Finite Group Databasebeta

← #13252773

Subgroups — #13252773

Order 1792.

686 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739521C211yesmaximal, characteristic
2C7×C4⋊#95C211yesmaximal, characteristic
3C4×C22⋊(C7⋊C8)C211yesmaximal, characteristic
4C2×#89247C214yesmaximal
5C22×C7×C4⋊C4—21no—
6C22×C42×C7C2211yescharacteristic
7C2×#6487C2212yes—
8C2×#6432C411yescharacteristic, complemented
9C2×C7×#95—21no—
10C2×C7×#95C2212yes—
11#89984—21no—
12#89984—21no—
13C2×C22⋊(C7⋊C8)C2212yes—
14#89707C411yescharacteristic, complemented
15#89701C412yescomplemented
16#89700—21no—
17#89700—21no—
18C2×C4×C7⋊C8—21no—
19#89319—21no—
20#89247—28no—
21#9679—71nomaximal, Sylow
22C23×C4×C7—22no—
23C23×C4×C7D411yescharacteristic
24C23×C4×C7D411yescharacteristic
25C23×C4×C7C2311yescharacteristic
26C22×Dic14C2×C412yes—
27C2×C7×C4⋊C4—24no—
28C2×C7×C4⋊C4—42no—
29C2×C7×C4⋊C4—42no—
30C2×C42×C7—42no—
31C2×C42×C7C2×C411yescharacteristic
32C2×C42×C7C2×C411yescharacteristic
33C2×C42×C7D411yescharacteristic
34C2×C42×C7D411yescharacteristic
35C2×C22⋊Dic7—22no—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7—21no—
38C2×C4⋊Dic7—21no—
39C2×C4⋊Dic7—21no—
40C2×C4⋊Dic7C2×C412yes—
41#6487—24no—
42#6487—24no—
43C2×Dic7⋊C4—22no—
44C22×C7⋊C8—22no—
45#6432—42no—
46C7×#95—24no—
47C7×#95—42no—
48C7⋊#95—22no—
49C7⋊#95—22no—
50C22⋊(C7⋊C8)—22no—
51C22⋊(C7⋊C8)D414yes—
52C4×C7⋊C8—42no—
53#2857—71no—
54C4×C22⋊C8—71no—
55C2×#328—74no—
56C4⋊#95D711yescharacteristic
57C24×C7C2×D411yescharacteristic
58C22×C4×C7—22no—
59C22×C4×C7—22no—
60C22×C4×C7—24no—
61C22×C4×C7—41no—
62C22×C4×C7—41no—
63C22×C4×C7—41no—
64C22×C4×C7—41no—
65C22×C4×C7—42no—
66C22×C4×C7—42no—
67C22×C4×C7—42no—
68C22×C4×C7—42no—
69C22×C4×C7—42no—
70C22×C4×C7—42no—
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22⋊C411yescharacteristic
74C22×C4×C7C22⋊C411yescharacteristic
75C22×C4×C7SD1612yes—
76C22×C4×C7SD1612yes—
77C22×C4×C7Q1612yes—
78C22×C4×C7Q1612yes—
79C22×C4×C7C22×C411yescharacteristic
80C22×C4×C7C2×D411yescharacteristic
81C22×C4×C7C2×D412yes—
82C22×C4×C7#4112yes—
83C22×Dic7—22no—
84C22×Dic7—22no—
85C2×Dic14—24no—
86C2×Dic14—42no—
87C2×Dic14—42no—
88C7×C4⋊C4—48no—
89C42×C7—22no—
90C42×C7—22no—
91C42×C7—41no—
92C42×C7—41no—
93C22⋊Dic7—42no—
94C22⋊Dic7—42no—
95C4⋊Dic7—24no—
96C4⋊Dic7—42no—
97C4⋊Dic7—42no—
98C4⋊Dic7—42no—
99C4⋊Dic7—42no—
100Dic7⋊C4—44no—
101C2×C7⋊C8—24no—
102C2×C7⋊C8—42no—
103C2×C7⋊C8—42no—
104C2×C4⋊Q8—71no—
105C2×C22⋊Q8—72no—
106C22×C4⋊C4—21no—
107C22×C42C2×D711yescharacteristic
108C2×C22⋊C8—72no—
109C2×C4×C8—141no—
110#391—72no—
111#389—141no—
112#389—141no—
113#384—71no—
114#380—141no—
115#380—141no—
116C2×#95—21no—
117C2×#95C2×D712yes—
118#336—141no—
119#328—148no—
120C23×C7—21no—
121C23×C7—21no—
122C23×C7—21no—
123C23×C7—21no—
