Finite Group Databasebeta

← C2×#11740959 #14230705

Subgroups — C2×#11740959 #14230705

Order 1792.

2374 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#547C211yesmaximal, characteristic, complemented
2C2×#90246C211yesmaximal, characteristic, complemented
3C2×#90010C212yesmaximal, complemented
4C2×#90004C212yesmaximal, complemented
5#11740959C2116yesmaximal, direct product factor
6C2×#89855C211yesmaximal, characteristic, complemented
7C2×#89853C211yesmaximal, characteristic, complemented
8C2×#89821C212yesmaximal, complemented
9C2×#89816C212yesmaximal, complemented
10C2×#89784C211yesmaximal, characteristic, complemented
11C2×#89779C211yesmaximal, characteristic, complemented
12C2×C4×#1141C211yesmaximal, characteristic, complemented
13C22×C7×#41C2212yes—
14C22×#1159—21no—
15C7×#547—24no—
16C7×#547C2218yescomplemented
17C2×C7×C4⋊Q8C2211yescharacteristic
18C2×C7×#123—22no—
19C2×C7×C22⋊Q8C2212yes—
20C2×C7×#121—21no—
21C2×C4×C7×D4C2211yescharacteristic
22C2×C4×C7×D4C2211yescharacteristic
23C22×C7×C4⋊C4—21no—
24C22×#1143C2212yes—
25C22×#1141C2211yescharacteristic
26C2×#6493C2212yes—
27C22×C4⋊Dic7C2212yes—
28C22×#1136C2212yes—
29#90246—24no—
30#90246C2218yescomplemented
31C2×#6460—21no—
32C2×#6449—22no—
33C2×C4×D28C2211yescharacteristic
34C2×#6432C2211yescharacteristic
35#90010C22116yescomplemented
36#90004C22116yescomplemented
37C2×#6409C2212yes—
38C2×#6409C2212yes—
39C2×#6409C2212yes—
40C2×#6406C2211yescharacteristic
41C2×#6406C2212yes—
42C2×C22⋊(C7⋊C8)C2212yes—
43#89855C2218yescomplemented
44#89853C2218yescomplemented
45#89821C22116yescomplemented
46#89816C22116yescomplemented
47C4×#1141C2218yescomplemented
48#89784C2218yescomplemented
49#89779C2218yescomplemented
50C2×#6383C2211yescharacteristic
51C2×#6381C2211yescharacteristic
52C2×#6381C2212yes—
53C2×C4⋊(C7⋊C8)C2211yescharacteristic
54C2×C4×C7⋊C8C2211yescharacteristic
55C2×#3330—71nomaximal, Sylow
56C2×C7×#41—24no—
57C2×C7×#41—28no—
58C2×C7×#41—44no—
59C2×C7×#41C2318yes—
60C22×C7×Q8C2312yes—
61C22×C7×D4—22no—
62C22×C7×D4D411yescharacteristic
63C22×C7×D4C2311yescharacteristic
64C23×C4×C7—22no—
65C23×C4×C7—21no—
66C23×C4×C7C2312yes—
67C22×C22⋊D7—22no—
68C23×Dic7—22no—
69C2×#1159—28no—
70C2×#1159—48no—
71C22×D28C2311yescharacteristic
72C22×C4×D7—21no—
73C22×Dic14—21no—
74C7×C4⋊Q8—22no—
75C7×C4⋊Q8C2314yes—
76C7×#123—216no—
77C7×C22⋊Q8—24no—
78C7×C22⋊Q8C2318yes—
79C7×#121—28no—
80C4×C7×D4—22no—
81C4×C7×D4D414yes—
82C4×C7×D4C2314yes—
83C4×C7×D4C2314yes—
84C2×C7×C4⋊C4—21no—
85C2×C7×C4⋊C4—22no—
86C2×C7×C4⋊C4—21no—
87C2×C7×C4⋊C4—28no—
88C2×C7×C4⋊C4D411yescharacteristic
89C2×C7×C4⋊C4C2311yescharacteristic
