Finite Group Databasebeta

← C2×#21460694 #30596801

Subgroups — C2×#21460694 #30596801

Order 15616.

1454 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840704C211yesmaximal, characteristic
2C22×(C2×#6923)⋊C4C211yesmaximal, characteristic
3#21460694C214yesmaximal, direct product factor
4C2×C22⋊C8×D61C211yesmaximal, characteristic
5C24×#6923—21no—
6C22×C4⋊#6923C412yescomplemented
7C22×C22⋊#6923—21no—
8#16840704—21no—
9#16840704—21no—
10#16840704C412yescomplemented
11#16840704C2212yes—
12C2×(C2×#6923)⋊C4—21no—
13C2×(C2×#6923)⋊C4—21no—
14C2×(C2×#6923)⋊C4—21no—
15C2×(C2×#6923)⋊C4—21no—
16C2×(C2×#6923)⋊C4C412yescomplemented
17C2×(C2×#6923)⋊C4C412yescomplemented
18C2×(C2×#6923)⋊C4C2212yes—
19C23×C4×D61C2211yescharacteristic
20C22×C8×D61—21no—
21C2×C22⋊#92418C411yescharacteristic, complemented
22C2×#14519689—21no—
23C22⋊C8×D61—21no—
24C22⋊C8×D61—21no—
25C22⋊C8×D61C412yescomplemented
26C22⋊C8×D61C2212yes—
27C2×C22⋊C8×C61C411yescharacteristic, complemented
28C23×#6923—28no—
29C23×#6923—22no—
30C23×#6923—22no—
31C23×#6923—22no—
32C23×#6923—22no—
33C23×#6923—44no—
34C23×#6923—42no—
35C23×#6923—42no—
36C2×C4⋊#6923—22no—
37C2×C4⋊#6923—44no—
38C2×C4⋊#6923C2×C414yescomplemented
39C2×C22⋊#6923—22no—
40C2×C22⋊#6923—22no—
41C2×C22⋊#6923—42no—
42C2×C22⋊#6923—42no—
43(C2×#6923)⋊C4—22no—
44(C2×#6923)⋊C4—22no—
45(C2×#6923)⋊C4—22no—
46(C2×#6923)⋊C4—22no—
47(C2×#6923)⋊C4—22no—
48(C2×#6923)⋊C4C2×C414yescomplemented
49C24×D61D411yescharacteristic
50C23×Dic61Q811yescharacteristic
51C22×C4×D61—44no—
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61C2×C411yescharacteristic
55C22×C4×D61C2×C411yescharacteristic
56C22×C4×D61C2×C411yescharacteristic
57C22×C4×D61D411yescharacteristic
58C22×C4×D61D411yescharacteristic
59C22×C4×D61D411yescharacteristic
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61Q811yescharacteristic
63C22×C4×D61C2311yescharacteristic
64C22×#92418—21no—
65C2×C8×D61—22no—
66C2×C8×D61—22no—
67C2×C8×D61—44no—
68C22⋊#92418—21no—
69C22⋊#92418C2×C412yescomplemented
70#14519689—22no—
71#14519689—22no—
72C23×C4×C61C2×C411yescharacteristic
73C22×C8×C61—21no—
74C22⋊C8×C61—21no—
75C22⋊C8×C61C2×C412yescomplemented
76C24×C61C4⋊C411yescharacteristic
77C23×D61—24no—
78C23×D61—24no—
79C23×D61C22⋊C411yescharacteristic
80C23×D61C22⋊C411yescharacteristic
81C23×D61C22⋊C411yescharacteristic
82C23×D61C22⋊C411yescharacteristic
83C23×D61C4⋊C411yescharacteristic
84C23×D61D812yes—
85C23×D61SD1612yes—
86C23×D61SD1612yes—
87C23×D61Q1612yes—
88C23×D61C2×D411yescharacteristic
89C22×#6923—28no—
90C22×#6923—28no—
91C22×#6923—28no—
92C22×#6923—24no—
93C22×#6923—24no—
94C22×#6923—44no—
95C22×#6923—416no—
96C22×#6923—416no—
97C22×#6923—44no—
98C22×#6923—44no—
99C22×#6923—44no—
100C22×#6923—44no—
101C22×#6923—42no—
102C22×#6923—42no—
103C22×#6923—44no—
104C22×#6923—44no—
