Finite Group Databasebeta

← #13382888

Subgroups — #13382888

Order 1792.

950 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#389C211yesmaximal, characteristic
2C2×#89736C211yesmaximal, characteristic
3#11739514C211yesmaximal, characteristic
4C2×#89696C211yesmaximal, characteristic
5#11729312C211yesmaximal, characteristic
6#11729312C211yesmaximal, characteristic
7#11729312C211yesmaximal, characteristic
8#11727378C212yesmaximal, complemented
9#11727377C212yesmaximal, complemented
10#11727376C212yesmaximal, complemented
11#11727364C212yesmaximal, complemented
12C22×C7×C4⋊C4—21no—
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C2×#6489C2211yescharacteristic
17C2×#6489C2211yescharacteristic
18C22×#1136C2211yescharacteristic
19C22×#1136C2211yescharacteristic
20C7×#389—21no—
21C7×#389—21no—
22C7×#389C2212yes—
23C7×#389C2212yes—
24C2×C7×#95—21no—
25#89982—21no—
26#89982—21no—
27#89736—24no—
28C2×#6382C2212yes—
29C2×#6381C2212yes—
30C4×Dic7⋊C4—21no—
31C4×Dic7⋊C4—21no—
32#89700C2211yescharacteristic
33#89700C2211yescharacteristic
34#89700C2211yescharacteristic
35#89700C2211yescharacteristic
36#89696—24no—
37C2×C4⋊(C7⋊C8)C2212yes—
38C2×C4⋊(C7⋊C8)C2212yes—
39#89324C2212yes—
40#89324C2212yes—
41#89324C2212yes—
42#89324C2212yes—
43#89324C2212yes—
44#89324C2212yes—
45#23670—71nomaximal, Sylow
46C23×C4×C7—21no—
47C23×C4×C7—21no—
48C23×C4×C7D411yescharacteristic
49C23×C4×C7D411yescharacteristic
50C23×C4×C7C2311yescharacteristic
51C2×C7×C4⋊C4—21no—
52C2×C7×C4⋊C4—22no—
53C2×C7×C4⋊C4—22no—
54C2×C7×C4⋊C4—22no—
55C2×C7×C4⋊C4—22no—
56C2×C7×C4⋊C4—22no—
57C2×C7×C4⋊C4—21no—
58C2×C7×C4⋊C4—44no—
59C2×C7×C4⋊C4Q814yes—
60C2×C7×C4⋊C4C2312yes—
61C2×C7×C4⋊C4C2312yes—
62C2×C42×C7—22no—
63C2×C42×C7—22no—
64C2×C42×C7D411yescharacteristic
65C2×C42×C7D411yescharacteristic
66C2×C42×C7C2311yescharacteristic
67C2×C42×C7C2311yescharacteristic
68C2×C22⋊Dic7—21no—
69C2×C22⋊Dic7—21no—
70#6489—22no—
71#6489—22no—
72#6489—22no—
73#6489Q814yes—
74C2×C4⋊Dic7C2311yescharacteristic
75C2×C4⋊Dic7C2311yescharacteristic
76C2×C4⋊Dic7C2311yescharacteristic
77C2×C4⋊Dic7C2311yescharacteristic
78C2×Dic7⋊C4—21no—
79C2×Dic7⋊C4—21no—
80C2×Dic7⋊C4—21no—
81C2×Dic7⋊C4—21no—
82C2×C4×Dic7—21no—
83C2×C4×Dic7—21no—
84C2×#1136—22no—
85C2×#1136—22no—
86C2×#1136—22no—
87C2×#1136—22no—
88C2×#1136—22no—
89C2×#1136D414yes—
90C22×C7⋊C8C2312yes—
91C22×C7⋊C8C2312yes—
92C7×#95—22no—
93C7×#95—22no—
94C7⋊#95—21no—
95C7⋊#95—21no—
96C7⋊#95—21no—
97C7⋊#95—21no—
98#6382—24no—
99#6381—24no—
100C4⋊(C7⋊C8)—24no—
101C4⋊(C7⋊C8)—24no—
102C2×#428—71no—
103C2×#423—71no—
104#2296—71no—
105C2×#389D711yescharacteristic
106#2088—72no—
107#2088—72no—
108#2087—72no—
109#2086—72no—
110#1736—71no—
111#1736—71no—
112#1736—71no—
113C24×C7C2×D411yescharacteristic
114C22×C4×C7—22no—
115C22×C4×C7—22no—
116C22×C4×C7—24no—
