Finite Group Databasebeta

← C2×#21447034 #29707604

Subgroups — C2×#21447034 #29707604

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×#16840333C211yesmaximal, characteristic
2C2×#16839802C211yesmaximal, characteristic, complemented
3C22×#14519704C211yesmaximal, characteristic
4C22×#14519695C211yesmaximal, characteristic, complemented
5C2×#16839667C211yesmaximal, characteristic, complemented
6#21447034C218yesmaximal, direct product factor
7C2×#16839523C211yesmaximal, characteristic, complemented
8C2×C61×#417C211yesmaximal, characteristic
9C23×Dic122C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11#16840333—22no—
12#16840333—22no—
13#16840333—22no—
14#16840333C2214yes—
15C2×#14519775—21no—
16C2×#14519764—21no—
17C2×#14519758—22no—
18C2×#14519756—21no—
19C2×#14519756—21no—
20C2×#14519736C2211yescharacteristic
21C22×C4×Dic61C2211yescharacteristic
22#16839802—22no—
23#16839802C2214yescomplemented
24C2×#14519710—21no—
25C2×#14519708—21no—
26C2×#14519704—24no—
27C2×#14519704C2214yes—
28C2×#14519695—24no—
29C2×#14519695C2214yescomplemented
30#16839667—22no—
31#16839667C2214yescomplemented
32C2×#14519684—22no—
33#16839523C2214yescomplemented
34C22×#41×C61C2211yescharacteristic
35C22×M16×C61C2211yescharacteristic
36C22×C4⋊C4×C61C2211yescharacteristic
37C61×#417—22no—
38C61×#417C2214yes—
39C2×#103×C61—21no—
40C2×#102×C61—21no—
41C22×Dic122—22no—
42C22×Dic122—21no—
43C22×Dic122—21no—
44C22×Dic122—21no—
45C22×Dic122—21no—
46C22×Dic122—22no—
47C22×Dic122—22no—
48C22×Dic122—22no—
49C22×Dic122D412yes—
50C22×Dic122C2312yes—
51C23×Dic61—21no—
52C23×Dic61D412yes—
53C2×#11758194—21no—
54C2×#11758194—22no—
55C2×#11758194D414yes—
56C2×#11758194C2312yes—
57C22×#92418—21no—
58#14519775—24no—
59#14519775—24no—
60#14519764—24no—
61#14519764—24no—
62#14519758—28no—
63#14519758—28no—
64#14519756—24no—
65#14519756—24no—
66#14519756—24no—
67#14519756—24no—
68#14519736—21no—
69#14519736—21no—
70#14519736D412yes—
71#14519736C2312yes—
72C2×C4⋊Dic61D411yescharacteristic
73C2×C4⋊Dic61D411yescharacteristic
74C2×#11758196—22no—
75C2×#11758196—22no—
76C2×C22⋊Dic61—22no—
77C2×C22⋊Dic61—22no—
78C2×C22⋊Dic61—21no—
79C2×C4×Dic61—21no—
80C2×C4×Dic61—22no—
81C2×C4×Dic61—22no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61C2312yes—
84#14519710—24no—
85#14519708—24no—
86#14519704—28no—
87#14519695—28no—
88#14519684—28no—
89C2×#41×C61—21no—
90C2×#41×C61—21no—
91C2×#41×C61—22no—
92C2×#41×C61—22no—
93C2×#41×C61—22no—
94C2×#41×C61—22no—
95C2×#41×C61D412yes—
96C2×#41×C61C2312yes—
97C22×Q8×C61D411yescharacteristic
98C22×D4×C61—21no—
99C22×D4×C61D411yescharacteristic
100C23×C4×C61—21no—
101C23×C4×C61—21no—
102C23×C4×C61C2311yescharacteristic
103C2×M16×C61—21no—
104C2×M16×C61—22no—
105C2×M16×C61—22no—
106C2×M16×C61C2312yes—
107C22×C8×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61C2312yes—
114#103×C61—24no—
115#102×C61—24no—
116C24×C61—21no—
117C24×C61C2×D411yescharacteristic
118#41×C61—24no—
119#41×C61—24no—
120#41×C61—22no—
121#41×C61—22no—
122#41×C61—22no—
123#41×C61—22no—
124#41×C61—42no—
125#41×C61—42no—
126#41×C61—42no—
127#41×C61—42no—
128C2×Q8×C61—21no—
129C2×Q8×C61—22no—
130C2×Q8×C61—22no—
131C2×Q8×C61C2×D412yes—
132C2×D4×C61—22no—
133C2×D4×C61—22no—
134C2×D4×C61—21no—
135C2×D4×C61—22no—
136C2×D4×C61—22no—
137C2×D4×C61—42no—
138C2×D4×C61—42no—
139C2×D4×C61C2×D412yes—
