Finite Group Databasebeta

← C2×#11739321 #14225066

Subgroups — C2×#11739321 #14225066

Order 1792.

2146 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D7×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#90371C211yesmaximal, characteristic
3C2×C7×#497C211yesmaximal, characteristic, complemented
4C2×#89958C212yesmaximal, complemented
5C2×#89954C212yesmaximal, complemented
6C2×#89942C212yesmaximal
7C2×#89934C212yesmaximal, complemented
8C2×#89854C211yesmaximal, characteristic, complemented
9C2×#89832C211yesmaximal, characteristic, complemented
10#11739321C2116yesmaximal, direct product factor
11C2×#89475C211yesmaximal, characteristic, complemented
12C2×#89477C211yesmaximal, characteristic, complemented
13C22×Q8×D7C2212yes—
14C22×C7×Q16C2212yes—
15C22×C7×SD16C2212yes—
16C2×C7×C4⋊Q8C2211yescharacteristic
17C2×C7×#124C2211yescharacteristic
18C2×#6509C2211yescharacteristic
19C2×Q8×Dic7C2211yescharacteristic
20C2×#6507C2212yes—
21C22×#1144C2212yes—
22C2×#6501C2211yescharacteristic
23C2×D4×Dic7C2211yescharacteristic
24C22×#1142C2212yes—
25D7×C4⋊Q8—24no—
26D7×C4⋊Q8C2218yescomplemented
27#90371—24no—
28#90371C2218yes—
29C2×D7×C4⋊C4—21no—
30C2×D7×C4⋊C4—21no—
31C2×#6451—21no—
32C2×#6451—21no—
33C2×#6446—21no—
34C2×(C22⋊D7)⋊C4—21no—
35C2×#6442—21no—
36C2×#6440—21no—
37C2×C42×D7C2211yescharacteristic
38C2×#6433C2211yescharacteristic
39C2×#6432C2211yescharacteristic
40C7×#497C2218yescomplemented
41C2×C7×#97C2211yescharacteristic
42C2×#6409C2212yes—
43C2×#6409C2212yes—
44#89958C22116yescomplemented
45#89954C22116yescomplemented
46#89942C22116yes—
47#89934C22116yescomplemented
48C2×(C2×D7)⋊C8C2212yes—
49C2×#6390C2212yes—
50C2×#6390C2212yes—
51C2×Dic7⋊C8C2212yes—
52#89854C2218yescomplemented
53#89832C2218yescomplemented
54C2×#6377C2211yescharacteristic
55#89477C2218yescomplemented
56#89475C2218yescomplemented
57C2×#3218—71nomaximal, Sylow
58C22×C7×Q8C2311yescharacteristic
59C22×C7×Q8C2312yes—
60C22×C7×D4C2311yescharacteristic
61C22×C22⋊D7—21no—
62C23×Dic7—21no—
63C2×Q8×D7—24no—
64C2×Q8×D7—44no—
65C2×Q8×D7—44no—
66C2×Q8×D7C2318yes—
67C22×C4×D7—22no—
68C22×C4×D7D411yescharacteristic
69C22×C4×D7D411yescharacteristic
70C22×C4×D7C2311yescharacteristic
71C22×Dic14—22no—
72C22×Dic14C2312yes—
73C2×C7×Q16—44no—
74C2×C7×Q16C2318yes—
75C2×C7×SD16—44no—
76C2×C7×SD16C2318yes—
77C22×C7×C8C2312yes—
78C7×C4⋊Q8—22no—
79C7×C4⋊Q8C2314yes—
80C7×#124—22no—
81C7×#124C2314yes—
82C2×C7×C4⋊C4—21no—
83C2×C7×C4⋊C4—21no—
84C2×C7×C22⋊C4—21no—
85C2×C7×C22⋊C4—21no—
86C2×C42×C7C2311yescharacteristic
87C2×C22⋊Dic7—21no—
88C2×C22⋊Dic7—21no—
89#6509—22no—
90#6509C2314yes—
