Finite Group Databasebeta

← C4×#89753 #13274971

Subgroups — C4×#89753 #13274971

Order 1792.

1742 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C4⋊C4C211yesmaximal, characteristic
2C2×#89753C212yesmaximal
3C2×C4×C4⋊Dic7C211yesmaximal, characteristic
4C2×C42×Dic7C211yesmaximal, characteristic
5#11729318C212yesmaximal
6C4×C7⋊#95C211yesmaximal, characteristic
7C4×C7⋊#95C211yesmaximal, characteristic
8C4×C7⋊#95C211yesmaximal, characteristic
9C4×C7⋊#95C211yesmaximal, characteristic
10#11727161C212yesmaximal
11#11727155C212yesmaximal
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C42×C7C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C22×C42×C7C2211yescharacteristic
17C22×C4⋊Dic7C2212yes—
18C22×C4×Dic7C2212yes—
19C22×C4×Dic7C2211yescharacteristic
20C22×C4×Dic7C2211yescharacteristic
21C22×C4×Dic7C2212yes—
22C22×C4×Dic7C2211yescharacteristic
23C22×C4×Dic7C2211yescharacteristic
24C4×C7×C4⋊C4C418yescomplemented
25C2×C7×#95C2211yescharacteristic
26C2×C7×#95C2211yescharacteristic
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36#89753C4116yesdirect product factor
37C4×C4⋊Dic7—24no—
38C42×Dic7—24no—
39C4×#387—71nomaximal, Sylow
40C23×C4×C7C2311yescharacteristic
41C23×C4×C7C2311yescharacteristic
42C23×C4×C7C2311yescharacteristic
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C23×Dic7C2312yes—
48C23×Dic7C2312yes—
49C23×Dic7C2312yes—
50C23×Dic7C2312yes—
51C2×C7×C4⋊C4—24no—
52C2×C7×C4⋊C4C2×C418yes—
53C2×C7×C4⋊C4C2×C414yes—
54C2×C7×C4⋊C4C2×C414yes—
55C2×C42×C7—22no—
56C2×C42×C7—22no—
57C2×C42×C7—22no—
58C2×C42×C7—22no—
59C2×C42×C7—22no—
60C2×C42×C7—22no—
61C2×C42×C7C2×C414yes—
62C2×C42×C7C2×C414yes—
63C2×C42×C7C2×C414yes—
64C2×C4⋊Dic7—24no—
65C2×C4⋊Dic7—24no—
66C2×C4⋊Dic7C2×C418yes—
67C2×C4×Dic7—22no—
68C2×C4×Dic7—24no—
69C2×C4×Dic7—22no—
70C2×C4×Dic7—22no—
71C2×C4×Dic7—22no—
72C2×C4×Dic7—24no—
73C2×C4×Dic7—24no—
74C2×C4×Dic7—24no—
75C2×C4×Dic7—24no—
76C2×C4×Dic7—22no—
77C2×C4×Dic7—22no—
78C2×C4×Dic7—22no—
79C2×C4×Dic7—22no—
80C2×C4×Dic7—22no—
81C2×C4×Dic7—22no—
82C2×C4×Dic7C2×C418yes—
83C2×C4×Dic7D414yes—
84C2×C4×Dic7Q814yes—
85C7×#95C2×C414yes—
86C7×#95C2×C414yes—
87C7⋊#95—24no—
88C7⋊#95—24no—
89C7⋊#95—24no—
90C7⋊#95—24no—
91C7⋊#95—24no—
92C7⋊#95C2×C418yes—
93C7⋊#95C2×C418yes—
94C7⋊#95C2×C418yes—
95C7⋊#95C2×C418yes—
96C2×#387—72no—
97C2×C4×C4⋊C4—71no—
98C2×C4×C4⋊C4D711yescharacteristic
99C2×C43—71no—
100#1436—72no—
101#1436—72no—
102#1434—72no—
103C4×#95—71no—
104C4×#95—71no—
105C4×#95—71no—
106C4×#95—71no—
