Finite Group Databasebeta

← C2×#21436837 #29468413

Subgroups — C2×#21436837 #29468413

Order 15104.

1842 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic118C211yesmaximal, characteristic, complemented
2C2×#16838124C211yesmaximal, characteristic
3#21436837C2116yesmaximal, direct product factor
4C2×#16837763C211yesmaximal, characteristic
5C2×#16837762C211yesmaximal, characteristic
6C2×#16837751C211yesmaximal, characteristic, complemented
7C2×#16837687C211yesmaximal, characteristic, complemented
8C2×#16837686C211yesmaximal, characteristic, complemented
9C2×#16837691C211yesmaximal, characteristic
10C2×#16837626C211yesmaximal, characteristic
11C2×#16837624C211yesmaximal, characteristic
12C2×#16837610C211yesmaximal, characteristic, complemented
13C2×#16837530C211yesmaximal, characteristic, complemented
14C2×#16837506C211yesmaximal, characteristic, complemented
15C2×#16837487C211yesmaximal, characteristic
16C2×C59×#441C211yesmaximal, characteristic, complemented
17C22×#11745672C2211yescharacteristic
18C22×#11745671C2211yescharacteristic
19Q8×Dic118—24no—
20Q8×Dic118C2218yescomplemented
21#16838124—24no—
22#16838124C2218yes—
23C2×#14273727—21no—
24C2×#14273727C2211yescharacteristic
25C2×#14273726—21no—
26C2×#14273726—21no—
27C2×#14273726C2211yescharacteristic
28C2×#14273726C2211yescharacteristic
29C2×#14273725C2211yescharacteristic
30C2×#14273722—21no—
31C2×#14273721—21no—
32C2×#14273716C2211yescharacteristic
33C2×#14273715C2211yescharacteristic
34C2×#14273705—21no—
35C2×Q8×Dic59C2211yescharacteristic
36C2×Q8×Dic59C2211yescharacteristic
37C2×C4×Dic118—21no—
38C2×C4×Dic118C2211yescharacteristic
39C2×#14273692C2211yescharacteristic
40C2×#14273689C2211yescharacteristic
41C2×#14273684—21no—
42#16837763C2218yes—
43#16837762C2218yes—
44#16837751C2218yescomplemented
45#16837691C2218yes—
46#16837687C2218yescomplemented
47#16837686C2218yescomplemented
48#16837626C2218yes—
49#16837624C2218yes—
50#16837610C2218yescomplemented
51#16837530C2218yescomplemented
52#16837506C2218yescomplemented
53#16837487C2218yes—
54C2×#14273658C2211yescharacteristic
55C2×#14273658C2211yescharacteristic
56C2×C4⋊(C59⋊C8)C2211yescharacteristic
57C2×Dic59⋊C8C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273649C2211yescharacteristic
66C2×#14273647C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×Q16×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic
71C2×C4×Q8×C59C2211yescharacteristic
72C59×#441C2218yescomplemented
73C2×#106×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#97×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118—21no—
80C22×Dic118D411yescharacteristic
