Finite Group Databasebeta

← C2×#21447038 #29707608

Subgroups — C2×#21447038 #29707608

Order 15616.

1434 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840338C211yesmaximal, characteristic
2C22×#14519703C211yesmaximal, characteristic
3C2×#16839761C211yesmaximal, characteristic
4C22×#14519695C211yesmaximal, characteristic, complemented
5C2×#16839667C211yesmaximal, characteristic, complemented
6#21447038C218yesmaximal, direct product factor
7C2×#16839521C211yesmaximal, characteristic, complemented
8C2×C61×#428C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C23×Dic122C2211yescharacteristic
11C22×#11758194C2211yescharacteristic
12#16840338—22no—
13#16840338—22no—
14#16840338—22no—
15#16840338C2214yes—
16C2×#14519777—21no—
17C2×#14519765—21no—
18C2×#14519761—22no—
19C2×#14519757—21no—
20C2×#14519757—21no—
21C22×C4×Dic61C2211yescharacteristic
22C2×#14519703—24no—
23C2×#14519703C2214yes—
24#16839761—22no—
25#16839761C2214yes—
26C2×#14519700—21no—
27C2×#14519697—21no—
28C2×#14519695—24no—
29C2×#14519695C2214yescomplemented
30#16839667—22no—
31#16839667C2214yescomplemented
32C2×#14519684—22no—
33#16839521C2214yescomplemented
34C22×M16×C61C2211yescharacteristic
35C2×#117×C61C2211yescharacteristic
36C22×C4⋊C4×C61C2211yescharacteristic
37C61×#428—22no—
38C61×#428C2214yescomplemented
39C2×#107×C61—21no—
40C2×#106×C61—21no—
41C2×#11758222—21no—
42C2×#11758222—21no—
43C2×#11758222—22no—
44C2×#11758222—22no—
45C2×#11758222—22no—
46C2×#11758222—22no—
47C2×#11758222D412yes—
48C2×#11758222C2312yes—
49C22×Dic122—22no—
50C22×Dic122—21no—
51C22×Dic122—21no—
52C22×Dic122—21no—
53C22×Dic122—21no—
54C22×Dic122—22no—
55C22×Dic122—22no—
56C22×Dic122—22no—
57C22×Dic122D412yes—
58C22×Dic122D411yescharacteristic
59C22×Dic122C2312yes—
60C22×D244D411yescharacteristic
61C22×C22⋊D61—21no—
62C23×Dic61—21no—
63C23×Dic61D412yes—
64C22×C4×D61—21no—
65C2×#11758194—21no—
66C2×#11758194—22no—
67C2×#11758194—22no—
68C2×#11758194C2312yes—
69C22×#92418—21no—
70#14519777—24no—
71#14519777—24no—
72#14519765—24no—
73#14519765—24no—
74#14519761—28no—
75#14519761—28no—
76#14519757—24no—
77#14519757—24no—
78#14519757—24no—
79#14519757—24no—
80C2×C4⋊Dic61—22no—
81C2×C4⋊Dic61—22no—
82C2×#11758198—22no—
83C2×#11758198—22no—
84C2×C4×Dic61—22no—
85C2×C4×Dic61—22no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61C2312yes—
88#14519703—28no—
89#14519700—24no—
90#14519697—24no—
91#14519695—28no—
92#14519684—28no—
93C23×C4×C61—21no—
94C23×C4×C61C2311yescharacteristic
95C2×M16×C61—21no—
96C2×M16×C61—22no—
97C2×M16×C61D414yes—
98C2×M16×C61C2312yes—
99C22×C8×C61—21no—
100#117×C61—21no—
101#117×C61—21no—
102#117×C61D412yes—
103#117×C61C2312yes—
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61D411yescharacteristic
110C2×C4⋊C4×C61D411yescharacteristic
111C2×C4⋊C4×C61C2312yes—
112C2×C22⋊C4×C61—21no—
