Finite Group Databasebeta

← C2×#21446337 #29681947

Subgroups — C2×#21446337 #29681947

Order 15616.

1698 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519808C211yesmaximal, characteristic
2C22×#14519783C211yesmaximal, characteristic
3C2×#16839761C211yesmaximal, characteristic
4C22×#14519696C211yesmaximal, characteristic, complemented
5#21446337C218yesmaximal, direct product factor
6C2×#16839531C211yesmaximal, characteristic, complemented
7C2×#16839527C211yesmaximal, characteristic, complemented
8C22×#103×C61C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C2×#14519808—22no—
11C2×#14519808—24no—
12C2×#14519808C418yescomplemented
13C2×#14519808C2214yes—
14C22×#11758202—21no—
15C22×#11758201—21no—
16C2×#14519783—24no—
17C2×#14519783—22no—
18C2×#14519783—24no—
19C2×#14519783C2214yes—
20C22×#11758194C2211yescharacteristic
21C22×#11758194C2211yescharacteristic
22C22×#11758194C2211yescharacteristic
23C22×#11758189—21no—
24C22×C8×D61—21no—
25#16839761—22no—
26#16839761C2214yes—
27C2×#14519700—21no—
28C2×#14519697—21no—
29C2×#14519696—24no—
30C2×#14519696C2214yescomplemented
31#16839531C2214yescomplemented
32#16839527C2214yescomplemented
33C23×Q8×C61C2211yescharacteristic
34C23×C8×C61C2211yescharacteristic
35C22×C4⋊C4×C61C2211yescharacteristic
36C2×#103×C61—21no—
37C2×#103×C61—21no—
38C2×#103×C61—22no—
39C2×#103×C61C2214yescomplemented
40C2×#11758222—22no—
41C2×#11758222—21no—
42C2×#11758222—22no—
43C2×#11758222—21no—
44C2×#11758222C2×C414yes—
45C2×#11758222D414yes—
46C2×#11758222D412yes—
47C2×#11758222C2312yes—
48C22×Dic122D411yescharacteristic
49C22×D244D411yescharacteristic
50C22×C22⋊D61—21no—
51C22×C4×D61—21no—
52#14519808—216no—
53#14519808—28no—
54#14519808C2×C4116yescomplemented
55C2×#11758202—28no—
56C2×#11758202—24no—
57C2×#11758201—28no—
58C2×#11758201—24no—
59#14519783—216no—
60#14519783—28no—
61#14519783—28no—
62C2×#11758194—22no—
63C2×#11758194—21no—
64C2×#11758194—22no—
65C2×#11758194—21no—
66C2×#11758194—21no—
67C2×#11758194—22no—
68C2×#11758194—22no—
69C2×#11758194C2×C414yes—
70C2×#11758194D414yes—
71C2×#11758194C2312yes—
72C2×#11758194C2312yes—
73C2×#11758194C2312yes—
74C2×#11758189—28no—
75C2×#11758189—24no—
76C22×#92418—21no—
77C22×#92418—21no—
78C22×#92418—21no—
79C2×C8×D61—28no—
80C2×C8×D61—24no—
81#14519700—24no—
82#14519697—24no—
83#14519696—28no—
84C22×Q8×C61—22no—
85C22×Q8×C61—21no—
86C22×Q8×C61—21no—
87C22×Q8×C61—21no—
88C22×Q8×C61—22no—
89C22×Q8×C61—21no—
90C22×Q8×C61—21no—
91C22×Q8×C61—22no—
92C22×Q8×C61C2×C414yes—
93C22×Q8×C61C2312yes—
94C23×C4×C61—21no—
95C23×C4×C61—21no—
96C23×C4×C61C2311yescharacteristic
97C22×C8×C61—22no—
98C22×C8×C61—22no—
99C22×C8×C61D411yescharacteristic
100C22×C8×C61D411yescharacteristic
101C22×C8×C61D412yes—
102C22×C8×C61C2312yes—