117C22×C4×C7—22no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
121C22×C4×C7—41no—
122C22×C4×C7—41no—
123C22×C4×C7—42no—
124C22×C4×C7—42no—
125C22×C4×C7—42no—
126C22×C4×C7—42no—
127C22×C4×C7—42no—
128C22×C4×C7C2×D411yescharacteristic
129C22×C4×C7C2×D411yescharacteristic
130C22×C4×C7C2×D411yescharacteristic
131C22×C4×C7C2×D411yescharacteristic
132C22×C4×C7C2×D411yescharacteristic
133C22×C4×C7C2×D412yes—
134C22×C4×C7C2×Q812yes—
135C22×C4×C7C2×Q812yes—
136C22×C4×C7#4112yes—
137C22×C4×C7#4112yes—
138C22×C4×C7#4112yes—
139C22×C4×C7C2411yescharacteristic
140C22×Dic7—21no—
141C22×Dic7—21no—
142C22×Dic7—21no—
143C22×Dic7—21no—
144C7×C4⋊C4—24no—
145C7×C4⋊C4—22no—
146C7×C4⋊C4—22no—
147C7×C4⋊C4—22no—
148C7×C4⋊C4—44no—
149C7×C4⋊C4—42no—
150C7×C4⋊C4—44no—
151C7×C4⋊C4C2×Q814yes—
152C42×C7—22no—
153C42×C7—22no—
154C42×C7—21no—
155C42×C7—21no—
156C42×C7—21no—
157C42×C7—21no—
158C22⋊Dic7—24no—
159C22⋊Dic7—42no—
160C4⋊Dic7—21no—
161C4⋊Dic7—21no—
162C4⋊Dic7—21no—
163C4⋊Dic7—21no—
164C4⋊Dic7—21no—
165C4⋊Dic7—21no—
166C4⋊Dic7C2×Q812yes—
167C4⋊Dic7C2×Q812yes—
168Dic7⋊C4—42no—
169Dic7⋊C4—42no—
170Dic7⋊C4—42no—
171Dic7⋊C4—42no—
172C4×Dic7—24no—
173C4×Dic7—42no—
174#1136—28no—
175#1136—44no—
176C2×C7⋊C8—22no—
177C2×C7⋊C8—22no—
178C2×C7⋊C8—22no—
179C2×C7⋊C8—22no—
180C2×C7⋊C8—22no—
181C2×C7⋊C8C2×D414yes—
182C22×M16—71no—
183C22×M16—71no—
184C2×#117—71no—
185C2×#117—71no—
186C22×C4⋊C4—21no—
187C22×C4⋊C4C2×D711yescharacteristic
188C22×C4⋊C4C2×D711yescharacteristic
189C22×C42C2×D711yescharacteristic
190#428—144no—
191C2×#107—72no—
192C2×#106—72no—
193#423—144no—
194C2×C4⋊C8—72no—
195C2×C4⋊C8—72no—
196#389—21no—
197#389—21no—
198#389—71no—
199#389—71no—
200#389—71no—
201#389—71no—
202#389C2×D712yes—
203#389C2×D712yes—
204#385—141no—
205#385—141no—
206C4×C4⋊C4—141no—
207C4×C4⋊C4—141no—
208C2×#95—21no—
209#340—72no—
210#340—72no—
211#340—72no—
212#340—72no—
213#340—72no—
214#340—72no—
215C23×C7—21no—
216C23×C7—21no—
217C23×C7—21no—
218C23×C7—21no—
219C23×C7#12112yes—
220C23×C7C22⋊Q812yes—
221C23×C7C22⋊Q812yes—
222C23×C7C22×D411yescharacteristic
223C2×C4×C7—21no—
224C2×C4×C7—21no—
225C2×C4×C7—21no—
226C2×C4×C7—21no—
227C2×C4×C7—21no—
228C2×C4×C7—21no—
229C2×C4×C7—24no—
230C2×C4×C7—21no—
231C2×C4×C7—21no—
232C2×C4×C7—21no—
233C2×C4×C7—21no—
234C2×C4×C7—44no—
235C2×C4×C7—44no—
236C2×C4×C7—48no—
237C2×C4×C7—42no—
238C2×C4×C7—42no—
239C2×C4×C7—42no—
240C2×C4×C7—42no—
241C2×C4×C7—42no—
242C2×C4×C7—84no—
243C2×C4×C7#12112yes—
244C2×C4×C7C22⋊Q812yes—
245C2×C4×C7C22⋊Q812yes—
246C2×C4×C7#12314yes—
247C2×C4×C7#12514yes—
248C2×C4×C7#12514yes—
249C2×C4×C7C4⋊Q814yes—
250C2×C4×C7AGL(1,ℤ/8)12yes—
251C2×C4×C7#13712yes—
252C2×C4×C7C22×D411yescharacteristic
253C2×C4×C7C22×Q811yescharacteristic
254C2×C4×C7C22×Q811yescharacteristic
255C2×C4×C7C2×#4111yescharacteristic
256C2×C4×C7C2×#4111yescharacteristic