113C2×C42×C61—21no—
114#107×C61—24no—
115#106×C61—24no—
116C24×C61C2×D411yescharacteristic
117C23×D61—21no—
118C22×C4×C61—21no—
119C22×C4×C61—21no—
120C22×C4×C61—22no—
121C22×C4×C61—44no—
122C22×C4×C61—41no—
123C22×C4×C61—41no—
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D412yes—
130C22×C4×C61#4112yes—
131C22×C4×C61#4112yes—
132C22×C4×C61#4112yes—
133C22×C4×C61C2411yescharacteristic
134C2×C22⋊D61—22no—
135C2×C22⋊D61—22no—
136C2×C22⋊D61—42no—
137C2×C22⋊D61—42no—
138C22×Dic61—24no—
139C22×Dic61—21no—
140C22×Dic61—22no—
141C22×Dic61—22no—
142C22×Dic61—24no—
143C22×Dic61—24no—
144C22×Dic61—22no—
145C22×Dic61—42no—
146C22×Dic61—42no—
147C22×Dic61C2×D414yes—
148#11758222—24no—
149#11758222—24no—
150#11758222—22no—
151#11758222—22no—
152#11758222—22no—
153#11758222—22no—
154#11758222—42no—
155#11758222—42no—
156#11758222—42no—
157#11758222—42no—
158C2×D244—22no—
159C2×D244—22no—
160C2×D244—21no—
161C2×D244C2×D412yes—
162C2×C4×D61—22no—
163C2×C4×D61—22no—
164C2×C4×D61—42no—
165C2×C4×D61—42no—
166C2×Dic122—22no—
167C2×Dic122—22no—
168C2×Dic122—22no—
169C2×Dic122—22no—
170C2×Dic122—21no—
171C2×Dic122—24no—
172C2×Dic122—24no—
173C2×Dic122—22no—
174C2×Dic122—22no—
175C2×Dic122—22no—
176C2×Dic122—22no—
177C2×Dic122—22no—
178C2×Dic122—22no—
179C2×Dic122—42no—
180C2×Dic122—42no—
181C2×Dic122—42no—
182C2×Dic122—42no—
183C2×Dic122—42no—
184C2×Dic122—42no—
185C2×Dic122—42no—
186C2×Dic122—42no—
187C2×Dic122C2×D412yes—
188M16×C61—24no—
189M16×C61—22no—
190M16×C61C2×D414yes—
191C2×C8×C61—24no—
192C2×C8×C61—22no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—22no—
196C4⋊C4×C61—22no—
197C4⋊C4×C61—41no—
198C4⋊C4×C61—41no—
199C4⋊C4×C61C2×D412yes—
200C4⋊C4×C61C2×D412yes—
201C22⋊C4×C61—22no—
202C22⋊C4×C61—22no—
203C42×C61—22no—
204C42×C61—22no—
205#11758198—28no—
206#11758198—28no—
207C4⋊Dic61—28no—
208C4⋊Dic61—28no—
209C4×Dic61—22no—
210C4×Dic61—22no—
211C4×Dic61—42no—
212#11758194—22no—
213#11758194—22no—
214#11758194—42no—
215C2×#92418—22no—
216C2×#92418—42no—
217C23×C61—22no—
218C23×C61—22no—
219C23×C61#12011yescharacteristic
220C23×C61#12011yescharacteristic
221C23×C61#12112yes—
222C23×C61#12312yes—
223C23×C61C22×D411yescharacteristic
224C22×D61—22no—
225C22×D61—42no—
226C22×D61—42no—
227C22×D61—42no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61—44no—
233C2×C4×C61—42no—
234C2×C4×C61—82no—
235C2×C4×C61—82no—
236C2×C4×C61#12011yescharacteristic
237C2×C4×C61#12011yescharacteristic
238C2×C4×C61#12112yes—
239C2×C4×C61#12112yes—
240C2×C4×C61#12112yes—
241C2×C4×C61#12112yes—
242C2×C4×C61#12112yes—
243C2×C4×C61#12312yes—
244C2×C4×C61#12312yes—
245C2×C4×C61#12312yes—
246C2×C4×C61#12412yes—
247C2×C4×C61#12412yes—
248C2×C4×C61C22×D411yescharacteristic
249C2×C4×C61C22×D411yescharacteristic
250C2×C4×C61C22×D411yescharacteristic
251C2×C4×C61C2×#4111yescharacteristic
