Finite Group Databasebeta

← #13276176

Subgroups — #13276176

Order 1792.

1282 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×Dic7C211yesmaximal, characteristic
2C2×#89423C212yesmaximal
3C7×C4⋊#95C211yesmaximal, characteristic
4#11729317C211yesmaximal, characteristic
5#11729317C211yesmaximal, characteristic
6#11729317C211yesmaximal, characteristic
7#11729289C211yesmaximal, characteristic
8C4×C7⋊#95C211yesmaximal, characteristic
9#11727172C212yesmaximal
10#11727171C212yesmaximal
11#11727157C212yesmaximal
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C42×C7C2211yescharacteristic
15C22×C4⋊Dic7C2211yescharacteristic
16C22×C4⋊Dic7C2211yescharacteristic
17C22×C4×Dic7C2211yescharacteristic
18C22×C4×Dic7C2212yes—
19C22×C4×Dic7C2211yescharacteristic
20C2×C7×#95C2212yes—
21C2×C7×#95C2212yes—
22C2×C7⋊#95C2211yescharacteristic
23C2×C7⋊#95C2212yes—
24C2×C7⋊#95C2212yes—
25C2×C7⋊#95C2212yes—
26C2×C7⋊#95C2211yescharacteristic
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2211yescharacteristic
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2211yescharacteristic
35C4⋊C4×Dic7C418yescomplemented
36#89423—28no—
37#13921—71nomaximal, Sylow
38C23×C4×C7C2312yes—
39C23×C4×C7C2312yes—
40C23×C4×C7C2311yescharacteristic
41C23×C4×C7C2311yescharacteristic
42C23×C4×C7C2311yescharacteristic
43C23×Dic7C2312yes—
44C23×Dic7C2312yes—
45C23×Dic7C2311yescharacteristic
46C23×Dic7C2311yescharacteristic
47C23×Dic7C2311yescharacteristic
48C23×Dic7C2311yescharacteristic
49C2×C7×C4⋊C4—22no—
50C2×C7×C4⋊C4—22no—
51C2×C7×C4⋊C4—22no—
52C2×C7×C4⋊C4—22no—
53C2×C7×C4⋊C4—22no—
54C2×C7×C4⋊C4C2×C414yes—
55C2×C42×C7—22no—
56C2×C42×C7—22no—
57C2×C42×C7—22no—
58C2×C4⋊Dic7—22no—
59C2×C4⋊Dic7—22no—
60C2×C4⋊Dic7—22no—
61C2×C4⋊Dic7—22no—
62C2×C4⋊Dic7—22no—
63C2×C4⋊Dic7C2×C414yes—
64C2×C4×Dic7—22no—
65C2×C4×Dic7—22no—
66C2×C4×Dic7—24no—
67C2×C4×Dic7—24no—
68C2×C4×Dic7—22no—
69C2×C4×Dic7—22no—
70C2×C4×Dic7—22no—
71C2×C4×Dic7C2×C414yes—
72C2×C4×Dic7C2×C418yes—
73C7×#95—24no—
74C7×#95—42no—
75C7⋊#95—24no—
76C7⋊#95—22no—
77C7⋊#95—24no—
78C7⋊#95—24no—
79C7⋊#95—24no—
80C7⋊#95—24no—
81C7⋊#95—22no—
82C7⋊#95—24no—
83C7⋊#95—22no—
84C7⋊#95—42no—
85C7⋊#95—42no—
86C7⋊#95C2×C418yes—
87C7⋊#95D414yes—
88C2×#383—72no—
89C2×C4×C4⋊C4—71no—
90#1443—72no—
91#1443—72no—
92C4⋊#95—71no—
93C4⋊#95—71no—
94C4⋊#95—71no—
95C4⋊#95—71no—
96C4⋊#95D711yescharacteristic
97#1434—72no—
98C4×#95—71no—
99C24×C7C2411yescharacteristic
100C22×C4×C7—22no—
101C22×C4×C7—21no—
102C22×C4×C7—21no—
103C22×C4×C7—22no—
104C22×C4×C7—21no—
105C22×C4×C7—21no—
106C22×C4×C7—21no—
107C22×C4×C7—21no—
108C22×C4×C7—21no—
109C22×C4×C7—21no—
110C22×C4×C7—22no—
111C22×C4×C7—22no—
112C22×C4×C7—22no—
113C22×C4×C7—21no—
114C22×C4×C7—22no—
