Finite Group Databasebeta

← C2×#11740962 #14232219

Subgroups — C2×#11740962 #14232219

Order 1792.

2158 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#547C211yesmaximal, characteristic
2C2×#90234C211yesmaximal, characteristic, complemented
3#11740962C2116yesmaximal, direct product factor
4C2×#89866C211yesmaximal, characteristic, complemented
5C2×#89851C211yesmaximal, characteristic, complemented
6C2×#89813C212yesmaximal, complemented
7C2×#89806C212yesmaximal, complemented
8C2×C4×#1142C211yesmaximal, characteristic, complemented
9C2×D4×C7⋊C8C211yesmaximal, characteristic, complemented
10C2×#89780C211yesmaximal, characteristic, complemented
11C2×#89743C212yesmaximal, complemented
12C22×#6382C212yesmaximal, complemented
13C22×C7×#41—21no—
14C7×#547—24no—
15C7×#547C2218yes—
16C2×C7×C4⋊Q8C2211yescharacteristic
17C2×C7×#123—22no—
18C2×C7×C22⋊Q8—21no—
19C2×C7×#121C2212yes—
20C2×C4×C7×D4C2211yescharacteristic
21C2×C4×C7×D4C2211yescharacteristic
22C22×C7×C4⋊C4C2212yes—
23C2×D4×Dic7—21no—
24C22×#1142C2211yescharacteristic
25C22×C4⋊Dic7C2212yes—
26C2×#6487C2212yes—
27C23×C7⋊C8C2212yes—
28#90234—24no—
29#90234C2218yescomplemented
30C2×#6453—21no—
31C2×#6441—22no—
32C2×#6432C2211yescharacteristic
33C2×C4×Dic14C2211yescharacteristic
34C2×#6406C2212yes—
35C2×#6406C2211yescharacteristic
36C2×C22⋊(C7⋊C8)C2212yes—
37#89866C2218yescomplemented
38#89851C2218yescomplemented
39#89813C22116yescomplemented
40#89806C22116yescomplemented
41C4×#1142C2218yescomplemented
42D4×C7⋊C8C2218yescomplemented
43#89780C2218yescomplemented
44#89743C22116yescomplemented
45C2×#6384C2211yescharacteristic
46C2×#6384C2212yes—
47C2×#6382C2212yes—
48C2×#6382C2211yescharacteristic
49C2×#6382C2212yes—
50C2×#6382C2212yes—
51C2×#6382C2212yes—
52C2×#6382C22116yescomplemented
53C2×C4⋊(C7⋊C8)C2211yescharacteristic
54C2×C4×C7⋊C8C2211yescharacteristic
55C2×#3335—71nomaximal, Sylow
56C2×C7×#41—28no—
57C2×C7×#41—48no—
58C22×C7×Q8—21no—
59C22×C7×D4—22no—
60C22×C7×D4D411yescharacteristic
61C22×C7×D4C2311yescharacteristic
62C23×C4×C7—22no—
63C23×C4×C7—21no—
64C23×C4×C7C2312yes—
65C23×Dic7—22no—
66C22×Dic14—21no—
67C22×Dic14C2311yescharacteristic
68C7×C4⋊Q8—22no—
69C7×C4⋊Q8C2314yes—
70C7×#123—216no—
71C7×C22⋊Q8—28no—
72C7×#121—24no—
73C7×#121C2318yes—
74C4×C7×D4—22no—
75C4×C7×D4D414yes—
76C4×C7×D4C2314yes—
77C4×C7×D4C2314yes—
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—24no—
80C2×C7×C4⋊C4—21no—
81C2×C7×C4⋊C4D411yescharacteristic
82C2×C7×C4⋊C4C2311yescharacteristic
83C2×C7×C4⋊C4C2312yes—
