Finite Group Databasebeta

← C2×#21458144 #30556944

Subgroups — C2×#21458144 #30556944

Order 15616.

2426 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840430C211yesmaximal, characteristic, complemented
2C2×#16840413C211yesmaximal, characteristic, complemented
3#21458144C2116yesmaximal, direct product factor
4C2×#16840107C211yesmaximal, characteristic, complemented
5C2×#16840082C211yesmaximal, characteristic, complemented
6C2×#16840046C211yesmaximal, characteristic, complemented
7C2×#16840016C211yesmaximal, characteristic, complemented
8C2×#16840013C211yesmaximal, characteristic, complemented
9C2×#16839956C211yesmaximal, characteristic, complemented
10C2×#16839909C211yesmaximal, characteristic, complemented
11C2×#16839908C211yesmaximal, characteristic, complemented
12C2×#16839849C211yesmaximal, characteristic, complemented
13C2×#16839837C211yesmaximal, characteristic, complemented
14C2×#16839761C211yesmaximal, characteristic, complemented
15C2×#16839760C211yesmaximal, characteristic, complemented
16C2×C61×#481C211yesmaximal, characteristic, complemented
17C22×#11758222—21no—
18C22×#11758222C2211yescharacteristic
19C22×#11758224C2211yescharacteristic
20C22×#11758190C2211yescharacteristic
21C22×D488C2211yescharacteristic
22C22×#11758199C2211yescharacteristic
23C22×#11758194C2211yescharacteristic
24C22×#11758189C2211yescharacteristic
25#16840430—24no—
26#16840430C2218yescomplemented
27#16840413—24no—
28#16840413C2218yescomplemented
29C2×#14519776C2211yescharacteristic
30C2×#14519773—21no—
31C2×#14519773C2211yescharacteristic
32C2×#14519762—21no—
33C2×#14519760—21no—
34C2×#14519755—21no—
35C2×#14519752C2211yescharacteristic
36C2×#14519752C2211yescharacteristic
37C2×#14519751C2211yescharacteristic
38C2×#14519750—21no—
39C2×#14519749—21no—
40C2×#14519742C2211yescharacteristic
41C2×#14519739C2211yescharacteristic
42C2×C4×C22⋊D61C2211yescharacteristic
43C2×#14519737—21no—
44C2×C4⋊C4×D61C2211yescharacteristic
45#16840107C2218yescomplemented
46#16840082C2218yescomplemented
47#16840046C2218yescomplemented
48#16840016C2218yescomplemented
49#16840013C2218yescomplemented
50#16839956C2218yescomplemented
51#16839909C2218yescomplemented
52#16839908C2218yescomplemented
53#16839849C2218yescomplemented
54#16839837C2218yescomplemented
55C2×#14519708C2211yescharacteristic
56C2×#14519706C2211yescharacteristic
57#16839761C2218yescomplemented
58#16839760C2218yescomplemented
59C2×#14519702C2211yescharacteristic
60C2×#14519700C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C2×#121×C61C2211yescharacteristic
70C22×C4⋊C4×C61C2211yescharacteristic
71C61×#481C2218yescomplemented
72C2×#106×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—28no—
79C2×#11758222—24no—
80C2×#11758222—42no—
81C2×#11758222—48no—
82C2×#11758222C2314yes—
83C2×#11758224—22no—
84C2×#11758224—24no—
85C2×#11758224—42no—
86C2×#11758224C2314yes—
87C22×Dic122—21no—
88C22×Dic122C2311yescharacteristic
89C22×D244—21no—
90C22×D244—21no—
91C22×D244C2311yescharacteristic
92C22×D244C2311yescharacteristic
93C22×C22⋊D61—21no—
94C22×C22⋊D61—21no—
95C22×C22⋊D61—21no—
96C22×C22⋊D61—21no—
97C22×C22⋊D61—21no—