81C22×Dic118C2311yescharacteristic
82C22×D236C2311yescharacteristic
83C22×C4×D59—21no—
84C2×#11745672—24no—
85C2×#11745672C2314yes—
86C2×#11745671—24no—
87C2×#11745671C2314yes—
88C22×C59⋊C8C2311yescharacteristic
89C22×C59⋊C8C2311yescharacteristic
90#14273727—22no—
91#14273727—28no—
92#14273727C2314yes—
93#14273726—28no—
94#14273726—28no—
95#14273726—22no—
96#14273726—22no—
97#14273726C2314yes—
98#14273726C2314yes—
99#14273725—22no—
100#14273725C2314yes—
101#14273722—28no—
102#14273721—28no—
103#14273716—22no—
104#14273716C2314yes—
105#14273715—22no—
106#14273715C2314yes—
107#14273705—28no—
108Q8×Dic59—22no—
109Q8×Dic59—22no—
110Q8×Dic59C2314yes—
111Q8×Dic59C2314yes—
112C4×Dic118—28no—
113C4×Dic118D414yes—
114C4×Dic118C2314yes—
115#14273692—22no—
116#14273692C2314yes—
117#14273689—22no—
118#14273689C2314yes—
119#14273684—28no—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59—21no—
122C2×C4⋊Dic59—21no—
123C2×C4⋊Dic59D411yescharacteristic
124C2×C4⋊Dic59C2311yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4D411yescharacteristic
132C2×Dic59⋊C4D411yescharacteristic
133C2×(C2×D59)⋊C4—21no—
134C2×(C2×D59)⋊C4—21no—
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×C4×Dic59—21no—
139C2×C4×Dic59—21no—
140C2×C4×Dic59—21no—
141C2×C4×Dic59C2311yescharacteristic
142C2×C4×Dic59C2311yescharacteristic
143#14273658C2314yes—
144#14273658C2314yes—
145C4⋊(C59⋊C8)C2314yes—
146Dic59⋊C8C2314yes—
147Dic59⋊C8C2314yes—
148#14273652C2314yes—
149#14273652C2314yes—
150#14273651C2314yes—
151#14273651C2314yes—
152#14273650C2314yes—
153#14273649C2314yes—
154#14273649C2314yes—
155#14273647C2314yes—
156#14273637C2314yes—
157C8×Dic59C2314yes—
158C22×Q8×C59C2311yescharacteristic
159C22×Q8×C59C2311yescharacteristic
160C2×Q16×C59—24no—
161C2×Q16×C59C2314yes—
162C22×C8×C59C2311yescharacteristic
163C22×C8×C59C2311yescharacteristic
164C4×Q8×C59—22no—
165C4×Q8×C59—22no—
166C4×Q8×C59C2314yes—
167C4×Q8×C59C2314yes—
168C2×C4⋊C4×C59—21no—
169C2×C4⋊C4×C59—21no—
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C42×C59—21no—
173C2×C42×C59—21no—
174C2×C42×C59C2311yescharacteristic
175#106×C59C2314yes—
176#103×C59C2314yes—
177#103×C59C2314yes—
178#97×C59C2314yes—
179C23×D59—21no—
180C2×Q8×C59—21no—
181C2×Q8×C59—21no—
182C2×Q8×C59—22no—
183C2×Q8×C59—22no—
184C2×Q8×C59—22no—
185C2×Q8×C59#4114yes—
186C2×Q8×C59C2412yes—
187C2×Q8×C59C2412yes—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2411yescharacteristic
195C22×Dic59—21no—
196C22×Dic59—21no—
197C22×Dic59—21no—
198C22×Dic59C2×D411yescharacteristic
199C22×Dic59C2×D411yescharacteristic
200C22×Dic59C2×D411yescharacteristic
201C22×Dic59C2×D411yescharacteristic