105C22×#6923—44no—
106C22×C4×C61—42no—
107C22×C4×C61C4211yescharacteristic
108C22×C4×C61C4211yescharacteristic
109C22×C4×C61C22⋊C411yescharacteristic
110C22×C4×C61C22⋊C411yescharacteristic
111C22×C4×C61C4⋊C411yescharacteristic
112C22×C4×C61C22×C411yescharacteristic
113C22×Dic61—42no—
114C22×Dic61C4⋊C411yescharacteristic
115C22×Dic61C4⋊C411yescharacteristic
116C22×Dic61C4⋊C411yescharacteristic
117C22×Dic61C4⋊C411yescharacteristic
118C22×Dic61C4⋊C411yescharacteristic
119C22×Dic61C2×Q811yescharacteristic
120C2×C4×D61—24no—
121C2×C4×D61—24no—
122C2×C4×D61—42no—
123C2×C4×D61—42no—
124C2×C4×D61—42no—
125C2×C4×D61—42no—
126C2×C4×D61—42no—
127C2×C4×D61—42no—
128C2×C4×D61—42no—
129C2×C4×D61—42no—
130C2×C4×D61—42no—
131C2×C4×D61—42no—
132C2×C4×D61C4211yescharacteristic
133C2×C4×D61C4211yescharacteristic
134C2×C4×D61C22⋊C411yescharacteristic
135C2×C4×D61C22⋊C411yescharacteristic
136C2×C4×D61C22⋊C411yescharacteristic
137C2×C4×D61C22⋊C411yescharacteristic
138C2×C4×D61C22⋊C411yescharacteristic
139C2×C4×D61C22⋊C411yescharacteristic
140C2×C4×D61C4⋊C411yescharacteristic
141C2×C4×D61C4⋊C411yescharacteristic
142C2×C4×D61C4⋊C411yescharacteristic
143C2×C4×D61C4⋊C411yescharacteristic
144C2×C4×D61C22×C411yescharacteristic
145C2×C4×D61C22×C411yescharacteristic
146C2×C4×D61C2×D411yescharacteristic
147C2×C4×D61C2×D411yescharacteristic
148C22⋊#6923—44no—
149C22⋊#6923—42no—
150C22⋊#6923—42no—
151C4⋊#6923—44no—
152C4⋊#6923—44no—
153C2×C8×C61—22no—
154C2×C8×C61—42no—
155C2×#92418—22no—
156C2×#92418—42no—
157C8×D61—44no—
158C8×D61—44no—
159C23×C61—22no—
160C23×C61—22no—
161C23×C61#9511yescharacteristic
162C23×C61#9511yescharacteristic
163C23×C61#10612yes—
164C23×C61#10712yes—
165C23×C61C2×C4⋊C411yescharacteristic
166C22×D61—22no—
167C22×D61—22no—
168C22×D61—28no—
169C22×D61—28no—
170C22×D61—28no—
171C22×D61—28no—
172C22×D61—22no—
173C22×D61—22no—
174C22×D61—22no—
175C22×D61—22no—
176C22×D61—22no—
177C22×D61—22no—
178C22×D61—22no—
179C22×D61—22no—
180C22×D61#9511yescharacteristic
181C22×D61#9511yescharacteristic
182C22×D61#9914yes—
183C22×D61#10212yes—
184C22×D61#10212yes—
185C22×D61#10212yes—
186C22×D61#10212yes—
187C22×D61#10312yes—
188C22×D61#10312yes—
189C22×D61#10312yes—
190C22×D61#10312yes—
191C22×D61#10414yes—
192C22×D61#10612yes—
193C22×D61#10712yes—
194C22×D61C2×C22⋊C411yescharacteristic
195C22×D61C2×C22⋊C411yescharacteristic
196C22×D61C2×D811yescharacteristic
197C22×D61C2×SD1611yescharacteristic
198C22×D61C2×SD1611yescharacteristic
199C22×D61C2×Q1611yescharacteristic
200C2×#6923—28no—
201C2×#6923—416no—
202C2×#6923—44no—
203C2×#6923—416no—
204C2×#6923—48no—
205C2×#6923—48no—
206C2×#6923—44no—
207C2×#6923—44no—
208C2×#6923—44no—
209C2×#6923—44no—
210C2×#6923—88no—
211C2×C4×C61—22no—
212C2×C4×C61—22no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61#9511yescharacteristic
