Finite Group Databasebeta

← C4×#89744 #13274987

Subgroups — C4×#89744 #13274987

Order 1792.

1918 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
1C2×C4×C7×C4⋊C4C211yesmaximal, characteristic
2C2×#89744C212yesmaximal
3C2×C4×Dic7⋊C4C211yesmaximal, characteristic
4C2×C4×Dic7⋊C4C211yesmaximal, characteristic
5C2×C4×Dic7⋊C4C211yesmaximal, characteristic
6C2×C42×Dic7C211yesmaximal, characteristic
7#11729318C212yesmaximal
8C4×C7⋊#95C211yesmaximal, characteristic
9C4×C7⋊#95C211yesmaximal, characteristic
10#11727159C212yesmaximal
11Dic7⋊#95C212yesmaximal
12C22×C7×C4⋊C4C2212yes—
13C22×C42×C7C2211yescharacteristic
14C22×C42×C7C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C22×Dic7⋊C4C2211yescharacteristic
17C22×Dic7⋊C4C2212yes—
18C22×Dic7⋊C4C2212yes—
19C22×Dic7⋊C4C2211yescharacteristic
20C22×C4×Dic7C2212yes—
21C22×C4×Dic7C2211yescharacteristic
22C22×C4×Dic7C2212yes—
23C22×C4×Dic7C2211yescharacteristic
24C22×C4×Dic7C2211yescharacteristic
25C22×C4×Dic7C2211yescharacteristic
26C4×C7×C4⋊C4—24no—
27C2×C7×#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2211yescharacteristic
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2211yescharacteristic
35C2×C7⋊#95C2212yes—
36#89744C4116yesdirect product factor
37C4×Dic7⋊C4—24no—
38C4×Dic7⋊C4—24no—
39C4×Dic7⋊C4C418yescomplemented
40C42×Dic7—24no—
41C4×#389—71nomaximal, Sylow
42C23×C4×C7C2311yescharacteristic
43C23×C4×C7C2312yes—
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2312yes—
46C23×C4×C7C2311yescharacteristic
47C23×Dic7C2312yes—
48C23×Dic7C2311yescharacteristic
49C23×Dic7C2311yescharacteristic
50C23×Dic7C2311yescharacteristic
51C23×Dic7C2312yes—
52C23×Dic7C2311yescharacteristic
53C2×C7×C4⋊C4—24no—
54C2×C7×C4⋊C4—24no—
55C2×C7×C4⋊C4C2×C418yes—
56C2×C42×C7—22no—
57C2×C42×C7—22no—
58C2×C42×C7—22no—
59C2×C42×C7—22no—
60C2×C42×C7—22no—
61C2×C42×C7—22no—
62C2×C42×C7—22no—
63C2×C42×C7C2×C414yes—
64C2×C42×C7D414yes—
65C2×Dic7⋊C4—24no—
66C2×Dic7⋊C4—24no—
67C2×Dic7⋊C4—24no—
68C2×Dic7⋊C4—24no—
69C2×Dic7⋊C4—24no—
70C2×Dic7⋊C4C2×C414yes—
71C2×Dic7⋊C4C2×C418yes—
72C2×Dic7⋊C4C2×C418yes—
73C2×Dic7⋊C4C2×C414yes—
74C2×Dic7⋊C4C2×C418yes—
75C2×C4×Dic7—22no—
76C2×C4×Dic7—22no—
77C2×C4×Dic7—24no—
78C2×C4×Dic7—22no—
79C2×C4×Dic7—22no—
80C2×C4×Dic7—24no—
81C2×C4×Dic7—24no—
82C2×C4×Dic7—24no—
83C2×C4×Dic7—24no—
84C2×C4×Dic7—22no—
85C2×C4×Dic7—22no—
86C2×C4×Dic7—22no—
87C2×C4×Dic7C2×C414yes—
88C2×C4×Dic7C2×C418yes—
89C2×C4×Dic7C2×C414yes—
90C2×C4×Dic7D414yes—
91C2×C4×Dic7Q814yes—
92C2×C4×Dic7Q814yes—
93C7×#95—24no—
94C7⋊#95—24no—
95C7⋊#95—24no—
