Finite Group Databasebeta

← #13272447

Subgroups — #13272447

Order 1792.

484 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 99 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#11739832C211yesmaximal, characteristic
2C7×#1799C211yesmaximal, characteristic
3C4×#6407C211yesmaximal, characteristic
4#11725500C212yesmaximal
5#11725500C212yesmaximal
6C2×C4×C7×D4C2211yescharacteristic
7C22×Dic7⋊C4C411yescharacteristic, complemented
8C2×C7×#99C2212yes—
9C7×#380—21no—
10#89992C2211yescharacteristic
11#89992C2211yescharacteristic
12C2×#6407C2212yes—
13#89984C411yescharacteristic, complemented
14#89982—21no—
15#89756—21no—
16#89720—21no—
17#89718C411yescharacteristic, complemented
18#89718C411yescharacteristic, complemented
19#89705—21no—
20C4×#1136—21no—
21C7×#342—21no—
22#89325—21no—
23#13294—71nomaximal, Sylow
24C22×C7×D4C2311yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C23×Dic7C2×C411yescharacteristic
28C23×Dic7C2×C411yescharacteristic
29C4×C7×D4—41no—
30C4×C7×D4—41no—
31C2×C7×C4⋊C4—41no—
32C2×C7×C4⋊C4D411yescharacteristic
33C2×C7×C22⋊C4—22no—
34C2×C7×C22⋊C4C2×C411yescharacteristic
35C2×C7×C22⋊C4D411yescharacteristic
36C2×C42×C7D411yescharacteristic
37C2×C22⋊Dic7—21no—
38C2×C22⋊Dic7—21no—
39C2×C22⋊Dic7C2×C411yescharacteristic
40C2×C22⋊Dic7C2×C411yescharacteristic
41C2×C4⋊Dic7—21no—
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—21no—
44C2×Dic7⋊C4—21no—
45C2×Dic7⋊C4—21no—
46C2×Dic7⋊C4—41no—
47C2×Dic7⋊C4—41no—
48C2×#1136—22no—
49C7×#99—24no—
50C7×#95—41no—
51#6407—22no—
52#6407Q814yes—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C7⋊#95—21no—
56C7⋊#95—21no—
57C7⋊#95—21no—
58#6377—41no—
59C4×C7⋊C8—41no—
60#2579—71no—
61#1799D711yescharacteristic
62C4×#100—71no—
63#1390—72no—
64#1390—72no—
65C24×C7C22×C411yescharacteristic
66C24×C7C2×D411yescharacteristic
67C2×C7×D4—41no—
68C2×C7×D4—41no—
69C2×C7×D4C2×Q812yes—
70C2×C7×D4#4112yes—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—21no—
74C22×C4×C7—21no—
75C22×C4×C7—42no—
76C22×C4×C7—81no—
77C22×C4×C7—81no—
78C22×C4×C7C22⋊C411yescharacteristic
79C22×C4×C7C22⋊C411yescharacteristic
80C22×C4×C7C22⋊C411yescharacteristic
81C22×C4×C7C22⋊C411yescharacteristic
82C22×C4×C7C2×D411yescharacteristic
83C22×Dic7—21no—
84C22×Dic7—21no—
85C22×Dic7—21no—
86C22×Dic7—21no—
87C22×Dic7—42no—
88C22×Dic7—41no—
89C22×Dic7—41no—
90C22×Dic7—81no—
91C7×C4⋊C4—41no—
92C7×C4⋊C4—82no—
93C7×C22⋊C4—41no—
94C7×C22⋊C4—41no—
95C7×C22⋊C4—42no—
96C7×C22⋊C4—42no—
97C42×C7—21no—
98C42×C7—21no—
99C22⋊Dic7—42no—
100C22⋊Dic7—41no—
101C22⋊Dic7—41no—
102C22⋊Dic7—81no—
103C4⋊Dic7—81no—
104Dic7⋊C4—42no—
105Dic7⋊C4—42no—
106Dic7⋊C4—41no—
107Dic7⋊C4—41no—
