Finite Group Databasebeta

← C2×#11739071 #14233524

Subgroups — C2×#11739071 #14233524

Order 1792.

1842 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×#90413C211yesmaximal, characteristic, complemented
2C2×#90423C211yesmaximal, characteristic
3C2×C7×#487C211yesmaximal, characteristic, complemented
4C2×#89862C211yesmaximal, characteristic, complemented
5C2×#89856C211yesmaximal, characteristic
6#11739071C2116yesmaximal, direct product factor
7C2×#89570C212yesmaximal
8C2×#89567C212yesmaximal
9C2×#89563C212yesmaximal, complemented
10C2×#89561C212yesmaximal, complemented
11C2×C4×#1132C211yesmaximal, characteristic
12C2×#89451C211yesmaximal, characteristic, complemented
13C2×C7×C4⋊Q8C2211yescharacteristic
14C2×C7×C4⋊Q8C2211yescharacteristic
15C2×#6510C2212yes—
16C2×Q8×Dic7C2212yes—
17C2×#6507—22no—
18C22×#1144C2212yes—
19C22×#1132C2211yescharacteristic
20#90423—24no—
21#90423C2218yes—
22#90413—24no—
23#90413C2218yescomplemented
24C2×#6461—22no—
25C2×#6460—21no—
26C2×#6455—21no—
27C2×#6451—21no—
28C2×#6451C2212yes—
29C2×#6450—21no—
30C2×#6450C2212yes—
31C2×C4×D28C2211yescharacteristic
32C2×C4×Dic14C2211yescharacteristic
33C2×C4×Dic14C2211yescharacteristic
34C7×#487C2218yescomplemented
35C2×C7×#103C2212yes—
36C2×C7×#103C2212yes—
37C2×C4×C7×C8C2211yescharacteristic
38C2×#6409C2212yes—
39C2×#6395C2211yescharacteristic
40C2×#6391C2211yescharacteristic
41C2×#6390C2211yescharacteristic
42C2×#6389C2212yes—
43C2×Dic7⋊C8C2212yes—
44#89862C2218yescomplemented
45#89856C2218yes—
46C2×#6383C2212yes—
47C2×#6382C2212yes—
48C2×C4⋊(C7⋊C8)C2211yescharacteristic
49#89570C22116yes—
50#89567C22116yes—
51#89563C22116yescomplemented
52#89561C22116yescomplemented
53C4×#1132C2218yes—
54#89451C2218yescomplemented
55C2×#3369—71nomaximal, Sylow
56C22×C7×Q8—21no—
57C22×C7×Q8C2312yes—
58C22×D28C2311yescharacteristic
59C22×C4×D7—21no—
60C22×Dic14—22no—
61C22×Dic14D411yescharacteristic
62C22×Dic14C2311yescharacteristic
63C22×C7×C8C2311yescharacteristic
64C22×C7×C8C2311yescharacteristic
65C7×C4⋊Q8—22no—
66C7×C4⋊Q8—22no—
67C7×C4⋊Q8C2314yes—
68C7×C4⋊Q8C2314yes—
69C2×C7×C4⋊C4—21no—
70C2×C7×C4⋊C4—21no—
71C2×C7×C4⋊C4—21no—
72C2×C7×C4⋊C4C2312yes—
73C2×C42×C7C2311yescharacteristic
74#6510—24no—
75#6510C2318yes—
76Q8×Dic7—24no—
77Q8×Dic7C2318yes—
78#6507—216no—
79C2×#1144—28no—
80C2×#1144C2318yes—
81C2×(C2×D7)⋊C4—21no—
82C2×(C2×D7)⋊C4—22no—
83C2×(C2×D7)⋊C4—22no—
84C2×C4⋊Dic7—22no—
85C2×C4⋊Dic7D411yescharacteristic
86C2×C4⋊Dic7C2311yescharacteristic
87C2×C4⋊Dic7C2311yescharacteristic
88C2×Dic7⋊C4—21no—
89C2×Dic7⋊C4—22no—
90C2×Dic7⋊C4—22no—
91C2×Dic7⋊C4D412yes—
92C2×C4×Dic7—21no—
93C2×C4×Dic7—22no—
94C2×C4×Dic7—22no—
95C2×C4×Dic7C2312yes—
96C22×C7⋊C8C2312yes—
97C2×#1132—24no—
98C2×#1132C2314yes—
99#6461—216no—
100#6460—28no—
101#6455—28no—
102#6451—28no—
103#6451—24no—
104#6451C2318yes—
