Finite Group Databasebeta

← C4×#90422 #13512941

Subgroups — C4×#90422 #13512941

Order 1792.

2070 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90422C211yesmaximal, characteristic
2C4×C7×C4⋊Q8C211yesmaximal, characteristic, complemented
3#11740672C211yesmaximal, characteristic, complemented
4C4×#6509C212yesmaximal
5C4×Q8×Dic7C212yesmaximal, complemented
6#11734056C212yesmaximal
7#11733928C212yesmaximal, complemented
8#11733423C214yesmaximal, complemented
9#11733420C214yesmaximal
10#11731803C211yesmaximal, characteristic
11#11731767C211yesmaximal, characteristic, complemented
12C4×#6452C214yesmaximal, complemented
13C4×#6461C214yesmaximal
14C4×#6433C211yesmaximal, characteristic, complemented
15C4×#6435C211yesmaximal, characteristic
16C2×C7×C4⋊Q8C2211yescharacteristic
17C2×C4×C7×Q8C2212yes—
18C2×#6509C2212yes—
19C2×Q8×Dic7C2212yes—
20C2×Q8×Dic7C2212yes—
21#90422C4116yesdirect product factor
22C2×#6461C2214yes—
23C2×#6452C2214yes—
24C2×#6435C2211yescharacteristic
25C2×#6435C2211yescharacteristic
26C2×C42×D7C2211yescharacteristic
27C2×#6433C2211yescharacteristic
28C7×#391C2212yes—
29C7×#389C2214yes—
30C7×#384C2211yescharacteristic
31C4×C7×C4⋊C4C2214yes—
32C43×C7C2211yescharacteristic
33#90002C2212yes—
34#89762C2214yes—
35#89761C2214yes—
36#89759C2212yes—
37#89753C2214yes—
38#89753C2214yes—
39#89750C2214yes—
40#89750C2214yes—
41#89750C2214yes—
42C4⋊C4×Dic7C2212yes—
43C4⋊C4×Dic7C2212yes—
44C4⋊C4×Dic7C2214yes—
45C4⋊C4×Dic7C2214yes—
46#89745C2212yes—
47#89744C2214yes—
48C4×(C2×D7)⋊C4C2214yes—
49C4×(C2×D7)⋊C4C2212yes—
50C4×(C2×D7)⋊C4C2212yes—
51#89708C2211yescharacteristic
52C4×C4⋊Dic7C2212yes—
53C4×C4⋊Dic7C2214yes—
54#89705C2214yes—
55#89704C2211yescharacteristic
56#89704C2211yescharacteristic
57C4×Dic7⋊C4C2214yes—
58C4×Dic7⋊C4C2212yes—
59C4×Dic7⋊C4C2212yes—
60C4×Dic7⋊C4C2214yes—
61C42×Dic7C2211yescharacteristic
62C42×Dic7C2214yes—
63#89700C2212yes—
64#89442C2214yes—
65#89441C2214yes—
66#89426C2214yes—
67#89425C2214yes—
68#89424C2214yes—
69#89423C2214yes—
70#89422C2214yes—
71#89419C2214yes—
72C4×#541—71nomaximal, Sylow
73C22×C7×Q8C2312yes—
74C22×C4×D7C2311yescharacteristic
75C22×C4×D7C2311yescharacteristic
76C22×C4×D7C2311yescharacteristic
77C7×C4⋊Q8C2×C418yescomplemented
78C4×C7×Q8—28no—
79C2×C7×C4⋊C4C2312yes—
80C2×C7×C4⋊C4C2314yes—
81C2×C7×C4⋊C4C2314yes—
82C2×C7×C4⋊C4C2314yes—
83C2×C42×C7C2311yescharacteristic
84C2×C42×C7C2314yes—
85C2×C42×C7C2312yes—
86C2×C42×C7C2312yes—