96C7⋊#95—24no—
97C7⋊#95—24no—
98C7⋊#95C2×C414yes—
99C7⋊#95C2×C414yes—
100C7⋊#95C2×C418yes—
101C7⋊#95C2×C418yes—
102C2×#389—72no—
103C2×C4×C4⋊C4—71no—
104C2×C4×C4⋊C4—71no—
105C2×C4×C4⋊C4—71no—
106C2×C4×C4⋊C4D711yescharacteristic
107C2×C43—71no—
108#1436—72no—
109#1436—72no—
110C4⋊#95—72no—
111C4×#95—71no—
112C4×#95—71no—
113C24×C7C2411yescharacteristic
114C22×C4×C7—22no—
115C22×C4×C7—21no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—21no—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
121C22×C4×C7—22no—
122C22×C4×C7—21no—
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—22no—
130C22×C4×C7—22no—
131C22×C4×C7C22×C412yes—
132C22×C4×C7C22×C414yes—
133C22×C4×C7C22×C412yes—
134C22×C4×C7C22×C414yes—
135C22×C4×C7C22×C414yes—
136C22×C4×C7C22×C412yes—
137C22×C4×C7C2×D414yes—
138C22×C4×C7C2×D412yes—
139C22×C4×C7C2×D412yes—
140C22×C4×C7C2×Q812yes—
141C22×C4×C7C2×Q812yes—
142C22×C4×C7#4114yes—
143C22×C4×C7#4112yes—
144C22×C4×C7#4112yes—
145C22×Dic7—22no—
146C22×Dic7—21no—
147C22×Dic7—21no—
148C22×Dic7—22no—
149C22×Dic7—22no—
150C22×Dic7—22no—
151C22×Dic7—22no—
152C22×Dic7—22no—
153C22×Dic7—22no—
154C22×Dic7—21no—
155C22×Dic7—22no—
156C22×Dic7—22no—
157C22×Dic7—22no—
158C22×Dic7—22no—
159C22×Dic7—21no—
160C22×Dic7—22no—
161C22×Dic7—22no—
162C22×Dic7—22no—
163C22×Dic7—22no—
164C22×Dic7C22×C412yes—
165C22×Dic7C22×C414yes—
166C22×Dic7C22×C412yes—
167C22×Dic7C22×C414yes—
168C22×Dic7C22×C412yes—
169C22×Dic7C22×C414yes—
170C22×Dic7C22×C412yes—
171C22×Dic7C22×C414yes—
172C22×Dic7C2×D412yes—
173C22×Dic7C2×D412yes—
174C22×Dic7C2×Q812yes—
175C22×Dic7C2×Q814yes—
176C22×Dic7C2×Q812yes—
177C22×Dic7#4114yes—
178C22×Dic7#4114yes—
179C7×C4⋊C4—216no—
180C42×C7—28no—
181C42×C7—28no—
182C42×C7—44no—
183Dic7⋊C4—216no—
184Dic7⋊C4—28no—
185Dic7⋊C4—216no—
186Dic7⋊C4C42116yescomplemented
187C4×Dic7—216no—
188C4×Dic7—28no—
189C4×Dic7—28no—
190C4×Dic7—216no—
191C4×Dic7—44no—
192C4×Dic7C4⋊C4116yescomplemented
193C22×C4⋊C4—71no—
194C22×C4⋊C4—71no—
195C22×C4⋊C4—72no—
196C22×C4⋊C4—72no—
197C22×C4⋊C4C2×D712yes—
198C22×C42—71no—
199C22×C42—72no—
200C22×C42—71no—
201C22×C42—71no—
202C22×C42—72no—
203C22×C42—71no—
204C22×C42C2×D711yescharacteristic
205C22×C42C2×D711yescharacteristic
206C22×C42C2×D711yescharacteristic
207#389—716no—
208C4×C4⋊C4—24no—
209C4×C4⋊C4—78no—
210C4×C4⋊C4—144no—
211C4×C4⋊C4—144no—
212C2×#95—72no—
213C2×#95—72no—
214C2×#95—71no—
215C2×#95—71no—
216C2×#95—72no—
217C2×#95—72no—
218C2×#95—72no—
219C2×#95—72no—
220C2×#95C2×D712yes—
221C43—144no—
222C23×C7C23×C411yescharacteristic
