Finite Group Databasebeta

← C2×#11726088 #13320935

Subgroups — C2×#11726088 #13320935

Order 1792.

1834 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90318C211yesmaximal, characteristic
2C2×#89498C211yesmaximal, characteristic, complemented
3C2×D7×#95C211yesmaximal, characteristic, complemented
4C2×C7×#328C211yesmaximal, characteristic, complemented
5C2×#89333C211yesmaximal, characteristic, complemented
6C2×#89265C211yesmaximal, characteristic, complemented
7C2×#89246C211yesmaximal, characteristic, complemented
8#11726088C218yesmaximal, direct product factor
9C22×#1161C411yescharacteristic, complemented
10C23×C4×D7—21no—
11C23×C4×D7C2211yescharacteristic
12C2×C7×C22⋊Q8C2211yescharacteristic
13C2×#6509C411yescharacteristic, complemented
14C2×#6493C2211yescharacteristic
15C22×#1131—21no—
16#90318—22no—
17#90318—22no—
18#90318C414yescomplemented
19#90318C2214yes—
20C2×#6458C411yescharacteristic, complemented
21C2×#6457—21no—
22C2×#6456—21no—
23C2×#6455C411yescharacteristic, complemented
24C2×#6445—21no—
25C2×(C22⋊D7)⋊C4—21no—
26C2×C7×C22⋊C8C2211yescharacteristic
27C2×C7×#95C2211yescharacteristic
28C2×C7⋊#95—21no—
29C2×C7⋊#95C2211yescharacteristic
30C2×C22⋊(C7⋊C8)C2211yescharacteristic
31C2×(C2×D7)⋊C8—21no—
32#89498—22no—
33#89498C2214yescomplemented
34D7×#95—22no—
35D7×#95C2214yescomplemented
36C7×#328C2214yescomplemented
37#89333C2214yescomplemented
38#89265C2214yescomplemented
39#89246C2214yescomplemented
40C2×#1504—71nomaximal, Sylow
41C24×D7D411yescharacteristic
42C22×C7×Q8C2×C411yescharacteristic, complemented
43C23×C4×C7—21no—
44C23×C4×C7C2311yescharacteristic
45C22×C22⋊D7—21no—
46C23×Dic7—21no—
47C23×Dic7D411yescharacteristic
48C2×#1161—22no—
49C2×#1161—44no—
50C2×#1161C2×C414yescomplemented
51C22×D28—21no—
52C22×D28—21no—
53C22×D28C2×C411yescharacteristic, complemented
54C22×C4×D7—28no—
55C22×C4×D7—24no—
56C22×C4×D7—21no—
57C22×C4×D7—44no—
58C22×C4×D7—44no—
59C22×C4×D7—44no—
60C22×C4×D7C2×C411yescharacteristic
61C22×C4×D7C2×C411yescharacteristic
62C22×C4×D7C2×C412yes—
63C22×C4×D7D411yescharacteristic
64C22×C4×D7D412yes—
65C22×C4×D7D411yescharacteristic
66C22×C4×D7D412yes—
67C22×C4×D7C2312yes—
68C22×C7×C8—21no—
69C7×C22⋊Q8—21no—
70C7×C22⋊Q8—21no—
71C7×C22⋊Q8C2×C412yescomplemented
72C7×C22⋊Q8C2312yes—
73C2×C7×C4⋊C4—21no—
74C2×C7×C4⋊C4C2×C411yescharacteristic, complemented
75C2×C7×C22⋊C4—21no—
76#6509—22no—
77#6509C2×C414yescomplemented
78#6493—21no—
79#6493—21no—
80#6493C2×C412yescomplemented