202C2×D236—22no—
203C2×D236—22no—
204C2×D236—21no—
205C2×D236C2412yes—
206C2×C4×D59—24no—
207C2×C4×D59—44no—
208C2×Dic118—24no—
209C2×Dic118—22no—
210C2×Dic118—22no—
211C2×Dic118—21no—
212C2×Dic118—24no—
213C2×Dic118—24no—
214C2×Dic118—24no—
215C2×Dic118—82no—
216C2×Dic118—82no—
217C2×Dic118—82no—
218C2×Dic118C2×D414yes—
219C2×Dic118C2412yes—
220Q16×C59—28no—
221C2×C8×C59—22no—
222C2×C8×C59—22no—
223C2×C8×C59C2412yes—
224C2×C8×C59C2412yes—
225C4⋊C4×C59—24no—
226C4⋊C4×C59—24no—
227C4⋊C4×C59—21no—
228C4⋊C4×C59—21no—
229C4⋊C4×C59C2412yes—
230C4⋊C4×C59C2412yes—
231C42×C59—24no—
232C42×C59—24no—
233C42×C59C2×D412yes—
234C42×C59C2412yes—
235#11745672—28no—
236#11745671—28no—
237(C2×D59)⋊C4—24no—
238(C2×D59)⋊C4—24no—
239(C2×D59)⋊C4—24no—
240(C2×D59)⋊C4—24no—
241(C2×D59)⋊C4—24no—
242C4⋊Dic59—24no—
243C4⋊Dic59—21no—
244C4⋊Dic59—21no—
245C4⋊Dic59—24no—
246C4⋊Dic59—24no—
247C4⋊Dic59C2×D414yes—
248C4⋊Dic59C2412yes—
249C4⋊Dic59C2412yes—
250Dic59⋊C4—24no—
251Dic59⋊C4—24no—
252Dic59⋊C4—24no—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4C2×D414yes—
256Dic59⋊C4C2×D414yes—
257C4×Dic59—24no—
258C4×Dic59—24no—
259C4×Dic59—24no—
260C4×Dic59C2×D412yes—
261C4×Dic59C2×D412yes—
262C4×Dic59C2412yes—
263C4×Dic59C2412yes—
264C2×C59⋊C8—22no—
265C2×C59⋊C8—22no—
266C2×C59⋊C8C2412yes—
267C2×C59⋊C8C2412yes—
268C23×C59C22×D411yescharacteristic
269C22×D59—22no—
270C22×D59—42no—
271C22×D59—42no—
272C22×D59—42no—
273Q8×C59—24no—
274Q8×C59—22no—
275Q8×C59—22no—
276Q8×C59—22no—
277Q8×C59—42no—
278Q8×C59C2×#4114yes—
279C2×C4×C59—24no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—42no—
287C2×C4×C59—42no—
288C2×C4×C59—42no—
289C2×C4×C59C22×D412yes—
290C2×C4×C59C22×D412yes—
291C2×C4×C59C22×D411yescharacteristic
292C2×C4×C59C2×#4112yes—
293C2×C4×C592−1+412yes—
294C2×C4×C59C2511yescharacteristic
295C2×Dic59—22no—
296C2×Dic59—22no—
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—22no—
300C2×Dic59—22no—
301C2×Dic59—42no—
302C2×Dic59—42no—
303C2×Dic59—42no—
304C2×Dic59#13714yes—
305C2×Dic59C22×D412yes—
306C2×Dic59C22×D412yes—
307C2×Dic59C22×D412yes—
308C2×Dic59C22×D412yes—
309D236—22no—
310D236—22no—
311D236—42no—
312C4×D59—48no—
313Dic118—28no—
314Dic118—22no—
315Dic118—22no—
316Dic118—42no—
317Dic118—84no—
318Dic118—84no—
319Dic118—84no—
320C8×C59—22no—
321C8×C59—22no—
322C59⋊C8—22no—
323C59⋊C8—22no—
324C2×#3369—591nomaximal, Sylow
325C22×C59#54812yes—
326C22×C59C2×#13712yes—
327C22×C59#57712yes—
328C22×C59C23×D411yescharacteristic
329C2×D59—42no—
330C2×D59—42no—
331C2×D59—42no—
332C2×D59—84no—
333C4×C59—24no—
334C4×C59—22no—
335C4×C59—22no—
336C4×C59—42no—
337C4×C59—42no—
338C4×C59—42no—
