Finite Group Databasebeta

← C2×#11737860 #14233372

Subgroups — C2×#11737860 #14233372

Order 1792.

1906 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90423C211yesmaximal, characteristic, complemented
2C2×#90234C211yesmaximal, characteristic, complemented
3C2×C7×#461C211yesmaximal, characteristic, complemented
4C2×#89937C212yesmaximal
5C2×SD16×Dic7C212yesmaximal, complemented
6C2×#89853C211yesmaximal, characteristic, complemented
7C2×C4×#1141C211yesmaximal, characteristic
8#11737860C2116yesmaximal, direct product factor
9C2×#89614C211yesmaximal, characteristic, complemented
10C2×#89602C211yesmaximal, characteristic, complemented
11C2×#89572C212yesmaximal, complemented
12C2×#89571C212yesmaximal, complemented
13C22×C7×SD16C2212yes—
14C2×C7×C4⋊Q8C2211yescharacteristic
15C2×C4×C7×D4C2211yescharacteristic
16C2×#6510C2212yes—
17C2×Q8×Dic7C2212yes—
18C2×D4×Dic7C2212yes—
19C22×#1141C2211yescharacteristic
20C22×C4⋊Dic7—21no—
21C2×#6487—21no—
22#90423—24no—
23#90423C2218yescomplemented
24#90234—24no—
25#90234C2218yescomplemented
26C2×#6461—22no—
27C2×#6460—21no—
28C2×#6455—21no—
29C2×#6453C2212yes—
30C2×#6441—22no—
31C2×C4×D28C2211yescharacteristic
32C2×#6432C2211yescharacteristic
33C2×C4×Dic14C2211yescharacteristic
34C7×#461C2218yescomplemented
35C2×C7×C4⋊C8C2211yescharacteristic
36C2×C7×#103C2212yes—
37C2×#6409C2212yes—
38C2×#6409C2212yes—
39C2×#6406C2211yescharacteristic
40#89937C22116yes—
41SD16×Dic7C22116yescomplemented
42C2×#6395C2212yes—
43C2×#6391C2212yes—
44C2×Dic7⋊C8C2212yes—
45C2×C8×Dic7C2212yes—
46#89853C2218yescomplemented
47C4×#1141C2218yes—
48C2×#6383C2211yescharacteristic
49C2×#6381C2211yescharacteristic
50C2×C4×C7⋊C8C2211yescharacteristic
51#89614C2218yescomplemented
52#89602C2218yescomplemented
53#89572C22116yescomplemented
54#89571C22116yescomplemented
55C2×#3360—71nomaximal, Sylow
56C22×C7×Q8C2312yes—
57C22×C7×D4C2311yescharacteristic
58C23×C4×C7—21no—
59C23×Dic7—22no—
60C22×D28C2311yescharacteristic
61C22×C4×D7—21no—
62C22×Dic14—21no—
63C22×Dic14D411yescharacteristic
64C2×C7×SD16—28no—
65C2×C7×SD16C2318yes—
66C22×C7×C8C2312yes—
67C7×C4⋊Q8—22no—
68C7×C4⋊Q8C2314yes—
69C4×C7×D4—22no—
70C4×C7×D4C2314yes—
71C2×C7×C4⋊C4—21no—
72C2×C7×C4⋊C4—21no—
73C2×C7×C4⋊C4C2311yescharacteristic
74C2×C7×C22⋊C4—21no—
75C2×C42×C7C2311yescharacteristic
76C2×C22⋊Dic7—22no—
77#6510—24no—
78#6510C2318yes—
79Q8×Dic7—24no—
80Q8×Dic7C2318yes—
81D4×Dic7—24no—
82D4×Dic7C2318yes—
83C2×#1141—24no—
84C2×#1141C2314yes—
85C2×(C2×D7)⋊C4—21no—
86C2×(C2×D7)⋊C4—22no—
87C2×(C2×D7)⋊C4—22no—
88C2×C4⋊Dic7—21no—
89C2×C4⋊Dic7—22no—
90C2×C4⋊Dic7—22no—
91C2×C4⋊Dic7—28no—
92C2×C4⋊Dic7D411yescharacteristic
93C2×C4⋊Dic7C2311yescharacteristic
94C2×C4⋊Dic7C2312yes—
95#6487—28no—
96C2×Dic7⋊C4—22no—
97C2×Dic7⋊C4D412yes—
98C2×C4×Dic7—22no—
99C2×C4×Dic7C2312yes—
100C22×C7⋊C8C2311yescharacteristic
101C22×C7⋊C8C2311yescharacteristic
102#6461—216no—
103#6460—28no—
104#6455—28no—
105#6453—24no—
106#6453C2318yes—
107#6441—216no—