81#6493C2312yes—
82C2×(C2×D7)⋊C4—21no—
83C2×(C2×D7)⋊C4—21no—
84C2×(C2×D7)⋊C4—21no—
85C2×(C2×D7)⋊C4—21no—
86C2×C4⋊Dic7C2×C411yescharacteristic, complemented
87C2×Dic7⋊C4—21no—
88C2×C4×Dic7—21no—
89C22×C7⋊C8—21no—
90C2×#1131—24no—
91C2×#1131—44no—
92#6458—22no—
93#6458C2×C414yescomplemented
94#6457—24no—
95#6457—24no—
96#6456—24no—
97#6456—24no—
98#6455—22no—
99#6455C2×C414yescomplemented
100#6445—24no—
101#6445—24no—
102(C22⋊D7)⋊C4—24no—
103(C22⋊D7)⋊C4—24no—
104C7×C22⋊C8—21no—
105C7×C22⋊C8C2312yes—
106C7×#95—21no—
107C7×#95C2312yes—
108C7⋊#95—21no—
109C7⋊#95—24no—
110C7⋊#95C2312yes—
111C22⋊(C7⋊C8)—21no—
112C22⋊(C7⋊C8)C2312yes—
113(C2×D7)⋊C8—24no—
114C2×#525—71no—
115C2×#407—71no—
116C22×#95—71no—
117#1504—78no—
118C2×#328—71no—
119C2×#328D711yescharacteristic, complemented
120C2×#327—71no—
121C2×#327—71no—
122C24×C7C2×D411yescharacteristic
123C23×D7—22no—
124C23×D7—22no—
125C23×D7—24no—
126C23×D7—24no—
127C23×D7—21no—
128C23×D7C22⋊C412yes—
129C23×D7C22⋊C411yescharacteristic
130C23×D7C22⋊C411yescharacteristic
131C23×D7C2×D412yes—
132C2×C7×Q8—21no—
133C2×C7×Q8—42no—
134C2×C7×Q8C22×C412yescomplemented
135C22×C4×C7—24no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—22no—
139C22×C4×C7—42no—
140C22×C4×C7—42no—
141C22×C4×C7—42no—
142C22×C4×C7C22×C411yescharacteristic
143C22×C4×C7C22×C411yescharacteristic
144C22×C4×C7C2×D411yescharacteristic
145C22×C4×C7C2×D411yescharacteristic
146C22×C4×C7C2×D411yescharacteristic
147C22×C4×C7C2411yescharacteristic
148C2×C22⋊D7—22no—
149C2×C22⋊D7—22no—
150C2×C22⋊D7—42no—
151C2×C22⋊D7—42no—
152C22×Dic7—24no—
153C22×Dic7—21no—
154C22×Dic7—22no—
155C22×Dic7—42no—
156C22×Dic7—42no—
157C22×Dic7—42no—
158C22×Dic7C22⋊C411yescharacteristic
159C22×Dic7C22⋊C411yescharacteristic
160C22×Dic7C22⋊C412yes—
161C22×Dic7C2×D412yes—
162#1161—48no—
163#1161—48no—
164C2×D28—24no—
165C2×D28—24no—
166C2×D28—21no—
167C2×D28—42no—
168C2×D28—44no—
169C2×D28—44no—
170C2×D28C22×C412yescomplemented
171C2×C4×D7—24no—
172C2×C4×D7—24no—
173C2×C4×D7—216no—
174C2×C4×D7—24no—
175C2×C4×D7—44no—
176C2×C4×D7—44no—
177C2×C4×D7—44no—
178C2×C4×D7—44no—
179C2×C4×D7—42no—
180C2×C4×D7—42no—
181C2×C4×D7—44no—
182C2×C4×D7—432no—
183C2×C4×D7—48no—
184C2×C4×D7—48no—
185C2×C4×D7C22⋊C412yes—
186C2×C4×D7C22⋊C412yes—
187C2×C4×D7C22⋊C412yes—
188C2×C4×D7C22⋊C412yes—
189C2×C4×D7C22×C412yes—
190C2×C4×D7C22×C412yes—
191C2×C4×D7C2×D412yes—
192C2×C4×D7C2×D412yes—
193C2×C7×C8—22no—
194C2×C7×C8—42no—
195C7×C4⋊C4—21no—
196C7×C4⋊C4—22no—
