Finite Group Databasebeta

← C2×#21445921 #29679855

Subgroups — C2×#21445921 #29679855

Order 15616.

1354 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840230C211yesmaximal, characteristic
2C2×#16839744C211yesmaximal, characteristic
3C2×#16839735C211yesmaximal, characteristic
4#21445921C218yesmaximal, direct product factor
5C2×#16839523C211yesmaximal, characteristic, complemented
6C2×#16839521C211yesmaximal, characteristic, complemented
7C2×#16839518C211yesmaximal, characteristic, complemented
8C2×C61×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11#16840230—22no—
12#16840230—22no—
13#16840230C414yescomplemented
14#16840230C2214yes—
15C2×#14519742—21no—
16C2×#14519739—21no—
17C2×#14519737—22no—
18C2×#14519736C2211yescharacteristic
19C2×#14519734C412yescomplemented
20C22×C4×Dic61C2211yescharacteristic
21C2×C42×D61C412yescomplemented
22#16839744—22no—
23#16839744C2214yes—
24C2×#14519695—21no—
25C2×#14519693—21no—
26#16839735—22no—
27#16839735C2214yes—
28C2×#14519691—22no—
29#16839523C2214yescomplemented
30#16839521C2214yescomplemented
31#16839518C2214yescomplemented
32C22×M16×C61C2211yescharacteristic
33C2×#117×C61C2211yescharacteristic
34C2×#117×C61C2211yescharacteristic
35C61×H(3,ℤ/4)C2214yescomplemented
36C2×#11758222—21no—
37C2×#11758222—21no—
38C2×#11758222—21no—
39C2×#11758222—21no—
40C2×#11758222—21no—
41C2×#11758222—21no—
42C2×#11758222—21no—
43C2×#11758222—21no—
44C2×#11758222C2×C412yes—
45C2×#11758222D412yes—
46C2×#11758222D412yes—
47C2×#11758222C2312yes—
48C22×Dic122D411yescharacteristic
49C22×D244D411yescharacteristic
50C22×C22⋊D61D412yes—
51C23×Dic61—21no—
52C22×C4×D61—22no—
53C22×C4×D61C2×C412yes—
54C2×#11758194—21no—
55C2×#11758194—21no—
56C2×#11758194—21no—
57C2×#11758194—21no—
58C2×#11758194—21no—
59C2×#11758194C2312yes—
60C22×#92418—21no—
61#14519742—24no—
62#14519742—24no—
63#14519739—24no—
64#14519739—24no—
65#14519737—28no—
66#14519737—28no—
67#14519736—21no—
68#14519736—21no—
69#14519736—21no—
70#14519736C2312yes—
71#14519734—24no—
72#14519734C2×C418yescomplemented
73C2×C4⋊Dic61—21no—
74C2×#11758196—22no—
75C2×C22⋊Dic61—21no—
76C2×#11758198—22no—
77C2×C4×Dic61—21no—
78C2×C4×Dic61—21no—
79C2×C4×Dic61—21no—
80C2×C4×Dic61—22no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61C2×C411yescharacteristic
83C2×C4×Dic61C2×C411yescharacteristic
84C2×C4×Dic61C2×C412yes—
85C2×C4×Dic61C2312yes—
86C42×D61—24no—
87C42×D61C2×C418yescomplemented
88#14519695—24no—
89#14519693—24no—
90#14519691—28no—
91C23×C4×C61C2311yescharacteristic
92C2×M16×C61—21no—
93C2×M16×C61—21no—
94C2×M16×C61—21no—
95C2×M16×C61—21no—
96C2×M16×C61—21no—
97C2×M16×C61C2312yes—
98C22×C8×C61—21no—
99#117×C61—21no—
100#117×C61—21no—
101#117×C61—21no—