90C2×C7×C22⋊C4—22no—
91C2×C7×C22⋊C4—21no—
92C2×C7×C22⋊C4D412yes—
93C2×C42×C7C2311yescharacteristic
94C2×#1143—44no—
95C2×#1143C2318yes—
96C2×#1141—24no—
97C2×#1141C2314yes—
98#6493—24no—
99#6493C2318yes—
100C2×(C2×D7)⋊C4—21no—
101C2×(C2×D7)⋊C4—22no—
102C2×C4⋊Dic7—21no—
103C2×C4⋊Dic7—22no—
104C2×C4⋊Dic7—24no—
105C2×C4⋊Dic7C2312yes—
106C2×C4⋊Dic7C2311yescharacteristic
107C2×C4⋊Dic7C2318yes—
108C2×#1136—44no—
109C2×#1136C2318yes—
110C22×C7⋊C8C2311yescharacteristic
111C22×C7⋊C8C2311yescharacteristic
112C22×C7⋊C8C2312yes—
113#6460—28no—
114#6449—216no—
115C4×D28—22no—
116C4×D28C2314yes—
117#6432—22no—
118#6432C2314yes—
119#6409C2318yes—
120#6409C2318yes—
121#6409C2318yes—
122#6406C2314yes—
123#6406C2318yes—
124C22⋊(C7⋊C8)C2318yes—
125#6383C2314yes—
126#6381C2318yes—
127#6381C2314yes—
128C4⋊(C7⋊C8)C2314yes—
129C4×C7⋊C8C2314yes—
130C2×#547—71no—
131C2×#547D711yescharacteristic, complemented
132#3330—716no—
133C2×#487—71no—
134C2×#484—72no—
135C2×#474—71no—
136C2×#468—72no—
137C2×#461—71no—
138C2×#449—72no—
139C2×C4×D8—71no—
140C2×#436—71no—
141C2×#417—72no—
142C24×C7—21no—
143C24×C7C2×D412yes—
144C23×D7—21no—
145C7×#41—216no—
146C7×#41—48no—
147C7×#41—416no—
148C2×C7×Q8—22no—
149C2×C7×Q8—24no—
150C2×C7×Q8—24no—
151C2×C7×Q8C2414yes—
152C2×C7×D4—28no—
153C2×C7×D4—24no—
154C2×C7×D4—21no—
155C2×C7×D4—22no—
156C2×C7×D4—48no—
157C2×C7×D4C2×D414yes—
158C2×C7×D4#4114yescomplemented
159C2×C7×D4C2412yes—
160C22×C4×C7—24no—
161C22×C4×C7—24no—
162C22×C4×C7—21no—
163C22×C4×C7—22no—
164C22×C4×C7—24no—
165C22×C4×C7—28no—
166C22×C4×C7—48no—
167C22×C4×C7—44no—
168C22×C4×C7C2×D411yescharacteristic
169C22×C4×C7C2×D412yes—
170C22×C4×C7C2×D414yes—
171C22×C4×C7C2×D411yescharacteristic
172C22×C4×C7C2414yes—
173C22×C4×C7C2411yescharacteristic
174C2×C22⋊D7—28no—
175C2×C22⋊D7—48no—
176C22×Dic7—28no—
177C22×Dic7—22no—
178C22×Dic7—21no—
179C22×Dic7—48no—
180#1159—432no—
181C2×D28—22no—
182C2×D28—22no—
183C2×D28—21no—
184C2×D28C2412yes—
185C2×C4×D7—24no—
186C2×C4×D7—44no—
187C2×Dic14—24no—
188C2×Dic14—44no—
189C7×C4⋊C4—24no—
190C7×C4⋊C4—28no—
191C7×C4⋊C4—24no—
192C7×C4⋊C4—21no—
193C7×C4⋊C4C2×D414yes—
194C7×C4⋊C4C2412yes—
195C7×C22⋊C4—28no—
196C7×C22⋊C4—24no—
197C7×C22⋊C4C2×D418yes—
198C42×C7C2×D412yes—
199C42×C7C2412yes—
200#1143—48no—
201#1141—28no—
202(C2×D7)⋊C4—24no—
203(C2×D7)⋊C4—28no—
204C4⋊Dic7—22no—
205C4⋊Dic7—24no—
206C4⋊Dic7—21no—
207C4⋊Dic7—28no—
208C4⋊Dic7C2414yes—
209C4⋊Dic7C2412yes—
210#1136—48no—
211C2×C7⋊C8—22no—
212C2×C7⋊C8—22no—
213C2×C7⋊C8—24no—
214C2×C7⋊C8C2412yes—
215C2×C7⋊C8C2414yes—
216C2×C7⋊C8C2412yes—
217C22×#41—141no—
218C22×#41C2×D712yes—
219C22×SD16—72no—