218C2×C4×C61#9511yescharacteristic
219C2×C4×C61C2×C4211yescharacteristic
220C2×C4×C61C2×C22⋊C411yescharacteristic
221C2×Dic61—22no—
222C2×Dic61—22no—
223C2×Dic61—41no—
224C2×Dic61—41no—
225C2×Dic61—41no—
226C2×Dic61—41no—
227C2×Dic61#9511yescharacteristic
228C2×Dic61#9511yescharacteristic
229C2×Dic61C2×C4⋊C411yescharacteristic
230C2×Dic61C2×C4⋊C411yescharacteristic
231C4×D61—22no—
232C4×D61—22no—
233C4×D61—22no—
234C4×D61—22no—
235C4×D61—22no—
236C4×D61—22no—
237C4×D61—22no—
238C4×D61—22no—
239C4×D61—41no—
240C4×D61—41no—
241C4×D61—41no—
242C4×D61—41no—
243C4×D61—41no—
244C4×D61—41no—
245C4×D61—41no—
246C4×D61—41no—
247C8×C61—42no—
248#92418—42no—
249C2×#1294—611nomaximal, Sylow
250C22×C61—24no—
251C22×C61—24no—
252C22×C61—21no—
253C22×C61—21no—
254C22×C61—21no—
255C22×C61—21no—
256C22×C61#33912yes—
257C22×C61#34012yes—
258C22×C61#34012yes—
259C22×C61#34212yes—
260C22×C61C2×#9511yescharacteristic
261C22×C61C2×#10611yescharacteristic
262C22×C61C2×#10711yescharacteristic
263C2×D61—24no—
264C2×D61—24no—
265C2×D61—21no—
266C2×D61—21no—
267C2×D61—21no—
268C2×D61—21no—
269C2×D61—24no—
270C2×D61—24no—
271C2×D61—24no—
272C2×D61—24no—
273C2×D61—22no—
274C2×D61—24no—
275C2×D61—22no—
276C2×D61—22no—
277C2×D61—24no—
278C2×D61—22no—
279C2×D61#32718yes—
280C2×D61#32818yes—
281C2×D61#33912yes—
282C2×D61#34012yes—
283C2×D61#34012yes—
284C2×D61#34212yes—
285C2×D61C2×#9912yes—
286C2×D61C2×#10211yescharacteristic
287C2×D61C2×#10211yescharacteristic
288C2×D61C2×#10311yescharacteristic
289C2×D61C2×#10311yescharacteristic
290C2×D61C2×#10412yes—
291#6923—48no—
292#6923—84no—
293C4×C61—21no—
294C4×C61—21no—
295C4×C61—21no—
296C4×C61—21no—
297Dic61—21no—
298Dic61—21no—
299Dic61—21no—
300Dic61—21no—
301C22×C22⋊C8—611no—
302C2×#380—611no—
303C22×#95—611no—
304#1294—614no—
305C2×C61—22no—
306C2×C61—21no—
307C2×C61—21no—
308C2×C61#129414yescomplemented
309C2×C61C2×#33911yescharacteristic
310C2×C61C2×#34011yescharacteristic
311C2×C61C2×#34211yescharacteristic
312D61—21no—
313D61—22no—
314D61—21no—
315D61#129414yescomplemented
316D61C2×#32712yes—
317D61C2×#32812yes—
318C24×C4—611no—
319C24×C4—1221no—
320C23×C8—1221no—
321C22×C4⋊C4—612no—
322C22×C22⋊C4—1221no—
323C2×C22⋊C8—611no—
324C2×C22⋊C8—612no—
325C2×C22⋊C8—612no—
326C2×C22⋊C8—1221no—
327C2×C22⋊C8—1221no—
328C2×C22⋊C8—1221no—
329C2×C22⋊C8#692311yescharacteristic, complemented
330#380—612no—
331#380—612no—
332#380—1221no—
333#380—1221no—
334C2×#95—612no—
335C2×#95—612no—
336C2×#95—612no—
337C2×#95—1221no—
338C2×#95—1221no—
339C2×#95—1221no—
340C2×#95—1221no—
341C61C2×#129411yescharacteristic, complemented, Sylow
342C25—611no—
343C23×C4—611no—
344C23×C4—611no—
345C23×C4—611no—
346C23×C4—611no—
347C23×C4—611no—
348C23×C4—611no—
349C23×C4—611no—
350C23×C4—611no—
351C23×C4—611no—
352C23×C4—611no—
353C23×C4—611no—