105#6450—28no—
106#6450—24no—
107#6450C2318yes—
108C4×D28—22no—
109C4×D28C2314yes—
110C4×Dic14—22no—
111C4×Dic14D414yes—
112C4×Dic14C2314yes—
113C4×Dic14C2314yes—
114C7×#103C2318yes—
115C7×#103C2318yes—
116C4×C7×C8C2314yes—
117#6409C2318yes—
118#6395C2314yes—
119#6391C2314yes—
120#6390C2314yes—
121#6389C2318yes—
122Dic7⋊C8C2318yes—
123#6383C2318yes—
124#6382C2318yes—
125C4⋊(C7⋊C8)C2314yes—
126C2×Q82—71no—
127C2×#556—71no—
128#3369—716no—
129C2×#489—72no—
130C2×#487D711yescharacteristic, complemented
131C2×#475—72no—
132C2×#476—71no—
133C2×#464—72no—
134C2×#462—71no—
135C2×#446—71no—
136C2×#441—72no—
137C2×C4×SD16—71no—
138C23×D7—21no—
139C2×C7×Q8—22no—
140C2×C7×Q8—24no—
141C2×C7×Q8—24no—
142C2×C7×Q8—24no—
143C2×C7×Q8—82no—
144C2×C7×Q8C2414yes—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7C2×D411yescharacteristic
148C22×C4×C7C2×D411yescharacteristic
149C22×C4×C7C2411yescharacteristic
150C22×Dic7—21no—
151C22×Dic7—21no—
152C22×Dic7—21no—
153C22×Dic7C2×D412yes—
154C22×Dic7C2×D412yes—
155C2×D28—22no—
156C2×D28—22no—
157C2×D28—21no—
158C2×D28C2412yes—
159C2×C4×D7—24no—
160C2×C4×D7—44no—
161C2×Dic14—24no—
162C2×Dic14—21no—
163C2×Dic14—22no—
164C2×Dic14—28no—
165C2×Dic14—84no—
166C2×Dic14C2×D414yes—
167C2×Dic14#4114yes—
168C2×Dic14C2412yes—
169C2×C7×C8—22no—
170C2×C7×C8—22no—
171C2×C7×C8C2412yes—
172C2×C7×C8C2412yes—
173C7×C4⋊C4—24no—
174C7×C4⋊C4—22no—
175C7×C4⋊C4—24no—
176C7×C4⋊C4—24no—
177C7×C4⋊C4C2414yes—
178C42×C7C2×D412yes—
179C42×C7C2412yes—
180#1144—216no—
181(C2×D7)⋊C4—24no—
182(C2×D7)⋊C4—28no—
183(C2×D7)⋊C4—28no—
184C4⋊Dic7—21no—
185C4⋊Dic7—21no—
186C4⋊Dic7—28no—
187C4⋊Dic7C2×D414yes—
188C4⋊Dic7C2412yes—
189C4⋊Dic7C2412yes—
190Dic7⋊C4—24no—
191Dic7⋊C4—28no—
192Dic7⋊C4—28no—
193Dic7⋊C4C2×D418yes—
194C4×Dic7—24no—
195C4×Dic7—28no—
196C4×Dic7—28no—
197C4×Dic7C2×D414yes—
198C4×Dic7C2414yes—
199C2×C7⋊C8—24no—
200C2×C7⋊C8C2414yes—
201#1132—28no—
202C22×Q16—72no—
203C22×SD16—71no—
204Q82—78no—
205Q82—144no—
206#556—78no—
207#556—144no—
208C2×C4⋊Q8—72no—
209C2×C4⋊Q8—141no—
210C2×C4⋊Q8—142no—
211C2×C4⋊Q8C2×D711yescharacteristic
212C2×C4⋊Q8C2×D711yescharacteristic
213C2×#126—142no—
214C2×#124—72no—
215C2×C22⋊Q8—141no—
216C2×C4×Q8—71no—
217C2×C4×Q8—72no—
218C2×C4×Q8—72no—
219C2×C4×Q8—71no—
220C2×C4×Q8—141no—
221C2×C4×D4—71no—
222C2×#117—141no—
223#489—716no—
224#487C2×D718yescomplemented
225#476—78no—
226#475—716no—
227#464—716no—
228#462—78no—
229#446—78no—
230#441—716no—
231C4×SD16—78no—
232C2×#106—71no—
233C2×#106—72no—
234C2×C4⋊C8—72no—
235C2×C4⋊C8—71no—
236C2×#103—72no—
237C2×#103—71no—
238C2×#103C2×D712yes—
239C2×#103C2×D712yes—
240C2×#102—71no—
241C2×#102—72no—
242C2×#97—72no—
243C2×C4×C8C2×D711yescharacteristic
244C23×C7C22×D411yescharacteristic
245C22×D7—22no—
246C22×D7—42no—
247C22×D7—42no—
248C22×D7—42no—
249C7×Q8—24no—
250C7×Q8—24no—
251C7×Q8—44no—
