Finite Group Databasebeta

← #13249552

Subgroups — #13249552

Order 1792.

946 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2848C211yesmaximal, characteristic
2C2×#89984C211yesmaximal, characteristic
3#11729880C211yesmaximal, characteristic
4C2×#89333C212yesmaximal, complemented
5#11725430C212yesmaximal, complemented
6C24×C4×C7C2211yescharacteristic
7C2×C7×C22⋊Q8C412yescomplemented
8C2×C7×C22⋊Q8C2211yescharacteristic
9C22×C22⋊Dic7—21no—
10C22×C4⋊Dic7—21no—
11C7×#385—21no—
12C7×#385—22no—
13C7×#380C412yescomplemented
14C7×#380C2211yescharacteristic
15C7×#379—21no—
16#89984—24no—
17C2×C7⋊#95C2212yes—
18C2×C22⋊(C7⋊C8)—22no—
19C2×C22⋊(C7⋊C8)C2212yes—
20#89333—24no—
21#9151—71nomaximal, Sylow
22C25×C7D411yescharacteristic
23C22×C7×Q8C2×C411yescharacteristic
24C23×C4×C7—22no—
25C23×C4×C7—22no—
26C23×C4×C7—44no—
27C23×C4×C7C2×C412yes—
28C23×C4×C7D411yescharacteristic
29C23×C4×C7D412yes—
30C23×C4×C7C2311yescharacteristic
31C23×Dic7—22no—
32C7×C22⋊Q8—22no—
33C7×C22⋊Q8—22no—
34C7×C22⋊Q8—44no—
35C2×C7×C4⋊C4—22no—
36C2×C7×C4⋊C4—21no—
37C2×C7×C4⋊C4C2×C411yescharacteristic
38C2×C7×C4⋊C4C2×C412yes—
39C2×C7×C22⋊C4—22no—
40C2×C7×C22⋊C4—22no—
41C2×C7×C22⋊C4—21no—
42C2×C7×C22⋊C4—21no—
43C2×C22⋊Dic7—24no—
44C2×C22⋊Dic7—42no—
45C2×C22⋊Dic7—42no—
46C2×C4⋊Dic7—24no—
47C2×C4⋊Dic7—44no—
48C22×C7⋊C8—22no—
49C7×#95—22no—
50C7×#95—21no—
51C7⋊#95—22no—
52C7⋊#95D414yes—
53C22⋊(C7⋊C8)—22no—
54C22⋊(C7⋊C8)—22no—
55C22⋊(C7⋊C8)—44no—
56#2848D711yescharacteristic
57C2×#380—71no—
58#1779—71no—
59C2×#328—72no—
60#1294—72no—
61C24×C7—21no—
62C24×C7—21no—
63C24×C7—21no—
64C24×C7—21no—
65C24×C7—42no—
66C24×C7—42no—
67C24×C7C22⋊C412yes—
68C24×C7SD1612yes—
69C24×C7Q1612yes—
70C24×C7C2×D411yescharacteristic
71C2×C7×Q8—22no—
72C2×C7×Q8—42no—
73C22×C4×C7—21no—
74C22×C4×C7—21no—
75C22×C4×C7—24no—
76C22×C4×C7—24no—
77C22×C4×C7—24no—
78C22×C4×C7—24no—
79C22×C4×C7—24no—
80C22×C4×C7—21no—
81C22×C4×C7—22no—
82C22×C4×C7—21no—
83C22×C4×C7—42no—
84C22×C4×C7—42no—
85C22×C4×C7—42no—
86C22×C4×C7—48no—
87C22×C4×C7—48no—
88C22×C4×C7C22⋊C412yes—
89C22×C4×C7C22×C411yescharacteristic
90C22×C4×C7C2×D411yescharacteristic
91C22×C4×C7C2×D412yes—
92C22×C4×C7#4112yes—
93C22×Dic7—24no—
94C22×Dic7—44no—
95C22×Dic7—44no—
96C22×Dic7—42no—
97C22×Dic7—42no—
98C7×C4⋊C4—22no—
99C7×C4⋊C4—42no—
100C7×C4⋊C4—44no—
101C7×C4⋊C4—42no—
102C7×C22⋊C4—44no—
103C7×C22⋊C4—44no—
104C7×C22⋊C4—41no—
105C7×C22⋊C4—41no—
106C7×C22⋊C4—41no—
107C7×C22⋊C4—41no—
108C22⋊Dic7—48no—
109C4⋊Dic7—48no—
110C2×C7⋊C8—44no—
111C2×C7⋊C8—42no—
112C24×C4C2×D711yescharacteristic
113C2×C22⋊Q8Dic712yescomplemented
114C2×C22⋊Q8C2×D711yescharacteristic
115C22×C4⋊C4—141no—
116C22×C22⋊C4—141no—
117C2×C22⋊C8—72no—
118C2×C22⋊C8—142no—
119#385—21no—
120#385—22no—
121#380—144no—
122#380Dic712yescomplemented
123#380C2×D711yescharacteristic
124#379—21no—
125C2×#95—72no—
126#328—144no—
127C23×C7—22no—
128C23×C7—22no—