252C2×C4×C61C2×#4111yescharacteristic
253C2×C4×C61C2×#4111yescharacteristic
254C22⋊D61—42no—
255C22⋊D61—42no—
256C22⋊D61—44no—
257C2×Dic61—24no—
258C2×Dic61—22no—
259C2×Dic61—24no—
260C2×Dic61—24no—
261C2×Dic61—24no—
262C2×Dic61—42no—
263C2×Dic61—48no—
264C2×Dic61—42no—
265C2×Dic61—42no—
266C2×Dic61—44no—
267C2×Dic61—44no—
268D244—22no—
269D244—22no—
270D244—42no—
271C4×D61—42no—
272C4×D61—42no—
273C4×D61—44no—
274Dic122—22no—
275Dic122—22no—
276Dic122—42no—
277Dic122—42no—
278Dic122—42no—
279Dic122—42no—
280Dic122—44no—
281Dic122—44no—
282Dic122—42no—
283C8×C61—24no—
284#92418—42no—
285C2×#2038—611nomaximal, Sylow
286C22×C61—21no—
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—21no—
290C22×C61—24no—
291C22×C61—24no—
292C22×C61#39412yes—
293C22×C61#39412yes—
294C22×C61#45412yes—
295C22×C61#45612yes—
296C22×C61C2×#12011yescharacteristic
297C22×C61C2×#12111yescharacteristic
298C22×C61C2×#12311yescharacteristic
299C2×D61—42no—
300C2×D61—42no—
301C2×D61—42no—
302C2×D61—84no—
303C4×C61—42no—
304C4×C61—42no—
305C4×C61—82no—
306C4×C61#39412yes—
307C4×C61#39412yes—
308C4×C61C2×#12111yescharacteristic
309C4×C61C2×#12111yescharacteristic
310C4×C61C2×#12311yescharacteristic
311C4×C61C2×#12411yescharacteristic
312Dic61—44no—
313Dic61—42no—
314Dic61—44no—
315C2×#536—611no—
316C2×#428D6111yescharacteristic, complemented
317C22×#104—611no—
318C2×#417—611no—
319C22×#101—611no—
320C2×#391—611no—
321#2038—618no—
322C2×#339—611no—
323C2×C61—21no—
324C2×C61—21no—
325C2×C61—22no—
326C2×C61#203814yescomplemented
327C2×C61C2×#39411yescharacteristic
328C2×C61C2×#45411yescharacteristic
329C2×C61C2×#45611yescharacteristic
330D61—82no—
331C22×#41—611no—
332C23×Q8—611no—
333C22×M16—611no—
334C22×M16C2×D6111yescharacteristic
335#536—614no—
336#536—1222no—
337#536—1222no—
338#536—1222no—
339C2×C4⋊Q8—1221no—
340C2×#124—1221no—
341C2×#123—1222no—
342C2×C22⋊Q8—1221no—
343C2×C22⋊Q8—1221no—
344C2×#117C2×D6111yescharacteristic
345C22×C4⋊C4C2×D6111yescharacteristic
346C22×C42—611no—
347#428—22no—
348#428C2×D6114yescomplemented
349C2×#107—21no—
350C2×#106—21no—
351C2×#104—614no—
352C2×#104—1224no—
353#417—614no—
354#417—1222no—
355C2×#103—1221no—
356C2×#102—1221no—
357C2×#101—614no—
358C2×#101—1224no—
359#391—614no—
360#391—1222no—
361C2×#95—1222no—
362#339—614no—
363C61C2×#203811yescharacteristic, complemented, Sylow
364C2×#41—612no—
365C2×#41—612no—
366C2×#41—1221no—
367C2×#41—1221no—
368C2×#41—1222no—
369C2×#41—1222no—
370C2×#41—1222no—
371C2×#41—1222no—
372C22×Q8—612no—
373C22×Q8—612no—
374C22×Q8—611no—
375C22×Q8—1222no—
376C22×Q8—1222no—
377C22×Q8—1221no—
378C22×Q8—1221no—
379C22×Q8—1222no—
380C22×Q8—1222no—
381C22×Q8—1221no—
382C22×Q8—1221no—
383C22×D4—611no—
384C22×D4—1221no—
385C23×C4—21no—
386C23×C4—612no—
387C23×C4—1221no—
388C23×C4—1221no—
389C23×C4C22×D6111yescharacteristic