103C2×C4⋊C4×C61—21no—
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61C2312yes—
109#103×C61—24no—
110#103×C61—24no—
111C24×C61#4111yescharacteristic
112C23×D61—21no—
113C2×Q8×C61—24no—
114C2×Q8×C61—22no—
115C2×Q8×C61—24no—
116C2×Q8×C61—24no—
117C2×Q8×C61—24no—
118C2×Q8×C61—24no—
119C2×Q8×C61—22no—
120C2×Q8×C61—22no—
121C2×Q8×C61—22no—
122C2×Q8×C61—22no—
123C2×Q8×C61—42no—
124C2×Q8×C61—42no—
125C2×Q8×C61—41no—
126C2×Q8×C61—41no—
127C2×Q8×C61—42no—
128C2×Q8×C61—42no—
129C2×Q8×C61—42no—
130C2×Q8×C61C22×C414yes—
131C22×C4×C61—24no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—41no—
135C22×C4×C61—41no—
136C22×C4×C61—42no—
137C22×C4×C61—41no—
138C22×C4×C61—41no—
139C22×C4×C61—82no—
140C22×C4×C61C22×C412yes—
141C22×C4×C61C2×D412yes—
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D412yes—
147C22×C4×C61#4111yescharacteristic
148C22×C4×C61#4112yes—
149C22×C4×C61C2411yescharacteristic
150C2×C22⋊D61—24no—
151C2×C22⋊D61—22no—
152C2×C22⋊D61—24no—
153C2×C22⋊D61—22no—
154C22×Dic61—21no—
155#11758222—24no—
156#11758222—24no—
157#11758222—24no—
158#11758222—24no—
159#11758222—24no—
160#11758222—22no—
161#11758222—22no—
162#11758222C22⋊C418yes—
163#11758222C22×C414yes—
164#11758222C2×D414yes—
165C2×D244—22no—
166C2×D244—21no—
167C2×D244C22⋊C414yes—
168C2×D244C2×D412yes—
169C2×C4×D61—24no—
170C2×C4×D61—24no—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×Dic122—22no—
174C2×Dic122—21no—
175C2×Dic122C22⋊C414yes—
176C2×Dic122C2×D412yes—
177C2×C8×C61—22no—
178C2×C8×C61—22no—
179C2×C8×C61—24no—
180C2×C8×C61—22no—
181C2×C8×C61—22no—
182C2×C8×C61C2×D412yes—
183C2×C8×C61C2×D412yes—
184C4⋊C4×C61—22no—
185C4⋊C4×C61—22no—
186C4⋊C4×C61—41no—
187C4⋊C4×C61—41no—
188#11758202—216no—
189#11758201—216no—
190#11758194—24no—
191#11758194—24no—
192#11758194—22no—
193#11758194—22no—
194#11758194—22no—
195#11758194—22no—
196#11758194—42no—
197#11758194C22×C414yes—
198#11758194C2×D414yes—
199C2×#92418—24no—
200C2×#92418—24no—
201C2×#92418—22no—
202C2×#92418—22no—
203C2×#92418—22no—
204C2×#92418—42no—
205#11758189—216no—
206C8×D61—216no—
207C23×C61—22no—
208C23×C61—22no—
209C23×C61C4×D412yes—
210C23×C61#12111yescharacteristic
211C23×C61#12111yescharacteristic
212C23×C61#12312yes—
213C23×C61C2×#4111yescharacteristic
214C22×D61—22no—
215C22×D61—24no—
216C22×D61—42no—
217C22×D61—42no—
218Q8×C61—24no—
219Q8×C61—24no—
220Q8×C61—42no—
221Q8×C61—42no—
222Q8×C61—44no—
223Q8×C61—44no—
224C2×C4×C61—24no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61—44no—
228C2×C4×C61—44no—
229C2×C4×C61—42no—
230C2×C4×C61—82no—
231C2×C4×C61—82no—
232C2×C4×C61—82no—
233C2×C4×C61C2×C22⋊C412yes—
234C2×C4×C61C2×C22⋊C412yes—
235C2×C4×C61C4×D412yes—
236C2×C4×C61C4×D412yes—
237C2×C4×C61C4×D412yes—
238C2×C4×C61#12012yes—
