Finite Group Databasebeta

← C2×#11740362 #14217661

Subgroups — C2×#11740362 #14217661

Order 1792.

2870 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#525C211yesmaximal, characteristic
2C22×#6511C211yesmaximal, characteristic, complemented
3C23×#1136C211yesmaximal, characteristic, complemented
4C2×#90006C211yesmaximal, characteristic, complemented
5C2×#89979C211yesmaximal, characteristic, complemented
6#11740362C2116yesmaximal, direct product factor
7C2×#89784C214yesmaximal, complemented
8C2×#89783C214yesmaximal, complemented
9C2×#89771C211yesmaximal, characteristic, complemented
10C2×#89769C211yesmaximal, characteristic, complemented
11C22×C7×#41C2211yescharacteristic
12C24×C4×C7C2211yescharacteristic
13C7×#525C418yes—
14C7×#525C2218yes—
15C2×C7×#123C412yes—
16C2×C7×C22⋊Q8C412yes—
17C2×C7×#121C412yes—
18C2×C7×#120C412yes—
19C2×C4×C7×D4C2214yes—
20C2×C7×#117C2211yescharacteristic
21C2×#6511—28no—
22C2×#6511C2218yescomplemented
23C22×#1136—28no—
24C22×#1136C2211yescharacteristic
25C22×#1136C2212yes—
26C22×#1136C2212yes—
27C22×#1136C2211yescharacteristic
28C22×#1136C2218yescomplemented
29C22×#1136C2212yescomplemented
30C23×C7⋊C8C2211yescharacteristic
31C23×C7⋊C8C2211yescharacteristic
32C23×C7⋊C8C2212yescomplemented
33#90006C2218yescomplemented
34#89979C2218yescomplemented
35C2×C22⋊(C7⋊C8)C2214yes—
36C2×C22⋊(C7⋊C8)C2214yescomplemented
37#89784C22132yescomplemented
38#89783C22132yescomplemented
39#89771C2218yescomplemented
40#89769C2218yescomplemented
41C2×C4⋊(C7⋊C8)C2214yescomplemented
42C2×#6377C2212yescomplemented
43C2×C4×C7⋊C8C2212yescomplemented
44C2×#2930—71nomaximal, Sylow
45C25×C7C2×C411yescharacteristic
46C2×C7×#41—24no—
47C2×C7×#41—24no—
48C2×C7×#41C2×C414yes—
49C2×C7×#41C2314yes—
50C22×C7×Q8C2×C411yescharacteristic
51C22×C7×D4C2×C412yes—
52C22×C7×D4C2×C411yescharacteristic
53C22×C7×D4C2×C414yes—
54C23×C4×C7—24no—
55C23×C4×C7—24no—
56C23×C4×C7C2×C412yes—
57C23×C4×C7C2×C411yescharacteristic
58C23×C4×C7C2×C414yes—
59C23×C4×C7C2312yes—
60C23×C4×C7C2312yes—
61C23×C4×C7C2314yes—
62C23×C4×C7C2311yescharacteristic
63C7×#123C2×C4116yes—
64C7×C22⋊Q8C2×C4116yes—
65C7×#121C2×C4116yes—
66C7×#120C2×C4116yes—
67C4×C7×D4C2×C4116yes—
68C4×C7×D4C23116yes—
69C7×#117C2×C414yes—
70C7×#117C2314yes—
71C2×C7×C4⋊C4C2×C412yes—
72C2×C7×C4⋊C4C2×C414yes—
73C2×C7×C22⋊C4C2×C412yes—
74C2×C7×C22⋊C4C2×C414yes—
75C2×C7×C22⋊C4C2×C414yes—
76C2×C42×C7C2312yes—
77#6511—232no—