91Q8×Dic7—22no—
92Q8×Dic7C2314yes—
93#6507—24no—
94#6507C2318yes—
95C2×#1144—44no—
96C2×#1144C2318yes—
97#6501—22no—
98#6501C2314yes—
99D4×Dic7—22no—
100D4×Dic7C2314yes—
101C2×#1142—44no—
102C2×#1142C2318yes—
103C2×(C2×D7)⋊C4—21no—
104C2×C4⋊Dic7—21no—
105C2×C4⋊Dic7—21no—
106C2×C4⋊Dic7—21no—
107C2×C4⋊Dic7C2311yescharacteristic
108C2×C4⋊Dic7C2311yescharacteristic
109C2×Dic7⋊C4—21no—
110C2×Dic7⋊C4—21no—
111C2×Dic7⋊C4—21no—
112C2×Dic7⋊C4—22no—
113C2×Dic7⋊C4—22no—
114C2×C4×Dic7—21no—
115C2×C4×Dic7D411yescharacteristic
116C2×C4×Dic7D411yescharacteristic
117C2×C4×Dic7C2311yescharacteristic
118C22×C7⋊C8C2312yes—
119D7×C4⋊C4—28no—
120D7×C4⋊C4—28no—
121#6451—28no—
122#6451—28no—
123#6446—28no—
124(C22⋊D7)⋊C4—28no—
125#6442—28no—
126#6440—28no—
127C42×D7D414yes—
128C42×D7C2314yes—
129#6433—22no—
130#6433C2314yes—
131#6432—22no—
132#6432C2314yes—
133C7×#97C2314yes—
134#6409C2318yes—
135#6409C2318yes—
136(C2×D7)⋊C8C2318yes—
137#6390C2318yes—
138#6390C2318yes—
139Dic7⋊C8C2318yes—
140#6377C2314yes—
141C22×C4⋊Q8—71no—
142C2×#529—71no—
143#3218—716no—
144C2×#497—71no—
145C2×#497D711yescharacteristic, complemented
146C2×#491—71no—
147C2×#491—71no—
148C2×#462—72no—
149C2×#461—72no—
150C2×#451—72no—
151C2×#448—72no—
152C2×#432—71no—
153C24×C7—21no—
154C23×D7C2×D411yescharacteristic
155C2×C7×Q8—22no—
156C2×C7×Q8—21no—
157C2×C7×Q8—24no—
158C2×C7×Q8—24no—
159C2×C7×Q8—24no—
160C2×C7×Q8C2414yes—
161C2×C7×Q8C2412yes—
162C2×C7×D4—21no—
163C2×C7×D4—24no—
164C2×C7×D4C2412yes—
165C22×C4×C7—21no—
166C22×C4×C7—22no—
167C22×C4×C7C2×D411yescharacteristic
168C22×C4×C7C2×D411yescharacteristic
169C22×C4×C7C2411yescharacteristic
170C2×C22⋊D7—24no—
171C2×C22⋊D7—44no—
172C22×Dic7—21no—
173C22×Dic7—21no—
174C22×Dic7—22no—
175C22×Dic7—24no—
176C22×Dic7—44no—
177C22×Dic7C2×D411yescharacteristic
178C22×Dic7C2×D411yescharacteristic
179C22×Dic7C2×D411yescharacteristic
180Q8×D7—48no—
181Q8×D7—48no—
182Q8×D7—416no—
183C2×C4×D7—24no—
184C2×C4×D7—24no—
185C2×C4×D7—24no—
186C2×C4×D7—28no—
187C2×C4×D7—48no—
188C2×C4×D7C2×D412yes—
189C2×C4×D7C2×D414yes—
190C2×C4×D7C2×D414yes—
191C2×C4×D7C2412yes—
192C2×Dic14—24no—
193C2×Dic14—24no—
194C2×Dic14—22no—
195C2×Dic14—28no—
196C2×Dic14—48no—
197C2×Dic14C2414yes—
198C7×Q16—48no—
199C7×SD16—48no—
200C2×C7×C8—24no—
201C2×C7×C8C2414yes—
202C7×C4⋊C4—24no—
203C7×C4⋊C4—24no—
204C7×C22⋊C4—24no—
205C7×C22⋊C4—24no—
206C42×C7C2×D412yes—
207C42×C7C2412yes—
208C22⋊Dic7—24no—
209C22⋊Dic7—24no—
210#1144—48no—
211#1142—48no—
212(C2×D7)⋊C4—24no—
213C4⋊Dic7—24no—
214C4⋊Dic7—24no—
215C4⋊Dic7—21no—
216C4⋊Dic7—21no—
217C4⋊Dic7—24no—
218C4⋊Dic7C2412yes—
219C4⋊Dic7C2412yes—
