Finite Group Databasebeta

← C2×#11737148 #14233529

Subgroups — C2×#11737148 #14233529

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×#90276C211yesmaximal, characteristic
2C2×Q8×Dic14C211yesmaximal, characteristic, complemented
3C2×C4×C7×Q16C211yesmaximal, characteristic, complemented
4C2×#89957C212yesmaximal, complemented
5C2×#89799C211yesmaximal, characteristic
6C2×#89793C211yesmaximal, characteristic, complemented
7#11737148C2116yesmaximal, direct product factor
8C2×#89662C212yesmaximal, complemented
9C2×#89567C212yesmaximal, complemented
10C2×#89589C212yesmaximal, complemented
11C2×#89466C211yesmaximal, characteristic
12C2×#89451C211yesmaximal, characteristic, complemented
13C22×C7×Q16C2211yescharacteristic
14C2×C4×C7×Q8C2211yescharacteristic
15C2×C4×C7×Q8C2211yescharacteristic
16C2×#6510C2212yes—
17C2×Q8×Dic7C2212yes—
18C22×#1143C2212yes—
19#90276—24no—
20#90276C2218yes—
21Q8×Dic14—24no—
22Q8×Dic14C2218yescomplemented
23C2×#6457—22no—
24C2×#6456C2212yes—
25C2×#6451—22no—
26C2×#6451C2212yes—
27C2×#6438—21no—
28C2×#6437C2211yescharacteristic
29C2×C4×D28—21no—
30C2×#6432—21no—
31C2×#6432C2211yescharacteristic
32C2×C4×Dic14—21no—
33C2×C4×Dic14C2211yescharacteristic
34C4×C7×Q16C2218yescomplemented
35C2×C7×#107C2211yescharacteristic
36C2×C7×#103C2211yescharacteristic
37C2×C7×#103C2211yescharacteristic
38C2×C4×C7×C8C2211yescharacteristic
39C2×#6409C2212yes—
40#89957C22116yescomplemented
41C2×#6395C2212yes—
42C2×#6395C2212yes—
43C2×#6389C2212yes—
44C2×Dic7⋊C8C2212yes—
45#89799C2218yes—
46#89793C2218yescomplemented
47C2×#6383C2212yes—
48C2×#6381C2212yes—
49C2×C4⋊(C7⋊C8)C2211yescharacteristic
50#89662C22116yescomplemented
51#89589C22116yescomplemented
52#89567C22116yescomplemented
53#89466C2218yes—
54#89451C2218yescomplemented
55C2×#3375—71nomaximal, Sylow
56C22×C7×Q8C2311yescharacteristic
57C22×C7×Q8C2311yescharacteristic
58C22×D28—21no—
59C22×D28—21no—
60C22×D28C2312yes—
61C22×C4×D7—22no—
62C22×Dic14—21no—
63C22×Dic14—22no—
64C22×Dic14D411yescharacteristic
65C2×C7×Q16—24no—
66C2×C7×Q16C2314yes—
67C22×C7×C8C2311yescharacteristic
68C22×C7×C8C2311yescharacteristic
69C4×C7×Q8—22no—
70C4×C7×Q8—22no—
71C4×C7×Q8C2314yes—
72C4×C7×Q8C2314yes—
73C2×C7×C4⋊C4—21no—
74C2×C7×C4⋊C4—21no—
75C2×C7×C4⋊C4C2311yescharacteristic
76C2×C7×C4⋊C4C2311yescharacteristic
77C2×C42×C7—21no—
78C2×C42×C7—21no—
79C2×C42×C7C2311yescharacteristic
80#6510—24no—
81#6510C2318yes—
82Q8×Dic7—24no—
83Q8×Dic7C2318yes—
84C2×#1143—28no—
85C2×#1143C2318yes—
86C2×(C2×D7)⋊C4—22no—
87C2×(C2×D7)⋊C4—22no—
88C2×(C2×D7)⋊C4—22no—
89C2×C4⋊Dic7—21no—
90C2×C4⋊Dic7—22no—
91C2×C4⋊Dic7D411yescharacteristic
92C2×C4⋊Dic7C2312yes—
93C2×Dic7⋊C4—22no—
94C2×Dic7⋊C4D412yes—
95C2×C4×Dic7—22no—
96C2×C4×Dic7C2312yes—
97C22×C7⋊C8C2312yes—
