Finite Group Databasebeta

← C2×#21446852 #29706910

Subgroups — C2×#21446852 #29706910

Order 15616.

1998 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840333C211yesmaximal, characteristic
2C22×#14519775C211yesmaximal, characteristic, complemented
3C22×#14519704C211yesmaximal, characteristic
4C2×#16839771C211yesmaximal, characteristic, complemented
5C22×#14519695C211yesmaximal, characteristic, complemented
6#21446852C218yesmaximal, direct product factor
7C2×#16839523C211yesmaximal, characteristic, complemented
8C22×#137×C61C211yesmaximal, characteristic
9C23×Dic122C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11#16840333—22no—
12#16840333—22no—
13#16840333—22no—
14#16840333C2214yes—
15C2×#14519775—24no—
16C2×#14519775—24no—
17C2×#14519775—21no—
18C2×#14519775—22no—
19C2×#14519775C2214yescomplemented
20C2×#14519764—21no—
21C2×#14519758—22no—
22C2×#14519756—22no—
23C2×#14519736C2211yescharacteristic
24C22×#11758196—22no—
25C22×C4×Dic61C2211yescharacteristic
26C2×#14519704—24no—
27C2×#14519704C2214yes—
28#16839771—22no—
29#16839771C2214yescomplemented
30C2×#14519701—22no—
31C2×#14519695—24no—
32C2×#14519695C2214yescomplemented
33#16839523C2214yescomplemented
34C22×#41×C61C2211yescharacteristic
35C23×Q8×C61C2211yescharacteristic
36C2×#137×C61—22no—
37C2×#137×C61—24no—
38C2×#137×C61—24no—
39C2×#137×C61C2214yes—
40C22×Q16×C61—21no—
41C22×SD16×C61—21no—
42C22×M16×C61C2211yescharacteristic
43C22×Dic122—22no—
44C22×Dic122—21no—
45C22×Dic122—21no—
46C22×Dic122—22no—
47C22×Dic122—22no—
48C22×Dic122—21no—
49C22×Dic122—21no—
50C22×Dic122—22no—
51C22×Dic122D412yes—
52C22×Dic122C2312yes—
53C23×Dic61—21no—
54C23×Dic61D412yes—
55C2×#11758194—21no—
56C2×#11758194—22no—
57C2×#11758194—22no—
58C2×#11758194C2312yes—
59C22×#92418—21no—
60#14519775—216no—
61#14519775—24no—
62#14519775—28no—
63#14519775—24no—
64#14519775—28no—
65#14519764—24no—
66#14519764—24no—
67#14519758—28no—
68#14519758—28no—
69#14519756—28no—
70#14519756—28no—
71#14519736—21no—
72#14519736—21no—
73#14519736D412yes—
74#14519736C2312yes—
75C2×C4⋊Dic61D412yes—
76C2×#11758196—216no—
77C2×#11758196—24no—
78C2×#11758196—28no—
79C2×C22⋊Dic61—24no—
80C2×C22⋊Dic61—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61—22no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61D414yes—
85C2×C4×Dic61C2312yes—
86#14519704—28no—
87#14519701—28no—
88#14519695—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×C61—22no—
98C22×Q8×C61—21no—
99C22×Q8×C61—21no—
100C22×Q8×C61—21no—
101C22×Q8×C61—22no—
102C22×Q8×C61—21no—
103C22×Q8×C61—21no—
104C22×Q8×C61—22no—
105C22×Q8×C61D411yescharacteristic
106C22×Q8×C61D414yes—
107C22×Q8×C61C2312yes—
108C22×D4×C61—21no—
109C22×D4×C61D411yescharacteristic
110C23×C4×C61—21no—
111C23×C4×C61—21no—
112C23×C4×C61C2311yescharacteristic
113#137×C61—216no—
114#137×C61—28no—
115#137×C61—28no—
116C2×Q16×C61—28no—
117C2×Q16×C61—24no—
118C2×SD16×C61—28no—