220Dic7⋊C4—24no—
221Dic7⋊C4—24no—
222Dic7⋊C4—24no—
223Dic7⋊C4—28no—
224Dic7⋊C4—28no—
225C4×Dic7—24no—
226C4×Dic7C2×D412yes—
227C4×Dic7C2×D414yes—
228C4×Dic7C2×D414yes—
229C4×Dic7C2412yes—
230C2×C7⋊C8—24no—
231C2×C7⋊C8C2414yes—
232C23×Q8—72no—
233C22×Q16—72no—
234C22×Q16C2×D712yes—
235C22×SD16—72no—
236C22×SD16C2×D712yes—
237C2×C4⋊Q8—72no—
238C2×C4⋊Q8—78no—
239C2×C4⋊Q8—71no—
240C2×C4⋊Q8—141no—
241C2×C4⋊Q8—141no—
242C2×C4⋊Q8—144no—
243C2×C4⋊Q8C2×D711yescharacteristic
244#529—78no—
245#529—144no—
246C2×#126—141no—
247C2×#125—71no—
248C2×#124C2×D711yescharacteristic
249C2×#123—141no—
250C2×C22⋊Q8—71no—
251C2×#121—71no—
252C2×C4×Q8—71no—
253C2×C4×D4—71no—
254C2×C4×D4—141no—
255C2×#117—141no—
256C22×C4⋊C4—141no—
257C22×C4⋊C4—141no—
258C22×C42—71no—
259#497—78no—
260#497C2×D718yescomplemented
261#491—78no—
262#491—78no—
263#462—716no—
264#461—716no—
265#451—716no—
266#448—716no—
267#432—78no—
268C2×C4⋊C8—72no—
269C2×#103—72no—
270C2×#103—72no—
271C2×#103—72no—
272C2×#103—72no—
273C2×C22⋊C8—72no—
274C2×#97—71no—
275C2×#97C2×D711yescharacteristic
276C23×C7—22no—
277C23×C7—42no—
278C23×C7—42no—
279C23×C7—42no—
280C23×C7C22×D411yescharacteristic
281C22×D7—22no—
282C22×D7—22no—
283C22×D7#13714yes—
284C22×D7C22×D412yes—
285C7×Q8—24no—
286C7×Q8—24no—
287C7×Q8—24no—
288C7×Q8—44no—
289C7×Q8—42no—
290C7×D4—24no—
291C7×D4—42no—
292C2×C4×C7—22no—
293C2×C4×C7—22no—
294C2×C4×C7—22no—
295C2×C4×C7—24no—
296C2×C4×C7—44no—
297C2×C4×C7—42no—
298C2×C4×C7C22×D412yes—
299C2×C4×C7C22×D412yes—
300C2×C4×C7C22×D411yescharacteristic
301C2×C4×C7H(5,𝔽2)14yes—
302C2×C4×C7C2511yescharacteristic
303C22⋊D7—48no—
304C2×Dic7—22no—
305C2×Dic7—22no—
306C2×Dic7—22no—
307C2×Dic7—22no—
308C2×Dic7—24no—
309C2×Dic7—44no—
310C2×Dic7—42no—
311C2×Dic7—42no—
312C2×Dic7—48no—
313C2×Dic7#13714yes—
314C2×Dic7C22×D412yes—
315C2×Dic7C22×D412yes—
316C2×Dic7C22×D412yes—
317C4×D7—28no—
318C4×D7—24no—
319C4×D7—24no—
320C4×D7—28no—
321C4×D7—416no—
322Dic14—24no—
323Dic14—24no—
324Dic14—416no—
325Dic14—44no—
326C7×C8—24no—
327C7⋊C8—24no—
328C22×Q8—78no—
329C22×Q8—72no—
330C22×Q8—142no—
331C22×Q8—144no—
332C22×Q8—284no—
333C22×Q8—284no—
334C22×Q8C22×D711yescharacteristic
335C22×Q8C22×D712yes—
336C22×D4—141no—
337C22×D4C22×D711yescharacteristic
338C23×C4—71no—
339C23×C4—71no—
340C23×C4—71no—
341C23×C4—142no—
342C23×C4—141no—
343C2×Q16—44no—
344C2×Q16—78no—
345C2×Q16—284no—
346C2×Q16C22×D718yes—
347C2×SD16—44no—
348C2×SD16—78no—
349C2×SD16—284no—
350C2×SD16C22×D718yes—
351C22×C8—72no—
352C22×C8C22×D712yes—
353C4⋊Q8—22no—
354C4⋊Q8—78no—
355C4⋊Q8—74no—
356C4⋊Q8—148no—
357C4⋊Q8—148no—
358C4⋊Q8—144no—