87C2×C42×C7C2311yescharacteristic
88C2×C42×C7C2311yescharacteristic
89#6509C2×C4116yes—
90Q8×Dic7—28no—
91Q8×Dic7C2×C4116yescomplemented
92C2×(C2×D7)⋊C4C2312yes—
93C2×(C2×D7)⋊C4C2314yes—
94C2×(C2×D7)⋊C4C2312yes—
95C2×(C2×D7)⋊C4C2314yes—
96C2×C4⋊Dic7C2314yes—
97C2×C4⋊Dic7C2312yes—
98C2×C4⋊Dic7C2312yes—
99C2×C4⋊Dic7C2314yes—
100C2×Dic7⋊C4C2312yes—
101C2×Dic7⋊C4C2314yes—
102C2×Dic7⋊C4C2314yes—
103C2×Dic7⋊C4C2314yes—
104C2×Dic7⋊C4C2312yes—
105C2×Dic7⋊C4C2314yes—
106C2×C4×Dic7C2311yescharacteristic
107C2×C4×Dic7C2311yescharacteristic
108C2×C4×Dic7C2311yescharacteristic
109C2×C4×Dic7C2314yes—
110C2×C4×Dic7C2312yes—
111C2×C4×Dic7C2314yes—
112C2×C4×Dic7C2314yes—
113C2×C4×Dic7C2314yes—
114C2×C4×Dic7C2312yes—
115C2×C4×Dic7C2311yescharacteristic
116C2×C4×Dic7C2314yes—
117C2×C4×Dic7C2311yescharacteristic
118#6461C2×C4132yes—
119#6452C2×C4132yescomplemented
120#6435—24no—
121#6435C2×C418yes—
122C42×D7—24no—
123#6433C2×C418yescomplemented
124C7×#95C2314yes—
125C7×#95C2314yes—
126C7⋊#95C2314yes—
127C7⋊#95C2312yes—
128C7⋊#95C2314yes—
129C7⋊#95C2314yes—
130C7⋊#95C2312yes—
131C7⋊#95C2314yes—
132C7⋊#95C2314yes—
133C7⋊#95C2314yes—
134C7⋊#95C2314yes—
135C7⋊#95C2312yes—
136C7⋊#95C2312yes—
137C7⋊#95C2314yes—
138C7⋊#95C2314yes—
139C2×#541—71no—
140#2336—74no—
141#2334—74no—
142#2330—71no—
143#2327—71no—
144#2323—72no—
145#2320—72no—
146#2314—71no—
147C4×C4⋊Q8D711yescharacteristic, complemented
148C4×#125—74no—
149C4×#125—71no—
150C4×#126—74no—
151C4×C22⋊Q8—72no—
152C42×Q8—72no—
153C4×#117—71no—
154C23×D7C2411yescharacteristic
155C2×C7×Q8—24no—
156C2×C7×Q8—24no—
157C2×C7×Q8C22×C418yes—
158C22×C4×C7C2412yes—
159C22×C4×C7C2414yes—
160C22×C4×C7C2412yes—
161C22×C4×C7C2414yes—
162C22×C4×C7C2411yescharacteristic
163C22×C4×C7C2411yescharacteristic
164C22×C4×C7C2411yescharacteristic
165C22×Dic7C2411yescharacteristic
166C22×Dic7C2414yes—
167C22×Dic7C2411yescharacteristic
168C22×Dic7C2412yes—
169C22×Dic7C2414yes—
170C22×Dic7C2411yescharacteristic
171C22×Dic7C2412yes—
172C2×C4×D7—22no—
173C2×C4×D7—22no—
174C2×C4×D7—22no—
175C2×C4×D7—22no—
176C2×C4×D7—24no—
177C2×C4×D7—42no—
178C2×C4×D7C22×C414yes—
179C7×C4⋊C4—28no—
180C7×C4⋊C4—24no—
181C7×C4⋊C4—44no—
182C7×C4⋊C4C22×C4116yes—
183C42×C7—22no—
184C42×C7—28no—
185C42×C7—24no—
186C42×C7—42no—
187C42×C7C22×C414yes—
188C42×C7#4114yes—
189(C2×D7)⋊C4—24no—
190(C2×D7)⋊C4—44no—
191(C2×D7)⋊C4C22×C418yes—
192(C2×D7)⋊C4C22×C4116yes—
193C4⋊Dic7—24no—
194C4⋊Dic7—28no—
195C4⋊Dic7C22×C418yes—