354C23×C4—611no—
355C23×C4—611no—
356C23×C4—1222no—
357C23×C4—1222no—
358C23×C4—1222no—
359C23×C4—1228no—
360C23×C4—1222no—
361C23×C4—2444no—
362C23×C4—2442no—
363C23×C4—2442no—
364C23×C4—2444no—
365C23×C4C2×#692311yescharacteristic
366C22×C8—21no—
367C22×C8—1222no—
368C22×C8—1222no—
369C22×C8—1221no—
370C22×C8—2444no—
371C2×C4⋊C4—614no—
372C2×C4⋊C4—1222no—
373C2×C4⋊C4—2444no—
374C2×C22⋊C4—1222no—
375C2×C22⋊C4—1222no—
376C2×C22⋊C4—2442no—
377C2×C22⋊C4—2442no—
378C22⋊C8—21no—
379C22⋊C8—612no—
380C22⋊C8—1222no—
381C22⋊C8—1222no—
382C22⋊C8—1221no—
383C22⋊C8C2×#692312yescomplemented
384#95—614no—
385#95—1222no—
386#95—1222no—
387#95—1222no—
388#95—1222no—
389#95—1222no—
390C24—611no—
391C24—611no—
392C24—611no—
393C24—611no—
394C24—612no—
395C24—612no—
396C24—612no—
397C24—612no—
398C24—611no—
399C24—611no—
400C24—1224no—
401C24—1224no—
402C24C4⋊#692311yescharacteristic
403C22×C4—42no—
404C22×C4—611no—
405C22×C4—611no—
406C22×C4—611no—
407C22×C4—611no—
408C22×C4—611no—
409C22×C4—611no—
410C22×C4—611no—
411C22×C4—611no—
412C22×C4—611no—
413C22×C4—611no—
414C22×C4—611no—
415C22×C4—611no—
416C22×C4—611no—
417C22×C4—611no—
418C22×C4—611no—
419C22×C4—611no—
420C22×C4—611no—
421C22×C4—611no—
422C22×C4—611no—
423C22×C4—611no—
424C22×C4—611no—
425C22×C4—611no—
426C22×C4—1224no—
427C22×C4—1224no—
428C22×C4—1224no—
429C22×C4—1228no—
430C22×C4—1228no—
431C22×C4—1228no—
432C22×C4—1224no—
433C22×C4—2442no—
434C22×C4—2442no—
435C22×C4—2442no—
436C22×C4—2442no—
437C22×C4—2442no—
438C22×C4—2442no—
439C22×C4—2442no—
440C22×C4—2442no—
441C22×C4—2442no—
442C22×C4—2442no—
443C22×C4—2442no—
444C22×C4—2444no—
445C22×C4—2444no—
446C22×C4—2444no—
447C22×C4—2442no—
448C22×C4—2442no—
449C22×C4—2444no—
450C22×C4—2444no—
451C22×C4—2444no—
452C22×C4—2444no—
453C22×C4—24416no—
454C22×C4—24416no—
455C22×C4—2444no—
456C22×C4C4×#692311yescharacteristic
457C22×C4C4×#692311yescharacteristic
458C22×C4C4⋊#692311yescharacteristic
459C22×C4C22⋊#692311yescharacteristic
460C22×C4C22⋊#692311yescharacteristic
461C22×C4C22×#692311yescharacteristic
462C2×C8—22no—
463C2×C8—42no—
464C2×C8—1222no—
465C2×C8—2444no—
466C2×C8—2444no—
467C2×C8—2442no—
468C4⋊C4—2444no—
469C4⋊C4—2444no—
470C22⋊C4—2442no—
471C22⋊C4—2442no—
472C22⋊C4—2444no—
473C23—22no—
474C23—22no—
475C23—614no—
476C23—612no—
477C23—612no—
478C23—614no—
479C23—611no—
480C23—611no—
481C23—612no—
482C23—611no—
483C23—611no—
484C23—612no—
485C23—611no—
486C23—611no—
487C23—612no—
488C23—612no—
489C23—612no—
490C23—612no—
491C23—612no—
492C23—612no—
493C23—611no—
494C23—611no—
495C23—1222no—
496C23—1222no—
497C23—1222no—
498C23—1222no—
499C23—1222no—
500C23—1222no—
501C23—1228no—
502C23—1228no—
503C23—1228no—
504C23—1228no—
505C23—1222no—
506C23—1222no—
507C23—1222no—
508C23—1222no—
509C23(C2×#6923)⋊C411yescharacteristic
