Finite Group Databasebeta

← C2×#11726063 #13320898

Subgroups — C2×#11726063 #13320898

Order 1792.

1194 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90313C211yesmaximal, characteristic
2C2×#89490C211yesmaximal, characteristic
3C2×#89421C211yesmaximal, characteristic
4C2×C7×#328C211yesmaximal, characteristic
5C2×#89333C211yesmaximal, characteristic
6C2×#89262C211yesmaximal, characteristic
7C2×#89247C211yesmaximal, characteristic
8#11726063C218yesmaximal, direct product factor
9C2×C7×C22⋊Q8C2211yescharacteristic
10C2×Q8×Dic7C411yescharacteristic, complemented
11C2×#6507C411yescharacteristic, complemented
12C2×#6487C2211yescharacteristic
13C22×Dic7⋊C4—21no—
14C22×C4×Dic7—21no—
15C22×C4×Dic7C2211yescharacteristic
16#90313—22no—
17#90313—22no—
18#90313C414yescomplemented
19#90313C2214yes—
20C2×#6452—21no—
21C2×#6451C411yescharacteristic, complemented
22C2×#6450—21no—
23C2×#6450C411yescharacteristic, complemented
24C2×#6441—21no—
25C2×#6440—21no—
26C2×C7×C22⋊C8C2211yescharacteristic
27C2×C7×#95C2211yescharacteristic
28C2×C7⋊#95C2211yescharacteristic
29C2×C22⋊(C7⋊C8)C2211yescharacteristic
30C2×Dic7⋊C8—21no—
31C2×C8×Dic7—21no—
32#89490—22no—
33#89490C2214yes—
34#89421—22no—
35#89421C2214yes—
36C7×#328C2214yes—
37#89333C2214yes—
38#89262C2214yes—
39#89247C2214yes—
40C2×#1503—71nomaximal, Sylow
41C22×C7×Q8C2×C411yescharacteristic
42C23×C4×C7—21no—
43C23×C4×C7C2311yescharacteristic
44C23×Dic7—21no—
45C23×Dic7D411yescharacteristic
46C23×Dic7D411yescharacteristic
47C22×Dic14—21no—
48C22×Dic14C2×C411yescharacteristic
49C22×C7×C8—21no—
50C7×C22⋊Q8—21no—
51C7×C22⋊Q8—21no—
52C7×C22⋊Q8C2×C412yes—
53C7×C22⋊Q8C2312yes—
54C2×C7×C4⋊C4—21no—
55C2×C7×C4⋊C4C2×C411yescharacteristic
56C2×C7×C22⋊C4—21no—
57C2×C22⋊Dic7—21no—
58Q8×Dic7—22no—
59Q8×Dic7C2×C414yescomplemented
60#6507—22no—
61#6507C2×C414yescomplemented
62C2×C4⋊Dic7—21no—
63C2×C4⋊Dic7C2×C411yescharacteristic
64#6487—21no—
65#6487—21no—
66#6487C2×C412yes—
67#6487C2312yes—
68C2×Dic7⋊C4—28no—
69C2×Dic7⋊C4—21no—
70C2×Dic7⋊C4—21no—
71C2×Dic7⋊C4—21no—
72C2×Dic7⋊C4—21no—
73C2×Dic7⋊C4—21no—
74C2×Dic7⋊C4—24no—
75C2×C4×Dic7—21no—
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#6452—24no—
89#6452—24no—
90#6451—22no—
91#6451C2×C414yescomplemented
92#6450—24no—
93#6450—22no—
94#6450—24no—
95#6450C2×C414yescomplemented
96#6441—24no—
97#6441—24no—
98#6440—24no—
99#6440—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—
108Dic7⋊C8—24no—
109C8×Dic7—24no—
110C2×#533—71no—
111C2×#431—71no—
112C2×C4×C4⋊C4—71no—
113#1503—78no—
114C2×#328—71no—
115C2×#328—71no—
116C2×#328—71no—
117C2×#328D711yescharacteristic
118C24×C7C2×D411yescharacteristic
119C2×C7×Q8—21no—
120C2×C7×Q8—42no—
121C2×C7×Q8C22×C412yes—
122C22×C4×C7—24no—
123C22×C4×C7—21no—
124C22×C4×C7—21no—
125C22×C4×C7—22no—
126C22×C4×C7—42no—
127C22×C4×C7—42no—
