Finite Group Databasebeta

← #13249524

Subgroups — #13249524

Order 1792.

1010 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 1010 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
1#11741476C211yesmaximal, characteristic
2C2×C4×C22⋊Dic7C211yesmaximal, characteristic
3C7×#1779C211yesmaximal, characteristic
4C2×#89262C212yesmaximal, complemented
5#11725481C212yesmaximal, complemented
6C24×C4×C7C2211yescharacteristic
7C22×C22⋊Dic7—21no—
8C2×#6487C412yescomplemented
9C2×#6487C2211yescharacteristic
10C22×C4×Dic7—21no—
11C2×C7×C22⋊C8—22no—
12C2×C7×C22⋊C8C2212yes—
13#90019—21no—
14#89984C412yescomplemented
15#89984C2211yescharacteristic
16#89982—21no—
17#89982—22no—
18C4×C22⋊Dic7—24no—
19C2×C7⋊#95C2212yes—
20#89262—24no—
21#9146—71nomaximal, Sylow
22C25×C7D411yescharacteristic
23C23×C4×C7—22no—
24C23×C4×C7—22no—
25C23×C4×C7—44no—
26C23×C4×C7C2×C412yes—
27C23×C4×C7D411yescharacteristic
28C23×C4×C7D412yes—
29C23×C4×C7C2311yescharacteristic
30C23×Dic7—22no—
31C22×Dic14C2×C411yescharacteristic
32C22×C7×C8—22no—
33C2×C22⋊Dic7—24no—
34C2×C22⋊Dic7—28no—
35C2×C22⋊Dic7—22no—
36C2×C22⋊Dic7—22no—
37C2×C22⋊Dic7—21no—
38C2×C22⋊Dic7—21no—
39C2×C4⋊Dic7C2×C411yescharacteristic
40C2×C4⋊Dic7C2×C412yes—
41#6487—22no—
42#6487—22no—
43#6487—44no—
44C2×Dic7⋊C4—22no—
45C2×Dic7⋊C4—21no—
46C2×C4×Dic7—24no—
47C2×C4×Dic7—44no—
48C7×C22⋊C8—22no—
49C7×C22⋊C8—22no—
50C7×C22⋊C8—44no—
51C7⋊#95—22no—
52C7⋊#95—22no—
53C7⋊#95—21no—
54C7⋊#95D414yes—
55#2848—71no—
56C2×C4×C22⋊C4—71no—
57#1779D711yescharacteristic
58C2×#328—72no—
59#1294—72no—
60C24×C7—24no—
61C24×C7—21no—
62C24×C7—21no—
63C24×C7—22no—
64C24×C7—22no—
65C24×C7—42no—
66C24×C7C22⋊C412yes—
67C24×C7C2×D411yescharacteristic
68C22×C4×C7—21no—
69C22×C4×C7—21no—
70C22×C4×C7—24no—
71C22×C4×C7—24no—
72C22×C4×C7—24no—
73C22×C4×C7—24no—
74C22×C4×C7—24no—
75C22×C4×C7—42no—
76C22×C4×C7—42no—
77C22×C4×C7—42no—
78C22×C4×C7—48no—
79C22×C4×C7—48no—
80C22×C4×C7C22⋊C412yes—
81C22×C4×C7C22×C411yescharacteristic
82C22×C4×C7C2×D411yescharacteristic
83C22×C4×C7C2×D412yes—
84C22×C4×C7#4112yes—
85C22×Dic7—28no—
86C22×Dic7—24no—
87C22×Dic7—21no—
88C22×Dic7—22no—
89C22×Dic7—21no—
90C22×Dic7—44no—
91C22×Dic7—42no—
92C22×Dic7—42no—
93C2×Dic14—22no—
94C2×Dic14—42no—
95C2×C7×C8—44no—
96C2×C7×C8—42no—
97C22⋊Dic7—216no—
98C22⋊Dic7—44no—
99C22⋊Dic7—44no—
100C22⋊Dic7—41no—
101C22⋊Dic7—41no—
102C22⋊Dic7—42no—
103C4⋊Dic7—22no—
104C4⋊Dic7—42no—
105Dic7⋊C4—44no—
106Dic7⋊C4—42no—
107C4×Dic7—48no—
108C24×C4C2×D711yescharacteristic
109C2×C22⋊Q8—71no—
110C2×C22⋊Q8—72no—
111C22×C22⋊C4—141no—
112C22×C42—141no—
113C2×C22⋊C8—22no—
114C2×C22⋊C8C2×D712yes—