107C24×C7C2411yescharacteristic
108C22×C4×C7—21no—
109C22×C4×C7—21no—
110C22×C4×C7—21no—
111C22×C4×C7—22no—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7—21no—
115C22×C4×C7—21no—
116C22×C4×C7—21no—
117C22×C4×C7—21no—
118C22×C4×C7—21no—
119C22×C4×C7—22no—
120C22×C4×C7—21no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—21no—
125C22×C4×C7—21no—
126C22×C4×C7—21no—
127C22×C4×C7—22no—
128C22×C4×C7C22×C412yes—
129C22×C4×C7C22×C412yes—
130C22×C4×C7C22×C414yes—
131C22×C4×C7C22×C414yes—
132C22×C4×C7C22×C414yes—
133C22×C4×C7C22×C412yes—
134C22×C4×C7C22×C412yes—
135C22×C4×C7C22×C412yes—
136C22×C4×C7C22×C412yes—
137C22×C4×C7C22×C412yes—
138C22×C4×C7C2×D412yes—
139C22×C4×C7C2×Q812yes—
140C22×C4×C7#4114yes—
141C22×C4×C7#4112yes—
142C22×C4×C7#4112yes—
143C22×C4×C7#4112yes—
144C22×C4×C7#4112yes—
145C22×Dic7—22no—
146C22×Dic7—22no—
147C22×Dic7—22no—
148C22×Dic7—22no—
149C22×Dic7—22no—
150C22×Dic7—22no—
151C22×Dic7—22no—
152C22×Dic7—22no—
153C22×Dic7—22no—
154C22×Dic7—22no—
155C22×Dic7—22no—
156C22×Dic7—22no—
157C22×Dic7—22no—
158C22×Dic7—22no—
159C22×Dic7—22no—
160C22×Dic7—22no—
161C22×Dic7—22no—
162C22×Dic7—22no—
163C22×Dic7—22no—
164C22×Dic7—22no—
165C22×Dic7C22×C414yes—
166C22×Dic7C22×C414yes—
167C22×Dic7C22×C414yes—
168C22×Dic7C22×C414yes—
169C22×Dic7C2×D414yes—
170C22×Dic7C2×Q814yes—
171C22×Dic7#4114yes—
172C22×Dic7#4114yes—
173C7×C4⋊C4—28no—
174C7×C4⋊C4C42116yescomplemented
175C42×C7—28no—
176C42×C7—28no—
177C42×C7—28no—
178C4⋊Dic7—216no—
179C4×Dic7—216no—
180C4×Dic7—28no—
181C4×Dic7—28no—
182C4×Dic7—216no—
183C4×Dic7—44no—
184C4×Dic7—44no—
185C22×C4⋊C4—72no—
186C22×C4⋊C4C2×D711yescharacteristic
187C22×C4⋊C4C2×D711yescharacteristic
188C22×C42—72no—
189C22×C42—71no—
190C22×C42—71no—
191C22×C42—72no—
192C22×C42—71no—
193C22×C42—71no—
194C22×C42C2×D711yescharacteristic
195C22×C42C2×D711yescharacteristic
196C22×C42C2×D711yescharacteristic
197#387—716no—
198C4×C4⋊C4—144no—
199C4×C4⋊C4Dic718yescomplemented
200C2×#95—72no—
201C2×#95—72no—
202C2×#95—72no—
203C2×#95—72no—
204C2×#95—72no—
205C2×#95—72no—
206C2×#95—72no—
207C2×#95—72no—
208C2×#95—72no—
209C2×#95C2×D711yescharacteristic
210C2×#95C2×D711yescharacteristic
211C43—144no—
212C23×C7C23×C412yes—
213C23×C7C23×C411yescharacteristic
214C23×C7C22×D411yescharacteristic
215C23×C7C22×Q811yescharacteristic
216C23×C7C2×#4111yescharacteristic
217C23×C7C2×#4111yescharacteristic
218C23×C7C2×#4112yes—
219C23×C7C2×#4111yescharacteristic
220C23×C7C2×#4111yescharacteristic
221C23×C7C2×#4112yes—
