Finite Group Databasebeta

← C4×#89626 #13361378

Subgroups — C4×#89626 #13361378

Order 1792.

880 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89626C211yesmaximal, characteristic
2C4×#6451C211yesmaximal, characteristic
3C4×#6450C211yesmaximal, characteristic
4C4×C7×#106C211yesmaximal, characteristic
5#11728342C211yesmaximal, characteristic
6#11728317C211yesmaximal, characteristic
7#11728311C211yesmaximal, characteristic
8C4×#6390C211yesmaximal, characteristic
9C4×Dic7⋊C8C211yesmaximal, characteristic
10C4×#6382C211yesmaximal, characteristic
11C4×#6384C211yesmaximal, characteristic
12#11726661C211yesmaximal, characteristic
13#11726658C211yesmaximal, characteristic
14#11726554C211yesmaximal, characteristic
15#11726542C211yesmaximal, characteristic
16C2×#6451C2211yescharacteristic
17C2×#6450C2211yescharacteristic
18C2×#6450C2211yescharacteristic
19C2×C4×Dic14—21no—
20C2×C4×Dic14C2211yescharacteristic
21C2×C7×#106C2211yescharacteristic
22C2×C7×#106C2211yescharacteristic
23C2×C4×C7×C8C2211yescharacteristic
24C4×C7×C4⋊C4C2211yescharacteristic
25C4×C7×C4⋊C4C2211yescharacteristic
26C2×#6390C2211yescharacteristic
27C2×#6390C2211yescharacteristic
28C2×Dic7⋊C8C2211yescharacteristic
29C2×Dic7⋊C8C2211yescharacteristic
30#89757C2211yescharacteristic
31#89748C2211yescharacteristic
32C4⋊C4×Dic7C2211yescharacteristic
33C4⋊C4×Dic7C2211yescharacteristic
34#89745C2211yescharacteristic
35C2×#6384C2211yescharacteristic
36C2×#6384C2211yescharacteristic
37C2×#6382C2211yescharacteristic
38C2×#6382C2211yescharacteristic
39C4×C4⋊Dic7C2211yescharacteristic
40C4×Dic7⋊C4—21no—
41C4×Dic7⋊C4—21no—
42C42×Dic7—21no—
43C42×Dic7C2211yescharacteristic
44C2×C4×C7⋊C8C2211yescharacteristic
45#89626C418yesdirect product factor
46#89421—21no—
47#89421—21no—
48#89419—21no—
49#89418—21no—
50C7×#340C2211yescharacteristic
51C7×#340C2211yescharacteristic
52#89346C2211yescharacteristic
53#89346C2211yescharacteristic
54#89345C2211yescharacteristic
55#89345C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60C4×#475—71nomaximal, Sylow
61C22×Dic14—21no—
62C22×Dic14C2311yescharacteristic
63C22×C7×C8C2311yescharacteristic
64C22×C7×C8C2311yescharacteristic
65C2×C7×C4⋊C4C2311yescharacteristic
66C2×C7×C4⋊C4C2311yescharacteristic
67C2×C7×C4⋊C4C2311yescharacteristic
68C2×C7×C4⋊C4C2311yescharacteristic
69C2×C42×C7—21no—
70C2×C42×C7—21no—
71C2×C42×C7C2311yescharacteristic
72C2×C4⋊Dic7—21no—
73C2×C4⋊Dic7C2311yescharacteristic
74C2×C4⋊Dic7C2311yescharacteristic
75C2×C4⋊Dic7C2311yescharacteristic
76C2×Dic7⋊C4—21no—
77C2×Dic7⋊C4—21no—
78C2×Dic7⋊C4—21no—
79C2×Dic7⋊C4—21no—
80C2×Dic7⋊C4—21no—