98#6457—216no—
99#6456—24no—
100#6456C2318yes—
101#6451—216no—
102#6451—24no—
103#6451C2318yes—
104#6438—28no—
105#6437—22no—
106#6437C2314yes—
107C4×D28—28no—
108#6432—22no—
109#6432—28no—
110#6432C2314yes—
111C4×Dic14—28no—
112C4×Dic14D414yes—
113C4×Dic14C2314yes—
114C7×#107C2314yes—
115C7×#103C2314yes—
116C7×#103C2314yes—
117C4×C7×C8C2314yes—
118#6409C2318yes—
119#6395C2318yes—
120#6395C2318yes—
121#6389C2318yes—
122Dic7⋊C8C2318yes—
123#6383C2318yes—
124#6381C2318yes—
125C4⋊(C7⋊C8)C2314yes—
126C2×#559—71no—
127C2×Q82—71no—
128#3375—716no—
129C2×#489—72no—
130C2×#486—71no—
131C2×#477—71no—
132C2×#474—72no—
133C2×#464—72no—
134C2×#460—71no—
135C2×#446—71no—
136C2×#440—72no—
137C2×C4×Q16D711yescharacteristic, complemented
138C23×D7—22no—
139C2×C7×Q8—21no—
140C2×C7×Q8—21no—
141C2×C7×Q8—22no—
142C2×C7×Q8—22no—
143C2×C7×Q8—22no—
144C2×C7×Q8#4114yes—
145C2×C7×Q8C2412yes—
146C2×C7×Q8C2412yes—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7C2×D411yescharacteristic
152C22×C4×C7C2×D411yescharacteristic
153C22×C4×C7C2411yescharacteristic
154C22×Dic7—22no—
155C22×Dic7C2×D412yes—
156C22×Dic7C2×D412yes—
157C2×D28—24no—
158C2×D28—24no—
159C2×D28—24no—
160C2×D28—22no—
161C2×D28—24no—
162C2×D28—44no—
163C2×D28—82no—
164C2×D28C2414yes—
165C2×C4×D7—28no—
166C2×C4×D7—84no—
167C2×Dic14—24no—
168C2×Dic14—24no—
169C2×Dic14—28no—
170C2×Dic14—84no—
171C2×Dic14—82no—
172C2×Dic14C2×D414yes—
173C7×Q16—28no—
174C2×C7×C8—22no—
175C2×C7×C8—22no—
176C2×C7×C8C2412yes—
177C2×C7×C8C2412yes—
178C7×C4⋊C4—24no—
179C7×C4⋊C4—21no—
180C7×C4⋊C4—21no—
181C7×C4⋊C4—24no—
182C7×C4⋊C4C2412yes—
183C7×C4⋊C4C2412yes—
184C42×C7—24no—
185C42×C7—24no—
186C42×C7C2×D412yes—
187C42×C7C2412yes—
188#1143—216no—
189(C2×D7)⋊C4—28no—
190(C2×D7)⋊C4—28no—
191(C2×D7)⋊C4—28no—
192C4⋊Dic7—24no—
193C4⋊Dic7—22no—
194C4⋊Dic7—28no—
195C4⋊Dic7C2×D414yes—
196C4⋊Dic7C2414yes—
197Dic7⋊C4—28no—
198Dic7⋊C4C2×D418yes—
199C4×Dic7—28no—
200C4×Dic7C2×D414yes—
201C4×Dic7C2414yes—
202C2×C7⋊C8—24no—
203C2×C7⋊C8C2414yes—
204C22×Q16C2×D711yescharacteristic
205C22×SD16—72no—
206#559—78no—
207#559—144no—
208Q82—78no—
209Q82—144no—
210C2×C4⋊Q8—72no—
211C2×C4⋊Q8—71no—
212C2×C4⋊Q8—141no—
213C2×C4⋊Q8—142no—
214C2×#127—71no—
215C2×#124—72no—
216C2×#124—141no—
217C2×#123—142no—
218C2×C4×Q8—71no—
219C2×C4×Q8—72no—
220C2×C4×Q8—141no—
221C2×C4×Q8C2×D711yescharacteristic
222C2×C4×Q8C2×D711yescharacteristic
223C2×C4×D4—72no—
224C2×C4×D4—141no—
225#489—716no—
226#486—78no—
227#477—78no—
228#474—716no—
229#464—716no—
230#460—78no—
231#446—78no—
232#440—716no—
233C4×Q16C2×D718yescomplemented
234C2×#107—72no—
235C2×#107C2×D711yescharacteristic
236C2×C4⋊C8—72no—
237C2×C4⋊C8—71no—
238C2×#103—72no—
239C2×#103C2×D711yescharacteristic
240C2×#103C2×D711yescharacteristic
