Finite Group Databasebeta

← #13339136

Subgroups — #13339136

Order 1792.

644 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#477C211yesmaximal, characteristic, complemented
2#11740661C211yesmaximal, characteristic
3#11739886C211yesmaximal, characteristic
4#11739880C211yesmaximal, characteristic, complemented
5#11729528C211yesmaximal, characteristic, complemented
6#11728904C214yesmaximal, complemented
7#11728902C214yesmaximal, complemented
8#11728185C211yesmaximal, characteristic
9#11728175C211yesmaximal, characteristic, complemented
10C2×C7×C4⋊Q8C2211yescharacteristic
11C2×C4×C7×Q8C2211yescharacteristic
12C2×#6505—21no—
13#90168C2211yescharacteristic
14C7×#477—22no—
15C7×#477C2214yes—
16C2×C7×#107—21no—
17C2×C7×C4⋊C8C2211yescharacteristic
18C2×C7×#103—21no—
19#89860C2212yes—
20#89856—22no—
21#89851C2212yes—
22#89803C2212yes—
23#89800—22no—
24#89799C2212yes—
25Q8×C7⋊C8—22no—
26Q8×C7⋊C8C2214yes—
27#89740—22no—
28#89738—21no—
29#89697—22no—
30#89697C2211yescharacteristic
31#89697C2211yescharacteristic
32#89696C2211yescharacteristic
33#89341C2214yes—
34#89280C2212yes—
35#89277C2212yes—
36#89275C2214yes—
37#19403—71nomaximal, Sylow
38C22×C7×Q8—21no—
39C22×C7×Q8D411yescharacteristic
40C2×#1157—21no—
41C22×C7×C8—21no—
42C7×C4⋊Q8—21no—
43C7×C4⋊Q8—21no—
44C7×C4⋊Q8—21no—
45C7×C4⋊Q8C2312yes—
46C4×C7×Q8—21no—
47C4×C7×Q8—21no—
48C4×C7×Q8D412yes—
49C4×C7×Q8C2312yes—
50C2×C7×C4⋊C4—21no—
51C2×C7×C4⋊C4—21no—
52C2×C7×C4⋊C4—21no—
53C2×C7×C4⋊C4D411yescharacteristic
54C2×C42×C7—21no—
55C2×C42×C7C2311yescharacteristic
56C2×#1144—22no—
57#6505—44no—
58C2×#1143—22no—
59#6493—21no—
60#6493—21no—
61C2×#1136—21no—
62#6438—21no—
63#6437C2311yescharacteristic
64C4×D28—21no—
65C4×D28—21no—
66#6432C2311yescharacteristic
67C7×#107—24no—
68C7×C4⋊C8—21no—
69C7×C4⋊C8C2312yes—
70C7×#103—24no—
71C22⋊(C7⋊C8)—21no—
72C22⋊(C7⋊C8)D412yes—
73#6384—22no—
74#6383—22no—
75#6383—24no—
76#6382—24no—
77C4⋊(C7⋊C8)—21no—
78C4⋊(C7⋊C8)—24no—
79C4⋊(C7⋊C8)D412yes—
80C4⋊(C7⋊C8)C2312yes—
81C4⋊(C7⋊C8)C2312yes—
82C4×C7⋊C8—21no—
83C4×C7⋊C8—24no—
84C4×C7⋊C8C2312yes—
85#3227—71no—
86C2×#477D711yescharacteristic, complemented
87#3037—71no—
88#2982—71no—
89#1678—74no—
90#1672—74no—
91#1570—71no—
92#1548—71no—
93#1540—71no—
94C2×C7×Q8—21no—
95C2×C7×Q8—22no—
96C2×C7×Q8—22no—
97C2×C7×Q8—41no—
98C2×C7×Q8—82no—
99C2×C7×Q8SD1614yes—
100C2×C7×Q8C2×D412yes—
101C22×C4×C7—21no—
102C22×C4×C7—21no—
103C22×C4×C7—41no—
104C22×C4×C7C2×D411yescharacteristic
105C22×C4×C7C2×D411yescharacteristic
106C22×C4×C7#4111yescharacteristic
107C2×C22⋊D7—41no—
108#1157—42no—
109#1157—42no—
110C2×D28—21no—
111C2×D28—21no—
112C2×D28—21no—
113C2×C4×D7—41no—
114C2×Dic14—21no—
115C2×C7×C8—22no—
116C2×C7×C8—42no—
117C7×C4⋊C4—22no—
118C7×C4⋊C4—21no—