223C23×C7C23×C412yes—
224C23×C7C22×D411yescharacteristic
225C23×C7C22×D411yescharacteristic
226C23×C7C22×Q811yescharacteristic
227C23×C7C22×Q811yescharacteristic
228C23×C7C2×#4111yescharacteristic
229C23×C7C2×#4112yes—
230C23×C7C2×#4111yescharacteristic
231C23×C7C2×#4112yes—
232C23×C7C2×#4112yes—
233C2×C4×C7—24no—
234C2×C4×C7—22no—
235C2×C4×C7—24no—
236C2×C4×C7—24no—
237C2×C4×C7—22no—
238C2×C4×C7—24no—
239C2×C4×C7—24no—
240C2×C4×C7—24no—
241C2×C4×C7—24no—
242C2×C4×C7—24no—
243C2×C4×C7—22no—
244C2×C4×C7—24no—
245C2×C4×C7—22no—
246C2×C4×C7—24no—
247C2×C4×C7—22no—
248C2×C4×C7—24no—
249C2×C4×C7—42no—
250C2×C4×C7—42no—
251C2×C4×C7—42no—
252C2×C4×C7—42no—
253C2×C4×C7—42no—
254C2×C4×C7—42no—
255C2×C4×C7C2×C4214yes—
256C2×C4×C7C2×C4⋊C414yes—
257C2×C4×C7C4×D418yes—
258C2×C4×C7C4×D414yes—
259C2×C4×C7C4×Q814yes—
260C2×C4×C7#12114yes—
261C2×C4×C7C22⋊Q814yes—
262C2×C4×C7#12514yes—
263C2×C4×C7C4⋊Q814yes—
264C2×Dic7—22no—
265C2×Dic7—24no—
266C2×Dic7—24no—
267C2×Dic7—24no—
268C2×Dic7—22no—
269C2×Dic7—22no—
270C2×Dic7—24no—
271C2×Dic7—22no—
272C2×Dic7—24no—
273C2×Dic7—24no—
274C2×Dic7—24no—
275C2×Dic7—24no—
276C2×Dic7—24no—
277C2×Dic7—24no—
278C2×Dic7—22no—
279C2×Dic7—22no—
280C2×Dic7—24no—
281C2×Dic7—24no—
282C2×Dic7—22no—
283C2×Dic7—24no—
284C2×Dic7—42no—
285C2×Dic7—42no—
286C2×Dic7—42no—
287C2×Dic7—42no—
288C2×Dic7—42no—
289C2×Dic7—42no—
290C2×Dic7C2×C4214yes—
291C2×Dic7C2×C4214yes—
292C2×Dic7C2×C4⋊C414yes—
293C2×Dic7C2×C4⋊C414yes—
294C2×Dic7#11714yes—
295C2×Dic7C4×D418yes—
296C2×Dic7C4×Q818yes—
297C2×Dic7C4×Q818yes—
298C23×C4—71no—
299C23×C4—71no—
300C23×C4—71no—
301C23×C4—72no—
302C23×C4—72no—
303C23×C4—71no—
304C23×C4C22×D712yes—
305C23×C4C22×D711yescharacteristic
306C23×C4C22×D711yescharacteristic
307C23×C4C22×D712yes—
308C23×C4C22×D711yescharacteristic
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—74no—
312C2×C4⋊C4—78no—
313C2×C4⋊C4—74no—
314C2×C4⋊C4—78no—
315C2×C4⋊C4—78no—
316C2×C4⋊C4—144no—
317C2×C4⋊C4—144no—
318C2×C4⋊C4—144no—
319C2×C4⋊C4—144no—
320C2×C4⋊C4—144no—
321C2×C4⋊C4C4×D718yes—
322C2×C42—22no—
323C2×C42—22no—
324C2×C42—22no—
325C2×C42—22no—
326C2×C42—22no—
327C2×C42—22no—
328C2×C42—22no—
329C2×C42—74no—
330C2×C42—74no—
331C2×C42—74no—
332C2×C42—74no—
333C2×C42—78no—
334C2×C42—74no—
335C2×C42—144no—
336C2×C42—144no—
337C2×C42—144no—
338C2×C42—144no—
339C2×C42—144no—
340C2×C42—142no—
341C2×C42—142no—
342C2×C42—142no—
343C2×C42—142no—
344C2×C42—142no—
345C2×C42—142no—
346C2×C42—142no—
347C2×C42C4×D714yes—
348C2×C42C22⋊D714yes—
349#95—24no—
350#95—74no—
351#95—74no—
352#95—78no—