108C4×D28—22no—
109C4×D28C2314yes—
110#6432—22no—
111#6432C2314yes—
112C4×Dic14D414yes—
113C4×Dic14C2314yes—
114C7×C4⋊C8C2314yes—
115C7×#103C2318yes—
116#6409C2318yes—
117#6409C2318yes—
118#6406C2314yes—
119#6395C2318yes—
120#6391C2318yes—
121Dic7⋊C8C2318yes—
122C8×Dic7C2318yes—
123#6383C2314yes—
124#6381C2314yes—
125C4×C7⋊C8C2314yes—
126C2×#556—71no—
127C2×#554—71no—
128#3360—716no—
129C2×#488—72no—
130C2×#487—71no—
131C2×#479—72no—
132C2×#476—71no—
133C2×#463—72no—
134C2×#461D711yescharacteristic, complemented
135C2×C8×Q8—71no—
136C2×C4×SD16—72no—
137C2×C4×D8—71no—
138C24×C7—21no—
139C23×D7—21no—
140C2×C7×Q8—22no—
141C2×C7×Q8—24no—
142C2×C7×Q8—24no—
143C2×C7×Q8C2414yes—
144C2×C7×D4—21no—
145C2×C7×D4—22no—
146C2×C7×D4#4114yes—
147C2×C7×D4C2412yes—
148C22×C4×C7—22no—
149C22×C4×C7—21no—
150C22×C4×C7—24no—
151C22×C4×C7—44no—
152C22×C4×C7C2×D411yescharacteristic
153C22×C4×C7C2×D411yescharacteristic
154C22×C4×C7C2411yescharacteristic
155C22×Dic7—21no—
156C22×Dic7—22no—
157C22×Dic7—28no—
158C22×Dic7—84no—
159C22×Dic7C2×D412yes—
160C22×Dic7C2×D412yes—
161C2×D28—22no—
162C2×D28—22no—
163C2×D28—21no—
164C2×D28C2412yes—
165C2×C4×D7—24no—
166C2×C4×D7—44no—
167C2×Dic14—24no—
168C2×Dic14—24no—
169C2×Dic14—82no—
170C2×Dic14C2×D414yes—
171C7×SD16—216no—
172C2×C7×C8—24no—
173C2×C7×C8C2414yes—
174C7×C4⋊C4—21no—
175C7×C4⋊C4—24no—
176C7×C4⋊C4—24no—
177C7×C4⋊C4C2412yes—
178C7×C22⋊C4—24no—
179C42×C7C2×D412yes—
180C42×C7C2412yes—
181C22⋊Dic7—28no—
182#1141—28no—
183(C2×D7)⋊C4—24no—
184(C2×D7)⋊C4—28no—
185(C2×D7)⋊C4—28no—
186C4⋊Dic7—22no—
187C4⋊Dic7—24no—
188C4⋊Dic7—21no—
189C4⋊Dic7—28no—
190C4⋊Dic7—28no—
191C4⋊Dic7C2×D414yes—
192C4⋊Dic7C2412yes—
193C4⋊Dic7C2414yes—
194Dic7⋊C4—28no—
195Dic7⋊C4C2×D418yes—
196C4×Dic7—28no—
197C4×Dic7C2×D414yes—
198C4×Dic7C2414yes—
199C2×C7⋊C8—22no—
200C2×C7⋊C8—22no—
201C2×C7⋊C8C2412yes—
202C2×C7⋊C8C2412yes—
203C22×SD16C2×D712yes—
204C22×D8—71no—
205#556—78no—
206#556—144no—
207#554—78no—
208#554—144no—
209C2×C4⋊Q8—71no—
210C2×C4⋊Q8C2×D711yescharacteristic
211C2×#126—142no—
212C2×#125—72no—
213C2×#124—72no—
214C2×C22⋊Q8—142no—
215C2×C22⋊Q8—141no—
216C2×C22⋊Q8—141no—
217C2×C4×Q8—71no—
218C2×C4×Q8—72no—
219C2×C4×D4—72no—
220C2×C4×D4—71no—
221C2×C4×D4C2×D711yescharacteristic
222C2×#117—141no—
223C22×C4⋊C4—141no—
224#488—716no—
225#487—78no—
226#479—716no—
227#476—78no—
228#463—716no—
229#461C2×D718yescomplemented
230C8×Q8—78no—
231C4×SD16—716no—
232C4×D8—78no—
233C2×#107—71no—
234C2×#106—72no—
235C2×C4⋊C8—72no—
236C2×C4⋊C8C2×D711yescharacteristic
237C2×#103—72no—
238C2×#103—72no—
239C2×#103C2×D712yes—
240C2×#102—71no—
241C2×#102—72no—
242C2×#102—71no—
243C2×C4×C8—72no—
244C2×C4×C8—71no—
245C23×C7—24no—
246C23×C7—22no—
247C23×C7—42no—
248C23×C7—42no—
249C23×C7C22×D411yescharacteristic
250C22×D7—22no—
251C22×D7—42no—
252C22×D7—42no—
253C22×D7—42no—
254C7×Q8—24no—
255C7×Q8—24no—
256C7×Q8—44no—
257C7×D4—24no—
258C7×D4—22no—
259C7×D4C2×#4114yes—
260C2×C4×C7—22no—
261C2×C4×C7—24no—