98C22×C22⋊D61D411yescharacteristic
99C23×Dic61—21no—
100C22×C4×D61—21no—
101C22×C4×D61—21no—
102C22×C4×D61—21no—
103C22×C4×D61C2311yescharacteristic
104C2×#11758190—24no—
105C2×#11758190C2314yes—
106C2×D488—42no—
107C2×D488C2314yes—
108C2×#11758199—42no—
109C2×#11758199C2314yes—
110C2×#11758194—42no—
111C2×#11758194C2314yes—
112C2×#11758189—42no—
113C2×#11758189C2314yes—
114C22×#92418C2311yescharacteristic
115C22×#92418C2311yescharacteristic
116#14519776—22no—
117#14519776C2314yes—
118#14519773—28no—
119#14519773—22no—
120#14519773C2314yes—
121#14519762—28no—
122#14519760—28no—
123#14519755—28no—
124#14519752—22no—
125#14519752—22no—
126#14519752C2314yes—
127#14519752C2314yes—
128#14519751—22no—
129#14519751C2314yes—
130#14519750—28no—
131#14519749—28no—
132#14519742—22no—
133#14519742C2314yes—
134#14519739—22no—
135#14519739C2314yes—
136C4×C22⋊D61D414yes—
137C4×C22⋊D61C2314yes—
138#14519737—28no—
139C2×C4⋊Dic61C2311yescharacteristic
140C2×#11758196—21no—
141C2×#11758196—21no—
142C2×#11758196—21no—
143C2×#11758196D411yescharacteristic
144C4⋊C4×D61—22no—
145C4⋊C4×D61C2314yes—
146C2×C22⋊Dic61D411yescharacteristic
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×#11758198D411yescharacteristic
152C2×C4×Dic61—21no—
153C2×C4×Dic61C2311yescharacteristic
154#14519708C2314yes—
155#14519706C2314yes—
156#14519702C2314yes—
157#14519700C2314yes—
158#14519700C2314yes—
159#14519699C2314yes—
160#14519698C2314yes—
161#14519697C2314yes—
162#14519697C2314yes—
163#14519697C2314yes—
164#14519689C2314yes—
165C8×Dic61C2314yes—
166C22×D4×C61—21no—
167C22×D4×C61C2311yescharacteristic
168C23×C4×C61—21no—
169C23×C4×C61C2311yescharacteristic
170C22×C8×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172#121×C61—22no—
173#121×C61C2314yes—
174C2×C4⋊C4×C61—21no—
175C2×C4⋊C4×C61—22no—
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C4⋊C4×C61C2314yes—
180C2×C22⋊C4×C61—21no—
181#106×C61C2314yes—
182#106×C61C2314yes—
183#102×C61C2314yes—
184#102×C61C2314yes—
185C22⋊C8×C61C2314yes—
186C24×C61—21no—
187C24×C61C2×D411yescharacteristic
188C23×D61—21no—
189C23×D61—21no—
190C23×D61C2×D411yescharacteristic
191C2×D4×C61—24no—
192C2×D4×C61—21no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61—82no—
196C2×D4×C61C2412yes—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—24no—
203C22×C4×C61—44no—
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D412yes—
206C22×C4×C61C2412yes—
207C22×C4×C61C2411yescharacteristic
208C2×C22⋊D61—24no—
209C2×C22⋊D61—24no—
210C2×C22⋊D61—24no—
211C2×C22⋊D61—24no—
212C2×C22⋊D61—24no—
213C2×C22⋊D61—24no—
214C2×C22⋊D61—44no—
215C2×C22⋊D61—44no—
216C2×C22⋊D61—44no—
217C2×C22⋊D61—44no—
218C2×C22⋊D61—82no—
219C2×C22⋊D61C2×D414yes—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—24no—
223C22×Dic61—44no—
224C22×Dic61C2×D411yescharacteristic
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227#11758224—28no—
228#11758224—44no—
229#11758224—48no—
230#11758222—28no—
231#11758222—44no—
232#11758222—48no—
233#11758222—432no—
234C2×D244—22no—
235C2×D244—22no—
236C2×D244—22no—
237C2×D244—22no—
238C2×D244—24no—
239C2×D244—21no—
240C2×D244—21no—
241C2×D244—24no—
