Finite Group Databasebeta

← C4×#89751 #13275607

Subgroups — C4×#89751 #13275607

Order 1792.

1942 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic14C211yesmaximal, characteristic
2C2×C4×C7×C4⋊C4C211yesmaximal, characteristic
3C2×#89751C211yesmaximal, characteristic
4C2×C4×Dic7⋊C4C212yesmaximal
5#11729322C212yesmaximal
6#11729319C211yesmaximal, characteristic
7C4×C7⋊#95C212yesmaximal
8C4×C7⋊#95C211yesmaximal, characteristic
9#11727178C211yesmaximal, characteristic
10#11727174C211yesmaximal, characteristic
11#11727163C212yesmaximal
12C23×Dic14C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C22×C42×C7C2211yescharacteristic
17C22×C42×C7C2211yescharacteristic
18C22×C4⋊Dic7C2211yescharacteristic
19C22×Dic7⋊C4C2212yes—
20C22×Dic7⋊C4C2212yes—
21C22×Dic7⋊C4C2212yes—
22C22×C4×Dic7C2212yes—
23C22×C4×Dic7C2212yes—
24C2×C4×Dic14—24no—
25C2×C4×Dic14—28no—
26C4×C7×C4⋊C4—24no—
27C2×C7×#95C2211yescharacteristic
28C2×C7×#95C2211yescharacteristic
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2211yescharacteristic
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2211yescharacteristic
37C2×C7⋊#95C2212yes—
38#89751C418yesdirect product factor
39C4×Dic7⋊C4—28no—
40C4×#395—71nomaximal, Sylow
41C23×C4×C7C2311yescharacteristic
42C23×C4×C7C2311yescharacteristic
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2311yescharacteristic
48C23×Dic7C2312yes—
49C23×Dic7C2312yes—
50C23×Dic7C2312yes—
51C23×Dic7C2312yes—
52C22×Dic14—22no—
53C22×Dic14—22no—
54C22×Dic14—24no—
55C22×Dic14—24no—
56C22×Dic14C2×C414yes—
57C2×C7×C4⋊C4—22no—
58C2×C7×C4⋊C4—22no—
59C2×C7×C4⋊C4—22no—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4C2×C414yes—
63C2×C42×C7—24no—
64C2×C42×C7—22no—
65C2×C42×C7—22no—
66C2×C42×C7—24no—
67C2×C42×C7—22no—
68C2×C42×C7D414yes—
69C2×C42×C7Q814yescomplemented
70C2×C4⋊Dic7—22no—
71C2×C4⋊Dic7—24no—
72C2×Dic7⋊C4—24no—
73C2×Dic7⋊C4—24no—
74C2×Dic7⋊C4—24no—
75C2×Dic7⋊C4—24no—
76C2×Dic7⋊C4—24no—
77C2×Dic7⋊C4—24no—
78C2×Dic7⋊C4—24no—
79C2×Dic7⋊C4—24no—
80C2×Dic7⋊C4C2×C418yes—
81C2×C4×Dic7—24no—
82C2×C4×Dic7—24no—
83C2×C4×Dic7—24no—
84C2×C4×Dic7—24no—
85C2×C4×Dic7D418yes—
86C2×C4×Dic7Q818yescomplemented
87C4×Dic14—232no—
88C7×#95—22no—
89C7×#95—22no—
90C7⋊#95—22no—
91C7⋊#95—24no—
92C7⋊#95—24no—
93C7⋊#95—24no—
94C7⋊#95—24no—
95C7⋊#95—24no—
96C7⋊#95—24no—
97C7⋊#95C2×C418yes—
98C7⋊#95C2×C414yes—
99C22×C4×Q8—71no—
100C2×#395—71no—
101C2×C4×C4⋊C4—72no—
102C2×C4×C4⋊C4D711yescharacteristic
103#1446—71no—
104#1444—71no—
105#1444—72no—
106#1441—72no—
107#1441—71no—
108C4×#95—72no—
109C4×#95—71no—
110C24×C7C2411yescharacteristic
111C22×C4×C7—22no—
112C22×C4×C7—21no—
113C22×C4×C7—21no—
114C22×C4×C7—21no—
115C22×C4×C7—21no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—22no—
119C22×C4×C7—21no—
120C22×C4×C7—21no—
121C22×C4×C7—21no—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—21no—
129C22×C4×C7—21no—
130C22×C4×C7—21no—
131C22×C4×C7—21no—
132C22×C4×C7—21no—
133C22×C4×C7C22×C412yes—
134C22×C4×C7C22×C412yes—
135C22×C4×C7C22×C412yes—
136C22×C4×C7C2×D412yes—
