Finite Group Databasebeta

← #13247793

Subgroups — #13247793

Order 1792.

612 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739601C211yesmaximal, characteristic
2C7×#1441C211yesmaximal, characteristic
3#11729310C212yesmaximal
4C2×#89323C211yesmaximal, characteristic
5#11725418C212yesmaximal
6C22×C7×C4⋊C4C2211yescharacteristic
7C22×C7×C4⋊C4C2211yescharacteristic
8C2×#6489—21no—
9C2×C7×#95—21no—
10C2×C7×#95—21no—
11C2×C7×#95C2211yescharacteristic
12#89984—21no—
13#89984C2212yes—
14C2×C22⋊(C7⋊C8)C2212yes—
15#89757—22no—
16#89757—22no—
17C2×#6382—22no—
18#89324—22no—
19#89323C414yescomplemented
20#8857—71nomaximal, Sylow
21C23×C4×C7—21no—
22C23×C4×C7—21no—
23C23×C4×C7D411yescharacteristic
24C23×C4×C7D411yescharacteristic
25C23×C4×C7C2311yescharacteristic
26C2×C7×C4⋊C4—22no—
27C2×C7×C4⋊C4—22no—
28C2×C7×C4⋊C4—22no—
29C2×C7×C4⋊C4—42no—
30C2×C7×C4⋊C4C2×C412yes—
31C2×C7×C4⋊C4Q812yes—
32C2×C22⋊Dic7—22no—
33#6489—42no—
34#6489—42no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7—21no—
38C2×C4⋊Dic7—21no—
39C2×C4⋊Dic7D412yes—
40C2×C4⋊Dic7D412yes—
41C2×C4×Dic7—22no—
42C22×C7⋊C8—22no—
43C7×#95—22no—
44C7×#95—42no—
45C7×#95—42no—
46C7⋊#95—22no—
47C7⋊#95—22no—
48C22⋊(C7⋊C8)—22no—
49C22⋊(C7⋊C8)C2×C414yes—
50#6382—44no—
51#2316—71no—
52#1853—72no—
53C2×#324—71no—
54#1441D711yescharacteristic
55#1294—72no—
56C24×C7C2×D411yescharacteristic
57C22×C4×C7—21no—
58C22×C4×C7—21no—
59C22×C4×C7—21no—
60C22×C4×C7—21no—
61C22×C4×C7—21no—
62C22×C4×C7—21no—
63C22×C4×C7—22no—
64C22×C4×C7—22no—
65C22×C4×C7—41no—
66C22×C4×C7—41no—
67C22×C4×C7—41no—
68C22×C4×C7—41no—
69C22×C4×C7—41no—
70C22×C4×C7—41no—
71C22×C4×C7—41no—
72C22×C4×C7—41no—
73C22×C4×C7—41no—
74C22×C4×C7—41no—
75C22×C4×C7—41no—
76C22×C4×C7—41no—
77C22×C4×C7—41no—
78C22×C4×C7—41no—
79C22×C4×C7—41no—
80C22×C4×C7—41no—
81C22×C4×C7C4⋊C412yes—
82C22×C4×C7C4⋊C412yes—
83C22×C4×C7SD1612yes—
84C22×C4×C7SD1612yes—
85C22×C4×C7C22×C411yescharacteristic
86C22×C4×C7C2×D412yes—
87C22×C4×C7C2×Q811yescharacteristic
88C22×C4×C7#4112yes—
89C22×Dic7—22no—
90C22×Dic7—22no—
91C7×C4⋊C4—24no—
92C7×C4⋊C4—24no—
93C7×C4⋊C4—24no—
94C7×C4⋊C4—42no—
95C22⋊Dic7—42no—
96C22⋊Dic7—42no—
97C4⋊Dic7—42no—
98C4⋊Dic7—42no—
99C4⋊Dic7—42no—
100C4⋊Dic7—42no—
101C4⋊Dic7—81no—
102C4⋊Dic7—81no—
103C4×Dic7—44no—
104C2×C7⋊C8—24no—
105C2×C7⋊C8—42no—
106C2×C7⋊C8—42no—
107C2×#117—141no—
108C22×C4⋊C4C2×D711yescharacteristic
109C22×C4⋊C4C2×D711yescharacteristic
110C2×#106—142no—
111C2×C22⋊C8—72no—
112#389—142no—
113#389—142no—
114#380—72no—
115#380—141no—
116C2×#95—21no—
117C2×#95—21no—
118C2×#95C2×D711yescharacteristic
