Finite Group Databasebeta

← C2×#11726087 #13320889

Subgroups — C2×#11726087 #13320889

Order 1792.

1606 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90318C211yesmaximal, characteristic
2C2×D7×C22⋊C8C211yesmaximal, characteristic, complemented
3C2×#89438C211yesmaximal, characteristic, complemented
4C2×C7×#328C211yesmaximal, characteristic, complemented
5C2×#89333C211yesmaximal, characteristic, complemented
6C2×#89265C211yesmaximal, characteristic, complemented
7C2×#89246C211yesmaximal, characteristic, complemented
8#11726087C218yesmaximal, direct product factor
9C22×#1161C411yescharacteristic, complemented
10C23×C4×D7C2211yescharacteristic
11C2×C7×C22⋊Q8C2211yescharacteristic
12C2×#6509C411yescharacteristic, complemented
13C2×#6493C2211yescharacteristic
14C22×(C2×D7)⋊C4—21no—
15C22×C4×Dic7—21no—
16C22×C8×D7—21no—
17#90318—22no—
18#90318—22no—
19#90318C414yescomplemented
20#90318C2214yes—
21C2×#6458C411yescharacteristic, complemented
22C2×#6457—21no—
23C2×#6456—21no—
24C2×#6455C411yescharacteristic, complemented
25C2×#6445—21no—
26C2×(C22⋊D7)⋊C4—21no—
27C2×C7×C22⋊C8C2211yescharacteristic
28C2×C7×#95C2211yescharacteristic
29C2×C7⋊#95C2211yescharacteristic
30C2×C22⋊(C7⋊C8)C2211yescharacteristic
31C2×(C2×D7)⋊C8—21no—
32D7×C22⋊C8—22no—
33D7×C22⋊C8C2214yescomplemented
34#89438—22no—
35#89438C2214yescomplemented
36C7×#328C2214yescomplemented
37#89333C2214yescomplemented
38#89265C2214yescomplemented
39#89246C2214yescomplemented
40C2×#1501—71nomaximal, Sylow
41C24×D7D411yescharacteristic
42C22×C7×Q8C2×C411yescharacteristic
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
54C22×C4×D7—21no—
55C22×C4×D7—44no—
56C22×C4×D7C2×C411yescharacteristic
57C22×C4×D7C2×C411yescharacteristic
58C22×C4×D7C2×C412yes—
59C22×C4×D7D411yescharacteristic
60C22×C4×D7D412yes—
61C22×C4×D7D411yescharacteristic
62C22×C4×D7D412yes—
63C22×C4×D7C2312yes—
64C22×C7×C8—21no—
65C7×C22⋊Q8—21no—
66C7×C22⋊Q8—21no—
67C7×C22⋊Q8C2×C412yes—
68C7×C22⋊Q8C2312yes—
69C2×C7×C4⋊C4—21no—
70C2×C7×C4⋊C4C2×C411yescharacteristic
71C2×C7×C22⋊C4—21no—
72#6509—22no—
73#6509C2×C414yescomplemented
74#6493—21no—
75#6493—21no—
76#6493C2×C412yes—
77#6493C2312yes—
78C2×(C2×D7)⋊C4—28no—
79C2×(C2×D7)⋊C4—21no—
80C2×(C2×D7)⋊C4—21no—
81C2×(C2×D7)⋊C4—24no—
82C2×(C2×D7)⋊C4—21no—
83C2×(C2×D7)⋊C4—21no—
84C2×C4⋊Dic7C2×C411yescharacteristic
85C2×Dic7⋊C4—21no—
86C2×C4×Dic7—21no—
87C2×C4×Dic7—24no—
88C2×C4×Dic7—44no—
89C22×C7⋊C8—21no—
90C2×C8×D7—24no—
91C2×C8×D7—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⋊#95C2312yes—
110C22⋊(C7⋊C8)—21no—
111C22⋊(C7⋊C8)C2312yes—
112(C2×D7)⋊C8—24no—
113C2×#525—71no—
114C22×C22⋊C8—71no—
115C2×C4×C22⋊C4—71no—
116#1501—78no—
117C2×#328—71no—