339C4×C59#54812yes—
340C4×C59C22×#4111yescharacteristic
341C4×C59C2×2−1+411yescharacteristic
342Dic59—22no—
343Dic59—22no—
344Dic59—22no—
345Dic59—42no—
346Dic59—42no—
347Dic59—42no—
348Dic59C2×#13714yes—
349C2×Q82—591no—
350C2×#556—591no—
351#3369—5916no—
352C2×#489—591no—
353C2×#489—591no—
354C2×#487—591no—
355C2×#475—591no—
356C2×#475—591no—
357C2×#476—591no—
358C2×#464—591no—
359C2×#464—591no—
360C2×#462—591no—
361C2×#446—591no—
362C2×#441—591no—
363C2×#441D5911yescharacteristic, complemented
364C2×C4×SD16—591no—
365C2×C59#336914yescomplemented
366C2×C59C2×#54811yescharacteristic
367C2×C59C22×#13711yescharacteristic
368C2×C59C2×#57711yescharacteristic
369D59—82no—
370C22×Q16—591no—
371C22×Q16C2×D5911yescharacteristic
372C22×SD16—591no—
373Q82—598no—
374Q82—1184no—
375#556—598no—
376#556—1184no—
377C2×C4⋊Q8—591no—
378C2×C4⋊Q8—591no—
379C2×C4⋊Q8—591no—
380C2×C4⋊Q8—591no—
381C2×C4⋊Q8—1181no—
382C2×C4⋊Q8—1181no—
383C2×C4⋊Q8—1181no—
384C2×#126—1181no—
385C2×#126—1181no—
386C2×#124—591no—
387C2×#124—591no—
388C2×C22⋊Q8—1181no—
389C2×C4×Q8—591no—
390C2×C4×Q8—591no—
391C2×C4×Q8—591no—
392C2×C4×Q8—591no—
393C2×C4×Q8—1181no—
394C2×C4×Q8C2×D5911yescharacteristic
395C2×C4×Q8C2×D5911yescharacteristic
396C2×C4×D4—591no—
397C2×#117—1181no—
398#489—598no—
399#489—598no—
400#487—598no—
401#476—598no—
402#475—598no—
403#475—598no—
404#464—598no—
405#464—598no—
406#462—598no—
407#446—598no—
408#441—598no—
409#441C2×D5918yescomplemented
410C4×SD16—598no—
411C2×#106—591no—
412C2×#106—591no—
413C2×#106C2×D5911yescharacteristic
414C2×C4⋊C8—591no—
415C2×C4⋊C8—591no—
416C2×C4⋊C8—591no—
417C2×#103—591no—
418C2×#103—591no—
419C2×#103—591no—
420C2×#103—591no—
421C2×#103—591no—
422C2×#103C2×D5911yescharacteristic
423C2×#103C2×D5911yescharacteristic
424C2×#102—591no—
425C2×#102—591no—
426C2×#102—591no—
427C2×#97—591no—
428C2×#97C2×D5911yescharacteristic
429C2×C4×C8—591no—
430C59C2×#336911yescharacteristic, complemented, Sylow
431C22×Q8—591no—
432C22×Q8—591no—
433C22×Q8—1181no—
434C22×Q8—1181no—
435C22×Q8—1181no—
436C22×Q8C22×D5911yescharacteristic
437C22×Q8C22×D5911yescharacteristic
438C22×D4—591no—
439C23×C4—1181no—
440C2×Q16—24no—
441C2×Q16—594no—
442C2×Q16—1184no—
443C2×Q16C22×D5914yes—
444C2×SD16—594no—
445C2×SD16—1184no—
446C22×C8—591no—
447C22×C8—591no—
448C22×C8C22×D5911yescharacteristic
449C22×C8C22×D5911yescharacteristic
450C4⋊Q8—594no—
451C4⋊Q8—594no—
452C4⋊Q8—594no—
453C4⋊Q8—594no—
454C4⋊Q8—1188no—
455C4⋊Q8—1182no—
456C4⋊Q8—1182no—
457C4⋊Q8—1182no—
458C4⋊Q8—1188no—
459C4⋊Q8—1188no—
460C4⋊Q8—1182no—
461#126—1188no—
462#126—1188no—
463#124—594no—
464#124—594no—
465#124—1182no—