81C2×Dic7⋊C4—21no—
82C2×Dic7⋊C4—21no—
83C2×C4×Dic7—21no—
84C2×C4×Dic7—21no—
85C2×C4×Dic7—21no—
86C2×C4×Dic7—21no—
87C2×C4×Dic7—21no—
88C2×C4×Dic7—21no—
89C2×C4×Dic7D411yescharacteristic
90C2×C4×Dic7D411yescharacteristic
91C2×C4×Dic7D411yescharacteristic
92C2×C4×Dic7D411yescharacteristic
93C2×C4×Dic7C2311yescharacteristic
94C2×C4×Dic7C2311yescharacteristic
95C22×C7⋊C8C2311yescharacteristic
96C22×C7⋊C8C2311yescharacteristic
97#6451—22no—
98#6451C2×C414yes—
99#6450—22no—
100#6450—22no—
101#6450—22no—
102#6450C2×C414yes—
103C4×Dic14—22no—
104C4×Dic14—44no—
105C4×Dic14Q814yescomplemented
106C7×#106—22no—
107C7×#106C2×C414yes—
108C4×C7×C8—22no—
109C7×#95—21no—
110C7×#95—21no—
111C7⋊#95—21no—
112C7⋊#95—21no—
113C7⋊#95—21no—
114C7⋊#95—21no—
115C7⋊#95—21no—
116#6390—22no—
117#6390C2×C414yes—
118Dic7⋊C8—22no—
119Dic7⋊C8C2×C414yes—
120#6384—22no—
121#6384C2×C414yes—
122#6382—22no—
123#6382C2×C414yes—
124C4×C7⋊C8—22no—
125C2×#475—71no—
126C4×C4⋊Q8—71no—
127C42×Q8—71no—
128#1988—71no—
129#1948—71no—
130#1919—71no—
131#1919—71no—
132#1865—71no—
133#1865—71no—
134#1803—71no—
135C4×#106—71no—
136C4×#106D711yescharacteristic
137C4×C4⋊C8—71no—
138C4×#103—71no—
139C4×#103—71no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7C2×D411yescharacteristic
145C22×C4×C7C2×D411yescharacteristic
146C22×C4×C7C2411yescharacteristic
147C22×Dic7—21no—
148C22×Dic7—21no—
149C22×Dic7—21no—
150C22×Dic7—21no—
151C22×Dic7C2×D411yescharacteristic
152C22×Dic7C2×D411yescharacteristic
153C22×Dic7C2×D411yescharacteristic
154C22×Dic7C2×D411yescharacteristic
155C2×Dic14—21no—
156C2×Dic14—21no—
157C2×Dic14—21no—
158C2×Dic14—24no—
159C2×Dic14—42no—
160C2×Dic14—42no—
161C2×Dic14C22×C412yes—
162C2×Dic14C2×Q812yes—
163C2×Dic14#4112yes—
164C2×C7×C8—21no—
165C2×C7×C8—21no—
166C2×C7×C8—21no—
167C2×C7×C8—21no—
168C2×C7×C8—21no—
169C2×C7×C8C22×C412yes—
170C7×C4⋊C4—21no—
171C7×C4⋊C4—21no—
172C7×C4⋊C4—21no—
173C7×C4⋊C4—21no—
174C7×C4⋊C4—21no—
175C7×C4⋊C4C22×C412yes—
176C7×C4⋊C4C22×C412yes—
177C7×C4⋊C4#4112yes—
178C42×C7—42no—
179C42×C7—42no—
180C42×C7C2×Q812yes—
181C42×C7#4112yes—
182C4⋊Dic7—21no—
183C4⋊Dic7—21no—
184C4⋊Dic7—21no—
185C4⋊Dic7—21no—
186C4⋊Dic7—42no—
187C4⋊Dic7C22×C412yes—
188C4⋊Dic7C2×Q812yes—
189Dic7⋊C4—24no—
190Dic7⋊C4—24no—
191Dic7⋊C4—24no—
192Dic7⋊C4—24no—
193Dic7⋊C4—42no—
194Dic7⋊C4—42no—
195Dic7⋊C4—42no—
196C4×Dic7—24no—
197C4×Dic7—24no—
198C4×Dic7—22no—
199C4×Dic7—21no—
200C4×Dic7—21no—
201C4×Dic7—24no—
202C4×Dic7—22no—
203C4×Dic7—41no—
204C4×Dic7—42no—
205C4×Dic7—42no—
206C4×Dic7—42no—
207C4×Dic7SD1614yes—
208C4×Dic7C22×C412yes—
209C4×Dic7#4112yes—
210C2×C7⋊C8—21no—
