Finite Group Databasebeta

← C2×#21425735 #28741408

Subgroups — C2×#21425735 #28741408

Order 15104.

1398 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837909C211yesmaximal, characteristic
2C2×#16837386C211yesmaximal, characteristic, complemented
3#21425735C218yesmaximal, direct product factor
4C2×#16837191C212yesmaximal, complemented
5C2×#16837188C212yesmaximal, complemented
6C2×C59×#410C211yesmaximal, characteristic, complemented
7C23×C4×D59C411yescharacteristic, complemented
8C22×#11745664—21no—
9#16837909—22no—
10#16837909—22no—
11#16837909C414yescomplemented
12#16837909C2214yes—
13C2×#14273708C411yescharacteristic, complemented
14C2×#14273708C2211yescharacteristic
15C2×#14273703—21no—
16C2×#14273698—21no—
17C2×#14273695C411yescharacteristic, complemented
18C2×#14273695C2211yescharacteristic
19C2×C4×C22⋊D59—21no—
20C2×C4×C22⋊D59—21no—
21C2×#14273686C411yescharacteristic, complemented
22#16837386—22no—
23#16837386C2214yescomplemented
24C2×#14273646—21no—
25C2×#14273644C2212yes—
26#16837191C2218yescomplemented
27#16837188C2218yescomplemented
28C22×#41×C59C2211yescharacteristic
29C2×#117×C59—21no—
30C59×#410—22no—
31C59×#410C2214yescomplemented
32C2×#99×C59—21no—
33C2×#99×C59C2212yes—
34C24×D59C2×C411yescharacteristic
35C22×C22⋊D59—21no—
36C22×C22⋊D59—21no—
37C23×Dic59C2×C411yescharacteristic
38C22×C4×D59—21no—
39C22×C4×D59—22no—
40C22×C4×D59—21no—
41C22×C4×D59—42no—
42C22×C4×D59—41no—
43C22×C4×D59—41no—
44C22×C4×D59C2×C414yescomplemented
45C2×#11745664—22no—
46C2×#11745664—24no—
47C2×#11745664—41no—
48C2×#11745664—42no—
49C22×C59⋊C8—41no—
50#14273708—22no—
51#14273708—21no—
52#14273708—21no—
53#14273708C2×C412yes—
54#14273708C2×C414yescomplemented
55#14273708C2312yes—
56#14273703—24no—
57#14273703—24no—
58#14273698—24no—
59#14273698—24no—
60#14273695—22no—
61#14273695—21no—
62#14273695—21no—
63#14273695C2×C412yes—
64#14273695C2×C414yescomplemented
65#14273695C2312yes—
66C4×C22⋊D59—24no—
67C4×C22⋊D59—24no—
68C4×C22⋊D59—24no—
69C4×C22⋊D59—24no—
70#14273686—22no—
71#14273686C2×C414yescomplemented
72C2×C4⋊Dic59—21no—
73C2×Dic59⋊C4—21no—
74C2×Dic59⋊C4—21no—
75C2×C22⋊Dic59—21no—
76C2×C22⋊Dic59—21no—
77C2×C22⋊Dic59C2×C411yescharacteristic
78C2×C22⋊Dic59C2×C411yescharacteristic
79C2×(C2×D59)⋊C4—21no—
80C2×(C2×D59)⋊C4—21no—
81C2×C4×Dic59—21no—
82#14273646—24no—
83#14273644—22no—
84#14273644C2314yes—
85C2×#41×C59—41no—
86C2×#41×C59—41no—
87C2×#41×C59—42no—
88C2×#41×C59C2×C412yes—
89C2×#41×C59D412yes—
90C2×#41×C59D412yes—
91C2×#41×C59C2312yes—
92C22×Q8×C59D411yescharacteristic
93C22×D4×C59C2×C411yescharacteristic
94C22×D4×C59D411yescharacteristic
95C22×D4×C59C2311yescharacteristic
96C23×C4×C59C2×C411yescharacteristic
97C23×C4×C59D411yescharacteristic
98C23×C4×C59D411yescharacteristic
99#117×C59—24no—
100#117×C59—42no—
101C2×C4⋊C4×C59—41no—
102C2×C22⋊C4×C59—22no—
103C2×C42×C59—41no—
104#99×C59—24no—
105#99×C59—22no—
106#99×C59C2314yes—
107C24×C59C22⋊C411yescharacteristic