262C2×C4×C7—22no—
263C2×C4×C7—44no—
264C2×C4×C7—42no—
265C2×C4×C7—48no—
266C2×C4×C7#13514yes—
267C2×C4×C7C22×D412yes—
268C2×C4×C7C22×D411yescharacteristic
269C2×C4×C7C22×D412yes—
270C2×C4×C7C2×#4112yes—
271C2×C4×C72−1+412yes—
272C2×C4×C7C2511yescharacteristic
273C2×Dic7—24no—
274C2×Dic7—24no—
275C2×Dic7—22no—
276C2×Dic7—24no—
277C2×Dic7—42no—
278C2×Dic7—44no—
279C2×Dic7—88no—
280C2×Dic7C22×D414yes—
281C2×Dic7C22×D414yes—
282D28—22no—
283D28—22no—
284D28—42no—
285C4×D7—48no—
286Dic14—28no—
287Dic14—84no—
288C7×C8—24no—
289C7⋊C8—22no—
290C7⋊C8—22no—
291C22×Q8—71no—
292C22×Q8—141no—
293C22×Q8C22×D712yes—
294C22×D4—71no—
295C22×D4C22×D711yescharacteristic
296C23×C4—21no—
297C23×C4—142no—
298C23×C4—141no—
299C2×SD16—28no—
300C2×SD16C22×D718yes—
301C2×D8—74no—
302C2×D8—144no—
303C22×C8—71no—
304C22×C8—71no—
305C22×C8C22×D712yes—
306C4⋊Q8—22no—
307C4⋊Q8—74no—
308C4⋊Q8—142no—
309C4⋊Q8C22×D714yes—
310#126—1416no—
311#125—78no—
312#125—144no—
313#124—78no—
314#124—144no—
315C22⋊Q8—1416no—
316C22⋊Q8—148no—
317C22⋊Q8—148no—
318C4×Q8—74no—
319C4×Q8—74no—
320C4×Q8—78no—
321C4×Q8—144no—
322C4×D4—22no—
323C4×D4—78no—
324C4×D4—74no—
325C4×D4—144no—
326C4×D4—142no—
327C4×D4C22×D714yes—
328#117—148no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—71no—
332C2×C4⋊C4—72no—
333C2×C4⋊C4—71no—
334C2×C4⋊C4—72no—
335C2×C4⋊C4—148no—
336C2×C4⋊C4—142no—
337C2×C4⋊C4—142no—
338C2×C4⋊C4—142no—
339C2×C4⋊C4—141no—
340C2×C4⋊C4C22×D711yescharacteristic
341C2×C22⋊C4—21no—
342C2×C22⋊C4—142no—
343C2×C22⋊C4—142no—
344C2×C22⋊C4—142no—
345C2×C22⋊C4—141no—
346C2×C42—72no—
347C2×C42—142no—
348C2×C42C22×D711yescharacteristic
349#107—74no—
350#106—78no—
351C4⋊C8—78no—
352C4⋊C8C22×D714yes—
353#103—78no—
354#103—78no—
355#103C22×D718yes—
356#102—74no—
357#102—78no—
358#102—74no—
359C4×C8—78no—
360C4×C8—74no—
361C22×C7—24no—
362C22×C7—48no—
363C22×C7—42no—
364C22×C7—42no—
365C22×C7#54812yes—
366C22×C7C2×#13512yes—
367C22×C7#57712yes—
368C22×C7C23×D411yescharacteristic
369C2×D7—42no—
370C2×D7—42no—
371C2×D7—42no—
372C2×D7—84no—
373C4×C7—22no—
374C4×C7—44no—
375C4×C7—42no—
376C4×C7#54812yes—
377C4×C7C2×#13514yes—
378C4×C7C22×#4111yescharacteristic
379C4×C7C2×2−1+411yescharacteristic
380Dic7—24no—
381Dic7—24no—
382Dic7—42no—
383Dic7—44no—
384C24—21no—
385C24—141no—
386C2×Q8—22no—
387C2×Q8—24no—
388C2×Q8—24no—
389C2×Q8—74no—
390C2×Q8—144no—
391C2×Q8—144no—
392C2×Q8—562no—
393C2×Q8C23×D714yes—
394C2×D4—21no—
395C2×D4—22no—
396C2×D4—72no—
397C2×D4—141no—
398C2×D4—142no—
399C2×D4—142no—
400C2×D4#115914yes—
401C2×D4C23×D712yes—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—24no—
405C22×C4—44no—
406C22×C4—72no—
407C22×C4—72no—
408C22×C4—148no—
409C22×C4—141no—
410C22×C4—142no—
411C22×C4—144no—
412C22×C4—284no—
413C22×C4—564no—
414C22×C4D4×D711yescharacteristic
415C22×C4D4×D711yescharacteristic
416C22×C4C23×D711yescharacteristic
417SD16—216no—
418D8—148no—
419C2×C8—24no—
420C2×C8—72no—
421C2×C8—72no—
422C2×C8—142no—
423C2×C8—142no—
