Finite Group Databasebeta

← C2×#11741009 #14234269

Subgroups — C2×#11741009 #14234269

Order 1792.

2082 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×D4×Q8C211yesmaximal, characteristic, complemented
2C2×#90270C211yesmaximal, characteristic, complemented
3#11741009C2116yesmaximal, direct product factor
4C2×#89856C212yesmaximal, complemented
5C2×#89859C211yesmaximal, characteristic, complemented
6C2×#89852C212yesmaximal, complemented
7C2×#89851C211yesmaximal, characteristic, complemented
8C2×#89796C211yesmaximal, characteristic, complemented
9C2×#89781C212yesmaximal, complemented
10C2×#89780C211yesmaximal, characteristic, complemented
11C2×#89786C212yesmaximal
12C2×C4×#1141C211yesmaximal, characteristic
13C23×C7×Q8—21no—
14C7×D4×Q8—24no—
15C7×D4×Q8C2218yescomplemented
16C2×C7×C4⋊Q8C2211yescharacteristic
17C2×C7×C4⋊Q8C2212yes—
18C2×C7×C22⋊Q8—21no—
19C2×C7×C22⋊Q8—22no—
20C2×C4×C7×Q8C2211yescharacteristic
21C2×C4×C7×D4C2211yescharacteristic
22C2×C4×C7×D4C2212yes—
23C2×#6509—21no—
24C22×#1141C2211yescharacteristic
25#90270—24no—
26#90270C2218yescomplemented
27C2×#6459—22no—
28C2×D7×C4⋊C4—21no—
29C2×C4×D28C2211yescharacteristic
30C2×C4×D28C2212yes—
31C2×#6433C2212yes—
32C2×#6432C2211yescharacteristic
33C2×#6406C2211yescharacteristic
34C2×#6406C2212yes—
35#89859C2218yescomplemented
36#89856C22116yescomplemented
37#89852C22116yescomplemented
38#89851C2218yescomplemented
39#89796C2218yescomplemented
40#89786C22116yes—
41C4×#1141C2218yes—
42#89781C22116yescomplemented
43#89780C2218yescomplemented
44C2×#6383C2211yescharacteristic
45C2×#6383C2212yes—
46C2×#6382C2212yes—
47C2×#6382C2212yes—
48C2×#6382C2212yes—
49C2×#6381C2211yescharacteristic
50C2×#6381C2212yes—
51C2×C4⋊(C7⋊C8)C2211yescharacteristic
52C2×C4⋊(C7⋊C8)C2212yes—
53C2×#6377C2212yes—
54C2×C4×C7⋊C8C2211yescharacteristic
55C2×#3384—71nomaximal, Sylow
56C22×C7×Q8—28no—
57C22×C7×Q8—22no—
58C22×C7×Q8—21no—
59C22×C7×Q8—48no—
60C22×C7×Q8D411yescharacteristic
61C22×C7×D4C2311yescharacteristic
62C23×C4×C7—22no—
63C23×C4×C7—21no—
64C22×D28C2311yescharacteristic
65C22×C4×D7—21no—
66C22×C4×D7—22no—
67C22×Dic14—21no—
68C7×C4⋊Q8—22no—
69C7×C4⋊Q8—24no—
70C7×C4⋊Q8C2318yes—
71C7×C4⋊Q8C2314yes—
72C7×C22⋊Q8—28no—
73C7×C22⋊Q8—216no—
74C4×C7×Q8D414yes—
75C4×C7×Q8C2314yes—
76C4×C7×D4—22no—
77C4×C7×D4—24no—
78C4×C7×D4C2314yes—
79C4×C7×D4C2318yes—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—21no—
82C2×C7×C4⋊C4D411yescharacteristic
83C2×C7×C4⋊C4D412yes—