84C2×C7×C4⋊C4C2318yes—
85C2×C7×C22⋊C4—21no—
86C2×C7×C22⋊C4—22no—
87C2×C7×C22⋊C4D412yes—
88C2×C42×C7C2311yescharacteristic
89C2×C22⋊Dic7—22no—
90D4×Dic7—28no—
91C2×#1142—24no—
92C2×#1142C2314yes—
93C2×C4⋊Dic7—21no—
94C2×C4⋊Dic7—22no—
95C2×C4⋊Dic7—24no—
96C2×C4⋊Dic7C2311yescharacteristic
97C2×C4⋊Dic7C2312yes—
98C2×C4⋊Dic7C2318yes—
99#6487—24no—
100#6487C2318yes—
101C2×Dic7⋊C4—21no—
102C2×Dic7⋊C4—22no—
103C2×C4×Dic7—21no—
104C22×C7⋊C8—28no—
105C22×C7⋊C8C2311yescharacteristic
106C22×C7⋊C8C2312yes—
107C22×C7⋊C8C2318yes—
108C22×C7⋊C8C2311yescharacteristic
109#6453—28no—
110#6441—216no—
111#6432—22no—
112#6432C2314yes—
113C4×Dic14—22no—
114C4×Dic14C2314yes—
115#6406C2318yes—
116#6406C2314yes—
117C22⋊(C7⋊C8)C2318yes—
118#6384C2318yes—
119#6384C2314yes—
120#6382C2318yes—
121#6382C2314yes—
122#6382C2318yes—
123#6382C2318yes—
124#6382C2318yes—
125C4⋊(C7⋊C8)C2314yes—
126C4×C7⋊C8C2314yes—
127C2×#554—71no—
128C2×#547D711yescharacteristic
129#3335—716no—
130C2×#498—71no—
131C2×#481—72no—
132C2×#483—72no—
133C2×#475—71no—
134C2×#476—71no—
135C2×#465—72no—
136C2×C4×SD16—71no—
137C2×C8×D4—71no—
138C22×#106—72no—
139C24×C7—21no—
140C24×C7C2×D412yes—
141C7×#41—432no—
142C2×C7×Q8—24no—
143C2×C7×Q8—44no—
144C2×C7×D4—28no—
145C2×C7×D4—21no—
146C2×C7×D4—22no—
147C2×C7×D4—22no—
148C2×C7×D4—48no—
149C2×C7×D4SD1618yescomplemented
150C2×C7×D4C2×D414yes—
151C2×C7×D4C2412yes—
152C22×C4×C7—24no—
153C22×C4×C7—24no—
154C22×C4×C7—21no—
155C22×C4×C7—22no—
156C22×C4×C7—28no—
157C22×C4×C7—24no—
158C22×C4×C7—48no—
159C22×C4×C7—44no—
160C22×C4×C7C2×D412yes—
161C22×C4×C7C2×D411yescharacteristic
162C22×C4×C7C2×D414yes—
163C22×C4×C7C2×D411yescharacteristic
164C22×C4×C7C2414yes—
165C22×C4×C7C2411yescharacteristic
166C22×Dic7—21no—
167C22×Dic7—21no—
168C22×Dic7—22no—
169C22×Dic7—28no—
170C22×Dic7—84no—
171C2×Dic14—22no—
172C2×Dic14—22no—
173C2×Dic14—21no—
174C2×Dic14—24no—
175C2×Dic14—82no—
176C2×Dic14C2412yes—
177C7×C4⋊C4—21no—
178C7×C4⋊C4—22no—
179C7×C4⋊C4—28no—
180C7×C4⋊C4—24no—
181C7×C4⋊C4C2×D414yes—
182C7×C4⋊C4C2412yes—
183C7×C4⋊C4C2414yes—
184C7×C22⋊C4—24no—
185C7×C22⋊C4—28no—
186C7×C22⋊C4C2×D418yes—
187C42×C7C2×D412yes—
188C42×C7C2412yes—
189C22⋊Dic7—28no—
190#1142—28no—
191C4⋊Dic7—21no—
192C4⋊Dic7—22no—
193C4⋊Dic7—24no—
194C4⋊Dic7—28no—
195C4⋊Dic7C2412yes—
196C4⋊Dic7C2414yes—
197Dic7⋊C4—24no—
198Dic7⋊C4—28no—
199C4×Dic7—24no—
200C2×C7⋊C8—24no—
201C2×C7⋊C8—22no—
202C2×C7⋊C8—216no—
203C2×C7⋊C8#4114yescomplemented
204C2×C7⋊C8C2412yes—
205C2×C7⋊C8C2414yes—
206C2×C7⋊C8C2412yes—
207C22×#41—21no—