115C22×C4×C7—21no—
116C22×C4×C7—21no—
117C22×C4×C7—21no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7C22×C414yes—
126C22×C4×C7C22×C412yes—
127C22×C4×C7C2×D412yes—
128C22×C4×C7#4112yes—
129C22×C4×C7#4112yes—
130C22×C4×C7#4112yes—
131C22×C4×C7#4112yes—
132C22×C4×C7#4112yes—
133C22×C4×C7#4112yes—
134C22×C4×C7#4112yes—
135C22×Dic7—21no—
136C22×Dic7—21no—
137C22×Dic7—21no—
138C22×Dic7—21no—
139C22×Dic7—22no—
140C22×Dic7—22no—
141C22×Dic7—22no—
142C22×Dic7—21no—
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—22no—
156C22×Dic7—22no—
157C22×Dic7—21no—
158C22×Dic7—21no—
159C22×Dic7—21no—
160C22×Dic7—21no—
161C22×Dic7—21no—
162C22×Dic7—21no—
163C22×Dic7—22no—
164C22×Dic7—22no—
165C22×Dic7—22no—
166C22×Dic7—22no—
167C22×Dic7—22no—
168C22×Dic7—22no—
169C22×Dic7—22no—
170C22×Dic7C22×C412yes—
171C22×Dic7C22×C414yes—
172C22×Dic7C22×C412yes—
173C22×Dic7C2×D412yes—
174C22×Dic7C2×D412yes—
175C22×Dic7#4112yes—
176C22×Dic7#4112yes—
177C7×C4⋊C4—28no—
178C7×C4⋊C4—44no—
179C42×C7—44no—
180C4⋊Dic7—28no—
181C4⋊Dic7—44no—
182C4×Dic7—28no—
183C4×Dic7—216no—
184C4×Dic7—44no—
185C22×C4⋊C4—71no—
186C22×C4⋊C4—71no—
187C22×C4⋊C4C2×D711yescharacteristic
188C22×C4⋊C4C2×D711yescharacteristic
189C22×C42—71no—
190C22×C42—72no—
191C22×C42—71no—
192C22×C42C2×D711yescharacteristic
193#383—148no—
194C4×C4⋊C4—78no—
195C2×#95—71no—
196C2×#95—72no—
197C2×#95—71no—
198C2×#95—71no—
199C2×#95—71no—
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×#95C2×D712yes—
209C2×#95C2×D712yes—
210C23×C7C23×C411yescharacteristic
211C23×C7C22×D411yescharacteristic
212C23×C7C2×#4111yescharacteristic
213C23×C7C2×#4111yescharacteristic
214C23×C7C2×#4111yescharacteristic
215C23×C7C2×#4111yescharacteristic
216C23×C7C2×#4111yescharacteristic
217C23×C7C2×#4111yescharacteristic
218C23×C7C2×#4111yescharacteristic
219C23×C7C2×#4111yescharacteristic
220C23×C7C2×#4111yescharacteristic
221C23×C7H(5,𝔽2)11yescharacteristic
222C23×C72−1+411yescharacteristic
223C23×C72−1+411yescharacteristic
224C23×C72−1+411yescharacteristic
225C2×C4×C7—24no—
226C2×C4×C7—24no—
227C2×C4×C7—24no—
228C2×C4×C7—22no—
229C2×C4×C7—22no—
230C2×C4×C7—22no—
231C2×C4×C7—22no—
232C2×C4×C7—22no—
233C2×C4×C7—22no—
234C2×C4×C7—41no—
235C2×C4×C7—41no—
236C2×C4×C7—41no—
237C2×C4×C7—41no—
238C2×C4×C7—42no—
239C2×C4×C7—42no—
240C2×C4×C7—41no—
241C2×C4×C7—41no—
242C2×C4×C7—42no—
243C2×C4×C7—41no—
244C2×C4×C7—41no—
245C2×C4×C7—42no—
246C2×C4×C7—42no—
247C2×C4×C7—42no—
248C2×C4×C7—42no—
249C2×C4×C7—42no—
250C2×C4×C7—42no—
251C2×C4×C7—42no—
252C2×C4×C7—42no—
253C2×C4×C7#11714yes—
254C2×C4×C7#11714yes—
255C2×C4×C7#11714yes—
256C2×C4×C7#12614yes—
257C2×C4×C7#12614yes—
258C2×C4×C7#12614yes—
259C2×C4×C7#12614yes—
260C2×Dic7—22no—
261C2×Dic7—22no—
262C2×Dic7—22no—