84C2×C7×C4⋊C4C2311yescharacteristic
85C2×C7×C4⋊C4C2312yes—
86C2×C7×C22⋊C4—22no—
87C2×C7×C22⋊C4—21no—
88C2×C42×C7C2311yescharacteristic
89C2×C42×C7C2312yes—
90#6509—28no—
91C2×#1141Q818yescomplemented
92C2×#1141C2314yes—
93C2×(C2×D7)⋊C4—21no—
94C2×(C2×D7)⋊C4—22no—
95C2×C4⋊Dic7—21no—
96C2×C4⋊Dic7C2312yes—
97C2×C4⋊Dic7C2311yescharacteristic
98C2×Dic7⋊C4—22no—
99C2×Dic7⋊C4—22no—
100C22×C7⋊C8C2311yescharacteristic
101C22×C7⋊C8C2312yes—
102C22×C7⋊C8C2311yescharacteristic
103#6459—216no—
104D7×C4⋊C4—28no—
105C4×D28—24no—
106C4×D28—22no—
107C4×D28C2318yes—
108C4×D28C2314yes—
109#6433—24no—
110#6433C2318yes—
111#6432—22no—
112#6432C2314yes—
113#6406C2318yes—
114#6406C2314yes—
115#6383C2314yes—
116#6383C2318yes—
117#6382C2318yes—
118#6382C2318yes—
119#6382C2318yes—
120#6381C2318yes—
121#6381C2314yes—
122C4⋊(C7⋊C8)C2318yes—
123C4⋊(C7⋊C8)C2314yes—
124#6377C2318yes—
125C4×C7⋊C8C2314yes—
126C2×#554—71no—
127C2×D4×Q8D711yescharacteristic, complemented
128#3384—716no—
129C2×#501—72no—
130C2×#498—71no—
131C2×#478—72no—
132C2×#476—72no—
133C2×#476—71no—
134C2×#474—71no—
135C2×#446—71no—
136C2×#442—72no—
137C2×C4×D8—71no—
138C24×C7—21no—
139C23×D7—21no—
140C2×C7×Q8—24no—
141C2×C7×Q8—28no—
142C2×C7×Q8—24no—
143C2×C7×Q8—48no—
144C2×C7×Q8—432no—
145C2×C7×Q8—44no—
146C2×C7×Q8C2×D414yes—
147C2×C7×D4—21no—
148C2×C7×D4—22no—
149C2×C7×D4C2×Q814yes—
150C2×C7×D4C2412yes—
151C22×C4×C7—22no—
152C22×C4×C7—21no—
153C22×C4×C7—28no—
154C22×C4×C7—24no—
155C22×C4×C7—48no—
156C22×C4×C7—44no—
157C22×C4×C7C2×D412yes—
158C22×C4×C7C2×D412yes—
159C22×C4×C7C2×D411yescharacteristic
160C22×C4×C7C2×D411yescharacteristic
161C22×C4×C7C2411yescharacteristic
162C22×Dic7—21no—
163C22×Dic7—22no—
164C2×D28—21no—
165C2×D28—22no—
166C2×D28C2×Q814yescomplemented
167C2×D28C2412yes—
168C2×C4×D7—24no—
169C2×C4×D7—28no—
170C2×C4×D7—44no—
171C2×C4×D7—84no—
172C2×Dic14—24no—
173C2×Dic14—82no—
174C7×C4⋊C4—28no—
175C7×C4⋊C4—24no—
176C7×C4⋊C4—21no—
177C7×C4⋊C4—22no—
178C7×C4⋊C4C2×D414yes—
179C7×C4⋊C4C2×D418yes—
180C7×C4⋊C4C2412yes—
181C7×C4⋊C4C2414yes—
182C7×C22⋊C4—28no—
183C7×C22⋊C4—24no—
184C42×C7C2×D412yes—
185C42×C7C2×D414yes—
186C42×C7C2412yes—
187C42×C7C2414yes—
188#1141C2×Q8116yescomplemented
189(C2×D7)⋊C4—24no—
190(C2×D7)⋊C4—28no—
191C4⋊Dic7—22no—
192C4⋊Dic7—24no—
193C4⋊Dic7—21no—
194C4⋊Dic7C2414yes—
195C4⋊Dic7C2412yes—
196Dic7⋊C4—28no—
197Dic7⋊C4—28no—
198C2×C7⋊C8—22no—
199C2×C7⋊C8—24no—
200C2×C7⋊C8C2×Q814yescomplemented
201C2×C7⋊C8C2412yes—
202C2×C7⋊C8C2414yes—
