Finite Group Databasebeta

← #13264914

Subgroups — #13264914

Order 1792.

452 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 95 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#11739833C211yesmaximal, characteristic
2C7×#1799C211yesmaximal, characteristic
3#11729354C211yesmaximal, characteristic
4#11725298C212yesmaximal, complemented
5#11725296C212yesmaximal, complemented
6C2×C4×C7×D4C2211yescharacteristic
7C2×C4×Dic14C411yescharacteristic, complemented
8C2×C7×#99—21no—
9C7×#380—21no—
10#89993—21no—
11#89982—21no—
12#89982—21no—
13C2×C22⋊(C7⋊C8)—21no—
14#89745—21no—
15#89721C411yescharacteristic, complemented
16#89721C2211yescharacteristic
17#89719C411yescharacteristic, complemented
18#89719C2211yescharacteristic
19#89708C411yescharacteristic, complemented
20C7×#342C2212yes—
21#89323—21no—
22#89320C2212yes—
23#11897—71nomaximal, Sylow
24C22×C7×D4D411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C22×Dic14C2×C411yescharacteristic
28C4×C7×D4—41no—
29C4×C7×D4—41no—
30C2×C7×C4⋊C4—41no—
31C2×C7×C4⋊C4D411yescharacteristic
32C2×C7×C22⋊C4—22no—
33C2×C7×C22⋊C4C2×C411yescharacteristic
34C2×C7×C22⋊C4C2311yescharacteristic
35C2×C42×C7C2×C411yescharacteristic
36C2×C22⋊Dic7—21no—
37C2×C22⋊Dic7—21no—
38C2×C22⋊Dic7—21no—
39C2×C22⋊Dic7—21no—
40C2×C4⋊Dic7—21no—
41C2×C4⋊Dic7C2×C411yescharacteristic
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—21no—
44C2×Dic7⋊C4—21no—
45C2×C4×Dic7—21no—
46C22×C7⋊C8—41no—
47C4×Dic14—41no—
48C4×Dic14—41no—
49C7×#99—42no—
50C7×#95—41no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95C2×C411yescharacteristic
55C7⋊#95C2×C411yescharacteristic
56C22⋊(C7⋊C8)—22no—
57C22⋊(C7⋊C8)—41no—
58#2580—71no—
59#1799D711yescharacteristic
60#1459—71no—
61#1352—72no—
62#1351—72no—
63C24×C7C22⋊C411yescharacteristic
64C24×C7C2×D411yescharacteristic
65C2×C7×D4—41no—
66C2×C7×D4—41no—
67C2×C7×D4SD1612yes—
68C2×C7×D4Q1612yes—
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—
85C2×Dic14—41no—
86C2×Dic14—42no—
87C7×C4⋊C4—41no—
88C7×C4⋊C4—82no—
89C7×C22⋊C4—41no—
90C7×C22⋊C4—41no—
91C7×C22⋊C4—42no—
92C7×C22⋊C4—42no—
93C42×C7—21no—
94C42×C7—21no—
95C22⋊Dic7—42no—
96C22⋊Dic7—42no—
97C22⋊Dic7—81no—
98C22⋊Dic7—81no—
99C4⋊Dic7—42no—
100C4⋊Dic7—41no—
101Dic7⋊C4—41no—
102Dic7⋊C4—41no—
103Dic7⋊C4—81no—
104Dic7⋊C4—81no—
105C4×Dic7—42no—
106C2×C7⋊C8—42no—
107C2×C7⋊C8—82no—
108C2×C4×Q8—71no—
109C2×C4×D4C2×D711yescharacteristic
110C2×#99—21no—
111C2×C22⋊C8—141no—
112#399—71no—
113#399—71no—
114#393—71no—
115#393—71no—
116#390—141no—
117#389—141no—
118#385—141no—
119#385—141no—
120#382—71no—
121#380—21no—
122#342C2×D712yes—
123#324—141no—
124#323—72no—
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×C7#10312yes—
134C23×C7C2×C22⋊C411yescharacteristic
135C23×C7C2×SD1611yescharacteristic
136C23×C7C2×Q1611yescharacteristic
137C7×D4—42no—
138C7×D4—42no—
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×C4×C7#10312yes—
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—
169C2×Dic7—41no—
170Dic14—42no—
171Dic14—42no—
172C7⋊C8—82no—
173C22×Q8—71no—
174C22×D4C22⋊D711yescharacteristic
175C23×C4D2811yescharacteristic
176C23×C4C22⋊D711yescharacteristic
177C22×C8—281no—
178C4×Q8—281no—
179C4×Q8—281no—
180C4×D4—41no—
181C4×D4—41no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4—71no—
184C2×C4⋊C4—141no—
185C2×C4⋊C4—141no—
186C2×C4⋊C4—141no—
187C2×C4⋊C4—141no—
188C2×C4⋊C4D2811yescharacteristic
