Finite Group Databasebeta

← #13249406

Subgroups — #13249406

Order 1792.

614 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×M16C211yesmaximal, characteristic
2#11739519C211yesmaximal, characteristic
3#11729283C211yesmaximal, characteristic
4C2×#89260C212yesmaximal, complemented
5#11725465C212yesmaximal, complemented
6C22×C7×M16—21no—
7C22×C42×C7C2211yescharacteristic
8C2×#6433C2211yescharacteristic
9C4×C7×M16—24no—
10C2×C7×#97C2212yes—
11C2×C4×C7×C8—21no—
12#89984C411yescharacteristic
13#89984C411yescharacteristic
14#89982—21no—
15#89982—21no—
16C2×C22⋊(C7⋊C8)—21no—
17#89708C2211yescharacteristic
18#89705—21no—
19#89705—21no—
20#89700C411yescharacteristic
21#89700C411yescharacteristic
22C2×#6377C2212yes—
23#89319—21no—
24#89260—24no—
25#9122—71nomaximal, Sylow
26C23×C4×C7C2×C411yescharacteristic
27C23×C4×C7D411yescharacteristic
28C23×C4×C7D411yescharacteristic
29C2×C7×M16—24no—
30C2×C7×M16—24no—
31C2×C7×M16—24no—
32C22×C7×C8—22no—
33C2×C42×C7—22no—
34C2×C42×C7—22no—
35C2×C42×C7C2×C411yescharacteristic
36C2×C42×C7D411yescharacteristic
37C2×C42×C7D411yescharacteristic
38C2×C42×C7C2311yescharacteristic
39C2×C22⋊Dic7—21no—
40C2×C22⋊Dic7—21no—
41C2×C4⋊Dic7C2×C411yescharacteristic
42C2×C4⋊Dic7C2×C411yescharacteristic
43C2×C4⋊Dic7C2×C411yescharacteristic
44C2×C4⋊Dic7C2×C411yescharacteristic
45C2×Dic7⋊C4—21no—
46C2×Dic7⋊C4—21no—
47C2×Dic7⋊C4—21no—
48C2×Dic7⋊C4—21no—
49C22×C7⋊C8—22no—
50#6433—22no—
51#6433—22no—
52C7×#97—22no—
53C7×#97D414yes—
54C4×C7×C8—24no—
55C7⋊#95—21no—
56C7⋊#95—21no—
57C7⋊#95—21no—
58C7⋊#95—21no—
59C7⋊#95—21no—
60C7⋊#95—21no—
61C22⋊(C7⋊C8)—24no—
62#6377—22no—
63#6377—22no—
64C2×C4×M16D711yescharacteristic
65#2851—71no—
66#1749—71no—
67C2×#330—72no—
68#1295—72no—
69C24×C7C22⋊C411yescharacteristic
70C22×C4×C7—22no—
71C22×C4×C7—22no—
72C22×C4×C7—21no—
73C22×C4×C7—21no—
74C22×C4×C7—22no—
75C22×C4×C7—22no—
76C22×C4×C7—22no—
77C22×C4×C7—22no—
78C22×C4×C7—41no—
79C22×C4×C7—41no—
80C22×C4×C7C22⋊C411yescharacteristic
81C22×C4×C7C22⋊C411yescharacteristic
82C22×C4×C7C22⋊C411yescharacteristic
83C22×C4×C7C22×C411yescharacteristic
84C22×C4×C7C2×D411yescharacteristic
85C22×C4×C7C2×D411yescharacteristic
86C22×Dic7—21no—
87C22×Dic7—21no—
88C22×Dic7—21no—
89C22×Dic7—21no—
90C7×M16—216no—
91C2×C7×C8—24no—
92C2×C7×C8—24no—
93C2×C7×C8—24no—
94C42×C7—22no—
95C42×C7—21no—
96C42×C7—22no—
97C42×C7—21no—
98C42×C7C2×D412yes—
99C42×C7#4112yes—
100C22⋊Dic7—42no—
101C22⋊Dic7—42no—
102C4⋊Dic7—22no—
103C4⋊Dic7—22no—
104C4⋊Dic7—41no—
105C4⋊Dic7—41no—
106Dic7⋊C4—42no—
107Dic7⋊C4—42no—
108Dic7⋊C4—41no—
109Dic7⋊C4—42no—
110Dic7⋊C4—41no—
111C2×C7⋊C8—24no—