208C22×SD16—71no—
209C23×C8—72no—
210#554—78no—
211#554—144no—
212#547—24no—
213#547C2×D718yes—
214C2×C4⋊Q8—71no—
215C2×C4⋊Q8C2×D711yescharacteristic
216C2×#125—141no—
217C2×#123—22no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—72no—
220C2×C22⋊Q8—142no—
221C2×#121C2×D712yes—
222C2×C4×Q8—71no—
223C2×C4×D4—141no—
224C2×C4×D4C2×D711yescharacteristic
225C2×C4×D4C2×D711yescharacteristic
226C22×C4⋊C4—72no—
227C22×C4⋊C4C2×D712yes—
228#498—78no—
229#483—716no—
230#481—716no—
231#476—78no—
232#475—78no—
233#465—716no—
234C4×SD16—78no—
235C8×D4—78no—
236C2×#106—72no—
237C2×#106—716no—
238C2×#106—72no—
239C2×#106—72no—
240C2×#106—72no—
241C2×#106—71no—
242C2×C4⋊C8—71no—
243C2×#103—72no—
244C2×#103—71no—
245C2×#102—71no—
246C2×#102—72no—
247C2×C22⋊C8—72no—
248C2×C4×C8—71no—
249C23×C7—24no—
250C23×C7—24no—
251C23×C7—22no—
252C23×C7—42no—
253C23×C7—42no—
254C23×C7—42no—
255C23×C7C2×SD1618yes—
256C23×C7C22×D414yes—
257C23×C7C22×D411yescharacteristic
258C7×Q8—48no—
259C7×D4—22no—
260C7×D4—22no—
261C7×D4—416no—
262C7×D4—42no—
263C7×D4C2×SD16116yescomplemented
264C2×C4×C7—24no—
265C2×C4×C7—22no—
266C2×C4×C7—28no—
267C2×C4×C7—24no—
268C2×C4×C7—24no—
269C2×C4×C7—22no—
270C2×C4×C7—24no—
271C2×C4×C7—42no—
272C2×C4×C7—44no—
273C2×C4×C7—416no—
274C2×C4×C7—48no—
275C2×C4×C7C2×SD1614yes—
276C2×C4×C7C22×D414yes—
277C2×C4×C7C22×D412yes—
278C2×C4×C7C22×D411yescharacteristic
279C2×C4×C7C22×D412yes—
280C2×C4×C7C2×#4112yes—
281C2×C4×C72−1+412yes—
282C2×C4×C7C2511yescharacteristic
283C2×Dic7—22no—
284C2×Dic7—22no—
285C2×Dic7—24no—
286C2×Dic7—42no—
287C2×Dic7—44no—
288C2×Dic7—42no—
289C2×Dic7—88no—
290Dic14—22no—
291Dic14—22no—
292Dic14—42no—
293Dic14—84no—
294C7⋊C8—24no—
295C7⋊C8—22no—
296C7⋊C8C2×#4114yescomplemented
297C2×#41—28no—
298C2×#41—48no—
299C22×Q8—21no—
300C22×Q8—71no—
301C22×Q8—141no—
302C22×D4—22no—
303C22×D4C22⋊D711yescharacteristic
304C22×D4C22×D711yescharacteristic
305C23×C4—22no—
306C23×C4—21no—
307C23×C4—142no—
308C23×C4C22×D712yes—
309C2×SD16—74no—
310C2×SD16—144no—
311C22×C8—71no—
312C22×C8—72no—
313C22×C8—78no—
314C22×C8—71no—
315C22×C8—148no—
316C4⋊Q8—22no—
317C4⋊Q8—74no—
318C4⋊Q8—142no—
319C4⋊Q8C22×D714yes—
320#125—148no—
321#123—216no—
322C22⋊Q8—28no—
323C22⋊Q8—78no—
324C22⋊Q8—144no—
325C22⋊Q8—1416no—
326#121—24no—
327#121C22×D718yes—
328C4×Q8—74no—
329C4×Q8—142no—
330C4×D4—22no—
331C4×D4—148no—
332C4×D4C22⋊D714yes—
333C4×D4C22×D714yes—
334C4×D4C22×D714yes—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—71no—
339C2×C4⋊C4—72no—
340C2×C4⋊C4—78no—