108C24×C59C22×C411yescharacteristic
109C24×C59C2×D411yescharacteristic
110C23×D59—21no—
111C23×D59—21no—
112C23×D59—44no—
113C23×D59—41no—
114C23×D59—41no—
115C23×D59C22×C412yes—
116#41×C59—42no—
117#41×C59—42no—
118#41×C59—42no—
119#41×C59—42no—
120#41×C59—42no—
121#41×C59—42no—
122#41×C59—42no—
123#41×C59—42no—
124C2×Q8×C59—41no—
125C2×Q8×C59—41no—
126C2×Q8×C59C22⋊C412yes—
127C2×Q8×C59C2×D412yes—
128C2×D4×C59—41no—
129C2×D4×C59—41no—
130C2×D4×C59—41no—
131C2×D4×C59—41no—
132C2×D4×C59—41no—
133C2×D4×C59—41no—
134C2×D4×C59C22⋊C412yes—
135C2×D4×C59C22⋊C412yes—
136C2×D4×C59C22×C412yes—
137C2×D4×C59C22×C411yescharacteristic
138C2×D4×C59C2×D412yes—
139C2×D4×C59C2×D411yescharacteristic
140C2×D4×C59C2×D411yescharacteristic
141C2×D4×C59C2411yescharacteristic
142C22×C4×C59—21no—
143C22×C4×C59—21no—
144C22×C4×C59—22no—
145C22×C4×C59—22no—
146C22×C4×C59—21no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—22no—
151C22×C4×C59—42no—
152C22×C4×C59C22⋊C411yescharacteristic
153C22×C4×C59C22⋊C412yes—
154C22×C4×C59C22⋊C411yescharacteristic
155C22×C4×C59C22⋊C412yes—
156C22×C4×C59C22⋊C412yes—
157C22×C4×C59C22⋊C411yescharacteristic
158C22×C4×C59C22×C412yes—
159C22×C4×C59C2×D412yes—
160C22×C4×C59C2×D411yescharacteristic
161C22×C4×C59C2×D412yes—
162C2×C22⋊D59—22no—
163C2×C22⋊D59—24no—
164C2×C22⋊D59—22no—
165C2×C22⋊D59—44no—
166C2×C22⋊D59—44no—
167C22×Dic59—21no—
168C22×Dic59—21no—
169C22×Dic59—21no—
170C22×Dic59—21no—
171C22×Dic59—41no—
172C22×Dic59—41no—
173C22×Dic59C22×C412yes—
174C2×C4×D59—24no—
175C2×C4×D59—24no—
176C2×C4×D59—42no—
177C2×C4×D59—42no—
178C2×C4×D59—44no—
179C2×C4×D59—44no—
180C2×C4×D59—42no—
181C2×C4×D59—41no—
182C2×C4×D59—41no—
183C2×C4×D59—44no—
184C2×C4×D59—44no—
185C4⋊C4×C59—44no—
186C22⋊C4×C59—24no—
187C22⋊C4×C59—42no—
188C42×C59—44no—
189C22⋊Dic59—22no—
190C22⋊Dic59—24no—
191C22⋊Dic59—21no—
192C22⋊Dic59—21no—
193C22⋊Dic59—22no—
194C22⋊Dic59C22×C412yes—
195C22⋊Dic59C22×C412yes—
196(C2×D59)⋊C4—22no—
197(C2×D59)⋊C4—24no—
198(C2×D59)⋊C4—22no—
199C4⋊Dic59—24no—
200Dic59⋊C4—22no—
201Dic59⋊C4—24no—
202Dic59⋊C4—22no—
203C4×Dic59—24no—
204#11745664—24no—
205#11745664—42no—
206#11745664—44no—
207C2×C59⋊C8—42no—
208C2×C59⋊C8—44no—
209C23×C59—21no—
210C23×C59—21no—
211C23×C59—21no—
212C23×C59—21no—
213C23×C59—21no—
214C23×C59—21no—
215C23×C59—42no—
216C23×C59—42no—
217C23×C59—42no—
218C23×C59C2×C22⋊C411yescharacteristic
219C23×C59C2×C22⋊C411yescharacteristic
220C23×C59C2×C22⋊C411yescharacteristic
221C23×C59C2×C22⋊C412yes—
222C23×C59C23×C411yescharacteristic
223C23×C59C22×D411yescharacteristic
224C22×D59—24no—
225C22×D59—22no—
226C22×D59—44no—
227C22×D59—44no—
228C22×D59—42no—
229C22×D59—42no—
230C22×D59—48no—
231C22×D59—44no—
232C22×D59—41no—
233C22×D59—41no—
234C22×D59—42no—
235C22×D59—44no—
236Q8×C59—42no—
237Q8×C59—42no—
238D4×C59—42no—
239D4×C59—42no—
240D4×C59—42no—
241D4×C59—41no—
242D4×C59—41no—
243D4×C59—42no—
244D4×C59—41no—
245D4×C59—41no—