112C2×C7⋊C8—42no—
113C2×C7⋊C8—42no—
114C22×M16—21no—
115C2×#125—71no—
116C22×C42C2×D711yescharacteristic
117C2×C22⋊C8—141no—
118C4×M16—24no—
119C2×#97—72no—
120C2×#97C2×D712yes—
121C2×C4×C8—21no—
122#389—71no—
123#389—71no—
124#387—141no—
125#387—141no—
126#385—141no—
127#385—141no—
128#382—71no—
129#380—71no—
130#380—71no—
131#336—141no—
132#330—144no—
133C23×C7—21no—
134C23×C7—21no—
135C23×C7—21no—
136C23×C7—21no—
137C23×C7—21no—
138C23×C7—21no—
139C23×C7#10412yes—
140C23×C7C2×C22⋊C411yescharacteristic
141C2×C4×C7—24no—
142C2×C4×C7—24no—
143C2×C4×C7—21no—
144C2×C4×C7—21no—
145C2×C4×C7—21no—
146C2×C4×C7—21no—
147C2×C4×C7—21no—
148C2×C4×C7—21no—
149C2×C4×C7—21no—
150C2×C4×C7—21no—
151C2×C4×C7—21no—
152C2×C4×C7—21no—
153C2×C4×C7—21no—
154C2×C4×C7—21no—
155C2×C4×C7—44no—
156C2×C4×C7—44no—
157C2×C4×C7#10112yes—
158C2×C4×C7#10412yes—
159C2×C4×C7#10412yes—
160C2×C4×C7C4×D412yes—
161C2×C4×C7#12011yescharacteristic
162C2×C4×C7#12112yes—
163C2×C4×C7#12311yescharacteristic
164C2×Dic7—41no—
165C2×Dic7—41no—
166C2×Dic7—41no—
167C2×Dic7—41no—
168C2×Dic7—41no—
169C2×Dic7—41no—
170C2×Dic7—41no—
171C2×Dic7—41no—
172C2×Dic7—41no—
173C2×Dic7—41no—
174C2×Dic7—41no—
175C2×Dic7—41no—
176C7×C8—28no—
177C7⋊C8—44no—
178C23×C4C4×D711yescharacteristic
179C23×C4D2811yescharacteristic
180C23×C4C22⋊D711yescharacteristic
181C2×M16—24no—
182C2×M16—24no—
183C2×M16—24no—
184C22×C8—22no—
185C22×C8—142no—
186#125—142no—
187#125—142no—
188C2×C4⋊C4—71no—
189C2×C4⋊C4—71no—
190C2×C4⋊C4—71no—
191C2×C4⋊C4—71no—
192C2×C4⋊C4—141no—
193C2×C4⋊C4—141no—
194C2×C4⋊C4—141no—
195C2×C4⋊C4—141no—
196C2×C22⋊C4—141no—
197C2×C22⋊C4—141no—
198C2×C42—22no—
199C2×C42—22no—
200C2×C42C4×D711yescharacteristic
201C2×C42D2811yescharacteristic
202C2×C42C22⋊D711yescharacteristic
203C2×C42C22×D711yescharacteristic
204C22⋊C8—144no—
205#97—22no—
206#97—142no—
207#97—142no—
208#97C22⋊D714yes—
209C4×C8—24no—
210#95—141no—
211#95—141no—
212#95—141no—
213#95—141no—
214#95—141no—
215#95—141no—
216C22×C7—22no—
217C22×C7—22no—
218C22×C7—22no—
219C22×C7—41no—
220C22×C7—41no—
221C22×C7—41no—
222C22×C7—41no—
223C22×C7#38611yescharacteristic
224C22×C7C2×#10111yescharacteristic
225C22×C7#41311yescharacteristic
226C22×C7C2×#10411yescharacteristic
227C22×C7C2×#10411yescharacteristic
228C22×C7C2×#10411yescharacteristic
229C22×C7#42111yescharacteristic
230C4×C7—22no—
231C4×C7—22no—
232C4×C7—21no—
233C4×C7—22no—
234C4×C7—21no—
235C4×C7—22no—
236C4×C7—22no—
237Dic7—81no—
238Dic7—81no—
239Dic7—81no—
240Dic7—81no—
241C24(C2×D7)⋊C411yescharacteristic
242C22×C4—22no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—141no—
