Finite Group Databasebeta

← C2×#21456035 #30548278

Subgroups — C2×#21456035 #30548278

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×#16840374C211yesmaximal, characteristic, complemented
2C2×#16840242C211yesmaximal, characteristic
3#21456035C2116yesmaximal, direct product factor
4C2×#16840098C211yesmaximal, characteristic, complemented
5C2×#16840093C211yesmaximal, characteristic, complemented
6C2×#16840070C211yesmaximal, characteristic, complemented
7C2×#16840063C211yesmaximal, characteristic, complemented
8C2×#16839973C211yesmaximal, characteristic, complemented
9C2×#16839968C211yesmaximal, characteristic, complemented
10C2×#16839926C211yesmaximal, characteristic
11C2×#16839926C211yesmaximal, characteristic
12C2×#16839870C211yesmaximal, characteristic, complemented
13C2×#16839864C211yesmaximal, characteristic, complemented
14C2×C4×Dic244C211yesmaximal, characteristic, complemented
15C2×C4×#11758190C211yesmaximal, characteristic, complemented
16C2×C61×#433C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×Dic244C2211yescharacteristic
19C22×Dic244C2211yescharacteristic
20C22×#11758190C2211yescharacteristic
21C22×#11758190C2211yescharacteristic
22#16840374—24no—
23#16840374C2218yescomplemented
24C2×#14519777C2211yescharacteristic
25C2×#14519770—21no—
26C2×#14519770—21no—
27C2×#14519769C2211yescharacteristic
28C2×#14519767—21no—
29C2×#14519767—21no—
30C2×#14519756C2211yescharacteristic
31C2×#14519756C2211yescharacteristic
32#16840242—24no—
33#16840242C2218yes—
34C2×C4×Dic122C2211yescharacteristic
35C2×C4×Dic122C2211yescharacteristic
36C2×C4×Dic122C2211yescharacteristic
37C2×C4×Dic122C2211yescharacteristic
38C2×C4×D244C2211yescharacteristic
39C2×C4×D244C2211yescharacteristic
40C2×#14519737—21no—
41C2×#14519737—21no—
42C2×#14519735—21no—
43C22×C4⋊Dic61C2211yescharacteristic
44C2×C4⋊C4×D61—21no—
45#16840098C2218yescomplemented
46#16840093C2218yescomplemented
47#16840070C2218yescomplemented
48#16840063C2218yescomplemented
49#16839973C2218yescomplemented
50#16839968C2218yescomplemented
51#16839926C2218yes—
52#16839926C2218yes—
53#16839870C2218yescomplemented
54#16839864C2218yescomplemented
55C4×Dic244C2218yescomplemented
56C4×#11758190C2218yescomplemented
57C2×#14519711C2211yescharacteristic
58C2×#14519711C2211yescharacteristic
59C2×#14519709C2211yescharacteristic
60C2×#14519709C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519702C2211yescharacteristic
63C2×#14519702C2211yescharacteristic
64C2×#14519702C2211yescharacteristic
65C2×#14519702C2211yescharacteristic
66C2×#14519702C2211yescharacteristic
67C2×#14519699C2211yescharacteristic
68C2×#14519699C2211yescharacteristic
69C2×#117×C61C2211yescharacteristic
70C61×#433C2218yescomplemented
71C2×C4⋊C8×C61C2211yescharacteristic
72C2×C4⋊C8×C61C2211yescharacteristic
73C2×C22⋊C8×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×#97×C61C2211yescharacteristic
76C2×C4×C8×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—24no—
79C2×#11758222—24no—
80C2×#11758222C2314yes—
81C22×Dic122C2311yescharacteristic
82C22×Dic122C2311yescharacteristic