140C22×C4×C61—21no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—42no—
145C22×C4×C61—42no—
146C22×C4×C61—44no—
147C22×C4×C61—41no—
148C22×C4×C61—41no—
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D412yes—
155C22×C4×C61#4112yes—
156C22×C4×C61#4112yes—
157C22×C4×C61#4112yes—
158C22×C4×C61C2411yescharacteristic
159C22×Dic61—24no—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—24no—
165C22×Dic61—24no—
166C22×Dic61—22no—
167C22×Dic61—42no—
168C22×Dic61—42no—
169C22×Dic61C2×D414yes—
170C2×Dic122—22no—
171C2×Dic122—22no—
172C2×Dic122—24no—
173C2×Dic122—24no—
174C2×Dic122—22no—
175C2×Dic122—22no—
176C2×Dic122—22no—
177C2×Dic122—22no—
178C2×Dic122—22no—
179C2×Dic122—22no—
180C2×Dic122—42no—
181C2×Dic122—42no—
182C2×Dic122—42no—
183C2×Dic122—42no—
184C2×Dic122—42no—
185C2×Dic122—42no—
186C2×Dic122—42no—
187C2×Dic122—42no—
188M16×C61—22no—
189M16×C61—22no—
190M16×C61—42no—
191C2×C8×C61—22no—
192C2×C8×C61—42no—
193C4⋊C4×C61—22no—
194C4⋊C4×C61—22no—
195C4⋊C4×C61—41no—
196C4⋊C4×C61—41no—
197C22⋊Dic61—28no—
198C22⋊Dic61—28no—
199C22⋊Dic61—22no—
200C22⋊Dic61—22no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61C2×D412yes—
204C4⋊Dic61C2×D412yes—
205#11758196—28no—
206#11758196—28no—
207C4×Dic61—22no—
208C4×Dic61—22no—
209C4×Dic61—22no—
210C4×Dic61—22no—
211C4×Dic61—42no—
212#11758194—24no—
213#11758194—22no—
214#11758194C2×D414yes—
215C2×#92418—24no—
216C2×#92418—22no—
217C23×C61—22no—
218C23×C61—22no—
219C23×C61—22no—
220C23×C61—42no—
221C23×C61—42no—
222C23×C61—42no—
223C23×C61#12011yescharacteristic
224C23×C61#12011yescharacteristic
225C23×C61#12112yes—
226C23×C61#12312yes—
227C23×C61C22×D411yescharacteristic
228Q8×C61—22no—
229Q8×C61—22no—
230Q8×C61—42no—
231D4×C61—22no—
232D4×C61—22no—
233D4×C61—42no—
234D4×C61—42no—
235D4×C61—44no—
236D4×C61—42no—
237C2×C4×C61—22no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—44no—
242C2×C4×C61—44no—
243C2×C4×C61—42no—
244C2×C4×C61—82no—
245C2×C4×C61—82no—
246C2×C4×C61#12011yescharacteristic
247C2×C4×C61#12011yescharacteristic
248C2×C4×C61#12112yes—
249C2×C4×C61#12112yes—
250C2×C4×C61#12112yes—
251C2×C4×C61#12112yes—
252C2×C4×C61#12112yes—
253C2×C4×C61#12312yes—
254C2×C4×C61#12312yes—
255C2×C4×C61#12312yes—
256C2×C4×C61#12412yes—
257C2×C4×C61#12412yes—
258C2×C4×C61C22×D411yescharacteristic
259C2×C4×C61C22×D411yescharacteristic
260C2×C4×C61C22×D411yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C2×C4×C61C2×#4111yescharacteristic
264C2×Dic61—24no—
265C2×Dic61—22no—
266C2×Dic61—22no—
267C2×Dic61—24no—
268C2×Dic61—24no—
269C2×Dic61—24no—
270C2×Dic61—42no—
271C2×Dic61—48no—
272C2×Dic61—42no—
273C2×Dic61—44no—
274C2×Dic61—44no—
275C2×Dic61—42no—
276C2×Dic61—42no—
277Dic122—42no—
278Dic122—42no—
279Dic122—42no—
280Dic122—42no—
281Dic122—44no—
282Dic122—44no—
283C8×C61—42no—
284#92418—24no—
285C2×#2038—611nomaximal, Sylow
286C22×C61—21no—
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—21no—
290C22×C61—24no—
291C22×C61—24no—
292C22×C61—42no—
293C22×C61—42no—
294C22×C61—42no—
295C22×C61—84no—
296C22×C61#39412yes—
297C22×C61#39412yes—
298C22×C61#45412yes—
299C22×C61#45612yes—
300C22×C61C2×#12011yescharacteristic
301C22×C61C2×#12111yescharacteristic
302C22×C61C2×#12311yescharacteristic
303C4×C61—42no—
304C4×C61—82no—
305C4×C61#39412yes—
306C4×C61#39412yes—
307C4×C61C2×#12111yescharacteristic
308C4×C61C2×#12111yescharacteristic
