Finite Group Databasebeta

← #13263370

Subgroups — #13263370

Order 1792.

440 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 83 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#11739625C211yesmaximal, characteristic
2C2×C7×#324C211yesmaximal, characteristic, complemented
3#11729306C211yesmaximal, characteristic, complemented
4#11725260C212yesmaximal, complemented
5#11725258C212yesmaximal, complemented
6C22×C7×C4⋊C4C2211yescharacteristic
7C2×#6493C411yescharacteristic
8C2×C7×C22⋊C8—21no—
9#89985—21no—
10#89985—21no—
11C4×C22⋊Dic7C411yescharacteristic
12#89979—21no—
13#89765—21no—
14#89765—21no—
15#89760C411yescharacteristic
16#89760C2211yescharacteristic
17#89749C411yescharacteristic
18#89749C2211yescharacteristic
19C7×#324—21no—
20C7×#324C2212yes—
21#89323—21no—
22#89323C2212yes—
23#11553—71nomaximal, Sylow
24C23×C4×C7C2×C411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C22×C22⋊D7—21no—
28C22×D28C2×C411yescharacteristic
29C22×C7×C8—41no—
30C2×C7×C4⋊C4—41no—
31C2×C7×C4⋊C4—41no—
32C2×C7×C4⋊C4C2×C411yescharacteristic
33C2×C7×C4⋊C4D411yescharacteristic
34C2×C7×C4⋊C4D411yescharacteristic
35C2×C7×C4⋊C4C2311yescharacteristic
36C2×C22⋊Dic7—21no—
37#6493—41no—
38#6493—41no—
39C2×(C2×D7)⋊C4—21no—
40C2×(C2×D7)⋊C4—21no—
41C2×(C2×D7)⋊C4—21no—
42C2×(C2×D7)⋊C4—21no—
43C2×(C2×D7)⋊C4—21no—
44C2×C4⋊Dic7C2×C411yescharacteristic
45C2×C4×Dic7C2×C411yescharacteristic
46C2×C4×Dic7C2×C411yescharacteristic
47C2×#1136—41no—
48C7×C22⋊C8—22no—
49C7×C22⋊C8—41no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C22⋊(C7⋊C8)—22no—
56C22⋊(C7⋊C8)—41no—
57#2504—71no—
58#1463—71no—
59C2×#324D711yescharacteristic, complemented
60#1324—72no—
61#1318—72no—
62C24×C7C22⋊C411yescharacteristic
63C23×D7—21no—
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7—21no—
67C22×C4×C7—21no—
68C22×C4×C7—21no—
69C22×C4×C7—21no—
70C22×C4×C7—22no—
71C22×C4×C7—41no—
72C22×C4×C7—81no—
73C22×C4×C7—81no—
74C22×C4×C7C22⋊C411yescharacteristic
75C22×C4×C7C22⋊C411yescharacteristic
76C22×C4×C7C22⋊C411yescharacteristic
77C22×C4×C7C22×C411yescharacteristic
78C22×C4×C7C2×D411yescharacteristic
79C22×C4×C7C2×D411yescharacteristic
80C2×C22⋊D7—42no—
81C2×C22⋊D7—42no—
82C2×C22⋊D7—41no—
83C2×C22⋊D7—41no—
84C22×Dic7—21no—
85C22×Dic7—21no—
86C22×Dic7—21no—
87C2×D28—22no—
88C2×D28—41no—
89C2×D28—41no—
90C2×C7×C8—42no—
91C2×C7×C8—82no—
92C7×C4⋊C4—41no—
93C7×C4⋊C4—41no—
94C7×C4⋊C4—41no—
95C7×C4⋊C4—41no—
96C22⋊Dic7—42no—
97(C2×D7)⋊C4—42no—
98(C2×D7)⋊C4—81no—
99(C2×D7)⋊C4—81no—
100(C2×D7)⋊C4—81no—
101(C2×D7)⋊C4—81no—
102C4⋊Dic7—41no—
103C4×Dic7—22no—
104C4×Dic7—41no—
105#1136—82no—
106C2×C7⋊C8—42no—
107C2×#121—71no—
108C22×C4⋊C4C2×D711yescharacteristic
109#407—141no—
110C2×C22⋊C8—21no—
111#397—141no—
112#397—141no—
113#390—71no—
114#390—71no—
115#386—141no—
116#386—141no—
117#382—71no—
118#382—71no—
119C4×C22⋊C4—71no—
120#324—21no—
121#324—72no—
122#324—141no—
123#324C2×D712yes—
124C23×C7—22no—
125C23×C7—21no—
126C23×C7—21no—
127C23×C7—41no—
128C23×C7#9911yescharacteristic
129C23×C7#9911yescharacteristic
130C23×C7C2×C22⋊C411yescharacteristic
131C22×D7—41no—
132C22×D7—41no—
133C22×D7—41no—
134C22×D7—41no—
135C22×D7—41no—
136C22×D7—41no—
137C22×D7—41no—
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—21no—
147C2×C4×C7—42no—
148C2×C4×C7—42no—
149C2×C4×C7—42no—
150C2×C4×C7—42no—
151C2×C4×C7—41no—
152C2×C4×C7—41no—
153C2×C4×C7—41no—
154C2×C4×C7—41no—
155C2×C4×C7—81no—
156C2×C4×C7—81no—
157C2×C4×C7#13112yes—
158C22⋊D7—82no—
159C22⋊D7—82no—
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—
169D28—82no—
170C7×C8—82no—
171C7⋊C8—82no—
172C22×D4—71no—
173C22×D4—141no—
174C23×C4C4×D711yescharacteristic
175C23×C4D2811yescharacteristic