246C2×C4×C59—21no—
247C2×C4×C59—21no—
248C2×C4×C59—21no—
249C2×C4×C59—21no—
250C2×C4×C59—21no—
251C2×C4×C59—21no—
252C2×C4×C59—22no—
253C2×C4×C59—22no—
254C2×C4×C59—22no—
255C2×C4×C59—22no—
256C2×C4×C59—22no—
257C2×C4×C59—22no—
258C2×C4×C59—22no—
259C2×C4×C59—22no—
260C2×C4×C59—22no—
261C2×C4×C59—22no—
262C2×C4×C59—22no—
263C2×C4×C59—22no—
264C2×C4×C59—44no—
265C2×C4×C59—84no—
266C2×C4×C59#9912yes—
267C2×C4×C59#9911yescharacteristic
268C2×C4×C59#9911yescharacteristic
269C2×C4×C59C2×C22⋊C412yes—
270C2×C4×C59C2×C22⋊C411yescharacteristic
271C2×C4×C59C2×C22⋊C412yes—
272C2×C4×C59C2×C22⋊C412yes—
273C2×C4×C59C22×D411yescharacteristic
274C22⋊D59—44no—
275C22⋊D59—48no—
276C22⋊D59—44no—
277C2×Dic59—22no—
278C2×Dic59—22no—
279C2×Dic59—22no—
280C2×Dic59—42no—
281C2×Dic59—42no—
282C2×Dic59—42no—
283C2×Dic59—41no—
284C2×Dic59—41no—
285C2×Dic59—42no—
286C4×D59—48no—
287C4×D59—44no—
288C4×D59—44no—
289C59⋊C8—44no—
290C2×#2120—591nomaximal, Sylow
291C22×C59—22no—
292C22×C59—21no—
293C22×C59—21no—
294C22×C59—21no—
295C22×C59—22no—
296C22×C59—21no—
297C22×C59—42no—
298C22×C59—41no—
299C22×C59—41no—
300C22×C59—41no—
301C22×C59—41no—
302C22×C59—42no—
303C22×C59—42no—
304C22×C59—42no—
305C22×C59—42no—
306C22×C59—81no—
307C22×C59—81no—
308C22×C59C2×#9911yescharacteristic
309C22×C59C2×#9911yescharacteristic
310C22×C59C22×C22⋊C411yescharacteristic
311C2×D59—24no—
312C2×D59—42no—
313C2×D59—44no—
314C2×D59—48no—
315C2×D59—44no—
316C2×D59—42no—
317C2×D59—44no—
318C2×D59—44no—
319C4×C59—21no—
320C4×C59—22no—
321C4×C59—21no—
322C4×C59—22no—
323C4×C59—84no—
324C4×C59C2×#9912yes—
325C4×C59C2×#9912yes—
326Dic59—42no—
327Dic59—42no—
328Dic59—42no—
329C2×#525—591no—
330C2×#413—591no—
331C2×#410D5911yescharacteristic, complemented
332#2120—598no—
333C2×#352—592no—
334C2×AΣL(1,𝔽16)—592no—
335C2×C59—21no—
336C2×C59—21no—
337C2×C59—41no—
338C2×C59—41no—
339C2×C59—41no—
340C2×C59—41no—
341C2×C59—42no—
342C2×C59#212012yescomplemented
343C2×C59C22×#9911yescharacteristic
344D59—44no—
345C22×#41C2×D5911yescharacteristic
346C24×C4—591no—
347C22×M16—1181no—
348#525—594no—
349#525—594no—
350#525—1182no—
351#525—1182no—
352C2×#123—591no—
353C2×#123—591no—
354C2×C22⋊Q8—1181no—
355C2×#121—1181no—
356C2×#120—591no—
357C2×#120—591no—
358C2×C4×D4—1181no—
359C2×C4×D4—1181no—
360C2×#117—21no—
361C2×#117—591no—
362#413—594no—
363#413—1182no—
364C2×#101—1181no—
365C2×#100—592no—
366#410—22no—
367#410C2×D5914yescomplemented
368C2×#99—21no—
369C2×#99C2×D5912yes—
370#352—598no—
371AΣL(1,𝔽16)—598no—
372C59C2×#212011yescharacteristic, complemented, Sylow
373C25—591no—
374C2×#41—41no—
375C2×#41—42no—
376C2×#41—41no—
377C2×#41C4×D5912yes—
378C2×#41D23612yes—
379C2×#41C22⋊D5912yes—
380C2×#41C22×D5912yes—
381C22×Q8D23611yescharacteristic
382C22×D4—1181no—
383C22×D4—1181no—
384C22×D4C4×D5911yescharacteristic
385C22×D4C22⋊D5911yescharacteristic
386C22×D4C22×D5911yescharacteristic
387C23×C4—591no—
388C23×C4—594no—
389C23×C4—1181no—