242C2×D244—44no—
243C2×D244—82no—
244C2×D244C2412yes—
245C2×D244C2412yes—
246C2×C4×D61—22no—
247C2×C4×D61—22no—
248C2×C4×D61—24no—
249C2×C4×D61—24no—
250C2×C4×D61—24no—
251C2×C4×D61—44no—
252C2×C4×D61—44no—
253C2×C4×D61—44no—
254C2×C4×D61C2×D412yes—
255C2×C4×D61C2412yes—
256C2×Dic122—21no—
257C2×Dic122—22no—
258C2×Dic122—24no—
259C2×Dic122—44no—
260C2×Dic122#4114yescomplemented
261C2×Dic122C2412yes—
262C2×C8×C61—22no—
263C2×C8×C61—22no—
264C2×C8×C61C2412yes—
265C2×C8×C61C2412yes—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—24no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61C2412yes—
271C4⋊C4×C61C2412yes—
272C4⋊C4×C61C2412yes—
273C22⋊C4×C61—24no—
274C22⋊Dic61C2×D414yes—
275#11758199—44no—
276#11758198—24no—
277#11758198—24no—
278#11758198—24no—
279#11758198—24no—
280#11758198C2×D414yes—
281C4⋊Dic61—21no—
282C4⋊Dic61C2412yes—
283#11758196—24no—
284#11758196—24no—
285#11758196—24no—
286#11758196C2×D414yes—
287C4×Dic61—24no—
288C4×Dic61C2×D412yes—
289C4×Dic61C2412yes—
290#11758194—44no—
291C2×#92418—22no—
292C2×#92418—22no—
293C2×#92418C2412yes—
294C2×#92418C2412yes—
295D488—44no—
296#11758190—28no—
297#11758189—44no—
298C23×C61—22no—
299C23×C61—22no—
300C23×C61—22no—
301C23×C61—22no—
302C23×C61—42no—
303C23×C61—42no—
304C23×C61—42no—
305C23×C61C22×D412yes—
306C23×C61C22×D411yescharacteristic
307C22×D61—22no—
308C22×D61—22no—
309C22×D61—22no—
310C22×D61—22no—
311C22×D61—22no—
312C22×D61—42no—
313C22×D61—42no—
314C22×D61—42no—
315C22×D61—42no—
316C22×D61—42no—
317C22×D61—42no—
318C22×D61C22×D412yes—
319D4×C61—22no—
320D4×C61—22no—
321D4×C61—42no—
322D4×C61—84no—
323C2×C4×C61—22no—
324C2×C4×C61—24no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—48no—
331C2×C4×C61—42no—
332C2×C4×C61—42no—
333C2×C4×C61—42no—
334C2×C4×C61C22×D412yes—
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C2×#4112yes—
337C2×C4×C61H(5,𝔽2)12yes—
338C2×C4×C61C2511yescharacteristic
339C22⋊D61—28no—
340C22⋊D61—48no—
341C22⋊D61—48no—
342C22⋊D61—48no—
343C22⋊D61—48no—
344C22⋊D61—84no—
345C2×Dic61—24no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—48no—
351C2×Dic61—42no—
352C2×Dic61AGL(1,ℤ/8)14yes—
353C2×Dic61C22×D412yes—
354C2×Dic61C22×D412yes—
355C2×Dic61C22×D412yes—
356D244—22no—
357D244—22no—
358D244—22no—
359D244—22no—
360D244—48no—
361D244—42no—
362D244—42no—
363D244—84no—
364C4×D61—24no—
365C4×D61—22no—
366C4×D61—22no—
367C4×D61—48no—
368C4×D61—48no—
369C4×D61—48no—
370Dic122—24no—
371Dic122—22no—
372Dic122—48no—
373Dic122C2×#4114yescomplemented
374C8×C61—22no—
375C8×C61—22no—
376#92418—22no—
377#92418—22no—
378C2×#3332—611nomaximal, Sylow
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—44no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—84no—
387C22×C61#54612yes—
388C22×C61C2×AGL(1,ℤ/8)12yes—
389C22×C61#57712yes—
390C22×C61C23×D411yescharacteristic
391C2×D61—22no—
392C2×D61—22no—
393C2×D61—22no—
394C2×D61—44no—
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—42no—
401C2×D61—84no—
402C2×D61—84no—
403C4×C61—22no—
404C4×C61—42no—
405C4×C61—42no—
406C4×C61—42no—
407C4×C61#54612yes—
408C4×C61C22×#4111yescharacteristic
