Finite Group Databasebeta

← C2×#21458899 #30561034

Subgroups — C2×#21458899 #30561034

Order 15616.

1938 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840484C211yesmaximal, characteristic, complemented
2C2×#16840482C211yesmaximal, characteristic, complemented
3#21458899C2116yesmaximal, direct product factor
4C2×#16840156C211yesmaximal, characteristic, complemented
5C2×#16840153C211yesmaximal, characteristic, complemented
6C2×#16840143C211yesmaximal, characteristic
7C2×#16839987C211yesmaximal, characteristic, complemented
8C2×#16839983C211yesmaximal, characteristic, complemented
9C2×#16839972C211yesmaximal, characteristic, complemented
10C2×#16839971C211yesmaximal, characteristic, complemented
11C2×#16839977C211yesmaximal, characteristic
12C2×#16839976C211yesmaximal, characteristic
13C2×#16839890C211yesmaximal, characteristic, complemented
14C2×#16839861C211yesmaximal, characteristic, complemented
15C2×#16839856C211yesmaximal, characteristic, complemented
16C2×C61×#440C211yesmaximal, characteristic, complemented
17C22×Dic244C2211yescharacteristic
18C22×Dic244C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758202C2211yescharacteristic
21C22×#11758190C2211yescharacteristic
22C22×#11758190C2211yescharacteristic
23C22×#11758200C2211yescharacteristic
24C22×#11758199C2211yescharacteristic
25#16840484—24no—
26#16840484C2218yescomplemented
27#16840482—24no—
28#16840482C2218yescomplemented
29C2×#14519777C2211yescharacteristic
30C2×#14519775C2211yescharacteristic
31C2×#14519772—21no—
32C2×#14519771—21no—
33C2×#14519770—21no—
34C2×#14519770—21no—
35C2×#14519766C2211yescharacteristic
36C2×#14519765C2211yescharacteristic
37C2×#14519764C2211yescharacteristic
38C2×#14519764C2211yescharacteristic
39C2×#14519756—21no—
40C2×#14519755—21no—
41C2×C4×Dic122C2211yescharacteristic
42C2×#14519742C2211yescharacteristic
43C2×#14519742C2211yescharacteristic
44C2×#14519742C2211yescharacteristic
45C2×#14519739C2211yescharacteristic
46C2×#14519736—21no—
47C2×#14519734—21no—
48#16840156C2218yescomplemented
49#16840153C2218yescomplemented
50#16840143C2218yes—
51#16839987C2218yescomplemented
52#16839983C2218yescomplemented
53#16839977C2218yes—
54#16839976C2218yes—
55#16839972C2218yescomplemented
56#16839971C2218yescomplemented
57#16839890C2218yescomplemented
58#16839861C2218yescomplemented
59#16839856C2218yescomplemented
60C2×C4⋊#92418C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519706C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65C2×#14519700C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C61×#440C2218yescomplemented
73C2×#107×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C22×Dic122D411yescharacteristic
78C22×Dic122C2311yescharacteristic
79C22×Dic122C2311yescharacteristic
80C22×Dic122C2311yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C4×D61—21no—
83C2×Dic244—24no—
84C2×Dic244—42no—
85C2×Dic244C2314yes—
86C2×Dic244C2314yes—
87C2×#11758202—42no—
88C2×#11758202—42no—
89C2×#11758202C2314yes—
90C2×#11758202C2314yes—
91C2×#11758190—24no—
92C2×#11758190—42no—
93C2×#11758190C2314yes—
94C2×#11758190C2314yes—
95C2×#11758200—42no—
96C2×#11758200C2314yes—
97C2×#11758199—42no—
98C2×#11758199C2314yes—
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101#14519777—22no—