196C4⋊Dic7C22×C4116yes—
197Dic7⋊C4—24no—
198Dic7⋊C4—44no—
199Dic7⋊C4—44no—
200Dic7⋊C4C22×C4116yes—
201Dic7⋊C4C22×C418yes—
202Dic7⋊C4C22×C4116yes—
203C4×Dic7—22no—
204C4×Dic7—22no—
205C4×Dic7—22no—
206C4×Dic7—24no—
207C4×Dic7—28no—
208C4×Dic7—28no—
209C4×Dic7—42no—
210C4×Dic7—44no—
211C4×Dic7—44no—
212C4×Dic7C22×C414yes—
213C4×Dic7C22×C4116yes—
214C4×Dic7#4114yes—
215#541—716no—
216C2×C4⋊Q8C2×D711yescharacteristic
217C2×#126—74no—
218C2×#125—74no—
219C2×#125—71no—
220C2×C22⋊Q8—72no—
221C2×C4×Q8—72no—
222C2×C4×Q8—72no—
223C2×C4×Q8C2×D712yes—
224C2×#117—71no—
225C2×#117—71no—
226C22×C42—71no—
227#391—72no—
228#391C2×D712yes—
229#389—74no—
230#389—72no—
231#389—72no—
232#389—74no—
233#389C2×D714yes—
234#388—74no—
235#388—74no—
236#388—74no—
237#387—74no—
238#387—74no—
239#387—74no—
240#387—74no—
241#387—74no—
242#387—74no—
243#387—74no—
244#387—74no—
245#387—74no—
246#385—74no—
247#384C2×D711yescharacteristic
248#383—74no—
249#382—71no—
250#382—74no—
251#380—72no—
252C4×C4⋊C4—72no—
253C4×C4⋊C4—72no—
254C4×C4⋊C4—74no—
255C4×C4⋊C4—74no—
256C4×C4⋊C4—74no—
257C4×C4⋊C4—74no—
258C4×C4⋊C4—72no—
259C4×C4⋊C4—74no—
260C4×C4⋊C4—72no—
261C4×C4⋊C4—72no—
262C4×C4⋊C4C2×D714yes—
263C4×C22⋊C4—72no—
264C4×C22⋊C4—74no—
265C4×C22⋊C4—72no—
266#376—71no—
267#376—71no—
268C43—74no—
269C43—71no—
270C43C2×D711yescharacteristic
271C23×C7C2511yescharacteristic
272C22×D7—21no—
273C22×D7—21no—
274C22×D7—22no—
275C22×D7—22no—
276C22×D7C23×C412yes—
277C7×Q8—216no—
278C2×C4×C7—24no—
279C2×C4×C7—24no—
280C2×C4×C7—22no—
281C2×C4×C7—22no—
282C2×C4×C7—22no—
283C2×C4×C7—22no—
284C2×C4×C7—24no—
285C2×C4×C7—22no—
286C2×C4×C7—24no—
287C2×C4×C7—24no—
288C2×C4×C7—22no—
289C2×C4×C7C23×C418yes—
290C2×C4×C7C23×C414yes—
291C2×C4×C7C23×C412yes—
292C2×C4×C7C2×#4112yes—
293C2×C4×C7C2×#4112yes—
294C2×C4×C7C2×#4112yes—
295C2×C4×C7C2×#4112yes—
296C2×C4×C72−1+414yes—
297C2×Dic7—21no—
298C2×Dic7—21no—
299C2×Dic7—22no—
300C2×Dic7—24no—
301C2×Dic7—22no—
302C2×Dic7—22no—
303C2×Dic7—22no—
304C2×Dic7—24no—
305C2×Dic7—21no—
306C2×Dic7—21no—
307C2×Dic7—24no—
308C2×Dic7—24no—
309C2×Dic7—22no—
310C2×Dic7—24no—
311C2×Dic7—22no—
312C2×Dic7C23×C414yes—
313C2×Dic7C23×C418yes—
314C2×Dic7C23×C412yes—
315C2×Dic7C2×#4114yes—
316C4×D7—28no—
317C4×D7—44no—
318C4×D7—44no—
319C22×Q8C22×D712yes—
320C23×C4—71no—
321C23×C4—71no—
322C23×C4—71no—
323C4⋊Q8C4×D718yescomplemented
324#126—732no—
325#125—732no—
326#125—78no—
327C22⋊Q8—716no—
328C4×Q8—28no—
329C4×Q8—716no—
