Finite Group Databasebeta

← #13280453

Subgroups — #13280453

Order 1792.

1414 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6452C211yesmaximal, characteristic
2C2×C4⋊C4×Dic7C211yesmaximal, characteristic
3C2×#89423C211yesmaximal, characteristic
4C7×#1441C211yesmaximal, characteristic
5#11729320C211yesmaximal, characteristic
6#11729319C211yesmaximal, characteristic
7#11727175C212yesmaximal
8#11727175C212yesmaximal
9#11727164C211yesmaximal, characteristic
10#11727161C212yesmaximal
11#11727160C212yesmaximal
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C4⋊Dic7C2211yescharacteristic
15C22×C4⋊Dic7C2211yescharacteristic
16C22×Dic7⋊C4C2211yescharacteristic
17C22×Dic7⋊C4C2211yescharacteristic
18C22×Dic7⋊C4C2211yescharacteristic
19C22×Dic7⋊C4C2211yescharacteristic
20C22×C4×Dic7C2212yes—
21C22×C4×Dic7C2211yescharacteristic
22C2×#6452—24no—
23C2×#6452—24no—
24C2×#6452C418yescomplemented
25C2×C7×#95C2212yes—
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⋊#95C2211yescharacteristic
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C4⋊C4×Dic7—24no—
39#89423—24no—
40#14289—71nomaximal, Sylow
41C23×C4×C7C2312yes—
42C23×C4×C7C2311yescharacteristic
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2312yes—
45C23×C4×C7C2311yescharacteristic
46C23×Dic7C2312yes—
47C23×Dic7C2311yescharacteristic
48C23×Dic7C2311yescharacteristic
49C23×Dic7C2312yes—
50C23×Dic7C2311yescharacteristic
51C23×Dic7C2311yescharacteristic
52C2×C7×C4⋊C4—22no—
53C2×C7×C4⋊C4—22no—
54C2×C7×C4⋊C4—22no—
55C2×C7×C4⋊C4—24no—
56C2×C7×C4⋊C4C2×C414yes—
57C2×C4⋊Dic7—22no—
58C2×C4⋊Dic7—22no—
59C2×C4⋊Dic7—22no—
60C2×C4⋊Dic7—24no—
61C2×C4⋊Dic7C2×C414yes—
62C2×Dic7⋊C4—22no—
63C2×Dic7⋊C4—22no—
64C2×Dic7⋊C4—22no—
65C2×Dic7⋊C4—22no—
66C2×Dic7⋊C4—22no—
67C2×Dic7⋊C4—22no—
68C2×Dic7⋊C4—22no—
69C2×Dic7⋊C4—22no—
70C2×Dic7⋊C4C2×C414yes—
71C2×Dic7⋊C4C2×C414yes—
72C2×Dic7⋊C4C2×C414yes—
73C2×Dic7⋊C4C2×C414yes—
74C2×C4×Dic7—24no—
75C2×C4×Dic7—42no—
76C2×C4×Dic7—42no—
77C2×C4×Dic7C2×C414yes—
78C2×C4×Dic7D414yes—
79C2×C4×Dic7D414yes—
80#6452—232no—
81C7×#95—22no—
82C7×#95—24no—
83C7×#95—42no—
84C7⋊#95—22no—
85C7⋊#95—24no—
86C7⋊#95—24no—
87C7⋊#95—24no—
88C7⋊#95—24no—
89C7⋊#95—24no—
90C7⋊#95—24no—
91C7⋊#95—42no—
92C7⋊#95—42no—
93C7⋊#95—42no—
94C22×#125—71no—
95C2×#383—71no—
96C2×C4×C4⋊C4—71no—
97#1445—72no—
98#1445—72no—
99#1441—71no—
100#1441—71no—
101#1441—71no—
102#1441D711yescharacteristic
103#1436—72no—
104#1436—72no—
105C24×C7C2411yescharacteristic
106C22×C4×C7—22no—
107C22×C4×C7—22no—
108C22×C4×C7—22no—
109C22×C4×C7—21no—
110C22×C4×C7—21no—
111C22×C4×C7—21no—
112C22×C4×C7—21no—
113C22×C4×C7—22no—
114C22×C4×C7—22no—
115C22×C4×C7—22no—
116C22×C4×C7—21no—
117C22×C4×C7—22no—
118C22×C4×C7—21no—
119C22×C4×C7—22no—
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—22no—
