Finite Group Databasebeta

← C2×#11741164 #14233527

Subgroups — C2×#11741164 #14233527

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×C7×#559C211yesmaximal, characteristic
2C2×Q8×Dic14C211yesmaximal, characteristic, complemented
3#11741164C2116yesmaximal, direct product factor
4C2×#89847C211yesmaximal, characteristic
5C2×#89842C211yesmaximal, characteristic
6C2×#89826C212yesmaximal, complemented
7C2×#89827C212yesmaximal, complemented
8C2×#89796C211yesmaximal, characteristic, complemented
9C2×#89793C211yesmaximal, characteristic, complemented
10C2×C4×#1144C211yesmaximal, characteristic, complemented
11C2×#89779C212yesmaximal, complemented
12C2×#89790C212yesmaximal, complemented
13C7×#559—24no—
14C7×#559C2218yes—
15C2×C7×#127C2211yescharacteristic
16C2×C7×#124—21no—
17C2×C7×#124C2212yes—
18C2×C7×#123—22no—
19C2×C4×C7×Q8C2211yescharacteristic
20C2×C4×C7×Q8C2211yescharacteristic
21C2×C4×C7×D4—21no—
22C2×C4×C7×D4C2212yes—
23C2×Q8×Dic7—21no—
24C22×#1144C2211yescharacteristic
25C22×#1142C2212yes—
26Q8×Dic14—24no—
27Q8×Dic14C2218yescomplemented
28C2×#6451—21no—
29C2×#6451—22no—
30C2×#6432C2212yes—
31C2×#6432C2211yescharacteristic
32C2×C4×Dic14C2212yes—
33C2×C4×Dic14C2211yescharacteristic
34C2×#6409C2211yescharacteristic
35C2×#6409C2212yes—
36C2×#6406C2212yes—
37C2×#6406C2212yes—
38C2×#6406C2212yes—
39#89847C2218yes—
40#89842C2218yes—
41#89827C22116yescomplemented
42#89826C22116yescomplemented
43C4×#1144C2218yescomplemented
44#89796C2218yescomplemented
45#89793C2218yescomplemented
46#89790C22116yescomplemented
47#89779C22116yescomplemented
48C2×#6384C2211yescharacteristic
49C2×#6381C2212yes—
50C2×#6381C2211yescharacteristic
51C2×C4⋊(C7⋊C8)C2212yes—
52C2×C4⋊(C7⋊C8)C2211yescharacteristic
53C2×#6377C2212yes—
54C2×C4×C7⋊C8C2211yescharacteristic
55C2×#3375—71nomaximal, Sylow
56C22×C7×Q8D411yescharacteristic
57C22×C7×Q8C2311yescharacteristic
58C22×C7×D4—21no—
59C22×C7×D4—21no—
60C22×C7×D4C2312yes—
61C23×C4×C7—22no—
62C22×Dic14—22no—
63C22×Dic14—21no—
64C22×Dic14C2311yescharacteristic
65C7×#127—22no—
66C7×#127C2314yes—
67C7×#124—28no—
68C7×#124—24no—
69C7×#124C2318yes—
70C7×#123—216no—
71C4×C7×Q8—22no—
72C4×C7×Q8D414yes—
73C4×C7×Q8C2314yes—
74C4×C7×Q8C2314yes—
75C4×C7×D4—28no—
76C4×C7×D4—24no—
77C4×C7×D4C2318yes—
78C2×C7×C4⋊C4—21no—
79C2×C7×C4⋊C4D411yescharacteristic
80C2×C7×C4⋊C4D412yes—
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—22no—
85C2×C42×C7—21no—
86C2×C42×C7C2311yescharacteristic
87C2×C42×C7C2312yes—
88Q8×Dic7—28no—
89C2×#1144—24no—
90C2×#1144C2314yes—
91C2×#1142—28no—
92C2×#1142C2318yes—
93C2×C4⋊Dic7—22no—
94C2×C4⋊Dic7—21no—
95C2×C4⋊Dic7C2312yes—
96C2×C4⋊Dic7C2311yescharacteristic
97C2×Dic7⋊C4—22no—
98C2×Dic7⋊C4—21no—
99C2×C4×Dic7—22no—
100C2×C4×Dic7—21no—
101C22×C7⋊C8C2311yescharacteristic
102C22×C7⋊C8C2311yescharacteristic
103C22×C7⋊C8C2312yes—
104#6451—28no—
