Finite Group Databasebeta

← #13337741

Subgroups — #13337741

Order 1792.

608 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C8×#41C211yesmaximal, characteristic
2#11739980C212yesmaximal
3#11735887C211yesmaximal, characteristic, complemented
4#11728699C211yesmaximal, characteristic, complemented
5#11728698C211yesmaximal, characteristic, complemented
6#11728697C212yesmaximal, complemented
7#11728607C211yesmaximal, characteristic, complemented
8#11728606C211yesmaximal, characteristic, complemented
9#11728605C212yesmaximal, complemented
10#11728535C212yesmaximal, complemented
11#11727486C211yesmaximal, characteristic, complemented
12C4×C7×#41C2211yescharacteristic
13#90161C2212yes—
14C7×C8×Q8C2211yescharacteristic
15C7×C8×Q8C2211yescharacteristic
16C7×C8×D4—21no—
17C7×C8×D4—21no—
18C7×C8×D4C2211yescharacteristic
19C7×C8×D4C2211yescharacteristic
20C7×#431—21no—
21C7×#431C2211yescharacteristic
22C2×C4×C7×C8—21no—
23C2×C4×C7×C8C2211yescharacteristic
24#90011—22no—
25#89878—21no—
26#89878—21no—
27#89803C2212yes—
28#89802—22no—
29#89793C2212yes—
30#89791C2212yes—
31#89790—22no—
32#89780C2212yes—
33#89768—22no—
34#89698C2212yes—
35#89455—21no—
36#89455—21no—
37#89454C2211yescharacteristic
38#89454C2211yescharacteristic
39#89452C2212yes—
40#89281C2212yes—
41#89281C2212yes—
42#89276C2212yes—
43#89276C2212yes—
44#89253C2211yescharacteristic
45#89253C2211yescharacteristic
46#89252C2212yes—
47#19273—71nomaximal, Sylow
48C2×C7×#41D411yescharacteristic
49C22×C7×C8—21no—
50C22×C7×C8—21no—
51C22×C7×C8D411yescharacteristic
52C22×C7×C8D411yescharacteristic
53C4×C7×Q8D411yescharacteristic
54C4×C7×Q8C2311yescharacteristic
55C4×C7×D4—21no—
56C4×C7×D4—21no—
57C4×C7×D4D411yescharacteristic
58C4×C7×D4C2311yescharacteristic
59C7×#117—21no—
60C7×#117D411yescharacteristic
61C2×C42×C7—21no—
62C2×C42×C7C2311yescharacteristic
63C2×#1144—22no—
64C2×#1142—22no—
65#6489—22no—
66#6487—22no—
67#6487—22no—
68#6433—22no—
69#6432C2312yes—
70#6432C2312yes—
71C4×Dic14—22no—
72C4×Dic14—22no—
73C7×C4⋊C8—21no—
74C7×C4⋊C8—21no—
75C7×C4⋊C8C2311yescharacteristic
76C7×C4⋊C8C2311yescharacteristic
77C7×C22⋊C8—21no—
78C7×C22⋊C8—21no—
79C7×C22⋊C8—21no—
80C4×C7×C8—21no—
81C4×C7×C8—21no—
82C4×C7×C8—21no—
83C4×C7×C8D411yescharacteristic
84C4×C7×C8D411yescharacteristic
85C4×C7×C8C2311yescharacteristic
86C4×C7×C8C2311yescharacteristic
87#6409—22no—
88#6406—22no—
89C22⋊(C7⋊C8)—22no—
90#6392—21no—
91#6392—21no—
92#6392—21no—
93#6392—21no—
94#6391—22no—
95#6391—22no—
96#6384—22no—
97#6384—22no—
98#6382—22no—
99#6381—22no—
100C4⋊(C7⋊C8)C2312yes—
101C4⋊(C7⋊C8)C2312yes—
102#6377—22no—
103#3160—71no—
104#3116—72no—
105C8×#41D711yescharacteristic
106#1676—71no—
107#1675—71no—
108#1674—71no—
109#1673—71no—
110#1672—72no—
111#1671—72no—
112#1568—71no—
113#1554—72no—
114C7×#41—22no—
115C7×#41—22no—
116C2×C7×Q8C2×D411yescharacteristic
117C2×C7×D4—21no—
118C2×C7×D4C2×D411yescharacteristic
119C22×C4×C7—21no—
120C22×C4×C7—21no—
121C22×C4×C7—21no—
122C22×C4×C7C2×D411yescharacteristic
123C22×C4×C7C2×D411yescharacteristic
124C22×C4×C7#4111yescharacteristic
125C2×Dic14—22no—
126C2×Dic14—22no—
127C2×C7×C8—22no—
128C2×C7×C8—22no—
129C2×C7×C8—21no—
130C2×C7×C8—21no—
131C2×C7×C8—42no—
132C2×C7×C8—42no—
133C2×C7×C8C2×D411yescharacteristic
134C2×C7×C8C2×D411yescharacteristic