353#95—78no—
354#95—144no—
355#95—144no—
356#95—144no—
357#95—144no—
358C22×C7C22×C4211yescharacteristic
359C22×C7C22×C4⋊C411yescharacteristic
360C22×C7C2×#11711yescharacteristic
361C22×C7C2×C4×D412yes—
362C22×C7C2×C4×D411yescharacteristic
363C22×C7C2×C4×D412yes—
364C22×C7C2×C4×Q811yescharacteristic
365C22×C7C2×C4×Q812yes—
366C22×C7C2×C4×Q812yes—
367C22×C7C4×#4112yes—
368C22×C7C4×#4111yescharacteristic
369C22×C7C4×#4111yescharacteristic
370C22×C7C4×#4112yes—
371C22×C7C2×#12111yescharacteristic
372C22×C7C2×C22⋊Q811yescharacteristic
373C22×C7#52512yes—
374C22×C7C2×#12511yescharacteristic
375C22×C7#52912yes—
376C22×C7#52912yes—
377C22×C7C2×C4⋊Q811yescharacteristic
378C22×C7#53212yes—
379C22×C7#53312yes—
380C22×C7#53312yes—
381C4×C7—24no—
382C4×C7—28no—
383C4×C7—42no—
384C4×C7—44no—
385C4×C7#38918yescomplemented
386Dic7—24no—
387Dic7—24no—
388Dic7—28no—
389Dic7—42no—
390Dic7—44no—
391Dic7C4×C4⋊C418yescomplemented
392C24C23×D711yescharacteristic
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—72no—
411C22×C4—74no—
412C22×C4—72no—
413C22×C4—72no—
414C22×C4—74no—
415C22×C4—72no—
416C22×C4—74no—
417C22×C4—72no—
418C22×C4—74no—
419C22×C4—72no—
420C22×C4—72no—
421C22×C4—74no—
422C22×C4—74no—
423C22×C4—72no—
424C22×C4—74no—
425C22×C4—141no—
426C22×C4—142no—
427C22×C4—142no—
428C22×C4—142no—
429C22×C4—142no—
430C22×C4—142no—
431C22×C4—142no—
432C22×C4—142no—
433C22×C4—141no—
434C22×C4—141no—
435C22×C4—142no—
436C22×C4—142no—
437C22×C4—142no—
438C22×C4—142no—
439C22×C4—142no—
440C22×C4—142no—
441C22×C4—142no—
442C22×C4—141no—
443C22×C4—142no—
444C22×C4C2×C4×D712yes—
445C22×C4C2×C4×D714yes—
446C22×C4C2×C4×D712yes—
447C22×C4C2×C4×D714yes—
448C22×C4C2×C4×D714yes—
449C22×C4C2×C4×D712yes—
450C22×C4#115714yes—
451C22×C4#115712yes—
452C22×C4D4×D712yes—
453C22×C4#115912yes—
454C22×C4Q8×D712yes—
455C22×C4Q8×D712yes—
456C22×C4C2×C22⋊D714yes—
457C22×C4C2×C22⋊D712yes—
458C4⋊C4—216no—
459C4⋊C4—716no—
460C4⋊C4—148no—
461C4⋊C4—1416no—
462C4⋊C4—1416no—
463C42—28no—
464C42—28no—
465C42—44no—
466C42—716no—
467C42—1416no—
468C42—1416no—
469C42—148no—
470C42—148no—
471C42—284no—
472C2×C7C2×C4×C4⋊C411yescharacteristic
473C2×C7C42×D411yescharacteristic
474C2×C7C42×Q811yescharacteristic
475C2×C7C2×#38911yescharacteristic
476C2×C7#229311yescharacteristic
477C2×C7#229511yescharacteristic
478C2×C7#229611yescharacteristic
479C2×C7C4×#12112yes—
480C2×C7C4×C22⋊Q812yes—
481C2×C7C4×#12512yes—
482C2×C7C4×C4⋊Q812yes—
483C23C22×C4×D711yescharacteristic
484C23C22×C4×D712yes—
485C23C2×#115711yescharacteristic
