Finite Group Databasebeta

← C2×#11738584 #14233530

Subgroups — C2×#11738584 #14233530

Order 1792.

1906 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90413C211yesmaximal, characteristic, complemented
2C2×#90276C211yesmaximal, characteristic
3C2×C7×#477C211yesmaximal, characteristic, complemented
4C2×#89860C211yesmaximal, characteristic
5C2×C4×#1144C211yesmaximal, characteristic, complemented
6#11738584C2116yesmaximal, direct product factor
7C2×#89662C212yesmaximal, complemented
8C2×#89661C212yesmaximal, complemented
9C2×#89620C211yesmaximal, characteristic
10C2×#89603C211yesmaximal, characteristic, complemented
11C2×#89570C212yesmaximal, complemented
12C2×#89567C212yesmaximal, complemented
13C2×C7×C4⋊Q8C2211yescharacteristic
14C2×C4×C7×Q8C2211yescharacteristic
15C2×#6510C2212yes—
16C2×#6507—22no—
17C22×#1144C2211yescharacteristic
18C22×#1132C2212yes—
19#90413—24no—
20#90413C2218yescomplemented
21#90276—24no—
22#90276C2218yes—
23C2×#6457—22no—
24C2×#6456C2212yes—
25C2×#6451—21no—
26C2×#6451C2212yes—
27C2×#6450—21no—
28C2×#6450C2212yes—
29C2×#6438—21no—
30C2×#6437C2211yescharacteristic
31C2×C4×D28—21no—
32C2×C4×Dic14C2211yescharacteristic
33C2×C4×Dic14C2211yescharacteristic
34C7×#477C2218yescomplemented
35C2×C7×#107C2212yes—
36C2×C7×C4⋊C8C2211yescharacteristic
37C2×C7×#103C2212yes—
38C2×#6409C2211yescharacteristic
39C2×#6395C2212yes—
40C2×#6389C2212yes—
41C2×Dic7⋊C8C2212yes—
42#89860C2218yes—
43C4×#1144C2218yescomplemented
44C2×#6384C2211yescharacteristic
45C2×#6383C2212yes—
46C2×#6383C2212yes—
47C2×#6381C2211yescharacteristic
48C2×C4×C7⋊C8C2211yescharacteristic
49#89662C22116yescomplemented
50#89661C22116yescomplemented
51#89620C2218yes—
52#89603C2218yescomplemented
53#89570C22116yescomplemented
54#89567C22116yescomplemented
55C2×#3375—71nomaximal, Sylow
56C22×C7×Q8—21no—
57C22×C7×Q8C2311yescharacteristic
58C22×D28—21no—
59C22×D28—21no—
60C22×D28C2312yes—
61C22×C4×D7—22no—
62C22×Dic14—22no—
63C22×Dic14D411yescharacteristic
64C22×Dic14C2311yescharacteristic
65C22×C7×C8C2312yes—
66C7×C4⋊Q8—22no—
67C7×C4⋊Q8C2314yes—
68C4×C7×Q8—22no—
69C4×C7×Q8C2314yes—
70C2×C7×C4⋊C4—21no—
71C2×C7×C4⋊C4—21no—
72C2×C7×C4⋊C4C2312yes—
73C2×C7×C4⋊C4C2311yescharacteristic
74C2×C42×C7—21no—
75C2×C42×C7C2311yescharacteristic
76#6510—24no—
77#6510C2318yes—
78#6507—216no—
79C2×#1144—24no—
80C2×#1144C2314yes—
81C2×(C2×D7)⋊C4—22no—
82C2×(C2×D7)⋊C4—22no—
83C2×(C2×D7)⋊C4—22no—
84C2×C4⋊Dic7D411yescharacteristic
85C2×C4⋊Dic7C2311yescharacteristic
86C2×Dic7⋊C4—21no—
87C2×Dic7⋊C4—22no—
88C2×Dic7⋊C4—22no—
89C2×Dic7⋊C4D412yes—
90C2×C4×Dic7—21no—
91C2×C4×Dic7—22no—
92C2×C4×Dic7C2312yes—
93C22×C7⋊C8C2311yescharacteristic
94C22×C7⋊C8C2311yescharacteristic
95C2×#1132—28no—
96C2×#1132C2318yes—
97#6457—216no—
98#6456—24no—
99#6456C2318yes—
100#6451—28no—
101#6451—24no—
102#6451C2318yes—
103#6450—28no—
104#6450—24no—
105#6450C2318yes—