390C23×C4—1182no—
391C23×C4—1181no—
392C23×C4—2361no—
393C23×C4—2362no—
394C23×C4—2361no—
395C23×C4C4×D5911yescharacteristic
396C23×C4D23611yescharacteristic
397C23×C4C22⋊D5911yescharacteristic
398C2×M16—1182no—
399C2×M16—1184no—
400C2×M16—2361no—
401C2×M16—2362no—
402C22×C8—2361no—
403#123—592no—
404#123—594no—
405#123—592no—
406#123—1182no—
407#123—1181no—
408#123—1181no—
409C22⋊Q8—1184no—
410C22⋊Q8—1184no—
411#121—1184no—
412#121—1184no—
413#120—592no—
414#120—594no—
415#120—592no—
416#120—1182no—
417#120—1181no—
418#120—1181no—
419C4×D4—1184no—
420C4×D4—1184no—
421C4×D4—1184no—
422C4×D4—1184no—
423#117—24no—
424#117—42no—
425#117—594no—
426#117—1182no—
427C2×C4⋊C4—41no—
428C2×C4⋊C4—1181no—
429C2×C4⋊C4—1181no—
430C2×C4⋊C4—1181no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—591no—
433C2×C22⋊C4—591no—
434C2×C22⋊C4—1181no—
435C2×C22⋊C4—1181no—
436C2×C22⋊C4—1181no—
437C2×C22⋊C4—1181no—
438C2×C42—41no—
439C2×C42—1181no—
440#101—1184no—
441#100—594no—
442#100—1182no—
443#99—24no—
444#99—22no—
445#99C22×D5914yes—
446C24—592no—
447C24—1181no—
448C24—1181no—
449C24—2361no—
450C24—2361no—
451C24—2364no—
452C24(C2×D59)⋊C411yescharacteristic
453C24C2×C4×D5911yescharacteristic
454C24C2×C22⋊D5911yescharacteristic
455#41—42no—
456#41—42no—
457#41—42no—
458#41—42no—
459#41—42no—
460#41—42no—
461#41—42no—
462#41—42no—
463C2×Q8—41no—
464C2×Q8—41no—
465C2×Q8(C2×D59)⋊C412yes—
466C2×Q8C2×D23612yes—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—1182no—
474C2×D4—1184no—
475C2×D4—1182no—
476C2×D4—2364no—
477C2×D4—2364no—
478C2×D4(C2×D59)⋊C412yes—
479C2×D4(C2×D59)⋊C412yes—
480C2×D4C2×C4×D5912yes—
481C2×D4C2×C4×D5911yescharacteristic
482C2×D4C2×D23611yescharacteristic
483C2×D4C2×C22⋊D5911yescharacteristic
484C2×D4C2×C22⋊D5912yes—
485C2×D4C23×D5911yescharacteristic
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—42no—
496C22×C4—592no—
497C22×C4—1181no—
498C22×C4—1181no—
499C22×C4—1181no—
500C22×C4—1181no—
501C22×C4—1184no—
502C22×C4—1184no—
503C22×C4—2362no—
504C22×C4—2362no—
505C22×C4—2364no—
506C22×C4—2364no—
507C22×C4—2364no—
508C22×C4—2364no—
509C22×C4—2362no—
510C22×C4—2361no—
511C22×C4—2361no—
512C22×C4—2361no—
513C22×C4—2361no—
514C22×C4(C2×D59)⋊C411yescharacteristic
515C22×C4(C2×D59)⋊C411yescharacteristic
516C22×C4(C2×D59)⋊C412yes—
517C22×C4(C2×D59)⋊C412yes—
518C22×C4(C2×D59)⋊C412yes—
519C22×C4(C2×D59)⋊C411yescharacteristic
520C22×C4C2×C4×D5912yes—
521C22×C4C2×D23611yescharacteristic
522C22×C4C2×D23612yes—
523C22×C4C2×C22⋊D5912yes—
524M16—1184no—
525M16—2362no—
526M16—2364no—
527C2×C8—2362no—
528C2×C8—2364no—
529C4⋊C4—44no—
530C4⋊C4—1184no—
531C4⋊C4—1182no—
532C4⋊C4—1184no—
533C4⋊C4—1182no—
534C22⋊C4—24no—
535C22⋊C4—42no—
536C22⋊C4—592no—
537C22⋊C4—592no—
538C22⋊C4—1181no—
539C22⋊C4—1181no—
540C22⋊C4—1182no—
541C22⋊C4—1184no—
542C22⋊C4—1182no—
543C22⋊C4—1182no—
544C22⋊C4—1184no—
545C22⋊C4—1182no—
546C42—44no—
