Finite Group Databasebeta

← C2×#11727730 #13320937

Subgroups — C2×#11727730 #13320937

Order 1792.

1834 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90482C211yesmaximal, characteristic
2C2×C7×#407C211yesmaximal, characteristic, complemented
3C22×C7⋊#95C211yesmaximal, characteristic, complemented
4#11727730C218yesmaximal, direct product factor
5C2×#89262C212yesmaximal, complemented
6C2×#89265C212yesmaximal, complemented
7C24×C4×C7C2211yescharacteristic
8C24×Dic7—21no—
9C22×#1157C411yescharacteristic, complemented
10C22×C7×M16—21no—
11C2×#6516—21no—
12#90482—22no—
13#90482—22no—
14#90482C414yescomplemented
15#90482C2214yes—
16C2×#6493C411yescharacteristic, complemented
17C2×#6493C2211yescharacteristic
18C2×#6492—21no—
19C2×C4×C22⋊D7—21no—
20C2×C4×C22⋊D7—21no—
21C2×#6489C411yescharacteristic, complemented
22C2×#6487C411yescharacteristic, complemented
23C2×#6487C2211yescharacteristic
24C7×#407—22no—
25C7×#407C2214yescomplemented
26C2×C7×C22⋊C8—21no—
27C2×C7×C22⋊C8C2212yes—
28C2×C7⋊#95—22no—
29C2×C7⋊#95—21no—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2214yescomplemented
32#89265C2218yescomplemented
33#89262C2218yescomplemented
34C2×#1504—71nomaximal, Sylow
35C25×C7D411yescharacteristic
36C23×C4×C7—44no—
37C23×C4×C7C2×C411yescharacteristic
38C23×C4×C7C2×C411yescharacteristic
39C23×C4×C7C2×C412yes—
40C23×C4×C7D411yescharacteristic
41C23×C4×C7D412yes—
42C23×C4×C7D411yescharacteristic
43C23×C4×C7D411yescharacteristic
44C23×C4×C7D412yes—
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2312yes—
47C22×C22⋊D7—21no—
48C22×C22⋊D7—21no—
49C22×C22⋊D7—21no—
50C23×Dic7—28no—
51C23×Dic7—22no—
52C23×Dic7—24no—
53C23×Dic7—44no—
54C23×Dic7—44no—
55C2×#1157—22no—
56C2×#1157—44no—
57C2×#1157C2×C414yescomplemented
58C22×D28C2×C411yescharacteristic, complemented
59C22×C4×D7—21no—
60C22×Dic14C2×C411yescharacteristic, complemented
61C2×C7×M16—24no—
62C2×C7×M16—44no—
63C22×C7×C8—22no—
64#6516—24no—
65#6516—24no—
66C2×C22⋊Dic7—21no—
67C2×C22⋊Dic7—21no—
68C2×C22⋊Dic7—21no—
69#6493—22no—
70#6493—21no—
71#6493—21no—
72#6493C2×C414yescomplemented
73#6493C2×C412yescomplemented
74#6493C2312yes—
75#6492—24no—
76#6492—24no—
77C4×C22⋊D7—24no—
78C4×C22⋊D7—24no—
79C4×C22⋊D7—24no—
80C4×C22⋊D7—24no—
81C2×(C2×D7)⋊C4—21no—
82C2×(C2×D7)⋊C4—21no—
83#6489—22no—
84#6489C2×C414yescomplemented
85C2×C4⋊Dic7C2×C411yescharacteristic, complemented
86C2×C4⋊Dic7C2×C411yescharacteristic, complemented
87#6487—22no—
88#6487—21no—
89#6487—21no—
90#6487C2×C414yescomplemented
91#6487C2×C412yescomplemented
92#6487C2312yes—
93C2×Dic7⋊C4—21no—
94C2×Dic7⋊C4—21no—
95C2×C4×Dic7—21no—
96C7×C22⋊C8—24no—
97C7×C22⋊C8—22no—
98C7×C22⋊C8C2314yes—
99C7⋊#95—22no—
100C7⋊#95—24no—
101C7⋊#95C2314yes—
102C2×#525—71no—