390C2×M16—22no—
391C2×M16—21no—
392C2×M16—612no—
393C2×M16—1221no—
394C2×M16—1222no—
395C2×M16—1222no—
396C2×M16D24414yes—
397C2×M16C22×D6112yes—
398C22×C8—21no—
399C22×C8—1221no—
400C4⋊Q8—1224no—
401C4⋊Q8—1224no—
402#124—1224no—
403#124—1224no—
404#123—1228no—
405#123—1228no—
406C22⋊Q8—1224no—
407C22⋊Q8—1224no—
408C22⋊Q8—1224no—
409C22⋊Q8—1224no—
410#117—21no—
411#117—21no—
412#117C22⋊D6112yes—
413#117C22×D6112yes—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—1222no—
420C2×C4⋊C4—1222no—
421C2×C4⋊C4C22⋊D6111yescharacteristic
422C2×C4⋊C4C22⋊D6111yescharacteristic
423C2×C4⋊C4C22×D6112yes—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—1222no—
426C2×C22⋊C4—1222no—
427C2×C42—21no—
428C2×C42—612no—
429C2×C42—1222no—
430C2×C42—1222no—
431C2×C42—1221no—
432#107—24no—
433#106—24no—
434#104—1228no—
435#103—1224no—
436#102—1224no—
437#101—1228no—
438#95—1228no—
439C24—1221no—
440C24D4×D6111yescharacteristic
441#41—1222no—
442#41—1222no—
443#41—1222no—
444#41—1222no—
445#41—1224no—
446#41—1224no—
447#41—2442no—
448#41—2442no—
449#41—2442no—
450#41—2442no—
451C2×Q8—612no—
452C2×Q8—1222no—
453C2×Q8—1222no—
454C2×Q8—1222no—
455C2×Q8—1222no—
456C2×Q8—1222no—
457C2×Q8—1222no—
458C2×Q8—1222no—
459C2×Q8—1222no—
460C2×Q8—1221no—
461C2×Q8—1224no—
462C2×Q8—1224no—
463C2×Q8—1222no—
464C2×Q8—1222no—
465C2×Q8—2442no—
466C2×Q8—2442no—
467C2×Q8—2442no—
468C2×Q8—2442no—
469C2×Q8—2442no—
470C2×Q8—2442no—
471C2×Q8—2442no—
472C2×Q8—2442no—
473C2×D4—612no—
474C2×D4—1222no—
475C2×D4—1222no—
476C2×D4—1221no—
477C2×D4—1222no—
478C2×D4—1222no—
479C2×D4—2442no—
480C2×D4—2442no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—44no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—614no—
488C22×C4—1224no—
489C22×C4—1222no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4—1221no—
493C22×C4—1224no—
494C22×C4—1224no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—2442no—
498C22×C4—2442no—
499C22×C4—2442no—
500C22×C4—2442no—
501C22×C4C2×D24412yes—
502C22×C4#1175822212yes—
503C22×C4D4×D6111yescharacteristic
504C22×C4D4×D6111yescharacteristic
505C22×C4D4×D6111yescharacteristic
506C22×C4#1175822612yes—
507C22×C4#1175822612yes—
508C22×C4C2×C22⋊D6111yescharacteristic
509C22×C4C2×C22⋊D6111yescharacteristic
510C22×C4C23×D6111yescharacteristic
511M16—22no—
512M16—24no—
513M16—1222no—
514M16—1222no—
515M16—2442no—
516M16C2×D24414yes—
517C2×C8—22no—
518C2×C8—24no—
519C2×C8—1222no—
520C2×C8—2442no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4—1228no—
528C4⋊C4—1228no—
529C4⋊C4C2×C22⋊D6112yes—
530C4⋊C4C2×C22⋊D6112yes—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—1228no—
534C22⋊C4—1228no—
535C42—22no—
536C42—22no—
537C42—1222no—
538C42—1222no—
539C42—2442no—
540C23—22no—
541C23—22no—
542C23—1222no—
543C23—2442no—
544C23—2442no—
545C23—2442no—