102#117×C61—21no—
103#117×C61—21no—
104#117×C61C2×C412yes—
105#117×C61C2312yes—
106#117×C61C2312yes—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C22⋊C4×C61—21no—
110C2×C22⋊C4×C61—21no—
111C2×C42×C61—21no—
112C2×C42×C61C2×C412yes—
113C24×C61C2×D411yescharacteristic
114C23×D61C22⋊C412yes—
115C22×C4×C61—22no—
116C22×C4×C61—41no—
117C22×C4×C61C22×C411yescharacteristic
118C22×C4×C61C22×C411yescharacteristic
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61#4111yescharacteristic
123C22×C4×C61#4111yescharacteristic
124C22×C4×C61#4111yescharacteristic
125C22×C4×C61#4111yescharacteristic
126C22×C4×C61#4111yescharacteristic
127C22×C4×C61#4111yescharacteristic
128C22×C4×C61#4111yescharacteristic
129C22×C4×C61#4111yescharacteristic
130C22×C4×C61C2411yescharacteristic
131C2×C22⋊D61—22no—
132C2×C22⋊D61—22no—
133C2×C22⋊D61—22no—
134C2×C22⋊D61—22no—
135C2×C22⋊D61C22⋊C414yes—
136C2×C22⋊D61C2×D414yes—
137C22×Dic61—21no—
138C22×Dic61—21no—
139C22×Dic61—22no—
140C22×Dic61—22no—
141C22×Dic61—44no—
142C22×Dic61—41no—
143C22×Dic61C22⋊C412yes—
144#11758222—22no—
145#11758222—22no—
146#11758222—22no—
147#11758222—22no—
148#11758222—22no—
149#11758222—22no—
150#11758222—22no—
151#11758222—22no—
152#11758222—22no—
153#11758222—22no—
154#11758222—22no—
155#11758222—22no—
156#11758222—22no—
157#11758222—22no—
158#11758222—22no—
159#11758222—22no—
160C2×D244—21no—
161C2×D244—21no—
162C2×D244—21no—
163C2×D244—21no—
164C2×D244C22⋊C412yes—
165C2×D244C2×D412yes—
166C2×C4×D61—22no—
167C2×C4×D61—22no—
168C2×C4×D61—22no—
169C2×C4×D61—22no—
170C2×C4×D61—28no—
171C2×C4×D61—48no—
172C2×C4×D61C22⋊C414yes—
173C2×C4×D61C22×C414yes—
174C2×Dic122—21no—
175C2×Dic122—21no—
176C2×Dic122—21no—
177C2×Dic122—21no—
178C2×Dic122C22⋊C412yes—
179C2×Dic122C2×D412yes—
180M16×C61—22no—
181M16×C61—22no—
182M16×C61—41no—
183M16×C61—41no—
184C2×C8×C61—22no—
185C2×C8×C61—41no—
186C2×C8×C61—41no—
187C4⋊C4×C61—22no—
188C4⋊C4×C61—22no—
189C4⋊C4×C61—22no—
190C4⋊C4×C61—41no—
191C22⋊C4×C61—22no—
192C22⋊C4×C61—22no—
193C22⋊C4×C61—22no—
194C22⋊C4×C61—41no—
195C42×C61—22no—
196C42×C61—22no—
197C42×C61—41no—
198C42×C61C22×C414yes—
199C22⋊Dic61—22no—
200C22⋊Dic61—41no—
201#11758198—28no—
202C4⋊Dic61—22no—
203C4⋊Dic61—41no—
204#11758196—28no—
205C4×Dic61—21no—
206C4×Dic61—21no—
207C4×Dic61—22no—
208C4×Dic61—22no—
209C4×Dic61—28no—
210C4×Dic61—22no—
211C4×Dic61—41no—
212C4×Dic61C22×C412yes—
213C4×Dic61C22×C412yes—
214#11758194—22no—
215#11758194—22no—
216#11758194—41no—
217#11758194—41no—
218C2×#92418—22no—
219C2×#92418—41no—
220C2×#92418—41no—
221C23×C61—42no—
222C23×C61C2×C22⋊C411yescharacteristic
223C23×C61C2×C22⋊C411yescharacteristic
224C23×C61#12311yescharacteristic
