Finite Group Databasebeta

← #13245148

Subgroups — #13245148

Order 1792.

810 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C22×#6452C211yesmaximal, characteristic
2C2×C7×#324C211yesmaximal, characteristic
3C2×#89323C211yesmaximal, characteristic
4C2×#89264C212yesmaximal
5#11727664C212yesmaximal
6C22×C7×C4⋊C4C2211yescharacteristic
7C22×C4⋊Dic7C411yescharacteristic
8C22×Dic7⋊C4C411yescharacteristic
9C22×Dic7⋊C4C411yescharacteristic
10C22×Dic7⋊C4C411yescharacteristic
11C22×Dic7⋊C4C2211yescharacteristic
12C22×C4×Dic7C2211yescharacteristic
13C2×#6452—22no—
14C2×#6452—22no—
15C2×#6452—24no—
16C2×#6452—24no—
17C2×C7×C22⋊C8C2212yes—
18C2×C22⋊(C7⋊C8)C2212yes—
19C7×#324—22no—
20#89345—24no—
21#89323—22no—
22#89264—24no—
23#8306—71nomaximal, Sylow
24C23×C4×C7C2×C411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7C2311yescharacteristic
27C23×Dic7C2×C411yescharacteristic
28C23×Dic7C2×C411yescharacteristic
29C23×Dic7C2×C411yescharacteristic
30C23×Dic7C2×C411yescharacteristic
31C22×C7×C8—22no—
32C2×C7×C4⋊C4—22no—
33C2×C7×C4⋊C4—22no—
34C2×C7×C4⋊C4D412yes—
35C2×C7×C4⋊C4D412yes—
36C2×C4⋊Dic7—22no—
37C2×C4⋊Dic7—22no—
38C2×C4⋊Dic7—22no—
39C2×Dic7⋊C4—22no—
40C2×Dic7⋊C4—22no—
41C2×Dic7⋊C4—22no—
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—22no—
44C2×Dic7⋊C4—21no—
45C2×Dic7⋊C4—22no—
46C2×Dic7⋊C4—22no—
47C2×Dic7⋊C4—22no—
48C2×Dic7⋊C4—22no—
49C2×Dic7⋊C4—22no—
50C2×Dic7⋊C4—22no—
51C2×Dic7⋊C4D414yes—
52C2×C4×Dic7—21no—
53C2×C4×Dic7—22no—
54C2×C4×Dic7—21no—
55C2×C4×Dic7D414yes—
56C22×C7⋊C8—22no—
57#6452—216no—
58#6452—216no—
59C7×C22⋊C8—22no—
60C7×C22⋊C8—22no—
61C22⋊(C7⋊C8)—22no—
62C22⋊(C7⋊C8)—22no—
63C22×#125—71no—
64#1817—72no—
65C2×#324—72no—
66C2×#324—71no—
67C2×#324D711yescharacteristic
68C24×C7C22×C411yescharacteristic
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—22no—
74C22×C4×C7—22no—
75C22×C4×C7—42no—
76C22×C4×C7—42no—
77C22×C4×C7C22⋊C412yes—
78C22×C4×C7C22⋊C412yes—
79C22×C4×C7C2×D412yes—
80C22×C4×C7C2×D411yescharacteristic
81C22×C4×C7C2×D412yes—
82C22×C4×C7C2×D411yescharacteristic
83C22×Dic7—21no—
84C22×Dic7—21no—
85C22×Dic7—24no—
86C22×Dic7—21no—
87C22×Dic7—21no—
88C22×Dic7—21no—
89C22×Dic7—21no—
90C22×Dic7—21no—
91C22×Dic7—21no—
92C22×Dic7—22no—
93C22×Dic7—22no—
94C22×Dic7—22no—
95C22×Dic7—22no—
96C22×Dic7—42no—
97C22×Dic7C22⋊C412yes—
98C22×Dic7C22⋊C412yes—
99C22×Dic7C22⋊C412yes—
100C22×Dic7C22⋊C412yes—
101C2×C7×C8—44no—
102C2×C7×C8—42no—
103C7×C4⋊C4—24no—
104C7×C4⋊C4—24no—
105C4⋊Dic7—28no—
106Dic7⋊C4—28no—