222C23×C7C2×#4112yes—
223C2×C4×C7—22no—
224C2×C4×C7—22no—
225C2×C4×C7—24no—
226C2×C4×C7—24no—
227C2×C4×C7—22no—
228C2×C4×C7—22no—
229C2×C4×C7—22no—
230C2×C4×C7—24no—
231C2×C4×C7—24no—
232C2×C4×C7—24no—
233C2×C4×C7—24no—
234C2×C4×C7—22no—
235C2×C4×C7—22no—
236C2×C4×C7—22no—
237C2×C4×C7—24no—
238C2×C4×C7—24no—
239C2×C4×C7—22no—
240C2×C4×C7—22no—
241C2×C4×C7—22no—
242C2×C4×C7—22no—
243C2×C4×C7—22no—
244C2×C4×C7—22no—
245C2×C4×C7—42no—
246C2×C4×C7—42no—
247C2×C4×C7—42no—
248C2×C4×C7—42no—
249C2×C4×C7C2×C4214yes—
250C2×C4×C7C2×C4214yes—
251C2×C4×C7C2×C4214yes—
252C2×C4×C7#11714yes—
253C2×C4×C7#11714yes—
254C2×C4×C7C4×D414yes—
255C2×C4×C7C4×Q814yes—
256C2×C4×C7C22⋊Q814yes—
257C2×C4×C7#12314yes—
258C2×C4×C7#12514yes—
259C2×C4×C7#12614yes—
260C2×Dic7—24no—
261C2×Dic7—24no—
262C2×Dic7—24no—
263C2×Dic7—24no—
264C2×Dic7—24no—
265C2×Dic7—24no—
266C2×Dic7—24no—
267C2×Dic7—24no—
268C2×Dic7—24no—
269C2×Dic7—24no—
270C2×Dic7—24no—
271C2×Dic7—24no—
272C2×Dic7—24no—
273C2×Dic7—24no—
274C2×Dic7—24no—
275C2×Dic7—24no—
276C2×Dic7—24no—
277C2×Dic7—24no—
278C2×Dic7—42no—
279C2×Dic7—42no—
280C2×Dic7—42no—
281C2×Dic7—42no—
282C2×Dic7—42no—
283C2×Dic7—42no—
284C2×Dic7—42no—
285C2×Dic7—42no—
286C2×Dic7C4×D418yes—
287C2×Dic7C4×Q818yes—
288C23×C4—72no—
289C23×C4—72no—
290C23×C4—72no—
291C23×C4—72no—
292C23×C4C22×D711yescharacteristic
293C23×C4C22×D711yescharacteristic
294C23×C4C22×D711yescharacteristic
295C23×C4C22×D711yescharacteristic
296C23×C4C22×D711yescharacteristic
297C23×C4C22×D711yescharacteristic
298C23×C4C22×D711yescharacteristic
299C2×C4⋊C4—24no—
300C2×C4⋊C4—78no—
301C2×C4⋊C4—144no—
302C2×C4⋊C4—144no—
303C2×C4⋊C4C4×D718yes—
304C2×C4⋊C4C2×Dic714yes—
305C2×C4⋊C4C2×Dic714yes—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—22no—
309C2×C42—22no—
310C2×C42—22no—
311C2×C42—22no—
312C2×C42—78no—
313C2×C42—74no—
314C2×C42—74no—
315C2×C42—144no—
316C2×C42—144no—
317C2×C42—144no—
318C2×C42—144no—
319C2×C42—144no—
320C2×C42—142no—
321C2×C42—142no—
322C2×C42—142no—
323C2×C42—142no—
324C2×C42—142no—
325C2×C42—142no—
326C2×C42—142no—
327C2×C42—142no—
328C2×C42—142no—
329C2×C42—142no—
330C2×C42C2×Dic714yes—
331C2×C42C2×Dic714yes—
332C2×C42C2×Dic714yes—
333#95—78no—
334#95—78no—
335#95—78no—
336#95—78no—
337#95—144no—
338#95—144no—
339#95—144no—
340#95—144no—
341#95—144no—
342#95C2×Dic714yes—
343#95C2×Dic714yes—
344C22×C7C22×C4211yescharacteristic
345C22×C7C2×#11711yescharacteristic
346C22×C7C2×#11711yescharacteristic
347C22×C7C2×C4×D411yescharacteristic
