Finite Group Databasebeta

← #13255243

Subgroups — #13255243

Order 1792.

458 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 85 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×#2642C211yesmaximal, characteristic
2#11740652C211yesmaximal, characteristic
3#11740466C211yesmaximal, characteristic
4#11729530C211yesmaximal, characteristic
5#11729489C211yesmaximal, characteristic
6#11727187C211yesmaximal, characteristic
7#11725421C211yesmaximal, characteristic
8C2×C7×C4⋊Q8C2211yescharacteristic
9C2×C7×#125C2211yescharacteristic
10#90161C2211yescharacteristic
11C7×#400—22no—
12C7×#400—22no—
13C7×#391—21no—
14C7×#391—21no—
15C7×#376C2211yescharacteristic
16#89852—22no—
17#89851—21no—
18#89850—21no—
19#89841—21no—
20#89837—21no—
21#89835—22no—
22#89743—21no—
23#89742—21no—
24#89736—22no—
25#89698C2211yescharacteristic
26#89698C2211yescharacteristic
27C4×#1136C2211yescharacteristic
28#89342—22no—
29#89338—22no—
30#89247—22no—
31#10103—71nomaximal, Sylow
32C22×C7×Q8—21no—
33C7×C4⋊Q8—21no—
34C7×C4⋊Q8—21no—
35C7×C4⋊Q8—21no—
36C7×C4⋊Q8—21no—
37C7×#125—21no—
38C7×#125—21no—
39C7×#125—21no—
40C7×#125—21no—
41C2×C7×C4⋊C4—21no—
42C2×C7×C4⋊C4—21no—
43C2×C7×C4⋊C4—21no—
44C2×C7×C4⋊C4D412yes—
45C2×C7×C4⋊C4D411yescharacteristic
46C2×C7×C4⋊C4D411yescharacteristic
47C2×C42×C7—21no—
48C2×C42×C7C2311yescharacteristic
49#6489—21no—
50#6487—21no—
51#6487—21no—
52C2×#1136—21no—
53#6433—21no—
54#6432D411yescharacteristic
55#6432D411yescharacteristic
56C4×Dic14—21no—
57C4×Dic14—21no—
58C7×#95—24no—
59C7×#95—24no—
60C7×#95—21no—
61C7×#95D412yes—
62C22⋊(C7⋊C8)—21no—
63C22⋊(C7⋊C8)—21no—
64#6384—22no—
65#6384—22no—
66#6382—24no—
67#6382—22no—
68#6381—24no—
69#6381—22no—
70C4⋊(C7⋊C8)—21no—
71C4⋊(C7⋊C8)D412yes—
72#6377—21no—
73#6377—21no—
74#6377D412yes—
75C4×C7⋊C8—21no—
76#3236—71no—
77#3165—71no—
78#2642D711yescharacteristic
79#1556—71no—
80#1528—71no—
81#1506—71no—
82#1300—71no—
83C2×C7×Q8—44no—
84C2×C7×Q8—41no—
85C2×C7×Q8—41no—
86C22×C4×C7—22no—
87C22×C4×C7—21no—
88C22×C4×C7—21no—
89C22×C4×C7—22no—
90C22×C4×C7C2×D411yescharacteristic
91C22×C4×C7C2×D411yescharacteristic
92C22×C4×C7C2×D411yescharacteristic
93C2×Dic14—21no—
94C2×Dic14—21no—
95C7×C4⋊C4—21no—
96C7×C4⋊C4—21no—
97C7×C4⋊C4—22no—
98C7×C4⋊C4—21no—
99C7×C4⋊C4—21no—
100C7×C4⋊C4—22no—
101C7×C4⋊C4—41no—
102C7×C4⋊C4—41no—
103C7×C4⋊C4—41no—
104C7×C4⋊C4—41no—
105C7×C4⋊C4—41no—
106C7×C4⋊C4—41no—
107C42×C7—42no—
108C42×C7C2×D411yescharacteristic
109C42×C7C2×D411yescharacteristic
110C42×C7C2×D411yescharacteristic
111C42×C7#4111yescharacteristic
112C22⋊Dic7—41no—
113C4⋊Dic7—21no—
114C4⋊Dic7—21no—
115C4⋊Dic7—21no—
116C4⋊Dic7—21no—
117Dic7⋊C4—41no—
118Dic7⋊C4—41no—
119C4×Dic7—41no—
120#1136—24no—
121C2×C7⋊C8—22no—
122C2×C7⋊C8—22no—
123C2×C7⋊C8—41no—
124#533—71no—
125C2×C4⋊Q8C2×D711yescharacteristic
126C2×#125C2×D711yescharacteristic
127#501—142no—
128#501—141no—
129#500—141no—
130#498—141no—
131#491—141no—
132#484—141no—
133#483—141no—
134#479—142no—
135#432—71no—
136#432—71no—
137#428—142no—
138C4×M16—71no—
139#400—22no—
140#400—22no—
141#391—21no—
142#391—21no—
143#376C2×D711yescharacteristic
144#332—142no—
145#330—142no—
146#328—142no—
147C23×C7#12011yescharacteristic
148C7×Q8—82no—
149C7×Q8—82no—
150C2×C4×C7—22no—
151C2×C4×C7—22no—
152C2×C4×C7—41no—
153C2×C4×C7—42no—
154C2×C4×C7—42no—
155C2×C4×C7—42no—
156C2×C4×C7—44no—
157C2×C4×C7—41no—
158C2×C4×C7—41no—
159C2×C4×C7—42no—
160C2×C4×C7—42no—
161C2×C4×C7—42no—
162C2×C4×C7#12011yescharacteristic