466#124—1182no—
467C22⋊Q8—1188no—
468C4×Q8—22no—
469C4×Q8—22no—
470C4×Q8—594no—
471C4×Q8—594no—
472C4×Q8—594no—
473C4×Q8—594no—
474C4×Q8—594no—
475C4×Q8—1188no—
476C4×Q8—1182no—
477C4×Q8—1182no—
478C4×Q8—1182no—
479C4×Q8C22×D5914yes—
480C4×Q8C22×D5914yes—
481C4×D4—594no—
482C4×D4—1182no—
483#117—1188no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—591no—
487C2×C4⋊C4—591no—
488C2×C4⋊C4—591no—
489C2×C4⋊C4—591no—
490C2×C4⋊C4—591no—
491C2×C4⋊C4—1181no—
492C2×C4⋊C4—1181no—
493C2×C4⋊C4—1181no—
494C2×C4⋊C4—1181no—
495C2×C4⋊C4—1181no—
496C2×C4⋊C4—1181no—
497C2×C4⋊C4—1181no—
498C2×C4⋊C4—1181no—
499C2×C4⋊C4C22×D5911yescharacteristic
500C2×C4⋊C4C22×D5911yescharacteristic
501C2×C22⋊C4—1181no—
502C2×C22⋊C4—1181no—
503C2×C22⋊C4—1181no—
504C2×C22⋊C4—1181no—
505C2×C22⋊C4—1181no—
506C2×C42—21no—
507C2×C42—21no—
508C2×C42—591no—
509C2×C42—591no—
510C2×C42—1181no—
511C2×C42—1181no—
512C2×C42—1181no—
513C2×C42C22×D5911yescharacteristic
514#106—594no—
515#106—594no—
516#106C22×D5914yes—
517C4⋊C8—594no—
518C4⋊C8—594no—
519C4⋊C8—594no—
520#103—594no—
521#103—594no—
522#103—594no—
523#103—594no—
524#103—594no—
525#103C22×D5914yes—
526#103C22×D5914yes—
527#102—594no—
528#102—594no—
529#102—594no—
530#97—594no—
531#97C22×D5914yes—
532C4×C8—594no—
533C24—1181no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—594no—
540C2×Q8—592no—
541C2×Q8—1184no—
542C2×Q8—1184no—
543C2×Q8—1184no—
544C2×Q8—1184no—
545C2×Q8—1181no—
546C2×Q8—1182no—
547C2×Q8—1182no—
548C2×Q8—4722no—
549C2×Q8—4722no—
550C2×Q8—4722no—
551C2×Q8#1174568514yes—
552C2×Q8C23×D5912yes—
553C2×Q8C23×D5912yes—
554C2×D4—592no—
555C2×D4—1181no—
556C2×D4—1182no—
557C2×D4—1182no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—591no—
563C22×C4—591no—
564C22×C4—591no—
565C22×C4—591no—
566C22×C4—1184no—
567C22×C4—1181no—
568C22×C4—1181no—
569C22×C4—1181no—
570C22×C4—2364no—
571C22×C4D4×D5911yescharacteristic
572C22×C4D4×D5911yescharacteristic
573C22×C4C23×D5911yescharacteristic
574Q16—28no—
575Q16—1188no—
576SD16—1188no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—592no—
580C2×C8—592no—
581C2×C8—1182no—
582C2×C8—1182no—
583C2×C8C23×D5912yes—
584C2×C8C23×D5912yes—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—594no—
590C4⋊C4—594no—
591C4⋊C4—594no—
592C4⋊C4—592no—
593C4⋊C4—592no—
594C4⋊C4—1184no—
595C4⋊C4—1184no—
596C4⋊C4—1184no—
597C4⋊C4—1184no—
598C4⋊C4—1184no—
599C4⋊C4—1184no—
600C4⋊C4—1184no—
601C4⋊C4—1181no—
602C4⋊C4—1181no—
603C4⋊C4—1184no—
604C4⋊C4C23×D5912yes—
605C4⋊C4C23×D5912yes—
606C22⋊C4—1184no—
607C22⋊C4—1184no—
608C22⋊C4—1184no—
609C22⋊C4—1184no—
610C22⋊C4—1184no—
611C42—24no—
612C42—24no—
613C42—592no—