102#14519777C2314yes—
103#14519775—22no—
104#14519775C2314yes—
105#14519772—28no—
106#14519771—28no—
107#14519770—28no—
108#14519770—28no—
109#14519766—22no—
110#14519766C2314yes—
111#14519765—22no—
112#14519765C2314yes—
113#14519764—22no—
114#14519764—22no—
115#14519764C2314yes—
116#14519764C2314yes—
117#14519756—28no—
118#14519755—28no—
119C4×Dic122D414yes—
120C4×Dic122C2314yes—
121#14519742—22no—
122#14519742—22no—
123#14519742—22no—
124#14519742C2314yes—
125#14519742C2314yes—
126#14519742C2314yes—
127#14519739—22no—
128#14519739C2314yes—
129#14519736—28no—
130#14519734—28no—
131C2×C4⋊Dic61—21no—
132C2×C4⋊Dic61—21no—
133C2×C4⋊Dic61D411yescharacteristic
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196D411yescharacteristic
140C2×#11758196D411yescharacteristic
141C2×C22⋊Dic61—21no—
142C2×C22⋊Dic61—21no—
143C2×C22⋊Dic61—21no—
144C2×C22⋊Dic61—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×C4×Dic61—21no—
151C2×C4×Dic61—21no—
152C2×C4×Dic61—21no—
153C2×C4×Dic61C2311yescharacteristic
154C2×C4×Dic61C2311yescharacteristic
155C4⋊#92418C2314yes—
156#14519706C2314yes—
157#14519706C2314yes—
158#14519700C2314yes—
159#14519700C2314yes—
160#14519700C2314yes—
161#14519697C2314yes—
162#14519687C2314yes—
163C8×Dic61C2314yes—
164C22×Q8×C61C2311yescharacteristic
165C22×D4×C61C2311yescharacteristic
166C23×C4×C61—21no—
167C2×SD16×C61—24no—
168C2×SD16×C61C2314yes—
169C22×C8×C61C2311yescharacteristic
170C22×C8×C61C2311yescharacteristic
171C4×Q8×C61—22no—
172C4×Q8×C61C2314yes—
173C4×D4×C61—22no—
174C4×D4×C61C2314yes—
175C2×C4⋊C4×C61—21no—
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C22⋊C4×C61—21no—
179C2×C42×C61—21no—
180C2×C42×C61C2311yescharacteristic
181#107×C61C2314yes—
182#103×C61C2314yes—
183#102×C61C2314yes—
184#97×C61C2314yes—
185C24×C61—21no—
186C23×D61—21no—
187C2×Q8×C61—21no—
188C2×Q8×C61—22no—
189C2×Q8×C61—22no—
190C2×Q8×C61C2412yes—
191C2×D4×C61—21no—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61C2412yes—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—24no—
199C22×C4×C61—44no—
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2411yescharacteristic
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208C22×Dic61C2×D411yescharacteristic
209C22×Dic61C2×D411yescharacteristic
210C2×D244—22no—
211C2×D244—22no—
212C2×D244—21no—
213C2×D244C2412yes—
214C2×C4×D61—24no—
215C2×C4×D61—44no—
216C2×Dic122—22no—
217C2×Dic122—22no—
218C2×Dic122—22no—
219C2×Dic122—22no—
220C2×Dic122—22no—
221C2×Dic122—22no—
222C2×Dic122—21no—
223C2×Dic122—21no—
224C2×Dic122—21no—
225C2×Dic122—42no—
226C2×Dic122C2×D414yes—
227C2×Dic122C2412yes—
228C2×Dic122C2412yes—
229C2×Dic122C2412yes—
230SD16×C61—28no—
231C2×C8×C61—22no—
232C2×C8×C61#4114yes—
233C2×C8×C61C2412yes—
234C2×C8×C61C2412yes—
235C4⋊C4×C61—24no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61C2412yes—
239C4⋊C4×C61C2412yes—
240C22⋊C4×C61—24no—
241C42×C61—24no—
242C42×C61C2×D412yes—
243C42×C61C2412yes—
244C22⋊Dic61—24no—
245C22⋊Dic61—24no—
246C22⋊Dic61—24no—
247C22⋊Dic61—24no—
248#11758202—44no—
249#11758202—44no—
250#11758200—44no—
251#11758199—44no—
252#11758198—24no—
253#11758198—24no—
254#11758198—24no—
255#11758198—24no—
256#11758198—24no—
257C4⋊Dic61—24no—