241C2×#102—72no—
242C2×#102—72no—
243C2×#102—72no—
244C2×#97—72no—
245C2×C4×C8C2×D711yescharacteristic
246C23×C7C22×D411yescharacteristic
247C22×D7—24no—
248C22×D7—44no—
249C22×D7—44no—
250C22×D7—44no—
251C7×Q8—24no—
252C7×Q8—22no—
253C7×Q8—22no—
254C7×Q8—22no—
255C7×Q8—42no—
256C7×Q8C2×#4114yes—
257C2×C4×C7—24no—
258C2×C4×C7—22no—
259C2×C4×C7—22no—
260C2×C4×C7—22no—
261C2×C4×C7—22no—
262C2×C4×C7—22no—
263C2×C4×C7—42no—
264C2×C4×C7—42no—
265C2×C4×C7—42no—
266C2×C4×C7#13714yes—
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—24no—
276C2×Dic7—44no—
277C2×Dic7C22×D414yes—
278C2×Dic7C22×D414yes—
279D28—24no—
280D28—24no—
281D28—44no—
282D28—48no—
283D28—84no—
284C4×D7—88no—
285Dic14—28no—
286Dic14—88no—
287Dic14—84no—
288C7×C8—22no—
289C7×C8—22no—
290C7⋊C8—24no—
291C22×Q8—71no—
292C22×Q8—142no—
293C22×Q8—141no—
294C22×Q8C22×D711yescharacteristic
295C22×Q8C22×D711yescharacteristic
296C22×D4—72no—
297C22×D4—141no—
298C22×D4—141no—
299C23×C4—142no—
300C2×Q16—24no—
301C2×Q16C22×D714yes—
302C2×SD16—78no—
303C2×SD16—148no—
304C22×C8—72no—
305C22×C8C22×D711yescharacteristic
306C22×C8C22×D711yescharacteristic
307C4⋊Q8—78no—
308C4⋊Q8—74no—
309C4⋊Q8—148no—
310C4⋊Q8—144no—
311C4⋊Q8—1416no—
312C4⋊Q8—142no—
313#127—74no—
314#127—142no—
315#124—78no—
316#124—148no—
317#124—144no—
318#123—1416no—
319C4×Q8—22no—
320C4×Q8—22no—
321C4×Q8—74no—
322C4×Q8—74no—
323C4×Q8—78no—
324C4×Q8—148no—
325C4×Q8—144no—
326C4×Q8C22×D714yes—
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—72no—
336C2×C4⋊C4—142no—
337C2×C4⋊C4—142no—
338C2×C4⋊C4—141no—
339C2×C4⋊C4C22×D711yescharacteristic
340C2×C4⋊C4C22×D711yescharacteristic
341C2×C22⋊C4—142no—
342C2×C22⋊C4—142no—
343C2×C22⋊C4—142no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—72no—
347C2×C42—142no—
348C2×C42C22×D711yescharacteristic
349#107—78no—
350#107C22×D714yes—
351C4⋊C8—78no—
352C4⋊C8—74no—
353#103—78no—
354#103C22×D714yes—
355#103C22×D714yes—
356#102—78no—
357#102—78no—
358#102—78no—
359#97—78no—
360C4×C8C22×D714yes—
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—24no—
370C4×C7—22no—
371C4×C7—42no—
372C4×C7—42no—
373C4×C7—42no—
374C4×C7#54812yes—
375C4×C7C2×#13714yes—
376C4×C7C22×#4111yescharacteristic
377C4×C7C2×2−1+411yescharacteristic
378Dic7—24no—
379Dic7—24no—
380Dic7—44no—
381C24—142no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—74no—
388C2×Q8—148no—
389C2×Q8—144no—
390C2×Q8—144no—
391C2×Q8—562no—
392C2×Q8—564no—
393C2×Q8#115714yes—
394C2×Q8C23×D712yes—
395C2×Q8C23×D712yes—
396C2×D4—74no—
397C2×D4—144no—
398C2×D4—144no—
399C2×D4—142no—
400C2×D4—144no—
401C2×D4—144no—
402C2×D4—284no—
403C2×D4—562no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—72no—
409C22×C4—72no—
410C22×C4—148no—