263C2×Dic7—22no—
264C2×Dic7—22no—
265C2×Dic7—22no—
266C2×Dic7—22no—
267C2×Dic7—24no—
268C2×Dic7—24no—
269C2×Dic7—22no—
270C2×Dic7—24no—
271C2×Dic7—22no—
272C2×Dic7—22no—
273C2×Dic7—22no—
274C2×Dic7—22no—
275C2×Dic7—22no—
276C2×Dic7—22no—
277C2×Dic7—22no—
278C2×Dic7—41no—
279C2×Dic7—41no—
280C2×Dic7—42no—
281C2×Dic7—42no—
282C2×Dic7—42no—
283C2×Dic7—42no—
284C2×Dic7—41no—
285C2×Dic7—41no—
286C2×Dic7—41no—
287C2×Dic7—41no—
288C2×Dic7—41no—
289C2×Dic7—41no—
290C2×Dic7—41no—
291C2×Dic7—41no—
292C2×Dic7—41no—
293C2×Dic7—41no—
294C2×Dic7—42no—
295C2×Dic7—42no—
296C2×Dic7—42no—
297C2×Dic7—42no—
298C2×Dic7—42no—
299C2×Dic7—42no—
300C2×Dic7—42no—
301C2×Dic7C4×D414yes—
302C23×C4—71no—
303C23×C4—72no—
304C23×C4—71no—
305C23×C4—71no—
306C23×C4—71no—
307C23×C4—72no—
308C23×C4C22×D712yes—
309C23×C4C22×D712yes—
310C23×C4C22×D711yescharacteristic
311C23×C4C22×D711yescharacteristic
312C23×C4C22×D711yescharacteristic
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—74no—
319C2×C4⋊C4—142no—
320C2×C4⋊C4—142no—
321C2×C4⋊C4—142no—
322C2×C4⋊C4—142no—
323C2×C4⋊C4—142no—
324C2×C4⋊C4C4×D714yes—
325C2×C42—22no—
326C2×C42—22no—
327C2×C42—22no—
328C2×C42—78no—
329C2×C42—74no—
330C2×C42—144no—
331C2×C42—144no—
332C2×C42—142no—
333C2×C42—142no—
334C2×C42—142no—
335C2×C42—142no—
336C2×C42—142no—
337#95—24no—
338#95—42no—
339#95—78no—
340#95—74no—
341#95—142no—
342#95—142no—
343#95—144no—
344#95—144no—
345#95—144no—
346#95—144no—
347#95—144no—
348#95—142no—
349#95—144no—
350#95—282no—
351#95—282no—
352C22×C7C2×#11711yescharacteristic
353C22×C7C2×#11711yescharacteristic
354C22×C7C2×#11711yescharacteristic
355C22×C7C2×C4×D411yescharacteristic
356C22×C7C4×#4111yescharacteristic
357C22×C7#51911yescharacteristic
358C22×C7#52011yescharacteristic
359C22×C7C2×#12611yescharacteristic
360C22×C7C2×#12611yescharacteristic
361C22×C7C2×#12611yescharacteristic
362C22×C7C2×#12611yescharacteristic
363C22×C7#52911yescharacteristic
364C22×C7#52911yescharacteristic
365C22×C7#53211yescharacteristic
366C22×C7#53211yescharacteristic
367C22×C7#54111yescharacteristic
368C22×C7#54111yescharacteristic
369C22×C7#54211yescharacteristic
370C22×C7#54211yescharacteristic
371C22×C7#54711yescharacteristic
372C22×C7#54711yescharacteristic
373C22×C7#54711yescharacteristic
374C22×C7#55011yescharacteristic
375C22×C7#55211yescharacteristic
376C22×C7#55211yescharacteristic
377C22×C7#55211yescharacteristic
378C22×C7#55211yescharacteristic
379C22×C7#55311yescharacteristic
380C22×C7#55311yescharacteristic
381C22×C7#55511yescharacteristic
382C22×C7#55611yescharacteristic
383C22×C7#55611yescharacteristic
384C22×C7#55611yescharacteristic
385C22×C7#55611yescharacteristic
386C22×C7#55611yescharacteristic
387C4×C7—44no—