78C2×#1136—24no—
79C2×#1136—24no—
80C2×#1136—28no—
81C2×#1136—28no—
82C2×#1136—28no—
83C2×#1136—232no—
84C2×#1136C2318yes—
85C2×#1136C2318yes—
86C2×#1136C2314yes—
87C2×#1136C2314yes—
88C2×#1136C2318yescomplemented
89C22×C7⋊C8—24no—
90C22×C7⋊C8—28no—
91C22×C7⋊C8D418yescomplemented
92C22×C7⋊C8C2312yes—
93C22×C7⋊C8C2312yes—
94C22×C7⋊C8C2312yes—
95C22×C7⋊C8C2314yes—
96C22×C7⋊C8C2311yescharacteristic
97C22×C7⋊C8C2311yescharacteristic
98C22×C7⋊C8C2314yes—
99C22×C7⋊C8C2318yescomplemented
100C22⋊(C7⋊C8)C23116yes—
101C22⋊(C7⋊C8)C23116yescomplemented
102C4⋊(C7⋊C8)C23116yescomplemented
103#6377C2318yescomplemented
104C4×C7⋊C8C2318yescomplemented
105C22×#131—71no—
106C23×M16—71no—
107C2×#525D711yescharacteristic
108#2930—716no—
109C2×#436—74no—
110C2×#435—74no—
111C2×#424—71no—
112C2×#408—71no—
113C2×#407—71no—
114C2×#405—71no—
115C24×C7—24no—
116C24×C7—44no—
117C24×C7C22×C412yes—
118C24×C7C22×C412yes—
119C24×C7C22×C411yescharacteristic
120C24×C7C22×C414yes—
121C7×#41—216no—
122C7×#41—28no—
123C7×#41—28no—
124C2×C7×Q8—24no—
125C2×C7×Q8C22×C414yes—
126C2×C7×D4—28no—
127C2×C7×D4—24no—
128C2×C7×D4—48no—
129C2×C7×D4C22×C418yes—
130C2×C7×D4C22×C414yes—
131C2×C7×D4C22×C4116yes—
132C22×C4×C7—24no—
133C22×C4×C7—28no—
134C22×C4×C7—216no—
135C22×C4×C7—24no—
136C22×C4×C7—24no—
137C22×C4×C7—28no—
138C22×C4×C7—24no—
139C22×C4×C7—28no—
140C22×C4×C7—24no—
141C22×C4×C7C22×C414yes—
142C22×C4×C7C22×C412yes—
143C22×C4×C7C22×C412yes—
144C22×C4×C7C22×C414yes—
145C22×C4×C7C22×C414yes—
146C22×C4×C7C22×C418yes—
147C22×C4×C7C22×C414yes—
148C22×C4×C7C22×C411yescharacteristic
149C22×C4×C7C22×C412yes—
150C22×C4×C7C2×D414yes—
151C22×C4×C7#4114yes—
152C22×C4×C7C2414yes—
153C22×C4×C7C2414yes—
154C22×C4×C7C2412yes—
155C22×C4×C7C2411yescharacteristic
156C7×C4⋊C4C22×C418yes—
157C7×C4⋊C4C22×C4116yes—
158C7×C22⋊C4C22×C418yes—
159C7×C22⋊C4C22×C4116yes—
160C7×C22⋊C4C22×C4116yes—
161C42×C7C22×C414yes—
162C42×C7C2414yes—
163#1136—28no—
164#1136—28no—
165#1136—216no—
166#1136—216no—
167#1136—216no—
168C2×C7⋊C8—24no—
169C2×C7⋊C8—24no—
170C2×C7⋊C8—28no—
171C2×C7⋊C8—24no—
172C2×C7⋊C8—216no—
173C2×C7⋊C8C2×D414yes—
174C2×C7⋊C8C2×D414yes—
175C2×C7⋊C8C2×D4116yescomplemented
176C2×C7⋊C8C2414yes—
177C2×C7⋊C8C2414yes—
178C2×C7⋊C8C2414yes—
179C2×C7⋊C8C2412yes—
180C2×C7⋊C8C2412yes—
181C22×#41C2×D711yescharacteristic
182C24×C4C2×D711yescharacteristic
183C2×#131—78no—
184C2×#131—148no—
185C22×M16—71no—
