Finite Group Databasebeta

← #13249574

Subgroups — #13249574

Order 1792.

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

normal subgroups only

This group has 692 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#11739525C211yesmaximal, characteristic
2C2×#89708C211yesmaximal, characteristic, complemented
3C7×#1817C211yesmaximal, characteristic, complemented
4C2×#89265C212yesmaximal
5#11725481C212yesmaximal, complemented
6C22×C42×C7C2211yescharacteristic
7C2×#6493C2211yescharacteristic
8C2×#6492—21no—
9C22×C4⋊Dic7—21no—
10C2×C7×C22⋊C8C2212yes—
11#89985—21no—
12#89984C2211yescharacteristic
13C2×C7⋊#95—21no—
14C2×C7⋊#95C2212yes—
15#89712—22no—
16#89711C412yescomplemented
17#89708—24no—
18#89700C412yescomplemented
19C7×#336—22no—
20#89265—24no—
21#9156—71nomaximal, Sylow
22C23×C4×C7D411yescharacteristic
23C23×C4×C7D411yescharacteristic
24C23×C4×C7C2311yescharacteristic
25C22×C22⋊D7—21no—
26C23×Dic7—22no—
27C22×D28C2×C411yescharacteristic
28C22×C7×C8—22no—
29C2×C42×C7—22no—
30C2×C42×C7—22no—
31C2×C42×C7C2×C412yes—
32C2×C42×C7D412yes—
33C2×C22⋊Dic7—21no—
34#6493—22no—
35#6493—22no—
36#6492—42no—
37#6492—42no—
38C2×(C2×D7)⋊C4—22no—
39C2×(C2×D7)⋊C4—22no—
40C2×(C2×D7)⋊C4—21no—
41C2×C4⋊Dic7—24no—
42C2×C4⋊Dic7—42no—
43C2×C4⋊Dic7—42no—
44C2×C4⋊Dic7C2×C411yescharacteristic
45C2×C4⋊Dic7C2×C412yes—
46C2×Dic7⋊C4—22no—
47C7×C22⋊C8—22no—
48C7×C22⋊C8—22no—
49C7⋊#95—24no—
50C7⋊#95—22no—
51C7⋊#95—22no—
52C7⋊#95—21no—
53C7⋊#95D414yes—
54#2854—71no—
55C2×#382—71no—
56#1817D711yescharacteristic, complemented
57C2×#327—72no—
58#1294—72no—
59C24×C7C2×D411yescharacteristic
60C23×D7—21no—
61C22×C4×C7—21no—
62C22×C4×C7—21no—
63C22×C4×C7—21no—
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7—21no—
67C22×C4×C7—42no—
68C22×C4×C7—42no—
69C22×C4×C7C22⋊C412yes—
70C22×C4×C7C22⋊C412yes—
71C22×C4×C7D812yes—
72C22×C4×C7SD1612yes—
73C22×C4×C7C22×C411yescharacteristic
74C22×C4×C7C2×D411yescharacteristic
75C22×C4×C7C2×D412yes—
76C22×C4×C7#4112yes—
77C2×C22⋊D7—41no—
78C2×C22⋊D7—41no—
79C2×C22⋊D7—41no—
80C2×C22⋊D7—41no—
81C2×C22⋊D7—41no—
82C2×C22⋊D7—41no—
83C22×Dic7—21no—
84C22×Dic7—22no—
85C22×Dic7—24no—
86C22×Dic7—44no—
87C22×Dic7—44no—
88C22×Dic7—42no—
89C22×Dic7—42no—
90C2×D28—22no—
91C2×D28—42no—
92C2×C7×C8—44no—
93C2×C7×C8—42no—
94C42×C7—24no—
95C42×C7—24no—
96C22⋊Dic7—41no—
97C22⋊Dic7—41no—
98(C2×D7)⋊C4—44no—
99(C2×D7)⋊C4—44no—
100(C2×D7)⋊C4—42no—
101C4⋊Dic7—22no—
102C4⋊Dic7—48no—
103C4⋊Dic7—42no—
104Dic7⋊C4—44no—
105C2×#123—141no—
106C2×#121—71no—
107C22×C4⋊C4—141no—
108C22×C42C2×D711yescharacteristic
109C2×C22⋊C8C2×D712yes—
110#390—72no—
111#389—72no—
112#388—142no—
