Finite Group Databasebeta

← C2×#11738574 #14232537

Subgroups — C2×#11738574 #14232537

Order 1792.

1866 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90421C211yesmaximal, characteristic
2C2×#90275C211yesmaximal, characteristic
3C2×C7×#477C211yesmaximal, characteristic, complemented
4C2×#89851C211yesmaximal, characteristic, complemented
5C2×C4×#1144C211yesmaximal, characteristic, complemented
6#11738574C2116yesmaximal, direct product factor
7C2×#89660C212yesmaximal, complemented
8C2×#89653C212yesmaximal, complemented
9C2×#89623C211yesmaximal, characteristic, complemented
10C2×#89610C211yesmaximal, characteristic
11C2×#89577C212yesmaximal, complemented
12C2×#89588C212yesmaximal, complemented
13C2×C7×C4⋊Q8C2211yescharacteristic
14C2×C4×C7×Q8C2211yescharacteristic
15C2×#6509—22no—
16C2×#6509C2212yes—
17C22×#1144C2211yescharacteristic
18C22×#1131C2212yes—
19#90421—24no—
20#90421C2218yes—
21#90275—24no—
22#90275C2218yes—
23C2×#6461—22no—
24C2×#6460C2212yes—
25C2×#6456—21no—
26C2×#6455C2212yes—
27C2×D7×C4⋊C4C2212yes—
28C2×#6453—21no—
29C2×#6438—21no—
30C2×C4×D28C2211yescharacteristic
31C2×#6432C2211yescharacteristic
32C2×C4×Dic14—21no—
33C2×C4×Dic14C2211yescharacteristic
34C7×#477C2218yescomplemented
35C2×C7×#107C2212yes—
36C2×C7×C4⋊C8C2211yescharacteristic
37C2×C7×#103C2212yes—
38C2×#6409C2211yescharacteristic
39C2×(C2×D7)⋊C8C2212yes—
40C2×#6391C2212yes—
41C2×#6390C2212yes—
42#89851C2218yescomplemented
43C4×#1144C2218yescomplemented
44C2×#6384C2211yescharacteristic
45C2×#6382C2212yes—
46C2×#6382C2212yes—
47C2×#6381C2211yescharacteristic
48C2×C4×C7⋊C8C2211yescharacteristic
49#89660C22116yescomplemented
50#89653C22116yescomplemented
51#89623C2218yescomplemented
52#89610C2218yes—
53#89588C22116yescomplemented
54#89577C22116yescomplemented
55C2×#3356—71nomaximal, Sylow
56C22×C7×Q8—21no—
57C22×C7×Q8C2311yescharacteristic
58C22×D28D411yescharacteristic
59C22×C4×D7—22no—
60C22×C4×D7C2312yes—
61C22×Dic14—21no—
62C22×Dic14C2311yescharacteristic
63C22×C7×C8C2312yes—
64C7×C4⋊Q8—22no—
65C7×C4⋊Q8C2314yes—
66C4×C7×Q8—22no—
67C4×C7×Q8C2314yes—
68C2×C7×C4⋊C4—21no—
69C2×C7×C4⋊C4—21no—
70C2×C7×C4⋊C4C2312yes—
71C2×C7×C4⋊C4C2311yescharacteristic
72C2×C42×C7—21no—
73C2×C42×C7C2311yescharacteristic
74#6509—24no—
75#6509—216no—
76#6509C2318yes—
77C2×#1144—24no—
78C2×#1144C2314yes—
79C2×(C2×D7)⋊C4—22no—
80C2×(C2×D7)⋊C4—22no—
81C2×(C2×D7)⋊C4—22no—
82C2×(C2×D7)⋊C4D412yes—
83C2×C4⋊Dic7—21no—
84C2×C4⋊Dic7—22no—
85C2×C4⋊Dic7D411yescharacteristic
86C2×C4⋊Dic7C2312yes—
87C2×C4⋊Dic7C2311yescharacteristic
88C2×Dic7⋊C4—21no—
89C2×Dic7⋊C4—22no—
90C2×Dic7⋊C4—22no—
91C2×C4×Dic7—21no—
92C2×C4×Dic7—22no—
93C22×C7⋊C8C2311yescharacteristic
94C22×C7⋊C8C2311yescharacteristic
95C2×#1131—28no—
96C2×#1131C2318yes—
97#6461—216no—
98#6460—24no—
99#6460C2318yes—
100#6456—28no—
101#6455—24no—
102#6455C2318yes—
103D7×C4⋊C4—24no—
104D7×C4⋊C4C2318yes—