341C2×C4⋊C4—142no—
342C2×C4⋊C4—144no—
343C2×C4⋊C4—141no—
344C2×C4⋊C4—141no—
345C2×C4⋊C4—142no—
346C2×C4⋊C4C22⋊D711yescharacteristic
347C2×C4⋊C4C22×D711yescharacteristic
348C2×C4⋊C4C22×D712yes—
349C2×C4⋊C4C22×D718yes—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—142no—
353C2×C22⋊C4C22⋊D712yes—
354C2×C42—141no—
355C2×C42C22×D711yescharacteristic
356#106—74no—
357#106—78no—
358#106—78no—
359#106—78no—
360#106—78no—
361C4⋊C8—74no—
362#103—74no—
363#103—78no—
364#102—74no—
365#102—78no—
366C22⋊C8—78no—
367C4×C8—74no—
368C22×C7—216no—
369C22×C7—24no—
370C22×C7—24no—
371C22×C7—42no—
372C22×C7—42no—
373C22×C7—42no—
374C22×C7—84no—
375C22×C7#54712yes—
376C22×C7C22×SD1618yes—
377C22×C7C22×SD1612yes—
378C22×C7#57712yes—
379C22×C7C23×D411yescharacteristic
380C4×C7—24no—
381C4×C7—22no—
382C4×C7—42no—
383C4×C7—44no—
384C4×C7#54712yes—
385C4×C7C22×SD1614yes—
386C4×C7C22×#4111yescharacteristic
387C4×C7C2×2−1+411yescharacteristic
388Dic7—42no—
389Dic7—44no—
390Dic7—42no—
391C24—21no—
392C24C2×C22⋊D712yes—
393#41—432no—
394C2×Q8—24no—
395C2×Q8—44no—
396C2×Q8—72no—
397C2×Q8—141no—
398C2×Q8—144no—
399C2×Q8—142no—
400C2×Q8—142no—
401C2×Q8—562no—
402C2×D4—28no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—21no—
406C2×D4—48no—
407C2×D4#114218yescomplemented
408C2×D4C2×C22⋊D714yes—
409C2×D4C23×D712yes—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—28no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—48no—
417C22×C4—44no—
418C22×C4—141no—
419C22×C4—141no—
420C22×C4—142no—
421C22×C4—148no—
422C22×C4—564no—
423C22×C4C2×C22⋊D714yes—
424C22×C4C2×C22⋊D711yescharacteristic
425C22×C4C2×C22⋊D712yes—
426C22×C4C2×C22⋊D711yescharacteristic
427C22×C4C23×D714yes—
428C22×C4C23×D711yescharacteristic
429SD16—148no—
430C2×C8—74no—
431C2×C8—72no—
432C2×C8—72no—
433C2×C8—74no—
434C2×C8—1416no—
435C2×C8—144no—
436C2×C8—142no—
437C4⋊C4—21no—
438C4⋊C4—22no—
439C4⋊C4—28no—
440C4⋊C4—24no—
441C4⋊C4—72no—
442C4⋊C4—74no—
443C4⋊C4—144no—
444C4⋊C4—148no—
445C4⋊C4—141no—
446C4⋊C4—148no—
447C4⋊C4—142no—
448C4⋊C4—144no—
449C4⋊C4C2×C22⋊D714yes—
450C4⋊C4C23×D712yes—
451C4⋊C4C23×D714yes—
452C22⋊C4—24no—
453C22⋊C4—28no—
454C22⋊C4—148no—
455C22⋊C4C2×C22⋊D718yes—
456C42—144no—
457C42C2×C22⋊D712yes—
458C42C23×D712yes—
459C2×C7—28no—
460C2×C7—82no—
461C2×C7#333514yescomplemented
462C2×C7C2×#54711yescharacteristic
463C2×C7C23×SD1611yescharacteristic
464C2×C7C2×#57711yescharacteristic
465C23—24no—
466C23—24no—
467C23—22no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23C2×#114218yes—