486C23C2×#115712yes—
487C23C2×D4×D711yescharacteristic
488C23C2×#115911yescharacteristic
489C23C2×Q8×D711yescharacteristic
490C23C2×Q8×D711yescharacteristic
491C23D7×#4112yes—
492C23D7×#4112yes—
493C23C22×C22⋊D711yescharacteristic
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—74no—
517C2×C4—74no—
518C2×C4—74no—
519C2×C4—78no—
520C2×C4—78no—
521C2×C4—74no—
522C2×C4—74no—
523C2×C4—78no—
524C2×C4—142no—
525C2×C4—144no—
526C2×C4—142no—
527C2×C4—144no—
528C2×C4—144no—
529C2×C4—142no—
530C2×C4—144no—
531C2×C4—142no—
532C2×C4—144no—
533C2×C4—144no—
534C2×C4—144no—
535C2×C4—144no—
536C2×C4—144no—
537C2×C4—144no—
538C2×C4—142no—
539C2×C4—142no—
540C2×C4—142no—
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×C4C42×D714yes—
551C2×C4#645014yes—
552C2×C4#645214yes—
553C2×C4D7×C4⋊C414yes—
554C2×C4#645914yes—
555C2×C4C4×C22⋊D718yes—
556C2×C4C4×C22⋊D714yes—
557C2×C4#650214yes—
558C2×C4#650714yes—
559C7C4×#38911yescharacteristic, complemented, Sylow
560C22C2×C42×D711yescharacteristic
561C22C4×#115711yescharacteristic
562C22C4×#115712yes—
563C22C2×#645011yescharacteristic
564C22C2×#645211yescharacteristic
565C22C2×D7×C4⋊C411yescharacteristic
566C22C2×#645911yescharacteristic
567C22D7×#11711yescharacteristic
568C22#9021311yescharacteristic
569C22#9021912yes—
570C22C4×#115912yes—
571C22#9022912yes—
572C22C4×D4×D712yes—
573C22#9023812yes—
574C22C4×Q8×D712yes—
575C22C4×Q8×D712yes—
576C22#9026912yes—
577C22#9026912yes—
578C22C2×C4×C22⋊D711yescharacteristic
579C22C2×C4×C22⋊D712yes—
580C22C2×#650211yescharacteristic
581C22C2×#650711yescharacteristic
582C22#9052312yes—
583C4—24no—
584C4—28no—
585C4—42no—
586C4—44no—
587C4—78no—
588C4—144no—
589C4—148no—
590C4—144no—
591C4—282no—
592C4—284no—
593C4#8974418yesdirect product factor
594C2C4×#645011yescharacteristic
595C2#1173106411yescharacteristic
596C2C4×#645212yes—
597C2C4×D7×C4⋊C411yescharacteristic
598C2#1173120011yescharacteristic
599C2C4×#645912yes—
600C2C42×C22⋊D711yescharacteristic
601C2C2×#8974411yescharacteristic
602C2#1173967011yescharacteristic
603C2C4×#650212yes—
604C2C4×#650712yes—
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×#389
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
36. #89744C4direct (N × H)
39. C4×Dic7⋊C4C4semidirect
186. Dic7⋊C4C42semidirect
192. C4×Dic7C4⋊C4semidirect
385. C4×C7#389semidirect
391. Dic7C4×C4⋊C4semidirect
559. C7C4×#389semidirect
593. C4#89744direct (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×#897442
C2×C4×Dic7⋊C42
C2×C42×Dic72
#117293182
C4×C7⋊#952
#117271592
Dic7⋊#952
C4×#3897