119C2×SD16×C61—24no—
120C2×M16×C61—22no—
121C2×M16×C61—21no—
122C2×M16×C61D414yes—
123C2×M16×C61C2312yes—
124C22×C8×C61—21no—
125C24×C61—21no—
126C24×C61C2×D411yescharacteristic
127#41×C61—24no—
128#41×C61—24no—
129#41×C61—22no—
130#41×C61—22no—
131#41×C61—22no—
132#41×C61—22no—
133#41×C61—42no—
134#41×C61—42no—
135#41×C61—42no—
136#41×C61—42no—
137C2×Q8×C61—24no—
138C2×Q8×C61—21no—
139C2×Q8×C61—22no—
140C2×Q8×C61—24no—
141C2×Q8×C61—22no—
142C2×Q8×C61—24no—
143C2×Q8×C61—24no—
144C2×Q8×C61—24no—
145C2×Q8×C61—22no—
146C2×Q8×C61—22no—
147C2×Q8×C61—22no—
148C2×Q8×C61—22no—
149C2×Q8×C61—22no—
150C2×Q8×C61—41no—
151C2×Q8×C61—41no—
152C2×Q8×C61—42no—
153C2×Q8×C61—42no—
154C2×Q8×C61—42no—
155C2×Q8×C61—42no—
156C2×Q8×C61—42no—
157C2×Q8×C61C2×D412yes—
158C2×Q8×C61C2×D414yes—
159C2×D4×C61—22no—
160C2×D4×C61—22no—
161C2×D4×C61—22no—
162C2×D4×C61—21no—
163C2×D4×C61—22no—
164C2×D4×C61—42no—
165C2×D4×C61—42no—
166C2×D4×C61C2×D412yes—
167C22×C4×C61—21no—
168C22×C4×C61—24no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—41no—
173C22×C4×C61—41no—
174C22×C4×C61—42no—
175C22×C4×C61—42no—
176C22×C4×C61—42no—
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D412yes—
181C22×C4×C61C2×D412yes—
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D412yes—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61#4112yes—
186C22×C4×C61C2411yescharacteristic
187C22×Dic61—28no—
188C22×Dic61—24no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—24no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—24no—
195C22×Dic61C2×D414yes—
196C2×Dic122—22no—
197C2×Dic122—22no—
198C2×Dic122—24no—
199C2×Dic122—24no—
200C2×Dic122—22no—
201C2×Dic122—22no—
202C2×Dic122—22no—
203C2×Dic122—22no—
204C2×Dic122—22no—
205C2×Dic122—22no—
206C2×Dic122—42no—
207C2×Dic122—42no—
208C2×Dic122—42no—
209C2×Dic122—42no—
210C2×Dic122—42no—
211C2×Dic122—42no—
212C2×Dic122—42no—
213C2×Dic122—42no—
214Q16×C61—216no—
215SD16×C61—216no—
216M16×C61—24no—
217M16×C61—22no—
218M16×C61C2×D414yes—
219C2×C8×C61—24no—
220C2×C8×C61—22no—
221C22⋊Dic61—216no—
222C22⋊Dic61—22no—
223C22⋊Dic61—22no—
224C4⋊Dic61—22no—
225C4⋊Dic61C2×D414yes—
226#11758196—232no—
227#11758196—216no—
228C4×Dic61—24no—
229C4×Dic61—22no—
230C4×Dic61—22no—
231C4×Dic61—22no—
232C4×Dic61C2×D414yes—
233#11758194—22no—
234#11758194—22no—
235#11758194—42no—
236C2×#92418—22no—
237C2×#92418—42no—
238C23×C61—24no—
239C23×C61—22no—
240C23×C61—42no—
241C23×C61—44no—
242C23×C61#12011yescharacteristic
243C23×C61#12012yes—
244C23×C61#12011yescharacteristic
245C23×C61#12112yes—
246C23×C61C22×D411yescharacteristic
247Q8×C61—24no—
248Q8×C61—22no—
249Q8×C61—24no—
250Q8×C61—22no—
251Q8×C61—42no—
252Q8×C61—42no—
253Q8×C61—44no—
254Q8×C61—44no—
255Q8×C61—42no—
256D4×C61—22no—
257D4×C61—22no—
258D4×C61—42no—
259D4×C61—42no—
260D4×C61—44no—
261D4×C61—42no—
262C2×C4×C61—22no—
263C2×C4×C61—24no—
264C2×C4×C61—42no—
265C2×C4×C61—42no—
