Finite Group Databasebeta

← C2×#21456751 #30551212

Subgroups — C2×#21456751 #30551212

Order 15616.

2466 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840311C211yesmaximal, characteristic, complemented
2C2×#16840309C211yesmaximal, characteristic, complemented
3#21456751C2116yesmaximal, direct product factor
4C2×#16840137C211yesmaximal, characteristic, complemented
5C2×#16840133C211yesmaximal, characteristic, complemented
6C2×#16840111C211yesmaximal, characteristic, complemented
7C2×#16840107C211yesmaximal, characteristic, complemented
8C2×#16839978C211yesmaximal, characteristic, complemented
9C2×#16839977C211yesmaximal, characteristic, complemented
10C2×#16839974C211yesmaximal, characteristic, complemented
11C2×#16839910C211yesmaximal, characteristic, complemented
12C2×#16839908C211yesmaximal, characteristic, complemented
13C2×#16839906C211yesmaximal, characteristic, complemented
14C2×#16839904C211yesmaximal, characteristic, complemented
15C2×#16839814C211yesmaximal, characteristic, complemented
16C2×C61×#463C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758222—21no—
19C22×#11758224C2211yescharacteristic
20C22×#11758190C2211yescharacteristic
21C22×#11758200C2211yescharacteristic
22C22×#11758201C2211yescharacteristic
23C22×D488C2211yescharacteristic
24C22×#11758199C2211yescharacteristic
25C22×#11758199C2211yescharacteristic
26#16840311—24no—
27#16840311C2218yescomplemented
28#16840309—24no—
29#16840309C2218yescomplemented
30C2×#14519776C2211yescharacteristic
31C2×#14519775C2211yescharacteristic
32C2×#14519773C2211yescharacteristic
33C2×#14519773C2211yescharacteristic
34C2×#14519765C2211yescharacteristic
35C2×#14519763—21no—
36C2×#14519752C2211yescharacteristic
37C2×#14519750—21no—
38C2×#14519750—21no—
39C2×#14519750—21no—
40C2×#14519748C2211yescharacteristic
41C2×C4×D244C2211yescharacteristic
42C2×C4×C22⋊D61—21no—
43C2×#14519737—21no—
44C2×#14519737—21no—
45C2×C42×D61C2211yescharacteristic
46#16840137C2218yescomplemented
47#16840133C2218yescomplemented
48#16840111C2218yescomplemented
49#16840107C2218yescomplemented
50#16839978C2218yescomplemented
51#16839977C2218yescomplemented
52#16839974C2218yescomplemented
53#16839910C2218yescomplemented
54#16839908C2218yescomplemented
55#16839906C2218yescomplemented
56#16839904C2218yescomplemented
57#16839814C2218yescomplemented
58C2×C4⋊#92418C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519701C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519689C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×C8×Dic61C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C22×D8×C61C2211yescharacteristic
71C2×#124×C61C2211yescharacteristic
72C2×C4×D4×C61C2211yescharacteristic
73C61×#463C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758226—22no—
78C2×#11758226—42no—
79C2×#11758226—42no—
80C2×#11758226C2314yes—
81C2×#11758222—28no—
82C2×#11758222—48no—
83C2×#11758224—22no—
84C2×#11758224—42no—
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⋊D61—21no—
99C23×Dic61—21no—
100C22×C4×D61—21no—
101C22×C4×D61—21no—
102C22×C4×D61D411yescharacteristic
103C22×C4×D61D411yescharacteristic
104C22×C4×D61C2311yescharacteristic
105C2×#11758190—42no—