510C23(C2×#6923)⋊C411yescharacteristic
511C23#1451984512yes—
512C23#1451984612yes—
513C23C2×C4⋊#692311yescharacteristic
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—611no—
521C2×C4—611no—
522C2×C4—611no—
523C2×C4—611no—
524C2×C4—1222no—
525C2×C4—1222no—
526C2×C4—1222no—
527C2×C4—1222no—
528C2×C4—1222no—
529C2×C4—1222no—
530C2×C4—1222no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—1222no—
534C2×C4—1228no—
535C2×C4—4888no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2444no—
549C2×C4—2444no—
550C2×C4—2444no—
551C2×C4—2444no—
552C2×C4—2448no—
553C2×C4—2448no—
554C2×C4—24416no—
555C2×C4—2444no—
556C2×C4—24416no—
557C2×C4(C2×#6923)⋊C411yescharacteristic
558C2×C4(C2×#6923)⋊C411yescharacteristic
559C2×C4C2×C4×#692311yescharacteristic
560C2×C4C2×C22⋊#692311yescharacteristic
561C8—42no—
562C8—2442no—
563C22—21no—
564C22—21no—
565C22—24no—
566C22—24no—
567C22—21no—
568C22—21no—
569C22—612no—
570C22—612no—
571C22—618no—
572C22—618no—
573C22—612no—
574C22—612no—
575C22—611no—
576C22—612no—
577C22—611no—
578C22—611no—
579C22—612no—
580C22—611no—
581C22—1222no—
582C22—1222no—
583C22—1224no—
584C22—1222no—
585C22—1224no—
586C22—1224no—
587C22—1222no—
588C22—1224no—
589C22—1224no—
590C22—1224no—
591C22—1221no—
592C22—1221no—
593C22—1224no—
594C22—1224no—
595C22—1221no—
596C22—1221no—
597C22#1684063412yes—
598C22#1684063612yes—
599C22#1684063612yes—
600C22#1684063912yes—
601C22C2×(C2×#6923)⋊C411yescharacteristic
602C22C2×#1451984511yescharacteristic
603C22C2×#1451984611yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—21no—
608C4—1221no—
609C4—1221no—
610C4—1221no—
611C4—1221no—
612C4—4884no—
613C4—2448no—
614C2—21no—
615C2—21no—
616C2—22no—
617C2—612no—
618C2—614no—
619C2—612no—
620C2—1221no—
621C2—1222no—
622C2—1221no—
623C2#2146069414yesdirect product factor
624C2C2×#1684063411yescharacteristic
625C2C2×#1684063611yescharacteristic
626C2C2×#1684063911yescharacteristic
subgroupG/H
centerC23(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×C22⋊C8×C61C4
socleC23×C61#95
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenterC2×C22⋊C8#6923
hypocenterC61C2×#1294
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #21460694C2direct (N × H)
6. C22×C4⋊#6923C4semidirect
10. #16840704C4semidirect
16. C2×(C2×#6923)⋊C4C4semidirect
17. C2×(C2×#6923)⋊C4C4semidirect
21. C2×C22⋊#92418C4semidirect
25. C22⋊C8×D61C4semidirect
27. C2×C22⋊C8×C61C4semidirect
38. C2×C4⋊#6923C2×C4semidirect
48. (C2×#6923)⋊C4C2×C4semidirect
69. C22⋊#92418C2×C4semidirect
75. C22⋊C8×C61C2×C4semidirect
308. C2×C61#1294semidirect
315. D61#1294semidirect
329. C2×C22⋊C8#6923semidirect
341. C61C2×#1294semidirect
383. C22⋊C8C2×#6923semidirect
623. C2#21460694direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407042
C22×(C2×#6923)⋊C42
#214606942
C2×C22⋊C8×D612
C2×#129461