105#6453—28no—
106#6438—28no—
107C4×D28D414yes—
108C4×D28C2314yes—
109#6432—22no—
110#6432C2314yes—
111C4×Dic14—22no—
112C4×Dic14—28no—
113C4×Dic14C2314yes—
114C7×#107C2318yes—
115C7×C4⋊C8C2314yes—
116C7×#103C2318yes—
117#6409C2314yes—
118(C2×D7)⋊C8C2318yes—
119#6391C2318yes—
120#6390C2318yes—
121#6384C2314yes—
122#6382C2318yes—
123#6382C2318yes—
124#6381C2314yes—
125C4×C7⋊C8C2314yes—
126C2×#556—71no—
127C2×#554—71no—
128#3356—716no—
129C2×#498—71no—
130C2×#485—72no—
131C2×#483—72no—
132C2×#477D711yescharacteristic, complemented
133C2×#475—71no—
134C2×#470—72no—
135C2×C4×Q16—71no—
136C2×#436—71no—
137C2×#428—72no—
138C23×D7C2×D412yes—
139C2×C7×Q8—21no—
140C2×C7×Q8—24no—
141C2×C7×Q8—22no—
142C2×C7×Q8—22no—
143C2×C7×Q8—82no—
144C2×C7×Q8C2412yes—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—22no—
148C22×C4×C7C2×D411yescharacteristic
149C22×C4×C7C2×D411yescharacteristic
150C22×C4×C7C2411yescharacteristic
151C22×Dic7—21no—
152C22×Dic7—21no—
153C22×Dic7—22no—
154C22×Dic7C2×D412yes—
155C2×D28—24no—
156C2×D28C2×D414yes—
157C2×C4×D7—24no—
158C2×C4×D7—24no—
159C2×C4×D7—28no—
160C2×C4×D7—84no—
161C2×C4×D7C2×D414yes—
162C2×C4×D7C2414yes—
163C2×Dic14—22no—
164C2×Dic14—22no—
165C2×Dic14—24no—
166C2×Dic14—21no—
167C2×Dic14—44no—
168C2×Dic14C2412yes—
169C2×C7×C8—24no—
170C2×C7×C8C2414yes—
171C7×C4⋊C4—24no—
172C7×C4⋊C4—22no—
173C7×C4⋊C4—21no—
174C7×C4⋊C4—24no—
175C7×C4⋊C4C2414yes—
176C7×C4⋊C4C2412yes—
177C42×C7—24no—
178C42×C7C2×D412yes—
179C42×C7C2412yes—
180#1144—28no—
181(C2×D7)⋊C4—28no—
182(C2×D7)⋊C4—28no—
183(C2×D7)⋊C4—28no—
184(C2×D7)⋊C4C2×D418yes—
185C4⋊Dic7—21no—
186C4⋊Dic7—22no—
187C4⋊Dic7—24no—
188C4⋊Dic7—28no—
189C4⋊Dic7C2×D414yes—
190C4⋊Dic7C2412yes—
191C4⋊Dic7C2414yes—
192Dic7⋊C4—24no—
193Dic7⋊C4—28no—
194Dic7⋊C4—28no—
195C4×Dic7—24no—
196C4×Dic7—28no—
197C2×C7⋊C8—22no—
198C2×C7⋊C8#4114yes—
199C2×C7⋊C8C2412yes—
200C2×C7⋊C8C2412yes—
201#1131—216no—
202C22×Q16—71no—
203C22×M16—72no—
204#556—78no—
205#556—144no—
206#554—78no—
207#554—144no—
208C2×C4⋊Q8—71no—
209C2×C4⋊Q8C2×D711yescharacteristic
210C2×#126—142no—
211C2×#125—141no—
212C2×#124—141no—
213C2×C22⋊Q8—72no—
214C2×C22⋊Q8—72no—
215C2×C22⋊Q8—142no—
216C2×C4×Q8—71no—
217C2×C4×Q8—141no—
218C2×C4×Q8C2×D711yescharacteristic
219C2×C4×D4—71no—
220C2×C4×D4—141no—
221C2×#117—72no—
222C22×C4⋊C4—72no—
223#498—78no—
224#485—716no—
225#483—716no—
226#477C2×D718yescomplemented
227#475—78no—
228#470—716no—
229C4×Q16—78no—
230#436—78no—
231#428—716no—
232C2×#107—71no—
233C2×#107C2×D712yes—
234C2×#106—72no—
235C2×#106—72no—
236C2×#106—72no—
237C2×C4⋊C8C2×D711yescharacteristic
238C2×#103—71no—
239C2×#103—72no—
240C2×#103—71no—
241C2×#103C2×D712yes—
242C2×C22⋊C8—72no—
243C2×C4×C8—71no—
244C23×C7C22×D411yescharacteristic
245C22×D7—24no—
246C22×D7—24no—
247C22×D7—24no—
248C22×D7C22×D414yes—
249C7×Q8—22no—
250C7×Q8—22no—
251C7×Q8—42no—
252C7×Q8—84no—
253C2×C4×C7—22no—