211C2×C7⋊C8—21no—
212C2×C7⋊C8—21no—
213C2×C7⋊C8—21no—
214C2×C7⋊C8—21no—
215C2×C7⋊C8C22×C412yes—
216C2×C4⋊Q8—71no—
217C2×C4×Q8—71no—
218C2×C4×Q8—71no—
219C2×C4×Q8—71no—
220C2×C4×Q8—141no—
221#475—78no—
222C2×#106—71no—
223C2×#106—71no—
224C2×#106C2×D711yescharacteristic
225C2×#106C2×D711yescharacteristic
226C2×C4⋊C8—71no—
227C2×C4⋊C8—71no—
228C2×#103—71no—
229C2×#103—71no—
230C2×#103—71no—
231C2×#103—71no—
232C2×C4×C8—71no—
233C2×C4×C8C2×D711yescharacteristic
234#391—141no—
235#389—71no—
236#389—71no—
237#389—141no—
238#384—71no—
239C4×C4⋊C4—71no—
240C4×C4⋊C4—71no—
241C4×C4⋊C4—71no—
242C4×C4⋊C4—141no—
243C4×C4⋊C4—141no—
244C4×C4⋊C4—141no—
245C4×C4⋊C4—141no—
246C4×C4⋊C4C2×D711yescharacteristic
247C4×C4⋊C4C2×D711yescharacteristic
248C43—71no—
249C43—141no—
250#340—71no—
251#340—71no—
252#340—71no—
253#340—71no—
254#340—71no—
255#340—71no—
256#340C2×D711yescharacteristic
257#340C2×D711yescharacteristic
258#336—71no—
259#336—71no—
260C23×C7C22×D411yescharacteristic
261C2×C4×C7—21no—
262C2×C4×C7—21no—
263C2×C4×C7—22no—
264C2×C4×C7—22no—
265C2×C4×C7—22no—
266C2×C4×C7—41no—
267C2×C4×C7—41no—
268C2×C4×C7—41no—
269C2×C4×C7—41no—
270C2×C4×C7—41no—
271C2×C4×C7—41no—
272C2×C4×C7—41no—
273C2×C4×C7—41no—
274C2×C4×C7—41no—
275C2×C4×C7C22⋊Q812yes—
276C2×C4×C7C22⋊Q812yes—
277C2×C4×C7C2×SD1612yes—
278C2×C4×C7#13712yes—
279C2×C4×C7C23×C411yescharacteristic
280C2×C4×C7C22×Q811yescharacteristic
281C2×C4×C7C2×#4111yescharacteristic
282C2×C4×C7C2×#4111yescharacteristic
283C2×C4×C7C2×#4111yescharacteristic
284C2×C4×C7C2×#4111yescharacteristic
285C2×Dic7—22no—
286C2×Dic7—22no—
287C2×Dic7—21no—
288C2×Dic7—22no—
289C2×Dic7—21no—
290C2×Dic7—21no—
291C2×Dic7—21no—
292C2×Dic7—22no—
293C2×Dic7—22no—
294C2×Dic7—21no—
295C2×Dic7—21no—
296C2×Dic7—21no—
297C2×Dic7—41no—
298C2×Dic7—41no—
299C2×Dic7—41no—
300C2×Dic7—41no—
301C2×Dic7—41no—
302C2×Dic7—41no—
303C2×Dic7—41no—
304C2×Dic7C4×D412yes—
305C2×Dic7C4×D412yes—
306C2×Dic7C2×SD1612yes—
307C2×Dic7C2×SD1612yes—
308C2×Dic7#13512yes—
309Dic14—22no—
310Dic14—22no—
311Dic14—22no—
312Dic14—48no—
313Dic14C4×Q814yescomplemented
314C7×C8—22no—
315C7×C8—41no—
316C7⋊C8—22no—
317C7⋊C8—41no—
318C22×Q8—71no—
319C22×Q8—141no—
320C22×C8—71no—
321C22×C8—71no—
322C22×C8C22×D711yescharacteristic
323C22×C8C22×D711yescharacteristic
324C4⋊Q8—74no—
325C4⋊Q8—142no—
326C4×Q8—74no—
327C4×Q8—74no—
328C4×Q8—142no—
329C4×Q8—142no—
330C4×Q8—142no—
331C4×Q8—142no—
332C4×Q8—284no—
333C2×C4⋊C4—71no—
334C2×C4⋊C4—71no—
335C2×C4⋊C4—71no—
336C2×C4⋊C4—141no—
337C2×C4⋊C4—141no—
338C2×C4⋊C4—141no—
339C2×C4⋊C4—141no—
340C2×C4⋊C4—141no—
341C2×C4⋊C4—141no—