163C2×C4×C7#12011yescharacteristic
164C2×C4×C7#12111yescharacteristic
165C2×C4×C7#12111yescharacteristic
166C2×C4×C7#12111yescharacteristic
167C2×C4×C7#12711yescharacteristic
168C2×Dic7—41no—
169C2×Dic7—41no—
170Dic14—42no—
171Dic14—81no—
172C7⋊C8—24no—
173C7⋊C8—42no—
174C7⋊C8—81no—
175C22×Q8—21no—
176C2×M16—141no—
177C4⋊Q8—21no—
178C4⋊Q8—21no—
179C4⋊Q8—21no—
180C4⋊Q8—21no—
181C4⋊Q8—71no—
182C4⋊Q8—71no—
183#125—21no—
184#125—21no—
185#125—21no—
186#125—21no—
187#125—141no—
188C22⋊Q8—141no—
189C22⋊Q8—141no—
190C4×Q8—141no—
191C4×Q8—141no—
192#117—141no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4C22⋊D711yescharacteristic
197C2×C4⋊C4C22⋊D711yescharacteristic
198C2×C4⋊C4C22⋊D712yes—
199C2×C42—21no—
200C2×C42C22×D711yescharacteristic
201#107—144no—
202#107—142no—
203#106—144no—
204#106—142no—
205C4⋊C8—72no—
206C4⋊C8—141no—
207#103—142no—
208#103—142no—
209C22⋊C8—141no—
210C22⋊C8—141no—
211#97—72no—
212#97—141no—
213#97—141no—
214C4×C8—141no—
215#95—24no—
216#95—24no—
217#95—21no—
218#95C22⋊D712yes—
219C22×C7—21no—
220C22×C7—21no—
221C22×C7#39211yescharacteristic
222C22×C7#45612yes—
223C4×C7—21no—
224C4×C7—21no—
225C4×C7—21no—
226C4×C7—21no—
227C4×C7—21no—
228C4×C7—82no—
229C4×C7—82no—
230C4×C7—81no—
231C4×C7—81no—
232C4×C7#45412yes—
233Dic7—81no—
234Dic7—81no—
235C2×Q8—44no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—141no—
239C2×Q8—141no—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4C2×C22⋊D711yescharacteristic
245C22×C4C2×C22⋊D711yescharacteristic
246C22×C4C2×C22⋊D711yescharacteristic
247M16—144no—
248C2×C8—142no—
249C2×C8—142no—
250C2×C8—281no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—22no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—22no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—141no—
264C4⋊C4—141no—
265C4⋊C4—141no—
266C4⋊C4—141no—
267C4⋊C4—281no—
268C4⋊C4—281no—
269C22⋊C4—281no—
270C42—42no—
271C42—281no—
272C42D4×D711yescharacteristic
273C42D4×D711yescharacteristic
274C42D4×D711yescharacteristic
275C42#115911yescharacteristic
276C2×C7—22no—
277C2×C7#200311yescharacteristic
278C2×C7#200511yescharacteristic
279C2×C7#200911yescharacteristic
280C23#651611yescharacteristic
281Q8—82no—
282Q8—82no—
283Q8—282no—
284Q8—561no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—44no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—281no—
298C2×C4—281no—
299C2×C4#650011yescharacteristic
300C2×C4#650011yescharacteristic
301C2×C4#650111yescharacteristic
302C2×C4#650211yescharacteristic
303C2×C4#650211yescharacteristic
304C2×C4#650311yescharacteristic
305C8—144no—
306C8—282no—
307C8—561no—
308C7#1010311yescharacteristic, complemented, Sylow
309C22—21no—
310C22—21no—
311C22#8999511yescharacteristic
312C22#9001812yes—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—82no—
319C4—82no—
320C4—81no—
321C4—81no—
322C4—561no—
323C4—561no—
324C4#8983412yes—
325C2—22no—
326C2#1172948411yescharacteristic
327C2#1172962211yescharacteristic
328C2#1172962311yescharacteristic
subgroupG/H
centerC22#89995
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#2642C2
socleC22×C7#392
prime radicalC23×C7#120
hypercenter#2642D7
hypocenterC7#10103
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2642

Complements

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

NH ≅ G/Ntype
308. C7#10103semidirect

Maximal subgroups

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

subgroupindex
C7×#26422
#117406522
#117404662
#117295302
#117294892
#117271872
#117254212
#101037