266C2×C4×C61—42no—
267C2×C4×C61—44no—
268C2×C4×C61—44no—
269C2×C4×C61—42no—
270C2×C4×C61—42no—
271C2×C4×C61—44no—
272C2×C4×C61#12012yes—
273C2×C4×C61#12012yes—
274C2×C4×C61#12011yescharacteristic
275C2×C4×C61#12012yes—
276C2×C4×C61#12011yescharacteristic
277C2×C4×C61#12112yes—
278C2×C4×C61#12112yes—
279C2×C4×C61#12112yes—
280C2×C4×C61#12112yes—
281C2×C4×C61#12112yes—
282C2×C4×C61#12712yes—
283C2×C4×C61#12712yes—
284C2×C4×C61C22×D411yescharacteristic
285C2×C4×C61C22×D411yescharacteristic
286C2×C4×C61C22×D411yescharacteristic
287C2×C4×C61C22×D411yescharacteristic
288C2×C4×C61C22×D411yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×Dic61—28no—
291C2×Dic61—216no—
292C2×Dic61—24no—
293C2×Dic61—24no—
294C2×Dic61—24no—
295C2×Dic61—24no—
296C2×Dic61—24no—
297C2×Dic61—44no—
298C2×Dic61—44no—
299C2×Dic61—44no—
300Dic122—42no—
301Dic122—42no—
302Dic122—42no—
303Dic122—42no—
304Dic122—44no—
305Dic122—44no—
306C8×C61—24no—
307#92418—42no—
308C2×#2005—611nomaximal, Sylow
309C22×C61—22no—
310C22×C61—22no—
311C22×C61—24no—
312C22×C61—24no—
313C22×C61—42no—
314C22×C61—44no—
315C22×C61—84no—
316C22×C61#39212yes—
317C22×C61#39212yes—
318C22×C61#45614yes—
319C22×C61C2×#12011yescharacteristic
320C22×C61C2×#12011yescharacteristic
321C22×C61C2×#12111yescharacteristic
322C4×C61—42no—
323C4×C61—44no—
324C4×C61#39212yes—
325C4×C61#39212yes—
326C4×C61C2×#12011yescharacteristic
327C4×C61C2×#12111yescharacteristic
328C4×C61C2×#12111yescharacteristic
329C4×C61C2×#12711yescharacteristic
330Dic61—28no—
331Dic61—44no—
332Dic61—44no—
333C22×#137D6111yescharacteristic
334C2×#536—611no—
335C22×C4⋊Q8—611no—
336C22×#104—611no—
337C2×#419—611no—
338C22×#101—611no—
339#2005—618no—
340C2×#339—611no—
341C2×C61—21no—
342C2×C61—21no—
343C2×C61—22no—
344C2×C61—82no—
345C2×C61#200514yescomplemented
346C2×C61C2×#39211yescharacteristic
347C2×C61C2×#45612yes—
348C22×#41C2×D6111yescharacteristic
349C23×Q8—611no—
350C23×Q8C2×D6111yescharacteristic
351C2×#137—22no—
352C2×#137—24no—
353C2×#137—24no—
354C2×#137C2×D6114yes—
355C22×Q16—21no—
356C22×SD16—21no—
357C22×M16—611no—
358C22×M16C2×D6111yescharacteristic
359#536—614no—
360#536—1222no—
361#536—1222no—
362#536—1222no—
363C2×C4⋊Q8—614no—
364C2×C4⋊Q8—1224no—
365C2×C4⋊Q8—1222no—
366C2×C4⋊Q8—1224no—
367C2×C4⋊Q8—1221no—
368C2×#124—1221no—
369C2×#123—1222no—
370C2×C22⋊Q8—1222no—
371C2×#117—611no—
372C22×C4⋊C4—1222no—
373C22×C42—611no—
374C2×#104—614no—
375C2×#104—1224no—
376#419—614no—
377#419—1222no—
378C2×#103—1222no—
379C2×#101—614no—
380C2×#101—1224no—
381#339—614no—
382C61C2×#200511yescharacteristic, complemented, Sylow
383C2×#41—21no—
384C2×#41—21no—
385C2×#41—22no—
386C2×#41—22no—
387C2×#41—22no—
388C2×#41—22no—
389C2×#41C22⋊D6112yes—
390C2×#41C22×D6112yes—
391C22×Q8—21no—
392C22×Q8—22no—
393C22×Q8—21no—
394C22×Q8—21no—
395C22×Q8—22no—
396C22×Q8—21no—
397C22×Q8—21no—
398C22×Q8—22no—
399C22×Q8—612no—
400C22×Q8—612no—
401C22×Q8—1221no—