124C23×C7C2×C22⋊C411yescharacteristic
125C23×C7#12411yescharacteristic
126C23×C7#12711yescharacteristic
127C23×C7C2×SD1611yescharacteristic
128C23×C7C2×SD1611yescharacteristic
129C23×C7C2×Q1611yescharacteristic
130C23×C7C2×Q1611yescharacteristic
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—21no—
140C2×C4×C7—21no—
141C2×C4×C7—24no—
142C2×C4×C7—24no—
143C2×C4×C7—42no—
144C2×C4×C7—42no—
145C2×C4×C7—42no—
146C2×C4×C7—42no—
147C2×C4×C7—44no—
148C2×C4×C7—44no—
149C2×C4×C7—44no—
150C2×C4×C7—82no—
151C2×C4×C7—82no—
152C2×C4×C7—82no—
153C2×C4×C7—82no—
154C2×C4×C7#9912yes—
155C2×C4×C7#10312yes—
156C2×C4×C7#10312yes—
157C2×C4×C7#10312yes—
158C2×C4×C7#10312yes—
159C2×C4×C7#10412yes—
160C2×C4×C7C4×D412yes—
161C2×C4×C7#12112yes—
162C2×Dic7—42no—
163C2×Dic7—42no—
164C2×Dic7—42no—
165C2×Dic7—42no—
166C2×Dic7—42no—
167C2×Dic7—42no—
168Dic14—84no—
169C7⋊C8—44no—
170C22×Q8—72no—
171C23×C4—22no—
172C23×C4C22⋊D711yescharacteristic
173C23×C4C22⋊D711yescharacteristic
174C23×C4C22×D711yescharacteristic
175C22×C8—142no—
176C4⋊Q8—282no—
177C22⋊Q8—144no—
178C22⋊Q8—144no—
179C2×C4⋊C4—24no—
180C2×C4⋊C4—42no—
181C2×C4⋊C4—42no—
182C2×C4⋊C4—72no—
183C2×C4⋊C4—141no—
184C2×C4⋊C4—141no—
185C2×C4⋊C4—141no—
186C2×C4⋊C4—141no—
187C2×C4⋊C4—142no—
188C2×C22⋊C4—142no—
189C2×C42—42no—
190C2×C42C4×D711yescharacteristic
191C2×C42C4×D711yescharacteristic
192C2×C42D2811yescharacteristic
193C2×C42D2811yescharacteristic
194C22⋊C8—74no—
195C22⋊C8—142no—
196C4×C8—282no—
197#95—24no—
198#95—42no—
199#95—142no—
200#95—142no—
201C22×C7—21no—
202C22×C7—21no—
203C22×C7—21no—
204C22×C7—21no—
205C22×C7—21no—
206C22×C7—21no—
207C22×C7—21no—
208C22×C7—21no—
209C22×C7—21no—
210C22×C7—21no—
211C22×C7—21no—
212C22×C7—21no—
213C22×C7#39011yescharacteristic
214C22×C7C2×#9911yescharacteristic
215C22×C7#41011yescharacteristic
216C22×C7C2×#10311yescharacteristic
217C22×C7C2×#10311yescharacteristic
218C22×C7C2×#10411yescharacteristic
219C22×C7#42111yescharacteristic
220C22×C7#48711yescharacteristic
221C22×C7#48711yescharacteristic
222C22×C7#49211yescharacteristic
223C22×C7#49411yescharacteristic
224C4×C7—22no—
225C4×C7—22no—
226C4×C7—22no—
227C4×C7—22no—
228C4×C7—22no—
229C4×C7—84no—
230C4×C7#32814yescomplemented
231Dic7—82no—
232Dic7—82no—
233C24C2×C22⋊D711yescharacteristic
234C2×Q8—144no—
235C2×Q8—282no—
236C2×Q8—282no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—24no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—142no—
251C22×C4—142no—
252C22×C4(C2×D7)⋊C411yescharacteristic
253C22×C4(C2×D7)⋊C411yescharacteristic
254C22×C4(C2×D7)⋊C411yescharacteristic
255C22×C4(C2×D7)⋊C411yescharacteristic
256C22×C4#114212yes—
257C22×C4#114212yes—
258C22×C4#114412yes—
259C22×C4#114412yes—
260C22×C4C2×C4×D711yescharacteristic
261C22×C4C2×D2811yescharacteristic
