Finite Group Databasebeta

← C2×#21446237 #29681664

Subgroups — C2×#21446237 #29681664

Order 15616.

1870 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840269C211yesmaximal, characteristic
2C2×#16839746C211yesmaximal, characteristic, complemented
3C2×#16839725C212yesmaximal, complemented
4#21446237C218yesmaximal, direct product factor
5C2×#16839533C212yesmaximal, complemented
6C2×C61×#568C211yesmaximal, characteristic, complemented
7C23×C4×D61C2211yescharacteristic
8C22×#11758194C2212yes—
9#16840269—22no—
10#16840269—22no—
11#16840269C414yes—
12#16840269C2214yes—
13C2×#14519758C412yes—
14C2×#14519753—21no—
15C2×#14519748—21no—
16C2×#14519745C412yes—
17C2×C4×C22⋊D61—22no—
18C2×#14519736C2211yescharacteristic
19#16839746—22no—
20#16839746C2214yescomplemented
21C2×#14519696—21no—
22C2×#14519694—21no—
23#16839725—24no—
24#16839725C2218yescomplemented
25C2×#14519689—24no—
26#16839533C2218yescomplemented
27C22×#41×C61C2211yescharacteristic
28C61×#568—22no—
29C61×#568—24no—
30C61×#568C2214yescomplemented
31C2×#131×C61—24no—
32C22×M16×C61—22no—
33C22×M16×C61C2212yes—
34C24×D61C2×C411yescharacteristic
35C22×C22⋊D61—22no—
36C23×Dic61C2×C411yescharacteristic
37C22×C4×D61—21no—
38C22×C4×D61—22no—
39C22×C4×D61—22no—
40C22×C4×D61—21no—
41C22×C4×D61—21no—
42C22×C4×D61—21no—
43C22×C4×D61—22no—
44C22×C4×D61—22no—
45C22×C4×D61C2×C412yes—
46C22×C4×D61C2312yes—
47C2×#11758194—22no—
48C2×#11758194—22no—
49C2×#11758194—22no—
50C2×#11758194—22no—
51C2×#11758194—22no—
52C2×#11758194C2314yes—
53C22×#92418—22no—
54#14519758—24no—
55#14519758C2×C418yes—
56#14519753—24no—
57#14519753—24no—
58#14519748—24no—
59#14519748—24no—
60#14519745—24no—
61#14519745C2×C418yes—
62C4×C22⋊D61—28no—
63C4×C22⋊D61—28no—
64#14519736—21no—
65#14519736—21no—
66#14519736C2×C412yes—
67#14519736C2312yes—
68C2×C4⋊Dic61—21no—
69C2×#11758196—22no—
70C2×C22⋊Dic61—22no—
71C2×C22⋊Dic61C2×C412yes—
72C2×#11758198—22no—
73C2×C4×Dic61—21no—
74#14519696—24no—
75#14519694—24no—
76#14519689—216no—
77C2×#41×C61—22no—
78C2×#41×C61—22no—
79C2×#41×C61—22no—
80C2×#41×C61—22no—
81C2×#41×C61C2×C412yes—
82C2×#41×C61D412yes—
83C2×#41×C61D412yes—
84C2×#41×C61C2312yes—
85C22×Q8×C61D411yescharacteristic
86C22×D4×C61C2×C412yes—
87C22×D4×C61D411yescharacteristic
88C23×C4×C61D412yes—
89C23×C4×C61C2311yescharacteristic
90#131×C61—216no—
91#131×C61—216no—
92C2×M16×C61—24no—
93C2×M16×C61—28no—
94C2×M16×C61—22no—
95C2×M16×C61—28no—
96C2×M16×C61—22no—
97C2×M16×C61—22no—
98C2×M16×C61—22no—
99C2×M16×C61D414yescomplemented
100C2×M16×C61C2314yes—
101C22×C8×C61—24no—
102C22×C8×C61D414yescomplemented
103C24×C61C22⋊C412yes—
104C24×C61C22×C411yescharacteristic
105C23×D61—21no—
106C23×D61—22no—
107C23×D61—21no—
108C23×D61—22no—
109C23×D61—44no—
110C23×D61C22×C412yes—