128C22×C4×C7—42no—
129C22×C4×C7C22×C411yescharacteristic
130C22×C4×C7C22×C411yescharacteristic
131C22×C4×C7C2×D411yescharacteristic
132C22×C4×C7C2×D411yescharacteristic
133C22×C4×C7C2×D411yescharacteristic
134C22×C4×C7C2411yescharacteristic
135C22×Dic7—24no—
136C22×Dic7—24no—
137C22×Dic7—21no—
138C22×Dic7—21no—
139C22×Dic7—22no—
140C22×Dic7—42no—
141C22×Dic7—42no—
142C22×Dic7C22⋊C412yes—
143C22×Dic7C22⋊C411yescharacteristic
144C22×Dic7C22⋊C412yes—
145C22×Dic7C22⋊C411yescharacteristic
146C22×Dic7C22⋊C411yescharacteristic
147C22×Dic7C22⋊C411yescharacteristic
148C22×Dic7SD1614yes—
149C22×Dic7Q1614yes—
150C22×Dic7C2×D412yes—
151C22×Dic7C2×D412yes—
152C2×Dic14—21no—
153C2×Dic14—24no—
154C2×Dic14—44no—
155C2×Dic14—42no—
156C2×Dic14C22×C412yes—
157C2×C7×C8—22no—
158C2×C7×C8—42no—
159C7×C4⋊C4—21no—
160C7×C4⋊C4—22no—
161C7×C4⋊C4—22no—
162C7×C4⋊C4C22×C412yes—
163C7×C22⋊C4—22no—
164C7×C22⋊C4—22no—
165C22⋊Dic7—22no—
166C22⋊Dic7—22no—
167C4⋊Dic7—21no—
168C4⋊Dic7—24no—
169C4⋊Dic7C22×C412yes—
170Dic7⋊C4—216no—
171Dic7⋊C4—22no—
172Dic7⋊C4—22no—
173Dic7⋊C4—24no—
174Dic7⋊C4—24no—
175Dic7⋊C4—24no—
176Dic7⋊C4—24no—
177C4×Dic7—24no—
178C4×Dic7—24no—
179C4×Dic7—48no—
180C4×Dic7C22⋊C412yes—
181C4×Dic7C22⋊C412yes—
182C4×Dic7C22⋊C412yes—
183C4×Dic7C22⋊C412yes—
184C4×Dic7C22×C412yes—
185C4×Dic7C22×C412yes—
186C4×Dic7C2×D412yes—
187C4×Dic7C2×D412yes—
188C2×C7⋊C8—22no—
189C2×C7⋊C8—42no—
190#533—74no—
191#533—74no—
192#533—142no—
193#533—142no—
194C2×C4⋊Q8—71no—
195C2×C4⋊Q8—71no—
196C2×#125—141no—
197C2×C22⋊Q8—71no—
198C2×C22⋊Q8—141no—
199C2×C22⋊Q8C2×D711yescharacteristic
200C2×C4×Q8—71no—
201C2×C4×Q8—71no—
202C2×C4×Q8—141no—
203C2×#117—141no—
204C22×C4⋊C4—141no—
205C22×C42—71no—
206C22×C42—141no—
207#431—74no—
208#431—142no—
209C2×C4⋊C8—141no—
210C2×C22⋊C8—71no—
211C2×C22⋊C8C2×D711yescharacteristic
212C2×C4×C8—141no—
213C4×C4⋊C4—74no—
214C4×C4⋊C4—142no—
215C2×#95—71no—
216C2×#95C2×D711yescharacteristic
217#328—74no—
218#328—74no—
219#328—74no—
220#328C2×D714yes—
221C23×C7—22no—
222C23×C7—22no—
223C23×C7C2×C22⋊C411yescharacteristic
224C23×C7C2×C22⋊C411yescharacteristic
225C23×C7C2×SD1612yes—
226C23×C7C2×Q1612yes—
227C23×C7C22×D411yescharacteristic
228C7×Q8—42no—
229C7×Q8—42no—
230C2×C4×C7—22no—
231C2×C4×C7—22no—
232C2×C4×C7—24no—
233C2×C4×C7—22no—
234C2×C4×C7—22no—
235C2×C4×C7—41no—
236C2×C4×C7—41no—
237C2×C4×C7—41no—
238C2×C4×C7—41no—
239C2×C4×C7—42no—
240C2×C4×C7—48no—
241C2×C4×C7—42no—
242C2×C4×C7—42no—
243C2×C4×C7—42no—
244C2×C4×C7C2×C22⋊C411yescharacteristic
245C2×C4×C7C2×C22⋊C411yescharacteristic
246C2×C4×C7C23×C411yescharacteristic
247C2×C4×C7C22×D411yescharacteristic
248C2×Dic7—22no—
249C2×Dic7—24no—
250C2×Dic7—24no—
251C2×Dic7—24no—
252C2×Dic7—22no—
253C2×Dic7—22no—
254C2×Dic7—42no—
255C2×Dic7—48no—
256C2×Dic7—42no—
257C2×Dic7—42no—
258C2×Dic7—42no—
259C2×Dic7#10318yes—