106C2×#11758190C2314yes—
107C2×#11758200—42no—
108C2×#11758200C2314yes—
109C2×#11758201—42no—
110C2×#11758201C2314yes—
111C2×D488—42no—
112C2×D488C2314yes—
113C2×#11758199—42no—
114C2×#11758199—42no—
115C2×#11758199C2314yes—
116C2×#11758199C2314yes—
117C22×#92418C2311yescharacteristic
118C22×#92418C2311yescharacteristic
119#14519776—22no—
120#14519776C2314yes—
121#14519775—22no—
122#14519775C2314yes—
123#14519773—22no—
124#14519773—22no—
125#14519773C2314yes—
126#14519773C2314yes—
127#14519765—22no—
128#14519765C2314yes—
129#14519763—28no—
130#14519752—22no—
131#14519752C2314yes—
132#14519750—28no—
133#14519750—28no—
134#14519750—28no—
135#14519748—22no—
136#14519748C2314yes—
137C4×D244—22no—
138C4×D244C2314yes—
139C4×C22⋊D61—28no—
140#14519737—28no—
141#14519737—28no—
142C2×C4⋊Dic61C2311yescharacteristic
143C2×#11758196—21no—
144C2×#11758196—21no—
145C2×#11758196—21no—
146C2×C22⋊Dic61—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×C4×Dic61D411yescharacteristic
152C2×C4×Dic61D411yescharacteristic
153C2×C4×Dic61C2311yescharacteristic
154C42×D61D414yes—
155C42×D61C2314yes—
156C4⋊#92418C2314yes—
157#14519702C2314yes—
158#14519701C2314yes—
159#14519700C2314yes—
160#14519699C2314yes—
161#14519698C2314yes—
162#14519697C2314yes—
163#14519689C2314yes—
164#14519689C2314yes—
165C8×Dic61C2314yes—
166C8×Dic61C2314yes—
167C22×Q8×C61C2311yescharacteristic
168C22×D4×C61C2311yescharacteristic
169C22×D4×C61C2311yescharacteristic
170C23×C4×C61—21no—
171C2×SD16×C61—42no—
172C2×SD16×C61C2314yes—
173C2×D8×C61—42no—
174C2×D8×C61C2314yes—
175C22×C8×C61C2311yescharacteristic
176C22×C8×C61C2311yescharacteristic
177#124×C61—22no—
178#124×C61C2314yes—
179C4×D4×C61—22no—
180C4×D4×C61C2314yes—
181C2×C4⋊C4×C61C2311yescharacteristic
182C2×C22⋊C4×C61—21no—
183C2×C22⋊C4×C61—21no—
184C2×C22⋊C4×C61—21no—
185C2×C42×C61C2311yescharacteristic
186C4⋊C8×C61C2314yes—
187#103×C61C2314yes—
188#102×C61C2314yes—
189C24×C61—21no—
190C24×C61—21no—
191C23×D61—21no—
192C23×D61—21no—
193C23×D61C2×D411yescharacteristic
194C2×Q8×C61—21no—
195C2×Q8×C61—22no—
196C2×Q8×C61—22no—
197C2×Q8×C61C2412yes—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—22no—
201C2×D4×C61—22no—
202C2×D4×C61—22no—
203C2×D4×C61—22no—
204C2×D4×C61C2412yes—
205C2×D4×C61C2412yes—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—24no—
209C22×C4×C61—44no—
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2411yescharacteristic
213C2×C22⋊D61—24no—
214C2×C22⋊D61—24no—
215C2×C22⋊D61—24no—
216C2×C22⋊D61—24no—
217C2×C22⋊D61—24no—
218C2×C22⋊D61—24no—
219C2×C22⋊D61—44no—
220C2×C22⋊D61—44no—
221C2×C22⋊D61—44no—
222C2×C22⋊D61—44no—
223C2×C22⋊D61—44no—
224C2×C22⋊D61—44no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—24no—
228C22×Dic61—44no—
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232#11758226—44no—
233#11758226—44no—
234#11758226—48no—
235#11758224—44no—
236#11758224—44no—
237#11758224—48no—
238#11758222—432no—
239C2×D244—22no—
240C2×D244—22no—
241C2×D244—22no—
242C2×D244—22no—
243C2×D244—24no—
244C2×D244—24no—
245C2×D244—21no—
246C2×D244—21no—
247C2×D244—44no—
248C2×D244—44no—
249C2×D244C2412yes—
250C2×D244C2412yes—
251C2×C4×D61—22no—