388C4×C7—42no—
389C4×C7—42no—
390C4×C7—82no—
391C4×C7#38318yescomplemented
392Dic7—24no—
393Dic7—42no—
394Dic7—42no—
395Dic7—42no—
396Dic7—44no—
397Dic7—82no—
398C24C23×D711yescharacteristic
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—72no—
425C22×C4—72no—
426C22×C4—72no—
427C22×C4—72no—
428C22×C4—74no—
429C22×C4—72no—
430C22×C4—72no—
431C22×C4—141no—
432C22×C4—141no—
433C22×C4—141no—
434C22×C4—141no—
435C22×C4—141no—
436C22×C4—141no—
437C22×C4—141no—
438C22×C4—141no—
439C22×C4—142no—
440C22×C4—141no—
441C22×C4—141no—
442C22×C4—142no—
443C22×C4—141no—
444C22×C4—141no—
445C22×C4—141no—
446C22×C4—142no—
447C22×C4—141no—
448C22×C4—141no—
449C22×C4—141no—
450C22×C4—142no—
451C22×C4—141no—
452C22×C4—141no—
453C22×C4—142no—
454C22×C4—141no—
455C22×C4—142no—
456C22×C4—141no—
457C22×C4—141no—
458C22×C4—141no—
459C22×C4—142no—
460C22×C4—142no—
461C22×C4—142no—
462C22×C4—142no—
463C22×C4—142no—
464C22×C4—142no—
465C22×C4—142no—
466C22×C4C2×C4×D714yes—
467C22×C4C2×C4×D712yes—
468C22×C4#115712yes—
469C22×C4#115712yes—
470C22×C4D4×D712yes—
471C22×C4#115912yes—
472C22×C4#115912yes—
473C22×C4#115912yes—
474C22×C4#116112yes—
475C22×C4#116112yes—
476C4⋊C4—28no—
477C4⋊C4—44no—
478C4⋊C4—148no—
479C4⋊C4—284no—
480C42—44no—
481C42—1416no—
482C42—148no—
483C42—284no—
484C2×C7C2×#38311yescharacteristic
485C2×C7#229311yescharacteristic
486C2×C7#232011yescharacteristic
487C2×C7#234411yescharacteristic
488C2×C7#234711yescharacteristic
489C2×C7#235411yescharacteristic
490C2×C7#235611yescharacteristic
491C2×C7#249511yescharacteristic
492C2×C7#249511yescharacteristic
493C2×C7#249611yescharacteristic
494C2×C7#249611yescharacteristic
495C2×C7#251211yescharacteristic
496C2×C7#251211yescharacteristic
497C2×C7#251411yescharacteristic
498C2×C7#251411yescharacteristic
499C23C22×C4×D711yescharacteristic
500C23C2×#115711yescharacteristic
501C23C2×#115711yescharacteristic
502C23C2×D4×D711yescharacteristic
503C23C2×#115911yescharacteristic
504C23C2×#115911yescharacteristic
505C23C2×#115911yescharacteristic
506C23#654811yescharacteristic
507C23C2×#116111yescharacteristic
508C23C2×#116111yescharacteristic
509C23#655111yescharacteristic
510C23D7×#4111yescharacteristic
511C23D7×#4111yescharacteristic
512C23#655411yescharacteristic
513C23#655411yescharacteristic
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—74no—
543C2×C4—142no—
544C2×C4—142no—
545C2×C4—142no—
546C2×C4—142no—
547C2×C4—142no—
548C2×C4—142no—
549C2×C4—142no—
550C2×C4—142no—
551C2×C4—142no—
552C2×C4—144no—
553C2×C4—144no—
554C2×C4—142no—
555C2×C4—142no—
556C2×C4—142no—
557C2×C4—142no—
558C2×C4—144no—
559C2×C4—142no—
560C2×C4—142no—
561C2×C4—282no—
562C2×C4—281no—
563C2×C4—282no—
564C2×C4—281no—
565C2×C4—281no—