203C2×C7⋊C8C2412yes—
204C23×Q8—21no—
205C22×D8—71no—
206#554—78no—
207#554—144no—
208D4×Q8—24no—
209D4×Q8C2×D718yescomplemented
210C2×C4⋊Q8—71no—
211C2×C4⋊Q8C2×D711yescharacteristic
212C2×C4⋊Q8C2×D712yes—
213C2×#125—72no—
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8—22no—
216C2×C22⋊Q8—141no—
217C2×C22⋊Q8—142no—
218C2×C4×Q8C2×D711yescharacteristic
219C2×C4×D4—71no—
220C2×C4×D4—72no—
221C2×C4×D4C2×D712yes—
222C2×C4×D4C2×D711yescharacteristic
223C22×C4⋊C4—141no—
224#501—716no—
225#498—78no—
226#478—716no—
227#476—716no—
228#476—78no—
229#474—78no—
230#446—78no—
231#442—716no—
232C4×D8—78no—
233C2×#107—72no—
234C2×#107—71no—
235C2×#106—72no—
236C2×#106—72no—
237C2×#106—72no—
238C2×C4⋊C8—72no—
239C2×C4⋊C8—71no—
240C2×#102—71no—
241C2×#102—72no—
242C2×#102—71no—
243C2×#102—72no—
244C2×#97—72no—
245C2×C4×C8—71no—
246C23×C7—24no—
247C23×C7—22no—
248C23×C7—42no—
249C23×C7—42no—
250C23×C7C22×D411yescharacteristic
251C22×D7—24no—
252C22×D7—22no—
253C22×D7—42no—
254C22×D7—42no—
255C7×Q8—28no—
256C7×Q8—416no—
257C7×Q8—48no—
258C7×D4—24no—
259C7×D4—22no—
260C7×D4C22×Q814yes—
261C2×C4×C7—24no—
262C2×C4×C7—22no—
263C2×C4×C7—24no—
264C2×C4×C7—24no—
265C2×C4×C7—22no—
266C2×C4×C7—416no—
267C2×C4×C7—44no—
268C2×C4×C7—42no—
269C2×C4×C7—48no—
270C2×C4×C7AGL(1,ℤ/8)14yes—
271C2×C4×C7C22×D414yes—
272C2×C4×C7C22×D414yes—
273C2×C4×C7C22×D412yes—
274C2×C4×C7C22×D411yescharacteristic
275C2×C4×C7C22×D412yes—
276C2×C4×C7C22×Q812yes—
277C2×C4×C72−1+412yes—
278C2×C4×C7C2511yescharacteristic
279C2×Dic7—22no—
280C2×Dic7—24no—
281C2×Dic7—42no—
282C2×Dic7—44no—
283D28—24no—
284D28—22no—
285D28C22×Q814yescomplemented
286C4×D7—48no—
287C4×D7—88no—
288Dic14—84no—
289C7⋊C8—22no—
290C7⋊C8—24no—
291C7⋊C8C22×Q814yescomplemented
292C22×Q8—28no—
293C22×Q8—22no—
294C22×Q8—21no—
295C22×Q8—48no—
296C22×Q8—141no—
297C22×Q8C22⋊D711yescharacteristic
298C22×D4—71no—
299C22×D4C22×D711yescharacteristic
300C23×C4—22no—
301C23×C4—21no—
302C23×C4—141no—
303C23×C4—142no—
304C2×D8—78no—
305C2×D8—74no—
306C22×C8—71no—
307C22×C8—71no—
308C22×C8—72no—
309C4⋊Q8—24no—
310C4⋊Q8—22no—
311C4⋊Q8—74no—
312C4⋊Q8—142no—
313C4⋊Q8C22×D714yes—
314C4⋊Q8C22×D718yes—
315#125—78no—
316#125—144no—
317C22⋊Q8—28no—
318C22⋊Q8—216no—
319C22⋊Q8—148no—
320C22⋊Q8—1416no—
321C4×Q8C22⋊D714yes—
322C4×Q8C22×D714yes—
323C4×D4—24no—
324C4×D4—22no—
325C4×D4—74no—
326C4×D4—78no—
327C4×D4—144no—
328C4×D4—142no—
329C4×D4C22×D714yes—
330C4×D4C22×D718yes—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—71no—