614C42—592no—
615C42—592no—
616C42—592no—
617C42—1184no—
618C42—1184no—
619C42—1184no—
620C42D4×D5912yes—
621C42C23×D5912yes—
622C23—1182no—
623C23—2362no—
624C23—2362no—
625C23—2362no—
626C23C2×D4×D5911yescharacteristic
627Q8—22no—
628Q8—24no—
629Q8—22no—
630Q8—22no—
631Q8—42no—
632Q8—1188no—
633Q8—1182no—
634Q8—1182no—
635Q8—4724no—
636Q8—4724no—
637Q8—4724no—
638Q8—2362no—
639Q8C2×#1174568514yes—
640D4—1182no—
641D4—1182no—
642D4—2362no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—594no—
654C2×C4—592no—
655C2×C4—592no—
656C2×C4—592no—
657C2×C4—592no—
658C2×C4—1182no—
659C2×C4—1182no—
660C2×C4—1182no—
661C2×C4—1182no—
662C2×C4—1182no—
663C2×C4—1182no—
664C2×C4—2368no—
665C2×C4—2362no—
666C2×C4—2362no—
667C2×C4—2362no—
668C2×C4C2×D4×D5912yes—
669C2×C4C2×D4×D5912yes—
670C2×C4C2×D4×D5911yescharacteristic
671C2×C4C2×#1174568512yes—
672C2×C4#1427377412yes—
673C2×C4C24×D5911yescharacteristic
674C8—22no—
675C8—22no—
676C8—1182no—
677C8—1182no—
678C22—4724no—
679C22—2362no—
680C22—2362no—
681C22—2362no—
682C22#1683806112yes—
683C22#137×D5912yes—
684C22#1683821112yes—
685C22C22×D4×D5911yescharacteristic
686C4—22no—
687C4—24no—
688C4—22no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—594no—
693C4—1182no—
694C4—1182no—
695C4—1182no—
696C4—2362no—
697C4—2362no—
698C4—2362no—
699C4#1683806112yes—
700C4C22×#1174568511yescharacteristic
701C4C2×#1427377411yescharacteristic
702C2—4722no—
703C2#2143683714yesdirect product factor
704C2C2×#1683806111yescharacteristic
705C2C2×#137×D5911yescharacteristic
706C2C2×#1683821111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#441C2
socleC23×C59C22×D4
prime radicalC22×D236C23
hypercenterC2×#441D59
hypocenterC59C2×#3369
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic118C2semidirect
3. #21436837C2direct (N × H)
6. C2×#16837751C2semidirect
7. C2×#16837687C2semidirect
8. C2×#16837686C2semidirect
12. C2×#16837610C2semidirect
13. C2×#16837530C2semidirect
14. C2×#16837506C2semidirect
16. C2×C59×#441C2semidirect
20. Q8×Dic118C22semidirect
44. #16837751C22semidirect
46. #16837687C22semidirect
47. #16837686C22semidirect
50. #16837610C22semidirect
51. #16837530C22semidirect
52. #16837506C22semidirect
72. C59×#441C22semidirect
363. C2×#441D59semidirect
365. C2×C59#3369semidirect
409. #441C2×D59semidirect
430. C59C2×#3369semidirect
703. C2#21436837direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic1182
C2×#168381242
#214368372
C2×#168377632
C2×#168377622
C2×#168377512
C2×#168376872
C2×#168376862
C2×#168376912
C2×#168376262
C2×#168376242
C2×#168376102
C2×#168375302
C2×#168375062
C2×#168374872
C2×C59×#4412
C2×#336959