118C2×#328D711yescharacteristic, complemented
119C2×#327—71no—
120C2×#327—71no—
121C24×C7C2×D411yescharacteristic
122C23×D7—22no—
123C23×D7—22no—
124C23×D7—24no—
125C23×D7—21no—
126C23×D7—42no—
127C23×D7C22⋊C411yescharacteristic
128C23×D7C22⋊C412yes—
129C23×D7C22⋊C411yescharacteristic
130C23×D7C2×D412yes—
131C2×C7×Q8—21no—
132C2×C7×Q8—42no—
133C2×C7×Q8C22×C412yes—
134C22×C4×C7—24no—
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7—22no—
138C22×C4×C7—42no—
139C22×C4×C7—42no—
140C22×C4×C7—42no—
141C22×C4×C7C22×C411yescharacteristic
142C22×C4×C7C22×C411yescharacteristic
143C22×C4×C7C2×D411yescharacteristic
144C22×C4×C7C2×D411yescharacteristic
145C22×C4×C7C2×D411yescharacteristic
146C22×C4×C7C2411yescharacteristic
147C2×C22⋊D7—22no—
148C2×C22⋊D7—22no—
149C2×C22⋊D7—42no—
150C2×C22⋊D7—42no—
151C22×Dic7—24no—
152C22×Dic7—24no—
153C22×Dic7—21no—
154C22×Dic7—22no—
155C22×Dic7—42no—
156C22×Dic7—42no—
157C22×Dic7C22⋊C412yes—
158C22×Dic7C22⋊C411yescharacteristic
159C22×Dic7C22⋊C411yescharacteristic
160C22×Dic7C2×D412yes—
161#1161—48no—
162#1161—48no—
163C2×D28—24no—
164C2×D28—24no—
165C2×D28—21no—
166C2×D28—42no—
167C2×D28—44no—
168C2×D28—44no—
169C2×D28C22×C412yes—
170C2×C4×D7—24no—
171C2×C4×D7—24no—
172C2×C4×D7—24no—
173C2×C4×D7—44no—
174C2×C4×D7—44no—
175C2×C4×D7—44no—
176C2×C4×D7—44no—
177C2×C4×D7—42no—
178C2×C4×D7—42no—
179C2×C4×D7—44no—
180C2×C4×D7C22⋊C412yes—
181C2×C4×D7C22⋊C412yes—
182C2×C4×D7C22⋊C412yes—
183C2×C4×D7C22⋊C412yes—
184C2×C4×D7C22×C412yes—
185C2×C4×D7C22×C412yes—
186C2×C4×D7C2×D412yes—
187C2×C4×D7C2×D412yes—
188C2×C7×C8—22no—
189C2×C7×C8—42no—
190C7×C4⋊C4—21no—
191C7×C4⋊C4—22no—
192C7×C4⋊C4—22no—
193C7×C4⋊C4C22×C412yes—
194C7×C22⋊C4—22no—
195C7×C22⋊C4—22no—
196(C2×D7)⋊C4—216no—
197(C2×D7)⋊C4—24no—
198(C2×D7)⋊C4—24no—
199(C2×D7)⋊C4—22no—
200(C2×D7)⋊C4—22no—
201(C2×D7)⋊C4—24no—
202C4⋊Dic7—21no—
203C4⋊Dic7C22×C412yes—
204Dic7⋊C4—24no—
205C4×Dic7—24no—
206C4×Dic7—48no—
207C2×C7⋊C8—22no—
208C2×C7⋊C8—42no—
209C8×D7—48no—
210C22×#41—71no—
211C24×C4—71no—
212C23×C8—141no—
213#525—74no—
214#525—74no—
215#525—142no—
216#525—142no—
217C2×#123—141no—
218C2×C22⋊Q8—71no—
219C2×C22⋊Q8C2×D711yescharacteristic
220C2×#121—71no—
221C2×#121—71no—
222C2×#120—141no—
223C2×C4×D4—141no—
224C2×C4×D4—141no—
225C2×#117—71no—
226C22×C22⋊C4—141no—
227C22×C42—141no—
228C2×C22⋊C8—71no—
229C2×C22⋊C8—74no—
230C2×C22⋊C8—142no—
231C2×C22⋊C8—141no—
232C2×C22⋊C8C2×D711yescharacteristic
233C4×C22⋊C4—74no—
234C4×C22⋊C4—142no—
235C2×#95—71no—
236C2×#95C2×D711yescharacteristic
237#328—74no—
238#328C2×D714yescomplemented
239#327—74no—
240#327—74no—
241C23×C7—22no—
242C23×C7—22no—
243C23×C7C2×C22⋊C411yescharacteristic
244C23×C7C2×C22⋊C411yescharacteristic