257C2×C4×C7C2×#4111yescharacteristic
258C2×Dic7—22no—
259C2×Dic7—22no—
260C2×Dic7—41no—
261C2×Dic7—41no—
262C2×Dic7—41no—
263C2×Dic7—41no—
264C2×Dic7—41no—
265C2×Dic7—41no—
266C2×Dic7—41no—
267C2×Dic7—41no—
268C2×Dic7—41no—
269C2×Dic7—41no—
270C7⋊C8—24no—
271C7⋊C8—42no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4C22⋊D711yescharacteristic
275C23×C4C22⋊D711yescharacteristic
276C23×C4C22×D711yescharacteristic
277C2×M16—74no—
278C2×M16—142no—
279C2×M16—142no—
280C2×M16—142no—
281C2×M16—142no—
282C2×M16—142no—
283C22×C8—72no—
284C22×C8—72no—
285#117—74no—
286#117—142no—
287#117—142no—
288#117—142no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—71no—
298C2×C4⋊C4—71no—
299C2×C4⋊C4—71no—
300C2×C4⋊C4—71no—
301C2×C4⋊C4—141no—
302C2×C4⋊C4—141no—
303C2×C4⋊C4—141no—
304C2×C4⋊C4—141no—
305C2×C4⋊C4Dic1414yes—
306C2×C4⋊C4C22×D712yes—
307C2×C4⋊C4C22×D712yes—
308C2×C22⋊C4—141no—
309C2×C22⋊C4—141no—
310C2×C42—22no—
311C2×C42—22no—
312C2×C42—141no—
313C2×C42—141no—
314C2×C42C22⋊D711yescharacteristic
315C2×C42C22⋊D711yescharacteristic
316C2×C42C22×D711yescharacteristic
317C2×C42C22×D711yescharacteristic
318#107—144no—
319#106—144no—
320C4⋊C8—144no—
321C4⋊C8—144no—
322#95—22no—
323#95—22no—
324#95—141no—
325#95—141no—
326#95—141no—
327#95—141no—
328C22×C7—22no—
329C22×C7—22no—
330C22×C7—22no—
331C22×C7—22no—
332C22×C7—22no—
333C22×C7—22no—
334C22×C7#39814yes—
335C22×C7C2×#12111yescharacteristic
336C22×C7C2×C22⋊Q811yescharacteristic
337C22×C7C2×C22⋊Q811yescharacteristic
338C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C7C2×#13711yescharacteristic
340C22×C7#57511yescharacteristic
341C22×C7#57511yescharacteristic
342C4×C7—22no—
343C4×C7—22no—
344C4×C7—44no—
345C4×C7—41no—
346C4×C7—41no—
347C4×C7—82no—
348C4×C7#39814yes—
349C4×C7C2×#12311yescharacteristic
350C4×C7C2×#12511yescharacteristic
351C4×C7C2×#12511yescharacteristic
352C4×C7C2×C4⋊Q811yescharacteristic
353Dic7—42no—
354Dic7—42no—
355Dic7—81no—
356Dic7—81no—
357C24C2×C22⋊D711yescharacteristic
358C22×C4—24no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—141no—
373C22×C4—141no—
374C22×C4—141no—
375C22×C4—141no—
376C22×C4C2×Dic1412yes—
377C22×C4#115712yes—
378C22×C4D4×D712yes—
379C22×C4#115912yes—
380C22×C4Q8×D712yes—
381C22×C4#116112yes—
382C22×C4C2×C22⋊D711yescharacteristic
383C22×C4C2×C22⋊D711yescharacteristic
384C22×C4C2×C22⋊D711yescharacteristic
385C22×C4C2×C22⋊D711yescharacteristic
386C22×C4C2×C22⋊D711yescharacteristic
387C22×C4C23×D711yescharacteristic
388M16—148no—
389M16—284no—
390C2×C8—74no—
391C2×C8—142no—
392C2×C8—142no—
393C2×C8—142no—
394C2×C8—142no—
395C2×C8—142no—
396C4⋊C4—24no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—44no—
401C4⋊C4—44no—
402C4⋊C4—42no—
403C4⋊C4—72no—
404C4⋊C4—72no—
405C4⋊C4—141no—
406C4⋊C4—141no—
407C4⋊C4—141no—
408C4⋊C4—141no—