135C2×C7×C8C2×D411yescharacteristic
136C2×C7×C8C2×D411yescharacteristic
137C7×C4⋊C4—21no—
138C7×C4⋊C4—21no—
139C7×C4⋊C4C2×D411yescharacteristic
140C7×C4⋊C4C2×D411yescharacteristic
141C7×C22⋊C4—21no—
142C7×C22⋊C4—21no—
143C7×C22⋊C4—21no—
144C42×C7—21no—
145C42×C7—21no—
146C42×C7—21no—
147C42×C7C2×D411yescharacteristic
148C42×C7C2×D411yescharacteristic
149C42×C7#4111yescharacteristic
150C42×C7C2411yescharacteristic
151C22⋊Dic7—42no—
152#1144—44no—
153#1142—44no—
154C4⋊Dic7—22no—
155C4⋊Dic7—22no—
156C4⋊Dic7—22no—
157C4⋊Dic7—22no—
158Dic7⋊C4—42no—
159Dic7⋊C4—42no—
160C4×Dic7—42no—
161C2×C7⋊C8—22no—
162C2×C7⋊C8—22no—
163#533—72no—
164C4×#41C2×D711yescharacteristic
165#500—71no—
166#500—71no—
167#499—141no—
168#499—141no—
169#498—72no—
170#485—142no—
171#477—72no—
172#476—72no—
173#462—72no—
174#461—72no—
175#452—142no—
176C8×Q8C2×D711yescharacteristic
177C8×Q8C2×D711yescharacteristic
178#441—142no—
179#440—142no—
180C8×D4—21no—
181C8×D4—21no—
182C8×D4C2×D711yescharacteristic
183C8×D4C2×D711yescharacteristic
184#432—72no—
185#431—21no—
186#431C2×D711yescharacteristic
187#427—141no—
188#427—141no—
189C2×C4×C8—21no—
190C2×C4×C8C2×D711yescharacteristic
191#335—71no—
192#335—71no—
193#334—72no—
194#333—72no—
195#333—72no—
196#332—72no—
197#332—72no—
198C23×C7—21no—
199C23×C7#12111yescharacteristic
200C7×Q8—21no—
201C7×Q8#13512yes—
202C7×D4—24no—
203C7×D4—21no—
204C7×D4#13512yes—
205C2×C4×C7—24no—
206C2×C4×C7—21no—
207C2×C4×C7—21no—
208C2×C4×C7—21no—
209C2×C4×C7—21no—
210C2×C4×C7—21no—
211C2×C4×C7—21no—
212C2×C4×C7—21no—
213C2×C4×C7—41no—
214C2×C4×C7—42no—
215C2×C4×C7—41no—
216C2×C4×C7—41no—
217C2×C4×C7#12111yescharacteristic
218C2×C4×C7#12111yescharacteristic
219C2×C4×C7#12111yescharacteristic
220C2×C4×C7C22×D411yescharacteristic
221C2×C4×C7C22×D411yescharacteristic
222C2×C4×C7C2×#4111yescharacteristic
223C2×Dic7—42no—
224C2×Dic7—42no—
225Dic14—42no—
226Dic14—42no—
227Dic14—82no—
228C7×C8—21no—
229C7×C8—21no—
230C7×C8—41no—
231C7×C8—41no—
232C7×C8#13712yes—
233C7×C8#13712yes—
234C7⋊C8—42no—
235C7⋊C8—42no—
236C2×#41D2811yescharacteristic
237C2×Q16—142no—
238C2×SD16—142no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8C22⋊D711yescharacteristic
242C22×C8C22⋊D711yescharacteristic
243C4⋊Q8—72no—
244C4⋊Q8—72no—
245#125—142no—
246C22⋊Q8—142no—
247C22⋊Q8—142no—
248C4×Q8—142no—
249C4×Q8—142no—
250C4×Q8D2811yescharacteristic
251C4×Q8C22×D711yescharacteristic
252C4×D4—21no—
253C4×D4—21no—
254C4×D4D2811yescharacteristic
255C4×D4C22×D711yescharacteristic
256#117—21no—
257#117—142no—
258#117D2811yescharacteristic
259C2×C42—21no—
260C2×C42C22×D711yescharacteristic
261#107—141no—
262#107—141no—
263#107—141no—
264#107—141no—
265#107—142no—
266#106—142no—
267#106—142no—
268#106—142no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—72no—
272C4⋊C8—72no—
273C4⋊C8C22×D711yescharacteristic
274C4⋊C8C22×D711yescharacteristic
275#103—142no—
276#103—142no—
277#103—142no—
278#102—142no—
279C22⋊C8—21no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—142no—
283#97—142no—
284C4×C8—21no—
285C4×C8—21no—
286C4×C8—21no—
287C4×C8C22⋊D711yescharacteristic
288C4×C8C22⋊D711yescharacteristic
289C4×C8C22×D711yescharacteristic
290C4×C8C22×D711yescharacteristic
291C22×C7—21no—
292C22×C7—21no—
293C22×C7—22no—
294C22×C7—21no—
295C22×C7—41no—
296C22×C7—41no—
