Finite Group Databasebeta

← #13251810

Subgroups — #13251810

Order 1792.

518 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2975C211yesmaximal, characteristic
2#11739832C211yesmaximal, characteristic
3#11729356C211yesmaximal, characteristic
4#11727725C212yesmaximal, complemented
5#11725491C212yesmaximal, complemented
6C2×C4×C7×D4C2211yescharacteristic
7C22×Dic7⋊C4C2211yescharacteristic
8C7×#436—24no—
9C7×#431—21no—
10C7×#407—21no—
11C7×#407C2212yes—
12#89992C411yescharacteristic
13#89992C411yescharacteristic
14#89984C2211yescharacteristic
15#89982—21no—
16#89979C2212yes—
17#89756—21no—
18#89720—21no—
19#89718C411yescharacteristic
20#89718C411yescharacteristic
21#89705—21no—
22#89323—21no—
23#89320—21no—
24#89264—24no—
25#9518—71nomaximal, Sylow
26C22×C7×D4C2×C411yescharacteristic
27C23×C4×C7D411yescharacteristic
28C23×C4×C7C2311yescharacteristic
29C23×Dic7C2×C411yescharacteristic
30C23×Dic7C2×C411yescharacteristic
31C2×C7×M16—22no—
32C2×C7×M16—22no—
33C4×C7×D4—22no—
34C4×C7×D4—22no—
35C2×C7×C4⋊C4D411yescharacteristic
36C2×C7×C22⋊C4C2×C411yescharacteristic
37C2×C7×C22⋊C4D411yescharacteristic
38C2×C42×C7D411yescharacteristic
39C2×C22⋊Dic7—21no—
40C2×C22⋊Dic7—21no—
41C2×C22⋊Dic7C2×C411yescharacteristic
42C2×C22⋊Dic7C2×C411yescharacteristic
43C2×C4⋊Dic7—21no—
44C2×Dic7⋊C4—21no—
45C2×Dic7⋊C4—21no—
46C2×Dic7⋊C4—21no—
47C2×Dic7⋊C4—22no—
48C2×Dic7⋊C4—22no—
49C2×Dic7⋊C4—21no—
50C2×#1136—22no—
51C7×C4⋊C8—22no—
52C7×C22⋊C8—22no—
53C7×C22⋊C8—22no—
54C7×C22⋊C8D414yes—
55C4×C7×C8—22no—
56C7⋊#95—21no—
57C7⋊#95—21no—
58C7⋊#95—21no—
59C7⋊#95—21no—
60C7⋊#95—21no—
61C22⋊(C7⋊C8)—22no—
62C22⋊(C7⋊C8)—22no—
63#2975D711yescharacteristic
64#2579—71no—
65#1465—71no—
66#1463—72no—
67#1305—72no—
68C24×C7C22⋊C411yescharacteristic
69C24×C7C22×C411yescharacteristic
70C2×C7×D4—22no—
71C2×C7×D4—22no—
72C2×C7×D4—41no—
73C22×C4×C7—21no—
74C22×C4×C7—21no—
75C22×C4×C7—81no—
76C22×C4×C7—81no—
77C22×C4×C7C22⋊C411yescharacteristic
78C22×C4×C7C22⋊C411yescharacteristic
79C22×C4×C7C22⋊C411yescharacteristic
80C22×C4×C7C2×D412yes—
81C22×C4×C7C2×D411yescharacteristic
82C22×C4×C7C2×D411yescharacteristic
83C22×C4×C7#4112yes—
84C22×Dic7—21no—
85C22×Dic7—22no—
86C22×Dic7—21no—
87C22×Dic7—21no—
88C22×Dic7—21no—
89C22×Dic7—22no—
90C22×Dic7—42no—
91C22×Dic7—81no—
92C7×M16—82no—
93C7×M16—82no—
94C2×C7×C8—24no—
95C7×C4⋊C4—22no—
96C7×C22⋊C4—22no—
97C7×C22⋊C4—22no—
98C42×C7—21no—
99C42×C7—21no—
100C22⋊Dic7—42no—
101C22⋊Dic7—41no—
102C22⋊Dic7—41no—
103C22⋊Dic7—81no—
104C4⋊Dic7—81no—
105Dic7⋊C4—42no—
106Dic7⋊C4—41no—
107Dic7⋊C4—42no—
108Dic7⋊C4—41no—
109Dic7⋊C4—81no—
110#1136—82no—
111C2×C7⋊C8—42no—
112C2×C4×D4C2×D711yescharacteristic
113C22×C4⋊C4—71no—
114#436—24no—
115#431—21no—
116#407—21no—
117#407—72no—
118#407C2×D712yes—
119#398—141no—
120#396—141no—
121#387—141no—
122#386—71no—
123#386—71no—
124#385—71no—
125#385—71no—
126#385—141no—
127#380—71no—
128#324—141no—
129#324—144no—
130#323—141no—
131C23×C7—21no—
132C23×C7—21no—
133C23×C7—21no—
134C23×C7—21no—
135C23×C7—21no—
136C23×C7—41no—
137C23×C7—41no—
138C23×C7—41no—
139C23×C7—41no—
140C23×C7C2×C22⋊C411yescharacteristic
141C23×C7C4×D412yes—
142C7×D4—44no—
143C2×C4×C7—21no—
144C2×C4×C7—21no—
145C2×C4×C7—21no—
146C2×C4×C7—21no—
147C2×C4×C7—42no—
148C2×C4×C7—41no—
149C2×C4×C7—42no—
150C2×C4×C7—41no—
151C2×C4×C7—42no—
152C2×C4×C7—41no—
153C2×C4×C7—41no—
154C2×C4×C7—81no—
155C2×C4×C7#10112yes—
156C2×C4×C7#12011yescharacteristic
157C2×C4×C7#12112yes—
158C2×C4×C7#12311yescharacteristic
159C2×Dic7—22no—
160C2×Dic7—24no—
161C2×Dic7—41no—
162C2×Dic7—42no—
163C2×Dic7—41no—
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—82no—
174C7×C8—44no—
175C7⋊C8—82no—
176C22×D4C4×D711yescharacteristic
177C23×C4—71no—
178C23×C4—71no—
179C23×C4C22⋊D711yescharacteristic
