Finite Group Databasebeta

← #13264590

Subgroups — #13264590

Order 1792.

418 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 79 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#11739836C211yesmaximal, characteristic
2C7×#1799C211yesmaximal, characteristic
3#11729356C211yesmaximal, characteristic
4#11725298C212yesmaximal, complemented
5#11725297C212yesmaximal, complemented
6C2×C4×C7×D4C2211yescharacteristic
7C2×#6433C411yescharacteristic, complemented
8C2×C7×#99—21no—
9C7×#380—21no—
10#89994—21no—
11#89982—21no—
12#89982—21no—
13#89979—21no—
14#89752—21no—
15#89725C411yescharacteristic, complemented
16#89725C2211yescharacteristic
17#89721C411yescharacteristic, complemented
18#89721C2211yescharacteristic
19#89709C411yescharacteristic, complemented
20C7×#342C2212yes—
21#89323—21no—
22#89320C2212yes—
23#11827—71nomaximal, Sylow
24C22×C7×D4D411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C4×C7×D4—41no—
28C4×C7×D4—41no—
29C2×C7×C4⋊C4—41no—
30C2×C7×C4⋊C4D411yescharacteristic
31C2×C7×C22⋊C4—22no—
32C2×C7×C22⋊C4C2×C411yescharacteristic
33C2×C7×C22⋊C4C2311yescharacteristic
34C2×C42×C7C2×C411yescharacteristic
35C2×C22⋊Dic7—21no—
36C2×C22⋊Dic7—21no—
37C2×C22⋊Dic7—21no—
38C2×C22⋊Dic7—21no—
39C2×C4⋊Dic7C2×C411yescharacteristic
40C2×C4⋊Dic7C2×C411yescharacteristic
41C2×Dic7⋊C4—21no—
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—21no—
44C2×Dic7⋊C4—21no—
45C2×#1136—41no—
46#6433—41no—
47#6433—41no—
48C7×#99—42no—
49C7×#95—41no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95C2×C411yescharacteristic
55C7⋊#95C2×C411yescharacteristic
56C22⋊(C7⋊C8)—22no—
57C22⋊(C7⋊C8)—41no—
58#2633—71no—
59#1799D711yescharacteristic
60#1465—71no—
61#1352—72no—
62#1344—72no—
63C24×C7C22⋊C411yescharacteristic
64C24×C7C2×D411yescharacteristic
65C2×C7×D4—21no—
66C2×C7×D4—21no—
67C2×C7×D4—41no—
68C2×C7×D4—41no—
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—42no—
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×Dic7—21no—
82C22×Dic7—21no—
83C22×Dic7—21no—
84C22×Dic7—21no—
85C7×C4⋊C4—41no—
86C7×C4⋊C4—82no—
87C7×C22⋊C4—41no—
88C7×C22⋊C4—41no—
89C7×C22⋊C4—42no—
90C7×C22⋊C4—42no—
91C42×C7—21no—
92C42×C7—21no—
93C22⋊Dic7—42no—
94C22⋊Dic7—41no—
95C22⋊Dic7—41no—
96C22⋊Dic7—81no—
97C22⋊Dic7—81no—
98C4⋊Dic7—41no—
99C4⋊Dic7—41no—
100Dic7⋊C4—42no—
101Dic7⋊C4—41no—
102Dic7⋊C4—41no—
103Dic7⋊C4—81no—
104Dic7⋊C4—81no—
105#1136—82no—
106C2×C7⋊C8—42no—
107C2×#125—71no—
108C2×C4×D4C2×D711yescharacteristic
109C2×#99—21no—
110#407—141no—
111#399—71no—
112#399—71no—
113#398—141no—
114#397—71no—
115#397—71no—
116#394—141no—
117#385—141no—
118#385—141no—
119#383—71no—
120#380—21no—
121#342C2×D712yes—
122#324—141no—
123#323—72no—
124C23×C7—21no—
125C23×C7—21no—
126C23×C7—21no—
127C23×C7—21no—
128C23×C7—21no—
129C23×C7—41no—
130C23×C7—41no—
131C23×C7—41no—
132C23×C7—41no—
133C23×C7C2×C22⋊C411yescharacteristic
134C23×C7AGL(1,ℤ/8)11yescharacteristic
135C23×C7#13711yescharacteristic
136C7×D4—42no—
137C7×D4—42no—
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—41no—
145C2×C4×C7—42no—
146C2×C4×C7—42no—
147C2×C4×C7—41no—
148C2×C4×C7—41no—
149C2×C4×C7—41no—
150C2×C4×C7—81no—
151C2×C4×C7—81no—
152C2×C4×C7—82no—
153C2×C4×C7—82no—
154C2×C4×C7—82no—
155C2×C4×C7#9911yescharacteristic
156C2×C4×C7#9911yescharacteristic
157C2×Dic7—41no—
158C2×Dic7—41no—
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—
169C7⋊C8—82no—
170C22×D4C22⋊D711yescharacteristic
171C23×C4D2811yescharacteristic
