Finite Group Databasebeta

← C2×#11738474 #14232298

Subgroups — C2×#11738474 #14232298

Order 1792.

1854 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90423C211yesmaximal, characteristic
2C2×#90275C211yesmaximal, characteristic
3C2×C7×#475C211yesmaximal, characteristic, complemented
4C2×#89850C211yesmaximal, characteristic, complemented
5C2×C4×#1144C211yesmaximal, characteristic, complemented
6#11738474C2116yesmaximal, direct product factor
7C2×#89632C212yesmaximal, complemented
8C2×#89639C212yesmaximal, complemented
9C2×#89623C211yesmaximal, characteristic, complemented
10C2×#89606C211yesmaximal, characteristic
11C2×#89587C212yesmaximal, complemented
12C2×#89585C212yesmaximal, complemented
13C2×C7×C4⋊Q8C2211yescharacteristic
14C2×C4×C7×Q8C2211yescharacteristic
15C2×#6510—21no—
16C2×#6509C2212yes—
17C2×Q8×Dic7—21no—
18C22×#1144C2211yescharacteristic
19C22×C8×D7C2212yes—
20#90423—24no—
21#90423C2218yes—
22#90275—24no—
23#90275C2218yes—
24C2×#6461—22no—
25C2×#6461—22no—
26C2×#6460C2212yes—
27C2×#6455C2212yes—
28C2×#6455C2212yes—
29C2×#6438—21no—
30C2×C4×D28C2211yescharacteristic
31C2×#6432C2211yescharacteristic
32C2×C4×Dic14—21no—
33C2×C4×Dic14C2211yescharacteristic
34C7×#475C2218yescomplemented
35C2×C7×#106C2212yes—
36C2×C7×C4⋊C8C2211yescharacteristic
37C2×C7×#103C2212yes—
38C2×#6409C2211yescharacteristic
39C2×(C2×D7)⋊C8C2212yes—
40C2×#6391C2212yes—
41C2×#6390C2212yes—
42#89850C2218yescomplemented
43C4×#1144C2218yescomplemented
44C2×#6384C2211yescharacteristic
45C2×#6381C2212yes—
46C2×#6381C2212yes—
47C2×#6381C2211yescharacteristic
48C2×C4×C7⋊C8C2211yescharacteristic
49#89639C22116yescomplemented
50#89632C22116yescomplemented
51#89623C2218yescomplemented
52#89606C2218yes—
53#89587C22116yescomplemented
54#89585C22116yescomplemented
55C2×#3342—71nomaximal, Sylow
56C22×C7×Q8—21no—
57C22×C7×Q8C2311yescharacteristic
58C22×D28D411yescharacteristic
59C22×C4×D7C2312yes—
60C22×Dic14—21no—
61C22×Dic14C2311yescharacteristic
62C22×C7×C8C2312yes—
63C7×C4⋊Q8—22no—
64C7×C4⋊Q8C2314yes—
65C4×C7×Q8—22no—
66C4×C7×Q8C2314yes—
67C2×C7×C4⋊C4—21no—
68C2×C7×C4⋊C4—21no—
69C2×C7×C4⋊C4C2311yescharacteristic
70C2×C7×C4⋊C4C2312yes—
71C2×C42×C7—21no—
72C2×C42×C7C2311yescharacteristic
73#6510—28no—
74#6509—24no—
75#6509C2318yes—
76Q8×Dic7—28no—
77C2×#1144—24no—
78C2×#1144C2314yes—
79C2×(C2×D7)⋊C4—22no—
80C2×(C2×D7)⋊C4—22no—
81C2×(C2×D7)⋊C4—22no—
82C2×(C2×D7)⋊C4—22no—
83C2×(C2×D7)⋊C4D412yes—
84C2×C4⋊Dic7—21no—
85C2×C4⋊Dic7—22no—
86C2×C4⋊Dic7D411yescharacteristic
87C2×C4⋊Dic7C2312yes—
88C2×C4⋊Dic7C2311yescharacteristic
89C2×Dic7⋊C4—21no—
90C2×Dic7⋊C4—22no—
91C2×C4×Dic7—21no—
92C2×C4×Dic7—22no—
93C2×C4×Dic7—22no—
94C22×C7⋊C8C2311yescharacteristic
95C22×C7⋊C8C2311yescharacteristic
96C2×C8×D7—28no—
97C2×C8×D7C2318yes—
98#6461—216no—
99#6461—216no—
100#6460—24no—
101#6460C2318yes—
102#6455—24no—
103#6455—24no—