129C23×C7—22no—
130C23×C7—22no—
131C23×C7—22no—
132C23×C7—22no—
133C23×C7—22no—
134C23×C7—22no—
135C23×C7—22no—
136C23×C7—22no—
137C23×C7—22no—
138C23×C7—22no—
139C23×C7—44no—
140C23×C7—44no—
141C23×C7—42no—
142C23×C7—42no—
143C23×C7—42no—
144C23×C7—42no—
145C23×C7—44no—
146C23×C7—44no—
147C23×C7#10314yes—
148C23×C7C2×C22⋊C411yescharacteristic
149C23×C7#12011yescharacteristic
150C23×C7#12311yescharacteristic
151C23×C7C2×SD1611yescharacteristic
152C23×C7C2×Q1611yescharacteristic
153C23×C7AGL(1,ℤ/8)11yescharacteristic
154C23×C7#13711yescharacteristic
155C7×Q8—82no—
156C2×C4×C7—24no—
157C2×C4×C7—24no—
158C2×C4×C7—22no—
159C2×C4×C7—22no—
160C2×C4×C7—22no—
161C2×C4×C7—22no—
162C2×C4×C7—42no—
163C2×C4×C7—42no—
164C2×C4×C7—48no—
165C2×C4×C7—48no—
166C2×C4×C7—41no—
167C2×C4×C7—41no—
168C2×C4×C7—42no—
169C2×C4×C7—42no—
170C2×C4×C7—42no—
171C2×C4×C7—42no—
172C2×C4×C7—42no—
173C2×C4×C7#9914yes—
174C2×C4×C7C4×D412yes—
175C2×C4×C7#12112yes—
176C2×Dic7—44no—
177C2×Dic7—44no—
178C2×Dic7—44no—
179C2×Dic7—84no—
180C2×Dic7—84no—
181C7⋊C8—82no—
182C25C22⋊D711yescharacteristic
183C22×Q8C2×Dic711yescharacteristic
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—44no—
187C23×C4—142no—
188C23×C4C2×Dic712yes—
189C23×C4C22⋊D711yescharacteristic
190C23×C4C22⋊D712yes—
191C23×C4C22×D711yescharacteristic
192C22×C8—142no—
193C22⋊Q8—22no—
194C22⋊Q8—22no—
195C22⋊Q8—44no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—144no—
199C2×C4⋊C4—284no—
200C2×C4⋊C4C2×Dic711yescharacteristic
201C2×C4⋊C4C2×Dic712yes—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—144no—
207C2×C22⋊C4—282no—
208C2×C22⋊C4—282no—
209C22⋊C8—142no—
210C22⋊C8—142no—
211C22⋊C8—284no—
212#95—22no—
213#95—21no—
214#95—74no—
215#95—142no—
216C22×C7—21no—
217C22×C7—21no—
218C22×C7—21no—
219C22×C7—21no—
220C22×C7—22no—
221C22×C7—22no—
222C22×C7—22no—
223C22×C7—22no—
224C22×C7—24no—
225C22×C7—24no—
226C22×C7—24no—
227C22×C7—44no—
228C22×C7—44no—
229C22×C7—44no—
230C22×C7—44no—
231C22×C7—42no—
232C22×C7—42no—
233C22×C7—42no—
234C22×C7—42no—
235C22×C7#38611yescharacteristic
236C22×C7C2×#9912yes—
237C22×C7C2×#10311yescharacteristic
238C22×C7#41711yescharacteristic
239C22×C7#42112yes—
240C22×C7#45011yescharacteristic
241C22×C7#45111yescharacteristic
242C22×C7#48311yescharacteristic
243C22×C7#48411yescharacteristic
244C4×C7—22no—
245C4×C7—24no—
246C4×C7—22no—
247C4×C7—81no—
248C4×C7—81no—
249C4×C7—82no—
250Dic7—84no—
251C24—21no—
252C24—21no—
253C24—21no—
254C24—21no—
255C24—42no—
256C24—42no—
257C24#114312yes—
258C24#114412yes—
259C24C22⋊Dic712yes—
260C24C2×C22⋊D711yescharacteristic
261C2×Q8—22no—
262C2×Q8—42no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—24no—
268C22×C4—24no—
269C22×C4—24no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—48no—
277C22×C4—48no—
278C22×C4—144no—
279C22×C4—284no—
280C22×C4—284no—
281C22×C4—282no—
282C22×C4—282no—