253C22×C4—141no—
254C22×C4—141no—
255C22×C4—141no—
256C22×C4(C2×D7)⋊C411yescharacteristic
257C22×C4(C2×D7)⋊C411yescharacteristic
258C22×C4(C2×D7)⋊C411yescharacteristic
259C22×C4C2×C4×D711yescharacteristic
260C22×C4C2×D2811yescharacteristic
261C22×C4C2×C22⋊D711yescharacteristic
262M16—216no—
263C2×C8—24no—
264C2×C8—24no—
265C2×C8—24no—
266C2×C8—144no—
267C2×C8—282no—
268C2×C8—282no—
269C4⋊C4—142no—
270C4⋊C4—142no—
271C4⋊C4—281no—
272C4⋊C4—281no—
273C4⋊C4—281no—
274C4⋊C4—282no—
275C4⋊C4—281no—
276C4⋊C4—282no—
277C4⋊C4—282no—
278C22⋊C4—282no—
279C22⋊C4—282no—
280C42—22no—
281C42—21no—
282C42—22no—
283C42—21no—
284C42#115712yes—
285C42C2×C22⋊D712yes—
286C2×C7—42no—
287C2×C7#152411yescharacteristic
288C2×C7#152611yescharacteristic
289C2×C7#152811yescharacteristic
290C2×C7#152911yescharacteristic
291C2×C7#187111yescharacteristic
292C2×C7#189611yescharacteristic
293C2×C7#190111yescharacteristic
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23#637912yes—
301C23C2×(C2×D7)⋊C411yescharacteristic
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—281no—
319C2×C4—281no—
320C2×C4—281no—
321C2×C4—281no—
322C2×C4—281no—
323C2×C4—281no—
324C2×C4—281no—
325C2×C4—281no—
326C2×C4—281no—
327C2×C4—281no—
328C2×C4—281no—
329C2×C4—281no—
330C2×C4#637912yes—
331C2×C4#639812yes—
332C2×C4#639912yes—
333C2×C4C4×C22⋊D712yes—
334C2×C4#649211yescharacteristic
335C2×C4#649312yes—
336C2×C4#651611yescharacteristic
337C8—28no—
338C8—284no—
339C7#912211yescharacteristic, complemented, Sylow
340C22—22no—
341C22—22no—
342C22—22no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22C2×#637911yescharacteristic
348C22C2×#637911yescharacteristic
349C22#8990411yescharacteristic
350C22C2×#639811yescharacteristic
351C22C2×#639911yescharacteristic
352C22#8991111yescharacteristic
353C22#8998511yescharacteristic
354C4—22no—
355C4—22no—
356C4—22no—
357C4—22no—
358C4—21no—
359C4—21no—
360C4—22no—
361C4—561no—
362C4—561no—
363C4—561no—
364C4—561no—
365C2—42no—
366C2#1172761211yescharacteristic
367C2#1172761511yescharacteristic
368C2#1172761611yescharacteristic
369C2#1172761711yescharacteristic
370C2#1172928611yescharacteristic
371C2#1172973811yescharacteristic
372C2#1172975711yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC2×C4×C7×M16C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C22⋊C4
cosocleC2×C42×C7C23
hypercenterC2×C4×M16D7
hypocenterC7#9122
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
4. C2×#89260C2semidirect
5. #11725465C2semidirect
339. C7#9122semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C7×M162
#117395192
#117292832
C2×#892602
#117254652
#91227