252C2×C4×D61—22no—
253C2×C4×D61—24no—
254C2×C4×D61—24no—
255C2×C4×D61—24no—
256C2×C4×D61—24no—
257C2×C4×D61—44no—
258C2×C4×D61—44no—
259C2×C4×D61C2×D414yes—
260C2×C4×D61C2×D414yes—
261C2×C4×D61C2×D412yes—
262C2×C4×D61C2412yes—
263C2×Dic122—22no—
264C2×Dic122—22no—
265C2×Dic122—21no—
266C2×Dic122—24no—
267C2×Dic122—44no—
268C2×Dic122C2412yes—
269SD16×C61—44no—
270D8×C61—44no—
271C2×C8×C61—22no—
272C2×C8×C61—22no—
273C2×C8×C61C2412yes—
274C2×C8×C61C2412yes—
275C4⋊C4×C61—21no—
276C4⋊C4×C61C2412yes—
277C22⋊C4×C61—24no—
278C22⋊C4×C61—24no—
279C22⋊C4×C61—24no—
280C42×C61C2×D412yes—
281C42×C61C2412yes—
282C22⋊Dic61—24no—
283#11758201—44no—
284#11758200—44no—
285#11758199—44no—
286#11758199—44no—
287#11758198—24no—
288#11758198—24no—
289#11758198—24no—
290#11758198—24no—
291C4⋊Dic61—21no—
292C4⋊Dic61C2412yes—
293#11758196—24no—
294#11758196—24no—
295#11758196—24no—
296C4×Dic61C2×D412yes—
297C4×Dic61C2×D414yes—
298C4×Dic61C2×D414yes—
299C4×Dic61C2412yes—
300C2×#92418—22no—
301C2×#92418—22no—
302C2×#92418C2412yes—
303C2×#92418C2412yes—
304D488—44no—
305#11758190—44no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—42no—
309C23×C61—42no—
310C23×C61—42no—
311C23×C61—42no—
312C23×C61—42no—
313C23×C61—42no—
314C23×C61C22×D411yescharacteristic
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—42no—
321C22×D61—42no—
322C22×D61—42no—
323C22×D61—42no—
324C22×D61—42no—
325C22×D61—42no—
326C22×D61C22×D412yes—
327Q8×C61—22no—
328Q8×C61—22no—
329Q8×C61—42no—
330D4×C61—22no—
331D4×C61—22no—
332D4×C61—22no—
333D4×C61—22no—
334D4×C61—42no—
335D4×C61—42no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—48no—
341C2×C4×C61—42no—
342C2×C4×C61—42no—
343C2×C4×C61C22×D412yes—
344C2×C4×C61C22×D412yes—
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61H(5,𝔽2)12yes—
347C2×C4×C61H(5,𝔽2)12yes—
348C2×C4×C61C2511yescharacteristic
349C22⋊D61—48no—
350C22⋊D61—48no—
351C22⋊D61—48no—
352C22⋊D61—48no—
353C22⋊D61—48no—
354C22⋊D61—48no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—48no—
359C2×Dic61—42no—
360C2×Dic61—42no—
361C2×Dic61#13514yes—
362C2×Dic61AGL(1,ℤ/8)14yes—
363C2×Dic61C22×D412yes—
364C2×Dic61C22×D412yes—
365C2×Dic61C22×D412yes—
366D244—22no—
367D244—22no—
368D244—22no—
369D244—22no—
370D244—48no—
371D244—48no—
372D244—42no—
373D244—42no—
374C4×D61—24no—
375C4×D61—22no—
376C4×D61—22no—
377C4×D61—28no—
378C4×D61—28no—
379C4×D61—48no—
380C4×D61—48no—
381Dic122—22no—
382Dic122—22no—
383Dic122—42no—
384Dic122—48no—
385C8×C61—22no—
386C8×C61—22no—
387#92418—22no—
388#92418—22no—
389C2×#3207—611nomaximal, Sylow
390C22×C61—42no—
391C22×C61—42no—
392C22×C61—42no—
393C22×C61—42no—
394C22×C61—42no—
395C22×C61—42no—
396C22×C61—84no—
397C22×C61—84no—
398C22×C61#53512yes—
399C22×C61C2×#13512yes—
400C22×C61C2×AGL(1,ℤ/8)12yes—
401C22×C61C23×D411yescharacteristic
402C2×D61—22no—
403C2×D61—22no—
404C2×D61—22no—
405C2×D61—44no—
406C2×D61—42no—
407C2×D61—42no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—84no—
413C2×D61—84no—
414C4×C61—22no—
415C4×C61—22no—
416C4×C61—42no—
417C4×C61—42no—
418C4×C61#53512yes—
419C4×C61C2×H(5,𝔽2)11yescharacteristic
420C4×C61C2×H(5,𝔽2)11yescharacteristic
421Dic61—22no—
422Dic61—42no—