104#6455C2318yes—
105#6455C2318yes—
106#6438—28no—
107C4×D28D414yes—
108C4×D28C2314yes—
109#6432—22no—
110#6432C2314yes—
111C4×Dic14—22no—
112C4×Dic14—28no—
113C4×Dic14C2314yes—
114C7×#106C2318yes—
115C7×C4⋊C8C2314yes—
116C7×#103C2318yes—
117#6409C2314yes—
118(C2×D7)⋊C8C2318yes—
119#6391C2318yes—
120#6390C2318yes—
121#6384C2314yes—
122#6381C2314yes—
123#6381C2318yes—
124#6381C2318yes—
125C4×C7⋊C8C2314yes—
126C2×#556—71no—
127C2×#556—71no—
128#3342—716no—
129C2×#500—71no—
130C2×#485—72no—
131C2×#485—72no—
132C2×#475—71no—
133C2×#475D711yescharacteristic, complemented
134C2×#467—72no—
135C2×C4×Q16—71no—
136C2×C8×D4—71no—
137C2×#427—72no—
138C23×D7C2×D412yes—
139C2×C7×Q8—24no—
140C2×C7×Q8—21no—
141C2×C7×Q8—22no—
142C2×C7×Q8—22no—
143C2×C7×Q8—44no—
144C2×C7×Q8C2412yes—
145C22×C4×C7—21no—
146C22×C4×C7—22no—
147C22×C4×C7—21no—
148C22×C4×C7C2×D411yescharacteristic
149C22×C4×C7C2×D411yescharacteristic
150C22×C4×C7C2411yescharacteristic
151C22×Dic7—21no—
152C22×Dic7—21no—
153C22×Dic7—22no—
154C22×Dic7C2×D412yes—
155C2×D28—24no—
156C2×D28C2×D414yes—
157C2×C4×D7—24no—
158C2×C4×D7—24no—
159C2×C4×D7C2×D414yes—
160C2×C4×D7C2414yes—
161C2×Dic14—22no—
162C2×Dic14—22no—
163C2×Dic14—24no—
164C2×Dic14—21no—
165C2×Dic14—44no—
166C2×Dic14C2412yes—
167C2×C7×C8—24no—
168C2×C7×C8C2414yes—
169C7×C4⋊C4—21no—
170C7×C4⋊C4—22no—
171C7×C4⋊C4—24no—
172C7×C4⋊C4—24no—
173C7×C4⋊C4C2414yes—
174C7×C4⋊C4C2412yes—
175C42×C7—24no—
176C42×C7C2×D412yes—
177C42×C7C2412yes—
178#1144—28no—
179(C2×D7)⋊C4—28no—
180(C2×D7)⋊C4—28no—
181(C2×D7)⋊C4—28no—
182(C2×D7)⋊C4—28no—
183(C2×D7)⋊C4C2×D418yes—
184C4⋊Dic7—21no—
185C4⋊Dic7—22no—
186C4⋊Dic7—24no—
187C4⋊Dic7—28no—
188C4⋊Dic7C2×D414yes—
189C4⋊Dic7C2412yes—
190C4⋊Dic7C2414yes—
191Dic7⋊C4—24no—
192Dic7⋊C4—28no—
193C4×Dic7—24no—
194C4×Dic7—28no—
195C4×Dic7—28no—
196C2×C7⋊C8—22no—
197C2×C7⋊C8#4114yes—
198C2×C7⋊C8C2412yes—
199C2×C7⋊C8C2412yes—
200C8×D7—216no—
201C22×Q16—71no—
202C23×C8—72no—
203#556—78no—
204#556—78no—
205#556—144no—
206#556—144no—
207C2×C4⋊Q8—71no—
208C2×C4⋊Q8C2×D711yescharacteristic
209C2×#126—142no—
210C2×#126—142no—
211C2×#124—141no—
212C2×#124—141no—
213C2×C22⋊Q8—72no—
214C2×C22⋊Q8—72no—
215C2×C4×Q8—71no—
216C2×C4×Q8—141no—
217C2×C4×Q8—141no—
218C2×C4×Q8C2×D711yescharacteristic
219C2×C4×D4—71no—
220C2×#117—72no—
221C2×#117—72no—
222#500—78no—
223#485—716no—
224#485—716no—
225#475—78no—
226#475C2×D718yescomplemented
227#467—716no—
228C4×Q16—78no—
229C8×D4—78no—
230#427—716no—
231C2×#107—72no—
232C2×#107—72no—
233C2×#107—71no—
234C2×#106—72no—
235C2×#106C2×D712yes—
236C2×C4⋊C8C2×D711yescharacteristic
237C2×#103—71no—
238C2×#103—72no—
239C2×#103—71no—
240C2×#103C2×D712yes—
241C2×C22⋊C8—72no—
242C2×C4×C8—71no—
243C23×C7C22×D411yescharacteristic
244C22×D7—24no—
245C22×D7—24no—
246C22×D7—24no—
247C22×D7C22×D414yes—
248C7×Q8—22no—
249C7×Q8—22no—
250C7×Q8—42no—