411C22×C4—142no—
412C22×C4—564no—
413C22×C4D4×D711yescharacteristic
414C22×C4D4×D711yescharacteristic
415C22×C4C23×D711yescharacteristic
416Q16—28no—
417SD16—1416no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—74no—
421C2×C8—144no—
422C2×C8C23×D712yes—
423C2×C8C23×D712yes—
424C4⋊C4—24no—
425C4⋊C4—24no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—78no—
429C4⋊C4—74no—
430C4⋊C4—74no—
431C4⋊C4—148no—
432C4⋊C4—148no—
433C4⋊C4—142no—
434C4⋊C4—144no—
435C4⋊C4C23×D712yes—
436C4⋊C4C23×D712yes—
437C22⋊C4—148no—
438C22⋊C4—148no—
439C22⋊C4—148no—
440C42—24no—
441C42—24no—
442C42—74no—
443C42—74no—
444C42—148no—
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—24no—
458Q8—22no—
459Q8—22no—
460Q8—22no—
461Q8—42no—
462Q8—148no—
463Q8—564no—
464Q8—568no—
465Q8C2×#115714yes—
466D4—144no—
467D4—144no—
468D4—288no—
469D4—284no—
470D4—564no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—74no—
481C2×C4—74no—
482C2×C4—144no—
483C2×C4—144no—
484C2×C4—144no—
485C2×C4—284no—
486C2×C4—568no—
487C2×C4#648114yes—
488C2×C4C2×#115712yes—
489C2×C4C2×D4×D712yes—
490C2×C4C2×D4×D712yes—
491C2×C4C2×D4×D711yescharacteristic
492C2×C4#655412yes—
493C2×C4C24×D711yescharacteristic
494C8—22no—
495C8—22no—
496C8—144no—
497C7C2×#337511yescharacteristic, complemented, Sylow
498C22—284no—
499C22—284no—
500C22—284no—
501C22—568no—
502C22#9024312yes—
503C22C2×#648112yes—
504C22#9046012yes—
505C22C22×D4×D711yescharacteristic
506C4—24no—
507C4—22no—
508C4—42no—
509C4—42no—
510C4—42no—
511C4—144no—
512C4—144no—
513C4—284no—
514C4#9024312yes—
515C4C2×#648114yes—
516C4C22×#115711yescharacteristic
517C4C2×#655411yescharacteristic
518C2—564no—
519C2#1173714814yesdirect product factor
520C2C2×#9024311yescharacteristic
521C2C22×#648111yescharacteristic
522C2C2×#9046011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C4×C7×Q16C2
socleC23×C7C22×D4
prime radicalC2×#6437C22
hypercenterC2×C4×Q16D7
hypocenterC7C2×#3375
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic14C2semidirect
3. C2×C4×C7×Q16C2semidirect
4. C2×#89957C2semidirect
6. C2×#89793C2semidirect
7. #11737148C2direct (N × H)
8. C2×#89662C2semidirect
9. C2×#89567C2semidirect
10. C2×#89589C2semidirect
12. C2×#89451C2semidirect
22. Q8×Dic14C22semidirect
34. C4×C7×Q16C22semidirect
40. #89957C22semidirect
46. #89793C22semidirect
50. #89662C22semidirect
51. #89589C22semidirect
52. #89567C22semidirect
54. #89451C22semidirect
137. C2×C4×Q16D7semidirect
233. C4×Q16C2×D7semidirect
447. C2×C7#3375semidirect
497. C7C2×#3375semidirect
519. C2#11737148direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902762
C2×Q8×Dic142
C2×C4×C7×Q162
C2×#899572
C2×#897992
C2×#897932
#117371482
C2×#896622
C2×#895672
C2×#895892
C2×#894662
C2×#894512
C2×#33757