245C23×C7#13512yes—
246C23×C7#13512yes—
247C23×C7C22×D411yescharacteristic
248C22×D7—22no—
249C22×D7—22no—
250C22×D7—22no—
251C22×D7—22no—
252C22×D7—22no—
253C22×D7—24no—
254C22×D7—22no—
255C22×D7—22no—
256C22×D7—24no—
257C22×D7—24no—
258C22×D7—22no—
259C22×D7—42no—
260C22×D7—42no—
261C22×D7—48no—
262C22×D7—48no—
263C22×D7—42no—
264C22×D7—42no—
265C22×D7—42no—
266C22×D7#10414yes—
267C22×D7C2×C22⋊C412yes—
268C22×D7C2×C22⋊C412yes—
269C7×Q8—42no—
270C7×Q8—42no—
271C2×C4×C7—22no—
272C2×C4×C7—22no—
273C2×C4×C7—24no—
274C2×C4×C7—22no—
275C2×C4×C7—22no—
276C2×C4×C7—41no—
277C2×C4×C7—41no—
278C2×C4×C7—41no—
279C2×C4×C7—41no—
280C2×C4×C7—42no—
281C2×C4×C7—48no—
282C2×C4×C7—42no—
283C2×C4×C7—42no—
284C2×C4×C7—42no—
285C2×C4×C7C2×C22⋊C411yescharacteristic
286C2×C4×C7C2×C22⋊C411yescharacteristic
287C2×C4×C7C23×C411yescharacteristic
288C2×C4×C7C22×D411yescharacteristic
289C22⋊D7—42no—
290C22⋊D7—42no—
291C22⋊D7—44no—
292C2×Dic7—22no—
293C2×Dic7—24no—
294C2×Dic7—24no—
295C2×Dic7—24no—
296C2×Dic7—22no—
297C2×Dic7—42no—
298C2×Dic7—48no—
299C2×Dic7—42no—
300C2×Dic7—42no—
301C2×Dic7#9914yes—
302C2×Dic7C2×C22⋊C412yes—
303C2×Dic7C2×C22⋊C412yes—
304D28—42no—
305D28—42no—
306D28—48no—
307D28—48no—
308C4×D7—24no—
309C4×D7—24no—
310C4×D7—24no—
311C4×D7—24no—
312C4×D7—42no—
313C4×D7—42no—
314C4×D7—42no—
315C4×D7—42no—
316C4×D7—48no—
317C7×C8—42no—
318C7⋊C8—42no—
319C25—71no—
320C2×#41—74no—
321C2×#41—142no—
322C2×#41—284no—
323C22×Q8C4×D711yescharacteristic
324C22×D4—71no—
325C22×D4—141no—
326C22×D4—141no—
327C22×D4—141no—
328C23×C4—21no—
329C23×C4—71no—
330C23×C4—71no—
331C23×C4—71no—
332C23×C4—71no—
333C23×C4—72no—
334C23×C4—71no—
335C23×C4—72no—
336C23×C4—72no—
337C23×C4—72no—
338C23×C4—141no—
339C23×C4—141no—
340C23×C4—284no—
341C23×C4C22×D711yescharacteristic
342C22×C8—21no—
343C22×C8—144no—
344C22×C8—141no—
345C22×C8—284no—
346#123—144no—
347#123—144no—
348C22⋊Q8—21no—
349C22⋊Q8—21no—
350C22⋊Q8—74no—
351C22⋊Q8—142no—
352C22⋊Q8C4×D712yes—
353C22⋊Q8C22×D712yes—
354#121—72no—
355#121—72no—
356#121—74no—
357#121—142no—
358#121—141no—
359#121—141no—
360#120—144no—
361#120—144no—
362C4×D4—144no—
363C4×D4—144no—
364C4×D4—144no—
365C4×D4—144no—
366#117—74no—
367#117—142no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—71no—
370C2×C4⋊C4—141no—
371C2×C4⋊C4C4×D711yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—141no—
374C2×C22⋊C4—144no—
375C2×C22⋊C4—141no—
376C2×C22⋊C4—141no—
377C2×C22⋊C4—148no—
378C2×C22⋊C4—141no—
379C2×C42—141no—
380C2×C42—144no—
381C2×C42—284no—
382C22⋊C8—21no—
383C22⋊C8—72no—
384C22⋊C8—144no—
385C22⋊C8—141no—
386C22⋊C8C22×D712yes—
387#95—21no—
388#95—72no—
389#95—141no—
390#95C22×D712yes—
391C22×C7—21no—
392C22×C7—21no—
