Finite Group Databasebeta

← C2×#11726065 #13320922

Subgroups — C2×#11726065 #13320922

Order 1792.

1206 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90315C211yesmaximal, characteristic
2C2×#89491C211yesmaximal, characteristic, complemented
3C2×#89421C211yesmaximal, characteristic, complemented
4C2×C7×#328C211yesmaximal, characteristic, complemented
5C2×#89333C211yesmaximal, characteristic, complemented
6C2×#89265C211yesmaximal, characteristic
7C2×#89246C211yesmaximal, characteristic
8#11726065C218yesmaximal, direct product factor
9C2×C7×C22⋊Q8C2211yescharacteristic
10C2×#6510C411yescharacteristic, complemented
11C2×Q8×Dic7C411yescharacteristic, complemented
12C2×#6493C2211yescharacteristic
13C22×Dic7⋊C4—21no—
14C22×C4×Dic7—21no—
15C22×C4×Dic7C2211yescharacteristic
16#90315—22no—
17#90315—22no—
18#90315C414yescomplemented
19#90315C2214yes—
20C2×#6461—21no—
21C2×#6456C411yescharacteristic, complemented
22C2×#6455—21no—
23C2×#6453C411yescharacteristic, complemented
24C2×#6449—21no—
25C2×(C22⋊D7)⋊C4—21no—
26C2×C7×C22⋊C8C2211yescharacteristic
27C2×C7×#95C2211yescharacteristic
28C2×C7⋊#95C2211yescharacteristic
29C2×C22⋊(C7⋊C8)C2211yescharacteristic
30C2×#6389—21no—
31C2×Dic7⋊C8—21no—
32#89491—22no—
33#89491C2214yescomplemented
34#89421—22no—
35#89421C2214yescomplemented
36C7×#328C2214yescomplemented
37#89333C2214yescomplemented
38#89265C2214yes—
39#89246C2214yes—
40C2×#1509—71nomaximal, Sylow
41C22×C7×Q8C2×C411yescharacteristic
42C23×C4×C7—21no—
43C23×C4×C7C2311yescharacteristic
44C22×C22⋊D7—21no—
45C23×Dic7—21no—
46C23×Dic7D411yescharacteristic
47C23×Dic7D411yescharacteristic
48C22×D28C2×C411yescharacteristic
49C22×C4×D7—21no—
50C22×C7×C8—21no—
51C7×C22⋊Q8—21no—
52C7×C22⋊Q8—21no—
53C7×C22⋊Q8C2×C412yes—
54C7×C22⋊Q8C2312yes—
55C2×C7×C4⋊C4—21no—
56C2×C7×C4⋊C4C2×C411yescharacteristic
57C2×C7×C22⋊C4—21no—
58#6510—22no—
59#6510C2×C414yescomplemented
60Q8×Dic7—22no—
61Q8×Dic7C2×C414yescomplemented
62#6493—21no—
63#6493—21no—
64#6493C2×C412yes—
65#6493C2312yes—
66C2×(C2×D7)⋊C4—21no—
67C2×(C2×D7)⋊C4—21no—
68C2×(C2×D7)⋊C4—21no—
69C2×(C2×D7)⋊C4—21no—
70C2×C4⋊Dic7—21no—
71C2×C4⋊Dic7—21no—
72C2×C4⋊Dic7C2×C411yescharacteristic
73C2×Dic7⋊C4—28no—
74C2×Dic7⋊C4—21no—
75C2×Dic7⋊C4—24no—
76C2×C4×Dic7—21no—
77C2×C4×Dic7—24no—
78C2×C4×Dic7—44no—
79C2×C4×Dic7C2×C411yescharacteristic
80C2×C4×Dic7C2×C411yescharacteristic
81C2×C4×Dic7C2×C412yes—
82C2×C4×Dic7D412yes—
83C2×C4×Dic7D411yescharacteristic
84C2×C4×Dic7D411yescharacteristic