220C22×D8—71no—
221C22×M16—72no—
222#547—24no—
223#547—78no—
224#547—144no—
225#547C2×D718yescomplemented
226C2×C4⋊Q8—71no—
227C2×C4⋊Q8C2×D711yescharacteristic
228C2×#123—22no—
229C2×#123—142no—
230C2×C22⋊Q8—141no—
231C2×C22⋊Q8C2×D712yes—
232C2×#121—21no—
233C2×#121—72no—
234C2×C4×D4—71no—
235C2×C4×D4C2×D711yescharacteristic
236C2×C4×D4C2×D711yescharacteristic
237C22×C4⋊C4—21no—
238C22×C4⋊C4—72no—
239#487—78no—
240#484—716no—
241#474—78no—
242#468—716no—
243#461—78no—
244#449—716no—
245C4×D8—78no—
246#436—78no—
247C2×#107—71no—
248C2×#107—72no—
249C2×C4⋊C8—71no—
250#417—716no—
251C2×#103—72no—
252C2×#103—72no—
253C2×#103—72no—
254C2×#102—71no—
255C2×#102—72no—
256C2×#102—71no—
257C2×C22⋊C8—72no—
258C2×C4×C8—71no—
259C23×C7—24no—
260C23×C7—24no—
261C23×C7—24no—
262C23×C7—24no—
263C23×C7—22no—
264C23×C7—42no—
265C23×C7—42no—
266C23×C7C22×D414yes—
267C23×C7C22×D411yescharacteristic
268C22×D7—22no—
269C22×D7—42no—
270C22×D7—42no—
271C22×D7—42no—
272C7×Q8—24no—
273C7×Q8—24no—
274C7×Q8—44no—
275C7×D4—24no—
276C7×D4—28no—
277C7×D4—22no—
278C7×D4—416no—
279C7×D4C2×#4114yescomplemented
280C2×C4×C7—24no—
281C2×C4×C7—22no—
282C2×C4×C7—28no—
283C2×C4×C7—24no—
284C2×C4×C7—24no—
285C2×C4×C7—22no—
286C2×C4×C7—24no—
287C2×C4×C7—416no—
288C2×C4×C7—44no—
289C2×C4×C7—42no—
290C2×C4×C7—48no—
291C2×C4×C7AGL(1,ℤ/8)14yes—
292C2×C4×C7C22×D412yes—
293C2×C4×C7C22×D414yes—
294C2×C4×C7C22×D411yescharacteristic
295C2×C4×C7C22×D412yes—
296C2×C4×C7C2×#4112yes—
297C2×C4×C7H(5,𝔽2)12yes—
298C2×C4×C7C2511yescharacteristic
299C22⋊D7—416no—
300C2×Dic7—24no—
301C2×Dic7—22no—
302C2×Dic7—416no—
303C2×Dic7—44no—
304C2×Dic7—42no—
305D28—22no—
306D28—22no—
307D28—42no—
308C4×D7—48no—
309Dic14—48no—
310C7⋊C8—22no—
311C7⋊C8—22no—
312C7⋊C8—24no—
313C2×#41—24no—
314C2×#41—28no—
315C2×#41—44no—
316C2×#41—148no—
317C2×#41—288no—
318C2×#41C22×D718yes—
319C22×Q8—141no—
320C22×Q8C22×D712yes—
321C22×D4—22no—
322C22×D4—71no—
323C22×D4—142no—
324C22×D4C22⋊D711yescharacteristic
325C22×D4C22×D711yescharacteristic
326C23×C4—21no—
327C23×C4—22no—
328C23×C4—142no—
329C23×C4—141no—
330C23×C4C22×D712yes—
331C2×SD16—78no—
332C2×SD16—284no—
333C2×D8—74no—
334C2×D8—144no—
335C2×M16—78no—
336C2×M16—284no—
337C22×C8—71no—
338C22×C8—72no—
339C22×C8—71no—
340C4⋊Q8—22no—
341C4⋊Q8—74no—
342C4⋊Q8—142no—
343C4⋊Q8C22×D714yes—
344#123—216no—
345#123—1416no—
346C22⋊Q8—24no—
347C22⋊Q8—148no—
348C22⋊Q8C22×D718yes—
349#121—28no—
350#121—78no—
351#121—144no—
352C4×D4—22no—
353C4×D4—74no—
354C4×D4—142no—
355C4×D4C22⋊D714yes—
356C4×D4C22×D714yes—
357C4×D4C22×D714yes—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—28no—
362C2×C4⋊C4—71no—