119C7×C4⋊C4—22no—
120C7×C4⋊C4—22no—
121C7×C4⋊C4—22no—
122C7×C4⋊C4—41no—
123C7×C4⋊C4—41no—
124C7×C4⋊C4C2×D412yes—
125C42×C7—22no—
126C42×C7—22no—
127C42×C7C2×D411yescharacteristic
128C42×C7C2×D411yescharacteristic
129C42×C7#4111yescharacteristic
130C42×C7C2411yescharacteristic
131#1144—44no—
132#1143—44no—
133(C2×D7)⋊C4—41no—
134(C2×D7)⋊C4—41no—
135C4⋊Dic7—21no—
136C4⋊Dic7—21no—
137#1136—42no—
138C2×C7⋊C8—22no—
139C2×C7⋊C8—22no—
140C2×C7⋊C8C2×D414yes—
141C2×#137—141no—
142#532—71no—
143C2×C4⋊Q8C2×D711yescharacteristic
144C2×C4×Q8C2×D711yescharacteristic
145#498—72no—
146#486—72no—
147#481—142no—
148#477—22no—
149#477C2×D714yes—
150#476—142no—
151#464—142no—
152#462—72no—
153#460—72no—
154C8×Q8—74no—
155C8×Q8—142no—
156#431—71no—
157#431—71no—
158#431—142no—
159C2×#107—21no—
160#423—71no—
161C2×C4⋊C8C2×D711yescharacteristic
162#417—141no—
163C2×#103—21no—
164#334—74no—
165#333—74no—
166#332—72no—
167#331—72no—
168C23×C7#12111yescharacteristic
169C22×D7—41no—
170C7×Q8—22no—
171C7×Q8—24no—
172C7×Q8—82no—
173C7×Q8—82no—
174C7×Q8C2×SD1614yes—
175C2×C4×C7—22no—
176C2×C4×C7—24no—
177C2×C4×C7—22no—
178C2×C4×C7—22no—
179C2×C4×C7—41no—
180C2×C4×C7—42no—
181C2×C4×C7—81no—
182C2×C4×C7—82no—
183C2×C4×C7#12111yescharacteristic
184C2×C4×C7#12111yescharacteristic
185C2×C4×C7#12111yescharacteristic
186C2×C4×C7C2×SD1612yes—
187C2×C4×C7#13512yes—
188C2×C4×C7C22×D411yescharacteristic
189C2×C4×C7C22×D411yescharacteristic
190C2×C4×C7C2×#4111yescharacteristic
191C22⋊D7—82no—
192C2×Dic7—41no—
193D28—41no—
194D28—41no—
195D28—42no—
196D28—81no—
197C4×D7—82no—
198Dic14—41no—
199Dic14—41no—
200C7×C8—42no—
201C7⋊C8—24no—
202C7⋊C8—42no—
203C7⋊C8—42no—
204C2×#41—141no—
205C22×Q8—21no—
206C22×Q8C22⋊D711yescharacteristic
207#137—284no—
208C2×Q16—142no—
209C2×SD16—142no—
210C2×M16—141no—
211C22×C8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—71no—
216C4⋊Q8C22×D712yes—
217#127—71no—
218#124—141no—
219#121—141no—
220#121—141no—
221C4×Q8—21no—
222C4×Q8—21no—
223C4×Q8C22⋊D712yes—
224C4×Q8C22×D712yes—
225C4×D4—141no—
226C4×D4—141no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4C22⋊D711yescharacteristic
231C2×C42—21no—
232C2×C42C22×D711yescharacteristic
233#107—24no—
234#106—144no—
235C4⋊C8—21no—
236C4⋊C8—72no—
237C4⋊C8—72no—
238C4⋊C8—72no—
239C4⋊C8—144no—
240C4⋊C8—141no—
241C4⋊C8C22×D712yes—
242#103—24no—
243#103—142no—
244#102—144no—
245#102—142no—
246C22⋊C8—72no—
247C22⋊C8—141no—
248C4×C8—72no—
249C4×C8—144no—
250C4×C8—141no—
251C22×C7—21no—
252C22×C7—21no—
253C22×C7#46512yes—
254C22×C7C2×#12111yescharacteristic
255C2×D7—81no—
256C2×D7—81no—
257C2×D7—81no—
258C4×C7—21no—
259C4×C7—24no—
260C4×C7—21no—
261C4×C7—21no—
262C4×C7—42no—
263C4×C7—82no—
264C4×C7#46512yes—
265C4×C7C22×SD1611yescharacteristic