472C23C22×C22⋊D714yes—
473C23C22×C22⋊D711yescharacteristic
474Q8—48no—
475Q8—142no—
476Q8—142no—
477Q8—282no—
478Q8—564no—
479D4—22no—
480D4—22no—
481D4—416no—
482D4—42no—
483D4C2×#1142116yescomplemented
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—28no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—42no—
492C2×C4—44no—
493C2×C4—416no—
494C2×C4—48no—
495C2×C4—142no—
496C2×C4—142no—
497C2×C4—144no—
498C2×C4—282no—
499C2×C4—282no—
500C2×C4—284no—
501C2×C4—568no—
502C2×C4C2×#114214yes—
503C2×C4D7×#4112yes—
504C2×C4#655412yes—
505C2×C4C22×C22⋊D712yes—
506C2×C4C22×C22⋊D714yes—
507C2×C4C22×C22⋊D712yes—
508C2×C4C22×C22⋊D711yescharacteristic
509C2×C4C24×D711yescharacteristic
510C8—74no—
511C8—144no—
512C8—142no—
513C7C2×#333511yescharacteristic, complemented, Sylow
514C22—216no—
515C22—24no—
516C22—24no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—84no—
521C22C22×#114218yes—
522C22C22×#114212yes—
523C22#9051512yes—
524C22#9052812yes—
525C22C23×C22⋊D711yescharacteristic
526C4—24no—
527C4—22no—
528C4—42no—
529C4—44no—
530C4—282no—
531C4—282no—
532C4—284no—
533C4C22×#114214yes—
534C4#9051512yes—
535C4C2×D7×#4111yescharacteristic
536C4C2×#655411yescharacteristic
537C2—28no—
538C2—82no—
539C2#1174096214yesdirect product factor
540C2C23×#114211yescharacteristic
541C2C2×#9051511yescharacteristic
542C2C2×#9052811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
Fitting, prime radicalC2×C7×#547C2
socleC23×C7C22×D4
hypercenterC2×#547D7
hypocenterC7C2×#3335
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
2. C2×#90234C2semidirect
3. #11740962C2direct (N × H)
4. C2×#89866C2semidirect
5. C2×#89851C2semidirect
6. C2×#89813C2semidirect
7. C2×#89806C2semidirect
8. C2×C4×#1142C2semidirect
9. C2×D4×C7⋊C8C2semidirect
10. C2×#89780C2semidirect
11. C2×#89743C2semidirect
12. C22×#6382C2semidirect
29. #90234C22semidirect
37. #89866C22semidirect
38. #89851C22semidirect
39. #89813C22semidirect
40. #89806C22semidirect
41. C4×#1142C22semidirect
42. D4×C7⋊C8C22semidirect
43. #89780C22semidirect
44. #89743C22semidirect
52. C2×#6382C22semidirect
149. C2×C7×D4SD16semidirect
203. C2×C7⋊C8#41semidirect
263. C7×D4C2×SD16semidirect
296. C7⋊C8C2×#41semidirect
407. C2×D4#1142semidirect
461. C2×C7#3335semidirect
483. D4C2×#1142semidirect
513. C7C2×#3335semidirect
539. C2#11740962direct (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×#902342
#117409622
C2×#898662
C2×#898512
C2×#898132
C2×#898062
C2×C4×#11422
C2×D4×C7⋊C82
C2×#897802
C2×#897432
C22×#63822
C2×#33357