402C22×Q8—1222no—
403C22×Q8—1221no—
404C22×Q8—1222no—
405C22×Q8—1221no—
406C22×Q8—1222no—
407C22×Q8—1221no—
408C22×Q8—1222no—
409C22×Q8C22⋊D6111yescharacteristic
410C22×Q8C22⋊D6114yes—
411C22×Q8C22×D6112yes—
412C22×D4—21no—
413C22×D4C22⋊D6111yescharacteristic
414C23×C4—21no—
415C23×C4—21no—
416C23×C4—612no—
417C23×C4—1221no—
418C23×C4C22×D6111yescharacteristic
419#137—216no—
420#137—28no—
421#137—28no—
422C2×Q16—28no—
423C2×Q16—24no—
424C2×SD16—28no—
425C2×SD16—24no—
426C2×M16—21no—
427C2×M16—22no—
428C2×M16—612no—
429C2×M16—1221no—
430C2×M16—1222no—
431C2×M16—1222no—
432C2×M16C22⋊D6114yes—
433C2×M16C22×D6112yes—
434C22×C8—21no—
435C22×C8—1221no—
436C4⋊Q8—1228no—
437C4⋊Q8—12216no—
438C4⋊Q8—1224no—
439C4⋊Q8—1228no—
440C4⋊Q8—1224no—
441#124—1224no—
442#124—1224no—
443#123—1228no—
444#123—1228no—
445C22⋊Q8—1228no—
446C22⋊Q8—1228no—
447#117—612no—
448#117—612no—
449#117—1221no—
450#117—1221no—
451C2×C4⋊C4—612no—
452C2×C4⋊C4—1228no—
453C2×C4⋊C4—12216no—
454C2×C4⋊C4—1224no—
455C2×C22⋊C4—1224no—
456C2×C22⋊C4—1221no—
457C2×C42—614no—
458C2×C42—612no—
459C2×C42—1221no—
460C2×C42—1221no—
461C2×C42—1222no—
462#104—1228no—
463#103—1228no—
464#101—1228no—
465C24—21no—
466C24D4×D6111yescharacteristic
467#41—22no—
468#41—22no—
469#41—22no—
470#41—22no—
471#41—24no—
472#41—24no—
473#41—42no—
474#41—42no—
475#41—42no—
476#41—42no—
477C2×Q8—22no—
478C2×Q8—24no—
479C2×Q8—21no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—24no—
485C2×Q8—22no—
486C2×Q8—24no—
487C2×Q8—24no—
488C2×Q8—24no—
489C2×Q8—22no—
490C2×Q8—41no—
491C2×Q8—41no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8—1222no—
498C2×Q8—1222no—
499C2×Q8—1222no—
500C2×Q8—1222no—
501C2×Q8—1222no—
502C2×Q8—1222no—
503C2×Q8—1222no—
504C2×Q8—1222no—
505C2×Q8—1224no—
506C2×Q8—1224no—
507C2×Q8—2442no—
508C2×Q8—2442no—
509C2×Q8—2442no—
510C2×Q8—2442no—
511C2×Q8—2442no—
512C2×Q8—2442no—
513C2×Q8—2442no—
514C2×Q8—2442no—
515C2×Q8C2×C22⋊D6112yes—
516C2×Q8C2×C22⋊D6114yes—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—21no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4C2×C22⋊D6112yes—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—614no—
536C22×C4—1228no—
537C22×C4—1222no—
538C22×C4—1224no—
539C22×C4—1224no—
540C22×C4—1222no—
541C22×C4—1222no—
542C22×C4—1222no—
543C22×C4—1224no—
544C22×C4D4×D6112yes—
545C22×C4D4×D6111yescharacteristic
546C22×C4D4×D6111yescharacteristic
547C22×C4D4×D6111yescharacteristic
548C22×C4#1175822412yes—
549C22×C4C2×C22⋊D6112yes—
550C22×C4C2×C22⋊D6111yescharacteristic
551C22×C4C2×C22⋊D6111yescharacteristic
552C22×C4C2×C22⋊D6112yes—
553C22×C4C23×D6111yescharacteristic
554Q16—216no—
555SD16—216no—
556M16—22no—
557M16—24no—
558M16—1222no—
559M16—1222no—
560M16—2442no—
561M16C2×C22⋊D6114yes—
562C2×C8—22no—
563C2×C8—24no—
564C2×C8—1222no—
565C2×C8—2442no—
566C4⋊C4—614no—
567C4⋊C4—12232no—
568C4⋊C4—12216no—
569C4⋊C4—1222no—
570C22⋊C4—12216no—