363C2×C4⋊C4—72no—
364C2×C4⋊C4—78no—
365C2×C4⋊C4—142no—
366C2×C4⋊C4—144no—
367C2×C4⋊C4—141no—
368C2×C4⋊C4C22⋊D711yescharacteristic
369C2×C4⋊C4C22×D711yescharacteristic
370C2×C22⋊C4—22no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—141no—
373C2×C22⋊C4—142no—
374C2×C22⋊C4C22⋊D712yes—
375C2×C42C22×D711yescharacteristic
376#107—74no—
377#107—78no—
378C4⋊C8—74no—
379#103—78no—
380#103—78no—
381#103—78no—
382#102—74no—
383#102—78no—
384#102—74no—
385C22⋊C8—78no—
386C4×C8—74no—
387C22×C7—24no—
388C22×C7—24no—
389C22×C7—24no—
390C22×C7—24no—
391C22×C7—48no—
392C22×C7—48no—
393C22×C7—42no—
394C22×C7—42no—
395C22×C7#54612yes—
396C22×C7C2×AGL(1,ℤ/8)12yes—
397C22×C7#57812yes—
398C22×C7C23×D411yescharacteristic
399C2×D7—42no—
400C2×D7—42no—
401C2×D7—42no—
402C2×D7—84no—
403C4×C7—24no—
404C4×C7—22no—
405C4×C7—44no—
406C4×C7—42no—
407C4×C7#54612yes—
408C4×C7C2×AGL(1,ℤ/8)14yes—
409C4×C7C22×#4111yescharacteristic
410C4×C7C2×H(5,𝔽2)11yescharacteristic
411Dic7—44no—
412Dic7—42no—
413C24—21no—
414C24—141no—
415C24C2×C22⋊D712yes—
416#41—216no—
417#41—48no—
418#41—416no—
419#41—2832no—
420C2×Q8—22no—
421C2×Q8—24no—
422C2×Q8—24no—
423C2×Q8—144no—
424C2×Q8—284no—
425C2×Q8C23×D714yes—
426C2×D4—28no—
427C2×D4—24no—
428C2×D4—22no—
429C2×D4—21no—
430C2×D4—48no—
431C2×D4—72no—
432C2×D4—148no—
433C2×D4—142no—
434C2×D4—142no—
435C2×D4—141no—
436C2×D4—288no—
437C2×D4#115914yescomplemented
438C2×D4C2×C22⋊D714yes—
439C2×D4C23×D712yes—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—24no—
445C22×C4—28no—
446C22×C4—48no—
447C22×C4—44no—
448C22×C4—148no—
449C22×C4—141no—
450C22×C4—142no—
451C22×C4—144no—
452C22×C4—288no—
453C22×C4—284no—
454C22×C4C2×C22⋊D714yes—
455C22×C4C2×C22⋊D711yescharacteristic
456C22×C4C2×C22⋊D712yes—
457C22×C4C2×C22⋊D711yescharacteristic
458C22×C4C23×D714yes—
459C22×C4C23×D711yescharacteristic
460SD16—288no—
461D8—148no—
462M16—288no—
463C2×C8—72no—
464C2×C8—72no—
465C2×C8—74no—
466C2×C8—142no—
467C2×C8—142no—
468C2×C8—144no—
469C4⋊C4—24no—
470C4⋊C4—28no—
471C4⋊C4—24no—
472C4⋊C4—21no—
473C4⋊C4—72no—
474C4⋊C4—74no—
475C4⋊C4—141no—
476C4⋊C4—142no—
477C4⋊C4—148no—
478C4⋊C4—144no—
479C4⋊C4C2×C22⋊D714yes—
480C4⋊C4C23×D712yes—
481C22⋊C4—28no—
482C22⋊C4—24no—
483C22⋊C4—144no—
484C22⋊C4—148no—
485C22⋊C4C2×C22⋊D718yes—
486C42C2×C22⋊D712yes—
487C42C23×D712yes—
488C2×C7—44no—
489C2×C7—44no—
490C2×C7#333014yescomplemented
491C2×C7C2×#54611yescharacteristic
492C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
493C2×C7C2×#57811yescharacteristic
494D7—82no—
495C23—24no—
496C23—24no—
497C23—24no—
498C23—24no—
499C23—22no—
500C23—42no—
501C23—42no—
502C23—142no—
