Finite Group Databasebeta

← #13284544

Subgroups — #13284544

Order 1792.

1130 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#398C211yesmaximal, characteristic
2C2×#89757C211yesmaximal, characteristic
3C2×#89753C211yesmaximal, characteristic
4#11729323C211yesmaximal, characteristic
5#11729323C212yesmaximal
6#11729319C211yesmaximal, characteristic
7#11729319C212yesmaximal
8#11727166C212yesmaximal
9#11727166C212yesmaximal
10#11727166C211yesmaximal, characteristic
11#11727155C211yesmaximal, characteristic
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2212yes—
15C22×C4⋊Dic7C2211yescharacteristic
16C22×C4⋊Dic7C2211yescharacteristic
17C22×C4⋊Dic7C2212yes—
18C22×C4×Dic7C2211yescharacteristic
19C7×#398C418yescomplemented
20C2×C7×#95C2211yescharacteristic
21C2×C7×#95C2212yes—
22C2×C7⋊#95C2211yescharacteristic
23C2×C7⋊#95C2211yescharacteristic
24C2×C7⋊#95C2211yescharacteristic
25C2×C7⋊#95C2212yes—
26C2×C7⋊#95C2211yescharacteristic
27C2×C7⋊#95C2211yescharacteristic
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36#89757—24no—
37#89753—24no—
38#14631—71nomaximal, Sylow
39C23×C4×C7C2311yescharacteristic
40C23×C4×C7C2312yes—
41C23×C4×C7C2312yes—
42C23×C4×C7C2311yescharacteristic
43C23×C4×C7C2311yescharacteristic
44C23×Dic7C2312yes—
45C23×Dic7C2311yescharacteristic
46C23×Dic7C2311yescharacteristic
47C23×Dic7C2312yes—
48C23×Dic7C2311yescharacteristic
49C23×Dic7C2311yescharacteristic
50C2×C7×C4⋊C4—22no—
51C2×C7×C4⋊C4—22no—
52C2×C7×C4⋊C4—22no—
53C2×C7×C4⋊C4—22no—
54C2×C7×C4⋊C4—42no—
55C2×C7×C4⋊C4—42no—
56C2×C7×C4⋊C4C2×C414yes—
57C2×C7×C4⋊C4C2×C414yes—
58C2×C7×C4⋊C4C2×C418yes—
59C2×C4⋊Dic7—22no—
60C2×C4⋊Dic7—22no—
61C2×C4⋊Dic7—24no—
62C2×C4⋊Dic7—42no—
63C2×C4⋊Dic7—42no—
64C2×C4⋊Dic7—42no—
65C2×C4⋊Dic7—42no—
66C2×C4×Dic7—42no—
67C2×C4×Dic7D414yes—
68C7×#95C2×C418yes—
69C7×#95C2×C414yes—
70C7⋊#95—22no—
71C7⋊#95—22no—
72C7⋊#95—22no—
73C7⋊#95—22no—
74C7⋊#95—22no—
75C7⋊#95—24no—
76C7⋊#95—42no—
77C7⋊#95—42no—
78C7⋊#95—42no—
79C7⋊#95—42no—
80C7⋊#95—42no—
81C7⋊#95—42no—
82C7⋊#95—42no—
83C7⋊#95—42no—
84C2×#398D711yescharacteristic
85C2×#389—71no—
86C2×#387—71no—
87#1445—71no—
88#1445—72no—
89#1442—72no—
90#1442—71no—
91#1442—72no—
92#1441—71no—
93#1441—72no—
94#1434—71no—
95C24×C7C2411yescharacteristic
96C22×C4×C7—22no—
97C22×C4×C7—22no—
98C22×C4×C7—21no—
99C22×C4×C7—21no—
100C22×C4×C7—22no—
101C22×C4×C7—21no—
102C22×C4×C7—22no—
103C22×C4×C7—21no—
104C22×C4×C7—21no—
105C22×C4×C7—22no—
106C22×C4×C7—22no—
107C22×C4×C7—22no—
108C22×C4×C7—22no—
109C22×C4×C7—22no—
110C22×C4×C7—22no—
111C22×C4×C7—22no—
112C22×C4×C7—21no—
113C22×C4×C7—21no—
114C22×C4×C7—22no—
115C22×C4×C7—22no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—21no—
119C22×C4×C7—22no—