119#340—142no—
120#324—74no—
121C23×C7—21no—
122C23×C7—21no—
123C23×C7—21no—
124C23×C7—21no—
125C23×C7C2×C4⋊C411yescharacteristic
126C23×C7#12011yescharacteristic
127C23×C7#12311yescharacteristic
128C23×C7C2×SD1611yescharacteristic
129C23×C7C2×SD1611yescharacteristic
130C23×C7AGL(1,ℤ/8)11yescharacteristic
131C23×C7#13711yescharacteristic
132C2×C4×C7—22no—
133C2×C4×C7—22no—
134C2×C4×C7—22no—
135C2×C4×C7—22no—
136C2×C4×C7—22no—
137C2×C4×C7—22no—
138C2×C4×C7—22no—
139C2×C4×C7—22no—
140C2×C4×C7—22no—
141C2×C4×C7—41no—
142C2×C4×C7—41no—
143C2×C4×C7—42no—
144C2×C4×C7—41no—
145C2×C4×C7—41no—
146C2×C4×C7—42no—
147C2×C4×C7—42no—
148C2×C4×C7—42no—
149C2×C4×C7—42no—
150C2×C4×C7—42no—
151C2×C4×C7—42no—
152C2×C4×C7—42no—
153C2×C4×C7—81no—
154C2×C4×C7—81no—
155C2×C4×C7—81no—
156C2×C4×C7—81no—
157C2×C4×C7—81no—
158C2×C4×C7—81no—
159C2×C4×C7—81no—
160C2×C4×C7—81no—
161C2×C4×C7—81no—
162C2×C4×C7#10614yescomplemented
163C2×C4×C7C4×D412yes—
164C2×C4×C7C22⋊Q812yes—
165C2×Dic7—42no—
166C2×Dic7—42no—
167C2×Dic7—42no—
168C2×Dic7—42no—
169C2×Dic7—42no—
170C2×Dic7—42no—
171C7⋊C8—44no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4C22⋊D711yescharacteristic
175C23×C4C22⋊D711yescharacteristic
176C23×C4C22×D711yescharacteristic
177C22×C8—142no—
178#117—282no—
179#117—282no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—72no—
185C2×C4⋊C4—72no—
186C2×C4⋊C4—141no—
187C2×C4⋊C4—141no—
188C2×C4⋊C4—141no—
189C2×C4⋊C4—141no—
190C2×C4⋊C4Dic1412yes—
191C2×C4⋊C4C4×D712yes—
192C2×C22⋊C4—142no—
193C2×C42—142no—
194#106—284no—
195C22⋊C8—74no—
196C22⋊C8—142no—
197#95—22no—
198#95—42no—
199#95—42no—
200#95—142no—
201#95—142no—
202C22×C7—21no—
203C22×C7—21no—
204C22×C7—21no—
205C22×C7—21no—
206C22×C7—21no—
207C22×C7—21no—
208C22×C7—21no—
209C22×C7—21no—
210C22×C7—21no—
211C22×C7—21no—
212C22×C7—21no—
213C22×C7—21no—
214C22×C7#38511yescharacteristic
215C22×C7C2×#10611yescharacteristic
216C22×C7#42811yescharacteristic
217C22×C7#44811yescharacteristic
218C22×C7#45011yescharacteristic
219C22×C7#45411yescharacteristic
220C22×C7#45611yescharacteristic
221C22×C7B(4,𝔽2)11yescharacteristic
222C22×C7#45811yescharacteristic
223C22×C7#48111yescharacteristic
224C22×C7#48311yescharacteristic
225C4×C7—24no—
226C4×C7—22no—
227C4×C7—22no—
228C4×C7—42no—
229C4×C7—82no—
230C4×C7—82no—
231Dic7—82no—
232Dic7—82no—
233C24C2×C22⋊D711yescharacteristic
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—142no—
259C22×C4—142no—
260C22×C4Dic7⋊C412yes—
261C22×C4Dic7⋊C412yes—
262C22×C4#114212yes—
263C22×C4#114312yes—
264C22×C4C2×Dic1411yescharacteristic