547C42—1184no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—1184no—
558C23—1182no—
559C23—2362no—
560C23—2362no—
561C23—2362no—
562C23—2364no—
563C23—2364no—
564C23—2364no—
565C23—2368no—
566C23—2364no—
567C23—2361no—
568C23—2361no—
569C23C2×(C2×D59)⋊C411yescharacteristic
570C23C2×(C2×D59)⋊C411yescharacteristic
571C23C2×(C2×D59)⋊C411yescharacteristic
572C23C2×(C2×D59)⋊C412yes—
573C23C22×C4×D5911yescharacteristic
574C23C22×C22⋊D5911yescharacteristic
575Q8—42no—
576Q8—42no—
577D4—42no—
578D4—42no—
579D4—42no—
580D4—41no—
581D4—41no—
582D4—42no—
583D4—41no—
584D4—41no—
585D4—2368no—
586D4—2364no—
587D4—2364no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—44no—
607C2×C4—84no—
608C2×C4—1182no—
609C2×C4—1182no—
610C2×C4—1182no—
611C2×C4—2368no—
612C2×C4—2362no—
613C2×C4—2362no—
614C2×C4—2362no—
615C2×C4—2361no—
616C2×C4—2361no—
617C2×C4—2364no—
618C2×C4—2364no—
619C2×C4—2362no—
620C2×C4#1427364111yescharacteristic
621C2×C4#1427364112yes—
622C2×C4#1427364111yescharacteristic
623C2×C4C2×(C2×D59)⋊C411yescharacteristic
624C2×C4C2×(C2×D59)⋊C412yes—
625C2×C4C2×(C2×D59)⋊C412yes—
626C2×C4C2×(C2×D59)⋊C412yes—
627C2×C4C22×D23611yescharacteristic
628C8—2364no—
629C22—22no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—22no—
634C22—21no—
635C22—42no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—81no—
645C22—81no—
646C22—1184no—
647C22—2362no—
648C22—2364no—
649C22—2364no—
650C22—2364no—
651C22—2368no—
652C22—2364no—
653C22—2362no—
654C22C2×#1427364111yescharacteristic
655C22C2×#1427364111yescharacteristic
656C22C22×(C2×D59)⋊C411yescharacteristic
657C4—21no—
658C4—22no—
659C4—21no—
660C4—22no—
661C4—84no—
662C4—2362no—
663C4—2362no—
664C4—2362no—
665C4C2×#1427364112yes—
666C4C2×#1427364112yes—
667C2—21no—
668C2—21no—
669C2—41no—
670C2—41no—
671C2—41no—
672C2—41no—
673C2—42no—
674C2—2364no—
675C2#2142573512yesdirect product factor
676C2C22×#1427364111yescharacteristic
subgroupG/H
centerC2×C4#14273641
commutatorC23×C59C23×C4
FrattiniC2×D4C23×D59
FittingC2×C59×#410C2
socleC22×C59C2×#99
prime radicalC2×#16837909C2
cosocleC2×D4×C59C24
hypercenterC2×#410D59
hypocenterC59C2×#2120
LCSG ▷ C23×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. C2×#16837386C2semidirect
3. #21425735C2direct (N × H)
4. C2×#16837191C2semidirect
5. C2×#16837188C2semidirect
6. C2×C59×#410C2semidirect
7. C23×C4×D59C4semidirect
11. #16837909C4semidirect
13. C2×#14273708C4semidirect
17. C2×#14273695C4semidirect
21. C2×#14273686C4semidirect
23. #16837386C22semidirect
26. #16837191C22semidirect
27. #16837188C22semidirect
31. C59×#410C22semidirect
44. C22×C4×D59C2×C4semidirect
54. #14273708C2×C4semidirect
64. #14273695C2×C4semidirect
71. #14273686C2×C4semidirect
331. C2×#410D59semidirect
342. C2×C59#2120semidirect
367. #410C2×D59semidirect
372. C59C2×#2120semidirect
675. C2#21425735direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379092
C2×#168373862
#214257352
C2×#168371912
C2×#168371882
C2×C59×#4102
C2×#212059