254C2×C4×C7—22no—
255C2×C4×C7—22no—
256C2×C4×C7—24no—
257C2×C4×C7—42no—
258C2×C4×C7—44no—
259C2×C4×C7—42no—
260C2×C4×C7#13714yes—
261C2×C4×C7C22×D412yes—
262C2×C4×C7C22×D411yescharacteristic
263C2×C4×C7C22×D412yes—
264C2×C4×C7C2×#4112yes—
265C2×C4×C72−1+412yes—
266C2×C4×C7C2511yescharacteristic
267C2×Dic7—24no—
268C2×Dic7—22no—
269C2×Dic7—22no—
270C2×Dic7—24no—
271C2×Dic7—42no—
272C2×Dic7—44no—
273C2×Dic7—42no—
274C2×Dic7C22×D414yes—
275D28—28no—
276C4×D7—28no—
277C4×D7—24no—
278C4×D7—24no—
279C4×D7—88no—
280Dic14—22no—
281Dic14—22no—
282Dic14—42no—
283Dic14—48no—
284C7×C8—24no—
285C7⋊C8—22no—
286C7⋊C8C2×#4114yes—
287C22×Q8—21no—
288C22×Q8—71no—
289C22×Q8—141no—
290C22×Q8C22×D711yescharacteristic
291C22×D4—71no—
292C23×C4—72no—
293C23×C4—142no—
294C2×Q16—74no—
295C2×Q16—144no—
296C2×M16—78no—
297C2×M16—148no—
298C22×C8—71no—
299C22×C8—71no—
300C22×C8C22×D712yes—
301C4⋊Q8—22no—
302C4⋊Q8—74no—
303C4⋊Q8—142no—
304C4⋊Q8C22×D714yes—
305#126—1416no—
306#125—148no—
307#124—148no—
308C22⋊Q8—78no—
309C22⋊Q8—78no—
310C22⋊Q8—1416no—
311C22⋊Q8—144no—
312C22⋊Q8—144no—
313C4×Q8—22no—
314C4×Q8—74no—
315C4×Q8—148no—
316C4×Q8—142no—
317C4×Q8C22×D714yes—
318C4×D4—74no—
319C4×D4—74no—
320C4×D4—148no—
321#117—78no—
322#117—144no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—71no—
326C2×C4⋊C4—71no—
327C2×C4⋊C4—72no—
328C2×C4⋊C4—78no—
329C2×C4⋊C4—144no—
330C2×C4⋊C4—142no—
331C2×C4⋊C4—142no—
332C2×C4⋊C4—142no—
333C2×C4⋊C4—141no—
334C2×C4⋊C4—141no—
335C2×C4⋊C4C22×D712yes—
336C2×C4⋊C4C22×D711yescharacteristic
337C2×C22⋊C4—72no—
338C2×C22⋊C4—142no—
339C2×C22⋊C4—142no—
340C2×C22⋊C4—142no—
341C2×C42—21no—
342C2×C42—142no—
343C2×C42—141no—
344C2×C42C22×D711yescharacteristic
345#107—74no—
346#107C22×D718yes—
347#106—78no—
348#106—78no—
349#106—78no—
350C4⋊C8C22×D714yes—
351#103—74no—
352#103—78no—
353#103—74no—
354#103C22×D718yes—
355C22⋊C8—78no—
356C4×C8—74no—
357C22×C7#54712yes—
358C22×C7C2×#13712yes—
359C22×C7#57712yes—
360C22×C7C23×D411yescharacteristic
361C2×D7—24no—
362C2×D7—24no—
363C2×D7—24no—
364C2×D7—48no—
365C4×C7—22no—
366C4×C7—42no—
367C4×C7—44no—
368C4×C7—42no—
369C4×C7#54712yes—
370C4×C7C2×#13714yes—
371C4×C7C22×#4111yescharacteristic
372C4×C7C2×2−1+411yescharacteristic
373Dic7—24no—
374Dic7—42no—
375Dic7—44no—
376Dic7—42no—
377C24—72no—
378C2×Q8—21no—
379C2×Q8—24no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—72no—
383C2×Q8—82no—
384C2×Q8—141no—
385C2×Q8—144no—
386C2×Q8—142no—
387C2×Q8—142no—
388C2×Q8—284no—
389C2×Q8C23×D712yes—
390C2×D4—74no—
391C2×D4—144no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—72no—
396C22×C4—74no—
397C22×C4—74no—
398C22×C4—148no—
399C22×C4—144no—
400C22×C4—144no—
401C22×C4—142no—
402C22×C4—141no—
403C22×C4—141no—
404C22×C4—564no—
405C22×C4D4×D711yescharacteristic
406C22×C4D4×D711yescharacteristic
407C22×C4C23×D711yescharacteristic
408Q16—148no—
409M16—1416no—