115#385—141no—
116#385—142no—
117#380—72no—
118#380—71no—
119#379—141no—
120C4×C22⋊C4—144no—
121C2×#95—72no—
122#328—144no—
123C23×C7—22no—
124C23×C7—22no—
125C23×C7—24no—
126C23×C7—24no—
127C23×C7—22no—
128C23×C7—22no—
129C23×C7—22no—
130C23×C7—22no—
131C23×C7—22no—
132C23×C7—22no—
133C23×C7—48no—
134C23×C7—48no—
135C23×C7—42no—
136C23×C7—42no—
137C23×C7—42no—
138C23×C7—42no—
139C23×C7#10414yes—
140C23×C7C2×C22⋊C411yescharacteristic
141C23×C7#12011yescharacteristic
142C23×C7#12311yescharacteristic
143C23×C7#13512yes—
144C23×C7#13712yes—
145C2×C4×C7—24no—
146C2×C4×C7—24no—
147C2×C4×C7—22no—
148C2×C4×C7—22no—
149C2×C4×C7—22no—
150C2×C4×C7—22no—
151C2×C4×C7—42no—
152C2×C4×C7—42no—
153C2×C4×C7—48no—
154C2×C4×C7—48no—
155C2×C4×C7#9914yes—
156C2×C4×C7C4×D412yes—
157C2×C4×C7#12112yes—
158C2×Dic7—28no—
159C2×Dic7—44no—
160C2×Dic7—48no—
161C2×Dic7—48no—
162C2×Dic7—44no—
163C2×Dic7—41no—
164C2×Dic7—41no—
165C2×Dic7—42no—
166C2×Dic7—42no—
167C2×Dic7—42no—
168C2×Dic7—42no—
169C2×Dic7—42no—
170Dic14—82no—
171C7×C8—82no—
172C25D2811yescharacteristic
173C22×Q8—71no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—44no—
177C23×C4—142no—
178C23×C4C4×D712yes—
179C23×C4D2811yescharacteristic
180C23×C4C22⋊D712yes—
181C23×C4C22×D711yescharacteristic
182C22×C8—22no—
183C22⋊Q8—142no—
184C22⋊Q8—142no—
185C22⋊Q8—284no—
186C2×C4⋊C4—71no—
187C2×C4⋊C4—72no—
188C2×C4⋊C4—142no—
189C2×C4⋊C4—141no—
190C2×C22⋊C4—148no—
191C2×C22⋊C4—144no—
192C2×C22⋊C4—142no—
193C2×C22⋊C4—142no—
194C2×C22⋊C4—141no—
195C2×C22⋊C4—141no—
196C2×C42—144no—
197C2×C42—284no—
198C22⋊C8—22no—
199C22⋊C8—22no—
200C22⋊C8—44no—
201#95—74no—
202#95—142no—
203#95—142no—
204#95—141no—
205C22×C7—21no—
206C22×C7—21no—
207C22×C7—21no—
208C22×C7—21no—
209C22×C7—24no—
210C22×C7—24no—
211C22×C7—24no—
212C22×C7—24no—
213C22×C7—24no—
214C22×C7—48no—
215C22×C7—48no—
216C22×C7—42no—
217C22×C7—42no—
218C22×C7—42no—
219C22×C7—42no—
220C22×C7#38611yescharacteristic
221C22×C7C2×#9912yes—
222C22×C7#41611yescharacteristic
223C22×C7#41911yescharacteristic
224C22×C7C2×#10412yes—
225C22×C7#45212yes—
226C22×C7#48512yes—
227C4×C7—22no—
228C4×C7—22no—
229C4×C7—24no—
230Dic7—48no—
231Dic7—81no—
232Dic7—81no—
233Dic7—82no—
234C24—21no—
235C24—21no—
236C24—24no—
237C24—22no—
238C24—22no—
239C24—42no—
240C24(C2×D7)⋊C412yes—
241C24C2×D2811yescharacteristic
242C2×Q8—142no—
243C2×Q8—282no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—24no—
247C22×C4—24no—
248C22×C4—24no—
249C22×C4—24no—
250C22×C4—24no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—48no—
255C22×C4—48no—
256C22×C4—148no—
257C22×C4—144no—