393C22×C7—21no—
394C22×C7—21no—
395C22×C7—24no—
396C22×C7—24no—
397C22×C7C2×#9912yes—
398C22×C7#41612yes—
399C22×C7#41612yes—
400C22×C7C2×#10412yes—
401C22×C7C22×C22⋊C411yescharacteristic
402C22×C7C2×#13511yescharacteristic
403C22×C7C2×#13511yescharacteristic
404C2×D7—22no—
405C2×D7—22no—
406C2×D7—28no—
407C2×D7—22no—
408C2×D7—22no—
409C2×D7—22no—
410C2×D7—44no—
411C2×D7—44no—
412C2×D7—48no—
413C2×D7—44no—
414C2×D7—42no—
415C2×D7—42no—
416C2×D7—42no—
417C2×D7—84no—
418C2×D7C2×#10414yes—
419C4×C7—21no—
420C4×C7—21no—
421C4×C7—21no—
422C4×C7—21no—
423C4×C7—44no—
424C4×C7—42no—
425C4×C7—42no—
426Dic7—22no—
427Dic7—44no—
428Dic7—42no—
429Dic7C2×#9914yes—
430C24—71no—
431C24—71no—
432C24—72no—
433C24—72no—
434C24—144no—
435C24—142no—
436C24—142no—
437C24—141no—
438C24—282no—
439C24D4×D711yescharacteristic
440#41—288no—
441#41—288no—
442C2×Q8—21no—
443C2×Q8—42no—
444C2×Q8C2×C4×D712yes—
445C2×D4—72no—
446C2×D4—144no—
447C2×D4—144no—
448C2×D4—142no—
449C2×D4—142no—
450C2×D4—141no—
451C2×D4—282no—
452C2×D4—284no—
453C2×D4—284no—
454C2×D4—282no—
455C2×D4—282no—
456C22×C4—24no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—71no—
464C22×C4—72no—
465C22×C4—71no—
466C22×C4—72no—
467C22×C4—72no—
468C22×C4—72no—
469C22×C4—72no—
470C22×C4—72no—
471C22×C4—72no—
472C22×C4—72no—
473C22×C4—72no—
474C22×C4—72no—
475C22×C4—144no—
476C22×C4—144no—
477C22×C4—144no—
478C22×C4—144no—
479C22×C4—144no—
480C22×C4—141no—
481C22×C4—142no—
482C22×C4—282no—
483C22×C4—282no—
484C22×C4—284no—
485C22×C4—284no—
486C22×C4—284no—
487C22×C4—284no—
488C22×C4—284no—
489C22×C4—282no—
490C22×C4—282no—
491C22×C4C2×C4×D711yescharacteristic
492C22×C4C2×C4×D711yescharacteristic
493C22×C4D4×D711yescharacteristic
494C22×C4D4×D711yescharacteristic
495C22×C4D4×D711yescharacteristic
496C22×C4C23×D711yescharacteristic
497C2×C8—22no—
498C2×C8—42no—
499C2×C8—142no—
500C2×C8—288no—
501C2×C8—282no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—72no—
506C4⋊C4—144no—
507C4⋊C4—141no—
508C4⋊C4C2×C4×D712yes—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—144no—
512C22⋊C4—144no—
513C22⋊C4—144no—
514C22⋊C4—1416no—
515C22⋊C4—142no—
516C22⋊C4—142no—
517C42—144no—
518C42—288no—
519C2×C7—21no—
520C2×C7—21no—
521C2×C7—22no—
522C2×C7#150114yescomplemented
523C2×C7C22×#9911yescharacteristic
524C2×C7C2×#41611yescharacteristic
525C2×C7C22×#10411yescharacteristic
526D7—24no—
527D7—42no—
528D7—82no—
529C23—22no—
530C23—22no—
531C23—72no—
532C23—74no—
533C23—72no—
534C23—144no—
535C23—144no—
536C23—142no—
537C23—142no—
538C23—142no—
539C23—142no—
540C23—142no—
541C23—144no—
542C23—142no—
543C23—142no—
544C23—142no—
545C23—282no—
546C23—282no—
547C23—288no—
548C23—288no—
549C23—282no—