197C7×C4⋊C4—22no—
198C7×C4⋊C4C22×C412yescomplemented
199C7×C22⋊C4—22no—
200C7×C22⋊C4—22no—
201(C2×D7)⋊C4—24no—
202(C2×D7)⋊C4—24no—
203(C2×D7)⋊C4—22no—
204(C2×D7)⋊C4—22no—
205(C2×D7)⋊C4—24no—
206C4⋊Dic7—21no—
207C4⋊Dic7C22×C412yescomplemented
208Dic7⋊C4—24no—
209C4×Dic7—24no—
210C2×C7⋊C8—22no—
211C2×C7⋊C8—42no—
212#1131—48no—
213C22×#41—71no—
214C24×C4—71no—
215C24×C4—141no—
216C22×M16—141no—
217#525—74no—
218#525—74no—
219#525—142no—
220#525—142no—
221C2×#123—141no—
222C2×C22⋊Q8—71no—
223C2×C22⋊Q8C2×D711yescharacteristic
224C2×#121—71no—
225C2×#121—71no—
226C2×#120—141no—
227C2×C4×D4—141no—
228C2×C4×D4—141no—
229C2×#117—71no—
230#407—74no—
231#407—142no—
232C2×C22⋊C8—71no—
233C2×C22⋊C8—141no—
234C2×C22⋊C8C2×D711yescharacteristic
235C2×#95—71no—
236C2×#95—74no—
237C2×#95—142no—
238C2×#95—141no—
239C2×#95C2×D711yescharacteristic
240#328—74no—
241#328C2×D714yescomplemented
242#327—74no—
243#327—74no—
244C23×C7—22no—
245C23×C7—22no—
246C23×C7C2×C22⋊C411yescharacteristic
247C23×C7C2×C22⋊C411yescharacteristic
248C23×C7AGL(1,ℤ/8)12yes—
249C23×C7#13712yes—
250C23×C7C22×D411yescharacteristic
251C22×D7—216no—
252C22×D7—216no—
253C22×D7—22no—
254C22×D7—22no—
255C22×D7—22no—
256C22×D7—24no—
257C22×D7—22no—
258C22×D7—22no—
259C22×D7—22no—
260C22×D7—24no—
261C22×D7—24no—
262C22×D7—24no—
263C22×D7—24no—
264C22×D7—22no—
265C22×D7—42no—
266C22×D7—42no—
267C22×D7—42no—
268C22×D7#9914yes—
269C22×D7#10414yes—
270C22×D7C2×C22⋊C412yes—
271C22×D7C2×C22⋊C412yes—
272C7×Q8—42no—
273C7×Q8—42no—
274C2×C4×C7—22no—
275C2×C4×C7—22no—
276C2×C4×C7—24no—
277C2×C4×C7—22no—
278C2×C4×C7—22no—
279C2×C4×C7—41no—
280C2×C4×C7—41no—
281C2×C4×C7—41no—
282C2×C4×C7—41no—
283C2×C4×C7—42no—
284C2×C4×C7—48no—
285C2×C4×C7—42no—
286C2×C4×C7—42no—
287C2×C4×C7—42no—
288C2×C4×C7C2×C22⋊C411yescharacteristic
289C2×C4×C7C2×C22⋊C411yescharacteristic
290C2×C4×C7C23×C411yescharacteristic
291C2×C4×C7C22×D411yescharacteristic
292C22⋊D7—42no—
293C22⋊D7—42no—
294C22⋊D7—44no—
295C2×Dic7—22no—
296C2×Dic7—22no—
297C2×Dic7—24no—
298C2×Dic7—22no—
299C2×Dic7—42no—
300C2×Dic7—42no—
301C2×Dic7—42no—
302C2×Dic7—48no—
303C2×Dic7—42no—
304C2×Dic7—42no—
305C2×Dic7C2×C22⋊C412yes—
306C2×Dic7C2×C22⋊C412yes—
307D28—42no—
308D28—42no—
309D28—48no—
310D28—48no—
311C4×D7—24no—
312C4×D7—24no—
313C4×D7—24no—
314C4×D7—24no—
315C4×D7—42no—
316C4×D7—42no—
317C4×D7—42no—
318C4×D7—42no—
319C4×D7—48no—
320C4×D7—432no—
321C7×C8—42no—
322C7⋊C8—42no—
323C25—71no—
324C2×#41—74no—
325C2×#41—142no—