107Dic7⋊C4—28no—
108Dic7⋊C4—28no—
109Dic7⋊C4—24no—
110Dic7⋊C4—24no—
111C4×Dic7—24no—
112C4×Dic7—24no—
113C2×C7⋊C8—44no—
114C2×C7⋊C8—42no—
115C2×#125—144no—
116C2×#125—144no—
117C2×#125—142no—
118C2×#125—142no—
119C22×C4⋊C4—71no—
120C22×C4⋊C4—71no—
121C22×C4⋊C4—71no—
122C22×C4⋊C4—71no—
123C22×C4⋊C4—71no—
124C22×C4⋊C4C2×D711yescharacteristic
125C22×C42—71no—
126C2×C22⋊C8—72no—
127C2×C22⋊C8C2×D712yes—
128#336—144no—
129#324—22no—
130#324—144no—
131#324—142no—
132C23×C7—22no—
133C23×C7—22no—
134C23×C7C2×C22⋊C411yescharacteristic
135C23×C7C2×C22⋊C411yescharacteristic
136C23×C7C2×C22⋊C411yescharacteristic
137C23×C7#13112yes—
138C23×C7#13112yes—
139C2×C4×C7—24no—
140C2×C4×C7—22no—
141C2×C4×C7—22no—
142C2×C4×C7—22no—
143C2×C4×C7—22no—
144C2×C4×C7—41no—
145C2×C4×C7—42no—
146C2×C4×C7—41no—
147C2×C4×C7—42no—
148C2×C4×C7—42no—
149C2×C4×C7—42no—
150C2×C4×C7—42no—
151C2×C4×C7—42no—
152C2×C4×C7#12012yes—
153C2×C4×C7#12012yes—
154C2×Dic7—24no—
155C2×Dic7—24no—
156C2×Dic7—22no—
157C2×Dic7—22no—
158C2×Dic7—22no—
159C2×Dic7—22no—
160C2×Dic7—22no—
161C2×Dic7—24no—
162C2×Dic7—24no—
163C2×Dic7—42no—
164C2×Dic7—41no—
165C2×Dic7—41no—
166C2×Dic7—41no—
167C2×Dic7—41no—
168C2×Dic7—42no—
169C2×Dic7—42no—
170C2×Dic7—42no—
171C2×Dic7—42no—
172C2×Dic7#10114yes—
173C7×C8—82no—
174C7⋊C8—82no—
175C23×C4—71no—
176C23×C4—71no—
177C23×C4—71no—
178C23×C4—71no—
179C23×C4C4×D711yescharacteristic
180C23×C4C4×D711yescharacteristic
181C23×C4C22×D711yescharacteristic
182C22×C8—22no—
183C22×C8—142no—
184#125—1416no—
185#125—1416no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—74no—
189C2×C4⋊C4—142no—
190C2×C4⋊C4—142no—
191C2×C4⋊C4—142no—
192C2×C4⋊C4—142no—
193C2×C4⋊C4—142no—
194C2×C4⋊C4—142no—
195C2×C4⋊C4—142no—
196C2×C4⋊C4—142no—
197C2×C4⋊C4—142no—
198C2×C4⋊C4—142no—
199C2×C4⋊C4—142no—
200C2×C4⋊C4—142no—
201C2×C4⋊C4—141no—
202C2×C4⋊C4—142no—
203C2×C4⋊C4—141no—
204C2×C4⋊C4D2812yes—
205C2×C4⋊C4C22⋊D712yes—
206C2×C42—74no—
207C2×C42—141no—
208C2×C42—142no—
209C2×C42—141no—
210C22⋊C8—22no—
211C22⋊C8—22no—
212C22⋊C8—142no—
213C22⋊C8—142no—
214C22×C7—24no—
215C22×C7—24no—
216C22×C7—21no—
217C22×C7—21no—
218C22×C7—21no—
219C22×C7—21no—
220C22×C7#37911yescharacteristic
221C22×C7#40811yescharacteristic
222C22×C7#40811yescharacteristic
223C22×C7#40812yes—
224C22×C7#40812yes—
225C22×C7#41012yes—
226C22×C7C2×#10112yes—
227C4×C7—22no—
228C4×C7—22no—
229C4×C7—42no—
230C4×C7—42no—
231Dic7—24no—
232Dic7—42no—
233Dic7—42no—
234Dic7—42no—
235C24C2×C4×D711yescharacteristic