342C2×C4⋊C4—141no—
343C2×C4⋊C4—141no—
344C2×C4⋊C4C22×D711yescharacteristic
345C2×C4⋊C4C22×D711yescharacteristic
346C2×C4⋊C4C22×D711yescharacteristic
347C2×C4⋊C4C22×D711yescharacteristic
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—71no—
351C2×C42—71no—
352C2×C42—71no—
353C2×C42—71no—
354C2×C42—71no—
355C2×C42—71no—
356C2×C42—141no—
357C2×C42—141no—
358C2×C42—141no—
359C2×C42—141no—
360C2×C42—141no—
361C2×C42—141no—
362C2×C42C22×D711yescharacteristic
363#106—22no—
364#106—74no—
365#106—142no—
366#106C4×D714yes—
367C4⋊C8—74no—
368C4⋊C8—142no—
369#103—74no—
370#103—74no—
371#103—142no—
372#103—142no—
373C4×C8—22no—
374C4×C8—142no—
375#95—21no—
376#95—21no—
377#95—141no—
378#95—141no—
379#95—141no—
380#95—141no—
381#95—141no—
382C22×C7C2×C4×D411yescharacteristic
383C22×C7C2×C22⋊Q811yescharacteristic
384C22×C7#52511yescharacteristic
385C22×C7C22×SD1611yescharacteristic
386C22×C7C2×#13511yescharacteristic
387C22×C7C2×#13711yescharacteristic
388C22×C7#57511yescharacteristic
389C4×C7—22no—
390C4×C7—42no—
391C4×C7—42no—
392C4×C7—42no—
393C4×C7—81no—
394C4×C7#47514yescomplemented
395C4×C7C2×C4×Q811yescharacteristic
396C4×C7C4×#4111yescharacteristic
397C4×C7#52911yescharacteristic
398C4×C7#53311yescharacteristic
399Dic7—22no—
400Dic7—22no—
401Dic7—24no—
402Dic7—42no—
403Dic7—41no—
404Dic7—42no—
405Dic7—81no—
406Dic7C4×SD1614yes—
407C2×Q8—72no—
408C2×Q8—72no—
409C2×Q8—72no—
410C2×Q8—144no—
411C2×Q8—141no—
412C2×Q8—141no—
413C2×Q8—141no—
414C2×Q8—282no—
415C2×Q8—282no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—71no—
421C22×C4—71no—
422C22×C4—71no—
423C22×C4—71no—
424C22×C4—141no—
425C22×C4—141no—
426C22×C4—141no—
427C22×C4—141no—
428C22×C4D4×D711yescharacteristic
429C22×C4D4×D711yescharacteristic
430C22×C4C23×D711yescharacteristic
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—72no—
437C2×C8—141no—
438C2×C8—141no—
439C2×C8—141no—
440C2×C8—141no—
441C2×C8—141no—
442C2×C8C2×C4×D712yes—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—72no—
449C4⋊C4—72no—
450C4⋊C4—144no—
451C4⋊C4—144no—
452C4⋊C4—144no—
453C4⋊C4—144no—
454C4⋊C4—141no—
455C4⋊C4—141no—
456C4⋊C4—141no—
457C4⋊C4—141no—
458C4⋊C4—282no—
459C4⋊C4—282no—
460C4⋊C4—282no—
461C4⋊C4—282no—
462C4⋊C4C2×C4×D712yes—
463C4⋊C4C2×C4×D712yes—
464C4⋊C4#115712yes—
465C42—42no—
466C42—42no—
467C42—74no—
468C42—72no—
469C42—72no—
470C42—142no—
471C42—144no—
472C42—144no—
473C42—144no—
474C42—142no—
475C42—141no—
476C42—141no—
477C42—281no—
478C42—282no—
479C42—282no—
480C42—282no—
481C42#115712yes—
482C42Q8×D712yes—
483C2×C7C4×C22⋊Q811yescharacteristic
484C2×C7C2×C4×SD1611yescharacteristic