409C4⋊C4—141no—
410C4⋊C4—141no—
411C4⋊C4—282no—
412C4⋊C4—282no—
413C4⋊C4—282no—
414C4⋊C4—282no—
415C4⋊C4C2×Dic1414yes—
416C22⋊C4—144no—
417C22⋊C4—282no—
418C42—22no—
419C42—22no—
420C42—21no—
421C42—21no—
422C42—21no—
423C42—21no—
424C42—144no—
425C42—282no—
426C2×C7—24no—
427C2×C7C2×#39811yescharacteristic
428C2×C7#305511yescharacteristic
429C2×C7#305611yescharacteristic
430C2×C7#307711yescharacteristic
431C2×C7#307811yescharacteristic
432C2×C7#307911yescharacteristic
433C2×C7#308011yescharacteristic
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23#648712yes—
439C23#650212yes—
440C23#650912yes—
441C23C22×C22⋊D711yescharacteristic
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—24no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—44no—
454C2×C4—44no—
455C2×C4—48no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—84no—
462C2×C4—142no—
463C2×C4—142no—
464C2×C4—281no—
465C2×C4—281no—
466C2×C4—281no—
467C2×C4—281no—
468C2×C4—281no—
469C2×C4—281no—
470C2×C4—281no—
471C2×C4—281no—
472C2×C4—281no—
473C2×C4—281no—
474C2×C4#645114yes—
475C2×C4#645214yes—
476C2×C4#645314yes—
477C2×C4#645714yes—
478C2×C4#648712yes—
479C2×C4#649512yes—
480C2×C4#650212yes—
481C2×C4#650512yes—
482C2×C4#650912yes—
483C2×C4C22×Dic1411yescharacteristic
484C2×C4C2×#115711yescharacteristic
485C2×C4C2×D4×D711yescharacteristic
486C2×C4C2×#115911yescharacteristic
487C2×C4C2×Q8×D711yescharacteristic
488C2×C4C2×#116111yescharacteristic
489C8—144no—
490C8—282no—
491C7#2367011yescharacteristic, complemented, Sylow
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22#8975614yes—
499C22C2×#648711yescharacteristic
500C22C2×#649511yescharacteristic
501C22C2×#650211yescharacteristic
502C22C2×#650511yescharacteristic
503C22C2×#650911yescharacteristic
504C22#9051311yescharacteristic
505C22#9051311yescharacteristic
506C4—22no—
507C4—22no—
508C4—41no—
509C4—44no—
510C4—41no—
511C4—82no—
512C4—282no—
513C4—282no—
514C4—561no—
515C4—561no—
516C4#8975614yes—
517C4C2×#645111yescharacteristic
518C4C2×#645211yescharacteristic
519C4C2×#645311yescharacteristic
520C4C2×#645711yescharacteristic
521C2—24no—
522C2C2×#8975611yescharacteristic
523C2#1173974111yescharacteristic
524C2#1173987611yescharacteristic
525C2#1174006611yescharacteristic
526C2#1174017711yescharacteristic
527C2#1174046211yescharacteristic
528C2#1174065711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#389C2
socleC23×C7C22×D4
prime radicalC24×C7C2×D4
hypercenterC2×#389D7
hypocenterC7#23670
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
8. #11727378C2semidirect
9. #11727377C2semidirect
10. #11727376C2semidirect
11. #11727364C2semidirect
491. C7#23670semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3892
C2×#897362
#117395142
C2×#896962
#117293122
#117273782
#117273772
#117273762
#117273642
#236707