309C4×C61C2×#12311yescharacteristic
310C4×C61C2×#12411yescharacteristic
311Dic61—44no—
312Dic61—44no—
313Dic61—42no—
314Dic61—42no—
315C2×#536—611no—
316C2×#428—611no—
317C22×#104—611no—
318C2×#417D6111yescharacteristic
319C22×#101—611no—
320C2×#391—611no—
321#2038—618no—
322C2×#339—611no—
323C2×C61—21no—
324C2×C61—21no—
325C2×C61—22no—
326C2×C61—82no—
327C2×C61#203814yescomplemented
328C2×C61C2×#39411yescharacteristic
329C2×C61C2×#45411yescharacteristic
330C2×C61C2×#45611yescharacteristic
331C22×#41C2×D6111yescharacteristic
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×#117—611no—
345C22×C4⋊C4C2×D6111yescharacteristic
346C22×C42—611no—
347#428—614no—
348#428—1222no—
349C2×#107—1221no—
350C2×#106—1221no—
351C2×#104—614no—
352C2×#104—1224no—
353#417—22no—
354#417C2×D6114yes—
355C2×#103—21no—
356C2×#102—21no—
357C2×#101—614no—
358C2×#101—1224no—
359#391—614no—
360#391—1222no—
361C2×#95—1222no—
362#339—614no—
363C61C2×#203811yescharacteristic, complemented, Sylow
364C2×#41—21no—
365C2×#41—21no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—22no—
369C2×#41—22no—
370C2×#41C22⋊D6112yes—
371C2×#41C22×D6112yes—
372C22×Q8—612no—
373C22×Q8—612no—
374C22×Q8—1222no—
375C22×Q8—1222no—
376C22×Q8—1221no—
377C22×Q8—1221no—
378C22×Q8—1222no—
379C22×Q8—1222no—
380C22×Q8—1221no—
381C22×Q8—1221no—
382C22×Q8C22⋊D6111yescharacteristic
383C22×D4—21no—
384C22×D4C22⋊D6111yescharacteristic
385C23×C4—21no—
386C23×C4—21no—
387C23×C4—612no—
388C23×C4—1221no—
389C23×C4C22×D6111yescharacteristic
390C2×M16—21no—
391C2×M16—22no—
392C2×M16—22no—
393C2×M16—614no—
394C2×M16—612no—
395C2×M16—1222no—
396C2×M16—1221no—
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—612no—
411#117—612no—
412#117—1221no—
413#117—1221no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—1222no—
422C2×C4⋊C4—1222no—
423C2×C4⋊C4C22×D6112yes—
424C2×C22⋊C4—1222no—
425C2×C22⋊C4—1222no—
426C2×C22⋊C4—1221no—
427C2×C42—612no—
428C2×C42—1221no—
429C2×C42—1222no—
430C2×C42—1222no—
431C2×C42—1221no—
432#107—1224no—
433#106—1224no—
434#104—1228no—
435#103—24no—
436#102—24no—
437#101—1228no—
438#95—1228no—
439C24—21no—
440C24D4×D6111yescharacteristic
441#41—22no—
442#41—22no—
443#41—22no—
444#41—22no—
445#41—24no—
446#41—24no—
447#41—42no—
448#41—42no—
449#41—42no—
450#41—42no—
451C2×Q8—21no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—1222no—
455C2×Q8—1222no—
456C2×Q8—1222no—
457C2×Q8—1222no—
458C2×Q8—1222no—
459C2×Q8—1222no—
460C2×Q8—1222no—
461C2×Q8—1222no—
462C2×Q8—1224no—
463C2×Q8—1224no—
464C2×Q8—2442no—
465C2×Q8—2442no—
466C2×Q8—2442no—
467C2×Q8—2442no—
468C2×Q8—2442no—
469C2×Q8—2442no—
470C2×Q8—2442no—
471C2×Q8—2442no—
472C2×Q8C2×C22⋊D6112yes—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—21no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4C2×C22⋊D6112yes—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—44no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—614no—
491C22×C4—1224no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—1221no—
495C22×C4—1221no—
496C22×C4—1222no—
497C22×C4—1224no—
498C22×C4—1224no—
499C22×C4—2442no—
500C22×C4—2442no—
501C22×C4#1175822212yes—
502C22×C4#1175822212yes—
503C22×C4D4×D6111yescharacteristic
504C22×C4D4×D6111yescharacteristic
505C22×C4D4×D6112yes—
506C22×C4D4×D6111yescharacteristic
507C22×C4#1175822412yes—
508C22×C4C2×C22⋊D6111yescharacteristic