485C2×C7C4×#13711yescharacteristic
486C2×C7C2×#47511yescharacteristic
487C2×C7#307611yescharacteristic
488C2×C7#310311yescharacteristic
489C2×C7#310711yescharacteristic
490C23C2×D4×D711yescharacteristic
491Q8—74no—
492Q8—142no—
493Q8—142no—
494Q8—142no—
495Q8—288no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—72no—
511C2×C4—72no—
512C2×C4—72no—
513C2×C4—72no—
514C2×C4—72no—
515C2×C4—141no—
516C2×C4—142no—
517C2×C4—141no—
518C2×C4—141no—
519C2×C4—142no—
520C2×C4—141no—
521C2×C4—142no—
522C2×C4—141no—
523C2×C4—142no—
524C2×C4—141no—
525C2×C4—142no—
526C2×C4—141no—
527C2×C4—281no—
528C2×C4—281no—
529C2×C4—281no—
530C2×C4—281no—
531C2×C4—281no—
532C2×C4—281no—
533C2×C4—281no—
534C2×C4#645912yes—
535C2×C4#645912yes—
536C2×C4D7×SD1612yes—
537C2×C4#647812yes—
538C2×C4C22×C4×D711yescharacteristic
539C2×C4C2×#115711yescharacteristic
540C2×C4C2×#115711yescharacteristic
541C2×C4C2×Q8×D711yescharacteristic
542C2×C4D7×#4111yescharacteristic
543C2×C4D7×#4111yescharacteristic
544C8—22no—
545C8—41no—
546C8—142no—
547C8—281no—
548C7C4×#47511yescharacteristic, complemented, Sylow
549C22C2×#645911yescharacteristic
550C22C4×D4×D711yescharacteristic
551C22#9023811yescharacteristic
552C22C2×D7×SD1611yescharacteristic
553C22C2×#647811yescharacteristic
554C22D7×#13511yescharacteristic
555C22#9045911yescharacteristic
556C4—22no—
557C4—42no—
558C4—42no—
559C4—42no—
560C4—74no—
561C4—81no—
562C4—142no—
563C4—144no—
564C4—142no—
565C4—282no—
566C4—281no—
567C4—282no—
568C4—561no—
569C4#8962614yesdirect product factor
570C4C4×#115711yescharacteristic
571C4#9021911yescharacteristic
572C4C4×Q8×D711yescharacteristic
573C4#9026911yescharacteristic
574C2C4×#645911yescharacteristic
575C2C2×#8962611yescharacteristic
576C2#1173664111yescharacteristic
577C2C4×D7×SD1611yescharacteristic
578C2C4×#647811yescharacteristic
579C2#1173709811yescharacteristic
580C2#1173710011yescharacteristic
subgroupG/H
centerC22×C4D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC4×C7×#106C2
socle, prime radicalC23×C7C22×D4
cosocleC22×C4×C7C24
hypercenterC4×#106D7
hypocenterC7C4×#475
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#106

Complements

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

NH ≅ G/Ntype
45. #89626C4direct (N × H)
105. C4×Dic14Q8semidirect
313. Dic14C4×Q8semidirect
394. C4×C7#475semidirect
548. C7C4×#475semidirect
569. C4#89626direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#896262
C4×#64512
C4×#64502
C4×C7×#1062
#117283422
#117283172
#117283112
C4×#63902
C4×Dic7⋊C82
C4×#63822
C4×#63842
#117266612
#117266582
#117265542
#117265422
C4×#4757