239C2×C4×C61#12012yes—
240C2×C4×C61#12112yes—
241C2×C4×C61#12112yes—
242C2×C4×C61#12111yescharacteristic
243C2×C4×C61#12111yescharacteristic
244C2×C4×C61#12312yes—
245C2×C4×C61C23×C411yescharacteristic
246C2×C4×C61C22×D411yescharacteristic
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61C22×D411yescharacteristic
249C2×C4×C61C22×D411yescharacteristic
250C2×C4×C61C2×#4111yescharacteristic
251C22⋊D61—24no—
252C22⋊D61—24no—
253C22⋊D61—28no—
254C2×Dic61—22no—
255C2×Dic61—24no—
256D244—22no—
257D244—24no—
258D244C2×C22⋊C414yes—
259C4×D61—24no—
260C4×D61—24no—
261C4×D61—28no—
262Dic122—22no—
263Dic122—24no—
264Dic122C2×C22⋊C414yes—
265C8×C61—22no—
266C8×C61—22no—
267#92418—24no—
268#92418—24no—
269#92418—42no—
270C2×#1908—611nomaximal, Sylow
271C22×C61—24no—
272C22×C61—24no—
273C22×C61—21no—
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—21no—
277C22×C61#38612yes—
278C22×C61#38612yes—
279C22×C61#47112yes—
280C22×C61#47312yes—
281C22×C61C2×C4×D411yescharacteristic
282C22×C61C2×#12111yescharacteristic
283C22×C61C2×#12311yescharacteristic
284C2×D61—24no—
285C2×D61—48no—
286C2×D61—42no—
287C2×D61—42no—
288C4×C61—44no—
289C4×C61—82no—
290C4×C61#38612yes—
291C4×C61#38612yes—
292C4×C61C22×C22⋊C411yescharacteristic
293C4×C61C2×C4×D411yescharacteristic
294C4×C61C2×#12011yescharacteristic
295C4×C61C2×#12111yescharacteristic
296Dic61—24no—
297C22×#137—611no—
298C22×#131—611no—
299C2×#417—611no—
300C22×#103D6111yescharacteristic, complemented
301C22×#101—611no—
302#1908—618no—
303C2×#343—611no—
304C2×#341—611no—
305C2×C61—21no—
306C2×C61—21no—
307C2×C61—22no—
308C2×C61#190814yescomplemented
309C2×C61C2×#38611yescharacteristic
310C2×C61C2×#47111yescharacteristic
311C2×C61C2×#47311yescharacteristic
312D61—44no—
313C22×#41—611no—
314C23×Q8C2×D6111yescharacteristic
315C2×#137—618no—
316C2×#137—614no—
317C2×#137—1224no—
318C2×#137—1222no—
319C22×Q16—1221no—
320C22×SD16—1221no—
321C2×#131—614no—
322C2×#131—1224no—
323C2×#131—1224no—
324C2×#131—1222no—
325C22×M16—611no—
326C22×M16—611no—
327C22×M16—611no—
328C22×M16—1221no—
329C23×C8—1221no—
330C23×C8C2×D6111yescharacteristic
331C22×C4⋊C4C2×D6111yescharacteristic
332#417—614no—
333#417—1222no—
334C2×#103—21no—
335C2×#103—21no—
336C2×#103—22no—
337C2×#103—1221no—
338C2×#103C2×D6114yescomplemented
339C2×#102—1221no—
340C2×#101—614no—
341C2×#101—1224no—
342#343—614no—
343#341—614no—
344C61C2×#190811yescharacteristic, complemented, Sylow
345C2×#41—614no—
346C2×#41—614no—
347C2×#41—612no—
348C2×#41—612no—
349C2×#41—1222no—
350C2×#41—1222no—
351C2×#41—1221no—
352C2×#41—1221no—
353C22×Q8—22no—
354C22×Q8—21no—
355C22×Q8—22no—
356C22×Q8—21no—
357C22×Q8—21no—
358C22×Q8—22no—
359C22×Q8—21no—
360C22×Q8—21no—
361C22×Q8—611no—
362C22×Q8C4×D6114yes—
363C22×Q8C22×D6112yes—
