Finite Group Databasebeta

← C2×#11740805 #14225874

Subgroups — C2×#11740805 #14225874

Order 1792.

1810 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#533C211yesmaximal, characteristic, complemented
2C2×#90170C211yesmaximal, characteristic
3#11740805C2116yesmaximal, direct product factor
4C2×#89863C211yesmaximal, characteristic, complemented
5C2×#89866C211yesmaximal, characteristic, complemented
6C2×#89856C211yesmaximal, characteristic, complemented
7C2×#89859C211yesmaximal, characteristic, complemented
8C2×#89836C212yesmaximal, complemented
9C2×#89840C212yesmaximal, complemented
10C2×#89768C212yesmaximal, complemented
11C2×#89775C212yesmaximal
12C2×#89697C211yesmaximal, characteristic, complemented
13C7×#533—24no—
14C7×#533C2218yescomplemented
15C2×C7×C4⋊Q8C2211yescharacteristic
16C2×C7×C4⋊Q8C2211yescharacteristic
17C2×C7×#125C2212yes—
18C2×C7×C22⋊Q8—21no—
19C2×C7×C22⋊Q8—21no—
20C2×C4×C7×Q8—21no—
21C2×C4×C7×Q8—21no—
22C2×C7×#117C2212yes—
23C22×C42×C7C2211yescharacteristic
24C2×#6493C2211yescharacteristic
25C2×#6492—21no—
26C2×C4×C22⋊D7—21no—
27C2×#6487C2211yescharacteristic
28#90170—24no—
29#90170C2218yes—
30C2×#6439—21no—
31C2×#6438C2211yescharacteristic
32C2×C4×D28C2211yescharacteristic
33C2×#6435—21no—
34C2×#6433C2211yescharacteristic
35C2×C4×Dic14C2211yescharacteristic
36C2×C22⋊(C7⋊C8)C2212yes—
37#89866C2218yescomplemented
38#89863C2218yescomplemented
39#89859C2218yescomplemented
40#89856C2218yescomplemented
41#89840C22116yescomplemented
42#89836C22116yescomplemented
43#89775C22116yes—
44#89768C22116yescomplemented
45C2×#6384C2212yes—
46C2×#6384C2212yes—
47C2×#6383C2212yes—
48C2×#6383C2212yes—
49C2×#6382C2212yes—
50C2×#6382C2212yes—
51C2×#6381C2212yes—
52C2×#6381C2212yes—
53#89697C2218yescomplemented
54C2×C4⋊(C7⋊C8)C2211yescharacteristic
55C2×C4⋊(C7⋊C8)C2211yescharacteristic
56C2×C4×C7⋊C8C2212yes—
57C2×#3233—71nomaximal, Sylow
58C22×C7×Q8—21no—
59C22×C7×Q8—21no—
60C23×C4×C7D411yescharacteristic
61C23×C4×C7D411yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C22×C22⋊D7—21no—
64C22×D28C2311yescharacteristic
65C22×C4×D7—21no—
66C22×Dic14C2311yescharacteristic
67C7×C4⋊Q8—22no—
68C7×C4⋊Q8—22no—
69C7×C4⋊Q8C2314yes—
70C7×C4⋊Q8C2314yes—
71C7×#125—24no—
72C7×#125C2318yes—
73C7×C22⋊Q8—28no—
74C7×C22⋊Q8—28no—
75C4×C7×Q8—28no—
76C4×C7×Q8—28no—
77C7×#117—24no—
78C7×#117C2318yes—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—21no—
82C2×C7×C4⋊C4—21no—
83C2×C7×C4⋊C4C2312yes—
84C2×C7×C4⋊C4C2312yes—
85C2×C7×C22⋊C4—22no—
86C2×C42×C7—22no—
87C2×C42×C7D411yescharacteristic