137C22×C4×C7C2×D412yes—
138C22×C4×C7C2×D414yes—
139C22×C4×C7C2×D412yes—
140C22×C4×C7C2×Q812yes—
141C22×C4×C7C2×Q812yes—
142C22×C4×C7C2×Q812yes—
143C22×C4×C7C2×Q814yes—
144C22×C4×C7#4112yes—
145C22×C4×C7#4112yes—
146C22×C4×C7#4112yes—
147C22×C4×C7#4112yes—
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×Dic7—22no—
166C22×Dic7—22no—
167C22×Dic7—22no—
168C22×Dic7C22×C414yes—
169C22×Dic7C22×C414yes—
170C22×Dic7C2×D414yes—
171C22×Dic7C2×D414yes—
172C22×Dic7C2×Q814yes—
173C22×Dic7C2×Q814yes—
174C22×Dic7#4114yes—
175C22×Dic7#4114yes—
176C2×Dic14—28no—
177C2×Dic14—216no—
178C2×Dic14—28no—
179C2×Dic14—28no—
180C2×Dic14—216no—
181C7×C4⋊C4—28no—
182C7×C4⋊C4—28no—
183C42×C7—28no—
184C42×C7—28no—
185C42×C7—44no—
186C4⋊Dic7—28no—
187Dic7⋊C4—216no—
188Dic7⋊C4—216no—
189Dic7⋊C4—216no—
190C4×Dic7—216no—
191C4×Dic7—216no—
192C23×Q8—71no—
193C2×C4×Q8—148no—
194C2×C4×Q8—144no—
195C22×C4⋊C4—72no—
196C22×C4⋊C4—72no—
197C22×C4⋊C4—71no—
198C22×C4⋊C4—72no—
199C22×C4⋊C4C2×D711yescharacteristic
200C22×C4⋊C4C2×D711yescharacteristic
201C22×C42—72no—
202C22×C42—72no—
203C22×C42C2×D711yescharacteristic
204C22×C42C2×D711yescharacteristic
205C22×C42C2×D711yescharacteristic
206#395—78no—
207C4×C4⋊C4—24no—
208C4×C4⋊C4—148no—
209C2×#95—72no—
210C2×#95—71no—
211C2×#95—72no—
212C2×#95—72no—
213C2×#95—72no—
214C2×#95—72no—
215C2×#95—71no—
216C2×#95—72no—
217C2×#95—72no—
218C2×#95C2×D711yescharacteristic
219C2×#95C2×D711yescharacteristic
220C23×C7C23×C411yescharacteristic
221C23×C7C22×D412yes—
222C23×C7C22×D411yescharacteristic
223C23×C7C22×Q811yescharacteristic
224C23×C7C22×Q812yes—
225C23×C7C2×#4111yescharacteristic
226C23×C7C2×#4111yescharacteristic
227C23×C7C2×#4111yescharacteristic
228C23×C7C2×#4111yescharacteristic
229C23×C7C2×#4112yes—
230C23×C7C2×#4112yes—
231C2×C4×C7—22no—
232C2×C4×C7—24no—
233C2×C4×C7—22no—
234C2×C4×C7—22no—
235C2×C4×C7—22no—
236C2×C4×C7—22no—
237C2×C4×C7—22no—
238C2×C4×C7—24no—
239C2×C4×C7—22no—
240C2×C4×C7—22no—
241C2×C4×C7—24no—
242C2×C4×C7—22no—
243C2×C4×C7—22no—
244C2×C4×C7—22no—
245C2×C4×C7—24no—
246C2×C4×C7—22no—
247C2×C4×C7—22no—
248C2×C4×C7—22no—
249C2×C4×C7—24no—
250C2×C4×C7—41no—
251C2×C4×C7—41no—
252C2×C4×C7—42no—
253C2×C4×C7—42no—
254C2×C4×C7—41no—
255C2×C4×C7—41no—
256C2×C4×C7—42no—
257C2×C4×C7—42no—
258C2×C4×C7—42no—
259C2×C4×C7—41no—
260C2×C4×C7—41no—
261C2×C4×C7C4×D414yes—
262C2×C4×C7C4×Q814yescomplemented
263C2×C4×C7#12014yes—
264C2×C4×C7C22⋊Q818yes—
265C2×C4×C7C22⋊Q814yes—
266C2×C4×C7C4⋊Q818yes—
267C2×C4×C7C4⋊Q814yes—
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—24no—
279C2×Dic7—24no—
280C2×Dic7—24no—
281C2×Dic7—24no—
282C2×Dic7—24no—
283C2×Dic7—24no—
284C2×Dic7—24no—
285C2×Dic7—24no—
286C2×Dic7—42no—
287C2×Dic7—42no—
288C2×Dic7—42no—
289C2×Dic7—42no—
290C2×Dic7—42no—
291C2×Dic7—42no—
292C2×Dic7—42no—
293C2×Dic7—42no—
294C2×Dic7C4×D418yes—
295C2×Dic7C4×Q818yescomplemented
296Dic14—232no—
297C22×Q8—74no—
298C22×Q8—144no—
299C22×Q8—144no—
300C22×Q8—142no—
301C22×Q8—142no—
302C23×C4—72no—
303C23×C4—72no—
304C23×C4—72no—
