Finite Group Databasebeta

← #13249513

Subgroups — #13249513

Order 1792.

738 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11740255C211yesmaximal, characteristic
2C2×#89421C211yesmaximal, characteristic
3C2×C7×#328C211yesmaximal, characteristic
4C2×#89333C211yesmaximal, characteristic
5#11727664C211yesmaximal, characteristic
6#11725481C211yesmaximal, characteristic
7#11725418C211yesmaximal, characteristic
8C2×C7×C22⋊Q8C2211yescharacteristic
9C22×Dic7⋊C4—21no—
10C22×C4×Dic7—21no—
11C22×C4×Dic7C2211yescharacteristic
12C2×C7×C22⋊C8C2211yescharacteristic
13C2×C7×#95C2211yescharacteristic
14#90002C412yescomplemented
15#89984C2211yescharacteristic
16C2×C7⋊#95C2211yescharacteristic
17C2×C22⋊(C7⋊C8)C2211yescharacteristic
18#89750—22no—
19#89745C412yescomplemented
20#89718—21no—
21#89715—21no—
22#89421—22no—
23#89421—22no—
24C7×#328—22no—
25#89345—22no—
26#89333—22no—
27#9144—71nomaximal, Sylow
28C22×C7×Q8C2×C411yescharacteristic
29C23×C4×C7—21no—
30C23×C4×C7C2311yescharacteristic
31C23×Dic7—21no—
32C23×Dic7D411yescharacteristic
33C23×Dic7D411yescharacteristic
34C22×C7×C8—21no—
35C7×C22⋊Q8—21no—
36C7×C22⋊Q8—21no—
37C7×C22⋊Q8—21no—
38C7×C22⋊Q8—21no—
39C2×C7×C4⋊C4—21no—
40C2×C7×C4⋊C4C2×C411yescharacteristic
41C2×C7×C22⋊C4—21no—
42C2×C22⋊Dic7—21no—
43C2×C4⋊Dic7C2×C412yes—
44C2×Dic7⋊C4—24no—
45C2×Dic7⋊C4—28no—
46C2×Dic7⋊C4—22no—
47C2×C4×Dic7—21no—
48C2×C4×Dic7—21no—
49C2×C4×Dic7—21no—
50C2×C4×Dic7—21no—
51C2×C4×Dic7—24no—
52C2×C4×Dic7—42no—
53C2×C4×Dic7—42no—
54C2×C4×Dic7C2×C412yes—
55C2×C4×Dic7D412yes—
56C22×C7⋊C8—21no—
57C7×C22⋊C8—21no—
58C7×C22⋊C8—21no—
59C7×#95—21no—
60C7×#95D412yes—
61C7⋊#95—21no—
62C7⋊#95—21no—
63C7⋊#95—22no—
64C7⋊#95—22no—
65C7⋊#95—22no—
66C7⋊#95D412yes—
67C22⋊(C7⋊C8)—21no—
68C22⋊(C7⋊C8)—21no—
69#2855—71no—
70C2×C4×C4⋊C4—71no—
71#1817—71no—
72C2×#328—71no—
73C2×#328D711yescharacteristic
74#1294—71no—
75#1294—71no—
76C24×C7C2×D411yescharacteristic
77C2×C7×Q8—21no—
78C2×C7×Q8—21no—
79C2×C7×Q8—42no—
80C22×C4×C7—24no—
81C22×C4×C7—22no—
82C22×C4×C7—21no—
83C22×C4×C7—21no—
84C22×C4×C7—42no—
85C22×C4×C7—42no—
86C22×C4×C7—41no—
87C22×C4×C7—41no—
88C22×C4×C7C22×C411yescharacteristic
89C22×C4×C7C2×D411yescharacteristic
90C22×C4×C7C2×D411yescharacteristic
91C22×C4×C7C2×D411yescharacteristic
92C22×C4×C7#4111yescharacteristic
93C22×C4×C7#4111yescharacteristic
94C22×Dic7—21no—
95C22×Dic7—21no—
96C22×Dic7—21no—
97C22×Dic7—21no—
98C22×Dic7—21no—
99C22×Dic7—21no—
100C22×Dic7—24no—
101C22×Dic7—24no—
102C22×Dic7—22no—
103C22×Dic7—22no—
104C22×Dic7—42no—
105C22×Dic7—41no—
106C22×Dic7—41no—
107C22×Dic7C22⋊C412yes—
108C22×Dic7C22⋊C412yes—
109C22×Dic7SD1612yes—
110C22×Dic7Q1612yes—
111C2×C7×C8—42no—
112C2×C7×C8—41no—
113C7×C4⋊C4—21no—
114C7×C4⋊C4—21no—
115C7×C4⋊C4—41no—
116C7×C4⋊C4—41no—
117C7×C22⋊C4—41no—
118C7×C22⋊C4—41no—
119C22⋊Dic7—41no—
120C22⋊Dic7—41no—
121C4⋊Dic7—42no—
122Dic7⋊C4—216no—
123Dic7⋊C4—44no—
124C4×Dic7—22no—
125C4×Dic7—22no—
126C4×Dic7—22no—
127C4×Dic7—22no—
128C4×Dic7—48no—
129C2×C7⋊C8—42no—
130C2×C7⋊C8—41no—
131C2×C22⋊Q8C2×D711yescharacteristic