409C4×C61C2×H(5,𝔽2)11yescharacteristic
410Dic61—24no—
411Dic61—22no—
412Dic61—22no—
413Dic61—42no—
414Dic61C2×AGL(1,ℤ/8)14yes—
415C2×#550—611no—
416C2×#547—611no—
417#3332—6116no—
418C2×#486—611no—
419C2×#481—611no—
420C2×#481D6111yescharacteristic, complemented
421C2×#475—611no—
422C2×#469—611no—
423C2×#469—611no—
424C2×#459—611no—
425C2×#449—611no—
426C2×#449—611no—
427C2×C4×SD16—611no—
428C2×#436—611no—
429C2×#417—611no—
430C2×#417—611no—
431C2×C61—42no—
432C2×C61—82no—
433C2×C61#333214yescomplemented
434C2×C61C2×#54611yescharacteristic
435C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
436C2×C61C2×#57711yescharacteristic
437D61—42no—
438D61—82no—
439D61—82no—
440C22×#41—611no—
441C22×#41—611no—
442C22×#41—1221no—
443C22×SD16—611no—
444C22×D8—611no—
445C22×D8—611no—
446C22×M16—611no—
447C22×M16—611no—
448#550—618no—
449#550—1224no—
450#547—618no—
451#547—1224no—
452C2×C4⋊Q8—611no—
453C2×#127—611no—
454C2×#127—1221no—
455C2×#123—1221no—
456C2×#123—1221no—
457C2×C22⋊Q8—1221no—
458C2×#121—611no—
459C2×#121—611no—
460C2×#121—611no—
461C2×#121—1221no—
462C2×#121—1221no—
463C2×#121C2×D6111yescharacteristic
464C2×C4×Q8—611no—
465C2×C4×D4—611no—
466C2×C4×D4—611no—
467C2×C4×D4—1221no—
468C22×C4⋊C4—611no—
469C22×C4⋊C4C2×D6111yescharacteristic
470#486—618no—
471#481—618no—
472#481C2×D6118yescomplemented
473#475—618no—
474#469—618no—
475#469—618no—
476#459—618no—
477#449—618no—
478#449—618no—
479C4×SD16—618no—
480#436—618no—
481C2×#106—611no—
482C2×#106C2×D6111yescharacteristic
483C2×#106C2×D6111yescharacteristic
484C2×C4⋊C8—611no—
485#417—618no—
486#417—618no—
487C2×#103—611no—
488C2×#103—611no—
489C2×#103—611no—
490C2×#102—611no—
491C2×#102—611no—
492C2×#102—611no—
493C2×#102—611no—
494C2×#102—611no—
495C2×#102C2×D6111yescharacteristic
496C2×#102C2×D6111yescharacteristic
497C2×C22⋊C8—611no—
498C2×C22⋊C8C2×D6111yescharacteristic
499C2×C4×C8—611no—
500C61C2×#333211yescharacteristic, complemented, Sylow
501C2×#41—614no—
502C2×#41—614no—
503C2×#41—1228no—
504C2×#41—1224no—
505C2×#41—1222no—
506C2×#41—1222no—
507C2×#41—1224no—
508C2×#41—2442no—
509C2×#41—2448no—
510C2×#41—2442no—
511C22×Q8—611no—
512C22×Q8—1221no—
513C22×D4—21no—
514C22×D4—611no—
515C22×D4—611no—
516C22×D4—611no—
517C22×D4—1221no—
518C22×D4—1221no—
519C22×D4—1221no—
520C22×D4—1221no—
521C22×D4—1221no—
522C22×D4—1221no—
523C22×D4—1221no—
524C22×D4C22×D6111yescharacteristic
525C23×C4—21no—
526C23×C4—611no—
527C23×C4—1221no—
528C23×C4—1221no—
529C23×C4—1221no—
530C23×C4—1221no—
531C23×C4C22×D6111yescharacteristic
532C2×SD16—614no—
533C2×SD16—1224no—
534C2×D8—614no—
535C2×D8—614no—
536C2×D8—2442no—
537C2×D8—2442no—
538C2×M16—614no—
539C2×M16—614no—
540C2×M16—2442no—
541C2×M16—2442no—
542C22×C8—611no—
543C22×C8—611no—
544C22×C8C22×D6111yescharacteristic
545C22×C8C22×D6111yescharacteristic
546C4⋊Q8—614no—
547C4⋊Q8—1222no—
548#127—614no—
549#127—1222no—
550#127—1228no—
551#123—1228no—
552#123—1228no—
553C22⋊Q8—1228no—
554#121—22no—
555#121—614no—
556#121—614no—
557#121—614no—
558#121—1228no—
559#121—1228no—
560#121—1222no—
561#121—1222no—
562#121—1222no—
563#121C22×D6114yes—
564C4×Q8—614no—
565C4×Q8—1222no—