330C4×Q8—148no—
331#117—78no—
332#117—144no—
333C2×C4⋊C4—72no—
334C2×C4⋊C4—72no—
335C2×C4⋊C4—74no—
336C2×C4⋊C4—74no—
337C2×C4⋊C4—74no—
338C2×C4⋊C4—72no—
339C2×C4⋊C4—72no—
340C2×C4⋊C4—74no—
341C2×C4⋊C4—74no—
342C2×C4⋊C4—74no—
343C2×C4⋊C4C22×D712yes—
344C2×C4⋊C4C22×D714yes—
345C2×C4⋊C4C22×D714yes—
346C2×C4⋊C4C22×D714yes—
347C2×C22⋊C4—72no—
348C2×C22⋊C4—74no—
349C2×C22⋊C4—72no—
350C2×C22⋊C4—74no—
351C2×C42—71no—
352C2×C42—71no—
353C2×C42—74no—
354C2×C42—74no—
355C2×C42—71no—
356C2×C42—71no—
357C2×C42—72no—
358C2×C42—74no—
359C2×C42—71no—
360C2×C42—72no—
361C2×C42—74no—
362C2×C42—74no—
363C2×C42—144no—
364C2×C42C22×D711yescharacteristic
365C2×C42C22×D714yes—
366C2×C42C22×D712yes—
367C2×C42C22×D712yes—
368C2×C42C22×D711yescharacteristic
369C2×C42C22×D711yescharacteristic
370#95—72no—
371#95—72no—
372#95—72no—
373#95—72no—
374#95—74no—
375#95—74no—
376#95—74no—
377#95—74no—
378#95—74no—
379#95—74no—
380#95—74no—
381#95—74no—
382#95—74no—
383#95C22×D714yes—
384#95C22×D714yes—
385C22×C7C24×C411yescharacteristic
386C22×C7C22×#4111yescharacteristic
387C22×C7C22×#4111yescharacteristic
388C22×C7C2×2−1+412yes—
389C22×C7#58512yes—
390C2×D7—22no—
391C2×D7—24no—
392C2×D7—41no—
393C2×D7—41no—
394C2×D7—42no—
395C4×C7—28no—
396C4×C7—24no—
397C4×C7—22no—
398C4×C7—44no—
399C4×C7—42no—
400C4×C7C4×#4114yes—
401C4×C7#54114yescomplemented
402Dic7—22no—
403Dic7—24no—
404Dic7—28no—
405Dic7—24no—
406Dic7—41no—
407Dic7—41no—
408Dic7—44no—
409C24—71no—
410C2×Q8—24no—
411C2×Q8—24no—
412C2×Q8C2×C4×D718yes—
413C22×C4—72no—
414C22×C4—72no—
415C22×C4—74no—
416C22×C4—71no—
417C22×C4—74no—
418C22×C4—71no—
419C22×C4—74no—
420C22×C4—71no—
421C22×C4—142no—
422C22×C4—142no—
423C22×C4—142no—
424C22×C4—142no—
425C22×C4—144no—
426C22×C4—282no—
427C22×C4C23×D712yes—
428C22×C4C23×D714yes—
429C22×C4C23×D712yes—
430C22×C4C23×D714yes—
431C22×C4C23×D711yescharacteristic
432C22×C4C23×D711yescharacteristic
433C22×C4C23×D711yescharacteristic
434C4⋊C4—28no—
435C4⋊C4—24no—
436C4⋊C4—44no—
437C4⋊C4—78no—
438C4⋊C4—716no—
439C4⋊C4—716no—
440C4⋊C4—78no—
441C4⋊C4—716no—
442C4⋊C4—144no—
443C4⋊C4—148no—
444C4⋊C4—144no—
445C4⋊C4—284no—
446C4⋊C4—284no—
447C4⋊C4C2×C4×D7116yes—
448C22⋊C4—78no—
449C22⋊C4—716no—
450C22⋊C4—144no—
451C22⋊C4—284no—
452C42—28no—
453C42—24no—
454C42—22no—
455C42—42no—
456C42—74no—
457C42—716no—
458C42—74no—
459C42—148no—
460C42—142no—
461C42—142no—
462C42—142no—
463C42—144no—
464C42—148no—
465C42—282no—
466C42—284no—
467C42—284no—