262C22×C4D4×D712yes—
263C22×C4#116112yes—
264C2×C8—144no—
265C2×C8—282no—
266C2×C8—282no—
267C4⋊C4—48no—
268C4⋊C4—144no—
269C4⋊C4—282no—
270C4⋊C4—282no—
271C4⋊C4—284no—
272C4⋊C4—282no—
273C4⋊C4—282no—
274C22⋊C4—282no—
275C22⋊C4—282no—
276C42—22no—
277C42—22no—
278C42—41no—
279C42—41no—
280C2×C7—21no—
281C2×C7—21no—
282C2×C7—21no—
283C2×C7—21no—
284C2×C7C2×#32811yescharacteristic
285C2×C7#150311yescharacteristic
286C2×C7#151811yescharacteristic
287C2×C7#152011yescharacteristic
288C2×C7#195611yescharacteristic
289C2×C7#196411yescharacteristic
290C2×C7#198011yescharacteristic
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23C2×(C2×D7)⋊C411yescharacteristic
296C23C2×#114211yescharacteristic
297C23C2×#114211yescharacteristic
298C23#650311yescharacteristic
299C23C2×#114411yescharacteristic
300C23C2×#114411yescharacteristic
301C23#651011yescharacteristic
302Q8—564no—
303C2×C4—21no—
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—24no—
314C2×C4—24no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—82no—
323C2×C4—82no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4—282no—
327C2×C4—282no—
328C2×C4—282no—
329C2×C4—282no—
330C2×C4—282no—
331C2×C4—282no—
332C2×C4#637912yes—
333C2×C4#638012yes—
334C2×C4#638412yes—
335C2×C4#638412yes—
336C2×C4#638412yes—
337C2×C4#638412yes—
338C2×C4#645612yes—
339C2×C4#645812yes—
340C8—284no—
341C7#967911yescharacteristic, complemented, Sylow
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22C2×#637911yescharacteristic
355C22C2×#638011yescharacteristic
356C22C2×#638411yescharacteristic
357C22C2×#638411yescharacteristic
358C22#8976011yescharacteristic
359C22#8977711yescharacteristic
360C22#8977811yescharacteristic
361C22#8984811yescharacteristic
362C22#8986411yescharacteristic
363C22#8986511yescharacteristic
364C22#8986511yescharacteristic
365C4—22no—
366C4—22no—
367C4—22no—
368C4—22no—
369C4—22no—
370C4—84no—
371C4—562no—
372C4—562no—
373C4#8924714yescomplemented
374C2—21no—
375C2—21no—
376C2—21no—
377C2—21no—
378C2C2×#8924711yescharacteristic
379C2#1172722511yescharacteristic
380C2#1172724611yescharacteristic
381C2#1172726411yescharacteristic
382C2#1172728211yescharacteristic
383C2#1172730011yescharacteristic
384C2#1172733311yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×C4⋊#95C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C2×D4
cosocleC23×C4×C7C23
hypercenterC4⋊#95D7
hypocenterC7#9679
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
8. C2×#6432C4semidirect
14. #89707C4semidirect
15. #89701C4semidirect
230. C4×C7#328semidirect
341. C7#9679semidirect
373. C4#89247semidirect

Maximal subgroups

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

subgroupindex
#117395212
C7×C4⋊#952
C4×C22⋊(C7⋊C8)2
C2×#892472
#96797