326C2×#41—284no—
327C22×Q8C4×D711yescharacteristic, complemented
328C22×D4—71no—
329C22×D4—141no—
330C22×D4—141no—
331C22×D4—141no—
332C23×C4—21no—
333C23×C4—71no—
334C23×C4—71no—
335C23×C4—71no—
336C23×C4—71no—
337C23×C4—72no—
338C23×C4—71no—
339C23×C4—72no—
340C23×C4—72no—
341C23×C4—72no—
342C23×C4—141no—
343C23×C4—144no—
344C23×C4—148no—
345C23×C4—141no—
346C23×C4—284no—
347C23×C4—284no—
348C23×C4—284no—
349C23×C4C22×D711yescharacteristic
350C2×M16—144no—
351C2×M16—284no—
352C22×C8—21no—
353C22×C8—141no—
354#123—144no—
355#123—144no—
356C22⋊Q8—21no—
357C22⋊Q8—21no—
358C22⋊Q8—74no—
359C22⋊Q8—142no—
360C22⋊Q8C4×D712yescomplemented
361C22⋊Q8C22×D712yes—
362#121—72no—
363#121—72no—
364#121—74no—
365#121—142no—
366#121—141no—
367#121—141no—
368#120—144no—
369#120—144no—
370C4×D4—144no—
371C4×D4—144no—
372C4×D4—144no—
373C4×D4—144no—
374#117—74no—
375#117—142no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—71no—
378C2×C4⋊C4—141no—
379C2×C4⋊C4C4×D711yescharacteristic, complemented
380C2×C22⋊C4—21no—
381C2×C22⋊C4—141no—
382C2×C22⋊C4—141no—
383C2×C22⋊C4—141no—
384C2×C22⋊C4—141no—
385C2×C42—141no—
386C22⋊C8—21no—
387C22⋊C8—72no—
388C22⋊C8—144no—
389C22⋊C8—141no—
390C22⋊C8C22×D712yes—
391#95—21no—
392#95—72no—
393#95—144no—
394#95—141no—
395#95C22×D712yes—
396C22×C7—21no—
397C22×C7—21no—
398C22×C7—21no—
399C22×C7—21no—
400C22×C7—24no—
401C22×C7—24no—
402C22×C7C2×#9912yes—
403C22×C7#41712yes—
404C22×C7#41712yes—
405C22×C7C2×#10412yes—
406C22×C7C22×C22⋊C411yescharacteristic
407C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
408C22×C7C2×#13711yescharacteristic
409C2×D7—28no—
410C2×D7—28no—
411C2×D7—216no—
412C2×D7—22no—
413C2×D7—22no—
414C2×D7—22no—
415C2×D7—22no—
416C2×D7—28no—
417C2×D7—28no—
418C2×D7—42no—
419C2×D7—42no—
420C2×D7—42no—
421C2×D7—84no—
422C2×D7C2×#9914yes—
423C2×D7C2×#10414yes—
424C4×C7—21no—
425C4×C7—21no—
426C4×C7—21no—
427C4×C7—21no—
428C4×C7—44no—
429C4×C7—42no—
430C4×C7—42no—
431Dic7—22no—
432Dic7—22no—
433Dic7—44no—
434Dic7—42no—
435C24—71no—
436C24—71no—
437C24—72no—
438C24—72no—
439C24—144no—
440C24—144no—
441C24—142no—
442C24—142no—
443C24—141no—
444C24D4×D711yescharacteristic
445#41—288no—
446#41—288no—
447C2×Q8—21no—
448C2×Q8—42no—
449C2×Q8C2×C4×D712yescomplemented
450C2×D4—72no—
451C2×D4—144no—
452C2×D4—144no—
453C2×D4—142no—
454C2×D4—142no—
455C2×D4—141no—
456C2×D4—282no—
457C2×D4—284no—
458C2×D4—284no—
459C2×D4—282no—
460C2×D4—282no—