260C2×Dic7#10314yes—
261C2×Dic7#10314yes—
262C2×Dic7#10414yes—
263C2×Dic7C2×C22⋊C412yes—
264C2×Dic7C2×C22⋊C412yes—
265C2×Dic7C2×C22⋊C412yes—
266C2×Dic7C2×C22⋊C412yes—
267C2×Dic7C2×SD1614yes—
268C2×Dic7C2×Q1614yes—
269Dic14—42no—
270Dic14—48no—
271Dic14—42no—
272C7×C8—42no—
273C7⋊C8—42no—
274C22×Q8—71no—
275C22×Q8—141no—
276C22×Q8C4×D711yescharacteristic
277C23×C4—21no—
278C23×C4—71no—
279C23×C4—71no—
280C23×C4—141no—
281C23×C4C22×D711yescharacteristic
282C22×C8—21no—
283C22×C8—141no—
284C4⋊Q8—74no—
285C4⋊Q8—74no—
286C4⋊Q8—142no—
287C4⋊Q8—142no—
288#125—144no—
289#125—144no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C22⋊Q8—72no—
293C22⋊Q8—72no—
294C22⋊Q8—144no—
295C22⋊Q8—144no—
296C22⋊Q8—141no—
297C22⋊Q8—141no—
298C22⋊Q8C4×D712yes—
299C22⋊Q8C22×D712yes—
300C4×Q8—74no—
301C4×Q8—74no—
302C4×Q8—142no—
303C4×Q8—144no—
304C4×Q8—144no—
305C4×Q8—142no—
306#117—144no—
307#117—144no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—71no—
310C2×C4⋊C4—144no—
311C2×C4⋊C4—141no—
312C2×C4⋊C4—141no—
313C2×C4⋊C4—141no—
314C2×C4⋊C4—141no—
315C2×C4⋊C4—141no—
316C2×C4⋊C4—148no—
317C2×C4⋊C4—141no—
318C2×C4⋊C4C4×D711yescharacteristic
319C2×C22⋊C4—21no—
320C2×C22⋊C4—141no—
321C2×C42—71no—
322C2×C42—71no—
323C2×C42—72no—
324C2×C42—71no—
325C2×C42—71no—
326C2×C42—72no—
327C2×C42—72no—
328C2×C42—72no—
329C2×C42—141no—
330C2×C42—141no—
331C2×C42—144no—
332C2×C42—284no—
333C4⋊C8—144no—
334C22⋊C8—21no—
335C22⋊C8—72no—
336C22⋊C8—141no—
337C22⋊C8C22×D712yes—
338C4×C8—144no—
339#95—21no—
340#95—72no—
341#95—141no—
342#95C22×D712yes—
343C22×C7—21no—
344C22×C7—21no—
345C22×C7—21no—
346C22×C7—21no—
347C22×C7—24no—
348C22×C7—24no—
349C22×C7#41012yes—
350C22×C7C2×#10312yes—
351C22×C7C2×#10312yes—
352C22×C7C2×#10412yes—
353C22×C7C22×C22⋊C411yescharacteristic
354C22×C7C22×SD1611yescharacteristic
355C22×C7C22×Q1611yescharacteristic
356C4×C7—21no—
357C4×C7—21no—
358C4×C7—21no—
359C4×C7—21no—
360C4×C7—44no—
361C4×C7—42no—
362C4×C7—42no—
363Dic7—22no—
364Dic7—44no—
365Dic7—42no—
366Dic7—42no—
367Dic7C2×#10314yes—
368Dic7C2×#10314yes—
369Dic7C2×#10414yes—
370C24D4×D711yescharacteristic
371C2×Q8—21no—
372C2×Q8—42no—
373C2×Q8—72no—
374C2×Q8—144no—
375C2×Q8—141no—
376C2×Q8—282no—
377C2×Q8—284no—
378C2×Q8C2×C4×D712yes—
379C22×C4—24no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—72no—
387C22×C4—71no—
388C22×C4—71no—
389C22×C4—71no—
390C22×C4—74no—
391C22×C4—74no—
392C22×C4—72no—
393C22×C4—72no—
394C22×C4—71no—
395C22×C4—72no—
396C22×C4—144no—
397C22×C4—144no—
398C22×C4—141no—
399C22×C4—141no—
400C22×C4—142no—
401C22×C4—282no—
402C22×C4—282no—
403C22×C4C2×C4×D711yescharacteristic
404C22×C4C2×C4×D711yescharacteristic
405C22×C4D4×D711yescharacteristic
406C22×C4D4×D711yescharacteristic
407C22×C4D4×D711yescharacteristic
408C22×C4C23×D711yescharacteristic
409C2×C8—22no—
410C2×C8—42no—
411C2×C8—142no—