423Dic61—42no—
424Dic61C2×#13514yes—
425Dic61C2×AGL(1,ℤ/8)14yes—
426C2×#532—611no—
427C2×#532—611no—
428#3207—6116no—
429C2×#493—611no—
430C2×#492—611no—
431C2×#487—611no—
432C2×#486—611no—
433C2×#463—611no—
434C2×#463—611no—
435C2×#463—611no—
436C2×#463D6111yescharacteristic, complemented
437C2×#449—611no—
438C2×#449—611no—
439C2×#449—611no—
440C2×#449—611no—
441C2×#431—611no—
442C2×C61—82no—
443C2×C61—82no—
444C2×C61#320714yescomplemented
445C2×C61C2×#53511yescharacteristic
446C2×C61C22×#13511yescharacteristic
447C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
448D61—42no—
449D61—82no—
450D61—82no—
451C22×#41—611no—
452C22×#41—611no—
453C22×#41—1221no—
454C22×SD16—611no—
455C22×SD16—611no—
456C22×SD16—611no—
457C22×SD16C2×D6111yescharacteristic
458C22×D8—611no—
459C22×D8—611no—
460C22×D8—611no—
461C22×D8C2×D6111yescharacteristic
462#532—618no—
463#532—618no—
464#532—1224no—
465#532—1224no—
466C2×C4⋊Q8—611no—
467C2×C4⋊Q8—611no—
468C2×#127—611no—
469C2×#127—611no—
470C2×#124—611no—
471C2×#124—1221no—
472C2×#124C2×D6111yescharacteristic
473C2×#121—611no—
474C2×#121—611no—
475C2×#121—1221no—
476C2×#121—1221no—
477C2×#121—1221no—
478C2×C4×D4—611no—
479C2×C4×D4—1221no—
480C2×C4×D4—1221no—
481C2×C4×D4—1221no—
482C2×C4×D4C2×D6111yescharacteristic
483C22×C42—611no—
484#493—618no—
485#492—618no—
486#487—618no—
487#486—618no—
488#463—618no—
489#463—618no—
490#463—618no—
491#463C2×D6118yescomplemented
492#449—618no—
493#449—618no—
494#449—618no—
495#449—618no—
496#431—618no—
497C2×C4⋊C8—611no—
498C2×C4⋊C8C2×D6111yescharacteristic
499C2×#103—611no—
500C2×#103—611no—
501C2×#103—611no—
502C2×#103C2×D6111yescharacteristic
503C2×#102—611no—
504C2×#102—611no—
505C2×#102—611no—
506C2×#102C2×D6111yescharacteristic
507C2×C22⋊C8—611no—
508C2×C22⋊C8—611no—
509C2×C4×C8—611no—
510C2×C4×C8—611no—
511C61C2×#320711yescharacteristic, complemented, Sylow
512C2×#41—614no—
513C2×#41—614no—
514C2×#41—1228no—
515C2×#41—1222no—
516C2×#41—1222no—
517C2×#41—2448no—
518C2×#41—2442no—
519C2×#41—2442no—
520C2×#41—2442no—
521C2×#41—2442no—
522C22×Q8—611no—
523C22×Q8—1221no—
524C22×Q8C22×D6111yescharacteristic
525C22×D4—611no—
526C22×D4—611no—
527C22×D4—1221no—
528C22×D4—1221no—
529C22×D4—1221no—
530C22×D4—1221no—
531C22×D4—1221no—
532C22×D4—1221no—
533C22×D4—1221no—
534C22×D4—1221no—
535C22×D4C22×D6111yescharacteristic
536C22×D4C22×D6111yescharacteristic
537C23×C4—21no—
538C23×C4—611no—
539C23×C4—611no—
540C23×C4—611no—
541C23×C4—1221no—
542C23×C4—1221no—
543C23×C4—1221no—
544C2×SD16—42no—
545C2×SD16—614no—
546C2×SD16—614no—
547C2×SD16—614no—
548C2×SD16—2442no—
549C2×SD16—2442no—
550C2×SD16—2442no—
551C2×SD16C22×D6114yes—
552C2×D8—42no—
553C2×D8—614no—
554C2×D8—614no—
555C2×D8—614no—
556C2×D8—2442no—
557C2×D8—2442no—
558C2×D8—2442no—
559C2×D8C22×D6114yes—
560C22×C8—611no—
561C22×C8—611no—
562C22×C8C22×D6111yescharacteristic
563C22×C8C22×D6111yescharacteristic
564C4⋊Q8—614no—
565C4⋊Q8—614no—
566C4⋊Q8—1222no—
567C4⋊Q8—1222no—
568#127—614no—
569#127—614no—
570#127—1222no—
571#127—1222no—
572#124—22no—
573#124—614no—
574#124—1228no—
575#124—1222no—
576#124C22×D6114yes—
577#121—614no—
578#121—614no—
579#121—1228no—