461C22×C4—24no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—71no—
469C22×C4—71no—
470C22×C4—72no—
471C22×C4—72no—
472C22×C4—72no—
473C22×C4—72no—
474C22×C4—72no—
475C22×C4—72no—
476C22×C4—72no—
477C22×C4—72no—
478C22×C4—72no—
479C22×C4—72no—
480C22×C4—144no—
481C22×C4—144no—
482C22×C4—144no—
483C22×C4—1416no—
484C22×C4—144no—
485C22×C4—141no—
486C22×C4—142no—
487C22×C4—282no—
488C22×C4—282no—
489C22×C4—284no—
490C22×C4—284no—
491C22×C4—284no—
492C22×C4—284no—
493C22×C4—284no—
494C22×C4—288no—
495C22×C4—2832no—
496C22×C4—288no—
497C22×C4—282no—
498C22×C4—282no—
499C22×C4—282no—
500C22×C4C2×C4×D711yescharacteristic
501C22×C4C2×C4×D711yescharacteristic
502C22×C4D4×D711yescharacteristic
503C22×C4D4×D711yescharacteristic
504C22×C4D4×D711yescharacteristic
505C22×C4C23×D711yescharacteristic
506M16—288no—
507C2×C8—22no—
508C2×C8—42no—
509C2×C8—142no—
510C2×C8—282no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—22no—
514C4⋊C4—72no—
515C4⋊C4—144no—
516C4⋊C4—141no—
517C4⋊C4C2×C4×D712yescomplemented
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—144no—
521C22⋊C4—144no—
522C22⋊C4—144no—
523C22⋊C4—142no—
524C22⋊C4—142no—
525C42—144no—
526C2×C7—21no—
527C2×C7—21no—
528C2×C7—22no—
529C2×C7#150414yescomplemented
530C2×C7C22×#9911yescharacteristic
531C2×C7C2×#41711yescharacteristic
532C2×C7C22×#10411yescharacteristic
533D7—24no—
534D7—24no—
535D7—82no—
536C23—22no—
537C23—22no—
538C23—72no—
539C23—72no—
540C23—74no—
541C23—74no—
542C23—144no—
543C23—144no—
544C23—144no—
545C23—144no—
546C23—1416no—
547C23—1416no—
548C23—142no—
549C23—142no—
550C23—142no—
551C23—144no—
552C23—142no—
553C23—142no—
554C23—142no—
555C23—142no—
556C23—282no—
557C23—282no—
558C23—282no—
559C23D7×C22⋊C411yescharacteristic
560C23D7×C22⋊C411yescharacteristic
561C23#647712yes—
562C23#648112yes—
563C23C2×D4×D711yescharacteristic
564Q8—42no—
565Q8—42no—
566D4—282no—
567D4—282no—
568D4—288no—
569D4—288no—
570D4—282no—
571D4—282no—
572D4—284no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—48no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—72no—
588C2×C4—72no—
589C2×C4—144no—
590C2×C4—144no—
591C2×C4—144no—
592C2×C4—144no—
593C2×C4—142no—
594C2×C4—142no—
595C2×C4—144no—
596C2×C4—142no—
597C2×C4—282no—
598C2×C4—282no—
599C2×C4—282no—
600C2×C4—282no—
601C2×C4—288no—
602C2×C4—2832no—
603C2×C4—282no—
604C2×C4—282no—
605C2×C4—288no—
606C2×C4—282no—
607C2×C4—282no—
608C2×C4—282no—
609C2×C4D7×C22⋊C411yescharacteristic
610C2×C4D7×C22⋊C411yescharacteristic