105#6451—216no—
106#6432—24no—
107#6432—22no—
108#6432C2318yes—
109#6432C2314yes—
110C4×Dic14—24no—
111C4×Dic14—22no—
112C4×Dic14C2318yes—
113C4×Dic14C2314yes—
114#6409C2318yes—
115#6409C2314yes—
116#6406C2318yes—
117#6406C2318yes—
118#6406C2318yes—
119#6384C2314yes—
120#6381C2314yes—
121#6381C2318yes—
122C4⋊(C7⋊C8)C2318yes—
123C4⋊(C7⋊C8)C2314yes—
124#6377C2318yes—
125C4×C7⋊C8C2314yes—
126C2×#559D711yescharacteristic
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×Q16—71no—
138C24×C7—22no—
139C2×C7×Q8—24no—
140C2×C7×Q8—21no—
141C2×C7×Q8—22no—
142C2×C7×Q8—22no—
143C2×C7×Q8C2×D414yes—
144C2×C7×Q8C2412yes—
145C2×C7×D4—22no—
146C2×C7×D4—24no—
147C2×C7×D4—24no—
148C2×C7×D4—24no—
149C2×C7×D4—24no—
150C2×C7×D4—44no—
151C2×C7×D4—82no—
152C2×C7×D4C2414yes—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—28no—
156C22×C4×C7—84no—
157C22×C4×C7C2×D412yes—
158C22×C4×C7C2×D412yes—
159C22×C4×C7C2×D411yescharacteristic
160C22×C4×C7C2×D411yescharacteristic
161C22×C4×C7C2411yescharacteristic
162C22×Dic7—21no—
163C22×Dic7—22no—
164C22×Dic7—21no—
165C2×Dic14—21no—
166C2×Dic14—22no—
167C2×Dic14—28no—
168C2×Dic14—24no—
169C2×Dic14—84no—
170C2×Dic14—82no—
171C2×Dic14#4114yes—
172C2×Dic14C2412yes—
173C7×C4⋊C4—24no—
174C7×C4⋊C4—21no—
175C7×C4⋊C4C2×D414yes—
176C7×C4⋊C4C2×D418yes—
177C7×C4⋊C4C2412yes—
178C7×C22⋊C4—28no—
179C7×C22⋊C4—28no—
180C7×C22⋊C4—28no—
181C42×C7—24no—
182C42×C7C2×D414yes—
183C42×C7C2×D412yes—
184C42×C7C2414yes—
185C42×C7C2412yes—
186#1144—28no—
187#1142—216no—
188C4⋊Dic7—22no—
189C4⋊Dic7—21no—
190C4⋊Dic7—28no—
191C4⋊Dic7—24no—
192C4⋊Dic7C2414yes—
193C4⋊Dic7C2412yes—
194Dic7⋊C4—28no—
195Dic7⋊C4—24no—
196C4×Dic7—28no—
197C4×Dic7—24no—
198C2×C7⋊C8—24no—
199C2×C7⋊C8—22no—
200C2×C7⋊C8—22no—
201C2×C7⋊C8C2412yes—
202C2×C7⋊C8C2412yes—
203C2×C7⋊C8C2414yes—
204C22×Q16—71no—
205C22×SD16—72no—
206#559—24no—
207#559C2×D718yes—
208Q82—78no—
209Q82—144no—
210C2×C4⋊Q8—71no—
211C2×C4⋊Q8—72no—
212C2×C4⋊Q8—141no—
213C2×C4⋊Q8—142no—
214C2×#127C2×D711yescharacteristic
215C2×#124—21no—
216C2×#124C2×D712yes—
217C2×#123—22no—
218C2×C4×Q8—71no—
219C2×C4×Q8—72no—
220C2×C4×Q8—141no—
221C2×C4×Q8C2×D711yescharacteristic
222C2×C4×Q8C2×D711yescharacteristic
223C2×C4×D4—21no—
224C2×C4×D4C2×D712yes—
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×Q16—78no—
234C2×#107—72no—
235C2×#107—71no—
236C2×C4⋊C8—71no—
237C2×C4⋊C8—72no—
238C2×#103—72no—
239C2×#103—71no—
240C2×#103—71no—
241C2×#102—72no—
242C2×#102—72no—
243C2×#102—72no—
244C2×#97—72no—
245C2×C4×C8—71no—
246C23×C7—24no—
247C23×C7—44no—
248C23×C7—44no—
249C23×C7—44no—
250C23×C7C22×D411yescharacteristic
251C7×Q8—28no—
252C7×Q8—22no—
253C7×Q8—22no—
254C7×Q8—42no—
255C7×D4—24no—
256C7×D4—24no—
257C7×D4—44no—
258C7×D4—48no—
259C7×D4—84no—
260C2×C4×C7—24no—
261C2×C4×C7—24no—
262C2×C4×C7—22no—
263C2×C4×C7—22no—
264C2×C4×C7—22no—