251C7×Q8—48no—
252C2×C4×C7—22no—
253C2×C4×C7—22no—
254C2×C4×C7—24no—
255C2×C4×C7—22no—
256C2×C4×C7—42no—
257C2×C4×C7—44no—
258C2×C4×C7—42no—
259C2×C4×C7#13514yes—
260C2×C4×C7C22×D412yes—
261C2×C4×C7C22×D411yescharacteristic
262C2×C4×C7C22×D412yes—
263C2×C4×C7C2×#4112yes—
264C2×C4×C72−1+412yes—
265C2×C4×C7C2511yescharacteristic
266C2×Dic7—24no—
267C2×Dic7—22no—
268C2×Dic7—22no—
269C2×Dic7—24no—
270C2×Dic7—42no—
271C2×Dic7—44no—
272C2×Dic7—42no—
273C2×Dic7C22×D414yes—
274D28—28no—
275C4×D7—28no—
276C4×D7—24no—
277C4×D7—24no—
278Dic14—22no—
279Dic14—22no—
280Dic14—42no—
281Dic14—48no—
282C7×C8—24no—
283C7⋊C8—22no—
284C7⋊C8C2×#4114yes—
285C22×Q8—21no—
286C22×Q8—71no—
287C22×Q8—141no—
288C22×Q8C22×D711yescharacteristic
289C22×D4—71no—
290C23×C4—72no—
291C2×Q16—74no—
292C2×Q16—144no—
293C22×C8—71no—
294C22×C8—71no—
295C22×C8—78no—
296C22×C8—148no—
297C22×C8C22×D712yes—
298C4⋊Q8—22no—
299C4⋊Q8—74no—
300C4⋊Q8—142no—
301C4⋊Q8C22×D714yes—
302#126—1416no—
303#126—1416no—
304#124—148no—
305#124—148no—
306C22⋊Q8—78no—
307C22⋊Q8—78no—
308C22⋊Q8—144no—
309C22⋊Q8—144no—
310C4×Q8—22no—
311C4×Q8—74no—
312C4×Q8—148no—
313C4×Q8—148no—
314C4×Q8—142no—
315C4×Q8C22×D714yes—
316C4×D4—74no—
317C4×D4—74no—
318#117—78no—
319#117—78no—
320#117—144no—
321#117—144no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—71no—
325C2×C4⋊C4—71no—
326C2×C4⋊C4—72no—
327C2×C4⋊C4—142no—
328C2×C4⋊C4—142no—
329C2×C4⋊C4—141no—
330C2×C4⋊C4—141no—
331C2×C4⋊C4C22×D711yescharacteristic
332C2×C4⋊C4C22×D712yes—
333C2×C22⋊C4—72no—
334C2×C22⋊C4—142no—
335C2×C22⋊C4—142no—
336C2×C22⋊C4—142no—
337C2×C22⋊C4—142no—
338C2×C42—21no—
339C2×C42—142no—
340C2×C42—142no—
341C2×C42—141no—
342C2×C42C22×D711yescharacteristic
343#107—74no—
344#107—78no—
345#107—78no—
346#106—78no—
347#106C22×D718yes—
348C4⋊C8C22×D714yes—
349#103—74no—
350#103—78no—
351#103—74no—
352#103C22×D718yes—
353C22⋊C8—78no—
354C4×C8—74no—
355C22×C7#54712yes—
356C22×C7C2×#13512yes—
357C22×C7#57812yes—
358C22×C7C23×D411yescharacteristic
359C2×D7—24no—
360C2×D7—24no—
361C2×D7—24no—
362C2×D7—48no—
363C4×C7—22no—
364C4×C7—42no—
365C4×C7—44no—
366C4×C7—42no—
367C4×C7#54712yes—
368C4×C7C2×#13514yes—
369C4×C7C22×#4111yescharacteristic
370C4×C7C2×2−1+411yescharacteristic
371Dic7—24no—
372Dic7—42no—
373Dic7—44no—
374Dic7—42no—
375C24—72no—
376C2×Q8—21no—
377C2×Q8—24no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—44no—
381C2×Q8—72no—
382C2×Q8—141no—
383C2×Q8—144no—
384C2×Q8—142no—
385C2×Q8—142no—
386C2×Q8—284no—
387C2×Q8C23×D712yes—
388C2×D4—74no—
389C2×D4—144no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—72no—
394C22×C4—74no—
395C22×C4—74no—
396C22×C4—144no—
397C22×C4—144no—
398C22×C4—141no—
399C22×C4—142no—
400C22×C4—141no—
401C22×C4D4×D711yescharacteristic
402C22×C4D4×D711yescharacteristic
403C22×C4C23×D711yescharacteristic
404Q16—148no—
405C2×C8—24no—
406C2×C8—74no—
