Finite Group Databasebeta

← #13277483

Subgroups — #13277483

Order 1792.

1442 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C4⋊C4C211yesmaximal, characteristic
2C2×#89745C211yesmaximal, characteristic
3C2×#89705C212yesmaximal
4C2×C4×Dic7⋊C4C211yesmaximal, characteristic
5#11729317C211yesmaximal, characteristic
6#11729317C211yesmaximal, characteristic
7#11729317C211yesmaximal, characteristic
8#11729289C211yesmaximal, characteristic
9#11729288C212yesmaximal
10#11727171C212yesmaximal
11#11727163C212yesmaximal
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C42×C7C2212yes—
15C22×C42×C7C2211yescharacteristic
16C22×C4⋊Dic7C2211yescharacteristic
17C22×C4⋊Dic7C2211yescharacteristic
18C22×Dic7⋊C4C2211yescharacteristic
19C22×Dic7⋊C4C2212yes—
20C22×Dic7⋊C4C2211yescharacteristic
21C22×C4×Dic7C2211yescharacteristic
22C22×C4×Dic7C2211yescharacteristic
23C4×C7×C4⋊C4—24no—
24C2×C7×#95C2212yes—
25C2×C7⋊#95C2212yes—
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2211yescharacteristic
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2211yescharacteristic
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36#89745C418yescomplemented
37#89705—28no—
38C4×Dic7⋊C4—24no—
39#14042—71nomaximal, Sylow
40C23×C4×C7C2312yes—
41C23×C4×C7C2311yescharacteristic
42C23×C4×C7C2312yes—
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2311yescharacteristic
45C23×Dic7C2312yes—
46C23×Dic7C2311yescharacteristic
47C23×Dic7C2312yes—
48C23×Dic7C2311yescharacteristic
49C23×Dic7C2311yescharacteristic
50C23×Dic7C2311yescharacteristic
51C2×C7×C4⋊C4—22no—
52C2×C7×C4⋊C4—22no—
53C2×C7×C4⋊C4—22no—
54C2×C7×C4⋊C4—22no—
55C2×C7×C4⋊C4C2×C414yes—
56C2×C7×C4⋊C4Q814yes—
57C2×C42×C7—22no—
58C2×C42×C7—22no—
59C2×C42×C7—24no—
60C2×C42×C7—24no—
61C2×C42×C7—24no—
62C2×C42×C7D414yes—
63C2×C4⋊Dic7—22no—
64C2×C4⋊Dic7—22no—
65C2×C4⋊Dic7—22no—
66C2×C4⋊Dic7—22no—
67C2×C4⋊Dic7—22no—
68C2×C4⋊Dic7C2×C414yes—
69C2×Dic7⋊C4—22no—
70C2×Dic7⋊C4—22no—
71C2×Dic7⋊C4—22no—
72C2×Dic7⋊C4—24no—
73C2×Dic7⋊C4—22no—
74C2×Dic7⋊C4—22no—
75C2×Dic7⋊C4—24no—
76C2×Dic7⋊C4C2×C418yes—
77C2×Dic7⋊C4D414yes—
78C2×C4×Dic7—22no—
79C2×C4×Dic7—22no—
80C2×C4×Dic7—22no—
81C2×C4×Dic7—22no—
82C2×C4×Dic7—22no—
83C2×C4×Dic7C2×C414yes—
84C7×#95—24no—
85C7⋊#95—22no—
86C7⋊#95—22no—
87C7⋊#95—24no—
88C7⋊#95—24no—
89C7⋊#95—24no—
90C7⋊#95—24no—
91C7⋊#95—24no—
92C7⋊#95—42no—
93C7⋊#95—42no—
94C7⋊#95—42no—
95C7⋊#95C2×C418yes—
96C2×#389—71no—
97C2×#387—72no—
98C2×C4×C4⋊C4—71no—
99C2×C4×C4⋊C4D711yescharacteristic
100#1443—72no—
101#1441—72no—
102C4⋊#95—71no—
103C4⋊#95—71no—
104C4⋊#95—71no—
105C4⋊#95—71no—
106#1434—72no—
107C24×C7C2411yescharacteristic
108C22×C4×C7—21no—
109C22×C4×C7—21no—
110C22×C4×C7—21no—
111C22×C4×C7—21no—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7—22no—
115C22×C4×C7—22no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—21no—
119C22×C4×C7—21no—
120C22×C4×C7—22no—
121C22×C4×C7—21no—