258C4⋊Dic61—24no—
259C4⋊Dic61C2×D414yes—
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×Dic61C2×D412yes—
271C4×Dic61C2×D412yes—
272C4×Dic61C2412yes—
273C4×Dic61C2412yes—
274C2×#92418—22no—
275C2×#92418—22no—
276C2×#92418C2412yes—
277C2×#92418C2412yes—
278Dic244—28no—
279Dic244—44no—
280#11758190—28no—
281#11758190—44no—
282C23×C61—22no—
283C23×C61—42no—
284C23×C61—42no—
285C23×C61—42no—
286C23×C61C22×D411yescharacteristic
287C22×D61—22no—
288C22×D61—42no—
289C22×D61—42no—
290C22×D61—42no—
291Q8×C61—22no—
292Q8×C61—22no—
293Q8×C61—42no—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—42no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—48no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61C22×D412yes—
307C2×C4×C61C22×D412yes—
308C2×C4×C61C22×D411yescharacteristic
309C2×C4×C61C2×#4112yes—
310C2×C4×C61H(5,𝔽2)12yes—
311C2×C4×C61C2511yescharacteristic
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61C22×D412yes—
323C2×Dic61C22×D412yes—
324C2×Dic61C22×D412yes—
325C2×Dic61C22×D412yes—
326D244—22no—
327D244—22no—
328D244—42no—
329C4×D61—48no—
330Dic122—22no—
331Dic122—22no—
332Dic122—22no—
333Dic122—22no—
334Dic122—22no—
335Dic122—22no—
336Dic122—44no—
337Dic122—42no—
338Dic122—42no—
339Dic122—42no—
340C8×C61—22no—
341C8×C61C2×#4114yes—
342#92418—22no—
343#92418—22no—
344C2×#3402—611nomaximal, Sylow
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—84no—
349C22×C61#55012yes—
350C22×C61#57512yes—
351C22×C61#57812yes—
352C22×C61C23×D411yescharacteristic
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—84no—
357C4×C61—22no—
358C4×C61—22no—
359C4×C61—42no—
360C4×C61—42no—
361C4×C61—42no—
362C4×C61#55012yes—
363C4×C61C22×#4111yescharacteristic
364C4×C61C2×H(5,𝔽2)11yescharacteristic
365Dic61—22no—
366Dic61—22no—
367Dic61—22no—
368Dic61—22no—
369Dic61—42no—
370Dic61—42no—
371Dic61—42no—
372C2×#556—611no—
373C2×#556—611no—
374#3402—6116no—
375C2×#497—611no—
376C2×#497—611no—
377C2×#495—611no—
378C2×#464—611no—
379C2×#464—611no—
380C2×#462—611no—
381C2×#462—611no—
382C2×#463—611no—
383C2×#463—611no—
384C2×#446—611no—
385C2×#440—611no—
386C2×#440D6111yescharacteristic, complemented
387C2×C4×Q16—611no—
388C2×C61—82no—
389C2×C61#340214yescomplemented
390C2×C61C2×#55011yescharacteristic
391C2×C61C2×#57511yescharacteristic
392C2×C61C2×#57811yescharacteristic
393D61—82no—
394C22×Q16—611no—
395C22×Q16—611no—
396C22×Q16—611no—
397C22×Q16—611no—
398C22×SD16—611no—
399C22×SD16—611no—
400C22×SD16—611no—
401C22×SD16C2×D6111yescharacteristic
402C22×D8—611no—
403#556—618no—
404#556—618no—
405#556—1224no—
406#556—1224no—
407C2×C4⋊Q8—611no—
408C2×C4⋊Q8—611no—
409C2×#126—1221no—
410C2×#126—1221no—
411C2×#126—1221no—
412C2×#126—1221no—
413C2×#124—611no—
414C2×#124—611no—
415C2×#124—611no—
416C2×#124—611no—
417C2×C22⋊Q8—1221no—
418C2×C22⋊Q8—1221no—
419C2×C4×Q8—611no—
420C2×C4×Q8—611no—
421C2×C4×Q8—611no—
422C2×C4×Q8—611no—
423C2×C4×Q8C2×D6111yescharacteristic
424C2×C4×D4—611no—
425C2×C4×D4C2×D6111yescharacteristic
426C2×#117—1221no—
427C2×#117—1221no—
428#497—618no—
429#497—618no—
430#495—618no—
431#464—618no—
432#464—618no—
433#463—618no—
434#463—618no—
435#462—618no—
436#462—618no—
437#446—618no—
438#440—618no—
439#440C2×D6118yescomplemented