111#41×C61—24no—
112#41×C61—24no—
113#41×C61—24no—
114#41×C61—24no—
115#41×C61—24no—
116#41×C61—24no—
117#41×C61—24no—
118#41×C61—24no—
119C2×Q8×C61—22no—
120C2×Q8×C61—22no—
121C2×Q8×C61C22⋊C412yes—
122C2×Q8×C61C2×D412yes—
123C2×D4×C61—24no—
124C2×D4×C61—24no—
125C2×D4×C61—22no—
126C2×D4×C61—22no—
127C2×D4×C61C22⋊C414yes—
128C2×D4×C61C22⋊C412yes—
129C2×D4×C61C22×C414yes—
130C2×D4×C61C2×D412yes—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61C22⋊C412yes—
136C22×C4×C61C22⋊C414yes—
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C2×D414yes—
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D412yes—
144C22×C4×C61C2×D412yes—
145C22×C4×C61#4112yes—
146C22×C4×C61#4112yes—
147C22×C4×C61C2411yescharacteristic
148C2×C22⋊D61—28no—
149C2×C22⋊D61—48no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61C22×C412yes—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—24no—
159C2×C4×D61—24no—
160C2×C4×D61—24no—
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—24no—
164C2×C4×D61—42no—
165C2×C4×D61—41no—
166C2×C4×D61—41no—
167C2×C4×D61—42no—
168C2×C4×D61—42no—
169C2×C4×D61—42no—
170C2×C4×D61—42no—
171C2×C4×D61—41no—
172C2×C4×D61—41no—
173C2×C4×D61—42no—
174M16×C61—216no—
175M16×C61—24no—
176M16×C61—24no—
177M16×C61—24no—
178M16×C61—24no—
179C2×C8×C61—216no—
180C2×C8×C61—24no—
181C2×C8×C61—24no—
182C2×C8×C61C2×D418yescomplemented
183C22⋊Dic61—28no—
184C22⋊Dic61—22no—
185C22⋊Dic61C22×C414yes—
186#11758198—28no—
187C4⋊Dic61—22no—
188C4⋊Dic61—22no—
189#11758196—28no—
190C4×Dic61—22no—
191C4×Dic61—22no—
192#11758194—24no—
193#11758194—24no—
194#11758194—42no—
195#11758194—42no—
196C2×#92418—24no—
197C2×#92418—42no—
198C2×#92418—42no—
199C23×C61—22no—
200C23×C61—22no—
201C23×C61—42no—
202C23×C61—44no—
203C23×C61C2×C22⋊C411yescharacteristic
204C23×C61C2×C22⋊C414yes—
205C23×C61C2×C22⋊C411yescharacteristic
206C23×C61C4×D412yes—
207C23×C61C4×D412yes—
208C23×C61C23×C411yescharacteristic
209C22×D61—24no—
210C22×D61—28no—
211C22×D61—22no—
212C22×D61—24no—
213C22×D61—44no—
214C22×D61—44no—
215C22×D61—48no—
216C22×D61—42no—
217C22×D61—44no—
218C22×D61—41no—
219C22×D61—42no—
220C22×D61—41no—
221Q8×C61—24no—
222Q8×C61—24no—
223D4×C61—28no—
224D4×C61—28no—
225D4×C61—24no—
226D4×C61—24no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—24no—
230C2×C4×C61—24no—
231C2×C4×C61—24no—
232C2×C4×C61—24no—
233C2×C4×C61C2×C22⋊C414yes—
234C2×C4×C61C2×C22⋊C411yescharacteristic
235C2×C4×C61C2×C22⋊C411yescharacteristic
236C2×C4×C61C4×D412yes—
237C2×C4×C61C4×D412yes—
238C2×C4×C61#12012yes—
239C2×C4×C61#12011yescharacteristic
240C2×C4×C61#12011yescharacteristic
241C2×C4×C61#12112yes—
242C2×C4×C61#12112yes—
243C2×C4×C61#12112yes—
244C2×C4×C61#12112yes—
245C2×C4×C61#12311yescharacteristic
246C2×C4×C61#12311yescharacteristic