566C2×C4—281no—
567C2×C4—281no—
568C2×C4—281no—
569C2×C4—281no—
570C2×C4—281no—
571C2×C4—281no—
572C2×C4—281no—
573C2×C4—282no—
574C2×C4—281no—
575C2×C4—282no—
576C2×C4—281no—
577C2×C4—282no—
578C2×C4—282no—
579C2×C4—282no—
580C2×C4—282no—
581C2×C4—282no—
582C2×C4—282no—
583C2×C4—282no—
584C2×C4#643514yes—
585C2×C4#644014yes—
586C2×C4#644214yes—
587C2×C4#644214yes—
588C2×C4#645514yes—
589C2×C4#646114yes—
590C2×C4#646114yes—
591C7#1392111yescharacteristic, complemented, Sylow
592C22C2×#643511yescharacteristic
593C22C2×#644011yescharacteristic
594C22C2×#644211yescharacteristic
595C22C2×#644211yescharacteristic
596C22C2×#645511yescharacteristic
597C22#9019811yescharacteristic
598C22C2×#646111yescharacteristic
599C22C2×#646111yescharacteristic
600C22#9020511yescharacteristic
601C22#9022011yescharacteristic
602C22#9022411yescharacteristic
603C22C4×D4×D711yescharacteristic
604C22#9023711yescharacteristic
605C22#9024211yescharacteristic
606C22#9024911yescharacteristic
607C22#9026311yescharacteristic
608C22C4×#116111yescharacteristic
609C22#9027211yescharacteristic
610C22#9027511yescharacteristic
611C22#9028711yescharacteristic
612C22#9029411yescharacteristic
613C22#9030211yescharacteristic
614C22#9030711yescharacteristic
615C22#9031511yescharacteristic
616C22#9031611yescharacteristic
617C22#9033011yescharacteristic
618C22#9033311yescharacteristic
619C22#9036211yescharacteristic
620C22#9036211yescharacteristic
621C22#9038211yescharacteristic
622C22#9038811yescharacteristic
623C22#9040911yescharacteristic
624C22#9041611yescharacteristic
625C22#9042311yescharacteristic
626C22#9042411yescharacteristic
627C4—42no—
628C4—42no—
629C4—44no—
630C4—82no—
631C4—144no—
632C4—282no—
633C4—284no—
634C4—282no—
635C4—282no—
636C4—562no—
637C4#8942318yescomplemented
638C2C2×#8942311yescharacteristic
639C2#1173107911yescharacteristic
640C2#1173121211yescharacteristic
641C2#1173136511yescharacteristic
642C2#1173136711yescharacteristic
643C2#1173161811yescharacteristic
644C2#1173177811yescharacteristic
645C2#1173340611yescharacteristic
646C2#1173341511yescharacteristic
647C2#1173368111yescharacteristic
648C2#1173368311yescharacteristic
649C2#1173374711yescharacteristic
650C2#1173378411yescharacteristic
651C2#1173393511yescharacteristic
652C2#1173397111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C4⋊#95C2
socle, prime radical, cosocleC24×C7C24
hypercenterC4⋊#95D7
hypocenterC7#13921
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
35. C4⋊C4×Dic7C4semidirect
391. C4×C7#383semidirect
591. C7#13921semidirect
637. C4#89423semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×Dic72
C2×#894232
C7×C4⋊#952
#117293172
#117292892
C4×C7⋊#952
#117271722
#117271712
#117271572
#139217