252C7×Q8—84no—
253C2×C4×C7—22no—
254C2×C4×C7—24no—
255C2×C4×C7—24no—
256C2×C4×C7—44no—
257C2×C4×C7—44no—
258C2×C4×C7#13714yes—
259C2×C4×C7C22×D412yes—
260C2×C4×C7C22×D411yescharacteristic
261C2×C4×C7C22×D412yes—
262C2×C4×C7C2×#4112yes—
263C2×C4×C72−1+412yes—
264C2×C4×C7C2511yescharacteristic
265C2×Dic7—24no—
266C2×Dic7—24no—
267C2×Dic7—24no—
268C2×Dic7—22no—
269C2×Dic7—22no—
270C2×Dic7—22no—
271C2×Dic7—42no—
272C2×Dic7—42no—
273C2×Dic7C22×D414yes—
274C2×Dic7C22×D414yes—
275D28—22no—
276D28—22no—
277D28—42no—
278C4×D7—48no—
279Dic14—24no—
280Dic14—28no—
281Dic14—22no—
282Dic14—88no—
283Dic14C2×#4114yes—
284C7×C8—22no—
285C7×C8—22no—
286C7⋊C8—24no—
287C22×Q8—21no—
288C22×Q8—71no—
289C22×Q8—71no—
290C22×Q8—142no—
291C22×Q8C22×D712yes—
292C22×D4—71no—
293C23×C4—141no—
294C2×Q16—78no—
295C2×Q16—148no—
296C2×SD16—74no—
297C2×SD16—144no—
298C22×C8—72no—
299C22×C8C22×D711yescharacteristic
300C22×C8C22×D711yescharacteristic
301C4⋊Q8—22no—
302C4⋊Q8—22no—
303C4⋊Q8—78no—
304C4⋊Q8—144no—
305C4⋊Q8—148no—
306C4⋊Q8—1416no—
307C4⋊Q8C22×D714yes—
308C4⋊Q8C22×D714yes—
309#126—1416no—
310#124—78no—
311#124—144no—
312C22⋊Q8—148no—
313C4×Q8—74no—
314C4×Q8—74no—
315C4×Q8—78no—
316C4×Q8—78no—
317C4×Q8—74no—
318C4×Q8—144no—
319C4×Q8—144no—
320C4×Q8—148no—
321C4×Q8—142no—
322C4×D4—74no—
323C4×D4—142no—
324#117—148no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—71no—
329C2×C4⋊C4—72no—
330C2×C4⋊C4—71no—
331C2×C4⋊C4—71no—
332C2×C4⋊C4—142no—
333C2×C4⋊C4—142no—
334C2×C4⋊C4—142no—
335C2×C4⋊C4—141no—
336C2×C4⋊C4C22×D712yes—
337C2×C22⋊C4—142no—
338C2×C22⋊C4—142no—
339C2×C22⋊C4—141no—
340C2×C42—72no—
341C2×C42—142no—
342C2×C42—142no—
343C2×C42—141no—
344C2×C42C22×D711yescharacteristic
345#106—74no—
346#106—78no—
347C4⋊C8—78no—
348C4⋊C8—74no—
349#103—78no—
350#103—74no—
351#103C22×D718yes—
352#103C22×D718yes—
353#102—74no—
354#102—78no—
355#97—78no—
356C4×C8C22×D714yes—
357C22×C7#54812yes—
358C22×C7C2×#13712yes—
359C22×C7#57712yes—
360C22×C7C23×D411yescharacteristic
361C2×D7—42no—
362C2×D7—42no—
363C2×D7—42no—
364C2×D7—84no—
365C4×C7—22no—
366C4×C7—44no—
367C4×C7—44no—
368C4×C7#54812yes—
369C4×C7C2×#13714yes—
370C4×C7C22×#4111yescharacteristic
371C4×C7C2×2−1+411yescharacteristic
372Dic7—24no—
373Dic7—24no—
374Dic7—24no—
375Dic7—42no—
376Dic7—42no—
377C24—141no—
378C2×Q8—22no—
379C2×Q8—24no—
380C2×Q8—24no—
381C2×Q8—24no—
382C2×Q8—74no—
383C2×Q8—74no—
384C2×Q8—72no—
385C2×Q8—82no—
386C2×Q8—148no—
387C2×Q8—144no—
388C2×Q8—141no—
389C2×Q8—142no—
390C2×Q8—564no—
391C2×Q8C23×D714yes—
392C2×D4—72no—
393C2×D4—141no—
394C2×D4—142no—
395C2×D4—142no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—72no—
399C22×C4—72no—
400C22×C4—141no—
401C22×C4—141no—
402C22×C4—141no—
403C22×C4—144no—
404C22×C4—284no—
405C22×C4D4×D711yescharacteristic
406C22×C4D4×D711yescharacteristic
407C22×C4C23×D711yescharacteristic