265C2×C4×C7—42no—
266C2×C4×C7—42no—
267C2×C4×C7—88no—
268C2×C4×C7#13714yes—
269C2×C4×C7C22×D414yes—
270C2×C4×C7C22×D414yes—
271C2×C4×C7C22×D412yes—
272C2×C4×C7C22×D411yescharacteristic
273C2×C4×C7C22×D412yes—
274C2×C4×C7C2×#4112yes—
275C2×C4×C72−1+412yes—
276C2×C4×C7C2511yescharacteristic
277C2×Dic7—24no—
278C2×Dic7—22no—
279C2×Dic7—24no—
280C2×Dic7—22no—
281C2×Dic7—42no—
282C2×Dic7—44no—
283Dic14—24no—
284Dic14—22no—
285Dic14—88no—
286Dic14—84no—
287Dic14C2×#4114yes—
288C7⋊C8—24no—
289C7⋊C8—22no—
290C7⋊C8—22no—
291C22×Q8—71no—
292C22×Q8—142no—
293C22×Q8—141no—
294C22×Q8C22⋊D711yescharacteristic
295C22×Q8C22×D711yescharacteristic
296C22×D4—21no—
297C22×D4—21no—
298C22×D4C22×D712yes—
299C23×C4—22no—
300C2×Q16—74no—
301C2×Q16—144no—
302C2×SD16—78no—
303C2×SD16—148no—
304C22×C8—72no—
305C22×C8—71no—
306C22×C8—71no—
307C4⋊Q8—78no—
308C4⋊Q8—74no—
309C4⋊Q8—148no—
310C4⋊Q8—1416no—
311C4⋊Q8—144no—
312C4⋊Q8—142no—
313#127—22no—
314#127C22×D714yes—
315#124—28no—
316#124—24no—
317#124C22×D718yes—
318#123—216no—
319C4×Q8—22no—
320C4×Q8—74no—
321C4×Q8—78no—
322C4×Q8—148no—
323C4×Q8—144no—
324C4×Q8—142no—
325C4×Q8C22⋊D714yes—
326C4×Q8C22×D714yes—
327C4×Q8C22×D714yes—
328C4×D4—28no—
329C4×D4—24no—
330C4×D4C22×D718yes—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—71no—
333C2×C4⋊C4—72no—
334C2×C4⋊C4—142no—
335C2×C4⋊C4—141no—
336C2×C4⋊C4—142no—
337C2×C4⋊C4—141no—
338C2×C4⋊C4C22⋊D711yescharacteristic
339C2×C4⋊C4C22⋊D712yes—
340C2×C4⋊C4C22×D711yescharacteristic
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C42—21no—
345C2×C42—142no—
346C2×C42—141no—
347C2×C42C22×D712yes—
348C2×C42C22×D711yescharacteristic
349#107—74no—
350#107—78no—
351C4⋊C8—74no—
352C4⋊C8—78no—
353#103—74no—
354#103—78no—
355#103—74no—
356#102—78no—
357#102—78no—
358#102—78no—
359#97—78no—
360C4×C8—74no—
361C22×C7—44no—
362C22×C7—44no—
363C22×C7—44no—
364C22×C7—88no—
365C22×C7#54812yes—
366C22×C7C2×#13712yes—
367C22×C7#57612yes—
368C22×C7C23×D411yescharacteristic
369C4×C7—24no—
370C4×C7—24no—
371C4×C7—22no—
372C4×C7—42no—
373C4×C7—42no—
374C4×C7#54812yes—
375C4×C7C2×#13714yes—
376C4×C7C22×#4111yescharacteristic
377C4×C7C2×2−1+411yescharacteristic
378Dic7—24no—
379Dic7—42no—
380Dic7—44no—
381C24—22no—
382C2×Q8—24no—
383C2×Q8—21no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—74no—
387C2×Q8—72no—
388C2×Q8—142no—
389C2×Q8—141no—
390C2×Q8—148no—
391C2×Q8—144no—
392C2×Q8—564no—
393C2×Q8—562no—
394C2×Q8C2×C22⋊D714yes—
395C2×Q8C23×D712yes—
396C2×D4—24no—
397C2×D4—24no—
398C2×D4—22no—
399C2×D4—24no—
400C2×D4—24no—
401C2×D4—44no—
402C2×D4—82no—
403C2×D4C23×D714yes—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—28no—
407C22×C4—84no—
408C22×C4—141no—
409C22×C4—142no—
410C22×C4—141no—
411C22×C4C2×C22⋊D712yes—
412C22×C4C2×C22⋊D712yes—
413C22×C4C2×C22⋊D711yescharacteristic
414C22×C4C2×C22⋊D711yescharacteristic