189C2×C22⋊C4—22no—
190C2×C22⋊C4—141no—
191C2×C22⋊C4—141no—
192C2×C22⋊C4—141no—
193C2×C22⋊C4—141no—
194C2×C22⋊C4C4×D711yescharacteristic
195C2×C22⋊C4C22×D711yescharacteristic
196C2×C42—141no—
197C2×C42C4×D711yescharacteristic
198#99—42no—
199C22⋊C8—142no—
200C22⋊C8—281no—
201#95—41no—
202#95—71no—
203#95—71no—
204#95—141no—
205#95—141no—
206#95—141no—
207C22×C7—21no—
208C22×C7—21no—
209C22×C7—21no—
210C22×C7—22no—
211C22×C7—21no—
212C22×C7—42no—
213C22×C7—41no—
214C22×C7—41no—
215C22×C7—41no—
216C22×C7—41no—
217C22×C7—41no—
218C22×C7—41no—
219C22×C7—81no—
220C22×C7—81no—
221C22×C7C2×#9911yescharacteristic
222C22×C7C2×#10311yescharacteristic
223C22×C7#42111yescharacteristic
224C4×C7—21no—
225C4×C7—21no—
226C4×C7—22no—
227C4×C7—41no—
228C4×C7—41no—
229C4×C7—41no—
230C4×C7—162no—
231Dic7—42no—
232Dic7—81no—
233Dic7—81no—
234Dic7—81no—
235C24(C2×D7)⋊C411yescharacteristic
236C24C2×C22⋊D711yescharacteristic
237C2×Q8—281no—
238C2×Q8—282no—
239C2×D4—41no—
240C2×D4—41no—
241C2×D4#114212yes—
242C2×D4#114412yes—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—42no—
248C22×C4—81no—
249C22×C4—81no—
250C22×C4—141no—
251C22×C4—141no—
252C22×C4—141no—
253C22×C4—141no—
254C22×C4(C2×D7)⋊C411yescharacteristic
255C22×C4(C2×D7)⋊C411yescharacteristic
256C22×C4(C2×D7)⋊C411yescharacteristic
257C22×C4C2×C4×D711yescharacteristic
258C22×C4C2×D2811yescharacteristic
259C2×C8—282no—
260C2×C8—562no—
261C4⋊C4—41no—
262C4⋊C4—82no—
263C4⋊C4—281no—
264C4⋊C4—282no—
265C4⋊C4—281no—
266C4⋊C4—281no—
267C4⋊C4—561no—
268C4⋊C4—561no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—282no—
274C22⋊C4—282no—
275C22⋊C4—561no—
276C22⋊C4—561no—
277C42—21no—
278C42—21no—
279C42—282no—
280C2×C7—21no—
281C2×C7—21no—
282C2×C7—41no—
283C2×C7—42no—
284C2×C7—41no—
285C2×C7#152011yescharacteristic
286C2×C7#212011yescharacteristic
287C2×C7#212711yescharacteristic
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23#638412yes—
297C23C2×(C2×D7)⋊C411yescharacteristic
298C23C2×#114211yescharacteristic
299C23C2×#114411yescharacteristic
300Q8—282no—
301Q8—282no—
302D4—42no—
303D4—42no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—82no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—142no—
321C2×C4—281no—
322C2×C4—281no—
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#638011yescharacteristic
333C2×C4#638011yescharacteristic
334C2×C4#638412yes—
335C8—562no—
336C7#1189711yescharacteristic, complemented, Sylow
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—42no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—81no—
351C22C2×#638011yescharacteristic
352C22C2×#638411yescharacteristic
353C22#8977711yescharacteristic
354C4—21no—
355C4—21no—
356C4—22no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—162no—
361C4—282no—
362C4—561no—
363C4—561no—
364C4—561no—
365C2—21no—
366C2—21no—
367C2—41no—
368C2—41no—
369C2—42no—
370C2#1172726411yescharacteristic
371C2#1172777311yescharacteristic
372C2#1172781011yescharacteristic
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#11897
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. #11725296C2semidirect
7. C2×C4×Dic14C4semidirect
15. #89721C4semidirect
17. #89719C4semidirect
19. #89708C4semidirect
336. C7#11897semidirect

Maximal subgroups

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

subgroupindex
#117398332
C7×#17992
#117293542
#117252982
#117252962
#118977