103C2×#407D711yescharacteristic, complemented
104C22×#95—71no—
105#1504—78no—
106C2×#328—72no—
107C2×#327—72no—
108C24×C7—24no—
109C24×C7—24no—
110C24×C7—22no—
111C24×C7—22no—
112C24×C7C22⋊C412yes—
113C24×C7C22⋊C411yescharacteristic
114C24×C7C22⋊C411yescharacteristic
115C24×C7C2×D412yes—
116C24×C7C2×D411yescharacteristic
117C23×D7—21no—
118C22×C4×C7—24no—
119C22×C4×C7—24no—
120C22×C4×C7—42no—
121C22×C4×C7—44no—
122C22×C4×C7—42no—
123C22×C4×C7—44no—
124C22×C4×C7—42no—
125C22×C4×C7—44no—
126C22×C4×C7—42no—
127C22×C4×C7—44no—
128C22×C4×C7C22⋊C411yescharacteristic
129C22×C4×C7C22⋊C411yescharacteristic
130C22×C4×C7C22⋊C412yes—
131C22×C4×C7C22⋊C412yes—
132C22×C4×C7C22⋊C412yes—
133C22×C4×C7C22⋊C412yes—
134C22×C4×C7C22⋊C412yes—
135C22×C4×C7C22×C411yescharacteristic
136C22×C4×C7C22×C412yes—
137C22×C4×C7C22×C411yescharacteristic
138C22×C4×C7C22×C412yes—
139C22×C4×C7C2×D411yescharacteristic
140C22×C4×C7C2×D412yes—
141C22×C4×C7C2×D411yescharacteristic
142C22×C4×C7C2×D412yes—
143C22×C4×C7C2×D411yescharacteristic
144C22×C4×C7C2×D412yes—
145C22×C4×C7C2411yescharacteristic
146C2×C22⋊D7—22no—
147C2×C22⋊D7—24no—
148C2×C22⋊D7—24no—
149C2×C22⋊D7—22no—
150C2×C22⋊D7—44no—
151C2×C22⋊D7—44no—
152C2×C22⋊D7—42no—
153C2×C22⋊D7—42no—
154C22×Dic7—28no—
155C22×Dic7—216no—
156C22×Dic7—21no—
157C22×Dic7—21no—
158C22×Dic7—21no—
159C22×Dic7—24no—
160C22×Dic7—432no—
161C22×Dic7—44no—
162C22×Dic7—48no—
163C22×Dic7—48no—
164C22×Dic7—44no—
165#1157—48no—
166#1157—48no—
167C2×D28—21no—
168C2×D28—42no—
169C2×D28C22×C412yescomplemented
170C2×C4×D7—24no—
171C2×C4×D7—44no—
172C2×Dic14—21no—
173C2×Dic14—42no—
174C2×Dic14C22×C412yescomplemented
175C7×M16—48no—
176C2×C7×C8—24no—
177C2×C7×C8—44no—
178C22⋊Dic7—22no—
179C22⋊Dic7—24no—
180C22⋊Dic7—24no—
181C22⋊Dic7—22no—
182(C2×D7)⋊C4—24no—
183(C2×D7)⋊C4—22no—
184(C2×D7)⋊C4—22no—
185C4⋊Dic7—21no—
186C4⋊Dic7—21no—
187C4⋊Dic7C22×C412yescomplemented
188C4⋊Dic7C22×C412yescomplemented
189Dic7⋊C4—24no—
190Dic7⋊C4—22no—
191Dic7⋊C4—22no—
192C4×Dic7—24no—
193C22×#41—71no—
194C24×C4—141no—
195C24×C4C2×D711yescharacteristic
196C22×M16—21no—
197#525—74no—
198#525—74no—
199#525—142no—
200#525—142no—
201C2×#123—141no—
202C2×C22⋊Q8—71no—
203C2×C22⋊Q8—71no—
204C2×#121—71no—
205C2×#121—71no—
206C2×#120—141no—
207C2×C4×D4—141no—
208C2×C4×D4—141no—
209C2×#117—71no—
210#407—22no—
211#407C2×D714yescomplemented
212C2×C22⋊C8—21no—
213C2×C22⋊C8C2×D712yes—
214C2×#95—72no—
215C2×#95—74no—
216C2×#95—141no—
217C2×#95—142no—
218#328—78no—
219#327—78no—
220C23×C7—216no—
221C23×C7—216no—
222C23×C7—22no—
223C23×C7—22no—
224C23×C7—24no—
225C23×C7—22no—
226C23×C7—24no—
227C23×C7—22no—
228C23×C7—24no—
229C23×C7—22no—
230C23×C7—22no—
231C23×C7—24no—
232C23×C7—22no—
233C23×C7—24no—
234C23×C7—22no—
235C23×C7#9914yes—
236C23×C7#10414yes—