122C22×C4×C7—21no—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—21no—
127C22×C4×C7—22no—
128C22×C4×C7—21no—
129C22×C4×C7—22no—
130C22×C4×C7C22×C414yes—
131C22×C4×C7C22×C412yes—
132C22×C4×C7C2×D412yes—
133C22×C4×C7C2×D412yes—
134C22×C4×C7C2×D412yes—
135C22×C4×C7C2×D412yes—
136C22×C4×C7C2×Q814yes—
137C22×C4×C7C2×Q812yes—
138C22×C4×C7#4112yes—
139C22×C4×C7#4112yes—
140C22×C4×C7#4112yes—
141C22×C4×C7#4112yes—
142C22×C4×C7#4112yes—
143C22×Dic7—21no—
144C22×Dic7—21no—
145C22×Dic7—21no—
146C22×Dic7—21no—
147C22×Dic7—21no—
148C22×Dic7—22no—
149C22×Dic7—21no—
150C22×Dic7—21no—
151C22×Dic7—21no—
152C22×Dic7—21no—
153C22×Dic7—21no—
154C22×Dic7—21no—
155C22×Dic7—21no—
156C22×Dic7—22no—
157C22×Dic7—21no—
158C22×Dic7—21no—
159C22×Dic7—22no—
160C22×Dic7—22no—
161C22×Dic7—21no—
162C22×Dic7—22no—
163C22×Dic7—21no—
164C22×Dic7—21no—
165C22×Dic7—21no—
166C22×Dic7—21no—
167C22×Dic7—22no—
168C22×Dic7—21no—
169C22×Dic7—21no—
170C22×Dic7—21no—
171C22×Dic7—22no—
172C22×Dic7—22no—
173C22×Dic7—22no—
174C22×Dic7—22no—
175C22×Dic7—22no—
176C22×Dic7—22no—
177C22×Dic7—22no—
178C22×Dic7C22×C412yes—
179C22×Dic7C22×C414yes—
180C22×Dic7C22×C412yes—
181C22×Dic7C2×D412yes—
182C22×Dic7C2×D412yes—
183C22×Dic7#4112yes—
184C22×Dic7#4112yes—
185C7×C4⋊C4—28no—
186C7×C4⋊C4—28no—
187C42×C7—28no—
188C42×C7—48no—
189C4⋊Dic7—28no—
190C4⋊Dic7—44no—
191Dic7⋊C4—28no—
192Dic7⋊C4—28no—
193Dic7⋊C4—216no—
194C4×Dic7—28no—
195C4×Dic7—44no—
196C22×C4⋊C4—72no—
197C22×C4⋊C4—71no—
198C22×C4⋊C4—71no—
199C22×C4⋊C4—71no—
200C22×C4⋊C4—71no—
201C22×C4⋊C4C2×D711yescharacteristic
202C22×C4⋊C4C2×D711yescharacteristic
203C22×C42—71no—
204C22×C42—71no—
205C22×C42C2×D712yes—
206C22×C42C2×D711yescharacteristic
207#389—78no—
208#387—148no—
209C4×C4⋊C4—24no—
210C4×C4⋊C4—144no—
211C2×#95—72no—
212C2×#95—71no—
213C2×#95—72no—
214C2×#95—72no—
215C2×#95—72no—
216C2×#95—72no—
217C2×#95—72no—
218C2×#95—71no—
219C2×#95—72no—
220C2×#95—72no—
221C2×#95—72no—
222C2×#95C2×D712yes—
223C23×C7C23×C411yescharacteristic
224C23×C7C22×D411yescharacteristic
225C23×C7C22×D411yescharacteristic
226C23×C7C22×Q811yescharacteristic
227C23×C7C2×#4111yescharacteristic
228C23×C7C2×#4111yescharacteristic
229C23×C7C2×#4111yescharacteristic
230C23×C7C2×#4111yescharacteristic
231C23×C7C2×#4111yescharacteristic
232C23×C7C2×#4111yescharacteristic
233C23×C7C2×#4111yescharacteristic
234C23×C7H(5,𝔽2)11yescharacteristic
235C23×C72−1+411yescharacteristic
236C23×C72−1+411yescharacteristic
237C23×C72−1+411yescharacteristic
238C2×C4×C7—22no—
239C2×C4×C7—22no—
240C2×C4×C7—22no—
241C2×C4×C7—22no—
242C2×C4×C7—22no—
243C2×C4×C7—22no—
244C2×C4×C7—24no—
245C2×C4×C7—24no—
246C2×C4×C7—24no—
247C2×C4×C7—24no—
248C2×C4×C7—22no—
249C2×C4×C7—22no—
250C2×C4×C7—22no—
251C2×C4×C7—24no—
252C2×C4×C7—24no—
253C2×C4×C7—42no—
254C2×C4×C7—42no—
255C2×C4×C7—42no—
256C2×C4×C7—42no—
257C2×C4×C7—42no—
258C2×C4×C7—42no—
259C2×C4×C7—42no—
260C2×C4×C7—41no—
261C2×C4×C7—41no—
262C2×C4×C7—41no—
263C2×C4×C7—41no—