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—72no—
245C22×C4—72no—
246C22×C4—72no—
247C22×C4—72no—
248C22×C4—144no—
249C22×C4—141no—
250C22×C4—141no—
251C22×C4—141no—
252C22×C4—141no—
253C22×C4—141no—
254C22×C4—142no—
255C22×C4—142no—
256C22×C4—142no—
257C22×C4—142no—
258C22×C4—141no—
259C22×C4—141no—
260C22×C4—141no—
261C22×C4—282no—
262C22×C4(C2×D7)⋊C412yes—
263C22×C4(C2×D7)⋊C412yes—
264C22×C4C2×D2811yescharacteristic
265C22×C4D4×D712yes—
266C22×C4D4×D712yes—
267C22×C4C2×C22⋊D711yescharacteristic
268C2×C8—44no—
269C2×C8—42no—
270C2×C8—284no—
271C2×C8—282no—
272C4⋊C4—24no—
273C4⋊C4—24no—
274C4⋊C4—148no—
275C4⋊C4—148no—
276C4⋊C4—148no—
277C4⋊C4—148no—
278C4⋊C4—144no—
279C4⋊C4—144no—
280C42—144no—
281C42—144no—
282C2×C7—21no—
283C2×C7—21no—
284C2×C7—22no—
285C2×C7#147014yes—
286C2×C7#178011yescharacteristic
287C2×C7#178211yescharacteristic
288C2×C7#178411yescharacteristic
289C23—22no—
290C23—22no—
291C23D7×C22⋊C411yescharacteristic
292C23D7×C22⋊C411yescharacteristic
293C23#646412yes—
294C23#647012yes—
295C23C2×(C2×D7)⋊C411yescharacteristic
296C2×C4—24no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—74no—
310C2×C4—144no—
311C2×C4—144no—
312C2×C4—142no—
313C2×C4—142no—
314C2×C4—142no—
315C2×C4—142no—
316C2×C4—142no—
317C2×C4—144no—
318C2×C4—144no—
319C2×C4—282no—
320C2×C4—281no—
321C2×C4—281no—
322C2×C4—281no—
323C2×C4—281no—
324C2×C4—282no—
325C2×C4—282no—
326C2×C4—282no—
327C2×C4—282no—
328C2×C4#644512yes—
329C2×C4#650012yes—
330C8—82no—
331C8—562no—
332C7#830611yescharacteristic, complemented, Sylow
333C22—24no—
334C22—24no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22#8949912yes—
340C22#8949912yes—
341C22#8951212yes—
342C22D7×#10112yes—
343C22#8972711yescharacteristic
344C22#8988211yescharacteristic
345C22#8990111yescharacteristic
346C4—22no—
347C4—22no—
348C4—42no—
349C4—42no—
350C4—144no—
351C4—282no—
352C4—282no—
353C4—282no—
354C2—21no—
355C2—21no—
356C2—22no—
357C2#1172588214yes—
358C2#1172771011yescharacteristic
359C2#1172778111yescharacteristic
360C2#1172786711yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutator, prime radicalC24×C7C22×C4
FrattiniC23×C4C22×D7
FittingC2×C7×#324C2
socleC23×C7C2×C22⋊C4
cosocleC23×C4×C7C23
hypercenterC2×#324D7
hypocenterC7#8306
LCSG ▷ C24×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
332. C7#8306semidirect

Maximal subgroups

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

subgroupindex
C22×#64522
C2×C7×#3242
C2×#893232
C2×#892642
#117276642
#83067