88C2×C42×C7D411yescharacteristic
89C2×C42×C7D414yes—
90C2×C42×C7C2311yescharacteristic
91C2×C42×C7C2311yescharacteristic
92C2×C42×C7C2314yes—
93C2×C22⋊Dic7—21no—
94#6493—22no—
95#6493C2314yes—
96#6492—28no—
97C4×C22⋊D7—28no—
98C2×(C2×D7)⋊C4—21no—
99C2×(C2×D7)⋊C4—21no—
100C2×(C2×D7)⋊C4—21no—
101C2×(C2×D7)⋊C4—21no—
102C2×C4⋊Dic7C2311yescharacteristic
103C2×C4⋊Dic7C2311yescharacteristic
104#6487—22no—
105#6487C2314yes—
106C2×Dic7⋊C4—21no—
107C2×Dic7⋊C4—21no—
108C2×Dic7⋊C4—21no—
109C2×Dic7⋊C4—21no—
110C2×C4×Dic7—21no—
111C22×C7⋊C8C2312yes—
112C22×C7⋊C8C2312yes—
113#6439—28no—
114#6438—22no—
115#6438C2314yes—
116C4×D28—22no—
117C4×D28C2314yes—
118#6435—28no—
119#6433—22no—
120#6433C2314yes—
121C4×Dic14—22no—
122C4×Dic14C2314yes—
123C22⋊(C7⋊C8)C2318yes—
124#6384C2318yes—
125#6384C2318yes—
126#6383C2318yes—
127#6383C2318yes—
128#6382C2318yes—
129#6382C2318yes—
130#6381C2318yes—
131#6381C2318yes—
132C4⋊(C7⋊C8)C2314yes—
133C4⋊(C7⋊C8)C2314yes—
134C4×C7⋊C8C2318yes—
135C2×#533D711yescharacteristic, complemented
136C2×#529—71no—
137#3233—716no—
138C2×#499—72no—
139C2×#488—72no—
140C2×#485—72no—
141C2×#482—72no—
142C2×#477—71no—
143C2×#475—71no—
144C2×#476—71no—
145C2×#474—71no—
146C2×#431—71no—
147C24×C7C2×D411yescharacteristic
148C23×D7—21no—
149C2×C7×Q8—24no—
150C2×C7×Q8—24no—
151C2×C7×Q8—44no—
152C2×C7×Q8—44no—
153C22×C4×C7—24no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—42no—
159C22×C4×C7C2×D411yescharacteristic
160C22×C4×C7C2×D411yescharacteristic
161C22×C4×C7C2×D411yescharacteristic
162C22×C4×C7C2×D411yescharacteristic
163C22×C4×C7C2×D412yes—
164C22×C4×C7C2×D414yes—
165C22×C4×C7C2×D414yes—
166C22×C4×C7C2×D411yescharacteristic
167C22×C4×C7C2412yes—
168C22×C4×C7C2411yescharacteristic
169C2×C22⋊D7—24no—
170C2×C22⋊D7—44no—
171C22×Dic7—21no—
172C22×Dic7—21no—
173C22×Dic7—21no—
174C2×D28—22no—
175C2×D28—22no—
176C2×D28—21no—
177C2×D28C2412yes—
178C2×C4×D7—24no—
179C2×C4×D7—44no—
180C2×Dic14—22no—
181C2×Dic14—22no—
182C2×Dic14—21no—
183C2×Dic14C2412yes—
184C7×C4⋊C4—28no—
185C7×C4⋊C4—28no—
186C7×C4⋊C4—24no—
187C7×C4⋊C4—24no—
188C7×C4⋊C4—22no—
189C7×C4⋊C4—22no—
190C7×C4⋊C4C2414yes—
191C7×C4⋊C4C2414yes—
192C7×C22⋊C4—28no—
193C42×C7—28no—
194C42×C7C2×D412yes—
195C42×C7C2×D412yes—
196C42×C7C2×D414yes—
197C42×C7C2×D414yes—
198C42×C7C2412yes—
199C42×C7C2412yes—
200C22⋊Dic7—24no—
201(C2×D7)⋊C4—24no—
202(C2×D7)⋊C4—24no—
203(C2×D7)⋊C4—24no—
204(C2×D7)⋊C4—24no—
205C4⋊Dic7—21no—
206C4⋊Dic7—21no—
207C4⋊Dic7C2412yes—
208C4⋊Dic7C2412yes—
209Dic7⋊C4—24no—
210Dic7⋊C4—24no—
211Dic7⋊C4—24no—
212Dic7⋊C4—24no—
213C4×Dic7—24no—