186C22×M16—71no—
187C22×M16—72no—
188C22×M16—72no—
189C22×M16—72no—
190C22×M16—78no—
191C22×M16—148no—
192C23×C8—71no—
193C23×C8—71no—
194C23×C8—72no—
195#525Dic718yes—
196#525C2×D718yes—
197C2×#123Dic712yes—
198C2×C22⋊Q8Dic712yes—
199C2×#121Dic712yes—
200C2×#120Dic712yes—
201C2×C4×D4C2×D714yes—
202C2×#117C2×D711yescharacteristic
203#436—732no—
204#435—732no—
205#424—78no—
206C2×C4⋊C8—74no—
207#408—78no—
208#407—78no—
209C2×C22⋊C8—74no—
210C2×C22⋊C8—74no—
211#405—78no—
212C2×#97—72no—
213C2×C4×C8—72no—
214C23×C7—24no—
215C23×C7—28no—
216C23×C7—24no—
217C23×C7—24no—
218C23×C7—24no—
219C23×C7—28no—
220C23×C7—24no—
221C23×C7—48no—
222C23×C7—416no—
223C23×C7C4×D414yes—
224C23×C7C23×C414yes—
225C23×C7C23×C414yes—
226C23×C7C23×C412yes—
227C23×C7C23×C411yescharacteristic
228C7×Q8—28no—
229C7×D4—216no—
230C7×D4—28no—
231C7×D4—416no—
232C2×C4×C7—28no—
233C2×C4×C7—24no—
234C2×C4×C7—24no—
235C2×C4×C7—28no—
236C2×C4×C7—28no—
237C2×C4×C7—216no—
238C2×C4×C7—28no—
239C2×C4×C7—24no—
240C2×C4×C7—24no—
241C2×C4×C7—24no—
242C2×C4×C7—24no—
243C2×C4×C7C4×D414yes—
244C2×C4×C7C4×D418yes—
245C2×C4×C7C23×C418yes—
246C2×C4×C7C23×C414yes—
247C2×C4×C7C23×C414yes—
248C2×C4×C7C23×C411yescharacteristic
249C2×C4×C7C23×C412yes—
250C2×C4×C7C22×D412yes—
251C2×C4×C7C22×D414yes—
252C2×C4×C7C2×#4112yes—
253C2×C4×C7C2×#4114yes—
254C2×C4×C7C2511yescharacteristic
255C7⋊C8—24no—
256C7⋊C8—24no—
257C7⋊C8—24no—
258C7⋊C8C22×D414yes—
259C7⋊C8C22×D414yes—
260C25C2×Dic711yescharacteristic
261C2×#41—24no—
262C2×#41—24no—
263C2×#41C2×Dic714yes—
264C2×#41C22×D714yes—
265C22×Q8C2×Dic711yescharacteristic
266C22×D4C2×Dic712yes—
267C22×D4C2×Dic711yescharacteristic
268C22×D4C2×Dic714yes—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4C2×Dic712yes—
272C23×C4C2×Dic711yescharacteristic
273C23×C4C2×Dic714yes—
274C23×C4C22×D714yes—
275C23×C4C22×D712yes—
276C23×C4C22×D712yes—
277C23×C4C22×D711yescharacteristic
278#131—1432no—
279C2×M16—78no—
280C2×M16—78no—
281C2×M16—74no—
282C2×M16—78no—
283C2×M16—74no—
284C2×M16—148no—
285C2×M16—148no—
286C2×M16—1432no—
287C2×M16—148no—
288C2×M16—144no—
289C2×M16—144no—
290C22×C8—78no—
291C22×C8—74no—
292C22×C8—71no—
293C22×C8—71no—
294C22×C8—74no—
295C22×C8—78no—
296C22×C8—72no—
297C22×C8—72no—
298C22×C8—72no—
299C22×C8—148no—
300C22×C8—144no—
301#123C2×Dic7116yes—
302C22⋊Q8C2×Dic7116yes—
303#121C2×Dic7116yes—
304#120C2×Dic7116yes—
305C4×D4C2×Dic7116yes—
306C4×D4C22×D7116yes—
