Finite Group Databasebeta

← #13257574

Subgroups — #13257574

Order 1792.

366 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 93 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
1#11736513C211yesmaximal, characteristic
2C7×#1570C211yesmaximal, characteristic
3#11728547C211yesmaximal, characteristic
4#11728540C211yesmaximal, characteristic
5#11728240C211yesmaximal, characteristic
6#11728191C211yesmaximal, characteristic
7#11725519C211yesmaximal, characteristic
8#90161C2211yescharacteristic
9C2×C4×Dic14C2211yescharacteristic
10C7×#431C2211yescharacteristic
11C7×#423C2211yescharacteristic
12C2×C7×C4⋊C8C2211yescharacteristic
13#89893—21no—
14#89892—21no—
15C2×#6390—21no—
16#89708C2211yescharacteristic
17#89697C2211yescharacteristic
18#89623—21no—
19#89622—21no—
20#89601—22no—
21C7×#334—22no—
22#89346—21no—
23#89281—21no—
24#89276—21no—
25#89264—22no—
26#89262—22no—
27#10470—71nomaximal, Sylow
28C22×Dic14D411yescharacteristic
29C2×C7×M16—21no—
30C22×C7×C8—21no—
31C2×C42×C7C2311yescharacteristic
32#6489—21no—
33C2×C4⋊Dic7—21no—
34C2×C4⋊Dic7D411yescharacteristic
35#6487—21no—
36#6487—21no—
37C2×Dic7⋊C4—21no—
38C2×C4×Dic7—21no—
39#6433—21no—
40#6432D411yescharacteristic
41#6432D411yescharacteristic
42C4×Dic14—21no—
43C4×Dic14—21no—
44C4×Dic14—21no—
45C4×Dic14—21no—
46C4×Dic14—21no—
47C4×Dic14—21no—
48C7×C4⋊C8—21no—
49C7×C4⋊C8—21no—
50C7×C4⋊C8—21no—
51C7×C4⋊C8—21no—
52C7×C4⋊C8D412yes—
53C7×C22⋊C8D412yes—
54C4×C7×C8—21no—
55C7⋊#95—21no—
56C7⋊#95—21no—
57C22⋊(C7⋊C8)—21no—
58#6392—22no—
59#6391—22no—
60#6390—22no—
61#6390—22no—
62#6390—42no—
63C4⋊(C7⋊C8)—21no—
64C4×C7⋊C8—21no—
65#3078—71no—
66#1805—71no—
67#1570D711yescharacteristic
68#1542—71no—
69#1518—71no—
70#1461—71no—
71#1286—71no—
72C22×C4×C7C2×D411yescharacteristic
73C22×C4×C7C2×D411yescharacteristic
74C22×C4×C7#4111yescharacteristic
75C22×Dic7—21no—
76C22×Dic7—21no—
77C22×Dic7—41no—
78C2×Dic14—21no—
79C2×Dic14—21no—
80C2×Dic14—21no—
81C2×Dic14—21no—
82C2×Dic14—21no—
83C2×Dic14—21no—
84C2×Dic14—21no—
85C2×Dic14SD1612yes—
86C7×M16—41no—
87C7×M16—41no—
88C2×C7×C8—22no—
89C2×C7×C8—22no—
90C2×C7×C8—41no—
91C2×C7×C8—41no—
92C2×C7×C8—41no—
93C42×C7C2×D411yescharacteristic
94C42×C7C2×D411yescharacteristic
95C42×C7#4111yescharacteristic
96C42×C7#4111yescharacteristic
97C22⋊Dic7—41no—
98C4⋊Dic7—21no—
99C4⋊Dic7—21no—
100C4⋊Dic7—21no—
101C4⋊Dic7—21no—
102C4⋊Dic7—21no—
103C4⋊Dic7—21no—
104C4⋊Dic7—41no—
105C4⋊Dic7—41no—
106Dic7⋊C4—41no—
107Dic7⋊C4—41no—
108Dic7⋊C4—41no—
109Dic7⋊C4—41no—
110C4×Dic7—41no—
111C4×Dic7—41no—
112C4×Dic7—41no—
113C2×C7⋊C8—41no—
114#533—71no—
115C2×C4×Q8—71no—
116#479—142no—
117#477—141no—
118#475—141no—
119#431—71no—
120#431C2×D711yescharacteristic
121#428—141no—
122#423C2×D711yescharacteristic
123C2×C4⋊C8C2×D711yescharacteristic
124#419—141no—
125C2×#103—141no—
126#382—71no—
127#340—141no—
128#334—22no—
129#333—141no—
130#332—141no—
131#328—142no—
132#324—142no—
133C23×C7#12111yescharacteristic
134C2×C4×C7—41no—
135C2×C4×C7—41no—
136C2×C4×C7#12011yescharacteristic
137C2×C4×C7#12111yescharacteristic
138C2×C4×C7#12111yescharacteristic
139C2×C4×C7#12311yescharacteristic
140C2×C4×C7#12311yescharacteristic
141C2×C4×C7#12411yescharacteristic
142C2×C4×C7C2×SD1611yescharacteristic
143C2×C4×C7#13511yescharacteristic
144C2×C4×C7#13711yescharacteristic
145C2×C4×C7#13711yescharacteristic
146C2×Dic7—22no—
147C2×Dic7—41no—
148C2×Dic7—41no—
149C2×Dic7—41no—
150C2×Dic7—41no—
151C2×Dic7—41no—
152C2×Dic7—81no—
153C2×Dic7—81no—
154C2×Dic7—81no—
155C2×Dic7—81no—
156Dic14—22no—
157Dic14—22no—
158Dic14—41no—
159Dic14—41no—
160Dic14—81no—
161Dic14—81no—
162C7×C8—42no—