237C23×C7C2×C22⋊C412yes—
238C23×C7C2×C22⋊C411yescharacteristic
239C23×C7C2×C22⋊C412yes—
240C23×C7C2×C22⋊C411yescharacteristic
241C23×C7AGL(1,ℤ/8)12yes—
242C23×C7#13712yes—
243C23×C7C22×D411yescharacteristic
244C22×D7—22no—
245C22×D7—42no—
246C22×D7—42no—
247C22×D7—42no—
248C2×C4×C7—22no—
249C2×C4×C7—24no—
250C2×C4×C7—22no—
251C2×C4×C7—22no—
252C2×C4×C7—24no—
253C2×C4×C7—24no—
254C2×C4×C7—24no—
255C2×C4×C7—22no—
256C2×C4×C7—42no—
257C2×C4×C7—42no—
258C2×C4×C7—42no—
259C2×C4×C7—41no—
260C2×C4×C7—42no—
261C2×C4×C7—41no—
262C2×C4×C7—42no—
263C2×C4×C7—41no—
264C2×C4×C7—42no—
265C2×C4×C7—41no—
266C2×C4×C7C2×C22⋊C412yes—
267C2×C4×C7C2×C22⋊C412yes—
268C2×C4×C7C2×C22⋊C411yescharacteristic
269C2×C4×C7C2×C22⋊C411yescharacteristic
270C2×C4×C7C23×C411yescharacteristic
271C2×C4×C7C22×D411yescharacteristic
272C22⋊D7—42no—
273C22⋊D7—42no—
274C22⋊D7—48no—
275C22⋊D7—44no—
276C22⋊D7—48no—
277C2×Dic7—28no—
278C2×Dic7—22no—
279C2×Dic7—22no—
280C2×Dic7—22no—
281C2×Dic7—432no—
282C2×Dic7—44no—
283C2×Dic7—416no—
284C2×Dic7—44no—
285C2×Dic7—42no—
286C2×Dic7—42no—
287C2×Dic7—42no—
288D28—42no—
289D28—42no—
290C4×D7—48no—
291Dic14—42no—
292Dic14—42no—
293C7×C8—44no—
294C25D2811yescharacteristic
295C2×#41—74no—
296C2×#41—142no—
297C2×#41—284no—
298C22×Q8—71no—
299C22×D4—71no—
300C22×D4—141no—
301C22×D4—141no—
302C22×D4—141no—
303C23×C4—44no—
304C23×C4—148no—
305C23×C4—144no—
306C23×C4—142no—
307C23×C4—141no—
308C23×C4—284no—
309C23×C4—284no—
310C23×C4C4×D711yescharacteristic
311C23×C4C4×D711yescharacteristic
312C23×C4C4×D712yes—
313C23×C4D2811yescharacteristic
314C23×C4D2812yes—
315C23×C4C22⋊D711yescharacteristic
316C23×C4C22⋊D711yescharacteristic
317C23×C4C22⋊D712yes—
318C23×C4C22×D711yescharacteristic
319C23×C4C22×D712yes—
320C2×M16—24no—
321C2×M16—44no—
322C22×C8—22no—
323#123—144no—
324#123—144no—
325C22⋊Q8—74no—
326C22⋊Q8—72no—
327C22⋊Q8—72no—
328C22⋊Q8—142no—
329C22⋊Q8—141no—
330C22⋊Q8—141no—
331#121—74no—
332#121—72no—
333#121—72no—
334#121—142no—
335#121—141no—
336#121—141no—
337#120—144no—
338#120—144no—
339C4×D4—144no—
340C4×D4—144no—
341C4×D4—144no—
342C4×D4—144no—
343#117—74no—
344#117—142no—
345C2×C4⋊C4—71no—
346C2×C4⋊C4—71no—
347C2×C4⋊C4—141no—
348C2×C4⋊C4—141no—
349C2×C22⋊C4—141no—
350C2×C22⋊C4—141no—
351C2×C22⋊C4—141no—
352C2×C22⋊C4—141no—
353C2×C22⋊C4—141no—
354C2×C42—141no—
355C22⋊C8—24no—
356C22⋊C8—22no—
357C22⋊C8C22×D714yes—
358#95—74no—
359#95—144no—
360#95—142no—
361C22×C7—28no—
362C22×C7—28no—
363C22×C7—216no—
364C22×C7—21no—
365C22×C7—21no—
366C22×C7—22no—
367C22×C7—22no—
368C22×C7—22no—
369C22×C7—21no—
370C22×C7—22no—
371C22×C7—21no—
372C22×C7—24no—
373C22×C7—28no—
374C22×C7—28no—
375C22×C7—24no—
376C22×C7C2×#9914yes—
377C22×C7C2×#9912yes—
378C22×C7#41712yes—
379C22×C7#41712yes—