132C22×C4⋊C4—141no—
133C22×C42—71no—
134C22×C42—141no—
135C2×C22⋊C8—71no—
136C2×C22⋊C8C2×D711yescharacteristic
137#391—72no—
138#389—72no—
139#387—142no—
140#385—141no—
141#381—141no—
142#380—71no—
143C4×C4⋊C4—142no—
144C4×C4⋊C4—142no—
145C2×#95—71no—
146C2×#95C2×D711yescharacteristic
147#336—142no—
148#328—22no—
149#328—142no—
150C23×C7—22no—
151C23×C7—22no—
152C23×C7C2×C22⋊C411yescharacteristic
153C23×C7#12011yescharacteristic
154C23×C7#12311yescharacteristic
155C23×C7C2×SD1611yescharacteristic
156C23×C7C2×Q1611yescharacteristic
157C23×C7AGL(1,ℤ/8)11yescharacteristic
158C23×C7#13711yescharacteristic
159C7×Q8—81no—
160C7×Q8—81no—
161C2×C4×C7—22no—
162C2×C4×C7—22no—
163C2×C4×C7—24no—
164C2×C4×C7—41no—
165C2×C4×C7—41no—
166C2×C4×C7—41no—
167C2×C4×C7—41no—
168C2×C4×C7—42no—
169C2×C4×C7—44no—
170C2×C4×C7—44no—
171C2×C4×C7—42no—
172C2×C4×C7—41no—
173C2×C4×C7—41no—
174C2×C4×C7—42no—
175C2×C4×C7—42no—
176C2×C4×C7C4×D411yescharacteristic
177C2×C4×C7C4×D411yescharacteristic
178C2×C4×C7#12111yescharacteristic
179C2×C4×C7#12111yescharacteristic
180C2×Dic7—24no—
181C2×Dic7—24no—
182C2×Dic7—22no—
183C2×Dic7—22no—
184C2×Dic7—22no—
185C2×Dic7—22no—
186C2×Dic7—22no—
187C2×Dic7—22no—
188C2×Dic7—22no—
189C2×Dic7—22no—
190C2×Dic7—24no—
191C2×Dic7—42no—
192C2×Dic7—44no—
193C2×Dic7—44no—
194C2×Dic7—42no—
195C2×Dic7—42no—
196C2×Dic7—42no—
197C2×Dic7—42no—
198C2×Dic7#10314yes—
199C2×Dic7#10414yes—
200C7×C8—81no—
201C7⋊C8—81no—
202C22×Q8C4×D711yescharacteristic
203C23×C4—21no—
204C23×C4—71no—
205C23×C4—71no—
206C23×C4—141no—
207C23×C4C22×D711yescharacteristic
208C22×C8—21no—
209C22×C8—141no—
210C22⋊Q8—21no—
211C22⋊Q8—21no—
212C22⋊Q8—21no—
213C22⋊Q8—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—72no—
216C2×C4⋊C4—148no—
217C2×C4⋊C4—144no—
218C2×C4⋊C4—142no—
219C2×C4⋊C4C4×D711yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—141no—
222C2×C42—72no—
223C2×C42—72no—
224C2×C42—141no—
225C2×C42—141no—
226C2×C42—141no—
227C2×C42—141no—
228C2×C42—144no—
229C2×C42—282no—
230C2×C42—282no—
231C22⋊C8—21no—
232C22⋊C8—21no—
233C22⋊C8—141no—
234C22⋊C8—141no—
235#95—21no—
236#95—72no—
237#95—142no—
238#95—142no—
239#95—142no—
240#95—141no—
241#95—141no—
242#95C22⋊D712yes—
243C22×C7—21no—
244C22×C7—21no—
245C22×C7—21no—
246C22×C7—21no—
247C22×C7—22no—
248C22×C7—22no—
249C22×C7—22no—
250C22×C7—22no—
251C22×C7#38611yescharacteristic
252C22×C7#41012yes—
253C22×C7C2×#10311yescharacteristic
254C22×C7#41711yescharacteristic
255C22×C7C2×#10412yes—
256C22×C7#45011yescharacteristic
257C22×C7#45111yescharacteristic
258C22×C7#48311yescharacteristic
259C22×C7#48411yescharacteristic
260C4×C7—21no—
261C4×C7—21no—
262C4×C7—21no—
263C4×C7—21no—
264C4×C7—44no—
265C4×C7—81no—
266C4×C7—81no—
267Dic7—24no—
268Dic7—24no—
269Dic7—44no—
270Dic7—82no—
271C24D4×D711yescharacteristic
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—42no—
275C22×C4—24no—
276C22×C4—22no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—72no—
284C22×C4—72no—
285C22×C4—72no—
286C22×C4—72no—
287C22×C4—144no—
288C22×C4—141no—
289C22×C4—141no—