412C2×C8—282no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—72no—
417C4⋊C4—144no—
418C4⋊C4—144no—
419C4⋊C4—144no—
420C4⋊C4—144no—
421C4⋊C4—144no—
422C4⋊C4—1416no—
423C4⋊C4—142no—
424C4⋊C4—141no—
425C4⋊C4—142no—
426C4⋊C4C2×C4×D712yes—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—142no—
430C22⋊C4—142no—
431C42—72no—
432C42—72no—
433C42—72no—
434C42—72no—
435C42—72no—
436C42—72no—
437C42—72no—
438C42—72no—
439C42—144no—
440C42—144no—
441C42—288no—
442C2×C7—21no—
443C2×C7—21no—
444C2×C7—22no—
445C2×C7#150314yescomplemented
446C2×C7C2×#41011yescharacteristic
447C2×C7C22×#10311yescharacteristic
448C2×C7C22×#10411yescharacteristic
449C23—22no—
450C23—22no—
451C23D7×C22⋊C411yescharacteristic
452C23D7×C22⋊C411yescharacteristic
453C23D7×SD1612yes—
454C23D7×Q1612yes—
455C23C2×D4×D711yescharacteristic
456Q8—42no—
457Q8—42no—
458Q8—282no—
459Q8—282no—
460Q8—288no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—48no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—72no—
476C2×C4—72no—
477C2×C4—72no—
478C2×C4—74no—
479C2×C4—74no—
480C2×C4—78no—
481C2×C4—74no—
482C2×C4—74no—
483C2×C4—74no—
484C2×C4—72no—
485C2×C4—144no—
486C2×C4—144no—
487C2×C4—142no—
488C2×C4—144no—
489C2×C4—142no—
490C2×C4—142no—
491C2×C4—282no—
492C2×C4—288no—
493C2×C4—282no—
494C2×C4—282no—
495C2×C4—282no—
496C2×C4D7×C22⋊C411yescharacteristic
497C2×C4D7×C22⋊C411yescharacteristic
498C2×C4C22×C4×D711yescharacteristic
499C2×C4C2×D4×D711yescharacteristic
500C8—42no—
501C8—282no—
502C7C2×#150311yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—24no—
508C22—24no—
509C22#8951212yes—
510C22D7×#10312yes—
511C22D7×#10312yes—
512C22D7×#10412yes—
513C22C2×D7×C22⋊C411yescharacteristic
514C22C2×D7×SD1611yescharacteristic
515C22C2×D7×Q1611yescharacteristic
516C4—21no—
517C4—21no—
518C4—21no—
519C4—21no—
520C4—44no—
521C4—42no—
522C4—42no—
523C4—74no—
524C4—74no—
525C4—74no—
526C4—142no—
527C4—284no—
528C4—282no—
529C4—282no—
530C2—21no—
531C2—21no—
532C2—22no—
533C2#1172606314yesdirect product factor
534C2C2×#8951211yescharacteristic
535C2C2×D7×#10311yescharacteristic
536C2C2×D7×#10411yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#328C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C2×D4
cosocleC22×C4×C7C24
hypercenterC2×#328D7
hypocenterC7C2×#1503
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
8. #11726063C2direct (N × H)
10. C2×Q8×Dic7C4semidirect
11. C2×#6507C4semidirect
18. #90313C4semidirect
21. C2×#6451C4semidirect
23. C2×#6450C4semidirect
59. Q8×Dic7C2×C4semidirect
61. #6507C2×C4semidirect
91. #6451C2×C4semidirect
95. #6450C2×C4semidirect
445. C2×C7#1503semidirect
502. C7C2×#1503semidirect
533. C2#11726063direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903132
C2×#894902
C2×#894212
C2×C7×#3282
C2×#893332
C2×#892622
C2×#892472
#117260632
C2×#15037