550C23—282no—
551C23—282no—
552C23D7×C22⋊C411yescharacteristic
553C23D7×C22⋊C411yescharacteristic
554C23#647912yes—
555C23#648212yes—
556C23C2×D4×D711yescharacteristic
557Q8—42no—
558Q8—42no—
559D4—282no—
560D4—282no—
561D4—288no—
562D4—288no—
563D4—282no—
564D4—282no—
565D4—284no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—48no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—72no—
581C2×C4—74no—
582C2×C4—72no—
583C2×C4—144no—
584C2×C4—144no—
585C2×C4—144no—
586C2×C4—144no—
587C2×C4—144no—
588C2×C4—144no—
589C2×C4—142no—
590C2×C4—144no—
591C2×C4—142no—
592C2×C4—282no—
593C2×C4—282no—
594C2×C4—282no—
595C2×C4—282no—
596C2×C4—288no—
597C2×C4—282no—
598C2×C4—288no—
599C2×C4—282no—
600C2×C4—282no—
601C2×C4D7×C22⋊C411yescharacteristic
602C2×C4D7×C22⋊C411yescharacteristic
603C2×C4C22×C4×D711yescharacteristic
604C2×C4C2×D4×D711yescharacteristic
605C8—42no—
606C8—282no—
607C7C2×#150111yescharacteristic, complemented, Sylow
608C22—24no—
609C22—24no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—74no—
615C22—148no—
616C22—142no—
617C22—142no—
618C22—142no—
619C22—142no—
620C22—142no—
621C22—284no—
622C22—284no—
623C22—288no—
624C22—284no—
625C22—282no—
626C22—282no—
627C22—282no—
628C22—564no—
629C22D7×#9912yes—
630C22#8957612yes—
631C22#8957612yes—
632C22D7×#10412yes—
633C22C2×D7×C22⋊C411yescharacteristic
634C22C2×#647911yescharacteristic
635C22C2×#648211yescharacteristic
636C4—21no—
637C4—21no—
638C4—21no—
639C4—21no—
640C4—44no—
641C4—42no—
642C4—42no—
643C4—74no—
644C4—142no—
645C4—284no—
646C4—282no—
647C2—21no—
648C2—21no—
649C2—22no—
650C2—144no—
651C2—282no—
652C2—562no—
653C2#1172608714yesdirect product factor
654C2C2×D7×#9911yescharacteristic
655C2C2×#8957611yescharacteristic
656C2C2×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×#1501
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×D7×C22⋊C8C2semidirect
3. C2×#89438C2semidirect
4. C2×C7×#328C2semidirect
5. C2×#89333C2semidirect
6. C2×#89265C2semidirect
7. C2×#89246C2semidirect
8. #11726087C2direct (N × H)
9. C22×#1161C4semidirect
12. C2×#6509C4semidirect
19. #90318C4semidirect
21. C2×#6458C4semidirect
24. C2×#6455C4semidirect
33. D7×C22⋊C8C22semidirect
35. #89438C22semidirect
36. C7×#328C22semidirect
37. #89333C22semidirect
38. #89265C22semidirect
39. #89246C22semidirect
50. C2×#1161C2×C4semidirect
73. #6509C2×C4semidirect
93. #6458C2×C4semidirect
99. #6455C2×C4semidirect
118. C2×#328D7semidirect
238. #328C2×D7semidirect
522. C2×C7#1501semidirect
607. C7C2×#1501semidirect
653. C2#11726087direct (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×D7×C22⋊C82
C2×#894382
C2×C7×#3282
C2×#893332
C2×#892652
C2×#892462
#117260872
C2×#15017