440C4×Q16—618no—
441C2×#107C2×D6111yescharacteristic
442C2×C4⋊C8—611no—
443C2×C4⋊C8—611no—
444C2×C4⋊C8—611no—
445C2×#103—611no—
446C2×#103—611no—
447C2×#103—611no—
448C2×#103C2×D6111yescharacteristic
449C2×#102—611no—
450C2×#102C2×D6111yescharacteristic
451C2×#97—611no—
452C2×#97C2×D6111yescharacteristic
453C2×C4×C8—611no—
454C61C2×#340211yescharacteristic, complemented, Sylow
455C22×Q8—611no—
456C22×Q8—611no—
457C22×Q8—611no—
458C22×Q8—611no—
459C22×Q8C22×D6111yescharacteristic
460C22×D4—611no—
461C22×D4C22×D6111yescharacteristic
462C23×C4—21no—
463C23×C4—1221no—
464C2×Q16—614no—
465C2×Q16—614no—
466C2×Q16—614no—
467C2×Q16—614no—
468C2×Q16—1224no—
469C2×Q16—2442no—
470C2×Q16—2442no—
471C2×Q16—2442no—
472C2×SD16—24no—
473C2×SD16—614no—
474C2×SD16—614no—
475C2×SD16—614no—
476C2×SD16—1224no—
477C2×SD16—2442no—
478C2×SD16—2442no—
479C2×SD16C22×D6114yes—
480C2×D8—614no—
481C2×D8—2442no—
482C22×C8—611no—
483C22×C8—611no—
484C22×C8C22×D6111yescharacteristic
485C22×C8C22×D6111yescharacteristic
486C4⋊Q8—614no—
487C4⋊Q8—614no—
488C4⋊Q8—1222no—
489C4⋊Q8—1222no—
490#126—1228no—
491#126—1228no—
492#126—1228no—
493#126—1228no—
494#124—614no—
495#124—614no—
496#124—614no—
497#124—614no—
498#124—1222no—
499#124—1222no—
500#124—1222no—
501#124—1222no—
502C22⋊Q8—1228no—
503C22⋊Q8—1228no—
504C4×Q8—22no—
505C4×Q8—614no—
506C4×Q8—614no—
507C4×Q8—614no—
508C4×Q8—614no—
509C4×Q8—614no—
510C4×Q8—1222no—
511C4×Q8—1222no—
512C4×Q8—1222no—
513C4×Q8C22×D6114yes—
514C4×D4—22no—
515C4×D4—614no—
516C4×D4—1222no—
517C4×D4C22×D6114yes—
518#117—1228no—
519#117—1228no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4C22×D6111yescharacteristic
532C2×C4⋊C4C22×D6111yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C42—21no—
544C2×C42—611no—
545C2×C42—611no—
546C2×C42—1221no—
547C2×C42—1221no—
548C2×C42—1221no—
549C2×C42C22×D6111yescharacteristic
550#107C22×D6114yes—
551C4⋊C8—614no—
552C4⋊C8—614no—
553C4⋊C8—614no—
554#103—614no—
555#103—614no—
556#103—614no—
557#103C22×D6114yes—
558#102—614no—
559#102C22×D6114yes—
560#97—614no—
561#97C22×D6114yes—
562C4×C8—614no—
563C24—21no—
564C24—1221no—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—614no—
569C2×Q8—612no—
570C2×Q8—612no—
571C2×Q8—612no—
572C2×Q8—1221no—
573C2×Q8—1221no—
574C2×Q8—1221no—
575C2×Q8—1222no—
576C2×Q8—1222no—
577C2×Q8—1222no—
578C2×Q8—1222no—
579C2×Q8—1222no—
580C2×Q8—1222no—
581C2×Q8—2442no—
582C2×Q8C23×D6112yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—612no—
587C2×D4—1221no—
588C2×D4—1222no—
589C2×D4—1222no—
590C2×D4C23×D6112yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—44no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—1224no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—2444no—
605C22×C4D4×D6111yescharacteristic
606C22×C4D4×D6111yescharacteristic
607C22×C4C23×D6111yescharacteristic
608Q16—1228no—
609Q16—2444no—
610Q16—2444no—
611Q16—2444no—
612SD16—28no—
613SD16—1228no—
614SD16—2444no—
615SD16—2444no—
616D8—2444no—
617C2×C8—22no—
618C2×C8—612no—
619C2×C8—612no—
620C2×C8—1222no—
621C2×C8—1222no—
622C2×C8#1175822214yes—
623C2×C8C23×D6112yes—
624C2×C8C23×D6112yes—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—614no—
629C4⋊C4—614no—
630C4⋊C4—614no—
631C4⋊C4—1224no—