225C23×C61#12311yescharacteristic
226C23×C61#12311yescharacteristic
227C23×C61#12311yescharacteristic
228C23×C61C22×D411yescharacteristic
229C22×D61—22no—
230C22×D61—22no—
231C22×D61—44no—
232C22×D61C2×C22⋊C414yes—
233C2×C4×C61—24no—
234C2×C4×C61—44no—
235C2×C4×C61—42no—
236C2×C4×C61—82no—
237C2×C4×C61C2×C22⋊C411yescharacteristic
238C2×C4×C61C2×C22⋊C411yescharacteristic
239C2×C4×C61#11711yescharacteristic
240C2×C4×C61#11711yescharacteristic
241C2×C4×C61#11711yescharacteristic
242C2×C4×C61#11711yescharacteristic
243C2×C4×C61#11711yescharacteristic
244C2×C4×C61#11711yescharacteristic
245C2×C4×C61#11711yescharacteristic
246C2×C4×C61#11711yescharacteristic
247C2×C4×C61#12311yescharacteristic
248C2×C4×C61#12311yescharacteristic
249C2×C4×C61#12311yescharacteristic
250C2×C4×C61#12311yescharacteristic
251C2×C4×C61#12311yescharacteristic
252C2×C4×C61#12311yescharacteristic
253C2×C4×C61#12311yescharacteristic
254C2×C4×C61#12311yescharacteristic
255C2×C4×C61#12311yescharacteristic
256C2×C4×C61#12311yescharacteristic
257C2×C4×C61#12311yescharacteristic
258C2×C4×C61#12311yescharacteristic
259C2×C4×C61C23×C411yescharacteristic
260C2×C4×C61C22×D411yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C2×C4×C61C2×#4111yescharacteristic
264C2×C4×C61C2×#4111yescharacteristic
265C22⋊D61—24no—
266C22⋊D61—24no—
267C22⋊D61—24no—
268C22⋊D61—24no—
269C2×Dic61—24no—
270C2×Dic61—22no—
271C2×Dic61—22no—
272C2×Dic61—22no—
273C2×Dic61—22no—
274C2×Dic61—44no—
275C2×Dic61—44no—
276C2×Dic61—42no—
277C2×Dic61—42no—
278C2×Dic61—82no—
279C2×Dic61C2×C22⋊C414yes—
280D244—22no—
281D244—22no—
282D244—22no—
283D244—22no—
284C4×D61—24no—
285C4×D61—24no—
286C4×D61—24no—
287C4×D61—24no—
288C4×D61—416no—
289Dic122—22no—
290Dic122—22no—
291Dic122—22no—
292Dic122—22no—
293C8×C61—42no—
294#92418—42no—
295C2×#1827—611nomaximal, Sylow
296C22×C61—22no—
297C22×C61—22no—
298C22×C61—22no—
299C22×C61—41no—
300C22×C61—41no—
301C22×C61—41no—
302C22×C61—41no—
303C22×C61#38111yescharacteristic
304C22×C61#38111yescharacteristic
305C22×C61#38111yescharacteristic
306C22×C61#38111yescharacteristic
307C22×C61C22×C22⋊C411yescharacteristic
308C22×C61C2×#12311yescharacteristic
309C22×C61C2×#12311yescharacteristic
310C2×D61—24no—
311C2×D61—44no—
312C2×D61—44no—
313C2×D61—44no—
314C4×C61—44no—
315C4×C61—82no—
316C4×C61#38111yescharacteristic
317C4×C61#38111yescharacteristic
318C4×C61#38111yescharacteristic
319C4×C61#38111yescharacteristic
320C4×C61C2×#11711yescharacteristic
321C4×C61C2×#11711yescharacteristic
322C4×C61C2×#12311yescharacteristic
323C4×C61C2×#12311yescharacteristic
324Dic61—24no—
325Dic61—24no—
326Dic61—42no—
327Dic61—82no—
328C2×C4×#41—611no—
329C2×#413—611no—
330C2×#410—611no—
331#1827—618no—