415C22×C4C23×D711yescharacteristic
416Q16—148no—
417SD16—1416no—
418C2×C8—72no—
419C2×C8—72no—
420C2×C8—74no—
421C2×C8—144no—
422C2×C8—142no—
423C2×C8—142no—
424C4⋊C4—24no—
425C4⋊C4—21no—
426C4⋊C4—74no—
427C4⋊C4—72no—
428C4⋊C4—148no—
429C4⋊C4—144no—
430C4⋊C4—141no—
431C4⋊C4—142no—
432C4⋊C4—148no—
433C4⋊C4—144no—
434C4⋊C4C2×C22⋊D714yes—
435C4⋊C4C2×C22⋊D718yes—
436C4⋊C4C23×D712yes—
437C22⋊C4—28no—
438C22⋊C4—28no—
439C22⋊C4—28no—
440C42—24no—
441C42—148no—
442C42—144no—
443C42C2×C22⋊D714yes—
444C42C2×C22⋊D712yes—
445C42C23×D712yes—
446C42C23×D714yes—
447C2×C7—84no—
448C2×C7#337514yescomplemented
449C2×C7C2×#54811yescharacteristic
450C2×C7C22×#13711yescharacteristic
451C2×C7C2×#57611yescharacteristic
452C23—24no—
453C23—44no—
454C23—44no—
455C23—44no—
456C23C22×C22⋊D711yescharacteristic
457Q8—28no—
458Q8—22no—
459Q8—22no—
460Q8—42no—
461Q8—74no—
462Q8—144no—
463Q8—142no—
464Q8—568no—
465Q8—564no—
466D4—24no—
467D4—24no—
468D4—48no—
469D4—44no—
470D4—84no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—88no—
479C2×C4—144no—
480C2×C4—142no—
481C2×C4—144no—
482C2×C4—142no—
483C2×C4—282no—
484C2×C4—284no—
485C2×C4#651414yes—
486C2×C4D7×#4112yes—
487C2×C4#655412yes—
488C2×C4C22×C22⋊D714yes—
489C2×C4C22×C22⋊D714yes—
490C2×C4C22×C22⋊D712yes—
491C2×C4C22×C22⋊D712yes—
492C2×C4C22×C22⋊D711yescharacteristic
493C2×C4C24×D711yescharacteristic
494C8—144no—
495C8—142no—
496C8—142no—
497C7C2×#337511yescharacteristic, complemented, Sylow
498C22—44no—
499C22—44no—
500C22—44no—
501C22—88no—
502C22C2×#651412yes—
503C22#9052212yes—
504C22#9052612yes—
505C22C23×C22⋊D711yescharacteristic
506C4—24no—
507C4—24no—
508C4—22no—
509C4—42no—
510C4—42no—
511C4—144no—
512C4—282no—
513C4—284no—
514C4C2×#651414yes—
515C4#9052212yes—
516C4C2×D7×#4111yescharacteristic
517C4C2×#655411yescharacteristic
518C2—84no—
519C2#1174116414yesdirect product factor
520C2C22×#651411yescharacteristic
521C2C2×#9052211yescharacteristic
522C2C2×#9052611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#559C2
socleC23×C7C22×D4
prime radicalC2×C7×#127C22
hypercenterC2×#559D7
hypocenterC7C2×#3375
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic14C2semidirect
3. #11741164C2direct (N × H)
6. C2×#89826C2semidirect
7. C2×#89827C2semidirect
8. C2×#89796C2semidirect
9. C2×#89793C2semidirect
10. C2×C4×#1144C2semidirect
11. C2×#89779C2semidirect
12. C2×#89790C2semidirect
27. Q8×Dic14C22semidirect
41. #89827C22semidirect
42. #89826C22semidirect
43. C4×#1144C22semidirect
44. #89796C22semidirect
45. #89793C22semidirect
46. #89790C22semidirect
47. #89779C22semidirect
448. C2×C7#3375semidirect
497. C7C2×#3375semidirect
519. C2#11741164direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5592
C2×Q8×Dic142
#117411642
C2×#898472
C2×#898422
C2×#898262
C2×#898272
C2×#897962
C2×#897932
C2×C4×#11442
C2×#897792
C2×#897902
C2×#33757