163C7×C8—42no—
164C7×C8—81no—
165C7⋊C8—81no—
166C22×Q8—71no—
167C2×M16—21no—
168C22×C8—21no—
169C4⋊Q8—71no—
170C4⋊Q8—71no—
171#125—141no—
172C22⋊Q8—141no—
173C22⋊Q8—141no—
174C4×Q8—141no—
175C4×Q8—141no—
176C4×Q8—141no—
177C4×Q8—141no—
178C4×Q8—141no—
179C4×Q8—141no—
180#117—141no—
181C2×C4⋊C4—71no—
182C2×C4⋊C4—141no—
183C2×C4⋊C4—141no—
184C2×C42—141no—
185C2×C42C22×D711yescharacteristic
186#107—142no—
187#106—142no—
188C4⋊C8—21no—
189C4⋊C8—21no—
190C4⋊C8—21no—
191C4⋊C8—21no—
192C4⋊C8—141no—
193C4⋊C8C22⋊D712yes—
194#103—142no—
195#103—142no—
196#103—282no—
197C22⋊C8—141no—
198C22⋊C8D2812yes—
199C4×C8—21no—
200C4×C8—141no—
201#95—141no—
202#95—141no—
203C22×C7—21no—
204C22×C7—21no—
205C22×C7#39411yescharacteristic
206C22×C7#46511yescharacteristic
207C22×C7#47011yescharacteristic
208C4×C7—21no—
209C4×C7—21no—
210C4×C7—21no—
211C4×C7—21no—
212C4×C7#44811yescharacteristic
213C4×C7#45211yescharacteristic
214C4×C7#48311yescharacteristic
215C4×C7#48511yescharacteristic
216Dic7—42no—
217Dic7—81no—
218Dic7—81no—
219Dic7—81no—
220Dic7—161no—
221C2×Q8—72no—
222C2×Q8—141no—
223C2×Q8—141no—
224C2×Q8—141no—
225C2×Q8—141no—
226C2×Q8—141no—
227C2×Q8—141no—
228C2×Q8—141no—
229C22×C4—141no—
230C22×C4—141no—
231C22×C4—281no—
232C22×C4C2×D2811yescharacteristic
233C22×C4D4×D711yescharacteristic
234C22×C4#116111yescharacteristic
235M16—41no—
236M16—41no—
237C2×C8—22no—
238C2×C8—22no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—281no—
243C4⋊C4—141no—
244C4⋊C4—141no—
245C4⋊C4—141no—
246C4⋊C4—141no—
247C4⋊C4—141no—
248C4⋊C4—141no—
249C4⋊C4—281no—
250C4⋊C4—281no—
251C4⋊C4—281no—
252C4⋊C4—281no—
253C4⋊C4—281no—
254C4⋊C4—281no—
255C22⋊C4—281no—
256C42—281no—
257C42—281no—
258C42—281no—
259C42#115711yescharacteristic
260C42D4×D711yescharacteristic
261C42#116111yescharacteristic
262C42C2×C22⋊D711yescharacteristic
263C2×C7—21no—
264C2×C7—21no—
265C2×C7#203511yescharacteristic
266C2×C7#204911yescharacteristic
267C2×C7#205311yescharacteristic
268C23#645811yescharacteristic
269Q8—142no—
270Q8—142no—
271Q8—281no—
272Q8—281no—
273Q8—561no—
274Q8—561no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—142no—
278C2×C4—281no—
279C2×C4—281no—
280C2×C4—281no—
281C2×C4—281no—
282C2×C4—281no—
283C2×C4—561no—
284C2×C4—561no—
285C2×C4—561no—
286C2×C4—561no—
287C2×C4#645711yescharacteristic
288C2×C4#645711yescharacteristic
289C2×C4#645811yescharacteristic
290C2×C4D7×SD1611yescharacteristic
291C2×C4#647811yescharacteristic
292C2×C4#647811yescharacteristic
293C2×C4#647911yescharacteristic
294C2×C4#649311yescharacteristic
295C2×C4#650011yescharacteristic
296C2×C4#651011yescharacteristic
297C8—42no—
298C8—42no—
299C8—81no—
300C8—561no—
301C7#1047011yescharacteristic, complemented, Sylow
302C22—21no—
303C22—21no—
304C22#8963611yescharacteristic
305C22#8964011yescharacteristic
306C22#8976311yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—282no—
312C4—561no—
313C4—561no—
314C4—561no—
315C4—1121no—
316C4#8963411yescharacteristic
317C4#8963911yescharacteristic
318C4#8994211yescharacteristic
319C4#8994511yescharacteristic
320C2—21no—
321C2—21no—
322C2#1172830111yescharacteristic
323C2#1172833611yescharacteristic
324C2#1172849111yescharacteristic
subgroupG/H
centerC22#89763
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1570C2
socleC22×C7#394
prime radicalC23×C7#121
hypercenter#1570D7
hypocenterC7#10470
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
301. C7#10470semidirect

Maximal subgroups

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

subgroupindex
#117365132
C7×#15702
#117285472
#117285402
#117282402
#117281912
#117255192
#104707