307#117C2×Dic714yes—
308#117C22×D714yes—
309C2×C4⋊C4C2×Dic712yes—
310C2×C4⋊C4C2×Dic714yes—
311C2×C22⋊C4C2×Dic712yes—
312C2×C22⋊C4C2×Dic714yes—
313C2×C22⋊C4C2×Dic714yes—
314C2×C42C22×D712yes—
315C4⋊C8—716no—
316C22⋊C8—716no—
317C22⋊C8—716no—
318#97—78no—
319C4×C8—78no—
320C22×C7—28no—
321C22×C7—24no—
322C22×C7—24no—
323C22×C7—24no—
324C22×C7—24no—
325C22×C7—28no—
326C22×C7—24no—
327C22×C7—416no—
328C22×C7—48no—
329C22×C7—48no—
330C22×C7C2×C4×D414yes—
331C22×C7C2×C4×D412yes—
332C22×C7#56814yes—
333C22×C7C24×C411yescharacteristic
334C4×C7—24no—
335C4×C7—24no—
336C4×C7—28no—
337C4×C7C2×C4×D412yes—
338C4×C7C2×C4×D414yes—
339C4×C7C23×D411yescharacteristic
340C4×C7C22×#4111yescharacteristic
341C24—24no—
342C24—44no—
343C24C22×Dic712yes—
344C24C22×Dic712yes—
345C24C22×Dic711yescharacteristic
346C24C22×Dic714yes—
347#41—216no—
348#41—28no—
349#41—28no—
350C2×Q8—24no—
351C2×Q8C22×Dic714yes—
352C2×D4—28no—
353C2×D4—24no—
354C2×D4—48no—
355C2×D4C22×Dic718yes—
356C2×D4C22×Dic714yes—
357C2×D4C22×Dic7116yes—
358C22×C4—24no—
359C22×C4—28no—
360C22×C4—216no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—28no—
364C22×C4—24no—
365C22×C4—28no—
366C22×C4—24no—
367C22×C4D4×D714yes—
368C22×C4#115914yes—
369C22×C4C22×Dic714yes—
370C22×C4C22×Dic712yes—
371C22×C4C22×Dic712yes—
372C22×C4C22×Dic714yes—
373C22×C4C22×Dic714yes—
374C22×C4C22×Dic718yes—
375C22×C4C22×Dic714yes—
376C22×C4C22×Dic711yescharacteristic
377C22×C4C22×Dic712yes—
378C22×C4C23×D714yes—
379C22×C4C23×D714yes—
380C22×C4C23×D712yes—
381C22×C4C23×D711yescharacteristic
382M16—1416no—
383M16—1416no—
384M16—1416no—
385M16—148no—
386M16—148no—
387C2×C8—74no—
388C2×C8—74no—
389C2×C8—716no—
390C2×C8—72no—
391C2×C8—72no—
392C2×C8—74no—
393C2×C8—74no—
394C2×C8—74no—
395C2×C8—1416no—
396C2×C8—144no—
397C2×C8—144no—
398C2×C8—148no—
399C2×C8—144no—
400C4⋊C4C22×Dic718yes—
401C4⋊C4C22×Dic7116yes—
402C22⋊C4C22×Dic718yes—
403C22⋊C4C22×Dic7116yes—
404C22⋊C4C22×Dic7116yes—
405C42C22×Dic714yes—
406C42C23×D714yes—
407C2×C7—24no—
408C2×C7—44no—
409C2×C7—44no—
410C2×C7#293014yescomplemented
411C2×C7C22×C4×D411yescharacteristic
412C2×C7C2×#56812yes—
413C23—24no—
414C23—28no—
415C23—24no—
416C23—24no—
417C23—24no—
418C23—28no—
419C23—24no—
420C23—48no—
421C23—416no—
422C23D4×Dic714yes—
423C23C23×Dic714yes—
424C23C23×Dic714yes—
425C23C23×Dic712yes—
426C23C23×Dic711yescharacteristic
427Q8—28no—
428D4—216no—
429D4—28no—
430D4—416no—