113#386—141no—
114#382—144no—
115#380—71no—
116C2×#95—72no—
117C2×#95—141no—
118#336—22no—
119#327—144no—
120C23×C7—22no—
121C23×C7—22no—
122C23×C7C2×C22⋊C411yescharacteristic
123C23×C7#12011yescharacteristic
124C23×C7#12311yescharacteristic
125C23×C7C2×D811yescharacteristic
126C23×C7C2×SD1611yescharacteristic
127C23×C7AGL(1,ℤ/8)11yescharacteristic
128C23×C7#13711yescharacteristic
129C22×D7—41no—
130C22×D7—42no—
131C22×D7—41no—
132C22×D7—41no—
133C22×D7—42no—
134C2×C4×C7—22no—
135C2×C4×C7—22no—
136C2×C4×C7—22no—
137C2×C4×C7—22no—
138C2×C4×C7—22no—
139C2×C4×C7—22no—
140C2×C4×C7—22no—
141C2×C4×C7—22no—
142C2×C4×C7—22no—
143C2×C4×C7—22no—
144C2×C4×C7—22no—
145C2×C4×C7—42no—
146C2×C4×C7—42no—
147C2×C4×C7—42no—
148C2×C4×C7—42no—
149C2×C4×C7#10214yes—
150C2×C4×C7C4×D412yes—
151C2×C4×C7#12112yes—
152C22⋊D7—81no—
153C22⋊D7—81no—
154C22⋊D7—81no—
155C22⋊D7—81no—
156C2×Dic7—44no—
157C2×Dic7—44no—
158C2×Dic7—41no—
159C2×Dic7—42no—
160C2×Dic7—41no—
161C2×Dic7—42no—
162C2×Dic7—41no—
163C2×Dic7—42no—
164C2×Dic7—44no—
165C2×Dic7—84no—
166C2×Dic7—84no—
167D28—82no—
168C7×C8—82no—
169C22×D4—71no—
170C22×D4—141no—
171C23×C4—142no—
172C23×C4D2811yescharacteristic
173C23×C4D2811yescharacteristic
174C23×C4C22×D711yescharacteristic
175C22×C8—22no—
176#123—282no—
177#123—282no—
178#121—142no—
179#121—142no—
180C2×C4⋊C4—71no—
181C2×C4⋊C4—72no—
182C2×C4⋊C4—144no—
183C2×C4⋊C4—142no—
184C2×C4⋊C4—282no—
185C2×C4⋊C4—282no—
186C2×C22⋊C4—141no—
187C2×C22⋊C4—142no—
188C2×C22⋊C4—142no—
189C2×C22⋊C4—141no—
190C2×C42—22no—
191C2×C42—22no—
192C2×C42C4×D712yes—
193C2×C42C22⋊D712yes—
194C22⋊C8—22no—
195C22⋊C8—22no—
196#95—74no—
197#95—144no—
198#95—142no—
199#95—142no—
200#95—141no—
201C22×C7—21no—
202C22×C7—21no—
203C22×C7—21no—
204C22×C7—21no—
205C22×C7—22no—
206C22×C7—22no—
207C22×C7—22no—
208C22×C7—22no—
209C22×C7#38611yescharacteristic
210C22×C7#41012yes—
211C22×C7C2×#10211yescharacteristic
212C22×C7#41711yescharacteristic
213C22×C7#42112yes—
214C22×C7#44711yescharacteristic
215C22×C7#44811yescharacteristic
216C22×C7#48011yescharacteristic
217C22×C7#48111yescharacteristic
218C2×D7—81no—
219C2×D7—81no—
220C2×D7—81no—
221C2×D7—82no—
222C2×D7—82no—
223C4×C7—24no—
224C4×C7—22no—
225C4×C7—22no—
226C4×C7—42no—
227Dic7—84no—
228Dic7—81no—
229Dic7—82no—
230C24—141no—
231C24C2×D2811yescharacteristic
232C2×D4—142no—
233C2×D4—282no—
234C2×D4—281no—
235C2×D4—281no—
236C2×D4—281no—
237C2×D4—281no—
238C2×D4—281no—
239C2×D4—281no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—144no—
249C22×C4—142no—
250C22×C4—141no—
251C22×C4—284no—
252C22×C4—284no—
253C22×C4—282no—
254C22×C4—282no—
255C22×C4#113212yes—