380C22×C7C2×#10414yes—
381C22×C7C2×#10412yes—
382C22×C7C22×C22⋊C411yescharacteristic
383C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
384C22×C7C2×#13711yescharacteristic
385C2×D7—42no—
386C2×D7—42no—
387C2×D7—42no—
388C2×D7—84no—
389C4×C7—21no—
390C4×C7—21no—
391C4×C7—21no—
392C4×C7—22no—
393C4×C7—21no—
394C4×C7—22no—
395Dic7—48no—
396Dic7—42no—
397Dic7—42no—
398Dic7—42no—
399C24—22no—
400C24—22no—
401C24—24no—
402C24—24no—
403C24—141no—
404C24(C2×D7)⋊C412yes—
405C24(C2×D7)⋊C411yescharacteristic
406C24(C2×D7)⋊C411yescharacteristic
407C24C2×D2812yes—
408C24C2×D2811yescharacteristic
409#41—288no—
410#41—288no—
411C2×Q8—72no—
412C2×Q8—141no—
413C2×Q8—282no—
414C2×D4—72no—
415C2×D4—142no—
416C2×D4—144no—
417C2×D4—144no—
418C2×D4—142no—
419C2×D4—141no—
420C2×D4—282no—
421C2×D4—282no—
422C2×D4—282no—
423C2×D4—284no—
424C2×D4—284no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—42no—
428C22×C4—44no—
429C22×C4—42no—
430C22×C4—44no—
431C22×C4—42no—
432C22×C4—44no—
433C22×C4—42no—
434C22×C4—44no—
435C22×C4—1416no—
436C22×C4—148no—
437C22×C4—141no—
438C22×C4—141no—
439C22×C4—141no—
440C22×C4—144no—
441C22×C4—144no—
442C22×C4—284no—
443C22×C4—2832no—
444C22×C4—288no—
445C22×C4—284no—
446C22×C4—288no—
447C22×C4—284no—
448C22×C4(C2×D7)⋊C412yes—
449C22×C4(C2×D7)⋊C412yes—
450C22×C4(C2×D7)⋊C411yescharacteristic
451C22×C4(C2×D7)⋊C411yescharacteristic
452C22×C4(C2×D7)⋊C412yes—
453C22×C4(C2×D7)⋊C412yes—
454C22×C4(C2×D7)⋊C412yes—
455C22×C4C2×C4×D712yes—
456C22×C4C2×C4×D711yescharacteristic
457C22×C4C2×C4×D711yescharacteristic
458C22×C4C2×C4×D712yes—
459C22×C4C2×D2812yes—
460C22×C4C2×D2811yescharacteristic
461C22×C4C2×C22⋊D712yes—
462C22×C4C2×C22⋊D711yescharacteristic
463C22×C4C2×C22⋊D712yes—
464C22×C4C2×C22⋊D711yescharacteristic
465C22×C4C23×D711yescharacteristic
466M16—48no—
467C2×C8—24no—
468C2×C8—44no—
469C4⋊C4—72no—
470C4⋊C4—72no—
471C4⋊C4—144no—
472C4⋊C4—142no—
473C4⋊C4—141no—
474C4⋊C4—141no—
475C4⋊C4—142no—
476C22⋊C4—144no—
477C22⋊C4—142no—
478C22⋊C4—144no—
479C22⋊C4—142no—
480C22⋊C4—144no—
481C22⋊C4—142no—
482C22⋊C4—142no—
483C42—144no—
484C2×C7—21no—
485C2×C7—21no—
486C2×C7—24no—
487C2×C7—22no—
488C2×C7—24no—
489C2×C7#150414yescomplemented
490C2×C7C22×#9911yescharacteristic
491C2×C7C2×#41711yescharacteristic
492C2×C7C22×#10411yescharacteristic
493D7—82no—
494C23—216no—
495C23—216no—
496C23—24no—
497C23—22no—
498C23—22no—
499C23—24no—
500C23—22no—
501C23—24no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—24no—
506C23—22no—
507C23—24no—
508C23—22no—
509C23—142no—
510C23—282no—
511C23—282no—
512C23—282no—
513C23#638014yes—
514C23#639914yes—
515C23#647112yes—
516C23#647212yes—
517C23C2×(C2×D7)⋊C411yescharacteristic
518C23C2×(C2×D7)⋊C412yes—
519C23C2×(C2×D7)⋊C412yes—