83C22×Dic122C2311yescharacteristic
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C23×Dic61—21no—
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C22×C4×D61—21no—
90C2×Dic244—24no—
91C2×Dic244—24no—
92C2×Dic244C2314yes—
93C2×Dic244C2314yes—
94C2×#11758190—24no—
95C2×#11758190—24no—
96C2×#11758190C2314yes—
97C2×#11758190C2314yes—
98#14519777—22no—
99#14519777C2314yes—
100#14519770—28no—
101#14519770—28no—
102#14519769—22no—
103#14519769C2314yes—
104#14519767—28no—
105#14519767—28no—
106#14519756—22no—
107#14519756—22no—
108#14519756C2314yes—
109#14519756C2314yes—
110C4×Dic122—22no—
111C4×Dic122—22no—
112C4×Dic122—22no—
113C4×Dic122—22no—
114C4×Dic122C2314yes—
115C4×Dic122C2314yes—
116C4×Dic122C2314yes—
117C4×Dic122C2314yes—
118C4×D244—22no—
119C4×D244—22no—
120C4×D244C2314yes—
121C4×D244C2314yes—
122#14519737—28no—
123#14519737—28no—
124#14519735—28no—
125C2×C4⋊Dic61—21no—
126C2×C4⋊Dic61—22no—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61C2311yescharacteristic
130C2×C4⋊Dic61C2311yescharacteristic
131C2×C4⋊Dic61C2314yes—
132C2×C4⋊Dic61C2311yescharacteristic
133C2×C4⋊Dic61C2311yescharacteristic
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×#11758196—21no—
141C2×#11758196—21no—
142C4⋊C4×D61—28no—
143C2×C22⋊Dic61—21no—
144C2×C22⋊Dic61—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×C4×Dic61—21no—
148C2×C4×Dic61—21no—
149C2×C4×Dic61—21no—
150C2×C4×Dic61—21no—
151#14519711C2314yes—
152#14519711C2314yes—
153#14519709C2314yes—
154#14519709C2314yes—
155#14519702C2314yes—
156#14519702C2314yes—
157#14519702C2314yes—
158#14519702C2314yes—
159#14519702C2314yes—
160#14519702C2314yes—
161#14519699C2314yes—
162#14519699C2314yes—
163C23×C4×C61C2311yescharacteristic
164C22×C8×C61C2311yescharacteristic
165C22×C8×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168#117×C61D414yes—
169#117×C61C2314yes—
170C2×C4⋊C4×C61D411yescharacteristic
171C2×C4⋊C4×C61D411yescharacteristic
172C2×C22⋊C4×C61D411yescharacteristic
173C2×C22⋊C4×C61D411yescharacteristic
174C2×C42×C61C2311yescharacteristic
175C2×C42×C61C2311yescharacteristic
176C4⋊C8×C61C2314yes—
177C4⋊C8×C61C2314yes—
178C22⋊C8×C61C2314yes—
179C22⋊C8×C61C2314yes—
180#97×C61C2314yes—
181C4×C8×C61C2314yes—
182C24×C61C2×D411yescharacteristic
183C23×D61—21no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D412yes—
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2412yes—
193C22×C4×C61C2411yescharacteristic
194C2×C22⋊D61—28no—
195C2×C22⋊D61—24no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—24no—
204C22×Dic61—82no—
205#11758222—216no—
206#11758222—28no—
207#11758222—28no—
208C2×D244—21no—
209C2×D244—22no—
210C2×D244#4114yes—
211C2×D244C2412yes—
212C2×C4×D61—28no—
213C2×C4×D61—24no—
214C2×C4×D61—24no—
215C2×C4×D61—24no—
216C2×C4×D61—82no—
217C2×C4×D61—82no—
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×C61—22no—
233C2×C8×C61—22no—
234C2×C8×C61C2412yes—
235C2×C8×C61C2412yes—
236C2×C8×C61C2412yes—
237C2×C8×C61C2412yes—
238C4⋊C4×C61C2×D414yes—
239C4⋊C4×C61C2×D414yes—
240C22⋊C4×C61C2×D414yes—