172C23×C4C22⋊D711yescharacteristic
173C2×M16—281no—
174#125—281no—
175#125—281no—
176C4×D4—41no—
177C4×D4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—71no—
180C2×C4⋊C4—71no—
181C2×C4⋊C4—141no—
182C2×C4⋊C4—141no—
183C2×C4⋊C4—141no—
184C2×C4⋊C4—141no—
185C2×C4⋊C4D2811yescharacteristic
186C2×C22⋊C4—22no—
187C2×C22⋊C4—141no—
188C2×C22⋊C4—141no—
189C2×C22⋊C4—141no—
190C2×C22⋊C4—141no—
191C2×C22⋊C4C4×D711yescharacteristic
192C2×C22⋊C4C22×D711yescharacteristic
193C2×C42C4×D711yescharacteristic
194#99—42no—
195C22⋊C8—142no—
196C22⋊C8—281no—
197#95—41no—
198#95—71no—
199#95—71no—
200#95—141no—
201#95—141no—
202#95—141no—
203#95—141no—
204C22×C7—21no—
205C22×C7—21no—
206C22×C7—21no—
207C22×C7—21no—
208C22×C7—41no—
209C22×C7—41no—
210C22×C7—42no—
211C22×C7—41no—
212C22×C7—41no—
213C22×C7—41no—
214C22×C7—41no—
215C22×C7—41no—
216C22×C7—81no—
217C22×C7—81no—
218C22×C7C2×#9911yescharacteristic
219C22×C7#41711yescharacteristic
220C22×C7#42111yescharacteristic
221C4×C7—21no—
222C4×C7—21no—
223C4×C7—41no—
224C4×C7—41no—
225C4×C7—41no—
226C4×C7—41no—
227C4×C7—162no—
228Dic7—81no—
229Dic7—81no—
230Dic7—81no—
231Dic7—81no—
232C24(C2×D7)⋊C411yescharacteristic
233C24C2×C22⋊D711yescharacteristic
234C2×D4—21no—
235C2×D4—21no—
236C2×D4—41no—
237C2×D4—41no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—42no—
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
254M16—562no—
255C2×C8—282no—
256C4⋊C4—41no—
257C4⋊C4—82no—
258C4⋊C4—281no—
259C4⋊C4—281no—
260C4⋊C4—282no—
261C4⋊C4—281no—
262C4⋊C4—281no—
263C4⋊C4—561no—
264C4⋊C4—561no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—42no—
268C22⋊C4—42no—
269C22⋊C4—282no—
270C22⋊C4—281no—
271C22⋊C4—281no—
272C22⋊C4—561no—
273C22⋊C4—561no—
274C42—21no—
275C42—21no—
276C2×C7—21no—
277C2×C7—21no—
278C2×C7—41no—
279C2×C7—41no—
280C2×C7—81no—
281C2×C7#151311yescharacteristic
282C2×C7#212311yescharacteristic
283C2×C7#212711yescharacteristic
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23C2×(C2×D7)⋊C411yescharacteristic
294C23#649511yescharacteristic
295C23#650511yescharacteristic
296D4—42no—
297D4—42no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—82no—
313C2×C4—82no—
314C2×C4—82no—
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—281no—
325C2×C4—281no—
326C2×C4—281no—
327C2×C4#638011yescharacteristic
328C2×C4#638011yescharacteristic
329C8—562no—
330C7#1182711yescharacteristic, complemented, Sylow
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—42no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—81no—
344C22—81no—
345C22C2×#638011yescharacteristic
346C22#8973811yescharacteristic
347C22#8977711yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—162no—
355C4—561no—
356C4—561no—
357C4—561no—
358C4—561no—
359C2—21no—
360C2—21no—
361C2—41no—
362C2—41no—
363C2—81no—
364C2#1172726211yescharacteristic
365C2#1172777311yescharacteristic
366C2#1172781211yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C22⋊C4C22×D7
FittingC7×#1799C2
socleC22×C7C2×#99
prime radicalC22×C7×D4D4
cosocleC2×C7×C22⋊C4C23
hypercenter#1799D7
hypocenterC7#11827
LCSG ▷ C22×C4×C7 ▷ C23×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
4. #11725298C2semidirect
5. #11725297C2semidirect
7. C2×#6433C4semidirect
15. #89725C4semidirect
17. #89721C4semidirect
19. #89709C4semidirect
330. C7#11827semidirect

Maximal subgroups

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

subgroupindex
#117398362
C7×#17992
#117293562
#117252982
#117252972
#118277