Finite Group Databasebeta

← #13264325

Subgroups — #13264325

Order 1792.

462 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 87 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#11739626C211yesmaximal, characteristic
2C2×C7×#343C211yesmaximal, characteristic
3#11729306C211yesmaximal, characteristic
4#11725301C212yesmaximal, complemented
5#11725300C212yesmaximal, complemented
6C22×C7×M16—21no—
7C22×C7×C4⋊C4C2211yescharacteristic
8C2×#6487C411yescharacteristic
9#89982—21no—
10#89982—21no—
11C4×C22⋊Dic7C411yescharacteristic
12#89979—21no—
13#89755C411yescharacteristic
14#89755C2211yescharacteristic
15#89751C411yescharacteristic
16#89751C2211yescharacteristic
17#89744—21no—
18#89744—21no—
19C7×#343—21no—
20C7×#343C2212yes—
21#89323—21no—
22#89323C2212yes—
23#11768—71nomaximal, Sylow
24C23×C4×C7C2×C411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C22×Dic14C2×C411yescharacteristic
28C2×C7×M16—24no—
29C2×C7×M16—22no—
30C2×C7×M16—41no—
31C2×C7×M16—42no—
32C22×C7×C8—41no—
33C2×C7×C4⋊C4—41no—
34C2×C7×C4⋊C4—41no—
35C2×C7×C4⋊C4C2×C411yescharacteristic
36C2×C7×C4⋊C4D411yescharacteristic
37C2×C7×C4⋊C4D411yescharacteristic
38C2×C7×C4⋊C4C2311yescharacteristic
39C2×C22⋊Dic7—21no—
40C2×C22⋊Dic7—21no—
41C2×C4⋊Dic7C2×C411yescharacteristic
42#6487—41no—
43#6487—41no—
44C2×Dic7⋊C4—21no—
45C2×Dic7⋊C4—21no—
46C2×Dic7⋊C4—21no—
47C2×Dic7⋊C4—21no—
48C2×Dic7⋊C4—21no—
49C2×C4×Dic7—21no—
50C2×#1136—41no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C7⋊#95C2×C411yescharacteristic
56C7⋊#95C2×C411yescharacteristic
57C22⋊(C7⋊C8)—22no—
58C22⋊(C7⋊C8)—41no—
59#2583—71no—
60C2×#343D711yescharacteristic
61#1463—71no—
62#1354—72no—
63#1346—72no—
64C24×C7C22⋊C411yescharacteristic
65C22×C4×C7—21no—
66C22×C4×C7—21no—
67C22×C4×C7—22no—
68C22×C4×C7—21no—
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—21no—
74C22×C4×C7—81no—
75C22×C4×C7—81no—
76C22×C4×C7C22⋊C411yescharacteristic
77C22×C4×C7C22⋊C411yescharacteristic
78C22×C4×C7C22⋊C411yescharacteristic
79C22×C4×C7C22×C411yescharacteristic
80C22×C4×C7C2×D411yescharacteristic
81C22×C4×C7C2×D411yescharacteristic
82C22×Dic7—21no—
83C22×Dic7—21no—
84C22×Dic7—21no—
85C22×Dic7—21no—
86C2×Dic14—41no—
87C2×Dic14—81no—
88C7×M16—24no—
89C7×M16—44no—
90C7×M16—42no—
91C2×C7×C8—44no—
92C2×C7×C8—42no—
93C7×C4⋊C4—41no—
94C7×C4⋊C4—41no—
95C7×C4⋊C4—41no—
96C7×C4⋊C4—41no—
97C22⋊Dic7—24no—
98C22⋊Dic7—41no—
99C22⋊Dic7—41no—
100C4⋊Dic7—41no—
101Dic7⋊C4—42no—
102Dic7⋊C4—42no—
103Dic7⋊C4—41no—
104Dic7⋊C4—41no—
105Dic7⋊C4—81no—
106Dic7⋊C4—81no—
107C4×Dic7—81no—
108#1136—82no—
109C2×C7⋊C8—42no—
110C22×M16—21no—
111C2×C22⋊Q8—71no—
112C22×C4⋊C4C2×D711yescharacteristic
113#407—141no—
114#398—71no—
115#398—71no—
116#395—71no—
117#395—71no—
118#389—141no—
119#389—141no—
120#385—141no—
121#385—141no—
122C4×C22⋊C4—71no—
123#343—21no—
124#343C2×D712yes—
125#324—72no—
126#324—141no—
127C23×C7—22no—
128C23×C7—21no—
129C23×C7—21no—
130C23×C7—41no—
131C23×C7#9911yescharacteristic
132C23×C7#9911yescharacteristic
133C23×C7C2×C22⋊C411yescharacteristic
134C2×C4×C7—22no—
135C2×C4×C7—22no—
136C2×C4×C7—22no—
137C2×C4×C7—22no—
138C2×C4×C7—21no—
139C2×C4×C7—21no—
140C2×C4×C7—21no—
141C2×C4×C7—21no—
142C2×C4×C7—21no—
143C2×C4×C7—21no—
144C2×C4×C7—21no—
145C2×C4×C7—21no—
146C2×C4×C7—42no—
147C2×C4×C7—41no—
148C2×C4×C7—41no—
149C2×C4×C7—41no—
150C2×C4×C7—41no—
151C2×C4×C7—81no—
152C2×C4×C7—81no—
153C2×C4×C7—81no—
154C2×C4×C7#10412yes—
155C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C7#13711yescharacteristic
157C2×Dic7—22no—
158C2×Dic7—22no—
159C2×Dic7—41no—
160C2×Dic7—41no—
161C2×Dic7—41no—
162C2×Dic7—41no—
163C2×Dic7—41no—
164C2×Dic7—41no—
165C2×Dic7—41no—
166C2×Dic7—41no—