120C22×C4×C7C22×C412yes—
121C22×C4×C7C22×C414yes—
122C22×C4×C7C22×C414yes—
123C22×C4×C7C22×C412yes—
124C22×C4×C7C22×C412yes—
125C22×C4×C7C2×D412yes—
126C22×C4×C7#4112yes—
127C22×Dic7—21no—
128C22×Dic7—22no—
129C22×Dic7—22no—
130C22×Dic7—21no—
131C22×Dic7—21no—
132C22×Dic7—22no—
133C22×Dic7—22no—
134C22×Dic7—21no—
135C22×Dic7—21no—
136C22×Dic7—21no—
137C22×Dic7—22no—
138C22×Dic7—22no—
139C22×Dic7—21no—
140C22×Dic7—21no—
141C22×Dic7—21no—
142C22×Dic7—22no—
143C22×Dic7—22no—
144C22×Dic7—22no—
145C22×Dic7—22no—
146C22×Dic7—22no—
147C22×Dic7—22no—
148C22×Dic7—22no—
149C22×Dic7—22no—
150C22×Dic7—22no—
151C22×Dic7—22no—
152C22×Dic7—22no—
153C22×Dic7—22no—
154C22×Dic7—22no—
155C22×Dic7—21no—
156C22×Dic7—22no—
157C22×Dic7—22no—
158C22×Dic7—22no—
159C22×Dic7C2×D412yes—
160C22×Dic7C2×D412yes—
161C7×C4⋊C4—28no—
162C7×C4⋊C4—28no—
163C7×C4⋊C4—48no—
164C4⋊Dic7—44no—
165C4⋊Dic7—48no—
166C4⋊Dic7—44no—
167C4×Dic7—44no—
168C22×C4⋊C4—72no—
169C22×C4⋊C4—71no—
170C22×C4⋊C4—71no—
171C22×C4⋊C4C2×D711yescharacteristic
172C22×C4⋊C4C2×D711yescharacteristic
173C22×C4⋊C4C2×D712yes—
174C22×C42—71no—
175#398Dic718yescomplemented
176#389—144no—
177#387—144no—
178C2×#95—71no—
179C2×#95—71no—
180C2×#95—71no—
181C2×#95—71no—
182C2×#95—72no—
183C2×#95—71no—
184C2×#95—72no—
185C2×#95—72no—
186C2×#95—72no—
187C2×#95—72no—
188C2×#95—72no—
189C2×#95—72no—
190C2×#95—72no—
191C2×#95—72no—
192C2×#95C2×D711yescharacteristic
193C2×#95C2×D712yes—
194C23×C7C23×C411yescharacteristic
195C23×C7C22×D411yescharacteristic
196C23×C7C2×#4111yescharacteristic
197C23×C7H(5,𝔽2)11yescharacteristic
198C23×C7H(5,𝔽2)11yescharacteristic
199C23×C7H(5,𝔽2)12yes—
200C23×C7H(5,𝔽2)11yescharacteristic
201C23×C72−1+412yes—
202C23×C72−1+412yes—
203C23×C72−1+412yes—
204C23×C72−1+411yescharacteristic
205C2×C4×C7—24no—
206C2×C4×C7—22no—
207C2×C4×C7—22no—
208C2×C4×C7—24no—
209C2×C4×C7—22no—
210C2×C4×C7—22no—
211C2×C4×C7—24no—
212C2×C4×C7—22no—
213C2×C4×C7—24no—
214C2×C4×C7—24no—
215C2×C4×C7—24no—
216C2×C4×C7—24no—
217C2×C4×C7—22no—
218C2×C4×C7—24no—
219C2×C4×C7—24no—
220C2×C4×C7—41no—
221C2×C4×C7—42no—
222C2×C4×C7—41no—
223C2×C4×C7—41no—
224C2×C4×C7—41no—
225C2×C4×C7—42no—
226C2×C4×C7—42no—
227C2×C4×C7—41no—
228C2×C4×C7—42no—
229C2×C4×C7—42no—
230C2×C4×C7—41no—
231C2×C4×C7—42no—
232C2×C4×C7—42no—
233C2×C4×C7—42no—
234C2×C4×C7—42no—
235C2×C4×C7C4×D414yes—
236C2×Dic7—22no—
237C2×Dic7—22no—
238C2×Dic7—22no—
239C2×Dic7—22no—
240C2×Dic7—22no—
241C2×Dic7—22no—
242C2×Dic7—42no—
243C2×Dic7—42no—
244C2×Dic7—42no—
245C2×Dic7—42no—
246C2×Dic7—42no—
247C2×Dic7—41no—
248C2×Dic7—42no—
249C2×Dic7—41no—
250C2×Dic7—42no—
251C2×Dic7—41no—
252C2×Dic7—41no—
253C2×Dic7—41no—
254C2×Dic7—41no—
255C2×Dic7—42no—
256C2×Dic7—42no—
257C2×Dic7—42no—
258C2×Dic7—42no—