305C23×C4—72no—
306C23×C4C22×D711yescharacteristic
307C23×C4C22×D711yescharacteristic
308C23×C4C22×D711yescharacteristic
309C23×C4C22×D711yescharacteristic
310C23×C4C22×D711yescharacteristic
311C23×C4C22×D711yescharacteristic
312C23×C4C22×D711yescharacteristic
313C4×Q8—1432no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—78no—
320C2×C4⋊C4—144no—
321C2×C4⋊C4—144no—
322C2×C4⋊C4—144no—
323C2×C4⋊C4—144no—
324C2×C4⋊C4—144no—
325C2×C4⋊C4—144no—
326C2×C4⋊C4—144no—
327C2×C4⋊C4—144no—
328C2×C4⋊C4—144no—
329C2×C4⋊C4—142no—
330C2×C4⋊C4C4×D714yes—
331C2×C42—22no—
332C2×C42—24no—
333C2×C42—22no—
334C2×C42—24no—
335C2×C42—22no—
336C2×C42—78no—
337C2×C42—78no—
338C2×C42—144no—
339C2×C42—144no—
340C2×C42—144no—
341C2×C42—144no—
342C2×C42Dic1414yescomplemented
343C2×C42C22⋊D714yes—
344#95—22no—
345#95—22no—
346#95—74no—
347#95—78no—
348#95—144no—
349#95—144no—
350#95—144no—
351#95—144no—
352#95—144no—
353#95—144no—
354#95—142no—
355C22×C7C2×C4×D411yescharacteristic
356C22×C7C2×C4×D412yes—
357C22×C7C2×C4×Q811yescharacteristic
358C22×C7C2×C4×Q812yes—
359C22×C7C4×#4111yescharacteristic
360C22×C7C2×#12011yescharacteristic
361C22×C7C2×C22⋊Q812yes—
362C22×C7C2×C22⋊Q811yescharacteristic
363C22×C7#52511yescharacteristic
364C22×C7#52512yes—
365C22×C7#52512yes—
366C22×C7#52511yescharacteristic
367C22×C7#52911yescharacteristic
368C22×C7#52912yes—
369C22×C7C2×C4⋊Q812yes—
370C22×C7C2×C4⋊Q811yescharacteristic
371C22×C7#53212yes—
372C22×C7#53211yescharacteristic
373C22×C7#53311yescharacteristic
374C22×C7#53312yes—
375C22×C7#53312yes—
376C22×C7#53312yes—
377C22×C7#53312yes—
378C4×C7—24no—
379C4×C7—24no—
380C4×C7—42no—
381C4×C7—42no—
382C4×C7—42no—
383C4×C7—42no—
384C4×C7#39518yescomplemented
385Dic7—28no—
386Dic7—28no—
387Dic7—44no—
388Dic7—44no—
389C24C23×D711yescharacteristic
390C2×Q8—1416no—
391C2×Q8—148no—
392C2×Q8—1416no—
393C2×Q8—148no—
394C2×Q8—148no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—74no—
418C22×C4—74no—
419C22×C4—74no—
420C22×C4—74no—
421C22×C4—74no—
422C22×C4—74no—
423C22×C4—74no—
424C22×C4—74no—
425C22×C4—142no—
426C22×C4—142no—
427C22×C4—142no—
428C22×C4—142no—
429C22×C4—142no—
430C22×C4—142no—
431C22×C4—142no—
432C22×C4—142no—
433C22×C4—142no—
434C22×C4—142no—
435C22×C4—142no—
436C22×C4—142no—
437C22×C4—142no—
438C22×C4—142no—
439C22×C4—142no—
440C22×C4—142no—
441C22×C4—142no—
442C22×C4—142no—
443C22×C4—142no—
444C22×C4—142no—
445C22×C4C2×Dic1412yes—
446C22×C4C2×Dic1412yes—
447C22×C4C2×Dic1412yes—
448C22×C4C2×C4×D712yes—
449C22×C4C2×C4×D712yes—
450C22×C4C2×C4×D712yes—
451C22×C4#115712yes—
452C22×C4#115712yes—
453C22×C4#115712yes—
454C22×C4#115712yes—
455C22×C4D4×D714yes—
456C22×C4Q8×D714yes—
457C22×C4C2×C22⋊D712yes—
458C22×C4C2×C22⋊D712yes—
459C22×C4C2×C22⋊D712yes—
460C4⋊C4—28no—
461C4⋊C4—28no—
462C4⋊C4—1416no—
463C4⋊C4—1416no—
464C4⋊C4—1416no—
465C4⋊C4—148no—
466C42—28no—
467C42—28no—
468C42—44no—
469C42—1416no—
470C42—1416no—
471C2×C7C4×#12011yescharacteristic
472C2×C7C4×C22⋊Q812yes—
473C2×C7C4×C22⋊Q811yescharacteristic
474C2×C7C4×C4⋊Q812yes—