214C2×C7⋊C8—24no—
215C2×C7⋊C8—24no—
216C2×C7⋊C8C2414yes—
217C2×C7⋊C8C2414yes—
218#533—24no—
219#533C2×D718yescomplemented
220C2×C4⋊Q8C2×D711yescharacteristic
221C2×C4⋊Q8C2×D711yescharacteristic
222#529—78no—
223#529—144no—
224C2×#126—141no—
225C2×#125—71no—
226C2×#125C2×D712yes—
227C2×#124—71no—
228C2×#123—141no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—71no—
232C2×#121—71no—
233C2×C4×Q8—21no—
234C2×C4×Q8—21no—
235C2×C4×Q8—71no—
236C2×C4×D4—71no—
237C2×C4×D4—141no—
238C2×#117—141no—
239C2×#117C2×D712yes—
240C22×C42C2×D711yescharacteristic
241#499—716no—
242#488—716no—
243#485—716no—
244#482—716no—
245#477—78no—
246#476—78no—
247#475—78no—
248#474—78no—
249#431—78no—
250C2×#107—72no—
251C2×#107—72no—
252C2×#106—72no—
253C2×#106—72no—
254C2×C4⋊C8—71no—
255C2×C4⋊C8—71no—
256C2×#103—72no—
257C2×#103—72no—
258C2×#102—72no—
259C2×#102—72no—
260C2×C22⋊C8—72no—
261C2×C4×C8—72no—
262C23×C7—22no—
263C23×C7—22no—
264C23×C7—22no—
265C23×C7C22×D412yes—
266C23×C7C22×D411yescharacteristic
267C22×D7—22no—
268C22×D7—42no—
269C22×D7—42no—
270C22×D7—42no—
271C7×Q8—48no—
272C7×Q8—48no—
273C2×C4×C7—22no—
274C2×C4×C7—22no—
275C2×C4×C7—22no—
276C2×C4×C7—22no—
277C2×C4×C7—24no—
278C2×C4×C7—28no—
279C2×C4×C7—22no—
280C2×C4×C7—22no—
281C2×C4×C7—24no—
282C2×C4×C7—24no—
283C2×C4×C7—44no—
284C2×C4×C7—44no—
285C2×C4×C7—44no—
286C2×C4×C7#13514yes—
287C2×C4×C7C22×D412yes—
288C2×C4×C7C22×D412yes—
289C2×C4×C7C22×D412yes—
290C2×C4×C7C22×D412yes—
291C2×C4×C7C22×D411yescharacteristic
292C2×C4×C7C22×D412yes—
293C2×C4×C72−1+412yes—
294C2×C4×C72−1+412yes—
295C2×C4×C7C2511yescharacteristic
296C22⋊D7—48no—
297C2×Dic7—22no—
298C2×Dic7—22no—
299C2×Dic7—22no—
300C2×Dic7—42no—
301C2×Dic7—42no—
302C2×Dic7—42no—
303D28—22no—
304D28—22no—
305D28—42no—
306C4×D7—48no—
307Dic14—22no—
308Dic14—22no—
309Dic14—42no—
310C7⋊C8—24no—
311C7⋊C8—24no—
312C22×Q8—21no—
313C22×Q8—21no—
314C22×Q8—71no—
315C22×D4—71no—
316C22×D4—141no—
317C23×C4—141no—
318C23×C4C22⋊D711yescharacteristic
319C23×C4C22⋊D711yescharacteristic
320C23×C4C22×D711yescharacteristic
321C22×C8—72no—
322C22×C8—72no—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8C22×D714yes—
326C4⋊Q8C22×D714yes—
327#126—148no—
328#125—24no—
329#125—74no—
330#125—142no—
331#125C22×D718yes—
332#124—74no—
333#124—142no—
334#123—148no—
335C22⋊Q8—28no—
336C22⋊Q8—28no—
337C22⋊Q8—74no—
338C22⋊Q8—142no—
339#121—74no—
340#121—142no—
341C4×Q8—28no—
342C4×Q8—28no—
343C4×Q8—74no—
344C4×Q8—142no—
345C4×D4—74no—
346C4×D4—148no—
347C4×D4—142no—
348#117—24no—
349#117—148no—
350#117C22×D718yes—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—71no—