468C42C2×C4×D714yes—
469C42#115914yes—
470C2×C7C2×C4×#4111yescharacteristic
471C2×C7C4×2−1+412yes—
472C2×C7C2×#54111yescharacteristic
473C2×C7#345511yescharacteristic
474C2×C7#346112yes—
475D7—42no—
476C23—72no—
477C23—141no—
478C23—142no—
479C23—141no—
480C23—142no—
481C23C24×D711yescharacteristic
482Q8—216no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—74no—
495C2×C4—78no—
496C2×C4—72no—
497C2×C4—74no—
498C2×C4—141no—
499C2×C4—142no—
500C2×C4—142no—
501C2×C4—144no—
502C2×C4—141no—
503C2×C4—142no—
504C2×C4—142no—
505C2×C4—144no—
506C2×C4—148no—
507C2×C4—141no—
508C2×C4—141no—
509C2×C4—144no—
510C2×C4—142no—
511C2×C4—144no—
512C2×C4—144no—
513C2×C4—142no—
514C2×C4—284no—
515C2×C4—284no—
516C2×C4C22×C4×D718yes—
517C2×C4C22×C4×D714yes—
518C2×C4C22×C4×D712yes—
519C2×C4C2×#115912yes—
520C2×C4C2×#115912yes—
521C2×C4C2×#115912yes—
522C2×C4#655114yes—
523C2×C4D7×#4112yes—
524C7C4×#54111yescharacteristic, complemented, Sylow
525C22—142no—
526C22—144no—
527C22—281no—
528C22—281no—
529C22—282no—
530C22C23×C4×D711yescharacteristic
531C22C22×#115911yescharacteristic
532C22C2×#655112yes—
533C22C2×D7×#4111yescharacteristic
534C22#9061612yes—
535C4—22no—
536C4—28no—
537C4—24no—
538C4—44no—
539C4—42no—
540C4—142no—
541C4—144no—
542C4—144no—
543C4—148no—
544C4—281no—
545C4—281no—
546C4—284no—
547C4C4×#115914yes—
548C4#9042214yesdirect product factor
549C2—282no—
550C2C2×C4×#115911yescharacteristic
551C2C4×#655112yes—
552C2C2×#9042211yescharacteristic
553C2#1174330411yescharacteristic
554C2#1174334312yes—
subgroupG/H
centerC22×C4C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC4×C7×C4⋊Q8C2
socle, cosocleC23×C7C25
prime radicalC23×D7C24
hypercenterC4×C4⋊Q8D7
hypocenterC7C4×#541
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C4×C7×C4⋊Q8C2semidirect
3. #11740672C2semidirect
5. C4×Q8×Dic7C2semidirect
7. #11733928C2semidirect
8. #11733423C2semidirect
11. #11731767C2semidirect
12. C4×#6452C2semidirect
14. C4×#6433C2semidirect
21. #90422C4direct (N × H)
77. C7×C4⋊Q8C2×C4semidirect
91. Q8×Dic7C2×C4semidirect
119. #6452C2×C4semidirect
123. #6433C2×C4semidirect
147. C4×C4⋊Q8D7semidirect
323. C4⋊Q8C4×D7semidirect
401. C4×C7#541semidirect
524. C7C4×#541semidirect
548. C4#90422direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904222
C4×C7×C4⋊Q82
#117406722
C4×#65092
C4×Q8×Dic72
#117340562
#117339282
#117334232
#117334202
#117318032
#117317672
C4×#64522
C4×#64612
C4×#64332
C4×#64352
C4×#5417