259C2×Dic7—42no—
260C2×Dic7—42no—
261C2×Dic7—42no—
262C2×Dic7—42no—
263C2×Dic7—42no—
264C2×Dic7—42no—
265C2×Dic7—42no—
266C2×Dic7—42no—
267C2×Dic7—42no—
268C2×Dic7—42no—
269C2×Dic7—42no—
270C23×C4—71no—
271C23×C4—71no—
272C23×C4—72no—
273C23×C4—71no—
274C23×C4—71no—
275C23×C4—72no—
276C23×C4C22×D712yes—
277C23×C4C22×D711yescharacteristic
278C23×C4C22×D711yescharacteristic
279C23×C4C22×D712yes—
280C23×C4C22×D711yescharacteristic
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—142no—
288C2×C4⋊C4—144no—
289C2×C4⋊C4—142no—
290C2×C4⋊C4—282no—
291C2×C4⋊C4—282no—
292C2×C4⋊C4—282no—
293C2×C4⋊C4—282no—
294C2×C4⋊C4C2×Dic714yes—
295C2×C4⋊C4C2×Dic714yes—
296C2×C4⋊C4C2×Dic718yes—
297C2×C42—74no—
298C2×C42—282no—
299#95—142no—
300#95—142no—
301#95—142no—
302#95—144no—
303#95—142no—
304#95—142no—
305#95—282no—
306#95—282no—
307#95—282no—
308#95—282no—
309#95—282no—
310#95—282no—
311#95—282no—
312#95—282no—
313#95C2×Dic718yes—
314#95C2×Dic714yes—
315C22×C7C2×C4×D411yescharacteristic
316C22×C7#51811yescharacteristic
317C22×C7#51912yes—
318C22×C7#52012yes—
319C22×C7#52011yescharacteristic
320C22×C7#53411yescharacteristic
321C22×C7#53511yescharacteristic
322C22×C7#53611yescharacteristic
323C22×C7#53611yescharacteristic
324C22×C7#53611yescharacteristic
325C22×C7#53711yescharacteristic
326C22×C7#53912yes—
327C22×C7#54011yescharacteristic
328C22×C7#54112yes—
329C22×C7#54211yescharacteristic
330C22×C7#56212yes—
331C22×C7#56212yes—
332C22×C7#56212yes—
333C22×C7#56312yes—
334C22×C7#56312yes—
335C22×C7#56312yes—
336C22×C7#56312yes—
337C22×C7#56412yes—
338C4×C7—24no—
339C4×C7—42no—
340C4×C7—42no—
341C4×C7—44no—
342C4×C7—44no—
343Dic7—42no—
344Dic7—42no—
345Dic7—82no—
346Dic7—81no—
347Dic7—82no—
348Dic7—81no—
349C24C23×D711yescharacteristic
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—72no—
375C22×C4—72no—
376C22×C4—141no—
377C22×C4—141no—
378C22×C4—142no—
379C22×C4—142no—
380C22×C4—142no—
381C22×C4—142no—
382C22×C4—141no—
383C22×C4—141no—
384C22×C4—141no—
385C22×C4—141no—
386C22×C4—142no—
387C22×C4—142no—
388C22×C4—141no—
389C22×C4—141no—
390C22×C4—142no—
391C22×C4—142no—
392C22×C4—142no—
393C22×C4—142no—
394C22×C4—142no—
395C22×C4—142no—
396C22×C4—142no—
397C22×C4—142no—
398C22×C4—141no—
399C22×C4—142no—
400C22×C4—142no—
401C22×C4—142no—
402C22×C4—142no—
403C22×C4—142no—
404C22×C4—142no—
405C22×C4—141no—
406C22×C4—142no—
407C22×C4—142no—
408C22×C4D4×D712yes—
409C22×C4#115912yes—
410C22×C4C22×Dic712yes—
411C22×C4C22×Dic714yes—
412C22×C4C22×Dic714yes—
413C22×C4C22×Dic712yes—
414C22×C4C22×Dic712yes—
415C4⋊C4—28no—
416C4⋊C4—28no—
417C4⋊C4—48no—
418C4⋊C4—284no—
419C4⋊C4—288no—
420C4⋊C4—284no—
421C42—284no—
422C2×C7#232211yescharacteristic
423C2×C7#232411yescharacteristic
