Finite Group Databasebeta

← #13272109

Subgroups — #13272109

Order 1792.

552 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 107 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#11739827C211yesmaximal, characteristic
2C4×C7×#99C211yesmaximal, characteristic
3#11729373C211yesmaximal, characteristic
4C2×#89268C214yesmaximal
5C2×C4×C7×D4C2211yescharacteristic
6C2×#6499C2212yes—
7C2×#6432C411yescharacteristic, complemented
8C2×C7×#99C2212yes—
9C4×C7×C22⋊C4—21no—
10C2×#6408C2212yes—
11#89984—21no—
12#89984—21no—
13#89984—21no—
14#89746C412yescomplemented
15#89725—21no—
16#89725—21no—
17C4×C4⋊Dic7C411yescharacteristic, complemented
18C7×#342—21no—
19#89321—21no—
20#89268—28no—
21#13224—71nomaximal, Sylow
22C22×C7×D4C2311yescharacteristic
23C23×C4×C7D411yescharacteristic
24C23×C4×C7D411yescharacteristic
25C22×Dic14C2×C412yes—
26C4×C7×D4—41no—
27C4×C7×D4—41no—
28C2×C7×C4⋊C4C2×C411yescharacteristic
29C2×C7×C22⋊C4—22no—
30C2×C7×C22⋊C4D411yescharacteristic
31C2×C7×C22⋊C4D411yescharacteristic
32C2×C42×C7—41no—
33C2×C42×C7C2×C411yescharacteristic
34C2×C22⋊Dic7—22no—
35C2×C22⋊Dic7—22no—
36C2×C22⋊Dic7—22no—
37#6499—24no—
38#6499—24no—
39C2×C4⋊Dic7—21no—
40C2×C4⋊Dic7—21no—
41C2×C4⋊Dic7—21no—
42C2×C4⋊Dic7—41no—
43C2×C4×Dic7C2×C412yes—
44#6432—41no—
45#6432—41no—
46C7×#99—22no—
47C7×#99D414yes—
48C7×#95—41no—
49#6408—24no—
50C7⋊#95—21no—
51C7⋊#95—22no—
52C7⋊#95—22no—
53C7⋊#95—41no—
54#2547—71no—
55C2×#354—74no—
56#1799—71no—
57C4×#99D711yescharacteristic
58C24×C7C2×D411yescharacteristic
59C24×C7C2×D411yescharacteristic
60C2×C7×D4—41no—
61C2×C7×D4—41no—
62C2×C7×D4C2×D412yes—
63C2×C7×D4#4112yes—
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7—21no—
67C22×C4×C7—21no—
68C22×C4×C7—42no—
69C22×C4×C7—42no—
70C22×C4×C7—42no—
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22⋊C411yescharacteristic
74C22×C4×C7C22⋊C411yescharacteristic
75C22×C4×C7C22×C411yescharacteristic
76C22×Dic7—22no—
77C22×Dic7—22no—
78C22×Dic7—42no—
79C2×Dic14—24no—
80C2×Dic14—42no—
81C2×Dic14—42no—
82C7×C4⋊C4—41no—
83C7×C22⋊C4—24no—
84C7×C22⋊C4—41no—
85C7×C22⋊C4—41no—
86C7×C22⋊C4—42no—
87C42×C7—21no—
88C42×C7—21no—
89C42×C7—82no—
90C22⋊Dic7—44no—
91C22⋊Dic7—42no—
92C22⋊Dic7—42no—
93C22⋊Dic7—42no—
94C22⋊Dic7—42no—
95C4⋊Dic7—42no—
96C4⋊Dic7—42no—
97C4⋊Dic7—41no—
98C4⋊Dic7—41no—
99C4⋊Dic7—82no—
100C4×Dic7—24no—
101C2×C4⋊Q8—71no—
102C2×#124—72no—
103C2×C4×D4C2×D711yescharacteristic
104C2×#99—72no—
105C2×#99C2×D712yes—
106#397—141no—
107#397—141no—
108#391—72no—
109#380—141no—
110#380—141no—
111#380—141no—
112C4×C4⋊C4—71no—
113C4×C22⋊C4—21no—
114#354—148no—
115#342—21no—
116#342—141no—
117C23×C7—21no—
118C23×C7—21no—
119C23×C7—21no—
120C23×C7—21no—
121C23×C7—41no—
122C23×C7—41no—
123C23×C7—41no—
124C23×C7—41no—
125C23×C7C2×C22⋊C411yescharacteristic
126C23×C7#12112yes—
127C23×C7#12411yescharacteristic
128C23×C7#12711yescharacteristic
129C7×D4—42no—
130C7×D4—42no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—22no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—42no—
138C2×C4×C7—42no—
139C2×C4×C7—41no—
140C2×C4×C7—41no—
141C2×C4×C7—41no—
142C2×C4×C7—44no—
143C2×C4×C7—81no—
144C2×C4×C7—81no—
145C2×C4×C7—82no—
146C2×C4×C7—82no—
147C2×C4×C7#9911yescharacteristic
148C2×C4×C7#9911yescharacteristic
149C2×C4×C7C4×D412yes—
150C2×Dic7—42no—
151C2×Dic7—42no—
152C2×Dic7—42no—
153C2×Dic7—42no—
154C2×Dic7—42no—
155C2×Dic7—42no—
156C2×Dic7—82no—
157C2×Dic7—82no—
158C2×Dic7—82no—
159Dic14—84no—
160C22×Q8—72no—
161C22×D4C22×D711yescharacteristic
162C23×C4D2811yescharacteristic
163C23×C4C22⋊D711yescharacteristic
164C4⋊Q8—281no—
165C4⋊Q8—281no—
166#124—144no—
167#124—144no—