85C2×C4×Dic7D412yes—
86C2×C4×Dic7C2312yes—
87C22×C7⋊C8—21no—
88#6461—24no—
89#6461—24no—
90#6456—22no—
91#6456C2×C414yescomplemented
92#6455—24no—
93#6455—24no—
94#6453—22no—
95#6453C2×C414yescomplemented
96#6449—24no—
97#6449—24no—
98(C22⋊D7)⋊C4—24no—
99(C22⋊D7)⋊C4—24no—
100C7×C22⋊C8—21no—
101C7×C22⋊C8C2312yes—
102C7×#95—21no—
103C7×#95C2312yes—
104C7⋊#95—21no—
105C7⋊#95C2312yes—
106C22⋊(C7⋊C8)—21no—
107C22⋊(C7⋊C8)C2312yes—
108#6389—24no—
109Dic7⋊C8—24no—
110C2×#529—71no—
111C2×#432—71no—
112C2×C4×C4⋊C4—71no—
113#1509—78no—
114C2×#328—71no—
115C2×#328D711yescharacteristic, complemented
116C2×#327—71no—
117C2×#327—71no—
118C24×C7C2×D411yescharacteristic
119C23×D7—21no—
120C2×C7×Q8—21no—
121C2×C7×Q8—42no—
122C2×C7×Q8C22×C412yes—
123C22×C4×C7—24no—
124C22×C4×C7—21no—
125C22×C4×C7—21no—
126C22×C4×C7—22no—
127C22×C4×C7—42no—
128C22×C4×C7—42no—
129C22×C4×C7—42no—
130C22×C4×C7C22×C411yescharacteristic
131C22×C4×C7C22×C411yescharacteristic
132C22×C4×C7C2×D411yescharacteristic
133C22×C4×C7C2×D411yescharacteristic
134C22×C4×C7C2×D411yescharacteristic
135C22×C4×C7C2411yescharacteristic
136C2×C22⋊D7—22no—
137C2×C22⋊D7—22no—
138C2×C22⋊D7—42no—
139C2×C22⋊D7—42no—
140C22×Dic7—22no—
141C22×Dic7—22no—
142C22×Dic7—24no—
143C22×Dic7—24no—
144C22×Dic7—21no—
145C22×Dic7—22no—
146C22×Dic7—42no—
147C22×Dic7—42no—
148C22×Dic7C22⋊C412yes—
149C22×Dic7C22⋊C412yes—
150C22×Dic7C22⋊C411yescharacteristic
151C22×Dic7C22⋊C411yescharacteristic
152C22×Dic7C22⋊C411yescharacteristic
153C22×Dic7C22⋊C411yescharacteristic
154C22×Dic7C2×D412yes—
155C22×Dic7C2×D412yes—
156C2×D28—21no—
157C2×D28—42no—
158C2×D28C22×C412yes—
159C2×C4×D7—24no—
160C2×C4×D7—44no—
161C2×C7×C8—22no—
162C2×C7×C8—42no—
163C7×C4⋊C4—21no—
164C7×C4⋊C4—22no—
165C7×C4⋊C4—22no—
166C7×C4⋊C4C22×C412yes—
167C7×C22⋊C4—22no—
168C7×C22⋊C4—22no—
169(C2×D7)⋊C4—22no—
170(C2×D7)⋊C4—22no—
171(C2×D7)⋊C4—24no—
172(C2×D7)⋊C4—24no—
173(C2×D7)⋊C4—24no—
174C4⋊Dic7—21no—
175C4⋊Dic7—24no—
176C4⋊Dic7—24no—
177C4⋊Dic7C22×C412yes—
178Dic7⋊C4—216no—
179Dic7⋊C4—24no—
180C4×Dic7—24no—
181C4×Dic7—48no—
182C4×Dic7C22⋊C412yes—
183C4×Dic7C22⋊C412yes—
184C4×Dic7C22⋊C412yes—
185C4×Dic7C22⋊C412yes—
186C4×Dic7C22×C412yes—
187C4×Dic7C22×C412yes—
188C4×Dic7C2×D412yes—
189C4×Dic7C2×D412yes—
190C2×C7⋊C8—22no—
191C2×C7⋊C8—42no—
192#529—74no—
193#529—74no—
194#529—142no—
195#529—142no—
196C2×#126—141no—
197C2×#125—71no—
198C2×#124—71no—
199C2×#123—141no—
200C2×C22⋊Q8C2×D711yescharacteristic
201C2×#121—71no—