264C2×C4×C7—42no—
265C2×C4×C7#11714yes—
266C2×C4×C7C4×D414yes—
267C2×C4×C7C4×Q814yes—
268C2×C4×C7#12114yes—
269C2×C4×C7C22⋊Q814yes—
270C2×C4×C7#12314yes—
271C2×C4×C7#12514yes—
272C2×C4×C7#12614yes—
273C2×Dic7—22no—
274C2×Dic7—22no—
275C2×Dic7—22no—
276C2×Dic7—22no—
277C2×Dic7—22no—
278C2×Dic7—22no—
279C2×Dic7—24no—
280C2×Dic7—22no—
281C2×Dic7—24no—
282C2×Dic7—22no—
283C2×Dic7—22no—
284C2×Dic7—24no—
285C2×Dic7—22no—
286C2×Dic7—22no—
287C2×Dic7—22no—
288C2×Dic7—22no—
289C2×Dic7—22no—
290C2×Dic7—22no—
291C2×Dic7—41no—
292C2×Dic7—41no—
293C2×Dic7—41no—
294C2×Dic7—41no—
295C2×Dic7—41no—
296C2×Dic7—41no—
297C2×Dic7—41no—
298C2×Dic7—41no—
299C2×Dic7—42no—
300C2×Dic7—42no—
301C2×Dic7—41no—
302C2×Dic7—41no—
303C2×Dic7—42no—
304C2×Dic7—41no—
305C2×Dic7—41no—
306C2×Dic7—42no—
307C2×Dic7—42no—
308C2×Dic7—42no—
309C2×Dic7—42no—
310C2×Dic7—42no—
311C2×Dic7—42no—
312C2×Dic7—42no—
313C2×Dic7—42no—
314C2×Dic7C4×D414yes—
315C23×C4—71no—
316C23×C4—72no—
317C23×C4—71no—
318C23×C4—71no—
319C23×C4—71no—
320C23×C4—72no—
321C23×C4C22×D712yes—
322C23×C4C22×D712yes—
323C23×C4C22×D711yescharacteristic
324C23×C4C22×D711yescharacteristic
325C23×C4C22×D711yescharacteristic
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—78no—
331C2×C4⋊C4—74no—
332C2×C4⋊C4—74no—
333C2×C4⋊C4—144no—
334C2×C4⋊C4—142no—
335C2×C4⋊C4—142no—
336C2×C4⋊C4—144no—
337C2×C4⋊C4—142no—
338C2×C4⋊C4—142no—
339C2×C4⋊C4—142no—
340C2×C4⋊C4—142no—
341C2×C4⋊C4—142no—
342C2×C4⋊C4—142no—
343C2×C4⋊C4—142no—
344C2×C4⋊C4—142no—
345C2×C4⋊C4Dic1414yes—
346C2×C4⋊C4C4×D714yes—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—24no—
350C2×C42—24no—
351C2×C42—24no—
352C2×C42—74no—
353C2×C42—142no—
354C2×C42—142no—
355C2×C42—142no—
356C2×C42—142no—
357C2×C42—142no—
358C2×C42C22⋊D714yes—
359#95—24no—
360#95—78no—
361#95—144no—
362#95—144no—
363#95—144no—
364#95—144no—
365#95—144no—
366#95—142no—
367#95—142no—
368#95—282no—
369#95—282no—
370#95—282no—
371C22×C7C2×#11711yescharacteristic
372C22×C7C2×C4×D411yescharacteristic
373C22×C7C2×C4×D411yescharacteristic
374C22×C7C2×C4×Q811yescharacteristic
375C22×C7C4×#4111yescharacteristic
376C22×C7#51911yescharacteristic
377C22×C7#52011yescharacteristic
378C22×C7C2×#12111yescharacteristic
379C22×C7C2×C22⋊Q811yescharacteristic
380C22×C7C2×#12311yescharacteristic
381C22×C7#52511yescharacteristic
382C22×C7C2×#12511yescharacteristic
383C22×C7C2×#12611yescharacteristic
384C22×C7#52911yescharacteristic
385C22×C7#53211yescharacteristic
386C22×C7#53611yescharacteristic
387C22×C7#53711yescharacteristic
388C22×C7#54111yescharacteristic
389C22×C7#54211yescharacteristic
390C22×C7#54711yescharacteristic
391C22×C7#54711yescharacteristic
392C22×C7D4×Q811yescharacteristic
393C22×C7#55011yescharacteristic
394C22×C7#55211yescharacteristic
395C22×C7#55211yescharacteristic
396C22×C7#55211yescharacteristic
397C22×C7#55311yescharacteristic
398C22×C7#55411yescharacteristic
399C22×C7#55511yescharacteristic