332C2×#339—611no—
333C2×#339—611no—
334C2×H(3,ℤ/4)—611no—
335C2×H(3,ℤ/4)D6111yescharacteristic, complemented
336C2×C61—21no—
337C2×C61—21no—
338C2×C61—21no—
339C2×C61—21no—
340C2×C61—21no—
341C2×C61—21no—
342C2×C61#182712yescomplemented
343C2×C61C2×#38111yescharacteristic
344D61—44no—
345C22×#41—611no—
346C22×M16—611no—
347C22×M16C2×D6111yescharacteristic
348C4×#41—614no—
349C4×#41—614no—
350C4×#41—1222no—
351C4×#41—1222no—
352C2×C4×Q8—1221no—
353C2×C4×D4—1222no—
354C2×C4×D4—1221no—
355C2×#117—612no—
356C2×#117—611no—
357C2×#117C2×D6111yescharacteristic
358C2×#117C2×D6111yescharacteristic
359C22×C42—611no—
360C22×C42—612no—
361#413—614no—
362#413—1222no—
363C2×#101—1221no—
364C2×#100—1221no—
365#410—614no—
366#410—1222no—
367C2×#99—1222no—
368#339—614no—
369#339—614no—
370H(3,ℤ/4)—614no—
371H(3,ℤ/4)C2×D6114yescomplemented
372C61C2×#182711yescharacteristic, complemented, Sylow
373C2×#41—612no—
374C2×#41—612no—
375C2×#41—612no—
376C2×#41—612no—
377C2×#41—1221no—
378C2×#41—1221no—
379C2×#41—1221no—
380C2×#41—1221no—
381C2×#41—1221no—
382C2×#41—1221no—
383C2×#41—1221no—
384C2×#41—1221no—
385C22×Q8—611no—
386C22×D4—612no—
387C22×D4—611no—
388C23×C4—612no—
389C23×C4—1222no—
390C23×C4—1221no—
391C23×C4C22×D6111yescharacteristic
392C2×M16—21no—
393C2×M16—21no—
394C2×M16—21no—
395C2×M16—21no—
396C2×M16—21no—
397C2×M16—612no—
398C2×M16—1221no—
399C2×M16—1221no—
400C2×M16—1221no—
401C2×M16—1221no—
402C2×M16—1221no—
403C2×M16C22×D6112yes—
404C22×C8—21no—
405C22×C8—1221no—
406C4×Q8—1224no—
407C4×Q8—1224no—
408C4×D4—1228no—
409C4×D4—1228no—
410C4×D4—1224no—
411C4×D4—1224no—
412#117—21no—
413#117—21no—
414#117—21no—
415#117—21no—
416#117—21no—
417#117—618no—
418#117—612no—
419#117—1224no—
420#117—1221no—
421#117—1221no—
422#117—1221no—
423#117C4×D6112yes—
424#117C22×D6112yes—
425#117C22×D6112yes—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—1222no—
429C2×C4⋊C4—1221no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—1222no—
433C2×C22⋊C4—1221no—
434C2×C42—21no—
435C2×C42—611no—
436C2×C42—612no—
437C2×C42—611no—
438C2×C42—612no—
439C2×C42—618no—
440C2×C42—1224no—
441C2×C42—1222no—
442C2×C42—1221no—
443C2×C42—1221no—
444C2×C42—1221no—
445C2×C42—1221no—
446C2×C42C4×D6112yes—
447#101—1224no—
448#100—1224no—
449#99—1228no—
450C24—612no—
451C24D4×D6111yescharacteristic
452#41—1222no—
453#41—1222no—
454#41—1222no—
455#41—1222no—
456#41—1222no—
457#41—1222no—
458#41—1222no—
459#41—1222no—
460#41—1222no—
461#41—1222no—
462#41—1222no—
463#41—1222no—
464#41—1222no—
465#41—1222no—
466#41—1222no—
467#41—1222no—
468C2×Q8—612no—
469C2×Q8—612no—
470C2×Q8—1221no—
471C2×Q8—1221no—
472C2×Q8—1221no—
473C2×Q8—1221no—
474C2×D4—614no—
475C2×D4—614no—
476C2×D4—612no—