566C4×D4—614no—
567C4×D4—614no—
568C4×D4—614no—
569C4×D4—1222no—
570C4×D4—1228no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—611no—
574C2×C4⋊C4—611no—
575C2×C4⋊C4—614no—
576C2×C4⋊C4—1222no—
577C2×C4⋊C4—1221no—
578C2×C4⋊C4—1221no—
579C2×C4⋊C4—1221no—
580C2×C4⋊C4C22×D6111yescharacteristic
581C2×C4⋊C4C22×D6111yescharacteristic
582C2×C4⋊C4C22×D6114yes—
583C2×C4⋊C4C22×D6111yescharacteristic
584C2×C22⋊C4—21no—
585C2×C22⋊C4—611no—
586C2×C22⋊C4—611no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C42—611no—
592C2×C42—1221no—
593#106—614no—
594#106C22×D6114yes—
595#106C22×D6114yes—
596C4⋊C8—614no—
597#103—614no—
598#103—614no—
599#103—614no—
600#102—614no—
601#102—614no—
602#102—614no—
603#102—614no—
604#102—614no—
605#102C22×D6114yes—
606#102C22×D6114yes—
607C22⋊C8—614no—
608C22⋊C8C22×D6114yes—
609C4×C8—614no—
610C24—21no—
611C24—611no—
612C24—1221no—
613C24—1221no—
614C24D4×D6111yescharacteristic
615#41—1228no—
616#41—1228no—
617#41—2444no—
618#41—2448no—
619#41—24432no—
620#41—2444no—
621#41—2448no—
622C2×Q8—614no—
623C2×Q8—612no—
624C2×Q8—1224no—
625C2×Q8—1221no—
626C2×Q8—1222no—
627C2×Q8—2444no—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—82no—
633C2×D4—614no—
634C2×D4—612no—
635C2×D4—612no—
636C2×D4—1224no—
637C2×D4—1224no—
638C2×D4—1224no—
639C2×D4—1224no—
640C2×D4—1224no—
641C2×D4—1224no—
642C2×D4—1224no—
643C2×D4—1224no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1222no—
647C2×D4—1222no—
648C2×D4—1222no—
649C2×D4—1222no—
650C2×D4—4882no—
651C2×D4—4882no—
652C2×D4—2444no—
653C2×D4—2444no—
654C2×D4—2444no—
655C2×D4—2444no—
656C2×D4—2444no—
657C2×D4C23×D6112yes—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—24no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—44no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—612no—
669C22×C4—612no—
670C22×C4—1224no—
671C22×C4—1224no—
672C22×C4—1224no—
673C22×C4—1221no—
674C22×C4—1222no—
675C22×C4—1222no—
676C22×C4—1221no—
677C22×C4—1224no—
678C22×C4—2444no—
679C22×C4—2444no—
680C22×C4—2444no—
681C22×C4—2444no—
682C22×C4D4×D6112yes—
683C22×C4D4×D6111yescharacteristic
684C22×C4C23×D6112yes—
685C22×C4C23×D6111yescharacteristic
686SD16—1228no—
687D8—2444no—
688D8—2444no—
689M16—2444no—
690M16—2444no—
691C2×C8—22no—
692C2×C8—22no—
693C2×C8—612no—
694C2×C8—612no—
695C2×C8—1222no—
696C2×C8—1222no—
697C2×C8C23×D6112yes—
698C2×C8C23×D6112yes—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—24no—
702C4⋊C4—21no—
703C4⋊C4—614no—
704C4⋊C4—612no—
705C4⋊C4—1224no—
706C4⋊C4—1224no—
707C4⋊C4—1224no—
708C4⋊C4—1221no—
709C4⋊C4C23×D6112yes—
710C4⋊C4C23×D6112yes—
711C4⋊C4C23×D6112yes—
712C22⋊C4—24no—
713C22⋊C4—614no—
714C22⋊C4—614no—
715C22⋊C4—1224no—
716C22⋊C4—1224no—
717C22⋊C4—1224no—
718C22⋊C4—1224no—
719C42—612no—
720C42—612no—
721C42—1224no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—612no—
730C23—1222no—
731C23—1222no—
732C23—1222no—
733C23—1222no—
734C23—1222no—
735C23—2442no—
736C23—2442no—
737C23—2442no—
738C23—2442no—
739C23—2442no—
740C23—2442no—
741C23C2×D4×D6112yes—
742C23C2×D4×D6111yescharacteristic
743Q8—614no—
744Q8—1222no—
745Q8—1224no—
746Q8—2448no—
747D4—22no—
748D4—22no—