297C22×C7C2×#12111yescharacteristic
298C4×C7—21no—
299C4×C7—21no—
300C4×C7—22no—
301C4×C7—21no—
302C4×C7—21no—
303C4×C7—41no—
304C4×C7—41no—
305C4×C7C2×#13511yescharacteristic
306C4×C7C2×#13511yescharacteristic
307C4×C7C2×#13711yescharacteristic
308C4×C7C2×#13711yescharacteristic
309Dic7—82no—
310Dic7—82no—
311#41—22no—
312#41—22no—
313C2×Q8—142no—
314C2×Q8—142no—
315C2×Q8C2×D2811yescharacteristic
316C2×D4—21no—
317C2×D4C2×D2811yescharacteristic
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4C2×D2811yescharacteristic
322C22×C4#115711yescharacteristic
323C22×C4C2×C22⋊D711yescharacteristic
324Q16—284no—
325SD16—284no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—42no—
331C2×C8—42no—
332C2×C8—142no—
333C2×C8—142no—
334C2×C8C2×C22⋊D711yescharacteristic
335C2×C8C2×C22⋊D711yescharacteristic
336C2×C8C2×C22⋊D711yescharacteristic
337C2×C8C2×C22⋊D711yescharacteristic
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—142no—
341C4⋊C4—142no—
342C4⋊C4—142no—
343C4⋊C4—142no—
344C4⋊C4—282no—
345C4⋊C4—282no—
346C4⋊C4C2×D2811yescharacteristic
347C4⋊C4C2×D2811yescharacteristic
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—282no—
352C42—21no—
353C42—21no—
354C42—21no—
355C42—282no—
356C42C2×D2811yescharacteristic
357C42#115711yescharacteristic
358C42C2×C22⋊D711yescharacteristic
359C42C23×D711yescharacteristic
360C2×C7—41no—
361C2×C7—42no—
362C2×C7#303911yescharacteristic
363C2×C7#305011yescharacteristic
364C2×C7#306711yescharacteristic
365C23—21no—
366C23#649311yescharacteristic
367Q8—21no—
368Q8—282no—
369Q8—282no—
370Q8—562no—
371Q8#646712yes—
372D4—24no—
373D4—21no—
374D4#646712yes—
375C2×C4—24no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—282no—
388C2×C4—282no—
389C2×C4#649311yescharacteristic
390C2×C4#649311yescharacteristic
391C2×C4#649311yescharacteristic
392C2×C4C22×D2811yescharacteristic
393C2×C4C2×#115711yescharacteristic
394C2×C4C22×C22⋊D711yescharacteristic
395C8—21no—
396C8—21no—
397C8—41no—
398C8—41no—
399C8—282no—
400C8—282no—
401C8#651412yes—
402C8#651412yes—
403C7#1927311yescharacteristic, complemented, Sylow
404C22—21no—
405C22—22no—
406C22—21no—
407C22—21no—
408C22—41no—
409C22—41no—
410C22C2×#649311yescharacteristic
411C4—21no—
412C4—22no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—41no—
417C4—41no—
418C4—562no—
419C4—562no—
420C4C2×#646711yescharacteristic
421C4C2×#646711yescharacteristic
422C4C2×#651411yescharacteristic
423C4C2×#651411yescharacteristic
424C2—41no—
425C2—42no—
426C2#1173997811yescharacteristic
427C2#1174118711yescharacteristic
428C2#1174125011yescharacteristic
subgroupG/H
centerC22C2×#6493
commutator, cosocleC42×C7C24
FrattiniC42C23×D7
FittingC7×C8×#41C2
socleC22×C7C2×#121
prime radicalC2×C7×#41D4
hypercenterC8×#41D7
hypocenterC7#19273
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
3. #11735887C2semidirect
4. #11728699C2semidirect
5. #11728698C2semidirect
6. #11728697C2semidirect
7. #11728607C2semidirect
8. #11728606C2semidirect
9. #11728605C2semidirect
10. #11728535C2semidirect
11. #11727486C2semidirect
403. C7#19273semidirect

Maximal subgroups

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

subgroupindex
C7×C8×#412
#117399802
#117358872
#117286992
#117286982
#117286972
#117286072
#117286062
#117286052
#117285352
#117274862
#192737