334C2×C4⋊C4—72no—
335C2×C4⋊C4—142no—
336C2×C4⋊C4—141no—
337C2×C4⋊C4—142no—
338C2×C4⋊C4—148no—
339C2×C4⋊C4C22⋊D711yescharacteristic
340C2×C4⋊C4C22⋊D712yes—
341C2×C4⋊C4C22×D712yes—
342C2×C4⋊C4C22×D711yescharacteristic
343C2×C22⋊C4—21no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—141no—
346C2×C22⋊C4—142no—
347C2×C42C22×D712yes—
348C2×C42C22×D711yescharacteristic
349#107—74no—
350#107—78no—
351#106—78no—
352#106—78no—
353#106—78no—
354C4⋊C8—74no—
355C4⋊C8—78no—
356#102—74no—
357#102—78no—
358#102—74no—
359#102—78no—
360#97—78no—
361C4×C8—74no—
362C22×C7—24no—
363C22×C7—48no—
364C22×C7—42no—
365C22×C7—42no—
366C22×C7D4×Q812yes—
367C22×C7C2×AGL(1,ℤ/8)12yes—
368C22×C7#57712yes—
369C22×C7C23×D411yescharacteristic
370C2×D7—24no—
371C2×D7—48no—
372C2×D7—42no—
373C2×D7—42no—
374C4×C7—24no—
375C4×C7—22no—
376C4×C7—24no—
377C4×C7—44no—
378C4×C7—42no—
379C4×C7D4×Q812yes—
380C4×C7C2×AGL(1,ℤ/8)14yes—
381C4×C7C23×Q811yescharacteristic
382C4×C7C2×2−1+411yescharacteristic
383Dic7—42no—
384Dic7—44no—
385C24—21no—
386C24—141no—
387C2×Q8—24no—
388C2×Q8—28no—
389C2×Q8—24no—
390C2×Q8—48no—
391C2×Q8—432no—
392C2×Q8—44no—
393C2×Q8—144no—
394C2×Q8—562no—
395C2×Q8C2×C22⋊D714yes—
396C2×D4—22no—
397C2×D4—21no—
398C2×D4—74no—
399C2×D4—72no—
400C2×D4—142no—
401C2×D4—141no—
402C2×D4Q8×D714yes—
403C2×D4C23×D712yes—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—28no—
407C22×C4—24no—
408C22×C4—48no—
409C22×C4—44no—
410C22×C4—141no—
411C22×C4—142no—
412C22×C4—144no—
413C22×C4—148no—
414C22×C4—284no—
415C22×C4—564no—
416C22×C4C2×C22⋊D711yescharacteristic
417C22×C4C2×C22⋊D712yes—
418C22×C4C2×C22⋊D712yes—
419C22×C4C2×C22⋊D711yescharacteristic
420C22×C4C23×D711yescharacteristic
421D8—716no—
422C2×C8—74no—
423C2×C8—72no—
424C2×C8—72no—
425C2×C8—74no—
426C2×C8—142no—
427C2×C8—144no—
428C4⋊C4—24no—
429C4⋊C4—28no—
430C4⋊C4—22no—
431C4⋊C4—21no—
432C4⋊C4—74no—
433C4⋊C4—72no—
434C4⋊C4—148no—
435C4⋊C4—148no—
436C4⋊C4—141no—
437C4⋊C4—142no—
438C4⋊C4—144no—
439C4⋊C4C2×C22⋊D714yes—
440C4⋊C4C2×C22⋊D718yes—
441C4⋊C4C23×D712yes—
442C4⋊C4C23×D714yes—
443C22⋊C4—24no—
444C22⋊C4—28no—
445C22⋊C4—144no—
446C22⋊C4—148no—
447C42C2×C22⋊D714yes—
448C42C2×C22⋊D712yes—
449C42C23×D712yes—
450C42C23×D714yes—
451C2×C7—44no—
452C2×C7#338414yescomplemented
453C2×C7C2×D4×Q811yescharacteristic
454C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
455C2×C7C2×#57711yescharacteristic
456D7—44no—
457C23—24no—
458C23—22no—
459C23—42no—
460C23—42no—