431C2×C4—28no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—28no—
435C2×C4—28no—
436C2×C4—216no—
437C2×C4—28no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4D4×Dic714yes—
443C2×C4D4×Dic718yes—
444C2×C4C2×D4×D712yes—
445C2×C4C2×D4×D714yes—
446C2×C4C2×#115912yes—
447C2×C4C2×#115914yes—
448C2×C4C23×Dic718yes—
449C2×C4C23×Dic714yes—
450C2×C4C23×Dic714yes—
451C2×C4C23×Dic711yescharacteristic
452C2×C4C23×Dic712yes—
453C2×C4C24×D711yescharacteristic
454C8—74no—
455C8—74no—
456C8—144no—
457C8—144no—
458C8—144no—
459C7C2×#293011yescharacteristic, complemented, Sylow
460C22—24no—
461C22—28no—
462C22—24no—
463C22—24no—
464C22—24no—
465C22—28no—
466C22—24no—
467C22—416no—
468C22—48no—
469C22—48no—
470C22C2×D4×Dic714yes—
471C22C2×D4×Dic712yes—
472C22#9051014yes—
473C22C24×Dic711yescharacteristic
474C4—24no—
475C4—24no—
476C4—28no—
477C4C2×D4×Dic712yes—
478C4C2×D4×Dic714yes—
479C4C22×D4×D711yescharacteristic
480C4C22×#115911yescharacteristic
481C2—24no—
482C2—44no—
483C2—44no—
484C2#1174036214yesdirect product factor
485C2C22×D4×Dic711yescharacteristic
486C2C2×#9051012yes—
subgroupG/H
centerC22×C4C23×D7
commutatorC22×C7C24×C4
FrattiniC2×C4C24×D7
Fitting, prime radicalC2×C7×#525C2
socleC23×C7C23×C4
cosocleC2×C4×C7C25
hypercenterC2×#525D7
hypocenterC7C2×#2930
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
2. C22×#6511C2semidirect
3. C23×#1136C2semidirect
4. C2×#90006C2semidirect
5. C2×#89979C2semidirect
6. #11740362C2direct (N × H)
7. C2×#89784C2semidirect
8. C2×#89783C2semidirect
9. C2×#89771C2semidirect
10. C2×#89769C2semidirect
22. C2×#6511C22semidirect
28. C22×#1136C22semidirect
29. C22×#1136C22semidirect
32. C23×C7⋊C8C22semidirect
33. #90006C22semidirect
34. #89979C22semidirect
36. C2×C22⋊(C7⋊C8)C22semidirect
37. #89784C22semidirect
38. #89783C22semidirect
39. #89771C22semidirect
40. #89769C22semidirect
41. C2×C4⋊(C7⋊C8)C22semidirect
42. C2×#6377C22semidirect
43. C2×C4×C7⋊C8C22semidirect
88. C2×#1136C23semidirect
91. C22×C7⋊C8D4semidirect
99. C22×C7⋊C8C23semidirect
101. C22⋊(C7⋊C8)C23semidirect
102. C4⋊(C7⋊C8)C23semidirect
103. #6377C23semidirect
104. C4×C7⋊C8C23semidirect
175. C2×C7⋊C8C2×D4semidirect
410. C2×C7#2930semidirect
459. C7C2×#2930semidirect
484. C2#11740362direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5252
C22×#65112
C23×#11362
C2×#900062
C2×#899792
#117403622
C2×#897842
C2×#897832
C2×#897712
C2×#897692
C2×#29307