424C2×C8C23×D714yes—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—21no—
428C4⋊C4—78no—
429C4⋊C4—74no—
430C4⋊C4—74no—
431C4⋊C4—72no—
432C4⋊C4—148no—
433C4⋊C4—148no—
434C4⋊C4—148no—
435C4⋊C4—141no—
436C4⋊C4—142no—
437C4⋊C4—144no—
438C4⋊C4C23×D712yes—
439C22⋊C4—24no—
440C22⋊C4—148no—
441C22⋊C4—148no—
442C22⋊C4—148no—
443C22⋊C4—144no—
444C42—74no—
445C42—74no—
446C42—148no—
447C42D4×D712yes—
448C42C23×D712yes—
449C2×C7—44no—
450C2×C7#336014yescomplemented
451C2×C7C2×#54811yescharacteristic
452C2×C7C22×#13511yescharacteristic
453C2×C7C2×#57711yescharacteristic
454D7—82no—
455C23—24no—
456C23—22no—
457C23—42no—
458C23—42no—
459C23—142no—
460C23—282no—
461C23—282no—
462C23—282no—
463C23C2×D4×D711yescharacteristic
464Q8—24no—
465Q8—24no—
466Q8—44no—
467Q8—148no—
468Q8—564no—
469D4—24no—
470D4—22no—
471D4—142no—
472D4—142no—
473D4—282no—
474D4C2×#115914yes—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—22no—
478C2×C4—42no—
479C2×C4—44no—
480C2×C4—48no—
481C2×C4—74no—
482C2×C4—74no—
483C2×C4—144no—
484C2×C4—144no—
485C2×C4—142no—
486C2×C4—144no—
487C2×C4—282no—
488C2×C4—284no—
489C2×C4—288no—
490C2×C4—568no—
491C2×C4#647914yes—
492C2×C4C2×D4×D712yes—
493C2×C4C2×D4×D712yes—
494C2×C4C2×D4×D711yescharacteristic
495C2×C4C2×#115912yes—
496C2×C4#655412yes—
497C2×C4C24×D711yescharacteristic
498C8—24no—
499C8—142no—
500C8—142no—
501C7C2×#336011yescharacteristic, complemented, Sylow
502C22—24no—
503C22—48no—
504C22—42no—
505C22—42no—
506C22—282no—
507C22—282no—
508C22—282no—
509C22—564no—
510C22#9028912yes—
511C22C2×#647912yes—
512C22#9046912yes—
513C22C22×D4×D711yescharacteristic
514C4—22no—
515C4—44no—
516C4—42no—
517C4—144no—
518C4—144no—
519C4—284no—
520C4—282no—
521C4#9028912yes—
522C4C2×#647914yes—
523C4C22×#115911yescharacteristic
524C4C2×#655411yescharacteristic
525C2—44no—
526C2—562no—
527C2#1173786014yesdirect product factor
528C2C2×#9028911yescharacteristic
529C2C22×#647911yescharacteristic
530C2C2×#9046911yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#461C2
socleC23×C7C22×D4
prime radicalC22×#1141C22
hypercenterC2×#461D7
hypocenterC7C2×#3360
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#90423C2semidirect
2. C2×#90234C2semidirect
3. C2×C7×#461C2semidirect
5. C2×SD16×Dic7C2semidirect
6. C2×#89853C2semidirect
8. #11737860C2direct (N × H)
9. C2×#89614C2semidirect
10. C2×#89602C2semidirect
11. C2×#89572C2semidirect
12. C2×#89571C2semidirect
23. #90423C22semidirect
25. #90234C22semidirect
34. C7×#461C22semidirect
41. SD16×Dic7C22semidirect
46. #89853C22semidirect
51. #89614C22semidirect
52. #89602C22semidirect
53. #89572C22semidirect
54. #89571C22semidirect
134. C2×#461D7semidirect
229. #461C2×D7semidirect
450. C2×C7#3360semidirect
501. C7C2×#3360semidirect
527. C2#11737860direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904232
C2×#902342
C2×C7×#4612
C2×#899372
C2×SD16×Dic72
C2×#898532
C2×C4×#11412
#117378602
C2×#896142
C2×#896022
C2×#895722
C2×#895712
C2×#33607