400C22×C7#55611yescharacteristic
401C22×C7#55611yescharacteristic
402C22×C7#55611yescharacteristic
403C22×C7#55611yescharacteristic
404C22×C7#55711yescharacteristic
405C22×C7#55711yescharacteristic
406C4×C7—24no—
407C4×C7—42no—
408C4×C7—44no—
409C4×C7—44no—
410C4×C7#38718yescomplemented
411Dic7—24no—
412Dic7—42no—
413Dic7—44no—
414Dic7—42no—
415Dic7—42no—
416Dic7—82no—
417C24C23×D711yescharacteristic
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—72no—
441C22×C4—72no—
442C22×C4—72no—
443C22×C4—72no—
444C22×C4—74no—
445C22×C4—72no—
446C22×C4—72no—
447C22×C4—141no—
448C22×C4—141no—
449C22×C4—141no—
450C22×C4—141no—
451C22×C4—141no—
452C22×C4—141no—
453C22×C4—141no—
454C22×C4—141no—
455C22×C4—141no—
456C22×C4—142no—
457C22×C4—142no—
458C22×C4—142no—
459C22×C4—141no—
460C22×C4—141no—
461C22×C4—141no—
462C22×C4—141no—
463C22×C4—142no—
464C22×C4—141no—
465C22×C4—142no—
466C22×C4—141no—
467C22×C4—141no—
468C22×C4—142no—
469C22×C4—141no—
470C22×C4—141no—
471C22×C4—141no—
472C22×C4—141no—
473C22×C4—141no—
474C22×C4—141no—
475C22×C4—142no—
476C22×C4—142no—
477C22×C4—142no—
478C22×C4—142no—
479C22×C4—142no—
480C22×C4—142no—
481C22×C4—142no—
482C22×C4C2×Dic1414yes—
483C22×C4C2×Dic1412yes—
484C22×C4C2×C4×D714yes—
485C22×C4C2×C4×D712yes—
486C22×C4#115712yes—
487C22×C4#115712yes—
488C22×C4#115712yes—
489C22×C4#115712yes—
490C22×C4D4×D712yes—
491C22×C4#115912yes—
492C22×C4C2×C22⋊D712yes—
493C22×C4C2×C22⋊D712yes—
494C22×C4C2×C22⋊D712yes—
495C4⋊C4—28no—
496C4⋊C4—28no—
497C4⋊C4—1416no—
498C4⋊C4—148no—
499C4⋊C4—148no—
500C4⋊C4—148no—
501C4⋊C4—284no—
502C42—28no—
503C42—48no—
504C42—148no—
505C42—284no—
506C2×C7C2×#38711yescharacteristic
507C2×C7C4×#12111yescharacteristic
508C2×C7#232311yescharacteristic
509C2×C7#235411yescharacteristic
510C2×C7#235611yescharacteristic
511C2×C7#236511yescharacteristic
512C2×C7#237011yescharacteristic
513C2×C7#248511yescharacteristic
514C2×C7#248611yescharacteristic
515C2×C7#250611yescharacteristic
516C2×C7#250811yescharacteristic
517C2×C7#251211yescharacteristic
518C2×C7#251411yescharacteristic
519C2×C7#253811yescharacteristic
520C2×C7#258111yescharacteristic
521C23C22×Dic1411yescharacteristic
522C23C22×C4×D711yescharacteristic
523C23C2×#115711yescharacteristic
524C23C2×#115711yescharacteristic
525C23C2×#115711yescharacteristic
526C23C2×#115711yescharacteristic
527C23C2×D4×D711yescharacteristic
528C23C2×#115911yescharacteristic
529C23#655111yescharacteristic
530C23#655111yescharacteristic
531C23D7×#4111yescharacteristic
532C23D7×#4111yescharacteristic
533C23#655311yescharacteristic
534C23#655411yescharacteristic
535C23C22×C22⋊D711yescharacteristic
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—74no—
564C2×C4—142no—
565C2×C4—142no—
566C2×C4—142no—
567C2×C4—142no—
568C2×C4—142no—
569C2×C4—142no—
570C2×C4—144no—
571C2×C4—142no—
572C2×C4—142no—
573C2×C4—142no—
574C2×C4—142no—
575C2×C4—142no—
576C2×C4—144no—
577C2×C4—142no—