503C23—282no—
504C23—282no—
505C23—282no—
506C23C22×C22⋊D714yes—
507C23C22×C22⋊D711yescharacteristic
508Q8—24no—
509Q8—24no—
510Q8—44no—
511Q8—288no—
512D4—24no—
513D4—28no—
514D4—22no—
515D4—416no—
516D4—142no—
517D4—142no—
518D4—2816no—
519D4—282no—
520D4C2×#115914yescomplemented
521C2×C4—24no—
522C2×C4—22no—
523C2×C4—28no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—416no—
529C2×C4—44no—
530C2×C4—42no—
531C2×C4—48no—
532C2×C4—142no—
533C2×C4—144no—
534C2×C4—2816no—
535C2×C4—282no—
536C2×C4—284no—
537C2×C4—288no—
538C2×C4#651214yes—
539C2×C4C2×#115912yes—
540C2×C4#654812yes—
541C2×C4C22×C22⋊D712yes—
542C2×C4C22×C22⋊D714yes—
543C2×C4C22×C22⋊D711yescharacteristic
544C2×C4C22×C22⋊D712yes—
545C2×C4C24×D711yescharacteristic
546C8—142no—
547C8—142no—
548C8—144no—
549C7C2×#333011yescharacteristic, complemented, Sylow
550C22—24no—
551C22—24no—
552C22—24no—
553C22—24no—
554C22—48no—
555C22—48no—
556C22—42no—
557C22—42no—
558C22—282no—
559C22—282no—
560C22—282no—
561C22—564no—
562C22#9049712yes—
563C22C2×#651212yes—
564C22#9052912yes—
565C22C23×C22⋊D711yescharacteristic
566C4—24no—
567C4—22no—
568C4—44no—
569C4—42no—
570C4—282no—
571C4—284no—
572C4#9049712yes—
573C4C2×#651214yes—
574C4C22×#115911yescharacteristic
575C4C2×#654811yescharacteristic
576C2—44no—
577C2—44no—
578C2—562no—
579C2#1174095914yesdirect product factor
580C2C2×#9049711yescharacteristic
581C2C22×#651211yescharacteristic
582C2C2×#9052911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#547C2
socleC23×C7C22×D4
hypercenterC2×#547D7
hypocenterC7C2×#3330
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×C7×#547C2semidirect
2. C2×#90246C2semidirect
3. C2×#90010C2semidirect
4. C2×#90004C2semidirect
5. #11740959C2direct (N × H)
6. C2×#89855C2semidirect
7. C2×#89853C2semidirect
8. C2×#89821C2semidirect
9. C2×#89816C2semidirect
10. C2×#89784C2semidirect
11. C2×#89779C2semidirect
12. C2×C4×#1141C2semidirect
16. C7×#547C22semidirect
30. #90246C22semidirect
35. #90010C22semidirect
36. #90004C22semidirect
43. #89855C22semidirect
44. #89853C22semidirect
45. #89821C22semidirect
46. #89816C22semidirect
47. C4×#1141C22semidirect
48. #89784C22semidirect
49. #89779C22semidirect
131. C2×#547D7semidirect
158. C2×C7×D4#41semidirect
225. #547C2×D7semidirect
279. C7×D4C2×#41semidirect
437. C2×D4#1159semidirect
490. C2×C7#3330semidirect
520. D4C2×#1159semidirect
549. C7C2×#3330semidirect
579. C2#11740959direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5472
C2×#902462
C2×#900102
C2×#900042
#117409592
C2×#898552
C2×#898532
C2×#898212
C2×#898162
C2×#897842
C2×#897792
C2×C4×#11412
C2×#33307