408Q16—1416no—
409SD16—148no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—74no—
413C2×C8—144no—
414C2×C8C23×D712yes—
415C2×C8C23×D712yes—
416C4⋊C4—24no—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—22no—
420C4⋊C4—78no—
421C4⋊C4—74no—
422C4⋊C4—72no—
423C4⋊C4—72no—
424C4⋊C4—148no—
425C4⋊C4—148no—
426C4⋊C4—148no—
427C4⋊C4—144no—
428C4⋊C4—141no—
429C4⋊C4—141no—
430C4⋊C4C23×D714yes—
431C22⋊C4—148no—
432C22⋊C4—148no—
433C22⋊C4—144no—
434C42—74no—
435C42—74no—
436C42—148no—
437C42—148no—
438C42—144no—
439C42D4×D712yes—
440C42C23×D712yes—
441C2×C7#336914yescomplemented
442C2×C7C2×#54811yescharacteristic
443C2×C7C22×#13711yescharacteristic
444C2×C7C2×#57711yescharacteristic
445D7—82no—
446C23—142no—
447C23—282no—
448C23—282no—
449C23—282no—
450C23C2×D4×D711yescharacteristic
451Q8—24no—
452Q8—24no—
453Q8—44no—
454Q8—74no—
455Q8—84no—
456Q8—144no—
457Q8—148no—
458Q8—142no—
459Q8—568no—
460D4—142no—
461D4—142no—
462D4—282no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—44no—
467C2×C4—44no—
468C2×C4—74no—
469C2×C4—74no—
470C2×C4—144no—
471C2×C4—144no—
472C2×C4—144no—
473C2×C4—142no—
474C2×C4—142no—
475C2×C4—142no—
476C2×C4—282no—
477C2×C4—282no—
478C2×C4—288no—
479C2×C4#648114yes—
480C2×C4C2×D4×D712yes—
481C2×C4C2×D4×D711yescharacteristic
482C2×C4C2×D4×D712yes—
483C2×C4D7×#4112yes—
484C2×C4#655412yes—
485C2×C4C24×D711yescharacteristic
486C8—22no—
487C8—22no—
488C8—144no—
489C7C2×#336911yescharacteristic, complemented, Sylow
490C22—282no—
491C22—282no—
492C22—282no—
493C22—564no—
494C22#9036812yes—
495C22#9045312yes—
496C22C2×#648112yes—
497C22C22×D4×D711yescharacteristic
498C4—22no—
499C4—44no—
500C4—44no—
501C4—144no—
502C4—144no—
503C4—144no—
504C4—282no—
505C4—282no—
506C4#9036812yes—
507C4C2×#648114yes—
508C4C2×D7×#4111yescharacteristic
509C4C2×#655411yescharacteristic
510C2—562no—
511C2#1173907114yesdirect product factor
512C2C2×#9036811yescharacteristic
513C2C2×#9045311yescharacteristic
514C2C22×#648111yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#487C2
socleC23×C7C22×D4
prime radicalC22×D28C23
hypercenterC2×#487D7
hypocenterC7C2×#3369
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
1. C2×#90413C2semidirect
3. C2×C7×#487C2semidirect
4. C2×#89862C2semidirect
6. #11739071C2direct (N × H)
9. C2×#89563C2semidirect
10. C2×#89561C2semidirect
12. C2×#89451C2semidirect
23. #90413C22semidirect
34. C7×#487C22semidirect
44. #89862C22semidirect
51. #89563C22semidirect
52. #89561C22semidirect
54. #89451C22semidirect
130. C2×#487D7semidirect
224. #487C2×D7semidirect
441. C2×C7#3369semidirect
489. C7C2×#3369semidirect
511. C2#11739071direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904132
C2×#904232
C2×C7×#4872
C2×#898622
C2×#898562
#117390712
C2×#895702
C2×#895672
C2×#895632
C2×#895612
C2×C4×#11322
C2×#894512
C2×#33697