176C23×C4C22⋊D711yescharacteristic
177C2×M16—281no—
178C22×C8—41no—
179#121—281no—
180#121—281no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4—71no—
184C2×C4⋊C4C4×D711yescharacteristic
185C2×C4⋊C4D2811yescharacteristic
186C2×C4⋊C4C22⋊D711yescharacteristic
187C2×C4⋊C4C22×D711yescharacteristic
188C2×C22⋊C4—141no—
189C2×C22⋊C4—141no—
190C2×C22⋊C4—141no—
191C2×C22⋊C4—141no—
192C2×C22⋊C4—141no—
193C2×C22⋊C4—141no—
194C2×C42—71no—
195C2×C42—71no—
196C22⋊C8—22no—
197C22⋊C8—41no—
198C22⋊C8—142no—
199C22⋊C8—281no—
200#95—141no—
201#95—141no—
202#95—141no—
203#95—141no—
204#95—141no—
205C22×C7—21no—
206C22×C7—21no—
207C22×C7—21no—
208C22×C7—21no—
209C22×C7—21no—
210C22×C7—21no—
211C22×C7—21no—
212C22×C7—42no—
213C22×C7—42no—
214C22×C7#35512yes—
215C22×C7#40811yescharacteristic
216C22×C7C2×#9911yescharacteristic
217C22×C7#41311yescharacteristic
218C2×D7—81no—
219C2×D7—81no—
220C2×D7—81no—
221C2×D7—81no—
222C2×D7—81no—
223C2×D7—81no—
224C2×D7—81no—
225C4×C7—22no—
226C4×C7—41no—
227C4×C7—41no—
228C4×C7—41no—
229C4×C7—41no—
230C4×C7—41no—
231Dic7—81no—
232Dic7—81no—
233Dic7—81no—
234C24—141no—
235C24(C2×D7)⋊C411yescharacteristic
236C2×D4—142no—
237C2×D4—281no—
238C2×D4—281no—
239C2×D4—282no—
240C2×D4—282no—
241C2×D4—281no—
242C2×D4—281no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—41no—
251C22×C4—81no—
252C22×C4—81no—
253C22×C4—141no—
254C22×C4—141no—
255C22×C4—141no—
256C22×C4(C2×D7)⋊C411yescharacteristic
257C22×C4(C2×D7)⋊C411yescharacteristic
258C22×C4(C2×D7)⋊C411yescharacteristic
259C22×C4C2×C4×D711yescharacteristic
260C22×C4C2×D2811yescharacteristic
261C22×C4C2×C22⋊D711yescharacteristic
262M16—562no—
263C2×C8—42no—
264C2×C8—82no—
265C2×C8—282no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—281no—
271C22⋊C4—282no—
272C22⋊C4—282no—
273C22⋊C4—561no—
274C22⋊C4—561no—
275C22⋊C4—561no—
276C22⋊C4—561no—
277C42—142no—
278C42—281no—
279C2×C7—21no—
280C2×C7—21no—
281C2×C7—22no—
282C2×C7—41no—
283C2×C7#146811yescharacteristic
284C2×C7#212711yescharacteristic
285C2×C7C2×#35511yescharacteristic
286D7—161no—
287C23—21no—
288C23—21no—
289C23—22no—
290C23—41no—
291C23—281no—
292C23—281no—
293C23—281no—
294C23—281no—
295C23—281no—
296C23—281no—
297C23—281no—
298C23#638011yescharacteristic
299C23#638011yescharacteristic
300C23C2×(C2×D7)⋊C411yescharacteristic
301D4—562no—
302D4—562no—
303D4—562no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—281no—
324C2×C4—281no—
325C2×C4—281no—
326C2×C4—281no—
327C2×C4—281no—
328C2×C4—281no—
329C2×C4—281no—
330C2×C4—281no—
331C2×C4—281no—
332C2×C4#646412yes—
333C8—82no—
334C8—562no—
335C7#1155311yescharacteristic, complemented, Sylow
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—42no—
344C22—42no—
345C22—561no—
346C22—561no—
347C22—561no—
348C22—561no—
349C22—561no—
350C22—561no—
351C22—561no—
352C22#8927212yes—
353C22C2×#638011yescharacteristic
354C22#8988211yescharacteristic
355C22#8990411yescharacteristic
356C4—22no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—561no—
363C4—561no—
364C4—561no—
365C2—21no—
366C2—21no—
367C2—22no—
368C2—41no—
369C2—1121no—
370C2#1172767411yescharacteristic
371C2#1172777311yescharacteristic
372C2C2×#8927211yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC2×C7×#324C2
socleC22×C7C2×#99
prime radicalC2×#6493C4
cosocleC2×C7×C4⋊C4C23
hypercenterC2×#324D7
hypocenterC7#11553
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. C2×C7×#324C2semidirect
3. #11729306C2semidirect
4. #11725260C2semidirect
5. #11725258C2semidirect
59. C2×#324D7semidirect
335. C7#11553semidirect

Maximal subgroups

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

subgroupindex
#117396252
C2×C7×#3242
#117293062
#117252602
#117252582
#115537