168C4×D4—41no—
169C4×D4—41no—
170C2×C4⋊C4—141no—
171C2×C4⋊C4—141no—
172C2×C4⋊C4—141no—
173C2×C4⋊C4—281no—
174C2×C4⋊C4C4×D711yescharacteristic
175C2×C22⋊C4—22no—
176C2×C22⋊C4—142no—
177C2×C22⋊C4—142no—
178C2×C22⋊C4—142no—
179C2×C22⋊C4D2811yescharacteristic
180C2×C22⋊C4C22⋊D711yescharacteristic
181C2×C42—41no—
182C2×C42—72no—
183C2×C42C4×D711yescharacteristic
184#99—22no—
185#99—144no—
186#99D2814yes—
187#95—41no—
188#95—141no—
189#95—142no—
190#95—142no—
191#95—281no—
192C22×C7—21no—
193C22×C7—21no—
194C22×C7—21no—
195C22×C7—22no—
196C22×C7—21no—
197C22×C7—42no—
198C22×C7—41no—
199C22×C7—41no—
200C22×C7—41no—
201C22×C7—41no—
202C22×C7—41no—
203C22×C7—41no—
204C22×C7—81no—
205C22×C7—81no—
206C22×C7#39011yescharacteristic
207C22×C7C2×#9911yescharacteristic
208C22×C7#41011yescharacteristic
209C4×C7—21no—
210C4×C7—22no—
211C4×C7—41no—
212C4×C7—41no—
213C4×C7—41no—
214C4×C7—84no—
215C4×C7#35412yescomplemented
216Dic7—82no—
217Dic7—82no—
218Dic7—162no—
219C24C2×D2811yescharacteristic
220C24C2×C22⋊D711yescharacteristic
221C2×Q8—144no—
222C2×Q8—282no—
223C2×Q8—282no—
224C2×D4—41no—
225C2×D4—41no—
226C2×D4C2×D2812yes—
227C2×D4#115712yes—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—142no—
236C22×C4—142no—
237C22×C4—282no—
238C22×C4(C2×D7)⋊C411yescharacteristic
239C22×C4(C2×D7)⋊C411yescharacteristic
240C22×C4(C2×D7)⋊C411yescharacteristic
241C22×C4(C2×D7)⋊C411yescharacteristic
242C22×C4C2×C4×D711yescharacteristic
243C4⋊C4—41no—
244C4⋊C4—282no—
245C4⋊C4—282no—
246C4⋊C4—281no—
247C4⋊C4—281no—
248C4⋊C4—562no—
249C22⋊C4—24no—
250C22⋊C4—41no—
251C22⋊C4—41no—
252C22⋊C4—42no—
253C22⋊C4—282no—
254C22⋊C4—282no—
255C22⋊C4—284no—
256C22⋊C4—282no—
257C22⋊C4—282no—
258C42—21no—
259C42—21no—
260C42—82no—
261C42—144no—
262C2×C7—21no—
263C2×C7—21no—
264C2×C7—41no—
265C2×C7—42no—
266C2×C7—41no—
267C2×C7#196411yescharacteristic
268C2×C7C2×#35411yescharacteristic
269C2×C7#212911yescharacteristic
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23#643711yescharacteristic
279C23#643811yescharacteristic
280C23C2×(C2×D7)⋊C411yescharacteristic
281C23#649312yes—
282Q8—564no—
283D4—42no—
284D4—42no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—44no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—82no—
300C2×C4—82no—
301C2×C4—282no—
302C2×C4—282no—
303C2×C4—282no—
304C2×C4—282no—
305C2×C4—282no—
306C2×C4—282no—
307C2×C4—562no—
308C2×C4—562no—
309C2×C4—562no—
310C2×C4#638011yescharacteristic
311C2×C4#638011yescharacteristic
312C2×C4C4×D2812yes—
313C7#1322411yescharacteristic, complemented, Sylow
314C22—21no—
315C22—21no—
316C22—22no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—42no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—81no—
327C22—81no—
328C22#8971111yescharacteristic
329C22C2×#638011yescharacteristic
330C22#8977811yescharacteristic
331C4—22no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—84no—
337C4—562no—
338C4—562no—
339C4—1122no—
340C4#8926812yescomplemented
341C2—21no—
342C2—21no—
343C2—42no—
344C2—41no—
345C2—41no—
346C2#1172721011yescharacteristic
347C2C2×#8926811yescharacteristic
348C2#1172781311yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC22×D4C22×D7
FittingC4×C7×#99C2
socleC22×C7C2×#99
prime radical, cosocleC22×C7×D4C23
hypercenterC4×#99D7
hypocenterC7#13224
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
7. C2×#6432C4semidirect
14. #89746C4semidirect
17. C4×C4⋊Dic7C4semidirect
215. C4×C7#354semidirect
313. C7#13224semidirect
340. C4#89268semidirect

Maximal subgroups

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

subgroupindex
#117398272
C4×C7×#992
#117293732
C2×#892682
#132247