129C22×C4×C7—22no—
130C22×C4×C7—22no—
131C22×C4×C7C22×C412yes—
132C22×C4×C7C22×C412yes—
133C22×C4×C7C22×C412yes—
134C22×C4×C7C2×D412yes—
135C22×C4×C7C2×D412yes—
136C22×C4×C7#4114yes—
137C22×Dic7—21no—
138C22×Dic7—21no—
139C22×Dic7—22no—
140C22×Dic7—22no—
141C22×Dic7—21no—
142C22×Dic7—21no—
143C22×Dic7—22no—
144C22×Dic7—21no—
145C22×Dic7—21no—
146C22×Dic7—21no—
147C22×Dic7—21no—
148C22×Dic7—22no—
149C22×Dic7—22no—
150C22×Dic7—22no—
151C22×Dic7—21no—
152C22×Dic7—21no—
153C22×Dic7—22no—
154C22×Dic7—22no—
155C22×Dic7—21no—
156C22×Dic7—21no—
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×Dic7C22×C412yes—
167C22×Dic7C22×C412yes—
168C22×Dic7C22×C412yes—
169C22×Dic7C22×C412yes—
170C22×Dic7C2×D412yes—
171C22×Dic7C2×D412yes—
172C22×Dic7C2×D412yes—
173C22×Dic7C2×D412yes—
174C22×Dic7#4114yes—
175C7×C4⋊C4—28no—
176C7×C4⋊C4—28no—
177C4⋊Dic7—28no—
178C4⋊Dic7—28no—
179Dic7⋊C4—28no—
180Dic7⋊C4—28no—
181Dic7⋊C4—28no—
182Dic7⋊C4—28no—
183C4×Dic7—48no—
184C4×Dic7C22⋊C4116yes—
185C2×#125—78no—
186C2×#125—144no—
187C2×#125—144no—
188C22×C4⋊C4—71no—
189C22×C4⋊C4—71no—
190C22×C4⋊C4—71no—
191C22×C4⋊C4—71no—
192C22×C4⋊C4—71no—
193C22×C4⋊C4—71no—
194C22×C4⋊C4C2×D711yescharacteristic
195C22×C4⋊C4C2×D711yescharacteristic
196C22×C42—71no—
197C22×C42—72no—
198#383—144no—
199C4×C4⋊C4—144no—
200C2×#95—72no—
201C2×#95—72no—
202C2×#95—72no—
203C2×#95—72no—
204C2×#95—71no—
205C2×#95—72no—
206C2×#95—72no—
207C2×#95—72no—
208C2×#95—72no—
209C2×#95—72no—
210C2×#95C2×D712yes—
211C2×#95C2×D711yescharacteristic
212C2×#95C2×D712yes—
213C23×C7C23×C411yescharacteristic
214C23×C7C22×D411yescharacteristic
215C23×C7C22×D411yescharacteristic
216C23×C7C2×#4112yes—
217C23×C7C2×#4112yes—
218C23×C7H(5,𝔽2)11yescharacteristic
219C23×C7H(5,𝔽2)11yescharacteristic
220C23×C72−1+412yes—
221C23×C72−1+411yescharacteristic
222C23×C72−1+412yes—
223C23×C72−1+411yescharacteristic
224C2×C4×C7—24no—
225C2×C4×C7—22no—
226C2×C4×C7—22no—
227C2×C4×C7—24no—
228C2×C4×C7—22no—
229C2×C4×C7—22no—
230C2×C4×C7—24no—
231C2×C4×C7—22no—
232C2×C4×C7—22no—
233C2×C4×C7—24no—
234C2×C4×C7—24no—
235C2×C4×C7—24no—
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—42no—
254C2×C4×C7C2×C22⋊C414yes—
255C2×Dic7—24no—
256C2×Dic7—22no—
257C2×Dic7—22no—
258C2×Dic7—22no—
259C2×Dic7—22no—
260C2×Dic7—24no—
261C2×Dic7—22no—
262C2×Dic7—22no—
263C2×Dic7—22no—
264C2×Dic7—22no—
265C2×Dic7—22no—
266C2×Dic7—22no—
267C2×Dic7—24no—
268C2×Dic7—22no—
269C2×Dic7—22no—
270C2×Dic7—24no—
271C2×Dic7—24no—
272C2×Dic7—24no—
273C2×Dic7—41no—
274C2×Dic7—41no—
275C2×Dic7—42no—
276C2×Dic7—42no—
277C2×Dic7—41no—
278C2×Dic7—42no—
279C2×Dic7—41no—
280C2×Dic7—41no—
281C2×Dic7—41no—
282C2×Dic7—42no—
283C2×Dic7—42no—
284C2×Dic7—42no—
285C2×Dic7—42no—
286C2×Dic7—42no—
287C2×Dic7—42no—
288C2×Dic7—42no—
289C2×Dic7—42no—
290C2×Dic7—42no—
