—1222no—
590C2×D4—2444no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—611no—
596C22×C4—612no—
597C22×C4—614no—
598C22×C4—614no—
599C22×C4—612no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—1224no—
603C22×C4—1224no—
604C22×C4—1224no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—4882no—
609C22×C4—2444no—
610C22×C4—2444no—
611C22×C4D4×D6111yescharacteristic
612C22×C4D4×D6111yescharacteristic
613C22×C4C23×D6111yescharacteristic
614M16—1228no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—612no—
618C2×C8—612no—
619C2×C8—1228no—
620C2×C8—1222no—
621C2×C8—1222no—
622C2×C8C23×D6112yes—
623C2×C8C23×D6112yes—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—614no—
631C4⋊C4—614no—
632C4⋊C4—612no—
633C4⋊C4—612no—
634C4⋊C4—1224no—
635C4⋊C4—1224no—
636C4⋊C4—1224no—
637C4⋊C4—1224no—
638C4⋊C4—1224no—
639C4⋊C4—1224no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4—1224no—
643C4⋊C4C23×D6112yes—
644C4⋊C4C23×D6112yes—
645C22⋊C4—614no—
646C22⋊C4—614no—
647C22⋊C4—1224no—
648C22⋊C4—1224no—
649C22⋊C4—1224no—
650C22⋊C4—1224no—
651C22⋊C4—1224no—
652C42—612no—
653C42—612no—
654C42—1224no—
655C42D4×D6112yes—
656C42C23×D6112yes—
657C23—614no—
658C23—612no—
659C23—1222no—
660C23—1222no—
661C23—1222no—
662C23—2442no—
663C23—2442no—
664C23—2442no—
665C23C2×D4×D6111yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—22no—
669Q8—22no—
670Q8—42no—
671Q8—42no—
672Q8—1222no—
673Q8—1222no—
674Q8—4884no—
675Q8—4884no—
676Q8—2448no—
677Q8—2442no—
678D4—1222no—
679D4—1222no—
680D4—2448no—
681D4—2442no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—614no—
693C2×C4—612no—
694C2×C4—618no—
695C2×C4—614no—
696C2×C4—614no—
697C2×C4—612no—
698C2×C4—612no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—4884no—
705C2×C4—2448no—
706C2×C4—2448no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4—2442no—
710C2×C4C2×D4×D6112yes—
711C2×C4C2×D4×D6112yes—
712C2×C4C2×D4×D6111yescharacteristic
713C2×C4#41×D6112yes—
714C2×C4#41×D6112yes—
715C2×C4C24×D6111yescharacteristic
716C8—22no—
717C8—22no—
718C8—1222no—
719C8—1222no—
720C22—614no—
721C22—1228no—
722C22—1222no—
723C22—1222no—
724C22—4884no—
725C22—2442no—
726C22—2442no—
727C22—2442no—
728C22#124×D6112yes—
729C22#1684057112yes—
730C22#1684057812yes—
731C22C22×D4×D6111yescharacteristic
732C4—22no—
733C4—22no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—614no—
739C4—1222no—
740C4—1222no—
741C4—2442no—
742C4—2442no—
743C4—2442no—
744C4#124×D6112yes—
745C4C2×#41×D6111yescharacteristic
746C4C2×#41×D6111yescharacteristic
747C2—1224no—
748C2—4882no—
749C2#2145618514yesdirect product factor
750C2C2×#124×D6111yescharacteristic
751C2C2×#1684057111yescharacteristic
752C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#491C2
socleC23×C61C22×D4
prime radicalC22×#11758226C22
hypercenterC2×#491D61
hypocenterC61C2×#3137
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
1. C2×#16840392C2semidirect
3. #21456185C2direct (N × H)
4. C2×#16840129C2semidirect
5. C2×#16840123C2semidirect
6. C2×#16840122C2semidirect
7. C2×#16840119C2semidirect
8. C2×#16840118C2semidirect
9. C2×#16840112C2semidirect
10. C2×#16840111C2semidirect
12. C2×#16839769C2semidirect
14. C2×#103×D61C2semidirect
15. C2×#16839719C2semidirect
16. C2×C61×#491C2semidirect
22. #16840392C22semidirect
42. #16840129C22semidirect
43. #16840123C22semidirect
44. #16840122C22semidirect
45. #16840119C22semidirect
46. #16840118C22semidirect
47. #16840112C22semidirect
48. #16840111C22semidirect
49. #16839769C22semidirect
60. #103×D61C22semidirect
65. #16839719C22semidirect
71. C61×#491C22semidirect
375. C2×#491D61semidirect
387. C2×C61#3137semidirect
421. #491C2×D61semidirect
453. C61C2×#3137semidirect
749. C2#21456185direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403922
C2×#168403372
#214561852
C2×#168401292
C2×#168401232
C2×#168401222
C2×#168401192
C2×#168401182
C2×#168401122
C2×#168401112
C2×#168397622
C2×#168397692
C2×#168397572
C2×#103×D612
C2×#168397192
C2×C61×#4912
C2×#313761