364C22×D4—611no—
365C22×D4—1221no—
366C23×C4—21no—
367C23×C4—21no—
368C23×C4—1221no—
369C23×C4C22×D6111yescharacteristic
370#137—6116no—
371#137—1228no—
372#137—12216no—
373C2×Q16—1224no—
374C2×Q16—1228no—
375C2×SD16—1224no—
376C2×SD16—1228no—
377#131—1228no—
378#131—1228no—
379#131—12216no—
380C2×M16—614no—
381C2×M16—614no—
382C2×M16—612no—
383C2×M16—612no—
384C2×M16—612no—
385C2×M16—1228no—
386C2×M16—1222no—
387C2×M16—1221no—
388C2×M16—1222no—
389C2×M16—1221no—
390C2×M16—1221no—
391C2×M16—1224no—
392C2×M16—1222no—
393C2×M16—1222no—
394C22×C8—22no—
395C22×C8—22no—
396C22×C8—1228no—
397C22×C8—1221no—
398C22×C8—1221no—
399C22×C8—1224no—
400C22×C8—1221no—
401C22×C8C22⋊D6111yescharacteristic
402C22×C8C22⋊D6111yescharacteristic
403C22×C8C22⋊D6112yes—
404C22×C8C22×D6112yes—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4C22×D6112yes—
411#103—24no—
412#103—24no—
413#103—1224no—
414#102—1224no—
415#101—1228no—
416C24—1221no—
417C24#1175822411yescharacteristic
418#41—614no—
419#41—614no—
420#41—618no—
421#41—1222no—
422#41—1222no—
423#41—1224no—
424#41—1224no—
425#41—1224no—
426#41—1224no—
427#41—1224no—
428C2×Q8—22no—
429C2×Q8—24no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—24no—
435C2×Q8—24no—
436C2×Q8—24no—
437C2×Q8—24no—
438C2×Q8—42no—
439C2×Q8—42no—
440C2×Q8—41no—
441C2×Q8—41no—
442C2×Q8—42no—
443C2×Q8—42no—
444C2×Q8—42no—
445C2×Q8—612no—
446C2×Q8—614no—
447C2×Q8—1221no—
448C2×Q8—1222no—
449C2×Q8C2×C4×D6114yes—
450C2×D4—612no—
451C2×D4—614no—
452C2×D4—1222no—
453C2×D4—1224no—
454C2×D4—1222no—
455C2×D4—1224no—
456C2×D4—1221no—
457C2×D4—1222no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—42no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—82no—
467C22×C4—1221no—
468C22×C4—1222no—
469C22×C4—1224no—
470C22×C4—1224no—
471C22×C4—1222no—
472C22×C4C2×C4×D6112yes—
473C22×C4#1175822212yes—
474C22×C4D4×D6112yes—
475C22×C4D4×D6111yescharacteristic
476C22×C4D4×D6111yescharacteristic
477C22×C4D4×D6112yes—
478C22×C4#1175822411yescharacteristic
479C22×C4C2×C22⋊D6111yescharacteristic
480C22×C4C2×C22⋊D6111yescharacteristic
481C22×C4C23×D6111yescharacteristic
482Q16—12216no—
483SD16—12216no—
484M16—614no—
485M16—614no—
486M16—12216no—
487M16—1222no—
488M16—1222no—
489M16—1224no—
490M16—1224no—
491M16—1222no—
492M16—1222no—
493M16—2442no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—24no—
499C2×C8—12216no—
500C2×C8—1222no—
501C2×C8—1222no—
502C2×C8—1224no—
503C2×C8—1224no—
504C2×C8—1222no—
505C2×C8—2442no—
506C2×C8C2×C22⋊D6112yes—
507C2×C8C2×C22⋊D6112yes—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C23—22no—
513C23—22no—
514C23—1222no—
515C23—1224no—
516C23—2442no—
517C23—2442no—
518C23#1451973712yes—
519C23#1451974811yescharacteristic
520C23#1451974811yescharacteristic