106#6438—28no—
107#6437—22no—
108#6437C2314yes—
109C4×D28—28no—
110C4×Dic14—22no—
111C4×Dic14D414yes—
112C4×Dic14C2314yes—
113C4×Dic14C2314yes—
114C7×#107C2318yes—
115C7×C4⋊C8C2314yes—
116C7×#103C2318yes—
117#6409C2314yes—
118#6395C2318yes—
119#6389C2318yes—
120Dic7⋊C8C2318yes—
121#6384C2314yes—
122#6383C2318yes—
123#6383C2318yes—
124#6381C2314yes—
125C4×C7⋊C8C2314yes—
126C2×#559—71no—
127C2×Q82—71no—
128#3375—716no—
129C2×#489—72no—
130C2×#486—71no—
131C2×#477D711yescharacteristic, complemented
132C2×#474—72no—
133C2×#464—72no—
134C2×#460—71no—
135C2×#446—71no—
136C2×#440—72no—
137C2×C4×Q16—71no—
138C23×D7—22no—
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—22no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7C2×D411yescharacteristic
149C22×C4×C7C2×D411yescharacteristic
150C22×C4×C7C2411yescharacteristic
151C22×Dic7—21no—
152C22×Dic7—21no—
153C22×Dic7C2×D412yes—
154C22×Dic7C2×D412yes—
155C2×D28—24no—
156C2×D28—24no—
157C2×D28—24no—
158C2×D28—22no—
159C2×D28—24no—
160C2×D28—44no—
161C2×D28—82no—
162C2×D28C2414yes—
163C2×C4×D7—28no—
164C2×C4×D7—84no—
165C2×Dic14—24no—
166C2×Dic14—21no—
167C2×Dic14—22no—
168C2×Dic14—28no—
169C2×Dic14—84no—
170C2×Dic14C2×D414yes—
171C2×Dic14#4114yes—
172C2×Dic14C2412yes—
173C2×C7×C8—24no—
174C2×C7×C8C2414yes—
175C7×C4⋊C4—24no—
176C7×C4⋊C4—22no—
177C7×C4⋊C4—21no—
178C7×C4⋊C4—24no—
179C7×C4⋊C4C2414yes—
180C7×C4⋊C4C2412yes—
181C42×C7—24no—
182C42×C7C2×D412yes—
183C42×C7C2412yes—
184#1144—28no—
185(C2×D7)⋊C4—28no—
186(C2×D7)⋊C4—28no—
187(C2×D7)⋊C4—28no—
188C4⋊Dic7—21no—
189C4⋊Dic7C2×D414yes—
190C4⋊Dic7C2412yes—
191Dic7⋊C4—24no—
192Dic7⋊C4—28no—
193Dic7⋊C4—28no—
194Dic7⋊C4C2×D418yes—
195C4×Dic7—24no—
196C4×Dic7—28no—
197C4×Dic7C2×D414yes—
198C4×Dic7C2414yes—
199C2×C7⋊C8—22no—
200C2×C7⋊C8—22no—
201C2×C7⋊C8C2412yes—
202C2×C7⋊C8C2412yes—
203#1132—216no—
204C22×Q16—71no—
205C22×SD16—72no—
206#559—78no—
207#559—144no—
208Q82—78no—
209Q82—144no—
210C2×C4⋊Q8—72no—
211C2×C4⋊Q8—141no—
212C2×C4⋊Q8—142no—
213C2×C4⋊Q8C2×D711yescharacteristic
214C2×#127—71no—
215C2×#124—72no—
216C2×#124—141no—
217C2×#123—142no—
218C2×C4×Q8—71no—
219C2×C4×Q8—72no—
220C2×C4×Q8—71no—
221C2×C4×Q8—141no—
222C2×C4×Q8C2×D711yescharacteristic
223C2×C4×D4—72no—
224C2×C4×D4—141no—
225#489—716no—
226#486—78no—
227#477C2×D718yescomplemented
228#474—716no—
229#464—716no—
230#460—78no—
231#446—78no—
232#440—716no—
233C4×Q16—78no—
234C2×#107—71no—
235C2×#107C2×D712yes—
236C2×C4⋊C8—72no—
237C2×C4⋊C8C2×D711yescharacteristic
238C2×#103—71no—
239C2×#103—71no—
240C2×#103C2×D712yes—
241C2×#102—72no—
242C2×#102—72no—
243C2×#102—72no—
244C2×#97—72no—
245C2×C4×C8—71no—
246C23×C7C22×D411yescharacteristic
247C22×D7—24no—
248C22×D7—44no—
249C22×D7—44no—
250C22×D7—44no—
251C7×Q8—22no—
252C7×Q8—22no—
253C7×Q8—42no—
254C7×Q8—84no—
255C2×C4×C7—22no—
256C2×C4×C7—24no—
257C2×C4×C7—22no—
258C2×C4×C7—22no—