571C22⋊C4—1222no—
572C22⋊C4—1222no—
573C42—614no—
574C42—1222no—
575C42—1222no—
576C42—1224no—
577C42—1222no—
578C23—24no—
579C23—22no—
580C23—44no—
581C23—42no—
582C23#1451974511yescharacteristic
583C23#1451974512yes—
584C23#1451974511yescharacteristic
585C23#1451974812yes—
586C23C2×D4×D6111yescharacteristic
587Q8—24no—
588Q8—22no—
589Q8—24no—
590Q8—22no—
591Q8—42no—
592Q8—42no—
593Q8—44no—
594Q8—44no—
595Q8—42no—
596Q8—2442no—
597Q8—2442no—
598Q8—2442no—
599Q8—2442no—
600Q8—2444no—
601Q8—2444no—
602D4—22no—
603D4—22no—
604D4—42no—
605D4—42no—
606D4—44no—
607D4—42no—
608C2×C4—22no—
609C2×C4—24no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—44no—
614C2×C4—44no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—44no—
618C2×C4—1228no—
619C2×C4—12216no—
620C2×C4—1224no—
621C2×C4—1224no—
622C2×C4—1224no—
623C2×C4—1224no—
624C2×C4—1224no—
625C2×C4—2444no—
626C2×C4—2444no—
627C2×C4—2444no—
628C2×C4#1451974511yescharacteristic
629C2×C4#1451974512yes—
630C2×C4#1451974511yescharacteristic
631C2×C4#1451974612yes—
632C2×C4#1451974612yes—
633C2×C4#1451974812yes—
634C2×C4#1451974912yes—
635C2×C4#1451974912yes—
636C2×C4#1451974912yes—
637C2×C4#1451974912yes—
638C2×C4#1451977312yes—
639C2×C4#1451977312yes—
640C2×C4C2×D4×D6111yescharacteristic
641C2×C4C2×D4×D6111yescharacteristic
642C2×C4C22×C22⋊D6111yescharacteristic
643C2×C4C22×C22⋊D6111yescharacteristic
644C2×C4C22×C22⋊D6111yescharacteristic
645C2×C4C2×#1175822411yescharacteristic
646C8—24no—
647C8—2442no—
648C22—22no—
649C22—22no—
650C22—24no—
651C22—24no—
652C22—42no—
653C22—44no—
654C22—84no—
655C22#1683967012yes—
656C22#1683967012yes—
657C22#1683994314yes—
658C22C2×#1451974511yescharacteristic
659C22C2×#1451974511yescharacteristic
660C22C2×#1451974811yescharacteristic
661C4—42no—
662C4—44no—
663C4—1228no—
664C4—2444no—
665C4—2444no—
666C4#1683967012yes—
667C4#1683967012yes—
668C4C2×#1451974611yescharacteristic
669C4C2×#1451974911yescharacteristic
670C4C2×#1451974911yescharacteristic
671C4C2×#1451977311yescharacteristic
672C2—21no—
673C2—21no—
674C2—22no—
675C2—82no—
676C2#2144685214yesdirect product factor
677C2C2×#1683967011yescharacteristic
678C2C2×#1683994312yes—
subgroupG/H
centerC23#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#137×C61C2
socleC23×C61#120
prime radicalC22×#41×C61C22
hypercenterC22×#137D61
hypocenterC61C2×#2005
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
2. C22×#14519775C2semidirect
4. C2×#16839771C2semidirect
5. C22×#14519695C2semidirect
6. #21446852C2direct (N × H)
7. C2×#16839523C2semidirect
19. C2×#14519775C22semidirect
29. #16839771C22semidirect
32. C2×#14519695C22semidirect
33. #16839523C22semidirect
345. C2×C61#2005semidirect
382. C61C2×#2005semidirect
676. C2#21446852direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403332
C22×#145197752
C22×#145197042
C2×#168397712
C22×#145196952
#214468522
C2×#168395232
C22×#137×C612
C2×#200561