477C2×D4—612no—
478C2×D4—1222no—
479C2×D4—1222no—
480C2×D4—1222no—
481C2×D4—1222no—
482C2×D4—1221no—
483C2×D4—1221no—
484C2×D4—1221no—
485C2×D4—1221no—
486C22×C4—22no—
487C22×C4—41no—
488C22×C4—612no—
489C22×C4—614no—
490C22×C4—614no—
491C22×C4—1228no—
492C22×C4—1221no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—1221no—
499C22×C4—1222no—
500C22×C4—2448no—
501C22×C4—2444no—
502C22×C4—2441no—
503C22×C4C2×C4×D6111yescharacteristic
504C22×C4C2×C4×D6111yescharacteristic
505C22×C4#1175822211yescharacteristic
506C22×C4#1175822211yescharacteristic
507C22×C4#1175822211yescharacteristic
508C22×C4#1175822211yescharacteristic
509C22×C4D4×D6111yescharacteristic
510C22×C4D4×D6111yescharacteristic
511C22×C4D4×D6111yescharacteristic
512C22×C4#1175822411yescharacteristic
513C22×C4#1175822411yescharacteristic
514C22×C4#1175822611yescharacteristic
515C22×C4#1175822611yescharacteristic
516C22×C4C23×D6111yescharacteristic
517M16—22no—
518M16—22no—
519M16—41no—
520M16—41no—
521M16—1222no—
522M16—1222no—
523M16—2441no—
524M16—2441no—
525C2×C8—22no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—1222no—
529C2×C8—2441no—
530C2×C8—2441no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—41no—
535C4⋊C4—1228no—
536C4⋊C4—1222no—
537C4⋊C4—2441no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—41no—
542C22⋊C4—1228no—
543C22⋊C4—1222no—
544C22⋊C4—2441no—
545C42—22no—
546C42—22no—
547C42—41no—
548C42—612no—
549C42—612no—
550C42—1228no—
551C42—1222no—
552C42—1221no—
553C42—1221no—
554C42—1222no—
555C42—1222no—
556C42—2441no—
557C42C2×C4×D6114yes—
558C23—42no—
559C23—614no—
560C23—1222no—
561C23—1222no—
562C23—2444no—
563C23C22⋊C4×D6111yescharacteristic
564C23C22⋊C4×D6111yescharacteristic
565C23#1451975911yescharacteristic
566C23#1451975911yescharacteristic
567C23#1451976211yescharacteristic
568C23#1451976211yescharacteristic
569C23C2×D4×D6111yescharacteristic
570Q8—1222no—
571Q8—1222no—
572Q8—1222no—
573Q8—1222no—
574D4—1224no—
575D4—1224no—
576D4—1224no—
577D4—1224no—
578D4—1222no—
579D4—1222no—
580D4—1222no—
581D4—1222no—
582C2×C4—24no—
583C2×C4—44no—
584C2×C4—42no—
585C2×C4—82no—
586C2×C4—614no—
587C2×C4—1224no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—1222no—
591C2×C4—1224no—
592C2×C4—1224no—
593C2×C4—1224no—
594C2×C4—1224no—
595C2×C4—1222no—
596C2×C4—4882no—
597C2×C4—24416no—
598C2×C4—2444no—
599C2×C4—2444no—
600C2×C4—2442no—
601C2×C4—2442no—
602C2×C4C22⋊C4×D6111yescharacteristic
603C2×C4C22⋊C4×D6111yescharacteristic
604C2×C4#1451973411yescharacteristic
605C2×C4#1451973411yescharacteristic
606C2×C4#1451973411yescharacteristic
607C2×C4#1451973411yescharacteristic
608C2×C4#1451973511yescharacteristic
609C2×C4#1451973511yescharacteristic