611C2×C4C22×C4×D711yescharacteristic
612C2×C4C2×D4×D711yescharacteristic
613C8—42no—
614C8—282no—
615C7C2×#150411yescharacteristic, complemented, Sylow
616C22—24no—
617C22—24no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—21no—
622C22—74no—
623C22—74no—
624C22—148no—
625C22—148no—
626C22—1416no—
627C22—148no—
628C22—148no—
629C22—142no—
630C22—142no—
631C22—142no—
632C22—142no—
633C22—282no—
634C22—282no—
635C22—282no—
636C22—564no—
637C22D7×#9912yes—
638C22#8957512yes—
639C22#8957512yes—
640C22D7×#10412yes—
641C22C2×D7×C22⋊C411yescharacteristic
642C22C2×#647711yescharacteristic
643C22C2×#648111yescharacteristic
644C4—21no—
645C4—21no—
646C4—21no—
647C4—21no—
648C4—44no—
649C4—42no—
650C4—42no—
651C4—142no—
652C4—142no—
653C4—284no—
654C4—282no—
655C2—21no—
656C2—21no—
657C2—22no—
658C2—144no—
659C2—144no—
660C2—562no—
661C2#1172608814yesdirect product factor
662C2C2×D7×#9911yescharacteristic
663C2C2×#8957511yescharacteristic
664C2C2×D7×#10411yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#328C2
socleC23×C7C2×C22⋊C4
prime radicalC2×#90318C2
cosocleC22×C4×C7C24
hypercenterC2×#328D7
hypocenterC7C2×#1504
LCSG ▷ C2×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. C2×#89498C2semidirect
3. C2×D7×#95C2semidirect
4. C2×C7×#328C2semidirect
5. C2×#89333C2semidirect
6. C2×#89265C2semidirect
7. C2×#89246C2semidirect
8. #11726088C2direct (N × H)
9. C22×#1161C4semidirect
13. C2×#6509C4semidirect
18. #90318C4semidirect
20. C2×#6458C4semidirect
23. C2×#6455C4semidirect
33. #89498C22semidirect
35. D7×#95C22semidirect
36. C7×#328C22semidirect
37. #89333C22semidirect
38. #89265C22semidirect
39. #89246C22semidirect
42. C22×C7×Q8C2×C4semidirect
50. C2×#1161C2×C4semidirect
53. C22×D28C2×C4semidirect
71. C7×C22⋊Q8C2×C4semidirect
74. C2×C7×C4⋊C4C2×C4semidirect
77. #6509C2×C4semidirect
80. #6493C2×C4semidirect
86. C2×C4⋊Dic7C2×C4semidirect
93. #6458C2×C4semidirect
99. #6455C2×C4semidirect
119. C2×#328D7semidirect
134. C2×C7×Q8C22×C4semidirect
170. C2×D28C22×C4semidirect
198. C7×C4⋊C4C22×C4semidirect
207. C4⋊Dic7C22×C4semidirect
241. #328C2×D7semidirect
327. C22×Q8C4×D7semidirect
360. C22⋊Q8C4×D7semidirect
379. C2×C4⋊C4C4×D7semidirect
449. C2×Q8C2×C4×D7semidirect
517. C4⋊C4C2×C4×D7semidirect
529. C2×C7#1504semidirect
615. C7C2×#1504semidirect
661. C2#11726088direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903182
C2×#894982
C2×D7×#952
C2×C7×#3282
C2×#893332
C2×#892652
C2×#892462
#117260882
C2×#15047