348C22×C7C2×C4×D412yes—
349C22×C7C2×C4×Q811yescharacteristic
350C22×C7C2×C4×Q812yes—
351C22×C7C4×#4112yes—
352C22×C7C4×#4112yes—
353C22×C7C4×#4112yes—
354C22×C7C4×#4111yescharacteristic
355C22×C7C4×#4111yescharacteristic
356C22×C7C4×#4112yes—
357C22×C7C2×C22⋊Q811yescharacteristic
358C22×C7C2×#12311yescharacteristic
359C22×C7#52512yes—
360C22×C7C2×#12511yescharacteristic
361C22×C7C2×#12611yescharacteristic
362C22×C7#52912yes—
363C22×C7#52912yes—
364C22×C7#52912yes—
365C22×C7#52912yes—
366C22×C7#53312yes—
367C4×C7—24no—
368C4×C7—24no—
369C4×C7—24no—
370C4×C7—24no—
371C4×C7—42no—
372C4×C7—42no—
373C4×C7#38718yescomplemented
374Dic7—28no—
375Dic7—28no—
376Dic7—44no—
377Dic7—44no—
378C24C23×D711yescharacteristic
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—74no—
400C22×C4—74no—
401C22×C4—74no—
402C22×C4—74no—
403C22×C4—74no—
404C22×C4—74no—
405C22×C4—74no—
406C22×C4—74no—
407C22×C4—142no—
408C22×C4—142no—
409C22×C4—142no—
410C22×C4—142no—
411C22×C4—142no—
412C22×C4—142no—
413C22×C4—142no—
414C22×C4—142no—
415C22×C4—142no—
416C22×C4—142no—
417C22×C4—142no—
418C22×C4—142no—
419C22×C4—142no—
420C22×C4—142no—
421C22×C4—142no—
422C22×C4—142no—
423C22×C4—142no—
424C22×C4—142no—
425C22×C4—142no—
426C22×C4—142no—
427C22×C4C2×C4×D714yes—
428C22×C4C2×C4×D714yes—
429C22×C4C2×C4×D714yes—
430C22×C4#115714yes—
431C22×C4#115712yes—
432C22×C4#115712yes—
433C22×C4D4×D712yes—
434C22×C4#115912yes—
435C22×C4Q8×D712yes—
436C22×C4#116112yes—
437C22×C4C22×Dic712yes—
438C22×C4C22×Dic712yes—
439C22×C4C22×Dic712yes—
440C22×C4C22×Dic712yes—
441C22×C4C22×Dic712yes—
442C22×C4C22×Dic712yes—
443C22×C4C22×Dic712yes—
444C4⋊C4—28no—
445C4⋊C4—1416no—
446C4⋊C4C4×Dic7116yescomplemented
447C42—28no—
448C42—28no—
449C42—28no—
450C42—1416no—
451C42—1416no—
452C42—148no—
453C42—148no—
454C42—284no—
455C42—284no—
456C2×C7C4×#11711yescharacteristic
457C2×C7C42×D411yescharacteristic
458C2×C7C42×Q811yescharacteristic
459C2×C7C2×#38711yescharacteristic
460C2×C7#229011yescharacteristic
461C2×C7#229511yescharacteristic
462C2×C7#229811yescharacteristic
463C2×C7C4×#12312yes—
464C2×C7C4×C22⋊Q812yes—
465C2×C7C4×#12612yes—
466C2×C7C4×#12512yes—
467C23C22×C4×D712yes—
468C23C2×#115711yescharacteristic
469C23C2×#115711yescharacteristic
470C23C2×#115712yes—
471C23C2×D4×D711yescharacteristic
472C23C2×#115911yescharacteristic
473C23C2×Q8×D711yescharacteristic
474C23C2×#116111yescharacteristic
475C23D7×#4112yes—
476C23D7×#4112yes—
477C23C23×Dic711yescharacteristic