180C23×C4C22×D711yescharacteristic
181C2×M16—22no—
182C2×M16—22no—
183C2×M16—142no—
184C4×D4—22no—
185C4×D4—22no—
186C2×C4⋊C4—141no—
187C2×C4⋊C4—141no—
188C2×C4⋊C4—142no—
189C2×C4⋊C4—142no—
190C2×C4⋊C4—141no—
191C2×C4⋊C4—141no—
192C2×C4⋊C4—141no—
193C2×C4⋊C4D2811yescharacteristic
194C2×C22⋊C4—71no—
195C2×C22⋊C4—71no—
196C2×C22⋊C4—141no—
197C2×C22⋊C4—141no—
198C2×C22⋊C4C4×D711yescharacteristic
199C2×C22⋊C4D2811yescharacteristic
200C2×C42C22⋊D711yescharacteristic
201C4⋊C8—22no—
202C22⋊C8—22no—
203C22⋊C8—22no—
204C22⋊C8—142no—
205C22⋊C8—142no—
206C22⋊C8C22⋊D714yes—
207C4×C8—22no—
208#95—141no—
209#95—141no—
210#95—141no—
211#95—141no—
212#95—141no—
213C22×C7—21no—
214C22×C7—21no—
215C22×C7—22no—
216C22×C7—22no—
217C22×C7—22no—
218C22×C7—42no—
219C22×C7—42no—
220C22×C7—42no—
221C22×C7—41no—
222C22×C7—41no—
223C22×C7—41no—
224C22×C7—81no—
225C22×C7#38611yescharacteristic
226C22×C7C2×#10111yescharacteristic
227C22×C7#41311yescharacteristic
228C4×C7—22no—
229C4×C7—22no—
230C4×C7—21no—
231C4×C7—21no—
232C4×C7—41no—
233C4×C7—41no—
234Dic7—42no—
235Dic7—81no—
236Dic7—81no—
237Dic7—81no—
238C24(C2×D7)⋊C411yescharacteristic
239C24C2×C4×D711yescharacteristic
240C2×D4—22no—
241C2×D4—22no—
242C2×D4—41no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—81no—
246C22×C4—81no—
247C22×C4—141no—
248C22×C4—142no—
249C22×C4—141no—
250C22×C4—141no—
251C22×C4—141no—
252C22×C4—142no—
253C22×C4—282no—
254C22×C4—561no—
255C22×C4(C2×D7)⋊C411yescharacteristic
256C22×C4(C2×D7)⋊C411yescharacteristic
257C22×C4(C2×D7)⋊C411yescharacteristic
258C22×C4C2×D2811yescharacteristic
259C22×C4#115712yes—
260C22×C4C2×C22⋊D711yescharacteristic
261C22×C4C2×C22⋊D712yes—
262M16—82no—
263M16—82no—
264M16—562no—
265C2×C8—24no—
266C2×C8—282no—
267C4⋊C4—22no—
268C4⋊C4—282no—
269C4⋊C4—281no—
270C4⋊C4—282no—
271C4⋊C4—281no—
272C4⋊C4—561no—
273C4⋊C4—561no—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C22⋊C4—282no—
277C22⋊C4—281no—
278C22⋊C4—281no—
279C22⋊C4—561no—
280C42—21no—
281C42—21no—
282C2×C7—21no—
283C2×C7—21no—
284C2×C7—42no—
285C2×C7—81no—
286C2×C7#189111yescharacteristic
287C2×C7#190111yescharacteristic
288C2×C7#191311yescharacteristic
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23C2×(C2×D7)⋊C411yescharacteristic
299C23C4×C22⋊D712yes—
300D4—44no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—81no—
313C2×C4—142no—
314C2×C4—144no—
315C2×C4—281no—
316C2×C4—282no—
317C2×C4—281no—
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—562no—
328C2×C4#639812yes—
329C2×C4#649211yescharacteristic
330C2×C4#649312yes—
331C2×C4#651611yescharacteristic
332C8—44no—
333C8—562no—
334C7#951811yescharacteristic, complemented, Sylow
335C22—21no—
336C22—21no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—42no—
341C22—42no—
342C22—42no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22#8990411yescharacteristic
348C22C2×#639811yescharacteristic
349C22#8998511yescharacteristic
350C4—21no—
351C4—22no—
352C4—21no—
353C4—22no—
354C4—41no—
355C4—41no—
356C4—282no—
357C4—561no—
358C4—561no—
359C4—561no—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—81no—
364C2#1172941011yescharacteristic
365C2#1172975711yescharacteristic
366C2#1172978311yescharacteristic
subgroupG/H
centerC22#89985
commutatorC24×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×#2975C2
socleC22×C7#386
prime radicalC22×C7×D4C2×C4
cosocleC23×C4×C7C23
hypercenter#2975D7
hypocenterC7#9518
LCSG ▷ C24×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2975

Complements

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

NH ≅ G/Ntype
4. #11727725C2semidirect
5. #11725491C2semidirect
334. C7#9518semidirect

Maximal subgroups

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

subgroupindex
C7×#29752
#117398322
#117293562
#117277252
#117254912
#95187