546C23#1451974511yescharacteristic
547C23#1451974511yescharacteristic
548C23#1451975212yes—
549C23#1451976212yes—
550C23C2×D4×D6111yescharacteristic
551Q8—1222no—
552Q8—1222no—
553Q8—2442no—
554Q8—2442no—
555Q8—2442no—
556Q8—2442no—
557Q8—2444no—
558Q8—2444no—
559Q8—2442no—
560D4—1222no—
561D4—1222no—
562D4—2442no—
563D4—2442no—
564D4—2444no—
565D4—2442no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—44no—
571C2×C4—42no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4—1224no—
575C2×C4—1224no—
576C2×C4—1222no—
577C2×C4—1224no—
578C2×C4—1224no—
579C2×C4—2442no—
580C2×C4—2448no—
581C2×C4—2442no—
582C2×C4—2444no—
583C2×C4—2444no—
584C2×C4—2442no—
585C2×C4—2442no—
586C2×C4—2442no—
587C2×C4—2444no—
588C2×C4#1451974511yescharacteristic
589C2×C4#1451974511yescharacteristic
590C2×C4#1451975112yes—
591C2×C4#1451975112yes—
592C2×C4#1451975212yes—
593C2×C4#1451975212yes—
594C2×C4#1451975212yes—
595C2×C4#1451976212yes—
596C2×C4#1451976212yes—
597C2×C4#1451976212yes—
598C2×C4#1451976612yes—
599C2×C4#1451976612yes—
600C2×C4C2×D4×D6111yescharacteristic
601C2×C4C22×C22⋊D6111yescharacteristic
602C2×C4C22×D24411yescharacteristic
603C2×C4C2×#1175822211yescharacteristic
604C2×C4C2×#1175822611yescharacteristic
605C2×C4C2×#1175822611yescharacteristic
606C8—24no—
607C8—2442no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—24no—
613C22—24no—
614C22—4884no—
615C22—2442no—
616C22—2442no—
617C22—2442no—
618C22#1683967912yes—
619C22#1683967912yes—
620C22#1683993312yes—
621C22#1683994312yes—
622C22C2×#1451974511yescharacteristic
623C22C2×#1451975211yescharacteristic
624C22C2×#1451976211yescharacteristic
625C4—42no—
626C4—42no—
627C4—82no—
628C4—2444no—
629C4—2444no—
630C4—2442no—
631C4#1683967912yes—
632C4#1683967912yes—
633C4C2×#1451975111yescharacteristic
634C4C2×#1451975211yescharacteristic
635C4C2×#1451976211yescharacteristic
636C4C2×#1451976611yescharacteristic
637C2—21no—
638C2—21no—
639C2—22no—
640C2—4882no—
641C2#2144703814yesdirect product factor
642C2C2×#1683967911yescharacteristic
643C2C2×#1683993311yescharacteristic
644C2C2×#1683994311yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#428C2
socleC23×C61#120
prime radicalC22×#11758222C22
hypercenterC2×#428D61
hypocenterC61C2×#2038
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
4. C22×#14519695C2semidirect
5. C2×#16839667C2semidirect
6. #21447038C2direct (N × H)
7. C2×#16839521C2semidirect
8. C2×C61×#428C2semidirect
29. C2×#14519695C22semidirect
31. #16839667C22semidirect
33. #16839521C22semidirect
38. C61×#428C22semidirect
316. C2×#428D61semidirect
326. C2×C61#2038semidirect
348. #428C2×D61semidirect
363. C61C2×#2038semidirect
641. C2#21447038direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403382
C22×#145197032
C2×#168397612
C22×#145196952
C2×#168396672
#214470382
C2×#168395212
C2×C61×#4282
C2×#203861