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—78no—
505C2×C4—78no—
506C2×C4—144no—
507C2×C4—144no—
508C2×C4—144no—
509C2×C4—144no—
510C2×C4—144no—
511C2×C4—144no—
512C2×C4—144no—
513C2×C4—144no—
514C2×C4—144no—
515C2×C4—144no—
516C2×C4—144no—
517C2×C4—144no—
518C2×C4—144no—
519C2×C4—144no—
520C2×C4—144no—
521C2×C4—144no—
522C2×C4—144no—
523C2×C4—144no—
524C2×C4—282no—
525C2×C4—282no—
526C2×C4—282no—
527C2×C4—282no—
528C2×C4—282no—
529C2×C4—282no—
530C2×C4—282no—
531C2×C4—282no—
532C2×C4#645214yes—
533C2×C4#645714yes—
534C2×C4#645914yes—
535C2×C4#646114yes—
536C2×C4C2×C4×Dic714yes—
537C2×C4C2×C4×Dic714yes—
538C2×C4C2×C4×Dic714yes—
539C2×C4#648914yes—
540C2×C4#648914yes—
541C2×C4D4×Dic714yes—
542C2×C4Q8×Dic714yes—
543C7C4×#38711yescharacteristic, complemented, Sylow
544C22C4×#115712yes—
545C22C4×#115712yes—
546C22C2×#645211yescharacteristic
547C22C2×#645711yescharacteristic
548C22C2×#645911yescharacteristic
549C22C2×#646111yescharacteristic
550C22#9021912yes—
551C22#9021912yes—
552C22C4×#115912yes—
553C22#9022912yes—
554C22C4×D4×D712yes—
555C22#9023812yes—
556C22C4×Q8×D712yes—
557C22C4×#116112yes—
558C22#9026912yes—
559C22#9027112yes—
560C22C22×C4×Dic711yescharacteristic
561C22C2×#648911yescharacteristic
562C22C2×#648911yescharacteristic
563C22C2×D4×Dic711yescharacteristic
564C22C2×Q8×Dic711yescharacteristic
565C22#41×Dic711yescharacteristic
566C22#41×Dic711yescharacteristic
567C4—24no—
568C4—24no—
569C4—24no—
570C4—24no—
571C4—42no—
572C4—42no—
573C4—148no—
574C4—148no—
575C4—284no—
576C4—284no—
577C4#8975318yesdirect product factor
578C2C4×#646112yes—
579C2C4×#645212yes—
580C2C4×#645712yes—
581C2C4×#645912yes—
582C2C4×#648911yescharacteristic
583C2C2×#8975311yescharacteristic
584C2#1173967411yescharacteristic
585C2C4×D4×Dic711yescharacteristic
586C2#1173976311yescharacteristic
587C2C4×Q8×Dic711yescharacteristic
588C2#1173989611yescharacteristic
subgroupG/H
centerC23×C4C22×D7
commutatorC22×C7C22×C42
FrattiniC24C23×D7
FittingC2×C4×C7×C4⋊C4C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×C4×C4⋊C4D7
hypocenterC7C4×#387
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
24. C4×C7×C4⋊C4C4semidirect
36. #89753C4direct (N × H)
174. C7×C4⋊C4C42semidirect
199. C4×C4⋊C4Dic7semidirect
373. C4×C7#387semidirect
446. C4⋊C4C4×Dic7semidirect
543. C7C4×#387semidirect
577. C4#89753direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C7×C4⋊C42
C2×#897532
C2×C4×C4⋊Dic72
C2×C42×Dic72
#117293182
C4×C7⋊#952
#117271612
#117271552
C4×#3877