461C23—144no—
462C23—142no—
463C23—282no—
464C23—282no—
465C23C22×C22⋊D711yescharacteristic
466Q8—28no—
467Q8—416no—
468Q8—48no—
469Q8—564no—
470D4—24no—
471D4—22no—
472D4—74no—
473D4—144no—
474D4—142no—
475D4C2×Q8×D714yes—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—416no—
482C2×C4—44no—
483C2×C4—42no—
484C2×C4—48no—
485C2×C4—142no—
486C2×C4—144no—
487C2×C4—282no—
488C2×C4—284no—
489C2×C4—288no—
490C2×C4—568no—
491C2×C4#649514yes—
492C2×C4C2×Q8×D712yes—
493C2×C4#655112yes—
494C2×C4C22×C22⋊D712yes—
495C2×C4C22×C22⋊D714yes—
496C2×C4C22×C22⋊D714yes—
497C2×C4C22×C22⋊D712yes—
498C2×C4C22×C22⋊D711yescharacteristic
499C2×C4C24×D711yescharacteristic
500C8—74no—
501C8—142no—
502C8—144no—
503C7C2×#338411yescharacteristic, complemented, Sylow
504C22—24no—
505C22—42no—
506C22—48no—
507C22—42no—
508C22—144no—
509C22—282no—
510C22—288no—
511C22—282no—
512C22C2×#649512yes—
513C22Q8×C22⋊D712yes—
514C22#9052812yes—
515C22C23×C22⋊D711yescharacteristic
516C4—24no—
517C4—24no—
518C4—22no—
519C4—44no—
520C4—42no—
521C4—282no—
522C4—284no—
523C4C2×#649514yes—
524C4Q8×C22⋊D712yes—
525C4C22×Q8×D711yescharacteristic
526C4C2×#655111yescharacteristic
527C2—44no—
528C2—284no—
529C2#1174100914yesdirect product factor
530C2C22×#649511yescharacteristic
531C2C2×Q8×C22⋊D711yescharacteristic
532C2C2×#9052811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×D4×Q8C2
socleC23×C7C22×D4
prime radicalC22×#1141C22
hypercenterC2×D4×Q8D7
hypocenterC7C2×#3384
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C7×D4×Q8C2semidirect
2. C2×#90270C2semidirect
3. #11741009C2direct (N × H)
4. C2×#89856C2semidirect
5. C2×#89859C2semidirect
6. C2×#89852C2semidirect
7. C2×#89851C2semidirect
8. C2×#89796C2semidirect
9. C2×#89781C2semidirect
10. C2×#89780C2semidirect
15. C7×D4×Q8C22semidirect
26. #90270C22semidirect
35. #89859C22semidirect
36. #89856C22semidirect
37. #89852C22semidirect
38. #89851C22semidirect
39. #89796C22semidirect
42. #89781C22semidirect
43. #89780C22semidirect
91. C2×#1141Q8semidirect
127. C2×D4×Q8D7semidirect
166. C2×D28C2×Q8semidirect
188. #1141C2×Q8semidirect
200. C2×C7⋊C8C2×Q8semidirect
209. D4×Q8C2×D7semidirect
285. D28C22×Q8semidirect
291. C7⋊C8C22×Q8semidirect
452. C2×C7#3384semidirect
503. C7C2×#3384semidirect
529. C2#11741009direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×D4×Q82
C2×#902702
#117410092
C2×#898562
C2×#898592
C2×#898522
C2×#898512
C2×#897962
C2×#897812
C2×#897802
C2×#897862
C2×C4×#11412
C2×#33847