359C4⋊Q8—142no—
360C4⋊Q8C22×D714yes—
361#126—148no—
362#125—74no—
363#125—142no—
364#124—22no—
365#124C22×D714yes—
366#123—148no—
367C22⋊Q8—74no—
368C22⋊Q8—142no—
369#121—74no—
370#121—142no—
371C4×Q8—74no—
372C4×Q8—142no—
373C4×D4—74no—
374C4×D4—142no—
375C4×D4—148no—
376#117—148no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—71no—
380C2×C4⋊C4—71no—
381C2×C4⋊C4—148no—
382C2×C4⋊C4—148no—
383C2×C4⋊C4—142no—
384C2×C4⋊C4—142no—
385C2×C4⋊C4—141no—
386C2×C4⋊C4—141no—
387C2×C4⋊C4—141no—
388C2×C4⋊C4—141no—
389C2×C4⋊C4—141no—
390C2×C4⋊C4—141no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—141no—
394C2×C22⋊C4—141no—
395C2×C22⋊C4—141no—
396C2×C42—71no—
397C2×C42—71no—
398C2×C42—71no—
399C2×C42—74no—
400C2×C42—74no—
401C2×C42—141no—
402C2×C42C22×D711yescharacteristic
403C4⋊C8—78no—
404#103—78no—
405#103—78no—
406#103—78no—
407#103—78no—
408C22⋊C8—78no—
409#97—74no—
410#97C22×D714yes—
411C22×C7—42no—
412C22×C7—42no—
413C22×C7—42no—
414C22×C7—84no—
415C22×C7#53512yes—
416C22×C7C2×#13712yes—
417C22×C7C2×#13712yes—
418C22×C7C23×D411yescharacteristic
419C2×D7—22no—
420C2×D7—28no—
421C2×D7—22no—
422C2×D7C2×#13714yes—
423C4×C7—22no—
424C4×C7—22no—
425C4×C7—44no—
426C4×C7—42no—
427C4×C7#53512yes—
428C4×C7C2×H(5,𝔽2)12yes—
429Dic7—22no—
430Dic7—22no—
431Dic7—44no—
432Dic7—42no—
433Dic7—42no—
434Dic7C2×#13714yes—
435C24—21no—
436C24—71no—
437C2×Q8—21no—
438C2×Q8—22no—
439C2×Q8—24no—
440C2×Q8—24no—
441C2×Q8—24no—
442C2×Q8—74no—
443C2×Q8—148no—
444C2×Q8—142no—
445C2×Q8—144no—
446C2×Q8—144no—
447C2×Q8—288no—
448C2×Q8—288no—
449C2×Q8—288no—
450C2×Q8—2816no—
451C2×Q8C23×D714yes—
452C2×Q8C23×D712yes—
453C2×D4—21no—
454C2×D4—24no—
455C2×D4—144no—
456C2×D4—284no—
457C2×D4C23×D712yes—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—71no—
461C22×C4—71no—
462C22×C4—71no—
463C22×C4—74no—
464C22×C4—74no—
465C22×C4—72no—
466C22×C4—72no—
467C22×C4—144no—
468C22×C4—144no—
469C22×C4—148no—
470C22×C4—144no—
471C22×C4—144no—
472C22×C4—141no—
473C22×C4—141no—
474C22×C4—142no—
475C22×C4—288no—
476C22×C4—284no—
477C22×C4D4×D711yescharacteristic
478C22×C4D4×D711yescharacteristic
479C22×C4C23×D711yescharacteristic
480Q16—48no—
481Q16—288no—
482SD16—48no—
483SD16—288no—
484C2×C8—24no—
485C2×C8—74no—
486C2×C8—144no—
487C2×C8C23×D714yes—
488C4⋊C4—24no—
489C4⋊C4—24no—
490C4⋊C4—72no—
491C4⋊C4—72no—
492C4⋊C4—148no—
493C4⋊C4—148no—
494C4⋊C4—144no—
495C4⋊C4—144no—
496C4⋊C4—144no—
497C4⋊C4—144no—
498C4⋊C4—141no—
499C4⋊C4—141no—
500C4⋊C4—144no—
501C4⋊C4—144no—
502C22⋊C4—24no—
503C22⋊C4—24no—
504C22⋊C4—144no—
505C22⋊C4—144no—
506C22⋊C4—144no—
507C42—74no—
508C42—72no—