410C2×C8—24no—
411C2×C8—74no—
412C2×C8—72no—
413C2×C8—72no—
414C2×C8—142no—
415C2×C8C23×D714yes—
416C4⋊C4—24no—
417C4⋊C4—24no—
418C4⋊C4—22no—
419C4⋊C4—21no—
420C4⋊C4—74no—
421C4⋊C4—74no—
422C4⋊C4—72no—
423C4⋊C4—148no—
424C4⋊C4—148no—
425C4⋊C4—148no—
426C4⋊C4—144no—
427C4⋊C4—141no—
428C4⋊C4—142no—
429C4⋊C4—144no—
430C4⋊C4C23×D712yes—
431C4⋊C4C23×D714yes—
432C22⋊C4—78no—
433C22⋊C4—148no—
434C22⋊C4—148no—
435C22⋊C4—148no—
436C42—24no—
437C42—148no—
438C42—144no—
439C42D4×D712yes—
440C42C23×D712yes—
441C2×C7#335614yescomplemented
442C2×C7C2×#54711yescharacteristic
443C2×C7C22×#13711yescharacteristic
444C2×C7C2×#57711yescharacteristic
445D7—44no—
446C23—74no—
447C23—144no—
448C23—144no—
449C23—144no—
450C23C2×D4×D711yescharacteristic
451Q8—22no—
452Q8—22no—
453Q8—42no—
454Q8—84no—
455Q8—142no—
456Q8—142no—
457Q8—288no—
458Q8—282no—
459D4—148no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—24no—
464C2×C4—42no—
465C2×C4—44no—
466C2×C4—42no—
467C2×C4—74no—
468C2×C4—144no—
469C2×C4—148no—
470C2×C4—144no—
471C2×C4—144no—
472C2×C4—144no—
473C2×C4—142no—
474C2×C4—142no—
475C2×C4—284no—
476C2×C4—282no—
477C2×C4—282no—
478C2×C4—568no—
479C2×C4#648114yes—
480C2×C4C2×D4×D712yes—
481C2×C4C2×D4×D712yes—
482C2×C4C2×D4×D711yescharacteristic
483C2×C4#655112yes—
484C2×C4D7×#4112yes—
485C2×C4C24×D711yescharacteristic
486C8—24no—
487C8—74no—
488C8—142no—
489C7C2×#335611yescharacteristic, complemented, Sylow
490C22—144no—
491C22—144no—
492C22—144no—
493C22—288no—
494C22#9032212yes—
495C22C2×#648112yes—
496C22#9046612yes—
497C22C22×D4×D711yescharacteristic
498C4—22no—
499C4—44no—
500C4—42no—
501C4—42no—
502C4—144no—
503C4—282no—
504C4—282no—
505C4—284no—
506C4#9032212yes—
507C4C2×#648114yes—
508C4C2×#655111yescharacteristic
509C4C2×D7×#4111yescharacteristic
510C2—284no—
511C2#1173857414yesdirect product factor
512C2C2×#9032211yescharacteristic
513C2C22×#648111yescharacteristic
514C2C2×#9046611yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#477C2
socleC23×C7C22×D4
prime radicalC22×D28D4
hypercenterC2×#477D7
hypocenterC7C2×#3356
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. C2×C7×#477C2semidirect
4. C2×#89851C2semidirect
5. C2×C4×#1144C2semidirect
6. #11738574C2direct (N × H)
7. C2×#89660C2semidirect
8. C2×#89653C2semidirect
9. C2×#89623C2semidirect
11. C2×#89577C2semidirect
12. C2×#89588C2semidirect
34. C7×#477C22semidirect
42. #89851C22semidirect
43. C4×#1144C22semidirect
49. #89660C22semidirect
50. #89653C22semidirect
51. #89623C22semidirect
53. #89588C22semidirect
54. #89577C22semidirect
132. C2×#477D7semidirect
226. #477C2×D7semidirect
441. C2×C7#3356semidirect
489. C7C2×#3356semidirect
511. C2#11738574direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904212
C2×#902752
C2×C7×#4772
C2×#898512
C2×C4×#11442
#117385742
C2×#896602
C2×#896532
C2×#896232
C2×#896102
C2×#895772
C2×#895882
C2×#33567