256C22×C4D5612yes—
257C22×C4(C2×D7)⋊C412yes—
258C22×C4(C2×D7)⋊C412yes—
259C22×C4C2×C4×D711yescharacteristic
260C22×C4D4×D712yes—
261C22×C4#115912yes—
262C22×C4C2×C22⋊D711yescharacteristic
263C2×C8—44no—
264C2×C8—42no—
265C4⋊C4—142no—
266C4⋊C4—282no—
267C4⋊C4—288no—
268C4⋊C4—284no—
269C22⋊C4—284no—
270C22⋊C4—281no—
271C22⋊C4—281no—
272C22⋊C4—282no—
273C22⋊C4—284no—
274C42—24no—
275C42—24no—
276C2×C7—21no—
277C2×C7—21no—
278C2×C7—21no—
279C2×C7—21no—
280C2×C7#151212yes—
281C2×C7#151712yes—
282C2×C7#187411yescharacteristic
283C2×C7#189711yescharacteristic
284C2×C7#189911yescharacteristic
285D7—161no—
286C23—22no—
287C23—22no—
288C23—281no—
289C23—281no—
290C23—282no—
291C23—281no—
292C23—282no—
293C23#644511yescharacteristic
294C23#644911yescharacteristic
295C23C2×#113211yescharacteristic
296C23C2×D5611yescharacteristic
297C23#647111yescharacteristic
298C23#647211yescharacteristic
299C23C2×(C2×D7)⋊C411yescharacteristic
300D4—562no—
301D4—561no—
302D4—561no—
303D4—561no—
304D4—561no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—284no—
321C2×C4—284no—
322C2×C4—282no—
323C2×C4—281no—
324C2×C4—281no—
325C2×C4—282no—
326C2×C4—281no—
327C2×C4—284no—
328C2×C4—282no—
329C2×C4—564no—
330C2×C4—564no—
331C2×C4#639514yes—
332C2×C4(C22⋊D7)⋊C412yes—
333C2×C4#650212yes—
334C8—82no—
335C7#915611yescharacteristic, complemented, Sylow
336C22—21no—
337C22—21no—
338C22—22no—
339C22—22no—
340C22—21no—
341C22—21no—
342C22—22no—
343C22—22no—
344C22—561no—
345C22—561no—
346C22—562no—
347C22—561no—
348C22—562no—
349C22#8950411yescharacteristic
350C22#8950711yescharacteristic
351C22#8950811yescharacteristic
352C22#8951011yescharacteristic
353C22#8973011yescharacteristic
354C22#8977812yes—
355C22C2×#639511yescharacteristic
356C22#8990511yescharacteristic
357C22#8991112yes—
358C4—24no—
359C4—22no—
360C4—22no—
361C4—42no—
362C4—564no—
363C4—561no—
364C4—562no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—1121no—
370C2#1172728911yescharacteristic
371C2#1172768611yescharacteristic
372C2#1172772011yescharacteristic
373C2#1172854412yes—
374C2#1172858812yes—
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×#1817C2
socleC23×C7C2×C22⋊C4
prime radicalC2×#6493C22
cosocleC23×C4×C7C23
hypercenter#1817D7
hypocenterC7#9156
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. C2×#89708C2semidirect
3. C7×#1817C2semidirect
5. #11725481C2semidirect
16. #89711C4semidirect
18. #89700C4semidirect
56. #1817D7semidirect
335. C7#9156semidirect

Maximal subgroups

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

subgroupindex
#117395252
C2×#897082
C7×#18172
C2×#892652
#117254812
#91567