580#121—1228no—
581#121—1228no—
582#121—1222no—
583#121—1222no—
584C4×D4—22no—
585C4×D4—614no—
586C4×D4—1228no—
587C4×D4—1228no—
588C4×D4—1228no—
589C4×D4—1222no—
590C4×D4C22×D6114yes—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—1221no—
593C2×C4⋊C4—1221no—
594C2×C4⋊C4—1221no—
595C2×C4⋊C4C22×D6111yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—1221no—
600C2×C22⋊C4—1221no—
601C2×C22⋊C4—1221no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604C2×C42—611no—
605C2×C42—611no—
606C2×C42—611no—
607C2×C42—614no—
608C2×C42—614no—
609C2×C42C22×D6111yescharacteristic
610C4⋊C8—614no—
611C4⋊C8C22×D6114yes—
612#103—614no—
613#103—614no—
614#103—614no—
615#103C22×D6114yes—
616#102—614no—
617#102—614no—
618#102—614no—
619#102C22×D6114yes—
620C22⋊C8—614no—
621C22⋊C8—614no—
622C4×C8—614no—
623C4×C8—614no—
624C24—21no—
625C24—21no—
626C24—611no—
627C24—1221no—
628C24—1221no—
629#41—24432no—
630#41—2444no—
631#41—2444no—
632#41—2448no—
633#41—2444no—
634#41—2444no—
635#41—2448no—
636C2×Q8—21no—
637C2×Q8—22no—
638C2×Q8—22no—
639C2×Q8—612no—
640C2×Q8—1224no—
641C2×Q8—1221no—
642C2×Q8—1222no—
643C2×Q8—1222no—
644C2×Q8—2444no—
645C2×Q8C23×D6112yes—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—22no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—612no—
653C2×D4—612no—
654C2×D4—1224no—
655C2×D4—1224no—
656C2×D4—1224no—
657C2×D4—1224no—
658C2×D4—1224no—
659C2×D4—1224no—
660C2×D4—1224no—
661C2×D4—1224no—
662C2×D4—1221no—
663C2×D4—1221no—
664C2×D4—1222no—
665C2×D4—1222no—
666C2×D4—1222no—
667C2×D4—1222no—
668C2×D4—2444no—
669C2×D4—2444no—
670C2×D4—2444no—
671C2×D4—2444no—
672C2×D4—2444no—
673C2×D4—2444no—
674C2×D4—2444no—
675C2×D4—2444no—
676C2×D4C23×D6112yes—
677C2×D4C23×D6112yes—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—24no—
681C22×C4—44no—
682C22×C4—611no—
683C22×C4—611no—
684C22×C4—611no—
685C22×C4—614no—
686C22×C4—614no—
687C22×C4—612no—
688C22×C4—612no—
689C22×C4—1224no—
690C22×C4—1224no—
691C22×C4—1224no—
692C22×C4—1224no—
693C22×C4—1222no—
694C22×C4—1222no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1224no—
698C22×C4—2444no—
699C22×C4—2444no—
700C22×C4—2444no—
701C22×C4D4×D6111yescharacteristic
702C22×C4D4×D6111yescharacteristic
703C22×C4C23×D6111yescharacteristic
704SD16—44no—
705SD16—2444no—
706SD16—2444no—
707SD16—2444no—
708D8—44no—
709D8—2444no—
710D8—2444no—
711D8—2444no—
712C2×C8—22no—
713C2×C8—22no—
714C2×C8—612no—
715C2×C8—612no—
716C2×C8—1222no—
717C2×C8—1222no—
718C2×C8C23×D6112yes—
719C2×C8C23×D6112yes—
720C4⋊C4—21no—
721C4⋊C4—612no—
722C4⋊C4—1224no—
723C4⋊C4—1224no—
724C4⋊C4—1224no—
725C4⋊C4—1221no—
726C4⋊C4C23×D6112yes—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—1224no—
731C22⋊C4—1224no—
732C22⋊C4—1224no—
733C22⋊C4—1224no—
734C22⋊C4—1224no—
735C42—614no—
736C42—614no—
737C42—612no—
738C42—612no—
739C42D4×D6112yes—
740C42C23×D6112yes—
741C23—22no—
742C23—22no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—612no—
750C23—1222no—
751C23—1222no—
752C23—1222no—
753C23—1222no—
754C23—1222no—
755C23—2442no—
756C23—2442no—
757C23—2442no—
758C23—2442no—
759C23—2442no—
760C23—2442no—
761C23C2×D4×D6111yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—42no—