475C2×C7C4×C4⋊Q811yescharacteristic
476C2×C7C2×#39511yescharacteristic
477C2×C7#238811yescharacteristic
478C2×C7#239612yes—
479C2×C7#239611yescharacteristic
480C2×C7#239911yescharacteristic
481C2×C7#239912yes—
482C23C22×Dic1411yescharacteristic
483C23C22×C4×D711yescharacteristic
484C23C2×#115711yescharacteristic
485C23C2×#115711yescharacteristic
486C23C2×#115711yescharacteristic
487C23C2×#115711yescharacteristic
488C23C2×D4×D712yes—
489C23C2×Q8×D712yes—
490C23D7×#4112yes—
491C23D7×#4112yes—
492C23C22×C22⋊D711yescharacteristic
493Q8—1432no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—78no—
525C2×C4—78no—
526C2×C4—144no—
527C2×C4—144no—
528C2×C4—144no—
529C2×C4—144no—
530C2×C4—144no—
531C2×C4—144no—
532C2×C4—144no—
533C2×C4—144no—
534C2×C4—144no—
535C2×C4—144no—
536C2×C4—144no—
537C2×C4—144no—
538C2×C4—144no—
539C2×C4—144no—
540C2×C4—144no—
541C2×C4—144no—
542C2×C4—144no—
543C2×C4—144no—
544C2×C4—282no—
545C2×C4—282no—
546C2×C4—282no—
547C2×C4—282no—
548C2×C4—282no—
549C2×C4—282no—
550C2×C4—282no—
551C2×C4—282no—
552C2×C4C4×Dic1414yescomplemented
553C2×C4#645118yes—
554C2×C4#645918yes—
555C2×C4#648714yes—
556C2×C4C4×C22⋊D714yes—
557C2×C4#650014yes—
558C2×C4#650714yes—
559C7C4×#39511yescharacteristic, complemented, Sylow
560C22C2×C4×Dic1411yescharacteristic
561C22#9016111yescharacteristic
562C22C4×#115711yescharacteristic
563C22#9017011yescharacteristic
564C22C2×#645112yes—
565C22C2×#645912yes—
566C22#9020812yes—
567C22#9021912yes—
568C22C4×D4×D712yes—
569C22#9023812yes—
570C22#9023812yes—
571C22#9023912yes—
572C22C4×Q8×D712yes—
573C22#9026912yes—
574C22#9026912yes—
575C22#9026912yes—
576C22C2×#648711yescharacteristic
577C22C2×C4×C22⋊D711yescharacteristic
578C22#9048211yescharacteristic
579C22C2×#650011yescharacteristic
580C22C2×#650711yescharacteristic
581C22#9051911yescharacteristic
582C22#9052311yescharacteristic
583C4—24no—
584C4—24no—
585C4—42no—
586C4—42no—
587C4—42no—
588C4—42no—
589C4—148no—
590C4—148no—
591C4—284no—
592C4—284no—
593C4#8975118yesdirect product factor
594C2C4×#645112yes—
595C2#1173111412yes—
596C2C4×#645912yes—
597C2#1173122312yes—
598C2C4×#648711yescharacteristic
599C2C2×#8975111yescharacteristic
600C2#1173969011yescharacteristic
601C2C4×#650011yescharacteristic
602C2#1173984511yescharacteristic
603C2C4×#650711yescharacteristic
604C2#1173991211yescharacteristic
subgroupG/H
centerC23×C4C22×D7
commutatorC23×C7C23×C4
FrattiniC24C23×D7
FittingC2×C4×C7×C4⋊C4C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×C4×C4⋊C4D7
hypocenterC7C4×#395
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
38. #89751C4direct (N × H)
69. C2×C42×C7Q8semidirect
86. C2×C4×Dic7Q8semidirect
262. C2×C4×C7C4×Q8semidirect
295. C2×Dic7C4×Q8semidirect
342. C2×C42Dic14semidirect
384. C4×C7#395semidirect
552. C2×C4C4×Dic14semidirect
559. C7C4×#395semidirect
593. C4#89751direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Dic142
C2×C4×C7×C4⋊C42
C2×#897512
C2×C4×Dic7⋊C42
#117293222
#117293192
C4×C7⋊#952
#117271782
#117271742
#117271632
C4×#3957