424C2×C7#232711yescharacteristic
425C2×C7#237812yes—
426C2×C7#238212yes—
427C2×C7#281411yescharacteristic
428C2×C7#281611yescharacteristic
429C2×C7#282111yescharacteristic
430C2×C7#282211yescharacteristic
431C2×C7#283612yes—
432C2×C7#283912yes—
433C23C2×D4×D711yescharacteristic
434C23C2×#115911yescharacteristic
435C23#654811yescharacteristic
436C23#654811yescharacteristic
437C23#655112yes—
438C23#655112yes—
439C23#655311yescharacteristic
440C23#655312yes—
441C23#655411yescharacteristic
442C23#655412yes—
443C23C23×Dic711yescharacteristic
444C2×C4—24no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—22no—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—142no—
475C2×C4—142no—
476C2×C4—142no—
477C2×C4—142no—
478C2×C4—142no—
479C2×C4—142no—
480C2×C4—282no—
481C2×C4—282no—
482C2×C4—282no—
483C2×C4—282no—
484C2×C4—282no—
485C2×C4—282no—
486C2×C4—282no—
487C2×C4—282no—
488C2×C4—282no—
489C2×C4—282no—
490C2×C4—281no—
491C2×C4—281no—
492C2×C4—282no—
493C2×C4—282no—
494C2×C4—282no—
495C2×C4—281no—
496C2×C4—281no—
497C2×C4—282no—
498C2×C4—282no—
499C2×C4—282no—
500C2×C4—282no—
501C2×C4—282no—
502C2×C4—282no—
503C2×C4—282no—
504C2×C4—281no—
505C2×C4—281no—
506C2×C4—282no—
507C2×C4—282no—
508C2×C4D4×Dic714yes—
509C7#1463111yescharacteristic, complemented, Sylow
510C22#9029411yescharacteristic
511C22#9029811yescharacteristic
512C22#9029911yescharacteristic
513C22#9031011yescharacteristic
514C22#9033712yes—
515C22#9033712yes—
516C22#9033812yes—
517C22#9033812yes—
518C22#9033911yescharacteristic
519C22#9034411yescharacteristic
520C22#9035612yes—
521C22C7⋊#56412yes—
522C22#9039012yes—
523C22#9039012yes—
524C22#9039112yes—
525C22#9041511yescharacteristic
526C22#9041511yescharacteristic
527C22#9042212yes—
528C22C2×D4×Dic711yescharacteristic
529C22#9048911yescharacteristic
530C22#9050312yes—
531C22#9051812yes—
532C22#9051811yescharacteristic
533C4—24no—
534C4—44no—
535C4—42no—
536C4—42no—
537C4—44no—
538C4—282no—
539C4—282no—
540C4—561no—
541C4—561no—
542C4—562no—
543C4—562no—
544C2#1173537011yescharacteristic
545C2#1173537111yescharacteristic
546C2#1173538312yes—
547C2#1173545111yescharacteristic
548C2#1173545211yescharacteristic
549C2#1173545912yes—
550C2#1174007811yescharacteristic
551C2#1174019512yes—
552C2#1174028111yescharacteristic
553C2#1174047212yes—
554C2#1174067211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#398C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×#398D7
hypocenterC7#14631
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
19. C7×#398C4semidirect
175. #398Dic7semidirect
509. C7#14631semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3982
C2×#897572
C2×#897532
#117293232
#117293192
#117271662
#117271552
#146317