202C2×C4×Q8—71no—
203C2×C4×D4—71no—
204C2×C4×D4—141no—
205C2×#117—141no—
206C22×C4⋊C4—141no—
207C22×C42—71no—
208C22×C42—141no—
209#432—74no—
210#432—142no—
211C2×C4⋊C8—141no—
212C2×C22⋊C8—71no—
213C2×C22⋊C8C2×D711yescharacteristic
214C2×#97—141no—
215C4×C4⋊C4—74no—
216C4×C4⋊C4—142no—
217C2×#95—71no—
218C2×#95C2×D711yescharacteristic
219#328—74no—
220#328C2×D714yescomplemented
221#327—74no—
222#327—74no—
223C23×C7—22no—
224C23×C7—22no—
225C23×C7C2×C22⋊C411yescharacteristic
226C23×C7C2×C22⋊C411yescharacteristic
227C23×C7AGL(1,ℤ/8)12yes—
228C23×C7#13712yes—
229C23×C7C22×D411yescharacteristic
230C22×D7—22no—
231C22×D7—42no—
232C22×D7—42no—
233C22×D7—42no—
234C7×Q8—42no—
235C7×Q8—42no—
236C2×C4×C7—22no—
237C2×C4×C7—22no—
238C2×C4×C7—24no—
239C2×C4×C7—22no—
240C2×C4×C7—22no—
241C2×C4×C7—41no—
242C2×C4×C7—41no—
243C2×C4×C7—41no—
244C2×C4×C7—41no—
245C2×C4×C7—42no—
246C2×C4×C7—48no—
247C2×C4×C7—42no—
248C2×C4×C7—42no—
249C2×C4×C7—42no—
250C2×C4×C7C2×C22⋊C411yescharacteristic
251C2×C4×C7C2×C22⋊C411yescharacteristic
252C2×C4×C7C23×C411yescharacteristic
253C2×C4×C7C22×D411yescharacteristic
254C22⋊D7—42no—
255C22⋊D7—42no—
256C22⋊D7—44no—
257C2×Dic7—22no—
258C2×Dic7—22no—
259C2×Dic7—24no—
260C2×Dic7—22no—
261C2×Dic7—22no—
262C2×Dic7—22no—
263C2×Dic7—24no—
264C2×Dic7—24no—
265C2×Dic7—24no—
266C2×Dic7—22no—
267C2×Dic7—42no—
268C2×Dic7—48no—
269C2×Dic7—42no—
270C2×Dic7—42no—
271C2×Dic7#10414yes—
272C2×Dic7C2×C22⋊C412yes—
273C2×Dic7C2×C22⋊C412yes—
274C2×Dic7C2×C22⋊C412yes—
275C2×Dic7C2×C22⋊C412yes—
276D28—42no—
277D28—42no—
278C4×D7—48no—
279C7×C8—42no—
280C7⋊C8—42no—
281C22×Q8C4×D711yescharacteristic
282C22×D4—71no—
283C22×D4—141no—
284C23×C4—21no—
285C23×C4—71no—
286C23×C4—71no—
287C23×C4—141no—
288C23×C4—141no—
289C23×C4C22×D711yescharacteristic
290C22×C8—21no—
291C22×C8—141no—
292#126—144no—
293#126—144no—
294#125—74no—
295#125—142no—
296#124—74no—
297#124—142no—
298#123—144no—
299#123—144no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8C4×D712yes—
303C22⋊Q8C22×D712yes—
304#121—72no—
305#121—72no—
306#121—141no—
307#121—141no—
308C4×Q8—74no—
309C4×Q8—142no—
310C4×D4—74no—
311C4×D4—142no—
312C4×D4—144no—
313C4×D4—144no—
314#117—144no—
315#117—144no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—71no—
318C2×C4⋊C4—144no—
319C2×C4⋊C4—141no—
320C2×C4⋊C4—141no—
321C2×C4⋊C4—141no—
322C2×C4⋊C4—148no—
323C2×C4⋊C4C4×D711yescharacteristic
324C2×C22⋊C4—21no—
325C2×C22⋊C4—141no—
326C2×C22⋊C4—141no—
327C2×C22⋊C4—141no—