259C2×C4×C7—42no—
260C2×C4×C7—44no—
261C2×C4×C7—42no—
262C2×C4×C7#13714yes—
263C2×C4×C7C22×D412yes—
264C2×C4×C7C22×D411yescharacteristic
265C2×C4×C7C22×D412yes—
266C2×C4×C7C2×#4112yes—
267C2×C4×C72−1+412yes—
268C2×C4×C7C2511yescharacteristic
269C2×Dic7—24no—
270C2×Dic7—24no—
271C2×Dic7—24no—
272C2×Dic7—22no—
273C2×Dic7—22no—
274C2×Dic7—42no—
275C2×Dic7C22×D414yes—
276C2×Dic7C22×D414yes—
277D28—24no—
278D28—24no—
279D28—44no—
280D28—48no—
281D28—84no—
282C4×D7—88no—
283Dic14—24no—
284Dic14—28no—
285Dic14—22no—
286Dic14—88no—
287Dic14C2×#4114yes—
288C7×C8—24no—
289C7⋊C8—22no—
290C7⋊C8—22no—
291C22×Q8—21no—
292C22×Q8—71no—
293C22×Q8—71no—
294C22×Q8—142no—
295C22×Q8C22×D711yescharacteristic
296C22×D4—72no—
297C22×D4—141no—
298C22×D4—141no—
299C23×C4—142no—
300C2×Q16—74no—
301C2×Q16—144no—
302C2×SD16—78no—
303C2×SD16—148no—
304C22×C8—71no—
305C22×C8—71no—
306C22×C8C22×D712yes—
307C4⋊Q8—22no—
308C4⋊Q8—78no—
309C4⋊Q8—144no—
310C4⋊Q8—148no—
311C4⋊Q8—1416no—
312C4⋊Q8C22×D714yes—
313#127—74no—
314#127—142no—
315#124—78no—
316#124—148no—
317#124—144no—
318#123—1416no—
319C4×Q8—22no—
320C4×Q8—74no—
321C4×Q8—74no—
322C4×Q8—78no—
323C4×Q8—74no—
324C4×Q8—144no—
325C4×Q8—148no—
326C4×Q8—142no—
327C4×Q8C22×D714yes—
328C4×D4—78no—
329C4×D4—148no—
330C4×D4—144no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—71no—
334C2×C4⋊C4—72no—
335C2×C4⋊C4—71no—
336C2×C4⋊C4—142no—
337C2×C4⋊C4—142no—
338C2×C4⋊C4—141no—
339C2×C4⋊C4C22×D711yescharacteristic
340C2×C4⋊C4C22×D712yes—
341C2×C22⋊C4—142no—
342C2×C22⋊C4—142no—
343C2×C22⋊C4—142no—
344C2×C42—21no—
345C2×C42—72no—
346C2×C42—142no—
347C2×C42—141no—
348C2×C42C22×D711yescharacteristic
349#107—74no—
350#107C22×D718yes—
351C4⋊C8—78no—
352C4⋊C8C22×D714yes—
353#103—74no—
354#103—74no—
355#103C22×D718yes—
356#102—78no—
357#102—78no—
358#102—78no—
359#97—78no—
360C4×C8—74no—
361C22×C7#54812yes—
362C22×C7C2×#13712yes—
363C22×C7#57612yes—
364C22×C7C23×D411yescharacteristic
365C2×D7—44no—
366C2×D7—44no—
367C2×D7—44no—
368C2×D7—88no—
369C4×C7—22no—
370C4×C7—42no—
371C4×C7—44no—
372C4×C7—42no—
373C4×C7#54812yes—
374C4×C7C2×#13714yes—
375C4×C7C22×#4111yescharacteristic
376C4×C7C2×2−1+411yescharacteristic
377Dic7—24no—
378Dic7—24no—
379Dic7—24no—
380Dic7—42no—
381C24—142no—
382C2×Q8—21no—
383C2×Q8—24no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—74no—
387C2×Q8—74no—
388C2×Q8—72no—
389C2×Q8—82no—
390C2×Q8—148no—
391C2×Q8—144no—
392C2×Q8—141no—
393C2×Q8—142no—
394C2×Q8—564no—
395C2×Q8C23×D712yes—
396C2×D4—74no—
397C2×D4—144no—
398C2×D4—142no—
399C2×D4—144no—
400C2×D4—144no—
401C2×D4—144no—
402C2×D4—284no—
403C2×D4—562no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—72no—
408C22×C4—72no—
409C22×C4—148no—
410C22×C4—141no—
411C22×C4—141no—
412C22×C4—564no—
413C22×C4D4×D711yescharacteristic
414C22×C4D4×D711yescharacteristic
415C22×C4C23×D711yescharacteristic
416Q16—148no—