291C2×Dic7C2×C22⋊C414yes—
292C2×Dic7C2×C22⋊C414yes—
293C23×C4—71no—
294C23×C4—71no—
295C23×C4—71no—
296C23×C4—71no—
297C23×C4—72no—
298C23×C4—72no—
299C23×C4C22×D712yes—
300C23×C4C22×D711yescharacteristic
301C23×C4C22×D711yescharacteristic
302C23×C4C22×D712yes—
303C23×C4C22×D711yescharacteristic
304#125—1432no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—74no—
310C2×C4⋊C4—74no—
311C2×C4⋊C4—74no—
312C2×C4⋊C4—74no—
313C2×C4⋊C4—74no—
314C2×C4⋊C4—142no—
315C2×C4⋊C4—142no—
316C2×C4⋊C4—142no—
317C2×C4⋊C4—142no—
318C2×C4⋊C4—142no—
319C2×C4⋊C4—142no—
320C2×C4⋊C4—142no—
321C2×C4⋊C4—142no—
322C2×C4⋊C4—144no—
323C2×C4⋊C4—142no—
324C2×C4⋊C4—142no—
325C2×C4⋊C4—142no—
326C2×C4⋊C4C4×D714yes—
327C2×C42—74no—
328C2×C42—74no—
329C2×C42—74no—
330C2×C42—144no—
331C2×C42—282no—
332C2×C42—282no—
333#95—22no—
334#95—24no—
335#95—42no—
336#95—144no—
337#95—144no—
338#95—144no—
339#95—144no—
340#95—144no—
341#95—142no—
342#95—144no—
343#95—282no—
344#95—282no—
345#95—282no—
346C22×C7C22×C22⋊C411yescharacteristic
347C22×C7C4×#4112yes—
348C22×C7#51912yes—
349C22×C7#52011yescharacteristic
350C22×C7#52011yescharacteristic
351C22×C7#52511yescharacteristic
352C22×C7#52511yescharacteristic
353C22×C7#53212yes—
354C22×C7#53511yescharacteristic
355C22×C7#53611yescharacteristic
356C22×C7#53612yes—
357C22×C7#53611yescharacteristic
358C22×C7#53611yescharacteristic
359C22×C7#53711yescharacteristic
360C22×C7#53711yescharacteristic
361C22×C7#53912yes—
362C22×C7#53912yes—
363C22×C7#53912yes—
364C22×C7#53912yes—
365C22×C7#54112yes—
366C22×C7#54112yes—
367C22×C7#54112yes—
368C22×C7#54112yes—
369C4×C7—24no—
370C4×C7—42no—
371C4×C7—44no—
372C4×C7—42no—
373C4×C7—82no—
374Dic7—24no—
375Dic7—24no—
376Dic7—42no—
377Dic7—44no—
378Dic7—42no—
379Dic7—82no—
380C24C23×D711yescharacteristic
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—72no—
407C22×C4—72no—
408C22×C4—72no—
409C22×C4—72no—
410C22×C4—72no—
411C22×C4—72no—
412C22×C4—72no—
413C22×C4—72no—
414C22×C4—74no—
415C22×C4—141no—
416C22×C4—142no—
417C22×C4—141no—
418C22×C4—141no—
419C22×C4—141no—
420C22×C4—142no—
421C22×C4—142no—
422C22×C4—141no—
423C22×C4—141no—
424C22×C4—141no—
425C22×C4—141no—
426C22×C4—142no—
427C22×C4—141no—
428C22×C4—142no—
429C22×C4—142no—
430C22×C4—141no—
431C22×C4—142no—
432C22×C4—142no—
433C22×C4—142no—
434C22×C4—141no—
435C22×C4—142no—
436C22×C4—141no—
437C22×C4—142no—
438C22×C4—142no—
439C22×C4—142no—
440C22×C4—142no—
441C22×C4—142no—
442C22×C4—142no—
443C22×C4—142no—
444C22×C4C2×C4×D712yes—
445C22×C4C2×C4×D712yes—
446C22×C4C2×C4×D712yes—
447C22×C4D4×D712yes—
448C22×C4D4×D712yes—
449C22×C4#115914yes—
450C4⋊C4—28no—
451C4⋊C4—28no—
452C4⋊C4—148no—
453C4⋊C4—148no—
454C4⋊C4—148no—
455C4⋊C4—148no—
456C4⋊C4—148no—
457C4⋊C4—148no—
458C42—716no—
459C42—288no—
460C2×C7#229711yescharacteristic
