Finite Group Databasebeta

← #13272078

Subgroups — #13272078

Order 1792.

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

normal subgroups only

This group has 536 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
1#11739818C211yesmaximal, characteristic
2C7×#1799C211yesmaximal, characteristic
3C4×#6407C211yesmaximal, characteristic
4C2×#89267C214yesmaximal
5C2×C4×C7×D4C2211yescharacteristic
6C2×#6498C2212yes—
7C22×C4⋊Dic7C411yescharacteristic, complemented
8C2×C7×#99C2212yes—
9C7×#380—21no—
10C2×#6407C2212yes—
11#89984—21no—
12#89984C411yescharacteristic, complemented
13#89755—21no—
14#89725—21no—
15#89715C412yescomplemented
16#89700—21no—
17C4×#1136—21no—
18C7×#342—21no—
19#89325—21no—
20#89267—28no—
21#13217—71nomaximal, Sylow
22C22×C7×D4C2311yescharacteristic
23C23×C4×C7C2×C411yescharacteristic
24C23×C4×C7D411yescharacteristic
25C23×Dic7C2×C412yes—
26C4×C7×D4—41no—
27C4×C7×D4—41no—
28C2×C7×C4⋊C4—41no—
29C2×C7×C4⋊C4D411yescharacteristic
30C2×C7×C22⋊C4—22no—
31C2×C7×C22⋊C4C2×C411yescharacteristic
32C2×C7×C22⋊C4D411yescharacteristic
33C2×C42×C7D411yescharacteristic
34C2×C22⋊Dic7—22no—
35C2×C22⋊Dic7C2×C412yes—
36#6498—24no—
37#6498—24no—
38C2×C4⋊Dic7—21no—
39C2×C4⋊Dic7—21no—
40C2×C4⋊Dic7—21no—
41C2×C4⋊Dic7—41no—
42C2×C4⋊Dic7—41no—
43C2×Dic7⋊C4—22no—
44C2×#1136—22no—
45C7×#99—24no—
46C7×#95—41no—
47#6407—22no—
48#6407D414yes—
49C7⋊#95—22no—
50C7⋊#95—22no—
51C7⋊#95—21no—
52#6377—41no—
53C4×C7⋊C8—41no—
54#2486—71no—
55C2×#352—74no—
56#1799D711yescharacteristic
57C4×#100—71no—
58C24×C7C22×C411yescharacteristic
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×C7C2×D411yescharacteristic
76C22×Dic7—22no—
77C22×Dic7—22no—
78C22×Dic7—24no—
79C22×Dic7—42no—
80C22×Dic7—42no—
81C7×C4⋊C4—41no—
82C7×C4⋊C4—82no—
83C7×C22⋊C4—41no—
84C7×C22⋊C4—41no—
85C7×C22⋊C4—42no—
86C7×C22⋊C4—42no—
87C42×C7—21no—
88C42×C7—21no—
89C22⋊Dic7—24no—
90C22⋊Dic7—42no—
91C22⋊Dic7—42no—
92C4⋊Dic7—42no—
93C4⋊Dic7—42no—
94C4⋊Dic7—41no—
95C4⋊Dic7—41no—
96Dic7⋊C4—44no—
97#1136—24no—
98#1136—42no—
99C2×C7⋊C8—42no—
100C2×#123—72no—
101C2×C4×D4C2×D711yescharacteristic
102C22×C4⋊C4—71no—
103C2×#100—72no—
104C2×#99C2×D712yes—
105C4×M16—141no—
106#398—141no—
107#397—141no—
108#389—141no—
109#381—72no—
110#380—21no—
111#380—71no—
112#380—141no—
113#352—148no—
114#343—141no—
115#342—21no—
116C23×C7—21no—
117C23×C7—21no—
118C23×C7—21no—
119C23×C7—21no—
120C23×C7—41no—
121C23×C7—41no—
122C23×C7—41no—
123C23×C7—41no—
124C23×C7C2×C22⋊C411yescharacteristic
125C23×C7C4×D412yes—
126C23×C7#12411yescharacteristic
127C23×C7#12711yescharacteristic
128C7×D4—42no—
129C7×D4—42no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—22no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—42no—
137C2×C4×C7—42no—
138C2×C4×C7—42no—
139C2×C4×C7—41no—
140C2×C4×C7—41no—
141C2×C4×C7—41no—
142C2×C4×C7—81no—
143C2×C4×C7—82no—
144C2×C4×C7—82no—
145C2×C4×C7—82no—
146C2×C4×C7#9911yescharacteristic
147C2×C4×C7#9911yescharacteristic
148C2×C4×C7#12112yes—
149C2×Dic7—42no—
150C2×Dic7—42no—
151C2×Dic7—42no—
152C2×Dic7—42no—
153C2×Dic7—42no—
154C2×Dic7—42no—
155C2×Dic7—84no—
156C7⋊C8—44no—
157C22×D4C22×D711yescharacteristic
158C23×C4—72no—
159C23×C4C4×D711yescharacteristic
160C23×C4C22⋊D711yescharacteristic
161C2×M16—142no—
162#123—144no—
163#123—144no—
164C4×D4—41no—
165C4×D4—41no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—141no—
168C2×C4⋊C4—141no—
169C2×C4⋊C4—141no—
170C2×C4⋊C4—142no—
171C2×C4⋊C4—281no—
172C2×C4⋊C4—281no—