521C23#1451975912yes—
522C23C2×#1175822411yescharacteristic
523Q8—24no—
524Q8—24no—
525Q8—42no—
526Q8—42no—
527Q8—44no—
528Q8—44no—
529Q8—614no—
530Q8—1222no—
531Q8—1224no—
532D4—614no—
533D4—1224no—
534D4—1224no—
535D4—1228no—
536D4—1222no—
537D4—1224no—
538C2×C4—24no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—44no—
542C2×C4—44no—
543C2×C4—42no—
544C2×C4—82no—
545C2×C4—82no—
546C2×C4—82no—
547C2×C4—1222no—
548C2×C4—1224no—
549C2×C4—1224no—
550C2×C4—1224no—
551C2×C4—1228no—
552C2×C4C22⋊C4×D6112yes—
553C2×C4C22⋊C4×D6112yes—
554C2×C4#1451973712yes—
555C2×C4C4×C22⋊D6112yes—
556C2×C4C4×C22⋊D6112yes—
557C2×C4#1451974512yes—
558C2×C4#1451974512yes—
559C2×C4#1451974811yescharacteristic
560C2×C4#1451974811yescharacteristic
561C2×C4#1451975012yes—
562C2×C4#1451975012yes—
563C2×C4#1451975912yes—
564C2×C4C22×C4×D6111yescharacteristic
565C2×C4C2×D4×D6111yescharacteristic
566C2×C4C2×D4×D6111yescharacteristic
567C2×C4C2×D4×D6111yescharacteristic
568C2×C4C22×C22⋊D6111yescharacteristic
569C2×C4C2×#1175822211yescharacteristic
570C8—22no—
571C8—22no—
572C8—1224no—
573C8—1224no—
574C8—2442no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—24no—
580C22—24no—
581C22—1224no—
582C22—2442no—
583C22—2442no—
584C22—2448no—
585C22#1683963812yes—
586C22#1683963812yes—
587C22#1684002212yes—
588C22#1684003412yes—
589C22C2×#1451973711yescharacteristic
590C22C2×#1451974811yescharacteristic
591C22C2×#1451975911yescharacteristic
592C4—44no—
593C4—82no—
594C4—1224no—
595C4#1683963812yes—
596C4#1683963812yes—
597C4C2×C22⋊C4×D6111yescharacteristic
598C4C2×C4×C22⋊D6111yescharacteristic
599C4C2×#1451974511yescharacteristic
600C4C2×#1451975011yescharacteristic
601C2—21no—
602C2—21no—
603C2—22no—
604C2—2444no—
605C2#2144633714yesdirect product factor
606C2C2×#1683963811yescharacteristic
607C2C2×#1684002211yescharacteristic
608C2C2×#1684003411yescharacteristic
subgroupG/H
centerC23#14519748
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC22×#103×C61C2
socleC23×C61#121
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenterC22×#103D61
hypocenterC61C2×#1908
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
4. C22×#14519696C2semidirect
5. #21446337C2direct (N × H)
6. C2×#16839531C2semidirect
7. C2×#16839527C2semidirect
8. C22×#103×C61C2semidirect
12. C2×#14519808C4semidirect
30. C2×#14519696C22semidirect
31. #16839531C22semidirect
32. #16839527C22semidirect
39. C2×#103×C61C22semidirect
54. #14519808C2×C4semidirect
300. C22×#103D61semidirect
308. C2×C61#1908semidirect
338. C2×#103C2×D61semidirect
344. C61C2×#1908semidirect
605. C2#21446337direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198082
C22×#145197832
C2×#168397612
C22×#145196962
#214463372
C2×#168395312
C2×#168395272
C22×#103×C612
C2×#190861