258C22×C4—142no—
259C22×C4—141no—
260C22×C4—141no—
261C22×C4—284no—
262C22×C4—282no—
263C22×C4—282no—
264C22×C4(C2×D7)⋊C412yes—
265C22×C4C2×C4×D711yescharacteristic
266C22×C4D4×D712yes—
267C22×C4#115912yes—
268C22×C4C2×C22⋊D711yescharacteristic
269C2×C8—44no—
270C2×C8—42no—
271C4⋊C4—142no—
272C4⋊C4—282no—
273C4⋊C4—282no—
274C4⋊C4—284no—
275C22⋊C4—1416no—
276C22⋊C4—284no—
277C22⋊C4—281no—
278C22⋊C4—281no—
279C22⋊C4—282no—
280C22⋊C4—284no—
281C42—288no—
282C2×C7—22no—
283C2×C7—22no—
284C2×C7—44no—
285C2×C7#150112yes—
286C2×C7#150812yes—
287C2×C7#187311yescharacteristic
288C2×C7#189611yescharacteristic
289C2×C7#189811yescharacteristic
290C23—22no—
291C23—22no—
292C23—24no—
293C23—24no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—22no—
298C23—22no—
299C23—22no—
300C23—48no—
301C23—48no—
302C23—42no—
303C23—42no—
304C23—42no—
305C23—42no—
306C23#639914yes—
307C23#644511yescharacteristic
308C23#644911yescharacteristic
309C23#646712yes—
310C23#647212yes—
311C23C2×(C2×D7)⋊C411yescharacteristic
312Q8—562no—
313C2×C4—24no—
314C2×C4—24no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—48no—
322C2×C4—48no—
323C2×C4—148no—
324C2×C4—284no—
325C2×C4—288no—
326C2×C4—288no—
327C2×C4—284no—
328C2×C4—282no—
329C2×C4—282no—
330C2×C4—282no—
331C2×C4—282no—
332C2×C4—282no—
333C2×C4—281no—
334C2×C4—281no—
335C2×C4#638014yes—
336C2×C4(C22⋊D7)⋊C412yes—
337C2×C4#650212yes—
338C8—82no—
339C7#914611yescharacteristic, complemented, Sylow
340C22—24no—
341C22—21no—
342C22—21no—
343C22—24no—
344C22—21no—
345C22—21no—
346C22—24no—
347C22—24no—
348C22—24no—
349C22—48no—
350C22—48no—
351C22—42no—
352C22—42no—
353C22—42no—
354C22—42no—
355C22#8949512yes—
356C22#8950512yes—
357C22C2×#638012yes—
358C22#8973011yescharacteristic
359C22#8988511yescharacteristic
360C22#8989211yescharacteristic
361C22C2×#639912yes—
362C4—22no—
363C4—24no—
364C4—22no—
365C4—288no—
366C4—562no—
367C4—561no—
368C4—561no—
369C2—22no—
370C2—22no—
371C2—44no—
372C2#1172725011yescharacteristic
373C2#1172768511yescharacteristic
374C2#1172769612yes—
375C2#1172771911yescharacteristic
376C2#1172773412yes—
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×#1779C2
socleC23×C7C2×C22⋊C4
prime radicalC25×C7D4
cosocleC23×C4×C7C23
hypercenter#1779D7
hypocenterC7#9146
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
4. C2×#89262C2semidirect
5. #11725481C2semidirect
8. C2×#6487C4semidirect
14. #89984C4semidirect
339. C7#9146semidirect

Maximal subgroups

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

subgroupindex
#117414762
C2×C4×C22⋊Dic72
C7×#17792
C2×#892622
#117254812
#91467