173C2×C4⋊C4D2811yescharacteristic
174C2×C22⋊C4—22no—
175C2×C22⋊C4—72no—
176C2×C22⋊C4—142no—
177C2×C22⋊C4C4×D711yescharacteristic
178C2×C22⋊C4C22⋊D711yescharacteristic
179C2×C42D2811yescharacteristic
180#100—74no—
181#100—142no—
182#99—24no—
183#97—281no—
184C4×C8—281no—
185#95—41no—
186#95—141no—
187#95—142no—
188#95—142no—
189C22×C7—21no—
190C22×C7—21no—
191C22×C7—22no—
192C22×C7—21no—
193C22×C7—21no—
194C22×C7—42no—
195C22×C7—41no—
196C22×C7—41no—
197C22×C7—42no—
198C22×C7—41no—
199C22×C7—41no—
200C22×C7—41no—
201C22×C7—41no—
202C22×C7—81no—
203C22×C7#39011yescharacteristic
204C22×C7C2×#9911yescharacteristic
205C22×C7#41011yescharacteristic
206C4×C7—21no—
207C4×C7—22no—
208C4×C7—41no—
209C4×C7—41no—
210C4×C7—41no—
211C4×C7—162no—
212C4×C7#35212yescomplemented
213Dic7—82no—
214Dic7—82no—
215C24C2×C4×D711yescharacteristic
216C24C2×C22⋊D711yescharacteristic
217C2×D4—41no—
218C2×D4—41no—
219C2×D4D4×D712yes—
220C2×D4#116112yes—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—142no—
229C22×C4—142no—
230C22×C4—144no—
231C22×C4—282no—
232C22×C4—282no—
233C22×C4(C2×D7)⋊C411yescharacteristic
234C22×C4(C2×D7)⋊C411yescharacteristic
235C22×C4(C2×D7)⋊C411yescharacteristic
236C22×C4(C2×D7)⋊C411yescharacteristic
237C22×C4C2×D2811yescharacteristic
238M16—144no—
239M16—282no—
240C2×C8—282no—
241C4⋊C4—41no—
242C4⋊C4—82no—
243C4⋊C4—282no—
244C4⋊C4—282no—
245C4⋊C4—284no—
246C4⋊C4—281no—
247C4⋊C4—281no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—144no—
253C22⋊C4—282no—
254C22⋊C4—282no—
255C42—21no—
256C42—21no—
257C2×C7—21no—
258C2×C7—21no—
259C2×C7—41no—
260C2×C7—42no—
261C2×C7—41no—
262C2×C7#196411yescharacteristic
263C2×C7C2×#35211yescharacteristic
264C2×C7#212311yescharacteristic
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—41no—
270C23—41no—
271C23—41no—
272C23—41no—
273C23#645612yes—
274C23C2×(C2×D7)⋊C411yescharacteristic
275C23#650311yescharacteristic
276C23#651011yescharacteristic
277D4—42no—
278D4—42no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—81no—
292C2×C4—82no—
293C2×C4—82no—
294C2×C4—82no—
295C2×C4—282no—
296C2×C4—282no—
297C2×C4—282no—
298C2×C4—282no—
299C2×C4—282no—
300C2×C4—282no—
301C2×C4—564no—
302C2×C4#638011yescharacteristic
303C2×C4#638011yescharacteristic
304C2×C4#645812yes—
305C8—284no—
306C7#1321711yescharacteristic, complemented, Sylow
307C22—21no—
308C22—21no—
309C22—21no—
310C22—22no—
311C22—21no—
312C22—42no—
313C22—41no—
314C22—41no—
315C22—42no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—81no—
321C22C2×#638011yescharacteristic
322C22#8976011yescharacteristic
323C22#8977811yescharacteristic
324C4—21no—
325C4—22no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—162no—
330C4—562no—
331C4—562no—
332C4#8926712yescomplemented
333C2—21no—
334C2—21no—
335C2—41no—
336C2—42no—
337C2—41no—
338C2#1172728211yescharacteristic
339C2C2×#8926711yescharacteristic
340C2#1172781211yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC24×C7C22×C4
FrattiniC22×D4C22×D7
FittingC7×#1799C2
socleC22×C7C2×#99
prime radical, cosocleC22×C7×D4C23
hypercenter#1799D7
hypocenterC7#13217
LCSG ▷ C24×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
7. C22×C4⋊Dic7C4semidirect
12. #89984C4semidirect
15. #89715C4semidirect
212. C4×C7#352semidirect
306. C7#13217semidirect
332. C4#89267semidirect

Maximal subgroups

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

subgroupindex
#117398182
C7×#17992
C4×#64072
C2×#892672
#132177