241C22⋊C4×C61C2×D414yes—
242C42×C61C2×D412yes—
243C42×C61C2×D412yes—
244C42×C61C2412yes—
245C42×C61C2412yes—
246C22⋊Dic61—24no—
247C22⋊Dic61—24no—
248#11758198—24no—
249#11758198—24no—
250C4⋊Dic61—24no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—24no—
254C4⋊Dic61—24no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61C2412yes—
258C4⋊Dic61C2412yes—
259C4⋊Dic61C2412yes—
260C4⋊Dic61C2412yes—
261#11758196—24no—
262#11758196—24no—
263#11758196—24no—
264#11758196—24no—
265#11758196—24no—
266#11758196—24no—
267#11758196—24no—
268#11758196—24no—
269C4×Dic61—24no—
270C4×Dic61—24no—
271C4×Dic61—24no—
272C4×Dic61—24no—
273Dic244—28no—
274Dic244—28no—
275#11758190—28no—
276#11758190—28no—
277C23×C61—22no—
278C23×C61—22no—
279C23×C61—22no—
280C23×C61C22×D412yes—
281C23×C61C22×D411yescharacteristic
282C22×D61—24no—
283C22×D61—22no—
284C22×D61—42no—
285C22×D61—42no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—24no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61C22×D412yes—
295C2×C4×C61C22×D412yes—
296C2×C4×C61C22×D412yes—
297C2×C4×C61C22×D412yes—
298C2×C4×C61C22×D412yes—
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C2×#4112yes—
301C2×C4×C61C2×#4112yes—
302C2×C4×C61C2511yescharacteristic
303C22⋊D61—216no—
304C2×Dic61—24no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—84no—
319D244—24no—
320D244—22no—
321D244C2×#4114yes—
322C4×D61—216no—
323C4×D61—84no—
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—
336C8×C61—22no—
337C8×C61—22no—
338C2×#3120—611nomaximal, Sylow
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—44no—
343C22×C61#52512yes—
344C22×C61#57712yes—
345C22×C61#57812yes—
346C22×C61C23×D411yescharacteristic
347C2×D61—24no—
348C2×D61—48no—
349C2×D61—42no—
350C2×D61—42no—
351C4×C61—22no—
352C4×C61—22no—
353C4×C61—22no—
354C4×C61—22no—
355C4×C61—22no—
356C4×C61#52512yes—
357C4×C61C22×#4111yescharacteristic
358C4×C61C22×#4111yescharacteristic
359Dic61—24no—
360Dic61—42no—
361Dic61—42no—
362Dic61—42no—
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×#478—611no—
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×#433D6111yescharacteristic, complemented
382C2×C61—42no—
383C2×C61#312014yescomplemented
384C2×C61C2×#52511yescharacteristic
385C2×C61C2×#57711yescharacteristic
386C2×C61C2×#57811yescharacteristic
387D61—44no—
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—611no—
399C2×#125—1221no—
400C2×#125—1221no—
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—611no—
411C2×C4×D4—1221no—
412C2×C4×D4—1221no—
413C2×#117—1221no—
414C2×#117C2×D6111yescharacteristic
415C22×C4⋊C4—611no—
416C22×C4⋊C4—1221no—
417#484—618no—
418#483—618no—
419#479—618no—
420#478—618no—
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#433C2×D6118yescomplemented
430C2×#107—611no—
431C2×#107—611no—
432C2×#106—611no—
433C2×#106—611no—
434C2×C4⋊C8C2×D6111yescharacteristic
435C2×C4⋊C8C2×D6111yescharacteristic
436C2×#103—611no—
437C2×#103—611no—
438C2×#103—611no—
439C2×#103—611no—
440C2×#103—611no—
441C2×#103—611no—
442C2×#102—611no—
443C2×#102—611no—
444C2×C22⋊C8C2×D6111yescharacteristic