407C2×C8—72no—
408C2×C8—72no—
409C2×C8—1416no—
410C2×C8—142no—
411C2×C8C23×D714yes—
412C4⋊C4—24no—
413C4⋊C4—24no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—74no—
417C4⋊C4—72no—
418C4⋊C4—74no—
419C4⋊C4—148no—
420C4⋊C4—148no—
421C4⋊C4—144no—
422C4⋊C4—141no—
423C4⋊C4—142no—
424C4⋊C4—144no—
425C4⋊C4C23×D712yes—
426C4⋊C4C23×D714yes—
427C22⋊C4—78no—
428C22⋊C4—148no—
429C22⋊C4—148no—
430C22⋊C4—148no—
431C22⋊C4—148no—
432C42—24no—
433C42—148no—
434C42—148no—
435C42—144no—
436C42D4×D712yes—
437C42C23×D712yes—
438C2×C7#334214yescomplemented
439C2×C7C2×#54711yescharacteristic
440C2×C7C22×#13511yescharacteristic
441C2×C7C2×#57811yescharacteristic
442D7—44no—
443C23—74no—
444C23—144no—
445C23—144no—
446C23—144no—
447C23C2×D4×D711yescharacteristic
448Q8—22no—
449Q8—22no—
450Q8—48no—
451Q8—42no—
452Q8—142no—
453Q8—142no—
454Q8—288no—
455Q8—282no—
456D4—148no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—44no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—74no—
465C2×C4—144no—
466C2×C4—148no—
467C2×C4—144no—
468C2×C4—144no—
469C2×C4—142no—
470C2×C4—144no—
471C2×C4—142no—
472C2×C4—284no—
473C2×C4—282no—
474C2×C4—282no—
475C2×C4#647914yes—
476C2×C4C2×D4×D712yes—
477C2×C4C2×D4×D712yes—
478C2×C4C2×D4×D711yescharacteristic
479C2×C4#655112yes—
480C2×C4D7×#4112yes—
481C2×C4C24×D711yescharacteristic
482C8—24no—
483C8—74no—
484C8—142no—
485C7C2×#334211yescharacteristic, complemented, Sylow
486C22—144no—
487C22—144no—
488C22—144no—
489C22—288no—
490C22#9032212yes—
491C22C2×#647912yes—
492C22#9047012yes—
493C22C22×D4×D711yescharacteristic
494C4—22no—
495C4—42no—
496C4—42no—
497C4—44no—
498C4—144no—
499C4—282no—
500C4—282no—
501C4—284no—
502C4#9032212yes—
503C4C2×#647914yes—
504C4C2×#655111yescharacteristic
505C4C2×D7×#4111yescharacteristic
506C2—284no—
507C2#1173847414yesdirect product factor
508C2C2×#9032211yescharacteristic
509C2C22×#647911yescharacteristic
510C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#475C2
socleC23×C7C22×D4
prime radicalC22×D28D4
hypercenterC2×#475D7
hypocenterC7C2×#3342
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. C2×C7×#475C2semidirect
4. C2×#89850C2semidirect
5. C2×C4×#1144C2semidirect
6. #11738474C2direct (N × H)
7. C2×#89632C2semidirect
8. C2×#89639C2semidirect
9. C2×#89623C2semidirect
11. C2×#89587C2semidirect
12. C2×#89585C2semidirect
34. C7×#475C22semidirect
42. #89850C22semidirect
43. C4×#1144C22semidirect
49. #89639C22semidirect
50. #89632C22semidirect
51. #89623C22semidirect
53. #89587C22semidirect
54. #89585C22semidirect
133. C2×#475D7semidirect
226. #475C2×D7semidirect
438. C2×C7#3342semidirect
485. C7C2×#3342semidirect
507. C2#11738474direct (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×#902752
C2×C7×#4752
C2×#898502
C2×C4×#11442
#117384742
C2×#896322
C2×#896392
C2×#896232
C2×#896062
C2×#895872
C2×#895852
C2×#33427