461C2×C7#231011yescharacteristic
462C2×C7#231111yescharacteristic
463C2×C7#233612yes—
464C2×C7#233612yes—
465C2×C7#263311yescharacteristic
466C2×C7#263311yescharacteristic
467C2×C7#263411yescharacteristic
468C2×C7#263411yescharacteristic
469C2×C7#266412yes—
470C2×C7#266412yes—
471C23C22×C4×D711yescharacteristic
472C23C2×D4×D711yescharacteristic
473C23C2×D4×D711yescharacteristic
474C23C2×#115912yes—
475C23#654811yescharacteristic
476C23#655112yes—
477C23#655111yescharacteristic
478C23D7×#4112yes—
479C23#655311yescharacteristic
480C23#655412yes—
481C23#655411yescharacteristic
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—74no—
513C2×C4—74no—
514C2×C4—142no—
515C2×C4—142no—
516C2×C4—142no—
517C2×C4—144no—
518C2×C4—142no—
519C2×C4—142no—
520C2×C4—144no—
521C2×C4—142no—
522C2×C4—142no—
523C2×C4—142no—
524C2×C4—144no—
525C2×C4—142no—
526C2×C4—142no—
527C2×C4—142no—
528C2×C4—142no—
529C2×C4—144no—
530C2×C4—144no—
531C2×C4—144no—
532C2×C4—282no—
533C2×C4—282no—
534C2×C4—281no—
535C2×C4—282no—
536C2×C4—282no—
537C2×C4—281no—
538C2×C4—281no—
539C2×C4—281no—
540C2×C4—281no—
541C2×C4—282no—
542C2×C4—281no—
543C2×C4—282no—
544C2×C4—282no—
545C2×C4—282no—
546C2×C4—282no—
547C2×C4—282no—
548C2×C4—282no—
549C2×C4—282no—
550C2×C4D7×C22⋊C414yes—
551C7#1428911yescharacteristic, complemented, Sylow
552C22C2×D7×C22⋊C411yescharacteristic
553C22#9019511yescharacteristic
554C22#9021411yescharacteristic
555C22C4×#115912yes—
556C22#9026312yes—
557C22#9027711yescharacteristic
558C22#9028712yes—
559C22#9029312yes—
560C22#9029811yescharacteristic
561C22#9029911yescharacteristic
562C22#9031612yes—
563C22#9031912yes—
564C22#9031911yescharacteristic
565C22#9032011yescharacteristic
566C22#9032912yes—
567C22#9034711yescharacteristic
568C22#9035612yes—
569C22#9036611yescharacteristic
570C22#9038312yes—
571C22#9038712yes—
572C22#9039212yes—
573C22#9041511yescharacteristic
574C22#9042212yes—
575C4—24no—
576C4—42no—
577C4—44no—
578C4—42no—
579C4—82no—
580C4—144no—
581C4—144no—
582C4—282no—
583C4—284no—
584C4—282no—
585C4—562no—
586C2#1173144811yescharacteristic
587C2#1173210311yescharacteristic
588C2#1173240312yes—
589C2#1173342312yes—
590C2#1173405511yescharacteristic
591C2#1173442311yescharacteristic
592C2#1173464911yescharacteristic
593C2#1173479012yes—
594C2#1173526711yescharacteristic
595C2#1173528412yes—
596C2#1173565511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1441C2
socle, prime radical, cosocleC24×C7C24
hypercenter#1441D7
hypocenterC7#14289
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
24. C2×#6452C4semidirect
551. C7#14289semidirect

Maximal subgroups

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

subgroupindex
C22×#64522
C2×C4⋊C4×Dic72
C2×#894232
C7×#14412
#117293202
#117293192
#117271752
#117271642
#117271612
#117271602
#142897