328C2×C22⋊C4—141no—
329C2×C42—71no—
330C2×C42—71no—
331C2×C42—72no—
332C2×C42—71no—
333C2×C42—71no—
334C2×C42—72no—
335C2×C42—72no—
336C2×C42—72no—
337C2×C42—141no—
338C2×C42—144no—
339C2×C42—284no—
340C4⋊C8—144no—
341C22⋊C8—21no—
342C22⋊C8—72no—
343C22⋊C8—141no—
344C22⋊C8C22×D712yes—
345#97—144no—
346#95—21no—
347#95—72no—
348#95—141no—
349#95C22×D712yes—
350C22×C7—21no—
351C22×C7—21no—
352C22×C7—21no—
353C22×C7—21no—
354C22×C7—24no—
355C22×C7—24no—
356C22×C7#41012yes—
357C22×C7#41712yes—
358C22×C7#41712yes—
359C22×C7C2×#10412yes—
360C22×C7C22×C22⋊C411yescharacteristic
361C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
362C22×C7C2×#13711yescharacteristic
363C2×D7—42no—
364C2×D7—42no—
365C2×D7—42no—
366C2×D7—84no—
367C4×C7—21no—
368C4×C7—21no—
369C4×C7—21no—
370C4×C7—21no—
371C4×C7—44no—
372C4×C7—42no—
373C4×C7—42no—
374Dic7—22no—
375Dic7—22no—
376Dic7—22no—
377Dic7—44no—
378Dic7—42no—
379Dic7C2×#10414yes—
380C24—141no—
381C24D4×D711yescharacteristic
382C2×Q8—21no—
383C2×Q8—42no—
384C2×Q8C2×C4×D712yes—
385C2×D4—72no—
386C2×D4—142no—
387C2×D4—142no—
388C2×D4—141no—
389C2×D4—282no—
390C2×D4—282no—
391C2×D4—282no—
392C22×C4—24no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—71no—
400C22×C4—72no—
401C22×C4—72no—
402C22×C4—71no—
403C22×C4—71no—
404C22×C4—71no—
405C22×C4—72no—
406C22×C4—72no—
407C22×C4—144no—
408C22×C4—144no—
409C22×C4—142no—
410C22×C4—142no—
411C22×C4—144no—
412C22×C4—141no—
413C22×C4—142no—
414C22×C4—284no—
415C22×C4—282no—
416C22×C4—282no—
417C22×C4C2×C4×D711yescharacteristic
418C22×C4C2×C4×D711yescharacteristic
419C22×C4D4×D711yescharacteristic
420C22×C4D4×D711yescharacteristic
421C22×C4D4×D711yescharacteristic
422C22×C4C23×D711yescharacteristic
423C2×C8—22no—
424C2×C8—42no—
425C2×C8—142no—
426C2×C8—282no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—72no—
431C4⋊C4—144no—
432C4⋊C4—144no—
433C4⋊C4—144no—
434C4⋊C4—1416no—
435C4⋊C4—141no—
436C4⋊C4C2×C4×D712yes—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—144no—
440C22⋊C4—144no—
441C22⋊C4—144no—
442C22⋊C4—142no—
443C22⋊C4—142no—
444C42—72no—
445C42—72no—
446C42—72no—
447C42—72no—
448C42—72no—
449C42—72no—
450C42—72no—
451C42—72no—
452C42—144no—
453C42—288no—
454C2×C7—21no—
455C2×C7—21no—
456C2×C7—22no—
457C2×C7#150914yescomplemented
458C2×C7C2×#41011yescharacteristic
459C2×C7C2×#41711yescharacteristic
460C2×C7C22×#10411yescharacteristic
461D7—82no—
462C23—22no—
463C23—22no—
464C23—142no—
465C23—282no—
466C23—282no—