356C2×C4⋊C4—71no—
357C2×C4⋊C4—141no—
358C2×C4⋊C4—141no—
359C2×C4⋊C4—141no—
360C2×C4⋊C4—141no—
361C2×C4⋊C4C22×D712yes—
362C2×C4⋊C4C22×D712yes—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—141no—
365C2×C22⋊C4—141no—
366C2×C22⋊C4—141no—
367C2×C22⋊C4—141no—
368C2×C22⋊C4—141no—
369C2×C42—22no—
370C2×C42—141no—
371C2×C42C22⋊D711yescharacteristic
372C2×C42C22⋊D711yescharacteristic
373C2×C42C22⋊D714yes—
374C2×C42C22×D711yescharacteristic
375C2×C42C22×D711yescharacteristic
376C2×C42C22×D714yes—
377#107—78no—
378#107—78no—
379#106—78no—
380#106—78no—
381C4⋊C8—74no—
382C4⋊C8—74no—
383#103—78no—
384#103—78no—
385#102—78no—
386#102—78no—
387C22⋊C8—78no—
388C4×C8—78no—
389C22×C7—22no—
390C22×C7—22no—
391C22×C7—22no—
392C22×C7—44no—
393C22×C7#53612yes—
394C22×C7C2×#13512yes—
395C22×C7#57512yes—
396C22×C7C23×D411yescharacteristic
397C2×D7—42no—
398C2×D7—42no—
399C2×D7—42no—
400C2×D7—84no—
401C4×C7—22no—
402C4×C7—22no—
403C4×C7—22no—
404C4×C7—22no—
405C4×C7—44no—
406C4×C7—44no—
407C4×C7#53612yes—
408C4×C7C2×#13514yes—
409C4×C7C2×2−1+411yescharacteristic
410C4×C7C2×2−1+411yescharacteristic
411Dic7—42no—
412Dic7—42no—
413Dic7—42no—
414C24—141no—
415C24C2×C22⋊D711yescharacteristic
416C2×Q8—24no—
417C2×Q8—24no—
418C2×Q8—44no—
419C2×Q8—44no—
420C2×Q8—72no—
421C2×Q8—141no—
422C2×Q8—142no—
423C2×Q8—142no—
424C2×D4—72no—
425C2×D4—144no—
426C2×D4—142no—
427C2×D4—142no—
428C2×D4—141no—
429C2×D4—284no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—42no—
436C22×C4—141no—
437C22×C4—141no—
438C22×C4—141no—
439C22×C4—144no—
440C22×C4—284no—
441C22×C4C2×C22⋊D712yes—
442C22×C4C2×C22⋊D714yes—
443C22×C4C2×C22⋊D711yescharacteristic
444C22×C4C2×C22⋊D711yescharacteristic
445C22×C4C2×C22⋊D711yescharacteristic
446C22×C4C2×C22⋊D711yescharacteristic
447C22×C4C2×C22⋊D714yes—
448C22×C4C2×C22⋊D711yescharacteristic
449C22×C4C23×D712yes—
450C22×C4C23×D711yescharacteristic
451C2×C8—74no—
452C2×C8—74no—
453C2×C8—144no—
454C2×C8—144no—
455C4⋊C4—28no—
456C4⋊C4—28no—
457C4⋊C4—24no—
458C4⋊C4—24no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—72no—
462C4⋊C4—72no—
463C4⋊C4—144no—
464C4⋊C4—144no—
465C4⋊C4—144no—
466C4⋊C4—144no—
467C4⋊C4—141no—
468C4⋊C4—141no—
469C4⋊C4C23×D714yes—
470C4⋊C4C23×D714yes—
471C22⋊C4—28no—
472C22⋊C4—144no—
473C22⋊C4—144no—
474C22⋊C4—144no—
475C22⋊C4—144no—
476C22⋊C4—144no—
477C42—28no—
478C42—144no—
479C42C2×C22⋊D714yes—
480C42C2×C22⋊D712yes—
481C42C2×C22⋊D714yes—
482C42C2×C22⋊D712yes—
483C42C23×D712yes—
484C42C23×D712yes—
485C2×C7—42no—
486C2×C7#323314yescomplemented