417SD16—1416no—
418C2×C8—24no—
419C2×C8—72no—
420C2×C8—72no—
421C2×C8—142no—
422C2×C8—142no—
423C2×C8C23×D714yes—
424C4⋊C4—24no—
425C4⋊C4—24no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—78no—
429C4⋊C4—74no—
430C4⋊C4—72no—
431C4⋊C4—148no—
432C4⋊C4—148no—
433C4⋊C4—144no—
434C4⋊C4—141no—
435C4⋊C4C23×D714yes—
436C4⋊C4C23×D712yes—
437C22⋊C4—148no—
438C22⋊C4—148no—
439C22⋊C4—148no—
440C42—24no—
441C42—74no—
442C42—74no—
443C42—148no—
444C42—144no—
445C42D4×D712yes—
446C42C23×D712yes—
447C2×C7#337514yescomplemented
448C2×C7C2×#54811yescharacteristic
449C2×C7C22×#13711yescharacteristic
450C2×C7C2×#57611yescharacteristic
451D7—84no—
452C23—144no—
453C23—284no—
454C23—284no—
455C23—284no—
456C23C2×D4×D711yescharacteristic
457Q8—22no—
458Q8—22no—
459Q8—42no—
460Q8—74no—
461Q8—84no—
462Q8—148no—
463Q8—144no—
464Q8—142no—
465Q8—568no—
466D4—144no—
467D4—144no—
468D4—288no—
469D4—284no—
470D4—564no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—42no—
476C2×C4—44no—
477C2×C4—42no—
478C2×C4—74no—
479C2×C4—74no—
480C2×C4—144no—
481C2×C4—144no—
482C2×C4—144no—
483C2×C4—142no—
484C2×C4—142no—
485C2×C4—282no—
486C2×C4—568no—
487C2×C4#648114yes—
488C2×C4C2×D4×D712yes—
489C2×C4C2×D4×D712yes—
490C2×C4C2×D4×D711yescharacteristic
491C2×C4#655112yes—
492C2×C4D7×#4112yes—
493C2×C4C24×D711yescharacteristic
494C8—24no—
495C8—142no—
496C8—142no—
497C7C2×#337511yescharacteristic, complemented, Sylow
498C22—284no—
499C22—284no—
500C22—284no—
501C22—568no—
502C22#9032412yes—
503C22C2×#648112yes—
504C22#9046512yes—
505C22C22×D4×D711yescharacteristic
506C4—22no—
507C4—42no—
508C4—44no—
509C4—42no—
510C4—144no—
511C4—144no—
512C4—144no—
513C4—282no—
514C4#9032412yes—
515C4C2×#648114yes—
516C4C2×#655111yescharacteristic
517C4C2×D7×#4111yescharacteristic
518C2—564no—
519C2#1173858414yesdirect product factor
520C2C2×#9032411yescharacteristic
521C2C22×#648111yescharacteristic
522C2C2×#9046511yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#477C2
socleC23×C7C22×D4
prime radicalC2×#6437C22
hypercenterC2×#477D7
hypocenterC7C2×#3375
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
1. C2×#90413C2semidirect
3. C2×C7×#477C2semidirect
5. C2×C4×#1144C2semidirect
6. #11738584C2direct (N × H)
7. C2×#89662C2semidirect
8. C2×#89661C2semidirect
10. C2×#89603C2semidirect
11. C2×#89570C2semidirect
12. C2×#89567C2semidirect
20. #90413C22semidirect
34. C7×#477C22semidirect
43. C4×#1144C22semidirect
49. #89662C22semidirect
50. #89661C22semidirect
52. #89603C22semidirect
53. #89570C22semidirect
54. #89567C22semidirect
131. C2×#477D7semidirect
227. #477C2×D7semidirect
447. C2×C7#3375semidirect
497. C7C2×#3375semidirect
519. C2#11738584direct (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×#902762
C2×C7×#4772
C2×#898602
C2×C4×#11442
#117385842
C2×#896622
C2×#896612
C2×#896202
C2×#896032
C2×#895702
C2×#895672
C2×#33757