509C42—74no—
510C42—72no—
511C42—144no—
512C42D4×D712yes—
513C42C23×D712yes—
514C2×C7—82no—
515C2×C7#321814yescomplemented
516C2×C7C2×#53511yescharacteristic
517C2×C7C22×#13711yescharacteristic
518C2×C7C22×#13711yescharacteristic
519D7—24no—
520C23—22no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—74no—
525C23—72no—
526C23—142no—
527C23—142no—
528C23C2×D4×D711yescharacteristic
529Q8—24no—
530Q8—24no—
531Q8—24no—
532Q8—42no—
533Q8—44no—
534Q8—144no—
535Q8—144no—
536Q8—2816no—
537Q8—284no—
538D4—24no—
539D4—42no—
540D4—288no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—74no—
548C2×C4—72no—
549C2×C4—72no—
550C2×C4—72no—
551C2×C4—148no—
552C2×C4—148no—
553C2×C4—142no—
554C2×C4—142no—
555C2×C4—144no—
556C2×C4—144no—
557C2×C4—142no—
558C2×C4—142no—
559C2×C4—144no—
560C2×C4—2816no—
561C2×C4—288no—
562C2×C4—284no—
563C2×C4—282no—
564C2×C4—282no—
565C2×C4C2×D4×D712yes—
566C2×C4C2×D4×D712yes—
567C2×C4C2×D4×D711yescharacteristic
568C2×C4#654814yes—
569C2×C4C24×D711yescharacteristic
570C8—24no—
571C8—144no—
572C7C2×#321811yescharacteristic, complemented, Sylow
573C22—42no—
574C22—42no—
575C22—42no—
576C22—74no—
577C22—84no—
578C22—142no—
579C22—142no—
580C22—148no—
581C22#9040612yes—
582C22D7×#13712yes—
583C22D7×#13712yes—
584C22C22×D4×D711yescharacteristic
585C4—22no—
586C4—22no—
587C4—44no—
588C4—42no—
589C4—74no—
590C4—142no—
591C4—142no—
592C4—282no—
593C4—282no—
594C4—284no—
595C4#9040612yes—
596C4C2×#654812yes—
597C2—82no—
598C2—144no—
599C2#1173932114yesdirect product factor
600C2C2×#9040611yescharacteristic
601C2C2×D7×#13711yescharacteristic
602C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#497C2
socleC23×C7C22×D4
prime radicalC2×#6501C22
hypercenterC2×#497D7
hypocenterC7C2×#3218
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C2×D7×C4⋊Q8C2semidirect
3. C2×C7×#497C2semidirect
4. C2×#89958C2semidirect
5. C2×#89954C2semidirect
7. C2×#89934C2semidirect
8. C2×#89854C2semidirect
9. C2×#89832C2semidirect
10. #11739321C2direct (N × H)
11. C2×#89475C2semidirect
12. C2×#89477C2semidirect
26. D7×C4⋊Q8C22semidirect
40. C7×#497C22semidirect
44. #89958C22semidirect
45. #89954C22semidirect
47. #89934C22semidirect
52. #89854C22semidirect
53. #89832C22semidirect
55. #89477C22semidirect
56. #89475C22semidirect
145. C2×#497D7semidirect
260. #497C2×D7semidirect
515. C2×C7#3218semidirect
572. C7C2×#3218semidirect
599. C2#11739321direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D7×C4⋊Q82
C2×#903712
C2×C7×#4972
C2×#899582
C2×#899542
C2×#899422
C2×#899342
C2×#898542
C2×#898322
#117393212
C2×#894752
C2×#894772
C2×#32187