578C2×C4—142no—
579C2×C4—142no—
580C2×C4—142no—
581C2×C4—144no—
582C2×C4—282no—
583C2×C4—281no—
584C2×C4—281no—
585C2×C4—281no—
586C2×C4—282no—
587C2×C4—281no—
588C2×C4—281no—
589C2×C4—281no—
590C2×C4—282no—
591C2×C4—281no—
592C2×C4—281no—
593C2×C4—282no—
594C2×C4—281no—
595C2×C4—281no—
596C2×C4—281no—
597C2×C4—281no—
598C2×C4—282no—
599C2×C4—282no—
600C2×C4—282no—
601C2×C4—282no—
602C2×C4—282no—
603C2×C4—282no—
604C2×C4—282no—
605C2×C4C4×Dic1414yes—
606C2×C4#643314yes—
607C2×C4#643514yes—
608C2×C4#643914yes—
609C2×C4#648714yes—
610C2×C4C4×C22⋊D714yes—
611C2×C4#649214yes—
612C2×C4#650114yes—
613C7#1404211yescharacteristic, complemented, Sylow
614C22C2×C4×Dic1411yescharacteristic
615C22C2×#643311yescharacteristic
616C22C2×#643511yescharacteristic
617C22C2×#643911yescharacteristic
618C22#9019811yescharacteristic
619C22#9019811yescharacteristic
620C22#9020411yescharacteristic
621C22#9020411yescharacteristic
622C22#9022011yescharacteristic
623C22#9022111yescharacteristic
624C22#9022311yescharacteristic
625C22#9022411yescharacteristic
626C22C4×#115911yescharacteristic
627C22D4×Dic1411yescharacteristic
628C22#9023311yescharacteristic
629C22#9023411yescharacteristic
630C22C4×D4×D711yescharacteristic
631C22#9023911yescharacteristic
632C22#9024411yescharacteristic
633C22#9024811yescharacteristic
634C22#9025911yescharacteristic
635C22#9025911yescharacteristic
636C22#9026011yescharacteristic
637C22#9026011yescharacteristic
638C22#9026311yescharacteristic
639C22#9026511yescharacteristic
640C22#9027311yescharacteristic
641C22#9027411yescharacteristic
642C22C2×#648711yescharacteristic
643C22C2×C4×C22⋊D711yescharacteristic
644C22C2×#649211yescharacteristic
645C22C2×#650111yescharacteristic
646C22#9050711yescharacteristic
647C22#9051911yescharacteristic
648C22#9052411yescharacteristic
649C4—24no—
650C4—42no—
651C4—44no—
652C4—44no—
653C4—144no—
654C4—282no—
655C4—282no—
656C4—284no—
657C4—282no—
658C4—562no—
659C4#8970518yescomplemented
660C2#1173108411yescharacteristic
661C2#1173108911yescharacteristic
662C2#1173109711yescharacteristic
663C2#1173110611yescharacteristic
664C2#1173112811yescharacteristic
665C2#1173113211yescharacteristic
666C2#1173113811yescharacteristic
667C2#1173114211yescharacteristic
668C2C2×#8970511yescharacteristic
669C2#1173964111yescharacteristic
670C2#1173972811yescharacteristic
671C2#1173982111yescharacteristic
672C2C4×#650111yescharacteristic
673C2#1173992611yescharacteristic
674C2#1173993311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C4×C7×C4⋊C4C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×C4×C4⋊C4D7
hypocenterC7#14042
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
36. #89745C4semidirect
410. C4×C7#387semidirect
613. C7#14042semidirect
659. C4#89705semidirect

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×#897452
C2×#897052
C2×C4×Dic7⋊C42
#117293172
#117292892
#117292882
#117271712
#117271632
#140427