445C2×C22⋊C8C2×D6111yescharacteristic
446C2×#97C2×D6111yescharacteristic
447C2×C4×C8C2×D6111yescharacteristic
448C61C2×#312011yescharacteristic, complemented, Sylow
449C2×#41—614no—
450C2×#41—1224no—
451C2×#41—1224no—
452C2×#41—1222no—
453C22×Q8—611no—
454C22×Q8—611no—
455C22×Q8—611no—
456C22×D4—611no—
457C22×D4—1221no—
458C23×C4—1221no—
459C23×C4—1221no—
460C23×C4—1221no—
461C23×C4—1221no—
462C23×C4C22×D6111yescharacteristic
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×C8C22×D6111yescharacteristic
472C22×C8C22×D6111yescharacteristic
473C22×C8C22×D6111yescharacteristic
474C22×C8C22×D6111yescharacteristic
475C4⋊Q8—614no—
476C4⋊Q8—1222no—
477#126—1228no—
478#126—1228no—
479#125—614no—
480#125—1228no—
481#125—1228no—
482#125—1222no—
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—614no—
496C4×D4—614no—
497C4×D4—1228no—
498C4×D4—1228no—
499C4×D4—1222no—
500C4×D4—1222no—
501#117—1228no—
502#117D24414yes—
503#117C22×D6114yes—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—614no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1222no—
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⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1228no—
522C2×C4⋊C4D24411yescharacteristic
523C2×C4⋊C4D24411yescharacteristic
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4D24411yescharacteristic
529C2×C22⋊C4D24411yescharacteristic
530C2×C42—1221no—
531C2×C42—1221no—
532C2×C42—1221no—
533C2×C42—1221no—
534C2×C42C22×D6111yescharacteristic
535C2×C42C22×D6111yescharacteristic
536#107—614no—
537#107—614no—
538#106—614no—
539#106—614no—
540C4⋊C8C22×D6114yes—
541C4⋊C8C22×D6114yes—
542#103—614no—
543#103—614no—
544#103—614no—
545#103—614no—
546#103—614no—
547#103—614no—
548#102—614no—
549#102—614no—
550C22⋊C8C22×D6114yes—
551C22⋊C8C22×D6114yes—
552#97C22×D6114yes—
553C4×C8C22×D6114yes—
554C24—1221no—
555C24C2×D24411yescharacteristic
556#41—1228no—
557#41—1228no—
558#41—12216no—
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—614no—
572C2×D4—612no—
573C2×D4—1228no—
574C2×D4—1224no—
575C2×D4—1221no—
576C2×D4—1222no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—1228no—
580C22×C4—1221no—
581C22×C4—1224no—
582C22×C4—1224no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1224no—
590C22×C4—1224no—
591C22×C4—4882no—
592C22×C4—4882no—
593C22×C4—4882no—
594C22×C4C2×D24412yes—
595C22×C4C2×D24411yescharacteristic
596C22×C4C2×D24411yescharacteristic
597C22×C4C2×D24411yescharacteristic
598C22×C4C2×D24411yescharacteristic
599C22×C4C2×D24411yescharacteristic
600C22×C4C23×D6112yes—
601C22×C4C23×D6111yescharacteristic
602Q16—1228no—
603Q16—1228no—
604SD16—1228no—
605SD16—1228no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8C23×D6112yes—
611C2×C8C23×D6112yes—
612C2×C8C23×D6112yes—
613C2×C8C23×D6112yes—
614C4⋊C4—612no—
615C4⋊C4—612no—
616C4⋊C4—612no—
617C4⋊C4—612no—
618C4⋊C4—1224no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1224no—
624C4⋊C4—1224no—
625C4⋊C4—1224no—
626C4⋊C4—1224no—
627C4⋊C4—1224no—
628C4⋊C4—1224no—
629C4⋊C4—1224no—
630C4⋊C4—1224no—