283C22×C4C22⋊Dic712yes—
284C22×C4D4×D712yes—
285C22×C4#115912yes—
286C22×C4C22×Dic711yescharacteristic
287C22×C4C2×C22⋊D711yescharacteristic
288C2×C8—284no—
289C2×C8—282no—
290C4⋊C4—22no—
291C4⋊C4—42no—
292C4⋊C4—44no—
293C4⋊C4—42no—
294C4⋊C4—288no—
295C22⋊C4—44no—
296C22⋊C4—44no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—288no—
302C2×C7—21no—
303C2×C7—21no—
304C2×C7—21no—
305C2×C7—21no—
306C2×C7—44no—
307C2×C7#151312yes—
308C2×C7#152012yes—
309C2×C7#187211yescharacteristic
310C2×C7#189711yescharacteristic
311C2×C7#189811yescharacteristic
312C23—22no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—22no—
318C23—22no—
319C23—22no—
320C23—22no—
321C23—22no—
322C23—22no—
323C23—22no—
324C23—44no—
325C23—44no—
326C23—42no—
327C23—42no—
328C23—44no—
329C23—44no—
330C23—42no—
331C23—42no—
332C23#640914yes—
333C23#649811yescharacteristic
334C23#650011yescharacteristic
335C23C2×#114311yescharacteristic
336C23C2×#114411yescharacteristic
337C23#651211yescharacteristic
338C23#651411yescharacteristic
339C23C2×C22⋊Dic711yescharacteristic
340Q8—82no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—48no—
350C2×C4—48no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—284no—
359C2×C4—284no—
360C2×C4—284no—
361C2×C4—564no—
362C2×C4—564no—
363C2×C4#640814yes—
364C2×C4D4×Dic712yes—
365C2×C4#650212yes—
366C8—562no—
367C7#915111yescharacteristic, complemented, Sylow
368C22—21no—
369C22—21no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—21no—
375C22—21no—
376C22—24no—
377C22—24no—
378C22—24no—
379C22—44no—
380C22—44no—
381C22—44no—
382C22—44no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22#8981511yescharacteristic
388C22#8981611yescharacteristic
389C22#8981811yescharacteristic
390C22#8982211yescharacteristic
391C22C2×#640812yes—
392C22#8999211yescharacteristic
393C22C2×#640911yescharacteristic
394C22#9000411yescharacteristic
395C22#9000812yes—
396C4—22no—
397C4—24no—
398C4—22no—
399C4—81no—
400C4—82no—
401C4—81no—
402C4—564no—
403C2—21no—
404C2—21no—
405C2—21no—
406C2—21no—
407C2—44no—
408C2#1172942411yescharacteristic
409C2#1172944412yes—
410C2#1172944611yescharacteristic
411C2#1172946312yes—
412C2#1172946611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic7
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×#2848C2
socleC23×C7C2×C22⋊C4
prime radicalC25×C7D4
cosocleC23×C4×C7C23
hypercenter#2848D7
hypocenterC7#9151
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2848

Complements

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

NH ≅ G/Ntype
4. C2×#89333C2semidirect
5. #11725430C2semidirect
7. C2×C7×C22⋊Q8C4semidirect
13. C7×#380C4semidirect
113. C2×C22⋊Q8Dic7semidirect
122. #380Dic7semidirect
367. C7#9151semidirect

Maximal subgroups

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

subgroupindex
C7×#28482
C2×#899842
#117298802
C2×#893332
#117254302
#91517