290C22×C4—141no—
291C22×C4—141no—
292C22×C4—141no—
293C22×C4—141no—
294C22×C4—144no—
295C22×C4—142no—
296C22×C4—142no—
297C22×C4—282no—
298C22×C4—281no—
299C22×C4—281no—
300C22×C4C2×C4×D711yescharacteristic
301C22×C4#115711yescharacteristic
302C22×C4D4×D711yescharacteristic
303C22×C4D4×D711yescharacteristic
304C22×C4#115911yescharacteristic
305C22×C4C2×C22⋊D711yescharacteristic
306C2×C8—42no—
307C2×C8—41no—
308C2×C8—282no—
309C2×C8—281no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—1416no—
315C4⋊C4—282no—
316C4⋊C4—284no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—281no—
320C22⋊C4—281no—
321C42—142no—
322C42—142no—
323C42—142no—
324C42—142no—
325C42—288no—
326C2×C7—21no—
327C2×C7—21no—
328C2×C7—21no—
329C2×C7—21no—
330C2×C7#150312yes—
331C2×C7#150912yes—
332C2×C7#187211yescharacteristic
333C2×C7#189611yescharacteristic
334C2×C7#189911yescharacteristic
335C23—22no—
336C23—22no—
337C23D7×C22⋊C411yescharacteristic
338C23#644611yescharacteristic
339C23D7×SD1611yescharacteristic
340C23#647711yescharacteristic
341C23D7×Q1611yescharacteristic
342C23#648111yescharacteristic
343C23#650011yescharacteristic
344Q8—81no—
345Q8—81no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—24no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—44no—
355C2×C4—44no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—74no—
362C2×C4—74no—
363C2×C4—144no—
364C2×C4—144no—
365C2×C4—142no—
366C2×C4—142no—
367C2×C4—142no—
368C2×C4—142no—
369C2×C4—142no—
370C2×C4—142no—
371C2×C4—142no—
372C2×C4—142no—
373C2×C4—144no—
374C2×C4—282no—
375C2×C4—284no—
376C2×C4—284no—
377C2×C4—282no—
378C2×C4—282no—
379C2×C4—282no—
380C2×C4—282no—
381C2×C4(C22⋊D7)⋊C411yescharacteristic
382C2×C4#644711yescharacteristic
383C2×C4C4×C22⋊D711yescharacteristic
384C2×C4#650111yescharacteristic
385C8—81no—
386C8—561no—
387C7#914411yescharacteristic, complemented, Sylow
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—22no—
393C22—22no—
394C22—22no—
395C22—22no—
396C22#8951212yes—
397C22D7×#10311yescharacteristic
398C22#8957511yescharacteristic
399C22#8957711yescharacteristic
400C22#8958111yescharacteristic
401C22D7×#10412yes—
402C22#8972811yescharacteristic
403C22#8994111yescharacteristic
404C22#8995811yescharacteristic
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—44no—
410C4—81no—
411C4—81no—
412C4—144no—
413C4—144no—
414C4—284no—
415C4—562no—
416C2—21no—
417C2—21no—
418C2—21no—
419C2—21no—
420C2#1172606312yes—
421C2#1172606512yes—
422C2#1172778311yescharacteristic
423C2#1172802211yescharacteristic
424C2#1172813611yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC2×C7×#328C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C2×D4
cosocleC23×C4×C7C23
hypercenterC2×#328D7
hypocenterC7#9144
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
14. #90002C4semidirect
19. #89745C4semidirect
387. C7#9144semidirect

Maximal subgroups

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

subgroupindex
#117402552
C2×#894212
C2×C7×#3282
C2×#893332
#117276642
#117254812
#117254182
#91447