509C22×C4C2×C22⋊D6111yescharacteristic
510C22×C4C23×D6111yescharacteristic
511M16—22no—
512M16—22no—
513M16—42no—
514M16—614no—
515M16—1222no—
516M16—1224no—
517C2×C8—22no—
518C2×C8—42no—
519C2×C8—1222no—
520C2×C8—1224no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—612no—
526C4⋊C4—612no—
527C4⋊C4—1228no—
528C4⋊C4—1228no—
529C4⋊C4—1221no—
530C4⋊C4—1221no—
531C22⋊C4—1228no—
532C22⋊C4—1228no—
533C22⋊C4—1222no—
534C22⋊C4—1222no—
535C42—1222no—
536C42—1222no—
537C42—1222no—
538C42—1222no—
539C42—2442no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23#1451974511yescharacteristic
547C23#1451974511yescharacteristic
548C23#1451975012yes—
549C23#1451975912yes—
550C23C2×D4×D6111yescharacteristic
551Q8—22no—
552Q8—22no—
553Q8—42no—
554Q8—2442no—
555Q8—2442no—
556Q8—2442no—
557Q8—2442no—
558Q8—2444no—
559Q8—2444no—
560D4—22no—
561D4—22no—
562D4—42no—
563D4—42no—
564D4—44no—
565D4—42no—
566C2×C4—22no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—44no—
571C2×C4—44no—
572C2×C4—42no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4—1224no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1224no—
579C2×C4—1224no—
580C2×C4—1224no—
581C2×C4—2442no—
582C2×C4—2448no—
583C2×C4—2442no—
584C2×C4—2442no—
585C2×C4—2444no—
586C2×C4—2444no—
587C2×C4—2442no—
588C2×C4#1451974511yescharacteristic
589C2×C4#1451974511yescharacteristic
590C2×C4#1451974912yes—
591C2×C4#1451974912yes—
592C2×C4#1451975012yes—
593C2×C4#1451975012yes—
594C2×C4#1451975012yes—
595C2×C4#1451975912yes—
596C2×C4#1451976012yes—
597C2×C4#1451976012yes—
598C2×C4#1451976312yes—
599C2×C4#1451976312yes—
600C2×C4C2×D4×D6111yescharacteristic
601C2×C4C2×D4×D6111yescharacteristic
602C2×C4C22×C22⋊D6111yescharacteristic
603C2×C4C2×#1175822411yescharacteristic
604C2×C4C2×#1175822211yescharacteristic
605C2×C4C2×#1175822211yescharacteristic
606C8—42no—
607C8—1224no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—24no—
613C22—24no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—84no—
618C22#1683967712yes—
619C22#1683967712yes—
620C22#1683993312yes—
621C22#1683994312yes—
622C22C2×#1451974511yescharacteristic
623C22C2×#1451975011yescharacteristic
624C22C2×#1451975911yescharacteristic
625C4—42no—
626C4—82no—
627C4—2444no—
628C4—2442no—
629C4—2442no—
630C4—2444no—
631C4#1683967712yes—
632C4#1683967712yes—
633C4C2×#1451974911yescharacteristic
634C4C2×#1451975011yescharacteristic
635C4C2×#1451976011yescharacteristic
636C4C2×#1451976311yescharacteristic
637C2—21no—
638C2—21no—
639C2—22no—
640C2—82no—
641C2#2144703414yesdirect product factor
642C2C2×#1683967711yescharacteristic
643C2C2×#1683993311yescharacteristic
644C2C2×#1683994311yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#417C2
socleC23×C61#120
prime radicalC22×#41×C61C22
hypercenterC2×#417D61
hypocenterC61C2×#2038
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#16839802C2semidirect
4. C22×#14519695C2semidirect
5. C2×#16839667C2semidirect
6. #21447034C2direct (N × H)
7. C2×#16839523C2semidirect
23. #16839802C22semidirect
29. C2×#14519695C22semidirect
31. #16839667C22semidirect
33. #16839523C22semidirect
327. C2×C61#2038semidirect
363. C61C2×#2038semidirect
641. C2#21447034direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403332
C2×#168398022
C22×#145197042
C22×#145196952
C2×#168396672
#214470342
C2×#168395232
C2×C61×#4172
C2×#203861