632C4⋊C4—1224no—
633C4⋊C4—1224no—
634C4⋊C4—1224no—
635C4⋊C4—1224no—
636C4⋊C4—1224no—
637C4⋊C4—1224no—
638C4⋊C4C23×D6112yes—
639C4⋊C4C23×D6112yes—
640C22⋊C4—24no—
641C22⋊C4—1224no—
642C22⋊C4—1224no—
643C22⋊C4—1224no—
644C22⋊C4—1224no—
645C22⋊C4—1224no—
646C22⋊C4—1224no—
647C22⋊C4—1224no—
648C22⋊C4—1224no—
649C22⋊C4—1224no—
650C42—24no—
651C42—612no—
652C42—612no—
653C42—612no—
654C42—612no—
655C42—1224no—
656C42—1224no—
657C42—1224no—
658C42D4×D6112yes—
659C42C23×D6112yes—
660C23—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—1222no—
665C23—2442no—
666C23—2442no—
667C23—2442no—
668C23C2×D4×D6111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—1222no—
673Q8—1222no—
674Q8—1222no—
675Q8—1222no—
676Q8—1222no—
677Q8—1222no—
678Q8—2444no—
679Q8—2442no—
680Q8—2442no—
681Q8—2442no—
682D4—22no—
683D4—22no—
684D4—42no—
685D4—1222no—
686D4—1222no—
687D4—2442no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—48no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—612no—
698C2×C4—612no—
699C2×C4—612no—
700C2×C4—612no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—2448no—
709C2×C4—2442no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4C2×D4×D6112yes—
713C2×C4C2×D4×D6112yes—
714C2×C4C2×D4×D6111yescharacteristic
715C2×C4C2×#1175822212yes—
716C2×C4#1451982312yes—
717C2×C4C24×D6111yescharacteristic
718C8—22no—
719C8—1222no—
720C8—1222no—
721C8C2×#1175822214yes—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—4884no—
727C22—2442no—
728C22—2442no—
729C22—2442no—
730C22#1684043312yes—
731C22#1684055812yes—
732C22#1684057812yes—
733C22C22×D4×D6111yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—1222no—
740C4—1222no—
741C4—1222no—
742C4—1222no—
743C4—2442no—
744C4—2442no—
745C4—2442no—
746C4#1684043312yes—
747C4C22×#1175822211yescharacteristic
748C4C2×#1451982311yescharacteristic
749C2—82no—
750C2—4882no—
751C2#2145889914yesdirect product factor
752C2C2×#1684043311yescharacteristic
753C2C2×#1684055811yescharacteristic
754C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
hypercenterC2×#440D61
hypocenterC61C2×#3402
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#16840484C2semidirect
2. C2×#16840482C2semidirect
3. #21458899C2direct (N × H)
4. C2×#16840156C2semidirect
5. C2×#16840153C2semidirect
7. C2×#16839987C2semidirect
8. C2×#16839983C2semidirect
9. C2×#16839972C2semidirect
10. C2×#16839971C2semidirect
13. C2×#16839890C2semidirect
14. C2×#16839861C2semidirect
15. C2×#16839856C2semidirect
16. C2×C61×#440C2semidirect
26. #16840484C22semidirect
28. #16840482C22semidirect
48. #16840156C22semidirect
49. #16840153C22semidirect
51. #16839987C22semidirect
52. #16839983C22semidirect
55. #16839972C22semidirect
56. #16839971C22semidirect
57. #16839890C22semidirect
58. #16839861C22semidirect
59. #16839856C22semidirect
72. C61×#440C22semidirect
386. C2×#440D61semidirect
389. C2×C61#3402semidirect
439. #440C2×D61semidirect
454. C61C2×#3402semidirect
751. C2#21458899direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404842
C2×#168404822
#214588992
C2×#168401562
C2×#168401532
C2×#168401432
C2×#168399872
C2×#168399832
C2×#168399722
C2×#168399712
C2×#168399772
C2×#168399762
C2×#168398902
C2×#168398612
C2×#168398562
C2×C61×#4402
C2×#340261