108Dic7⋊C4—81no—
109#1136—24no—
110#1136—42no—
111C2×C7⋊C8—42no—
112C2×C4×D4C2×D711yescharacteristic
113C22×C4⋊C4—71no—
114C2×#100—72no—
115C2×#99C2×D712yes—
116C4×M16—141no—
117#398—141no—
118#396—141no—
119#387—141no—
120#386—71no—
121#386—71no—
122#385—71no—
123#385—71no—
124#385—141no—
125#380—21no—
126#380—71no—
127#343—141no—
128#342—21no—
129C23×C7—21no—
130C23×C7—21no—
131C23×C7—21no—
132C23×C7—21no—
133C23×C7—41no—
134C23×C7—41no—
135C23×C7—41no—
136C23×C7—41no—
137C23×C7C2×C22⋊C411yescharacteristic
138C23×C7C4×Q812yes—
139C23×C7#12411yescharacteristic
140C23×C7C4⋊Q811yescharacteristic
141C7×D4—42no—
142C7×D4—42no—
143C2×C4×C7—21no—
144C2×C4×C7—21no—
145C2×C4×C7—21no—
146C2×C4×C7—21no—
147C2×C4×C7—21no—
148C2×C4×C7—41no—
149C2×C4×C7—42no—
150C2×C4×C7—41no—
151C2×C4×C7—41no—
152C2×C4×C7—41no—
153C2×C4×C7—81no—
154C2×C4×C7—81no—
155C2×C4×C7—81no—
156C2×C4×C7—82no—
157C2×C4×C7—82no—
158C2×C4×C7—82no—
159C2×C4×C7#9911yescharacteristic
160C2×C4×C7#9911yescharacteristic
161C2×C4×C7C22⋊Q812yes—
162C2×Dic7—22no—
163C2×Dic7—41no—
164C2×Dic7—42no—
165C2×Dic7—41no—
166C2×Dic7—42no—
167C2×Dic7—41no—
168C2×Dic7—41no—
169C2×Dic7—41no—
170C2×Dic7—41no—
171C2×Dic7—41no—
172C2×Dic7—41no—
173C2×Dic7—41no—
174C2×Dic7—41no—
175C2×Dic7—41no—
176C2×Dic7—82no—
177C7⋊C8—44no—
178C22×D4C22×D711yescharacteristic
179C23×C4—71no—
180C23×C4—71no—
181C23×C4C4×D711yescharacteristic
182C23×C4C22⋊D711yescharacteristic
183C2×M16—142no—
184C4×D4—41no—
185C4×D4—41no—
186C2×C4⋊C4—41no—
187C2×C4⋊C4—141no—
188C2×C4⋊C4—141no—
189C2×C4⋊C4—141no—
190C2×C4⋊C4—141no—
191C2×C4⋊C4—141no—
192C2×C4⋊C4—281no—
193C2×C4⋊C4—281no—
194C2×C4⋊C4D2811yescharacteristic
195C2×C22⋊C4—22no—
196C2×C22⋊C4—71no—
197C2×C22⋊C4—71no—
198C2×C22⋊C4—141no—
199C2×C22⋊C4—141no—
200C2×C22⋊C4C4×D711yescharacteristic
201C2×C22⋊C4C22⋊D711yescharacteristic
202C2×C42D2811yescharacteristic
203#100—74no—
204#100—142no—
205#99—24no—
206#97—281no—
207C4×C8—281no—
208#95—41no—
209#95—141no—
210#95—141no—
211#95—141no—
212#95—141no—
213#95—141no—
214C22×C7—21no—
215C22×C7—21no—
216C22×C7—21no—
217C22×C7—22no—
218C22×C7—21no—
219C22×C7—42no—
220C22×C7—41no—
221C22×C7—41no—
222C22×C7—42no—
223C22×C7—41no—
224C22×C7—41no—
225C22×C7—41no—
226C22×C7—41no—
227C22×C7—81no—
228C22×C7#39111yescharacteristic
229C22×C7C2×#9911yescharacteristic
230C22×C7#41011yescharacteristic
231C4×C7—21no—
232C4×C7—21no—
233C4×C7—22no—
234C4×C7—41no—
235C4×C7—41no—
236C4×C7—41no—
237C4×C7—162no—
238Dic7—42no—
239Dic7—81no—
240Dic7—81no—
241Dic7—81no—
242C24C2×C4×D711yescharacteristic
243C24C2×C22⋊D711yescharacteristic
244C2×D4—41no—
245C2×D4—41no—
246C2×D4#115912yes—