520C23C2×(C2×D7)⋊C411yescharacteristic
521C23C22×D2811yescharacteristic
522Q8—282no—
523Q8—282no—
524D4—282no—
525D4—282no—
526D4—284no—
527D4—288no—
528D4—282no—
529D4—282no—
530D4—288no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—148no—
550C2×C4—142no—
551C2×C4—142no—
552C2×C4—142no—
553C2×C4—288no—
554C2×C4—2832no—
555C2×C4—2816no—
556C2×C4—284no—
557C2×C4—282no—
558C2×C4—282no—
559C2×C4—284no—
560C2×C4—282no—
561C2×C4C2×(C2×D7)⋊C412yes—
562C2×C4C2×(C2×D7)⋊C411yescharacteristic
563C2×C4C2×(C2×D7)⋊C412yes—
564C2×C4C2×(C2×D7)⋊C411yescharacteristic
565C2×C4C22×C4×D711yescharacteristic
566C2×C4C22×C22⋊D711yescharacteristic
567C8—44no—
568C7C2×#150411yescharacteristic, complemented, Sylow
569C22—28no—
570C22—216no—
571C22—28no—
572C22—22no—
573C22—22no—
574C22—21no—
575C22—21no—
576C22—22no—
577C22—24no—
578C22—24no—
579C22—28no—
580C22—28no—
581C22—21no—
582C22—21no—
583C22—22no—
584C22—282no—
585C22—282no—
586C22—282no—
587C22—564no—
588C22C2×#638014yes—
589C22C2×#638012yes—
590C22#8990512yes—
591C22#8990512yes—
592C22C2×#639914yes—
593C22C2×#639912yes—
594C22C2×#647111yescharacteristic
595C22C2×#647211yescharacteristic
596C22C22×(C2×D7)⋊C411yescharacteristic
597C4—21no—
598C4—22no—
599C4—21no—
600C4—21no—
601C4—22no—
602C4—21no—
603C4—288no—
604C4—282no—
605C4—282no—
606C4—282no—
607C2—21no—
608C2—22no—
609C2—24no—
610C2—21no—
611C2—24no—
612C2—562no—
613C2#1172773014yesdirect product factor
614C2C22×#638011yescharacteristic
615C2C2×#8990511yescharacteristic
616C2C22×#639911yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#407C2
socleC23×C7C2×C22⋊C4
prime radicalC2×#90482C2
cosocleC22×C4×C7C24
hypercenterC2×#407D7
hypocenterC7C2×#1504
LCSG ▷ C2×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×C7×#407C2semidirect
3. C22×C7⋊#95C2semidirect
4. #11727730C2direct (N × H)
5. C2×#89262C2semidirect
6. C2×#89265C2semidirect
9. C22×#1157C4semidirect
14. #90482C4semidirect
16. C2×#6493C4semidirect
21. C2×#6489C4semidirect
22. C2×#6487C4semidirect
25. C7×#407C22semidirect
31. C2×C7⋊#95C22semidirect
32. #89265C22semidirect
33. #89262C22semidirect
57. C2×#1157C2×C4semidirect
58. C22×D28C2×C4semidirect
60. C22×Dic14C2×C4semidirect
72. #6493C2×C4semidirect
73. #6493C2×C4semidirect
84. #6489C2×C4semidirect
85. C2×C4⋊Dic7C2×C4semidirect
86. C2×C4⋊Dic7C2×C4semidirect
90. #6487C2×C4semidirect
91. #6487C2×C4semidirect
103. C2×#407D7semidirect
169. C2×D28C22×C4semidirect
174. C2×Dic14C22×C4semidirect
187. C4⋊Dic7C22×C4semidirect
188. C4⋊Dic7C22×C4semidirect
211. #407C2×D7semidirect
489. C2×C7#1504semidirect
568. C7C2×#1504semidirect
613. C2#11727730direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904822
C2×C7×#4072
C22×C7⋊#952
#117277302
C2×#892622
C2×#892652
C2×#15047