467C23—282no—
468C23D7×C22⋊C411yescharacteristic
469C23D7×C22⋊C411yescharacteristic
470C23#647712yes—
471C23#648112yes—
472C23C2×D4×D711yescharacteristic
473Q8—42no—
474Q8—42no—
475D4—282no—
476D4—282no—
477D4—282no—
478D4—282no—
479D4—284no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—48no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—72no—
495C2×C4—74no—
496C2×C4—72no—
497C2×C4—72no—
498C2×C4—72no—
499C2×C4—144no—
500C2×C4—144no—
501C2×C4—142no—
502C2×C4—142no—
503C2×C4—144no—
504C2×C4—142no—
505C2×C4—142no—
506C2×C4—142no—
507C2×C4—144no—
508C2×C4—142no—
509C2×C4—288no—
510C2×C4—282no—
511C2×C4—288no—
512C2×C4—282no—
513C2×C4—282no—
514C2×C4D7×C22⋊C411yescharacteristic
515C2×C4D7×C22⋊C411yescharacteristic
516C2×C4C22×C4×D711yescharacteristic
517C2×C4C2×D4×D711yescharacteristic
518C8—42no—
519C8—282no—
520C7C2×#150911yescharacteristic, complemented, Sylow
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—24no—
526C22—24no—
527C22—282no—
528C22—282no—
529C22—282no—
530C22—564no—
531C22#8951212yes—
532C22#8957512yes—
533C22#8957512yes—
534C22D7×#10412yes—
535C22C2×D7×C22⋊C411yescharacteristic
536C22C2×#647711yescharacteristic
537C22C2×#648111yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—44no—
543C4—42no—
544C4—42no—
545C4—74no—
546C4—142no—
547C4—142no—
548C4—142no—
549C4—284no—
550C4—282no—
551C2—21no—
552C2—21no—
553C2—22no—
554C2—562no—
555C2#1172606514yesdirect product factor
556C2C2×#8951211yescharacteristic
557C2C2×#8957511yescharacteristic
558C2C2×D7×#10411yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#328C2
socleC23×C7C2×C22⋊C4
prime radicalC2×#6493C22
cosocleC22×C4×C7C24
hypercenterC2×#328D7
hypocenterC7C2×#1509
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×#89491C2semidirect
3. C2×#89421C2semidirect
4. C2×C7×#328C2semidirect
5. C2×#89333C2semidirect
8. #11726065C2direct (N × H)
10. C2×#6510C4semidirect
11. C2×Q8×Dic7C4semidirect
18. #90315C4semidirect
21. C2×#6456C4semidirect
23. C2×#6453C4semidirect
33. #89491C22semidirect
35. #89421C22semidirect
36. C7×#328C22semidirect
37. #89333C22semidirect
59. #6510C2×C4semidirect
61. Q8×Dic7C2×C4semidirect
91. #6456C2×C4semidirect
95. #6453C2×C4semidirect
115. C2×#328D7semidirect
220. #328C2×D7semidirect
457. C2×C7#1509semidirect
520. C7C2×#1509semidirect
555. C2#11726065direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903152
C2×#894912
C2×#894212
C2×C7×#3282
C2×#893332
C2×#892652
C2×#892462
#117260652
C2×#15097