610C2×C4#1451973511yescharacteristic
611C2×C4#1451973511yescharacteristic
612C2×C4#1451975911yescharacteristic
613C2×C4#1451975911yescharacteristic
614C2×C4#1451975911yescharacteristic
615C2×C4#1451975911yescharacteristic
616C2×C4#1451975911yescharacteristic
617C2×C4#1451975911yescharacteristic
618C2×C4#1451976211yescharacteristic
619C2×C4#1451976211yescharacteristic
620C2×C4#1451976211yescharacteristic
621C2×C4#1451976211yescharacteristic
622C2×C4#1451976211yescharacteristic
623C2×C4#1451976211yescharacteristic
624C2×C4C22×C4×D6111yescharacteristic
625C2×C4C2×D4×D6111yescharacteristic
626C2×C4C2×#1175822411yescharacteristic
627C2×C4C2×#1175822211yescharacteristic
628C2×C4C2×#1175822211yescharacteristic
629C2×C4C2×#1175822611yescharacteristic
630C8—42no—
631C8—2442no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—1224no—
640C22—2444no—
641C22—2444no—
642C22—2444no—
643C22#1683962411yescharacteristic
644C22#1683962411yescharacteristic
645C22#1683962411yescharacteristic
646C22#1683962411yescharacteristic
647C22C2×C22⋊C4×D6111yescharacteristic
648C22C2×#1451975911yescharacteristic
649C22C2×#1451976211yescharacteristic
650C4—44no—
651C4—82no—
652C4—1224no—
653C4—1224no—
654C4—4882no—
655C4—2442no—
656C4#1683962411yescharacteristic
657C4#1683962411yescharacteristic
658C4#1683962411yescharacteristic
659C4#1683962411yescharacteristic
660C4C2×#1451973411yescharacteristic
661C4C2×#1451973511yescharacteristic
662C4C2×#1451975911yescharacteristic
663C4C2×#1451976211yescharacteristic
664C2—21no—
665C2—21no—
666C2—21no—
667C2—21no—
668C2—21no—
669C2—21no—
670C2—2444no—
671C2#2144592112yesdirect product factor
672C2C2×#1683962411yescharacteristic
subgroupG/H
centerC2×C4#14519734
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×H(3,ℤ/4)C2
socleC22×C61#381
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenterC2×H(3,ℤ/4)D61
hypocenterC61C2×#1827
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×#117 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. #21445921C2direct (N × H)
5. C2×#16839523C2semidirect
6. C2×#16839521C2semidirect
7. C2×#16839518C2semidirect
8. C2×C61×H(3,ℤ/4)C2semidirect
13. #16840230C4semidirect
19. C2×#14519734C4semidirect
21. C2×C42×D61C4semidirect
29. #16839523C22semidirect
30. #16839521C22semidirect
31. #16839518C22semidirect
35. C61×H(3,ℤ/4)C22semidirect
72. #14519734C2×C4semidirect
87. C42×D61C2×C4semidirect
335. C2×H(3,ℤ/4)D61semidirect
342. C2×C61#1827semidirect
371. H(3,ℤ/4)C2×D61semidirect
372. C61C2×#1827semidirect
671. C2#21445921direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402302
C2×#168397442
C2×#168397352
#214459212
C2×#168395232
C2×#168395212
C2×#168395182
C2×C61×H(3,ℤ/4)2
C2×#182761