247C2×C4×C61#12312yes—
248C2×C4×C61C22×D412yes—
249C2×C4×C61C22×D411yescharacteristic
250C2×C4×C61C22×D411yescharacteristic
251C2×C4×C61C2×#4112yes—
252C22⋊D61—416no—
253C2×Dic61—24no—
254C2×Dic61—22no—
255C2×Dic61—24no—
256C2×Dic61—44no—
257C2×Dic61—41no—
258C2×Dic61—42no—
259C2×Dic61—41no—
260C4×D61—42no—
261C4×D61—44no—
262C4×D61—42no—
263C4×D61—42no—
264C4×D61—42no—
265C4×D61—44no—
266C8×C61—28no—
267#92418—44no—
268C2×#1891—611nomaximal, Sylow
269C22×C61—22no—
270C22×C61—24no—
271C22×C61—24no—
272C22×C61—41no—
273C22×C61—42no—
274C22×C61—41no—
275C22×C61—44no—
276C22×C61—44no—
277C22×C61—82no—
278C22×C61#38611yescharacteristic
279C22×C61#38612yes—
280C22×C61#38611yescharacteristic
281C22×C61C22×C22⋊C411yescharacteristic
282C22×C61C2×C4×D412yes—
283C2×D61—24no—
284C2×D61—28no—
285C2×D61—42no—
286C2×D61—44no—
287C2×D61—44no—
288C2×D61—48no—
289C2×D61—44no—
290C2×D61—42no—
291C4×C61—24no—
292C4×C61#38611yescharacteristic
293C4×C61#38611yescharacteristic
294C4×C61#38612yes—
295C4×C61C2×#12011yescharacteristic
296C4×C61C2×#12112yes—
297C4×C61C2×#12311yescharacteristic
298Dic61—44no—
299Dic61—42no—
300C2×#568D6111yescharacteristic, complemented
301C2×#525—611no—
302C2×#413—611no—
303C2×#407—612no—
304#1891—618no—
305C2×#344—612no—
306C2×C61—21no—
307C2×C61—22no—
308C2×C61—21no—
309C2×C61—22no—
310C2×C61—44no—
311C2×C61#189112yescomplemented
312C2×C61C2×#38611yescharacteristic
313D61—44no—
314C22×#41C2×D6111yescharacteristic
315C24×C4—611no—
316#568—22no—
317#568—24no—
318#568C2×D6114yescomplemented
319C2×#131—24no—
320C22×M16—22no—
321C22×M16—612no—
322C22×M16C2×D6112yes—
323#525—614no—
324#525—614no—
325#525—1222no—
326#525—1222no—
327C2×#123—612no—
328C2×C22⋊Q8—1221no—
329C2×#121—1221no—
330C2×#120—612no—
331C2×C4×D4—1222no—
332C2×#117—611no—
333#413—614no—
334#413—1222no—
335C2×#101—1221no—
336C2×#100—1221no—
337#407—618no—
338#407—1224no—
339C2×C22⋊C8—1224no—
340#344—618no—
341C61C2×#189111yescharacteristic, complemented, Sylow
342C25—611no—
343C2×#41—22no—
344C2×#41—22no—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41C4×D6112yes—
348C2×#41D24412yes—
349C2×#41C22⋊D6112yes—
350C2×#41C22×D6112yes—
351C22×Q8D24411yescharacteristic
352C22×D4—1222no—
353C22×D4C4×D6112yes—
354C22×D4D24411yescharacteristic
355C23×C4—611no—
356C23×C4—612no—
357C23×C4—612no—
358C23×C4—1221no—
359C23×C4—1221no—
360C23×C4—1222no—
361C23×C4—1222no—
362C23×C4—1221no—
363C23×C4—1221no—
364C23×C4—1222no—
365C23×C4—1222no—
366C23×C4C22⋊D6112yes—
367C23×C4C22×D6111yescharacteristic
368#131—216no—
369#131—216no—
370C2×M16—24no—
371C2×M16—28no—
372C2×M16—22no—
373C2×M16—28no—
374C2×M16—22no—
375C2×M16—22no—
376C2×M16—22no—
377C2×M16—614no—
378C2×M16—1222no—
379C2×M16—1222no—
380C2×M16—1222no—