265C22×C4C2×C4×D711yescharacteristic
266C22×C4D4×D712yes—
267C22×C4#115912yes—
268C2×C8—144no—
269C2×C8—282no—
270C2×C8—282no—
271C4⋊C4—24no—
272C4⋊C4—24no—
273C4⋊C4—24no—
274C4⋊C4—42no—
275C4⋊C4—282no—
276C4⋊C4—282no—
277C4⋊C4—282no—
278C4⋊C4—282no—
279C4⋊C4—561no—
280C4⋊C4—561no—
281C22⋊C4—282no—
282C22⋊C4—282no—
283C42—284no—
284C2×C7—21no—
285C2×C7—21no—
286C2×C7—21no—
287C2×C7—21no—
288C2×C7#159911yescharacteristic
289C2×C7#160411yescharacteristic
290C2×C7#161111yescharacteristic
291C2×C7#161611yescharacteristic
292C2×C7#185311yescharacteristic
293C2×C7#185711yescharacteristic
294C2×C7#186711yescharacteristic
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23C2×Dic7⋊C411yescharacteristic
300C23C2×#114211yescharacteristic
301C23#649811yescharacteristic
302C23#650011yescharacteristic
303C23C2×#114311yescharacteristic
304C23#651211yescharacteristic
305C23#651411yescharacteristic
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—282no—
337C2×C4—282no—
338C2×C4—282no—
339C2×C4—282no—
340C2×C4—282no—
341C2×C4—282no—
342C2×C4#638214yescomplemented
343C2×C4#644112yes—
344C2×C4(C22⋊D7)⋊C412yes—
345C8—284no—
346C7#885711yescharacteristic, complemented, Sylow
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22#8971811yescharacteristic
360C22C2×#638211yescharacteristic
361C22#8976711yescharacteristic
362C22#8980411yescharacteristic
363C22#8980611yescharacteristic
364C22#8981211yescharacteristic
365C22#8981511yescharacteristic
366C22#8981811yescharacteristic
367C22#8982511yescharacteristic
368C22#8983411yescharacteristic
369C22#8986711yescharacteristic
370C4—24no—
371C4—22no—
372C4—22no—
373C4—42no—
374C4—82no—
375C4—82no—
376C4—562no—
377C4—562no—
378C2—21no—
379C2—21no—
380C2—21no—
381C2—21no—
382C2#1172725911yescharacteristic
383C2#1172735111yescharacteristic
384C2#1172742611yescharacteristic
385C2#1172745811yescharacteristic
386C2#1172746011yescharacteristic
387C2#1172746711yescharacteristic
388C2#1172747211yescharacteristic
subgroupG/H
centerC23#6500
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×#1441C2
socleC23×C7#120
prime radicalC24×C7C2×D4
cosocleC23×C4×C7C23
hypercenter#1441D7
hypocenterC7#8857
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1441

Complements

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

NH ≅ G/Ntype
19. #89323C4semidirect
162. C2×C4×C7#106semidirect
342. C2×C4#6382semidirect
346. C7#8857semidirect

Maximal subgroups

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

subgroupindex
#117396012
C7×#14412
#117293102
C2×#893232
#117254182
#88577