765Q8—1222no—
766Q8—1222no—
767Q8—2448no—
768Q8—2442no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—22no—
773D4—42no—
774D4—42no—
775D4—1222no—
776D4—1222no—
777D4—1222no—
778D4—1222no—
779D4—2448no—
780D4—2448no—
781D4—2448no—
782D4—2448no—
783D4—2448no—
784D4—2448no—
785D4—2448no—
786D4—2448no—
787D4—2442no—
788D4—2442no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—48no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—614no—
797C2×C4—614no—
798C2×C4—612no—
799C2×C4—612no—
800C2×C4—612no—
801C2×C4—1228no—
802C2×C4—1228no—
803C2×C4—1222no—
804C2×C4—1224no—
805C2×C4—1222no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—2448no—
810C2×C4—2448no—
811C2×C4—2448no—
812C2×C4—2442no—
813C2×C4—2442no—
814C2×C4C2×D4×D6112yes—
815C2×C4C2×D4×D6112yes—
816C2×C4C2×D4×D6111yescharacteristic
817C2×C4#1451982212yes—
818C2×C4#1451982312yes—
819C2×C4C24×D6111yescharacteristic
820C8—22no—
821C8—22no—
822C8—1222no—
823C8—1222no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—84no—
831C22—84no—
832C22—1222no—
833C22—1222no—
834C22—1222no—
835C22—4884no—
836C22—4884no—
837C22—2442no—
838C22—2442no—
839C22—2442no—
840C22—2442no—
841C22—2442no—
842C22—2442no—
843C22—2444no—
844C22#1684032812yes—
845C22#135×D6112yes—
846C22AGL(1,ℤ/8)×D6112yes—
847C22C22×D4×D6111yescharacteristic
848C4—22no—
849C4—22no—
850C4—42no—
851C4—42no—
852C4—614no—
853C4—614no—
854C4—1222no—
855C4—2442no—
856C4—2442no—
857C4#1684032812yes—
858C4C2×#1451982211yescharacteristic
859C4C2×#1451982311yescharacteristic
860C2—82no—
861C2—82no—
862C2—4882no—
863C2—4882no—
864C2—2442no—
865C2#2145675114yesdirect product factor
866C2C2×#1684032811yescharacteristic
867C2C2×#135×D6111yescharacteristic
868C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#463C2
socleC23×C61C22×D4
hypercenterC2×#463D61
hypocenterC61C2×#3207
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#16840311C2semidirect
2. C2×#16840309C2semidirect
3. #21456751C2direct (N × H)
4. C2×#16840137C2semidirect
5. C2×#16840133C2semidirect
6. C2×#16840111C2semidirect
7. C2×#16840107C2semidirect
8. C2×#16839978C2semidirect
9. C2×#16839977C2semidirect
10. C2×#16839974C2semidirect
11. C2×#16839910C2semidirect
12. C2×#16839908C2semidirect
13. C2×#16839906C2semidirect
14. C2×#16839904C2semidirect
15. C2×#16839814C2semidirect
16. C2×C61×#463C2semidirect
27. #16840311C22semidirect
29. #16840309C22semidirect
46. #16840137C22semidirect
47. #16840133C22semidirect
48. #16840111C22semidirect
49. #16840107C22semidirect
50. #16839978C22semidirect
51. #16839977C22semidirect
52. #16839974C22semidirect
53. #16839910C22semidirect
54. #16839908C22semidirect
55. #16839906C22semidirect
56. #16839904C22semidirect
57. #16839814C22semidirect
73. C61×#463C22semidirect
436. C2×#463D61semidirect
444. C2×C61#3207semidirect
491. #463C2×D61semidirect
511. C61C2×#3207semidirect
865. C2#21456751direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403112
C2×#168403092
#214567512
C2×#168401372
C2×#168401332
C2×#168401112
C2×#168401072
C2×#168399782
C2×#168399772
C2×#168399742
C2×#168399102
C2×#168399082
C2×#168399062
C2×#168399042
C2×#168398142
C2×C61×#4632
C2×#320761