Finite Group Databasebeta

← #13251460

Subgroups — #13251460

Order 1792.

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

normal subgroups only

This group has 486 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×#2983C211yesmaximal, characteristic, complemented
2#11739919C211yesmaximal, characteristic
3#11729379C211yesmaximal, characteristic, complemented
4#11728562C212yesmaximal
5#11725555C212yesmaximal, complemented
6C2×C4×C7×Q8C2211yescharacteristic
7C2×#6510C411yescharacteristic
8C2×#6507C411yescharacteristic
9C2×#6438C2211yescharacteristic
10C7×#446—24no—
11C7×#432—21no—
12C7×#432C2212yes—
13C7×#431—21no—
14#89766—21no—
15#89766—21no—
16#89760C411yescharacteristic
17#89746C411yescharacteristic
18#89712—21no—
19#89712—21no—
20C4×C4⋊Dic7C2211yescharacteristic
21#89698C2212yes—
22#89323—21no—
23#89323—21no—
24#89259—24no—
25#9448—71nomaximal, Sylow
26C22×C7×Q8C2×C411yescharacteristic
27C22×D28C2×C411yescharacteristic
28C22×Dic14C2×C411yescharacteristic
29C4×C7×Q8—22no—
30C4×C7×Q8—22no—
31C2×C7×C4⋊C4C2×C411yescharacteristic
32C2×C7×C4⋊C4D411yescharacteristic
33C2×C7×C4⋊C4D411yescharacteristic
34C2×C42×C7D411yescharacteristic
35C2×C42×C7D411yescharacteristic
36C2×C42×C7C2311yescharacteristic
37#6510—42no—
38#6507—42no—
39C2×(C2×D7)⋊C4—21no—
40C2×(C2×D7)⋊C4—21no—
41C2×(C2×D7)⋊C4—21no—
42C2×(C2×D7)⋊C4—21no—
43C2×(C2×D7)⋊C4—21no—
44C2×(C2×D7)⋊C4—21no—
45C2×C4⋊Dic7—21no—
46C2×Dic7⋊C4—21no—
47C2×Dic7⋊C4—21no—
48C2×C4×Dic7C2×C411yescharacteristic
49C2×C4×Dic7C2×C411yescharacteristic
50#6438—22no—
51#6438—22no—
52C7×C4⋊C8—22no—
53C7×C4⋊C8—22no—
54C7×C4⋊C8—22no—
55C7×C22⋊C8—22no—
56C7×#97—22no—
57C7×#97D414yes—
58C4×C7×C8—22no—
59C7⋊#95—21no—
60C7⋊#95—21no—
61C7⋊#95—21no—
62C22⋊(C7⋊C8)—22no—
63C4⋊(C7⋊C8)—22no—
64#6377—22no—
65#2983D711yescharacteristic, complemented
66#2545—71no—
67#1533—72no—
68#1467—71no—
69#1285—72no—
70C23×D7—21no—
71C2×C7×Q8—22no—
72C2×C7×Q8—22no—
73C2×C7×Q8—41no—
74C22×C4×C7C22⋊C411yescharacteristic
75C22×C4×C7C22⋊C411yescharacteristic
76C22×C4×C7C22⋊C411yescharacteristic
77C22×C4×C7C22⋊C411yescharacteristic
78C22×C4×C7C22×C411yescharacteristic
79C22×C4×C7C2×D411yescharacteristic
80C22×C4×C7C2×D411yescharacteristic
81C22×Dic7—21no—
82C22×Dic7—21no—
83C22×Dic7—21no—
84C2×D28—22no—
85C2×D28—41no—
86C2×D28—41no—
87C2×Dic14—22no—
88C2×Dic14—41no—
89C2×Dic14—41no—
90C2×C7×C8—24no—
91C7×C4⋊C4—22no—
92C7×C4⋊C4—22no—
93C7×C4⋊C4—22no—
94C42×C7—21no—
95C42×C7—21no—
96C42×C7—21no—
97C42×C7—21no—
98C42×C7C2×D412yes—
99C42×C7#4112yes—
100(C2×D7)⋊C4—42no—
101(C2×D7)⋊C4—42no—
102(C2×D7)⋊C4—42no—
103(C2×D7)⋊C4—42no—
104(C2×D7)⋊C4—41no—
105(C2×D7)⋊C4—42no—
106(C2×D7)⋊C4—41no—
107C4⋊Dic7—42no—
108Dic7⋊C4—42no—
109Dic7⋊C4—42no—
110C4×Dic7—41no—
111C4×Dic7—41no—
112C2×C7⋊C8—42no—
113C2×C4⋊Q8—71no—
114C2×#124—71no—
115C2×#124—71no—
116C2×C4×Q8C2×D711yescharacteristic
117#446—24no—
118#432—21no—
119#432—72no—
120#432C2×D712yes—
121#431—21no—
122#396—141no—
123#396—141no—
124#391—71no—
125#390—71no—
126#388—141no—
127#388—141no—
128C4×C4⋊C4—71no—
129#329—144no—
130#324—141no—
131#324—141no—
132C23×C7C2×C22⋊C411yescharacteristic
133C22×D7—41no—
134C22×D7—41no—
135C22×D7—41no—
136C22×D7—41no—
137C22×D7—41no—
138C22×D7—41no—
139C22×D7—41no—
140C7×Q8—44no—
141C2×C4×C7—21no—
142C2×C4×C7—21no—
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—41no—
151C2×C4×C7—41no—
152C2×C4×C7—41no—
153C2×C4×C7—41no—
154C2×C4×C7#10012yes—
155C2×C4×C7C4×D412yes—
156C2×C4×C7#12011yescharacteristic
157C2×C4×C7#12112yes—
158C2×C4×C7#12311yescharacteristic
159C2×Dic7—22no—
160C2×Dic7—41no—
161C2×Dic7—41no—
162C2×Dic7—41no—
163C2×Dic7—41no—
164C2×Dic7—41no—
165C2×Dic7—41no—
166C2×Dic7—41no—
167C2×Dic7—41no—
168D28—82no—
169Dic14—82no—
170C7×C8—44no—
171C7⋊C8—82no—
172C22×Q8—71no—