247C2×D4Q8×D712yes—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—42no—
253C22×C4—81no—
254C22×C4—81no—
255C22×C4—141no—
256C22×C4—141no—
257C22×C4—141no—
258C22×C4—141no—
259C22×C4—282no—
260C22×C4—281no—
261C22×C4—281no—
262C22×C4—561no—
263C22×C4(C2×D7)⋊C411yescharacteristic
264C22×C4(C2×D7)⋊C411yescharacteristic
265C22×C4(C2×D7)⋊C411yescharacteristic
266C22×C4(C2×D7)⋊C411yescharacteristic
267C22×C4C2×D2811yescharacteristic
268M16—144no—
269M16—282no—
270C2×C8—282no—
271C4⋊C4—41no—
272C4⋊C4—82no—
273C4⋊C4—282no—
274C4⋊C4—282no—
275C4⋊C4—281no—
276C4⋊C4—281no—
277C4⋊C4—561no—
278C4⋊C4—561no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C22⋊C4—282no—
284C22⋊C4—281no—
285C22⋊C4—281no—
286C22⋊C4—561no—
287C42—21no—
288C42—21no—
289C2×C7—21no—
290C2×C7—21no—
291C2×C7—41no—
292C2×C7—42no—
293C2×C7—41no—
294C2×C7#199611yescharacteristic
295C2×C7#212011yescharacteristic
296C2×C7#212111yescharacteristic
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23#645012yes—
306C23C2×(C2×D7)⋊C411yescharacteristic
307C23#649911yescharacteristic
308C23#650711yescharacteristic
309D4—42no—
310D4—42no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—142no—
328C2×C4—281no—
329C2×C4—282no—
330C2×C4—281no—
331C2×C4—282no—
332C2×C4—281no—
333C2×C4—281no—
334C2×C4—281no—
335C2×C4—281no—
336C2×C4—281no—
337C2×C4—281no—
338C2×C4—281no—
339C2×C4—281no—
340C2×C4—281no—
341C2×C4—562no—
342C2×C4#638011yescharacteristic
343C2×C4#638011yescharacteristic
344C2×C4#646012yes—
345C8—284no—
346C7#1329411yescharacteristic, complemented, Sylow
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—21no—
352C22—42no—
353C22—41no—
354C22—41no—
355C22—42no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22C2×#638011yescharacteristic
362C22#8974611yescharacteristic
363C22#8977811yescharacteristic
364C4—21no—
365C4—21no—
366C4—22no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—162no—
371C4—282no—
372C4—561no—
373C4—561no—
374C4—561no—
375C2—21no—
376C2—21no—
377C2—41no—
378C2—42no—
379C2—41no—
380C2#1172728311yescharacteristic
381C2#1172776911yescharacteristic
382C2#1172781011yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC24×C7C22×C4
FrattiniC22×D4C22×D7
FittingC7×#1799C2
socleC22×C7C2×#99
prime radical, cosocleC22×C7×D4C23
hypercenter#1799D7
hypocenterC7#13294
LCSG ▷ C24×C7 ▷ C22×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
7. C22×Dic7⋊C4C4semidirect
13. #89984C4semidirect
17. #89718C4semidirect
18. #89718C4semidirect
346. C7#13294semidirect

Maximal subgroups

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

subgroupindex
#117398322
C7×#17992
C4×#64072
#117255002
#132947