631C4⋊C4—1224no—
632C4⋊C4—1224no—
633C4⋊C4C2×D24414yes—
634C4⋊C4C2×D24414yes—
635C22⋊C4—1224no—
636C22⋊C4—1224no—
637C22⋊C4—1224no—
638C22⋊C4—1224no—
639C22⋊C4C2×D24414yes—
640C22⋊C4C2×D24414yes—
641C42—1224no—
642C42—1224no—
643C42—1224no—
644C42—1224no—
645C42C2×D24412yes—
646C42C2×D24412yes—
647C42C23×D6112yes—
648C42C23×D6112yes—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—1224no—
653C23—1222no—
654C23—2442no—
655C23—2442no—
656C23C22×D24412yes—
657C23C22×D24411yescharacteristic
658Q8—614no—
659Q8—1224no—
660Q8—1222no—
661Q8—1222no—
662Q8—1222no—
663Q8—1222no—
664Q8—1222no—
665Q8—2442no—
666Q8—2442no—
667D4—614no—
668D4—12216no—
669D4—1224no—
670D4—1222no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—12216no—
680C2×C4—1224no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—4884no—
689C2×C4—4884no—
690C2×C4—4884no—
691C2×C4—2442no—
692C2×C4—2442no—
693C2×C4—2442no—
694C2×C4—2442no—
695C2×C4—2442no—
696C2×C4—2442no—
697C2×C4C22×D24412yes—
698C2×C4C22×D24412yes—
699C2×C4C22×D24412yes—
700C2×C4C22×D24412yes—
701C2×C4C22×D24412yes—
702C2×C4C22×D24411yescharacteristic
703C2×C4#41×D6112yes—
704C2×C4#41×D6112yes—
705C2×C4C24×D6111yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—1224no—
715C22—2442no—
716C22—2442no—
717C22—2448no—
718C22#1684027412yes—
719C22#1684057412yes—
720C22#1684057912yes—
721C22C23×D24411yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—1224no—
728C4—2442no—
729C4—2442no—
730C4—2442no—
731C4—2442no—
732C4—2442no—
733C4—2442no—
734C4#1684027412yes—
735C4C2×#41×D6111yescharacteristic
736C4C2×#41×D6111yescharacteristic
737C2—42no—
738C2—2444no—
739C2#2145603514yesdirect product factor
740C2C2×#1684027411yescharacteristic
741C2C2×#1684057411yescharacteristic
742C2C2×#1684057911yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#433C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
hypercenterC2×#433D61
hypocenterC61C2×#3120
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#16840374C2semidirect
3. #21456035C2direct (N × H)
4. C2×#16840098C2semidirect
5. C2×#16840093C2semidirect
6. C2×#16840070C2semidirect
7. C2×#16840063C2semidirect
8. C2×#16839973C2semidirect
9. C2×#16839968C2semidirect
12. C2×#16839870C2semidirect
13. C2×#16839864C2semidirect
14. C2×C4×Dic244C2semidirect
15. C2×C4×#11758190C2semidirect
16. C2×C61×#433C2semidirect
23. #16840374C22semidirect
45. #16840098C22semidirect
46. #16840093C22semidirect
47. #16840070C22semidirect
48. #16840063C22semidirect
49. #16839973C22semidirect
50. #16839968C22semidirect
53. #16839870C22semidirect
54. #16839864C22semidirect
55. C4×Dic244C22semidirect
56. C4×#11758190C22semidirect
70. C61×#433C22semidirect
381. C2×#433D61semidirect
383. C2×C61#3120semidirect
429. #433C2×D61semidirect
448. C61C2×#3120semidirect
739. C2#21456035direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403742
C2×#168402422
#214560352
C2×#168400982
C2×#168400932
C2×#168400702
C2×#168400632
C2×#168399732
C2×#168399682
C2×#168399262
C2×#168398702
C2×#168398642
C2×C4×Dic2442
C2×C4×#117581902
C2×C61×#4332
C2×#312061