749D4—42no—
750D4—84no—
751D4—1228no—
752D4—1222no—
753D4—1222no—
754D4—1222no—
755D4—1222no—
756D4—4884no—
757D4—4884no—
758D4—2448no—
759D4—2448no—
760D4—2448no—
761D4—2448no—
762D4—2448no—
763D4—2442no—
764D4—2442no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—48no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—614no—
777C2×C4—612no—
778C2×C4—612no—
779C2×C4—612no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1224no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1224no—
787C2×C4—1222no—
788C2×C4—2448no—
789C2×C4—2448no—
790C2×C4—2448no—
791C2×C4—2448no—
792C2×C4—2442no—
793C2×C4C2×D4×D6112yes—
794C2×C4C2×D4×D6111yescharacteristic
795C2×C4#41×D6112yes—
796C2×C4#1451982312yes—
797C2×C4C24×D6111yescharacteristic
798C8—22no—
799C8—22no—
800C8—1222no—
801C8—1222no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—44no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—84no—
810C22—1222no—
811C22—1222no—
812C22—1222no—
813C22—4884no—
814C22—4884no—
815C22—2442no—
816C22—2442no—
817C22—2442no—
818C22—2442no—
819C22—2442no—
820C22—2442no—
821C22—2444no—
822C22#1684040412yes—
823C22AGL(1,ℤ/8)×D6112yes—
824C22#1684056812yes—
825C22C22×D4×D6111yescharacteristic
826C4—22no—
827C4—42no—
828C4—42no—
829C4—42no—
830C4—614no—
831C4—1222no—
832C4—1224no—
833C4—1222no—
834C4—2442no—
835C4#1684040412yes—
836C4C2×#41×D6111yescharacteristic
837C4C2×#1451982311yescharacteristic
838C2—42no—
839C2—82no—
840C2—4882no—
841C2—4882no—
842C2—2442no—
843C2#2145814414yesdirect product factor
844C2C2×#1684040411yescharacteristic
845C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
846C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#481C2
socleC23×C61C22×D4
hypercenterC2×#481D61
hypocenterC61C2×#3332
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#16840430C2semidirect
2. C2×#16840413C2semidirect
3. #21458144C2direct (N × H)
4. C2×#16840107C2semidirect
5. C2×#16840082C2semidirect
6. C2×#16840046C2semidirect
7. C2×#16840016C2semidirect
8. C2×#16840013C2semidirect
9. C2×#16839956C2semidirect
10. C2×#16839909C2semidirect
11. C2×#16839908C2semidirect
12. C2×#16839849C2semidirect
13. C2×#16839837C2semidirect
14. C2×#16839761C2semidirect
15. C2×#16839760C2semidirect
16. C2×C61×#481C2semidirect
26. #16840430C22semidirect
28. #16840413C22semidirect
45. #16840107C22semidirect
46. #16840082C22semidirect
47. #16840046C22semidirect
48. #16840016C22semidirect
49. #16840013C22semidirect
50. #16839956C22semidirect
51. #16839909C22semidirect
52. #16839908C22semidirect
53. #16839849C22semidirect
54. #16839837C22semidirect
57. #16839761C22semidirect
58. #16839760C22semidirect
71. C61×#481C22semidirect
260. C2×Dic122#41semidirect
373. Dic122C2×#41semidirect
420. C2×#481D61semidirect
433. C2×C61#3332semidirect
472. #481C2×D61semidirect
500. C61C2×#3332semidirect
843. C2#21458144direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404302
C2×#168404132
#214581442
C2×#168401072
C2×#168400822
C2×#168400462
C2×#168400162
C2×#168400132
C2×#168399562
C2×#168399092
C2×#168399082
C2×#168398492
C2×#168398372
C2×#168397612
C2×#168397602
C2×C61×#4812
C2×#333261