266C4×C7C2×#13511yescharacteristic
267C4×C7#57812yes—
268Dic7—81no—
269#41—282no—
270#41—282no—
271C2×Q8—21no—
272C2×Q8—22no—
273C2×Q8—22no—
274C2×Q8—41no—
275C2×Q8—82no—
276C2×Q8—141no—
277C2×Q8#114314yes—
278C2×Q8C2×C22⋊D712yes—
279C2×D4—141no—
280C2×D4—141no—
281C2×D4—141no—
282C2×D4—281no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—281no—
287C22×C4D4×D711yescharacteristic
288C22×C4#115911yescharacteristic
289C22×C4C2×C22⋊D711yescharacteristic
290Q16—284no—
291SD16—284no—
292M16—282no—
293C2×C8—22no—
294C2×C8—42no—
295C2×C8—74no—
296C2×C8—142no—
297C2×C8—142no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—141no—
306C4⋊C4—141no—
307C4⋊C4C2×C22⋊D712yes—
308C22⋊C4—281no—
309C22⋊C4—281no—
310C42—22no—
311C42—22no—
312C42D4×D711yescharacteristic
313C42#115911yescharacteristic
314C42C2×C22⋊D711yescharacteristic
315C42C23×D711yescharacteristic
316C2×C7—22no—
317C2×C7#304411yescharacteristic
318C2×C7C2×#46511yescharacteristic
319C2×C7#306811yescharacteristic
320D7—161no—
321C23—281no—
322C23#650211yescharacteristic
323Q8—22no—
324Q8—24no—
325Q8—82no—
326Q8—82no—
327Q8—281no—
328Q8—281no—
329Q8C2×#114314yes—
330D4—282no—
331D4—281no—
332D4—281no—
333D4—561no—
334D4—562no—
335C2×C4—22no—
336C2×C4—24no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—81no—
342C2×C4—82no—
343C2×C4—281no—
344C2×C4—562no—
345C2×C4#650211yescharacteristic
346C2×C4#650211yescharacteristic
347C2×C4#650211yescharacteristic
348C2×C4C2×#114312yes—
349C2×C4#651312yes—
350C2×C4C2×D4×D711yescharacteristic
351C2×C4C2×#115911yescharacteristic
352C2×C4C22×C22⋊D711yescharacteristic
353C8—42no—
354C8—144no—
355C8—282no—
356C8—282no—
357C7#1940311yescharacteristic, complemented, Sylow
358C22—21no—
359C22—21no—
360C22—561no—
361C22—561no—
362C22—561no—
363C22#8982012yes—
364C22C2×#650211yescharacteristic
365C4—24no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—42no—
370C4—82no—
371C4—561no—
372C4#8982012yes—
373C4#9045712yes—
374C4C22×#114311yescharacteristic
375C4C2×#651311yescharacteristic
376C2—22no—
377C2—1121no—
378C2C2×#8982011yescharacteristic
379C2#1174132211yescharacteristic
380C2#1174138811yescharacteristic
subgroupG/H
centerC22C2×#6502
commutator, cosocleC42×C7C24
FrattiniC42C23×D7
FittingC2×C7×#477C2
socleC22×C7C2×#121
prime radical#90168C22
hypercenterC2×#477D7
hypocenterC7#19403
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×C7×#477C2semidirect
4. #11739880C2semidirect
5. #11729528C2semidirect
6. #11728904C2semidirect
7. #11728902C2semidirect
9. #11728175C2semidirect
86. C2×#477D7semidirect
357. C7#19403semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4772
#117406612
#117398862
#117398802
#117295282
#117289042
#117289022
#117281852
#117281752
#194037