173C22×Q8C4×D711yescharacteristic
174C22×D4—71no—
175C4⋊Q8—282no—
176#124—142no—
177#124—142no—
178#124—282no—
179C4×Q8—22no—
180C4×Q8—22no—
181C2×C4⋊C4—141no—
182C2×C4⋊C4—141no—
183C2×C4⋊C4—141no—
184C2×C4⋊C4C4×D711yescharacteristic
185C2×C4⋊C4D2811yescharacteristic
186C2×C4⋊C4D2811yescharacteristic
187C2×C22⋊C4—141no—
188C2×C22⋊C4—141no—
189C2×C22⋊C4—141no—
190C2×C22⋊C4—141no—
191C2×C22⋊C4—141no—
192C2×C22⋊C4—141no—
193C2×C42—71no—
194C2×C42—71no—
195C2×C42C22⋊D711yescharacteristic
196C2×C42C22⋊D711yescharacteristic
197C2×C42C22×D711yescharacteristic
198C4⋊C8—22no—
199C4⋊C8—22no—
200C4⋊C8—22no—
201C4⋊C8—142no—
202C22⋊C8—22no—
203C22⋊C8—142no—
204#97—22no—
205#97—142no—
206#97C22⋊D714yes—
207C4×C8—22no—
208#95—141no—
209#95—141no—
210#95—141no—
211C22×C7—21no—
212C22×C7—21no—
213C22×C7#38611yescharacteristic
214C22×C7C2×#10011yescharacteristic
215C22×C7#41311yescharacteristic
216C2×D7—81no—
217C2×D7—81no—
218C2×D7—81no—
219C2×D7—81no—
220C2×D7—81no—
221C2×D7—81no—
222C2×D7—81no—
223C4×C7—22no—
224C4×C7—22no—
225C4×C7—22no—
226C4×C7—21no—
227C4×C7—21no—
228C4×C7—41no—
229C4×C7—41no—
230C4×C7—41no—
231Dic7—42no—
232Dic7—81no—
233Dic7—81no—
234C24—141no—
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8—41no—
238C2×Q8—142no—
239C2×Q8—281no—
240C2×Q8—281no—
241C2×D4—142no—
242C2×D4—281no—
243C2×D4—281no—
244C22×C4—141no—
245C22×C4—141no—
246C22×C4—141no—
247C22×C4(C2×D7)⋊C411yescharacteristic
248C22×C4(C2×D7)⋊C411yescharacteristic
249C22×C4(C2×D7)⋊C411yescharacteristic
250C22×C4(C2×D7)⋊C411yescharacteristic
251C22×C4C2×C4×D711yescharacteristic
252C22×C4C2×D2811yescharacteristic
253C22×C4C2×C22⋊D711yescharacteristic
254C2×C8—24no—
255C2×C8—282no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—282no—
260C4⋊C4—282no—
261C4⋊C4—282no—
262C22⋊C4—282no—
263C22⋊C4—282no—
264C22⋊C4—282no—
265C22⋊C4—281no—
266C22⋊C4—282no—
267C22⋊C4—281no—
268C22⋊C4—282no—
269C42—21no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—281no—
274C42—281no—
275C42#115712yes—
276C42C2×C22⋊D712yes—
277C2×C7—21no—
278C2×C7—21no—
279C2×C7#188411yescharacteristic
280C2×C7#190011yescharacteristic
281C2×C7#191211yescharacteristic
282D7—161no—
283C23—281no—
284C23—281no—
285C23—281no—
286C23—281no—
287C23—281no—
288C23—281no—
289C23—281no—
290C23C2×(C2×D7)⋊C411yescharacteristic
291Q8—44no—
292Q8—562no—
293D4—562no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—142no—
308C2×C4—281no—
309C2×C4—281no—
310C2×C4—281no—
311C2×C4—281no—
312C2×C4—281no—
313C2×C4—281no—
314C2×C4—281no—
315C2×C4—281no—
316C2×C4#639712yes—
317C2×C4C4×C22⋊D712yes—
318C2×C4#649211yescharacteristic
319C2×C4#649312yes—
320C2×C4#651611yescharacteristic
321C8—44no—
322C8—562no—
323C7#944811yescharacteristic, complemented, Sylow
324C22—21no—
325C22—21no—
326C22—561no—
327C22—561no—
328C22—561no—
329C22—561no—
330C22—561no—
331C22—561no—
332C22—561no—
333C22C2×#639711yescharacteristic
334C22#8990411yescharacteristic
335C22#8998511yescharacteristic
336C4—21no—
337C4—21no—
338C4—22no—
339C4—22no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—282no—
345C4—561no—
346C4—561no—
347C2—21no—
348C2—21no—
349C2—1121no—
350C2#1172941711yescharacteristic
351C2#1172975611yescharacteristic
352C2#1172977511yescharacteristic
subgroupG/H
centerC22#89985
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#2983C2
socleC22×C7#386
prime radicalC22×D28C2×C4
cosocleC2×C42×C7C23
hypercenter#2983D7
hypocenterC7#9448
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
1. C7×#2983C2semidirect
3. #11729379C2semidirect
5. #11725555C2semidirect
65. #2983D7semidirect
323. C7#9448semidirect

Maximal subgroups

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

subgroupindex
C7×#29832
#117399192
#117293792
#117285622
#117255552
#94487