381C2×M16—1222no—
382C2×M16—1222no—
383C2×M16C22⋊D6114yescomplemented
384C2×M16C22×D6114yes—
385C22×C8—24no—
386C22×C8—1222no—
387C22×C8C22⋊D6114yescomplemented
388#123—618no—
389#123—1224no—
390C22⋊Q8—1224no—
391C22⋊Q8—1224no—
392#121—1224no—
393#121—1224no—
394#120—618no—
395#120—1224no—
396C4×D4—1228no—
397C4×D4—1228no—
398#117—612no—
399#117—612no—
400#117—1221no—
401#117—1221no—
402C2×C4⋊C4—1222no—
403C2×C4⋊C4—1221no—
404C2×C22⋊C4—612no—
405C2×C22⋊C4—1222no—
406C2×C22⋊C4—1222no—
407C2×C42—1221no—
408#101—1224no—
409#100—1224no—
410C22⋊C8—12216no—
411C24—612no—
412C24—1221no—
413C24—1222no—
414C24—1221no—
415C24—1222no—
416C24—2444no—
417C24#1175819812yes—
418C24C2×C4×D6111yescharacteristic
419#41—24no—
420#41—24no—
421#41—24no—
422#41—24no—
423#41—24no—
424#41—24no—
425#41—24no—
426#41—24no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8#1175819812yes—
430C2×Q8C2×D24412yes—
431C2×D4—24no—
432C2×D4—24no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—1228no—
436C2×D4—2448no—
437C2×D4#1175819814yes—
438C2×D4#1175819812yes—
439C2×D4C2×C4×D6114yes—
440C2×D4C2×D24412yes—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—612no—
446C22×C4—1222no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4—1222no—
450C22×C4—1222no—
451C22×C4—1224no—
452C22×C4—1222no—
453C22×C4—1222no—
454C22×C4—1224no—
455C22×C4—1222no—
456C22×C4—1222no—
457C22×C4—1224no—
458C22×C4—1224no—
459C22×C4—2442no—
460C22×C4—2441no—
461C22×C4—2441no—
462C22×C4—2442no—
463C22×C4—2442no—
464C22×C4—2442no—
465C22×C4—2442no—
466C22×C4—2441no—
467C22×C4—2441no—
468C22×C4—2442no—
469C22×C4#1175819812yes—
470C22×C4#1175819814yes—
471C22×C4C2×C4×D6111yescharacteristic
472C22×C4C2×D24411yescharacteristic
473C22×C4C2×D24411yescharacteristic
474C22×C4#1175822212yes—
475C22×C4#1175822212yes—
476C22×C4C2×C22⋊D6114yes—
477C22×C4C2×C22⋊D6111yescharacteristic
478C22×C4C2×C22⋊D6111yescharacteristic
479C22×C4C2×C22⋊D6112yes—
480C22×C4C2×C22⋊D6112yes—
481C22×C4C23×D6111yescharacteristic
482M16—216no—
483M16—24no—
484M16—24no—
485M16—24no—
486M16—24no—
487M16—1224no—
488M16—1224no—
489M16—2442no—
490M16—2442no—
491C2×C8—216no—
492C2×C8—24no—
493C2×C8—24no—
494C2×C8—1224no—
495C2×C8—2442no—
496C2×C8—2442no—
497C2×C8C2×C22⋊D6118yescomplemented
498C4⋊C4—1222no—
499C4⋊C4—1228no—
500C4⋊C4—1222no—
501C22⋊C4—614no—
502C22⋊C4—1222no—
503C22⋊C4—1228no—
504C22⋊C4—1228no—
505C42—1222no—
506C42—1222no—
507C23—22no—
508C23—22no—
509C23—42no—
510C23—44no—
511C23—1224no—
512C23—1228no—
513C23—1222no—
514C23—1224no—
515C23—2442no—
516C23—2444no—
517C23—2444no—
518C23—2444no—
519C23—2448no—
520C23—2441no—
521C23—2442no—
522C23—2441no—
523C23C2×#1175819811yescharacteristic
524C23C2×#1175819814yes—
525C23C2×#1175819811yescharacteristic
526C23C4×C22⋊D6112yes—