167C2×Dic7—41no—
168C2×Dic7—41no—
169Dic14—82no—
170C7×C8—44no—
171C7⋊C8—82no—
172C22×Q8—71no—
173C23×C4C4×D711yescharacteristic
174C23×C4D2811yescharacteristic
175C23×C4C22⋊D711yescharacteristic
176C2×M16—24no—
177C2×M16—22no—
178C2×M16—41no—
179C2×M16—42no—
180C2×M16—281no—
181C22×C8—41no—
182C22⋊Q8—281no—
183C22⋊Q8—281no—
184C2×C4⋊C4—41no—
185C2×C4⋊C4—41no—
186C2×C4⋊C4—71no—
187C2×C4⋊C4—141no—
188C2×C4⋊C4—141no—
189C2×C4⋊C4—141no—
190C2×C4⋊C4—141no—
191C2×C4⋊C4—141no—
192C2×C4⋊C4C4×D711yescharacteristic
193C2×C4⋊C4D2811yescharacteristic
194C2×C4⋊C4C22⋊D711yescharacteristic
195C2×C4⋊C4C22×D711yescharacteristic
196C2×C22⋊C4—141no—
197C2×C22⋊C4—141no—
198C2×C42—141no—
199C22⋊C8—142no—
200C22⋊C8—281no—
201#95—71no—
202#95—71no—
203#95—141no—
204#95—141no—
205#95—141no—
206#95—141no—
207C22×C7—21no—
208C22×C7—21no—
209C22×C7—21no—
210C22×C7—21no—
211C22×C7—21no—
212C22×C7—21no—
213C22×C7—21no—
214C22×C7—42no—
215C22×C7—42no—
216C22×C7#35612yes—
217C22×C7C2×#9911yescharacteristic
218C22×C7#41711yescharacteristic
219C22×C7C2×#10411yescharacteristic
220C4×C7—21no—
221C4×C7—22no—
222C4×C7—21no—
223C4×C7—41no—
224C4×C7—41no—
225C4×C7—41no—
226C4×C7—41no—
227Dic7—42no—
228Dic7—42no—
229Dic7—81no—
230Dic7—81no—
231C24(C2×D7)⋊C411yescharacteristic
232C2×Q8—281no—
233C2×Q8—561no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—81no—
244C22×C4—81no—
245C22×C4—141no—
246C22×C4—141no—
247C22×C4—141no—
248C22×C4—141no—
249C22×C4(C2×D7)⋊C411yescharacteristic
250C22×C4(C2×D7)⋊C411yescharacteristic
251C22×C4(C2×D7)⋊C411yescharacteristic
252C22×C4C2×C4×D711yescharacteristic
253C22×C4C2×D2811yescharacteristic
254C22×C4C2×C22⋊D711yescharacteristic
255M16—24no—
256M16—44no—
257M16—42no—
258M16—562no—
259C2×C8—44no—
260C2×C8—42no—
261C2×C8—282no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—281no—
267C4⋊C4—282no—
268C4⋊C4—281no—
269C4⋊C4—281no—
270C4⋊C4—282no—
271C4⋊C4—561no—
272C4⋊C4—561no—
273C22⋊C4—144no—
274C22⋊C4—281no—
275C22⋊C4—281no—
276C42—561no—
277C2×C7—21no—
278C2×C7—21no—
279C2×C7—22no—
280C2×C7—41no—
281C2×C7#150411yescharacteristic
282C2×C7#212111yescharacteristic
283C2×C7C2×#35611yescharacteristic
284C23—21no—
285C23—21no—
286C23—22no—
287C23—41no—
288C23#638011yescharacteristic
289C23#638011yescharacteristic
290C23C2×(C2×D7)⋊C411yescharacteristic
291Q8—562no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—142no—
313C2×C4—142no—
314C2×C4—281no—
315C2×C4—281no—
316C2×C4—281no—
317C2×C4—281no—
318C2×C4—281no—
319C2×C4—281no—
320C2×C4—281no—
321C2×C4—281no—
322C2×C4—281no—
323C2×C4—281no—
324C2×C4#637912yes—
325C2×C4#649511yescharacteristic
326C2×C4#650511yescharacteristic
327C8—44no—
328C8—562no—
329C7#1176811yescharacteristic, complemented, Sylow
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—42no—
338C22—42no—
339C22#8927312yes—
340C22C2×#637911yescharacteristic
341C22C2×#638011yescharacteristic
342C22#8973811yescharacteristic
343C4—21no—
344C4—21no—
345C4—22no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—282no—
351C4—282no—
352C4—561no—
353C4—561no—
354C2—21no—
355C2—21no—
356C2—22no—
357C2—41no—
358C2#1172715211yescharacteristic
359C2#1172784811yescharacteristic
360C2C2×#8927311yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC2×C7×#343C2
socleC22×C7C2×#99
prime radicalC24×C7C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenterC2×#343D7
hypocenterC7#11768
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
4. #11725301C2semidirect
5. #11725300C2semidirect
329. C7#11768semidirect

Maximal subgroups

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

subgroupindex
#117396262
C2×C7×#3432
#117293062
#117253012
#117253002
#117687