487C2×C7C2×#53611yescharacteristic
488C2×C7C22×#13511yescharacteristic
489C2×C7C2×#57511yescharacteristic
490D7—82no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—142no—
495C23—282no—
496C23—282no—
497C23—282no—
498C23C22×C22⋊D712yes—
499C23C22×C22⋊D711yescharacteristic
500Q8—48no—
501Q8—48no—
502Q8—142no—
503Q8—142no—
504Q8—282no—
505D4—142no—
506D4—142no—
507D4—288no—
508D4—282no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—28no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—44no—
520C2×C4—44no—
521C2×C4—44no—
522C2×C4—142no—
523C2×C4—142no—
524C2×C4—142no—
525C2×C4—282no—
526C2×C4—282no—
527C2×C4—282no—
528C2×C4—288no—
529C2×C4#651314yes—
530C2×C4#655112yes—
531C2×C4#655112yes—
532C2×C4C22×C22⋊D712yes—
533C2×C4C22×C22⋊D712yes—
534C2×C4C22×C22⋊D712yes—
535C2×C4C22×C22⋊D712yes—
536C2×C4C22×C22⋊D711yescharacteristic
537C2×C4C22×C22⋊D712yes—
538C2×C4C24×D711yescharacteristic
539C8—144no—
540C8—144no—
541C7C2×#323311yescharacteristic, complemented, Sylow
542C22—22no—
543C22—22no—
544C22—22no—
545C22—44no—
546C22—282no—
547C22—282no—
548C22—282no—
549C22—564no—
550C22#9050712yes—
551C22C2×#651312yes—
552C22#9051312yes—
553C22C23×C22⋊D711yescharacteristic
554C4—22no—
555C4—22no—
556C4—22no—
557C4—22no—
558C4—44no—
559C4—44no—
560C4—282no—
561C4—282no—
562C4—282no—
563C4#9050712yes—
564C4C2×#651314yes—
565C4C2×#655111yescharacteristic
566C4C2×#655111yescharacteristic
567C2—42no—
568C2—562no—
569C2#1174080514yesdirect product factor
570C2C2×#9050711yescharacteristic
571C2C22×#651311yescharacteristic
572C2C2×#9051311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#533C2
socleC23×C7C22×D4
prime radicalC2×#6493C22
hypercenterC2×#533D7
hypocenterC7C2×#3233
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. C2×C7×#533C2semidirect
3. #11740805C2direct (N × H)
4. C2×#89863C2semidirect
5. C2×#89866C2semidirect
6. C2×#89856C2semidirect
7. C2×#89859C2semidirect
8. C2×#89836C2semidirect
9. C2×#89840C2semidirect
10. C2×#89768C2semidirect
12. C2×#89697C2semidirect
14. C7×#533C22semidirect
37. #89866C22semidirect
38. #89863C22semidirect
39. #89859C22semidirect
40. #89856C22semidirect
41. #89840C22semidirect
42. #89836C22semidirect
44. #89768C22semidirect
53. #89697C22semidirect
135. C2×#533D7semidirect
219. #533C2×D7semidirect
486. C2×C7#3233semidirect
541. C7C2×#3233semidirect
569. C2#11740805direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5332
C2×#901702
#117408052
C2×#898632
C2×#898662
C2×#898562
C2×#898592
C2×#898362
C2×#898402
C2×#897682
C2×#897752
C2×#896972
C2×#32337