527C23C4×C22⋊D6112yes—
528C23C22×C4×D6111yescharacteristic
529Q8—24no—
530Q8—24no—
531D4—28no—
532D4—28no—
533D4—24no—
534D4—24no—
535D4—24416no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—1224no—
543C2×C4—1222no—
544C2×C4—1224no—
545C2×C4—2444no—
546C2×C4—2441no—
547C2×C4—2442no—
548C2×C4—2441no—
549C2×C4—2442no—
550C2×C4—2444no—
551C2×C4—2442no—
552C2×C4—2442no—
553C2×C4—2442no—
554C2×C4—2444no—
555C2×C4C2×#1175819814yes—
556C2×C4C2×#1175819811yescharacteristic
557C2×C4C2×#1175819811yescharacteristic
558C2×C4C4×C22⋊D6112yes—
559C2×C4C4×C22⋊D6112yes—
560C2×C4#1451974612yes—
561C2×C4#1451974611yescharacteristic
562C2×C4#1451974611yescharacteristic
563C2×C4#1451975112yes—
564C2×C4#1451975112yes—
565C2×C4#1451975112yes—
566C2×C4#1451975112yes—
567C2×C4#1451976011yescharacteristic
568C2×C4#1451976011yescharacteristic
569C2×C4#1451976012yes—
570C2×C4C22×C22⋊D6112yes—
571C2×C4C22×C22⋊D6111yescharacteristic
572C2×C4C22×D24411yescharacteristic
573C2×C4C2×#1175822212yes—
574C8—28no—
575C8—2444no—
576C22—22no—
577C22—24no—
578C22—24no—
579C22—41no—
580C22—41no—
581C22—42no—
582C22—44no—
583C22—44no—
584C22—82no—
585C22—1224no—
586C22—1228no—
587C22—2442no—
588C22—2444no—
589C22—2444no—
590C22—2448no—
591C22—2442no—
592C22—2444no—
593C22#1683964111yescharacteristic
594C22#1683964112yes—
595C22#1683964111yescharacteristic
596C22C22×#1175819811yescharacteristic
597C22C2×C4×C22⋊D6112yes—
598C4—24no—
599C4—2444no—
600C4—2442no—
601C4#1683964111yescharacteristic
602C4#1683964111yescharacteristic
603C4#1683964112yes—
604C4C2×#1451974611yescharacteristic
605C4C2×#1451975112yes—
606C4C2×#1451976011yescharacteristic
607C2—21no—
608C2—21no—
609C2—22no—
610C2—22no—
611C2—44no—
612C2—2444no—
613C2#2144623712yesdirect product factor
614C2C2×#1683964111yescharacteristic
subgroupG/H
centerC2×C4#14519746
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#568C2
socleC22×C61#386
prime radicalC2×#16840269C2
cosocleC22×C4×C61C24
hypercenterC2×#568D61
hypocenterC61C2×#1891
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
2. C2×#16839746C2semidirect
3. C2×#16839725C2semidirect
4. #21446237C2direct (N × H)
5. C2×#16839533C2semidirect
6. C2×C61×#568C2semidirect
20. #16839746C22semidirect
24. #16839725C22semidirect
26. #16839533C22semidirect
30. C61×#568C22semidirect
99. C2×M16×C61D4semidirect
102. C22×C8×C61D4semidirect
182. C2×C8×C61C2×D4semidirect
300. C2×#568D61semidirect
311. C2×C61#1891semidirect
318. #568C2×D61semidirect
341. C61C2×#1891semidirect
383. C2×M16C22⋊D61semidirect
387. C22×C8C22⋊D61semidirect
497. C2×C8C2×C22⋊D61semidirect
613. C2#21446237direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402692
C2×#168397462
C2×#168397252
#214462372
C2×#168395332
C2×C61×#5682
C2×#189161