Finite Group Databasebeta

← #13249553

Subgroups — #13249553

Order 1792.

630 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11740255C211yesmaximal, characteristic
2C2×#89422C211yesmaximal, 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×Dic7C2211yescharacteristic
11C2×C7×C22⋊C8C2211yescharacteristic
12C2×C7×#95C2211yescharacteristic
13#90002C412yescomplemented
14#89984C2211yescharacteristic
15C2×C7⋊#95—21no—
16C2×C7⋊#95C2211yescharacteristic
17C2×C22⋊(C7⋊C8)C2211yescharacteristic
18#89750—22no—
19#89745C412yescomplemented
20#89718—21no—
21#89715—21no—
22#89422—22no—
23#89422—22no—
24C7×#328—22no—
25#89345—22no—
26#89333—22no—
27#9152—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—22no—
46C2×Dic7⋊C4—42no—
47C2×Dic7⋊C4—42no—
48C2×C4×Dic7—21no—
49C2×C4×Dic7—21no—
50C2×C4×Dic7—21no—
51C2×C4×Dic7—21no—
52C2×C4×Dic7C2×C412yes—
53C2×C4×Dic7D412yes—
54C22×C7⋊C8—21no—
55C7×C22⋊C8—21no—
56C7×C22⋊C8—21no—
57C7×#95—21no—
58C7×#95D412yes—
59C7⋊#95—24no—
60C7⋊#95—21no—
61C7⋊#95—21no—
62C7⋊#95—22no—
63C7⋊#95—22no—
64C7⋊#95—22no—
65C7⋊#95D412yes—
66C22⋊(C7⋊C8)—21no—
67C22⋊(C7⋊C8)—21no—
68#2855—71no—
69C2×#382—71no—
70#1817—71no—
71C2×#328—71no—
72C2×#328D711yescharacteristic
73#1294—71no—
74#1294—71no—
75C24×C7C2×D411yescharacteristic
76C2×C7×Q8—21no—
77C2×C7×Q8—21no—
78C2×C7×Q8—42no—
79C22×C4×C7—21no—
80C22×C4×C7—21no—
81C22×C4×C7—22no—
82C22×C4×C7—42no—
83C22×C4×C7—42no—
84C22×C4×C7—42no—
85C22×C4×C7—41no—
86C22×C4×C7—41no—
87C22×C4×C7C22×C411yescharacteristic
88C22×C4×C7C2×D411yescharacteristic
89C22×C4×C7C2×D411yescharacteristic
90C22×C4×C7C2×D411yescharacteristic
91C22×C4×C7#4111yescharacteristic
92C22×C4×C7#4111yescharacteristic
93C22×Dic7—21no—
94C22×Dic7—21no—
95C22×Dic7—21no—
96C22×Dic7—21no—
97C22×Dic7—21no—
98C22×Dic7—21no—
99C22×Dic7—22no—
100C22×Dic7—22no—
101C22×Dic7—42no—
102C22×Dic7—42no—
103C22×Dic7—42no—
104C22×Dic7—41no—
105C22×Dic7—41no—
106C22×Dic7C22⋊C412yes—
107C22×Dic7C22⋊C412yes—
108C22×Dic7SD1612yes—
109C22×Dic7Q1612yes—
110C2×C7×C8—42no—
111C2×C7×C8—41no—
112C7×C4⋊C4—21no—
113C7×C4⋊C4—21no—
114C7×C4⋊C4—41no—
115C7×C4⋊C4—41no—
116C7×C22⋊C4—41no—
117C7×C22⋊C4—41no—
118C22⋊Dic7—41no—
119C22⋊Dic7—41no—
120C4⋊Dic7—42no—
121Dic7⋊C4—44no—
122Dic7⋊C4—48no—
123C4×Dic7—22no—
124C4×Dic7—22no—
125C4×Dic7—22no—
126C4×Dic7—22no—
127C2×C7⋊C8—42no—
128C2×C7⋊C8—41no—
129C2×C22⋊Q8C2×D711yescharacteristic
130C22×C4⋊C4—141no—
131C22×C42—71no—
132C2×C22⋊C8—71no—
133C2×C22⋊C8C2×D711yescharacteristic
134#391—72no—
135#389—72no—
136#387—142no—
137#385—141no—
138#382—142no—
139#382—142no—
140#381—141no—
141#380—71no—
142C2×#95—71no—
143C2×#95—141no—
144C2×#95C2×D711yescharacteristic
145#336—142no—
146#328—22no—
147#328—142no—
148C23×C7—22no—
149C23×C7—22no—
150C23×C7C2×C22⋊C411yescharacteristic
151C23×C7#12011yescharacteristic
152C23×C7#12311yescharacteristic
153C23×C7C2×SD1611yescharacteristic
154C23×C7C2×Q1611yescharacteristic
155C23×C7AGL(1,ℤ/8)11yescharacteristic
156C23×C7#13711yescharacteristic
157C7×Q8—81no—
158C7×Q8—81no—
159C2×C4×C7—22no—
160C2×C4×C7—22no—
161C2×C4×C7—41no—
162C2×C4×C7—41no—
163C2×C4×C7—41no—
164C2×C4×C7—41no—
165C2×C4×C7—42no—
166C2×C4×C7—42no—
167C2×C4×C7—41no—
168C2×C4×C7—41no—
169C2×C4×C7—42no—
170C2×C4×C7—42no—
171C2×C4×C7—42no—
172C2×C4×C7—82no—
173C2×C4×C7—82no—
174C2×C4×C7C4×D411yescharacteristic
175C2×C4×C7C4×D411yescharacteristic
176C2×C4×C7#12111yescharacteristic
177C2×C4×C7#12111yescharacteristic
178C2×Dic7—22no—
179C2×Dic7—22no—
180C2×Dic7—22no—
181C2×Dic7—22no—
182C2×Dic7—22no—
183C2×Dic7—22no—
184C2×Dic7—22no—
185C2×Dic7—22no—
186C2×Dic7—22no—
187C2×Dic7—42no—
188C2×Dic7—42no—
189C2×Dic7—42no—
190C2×Dic7—42no—
191C2×Dic7—42no—
192C2×Dic7—42no—
193C2×Dic7—42no—
194C2×Dic7—42no—
195C2×Dic7—82no—
196C2×Dic7—82no—
197C2×Dic7#10314yes—
198C7×C8—81no—
199C7⋊C8—81no—
200C22×Q8C4×D711yescharacteristic
201C23×C4—21no—
202C23×C4—71no—
203C23×C4—71no—
204C23×C4—141no—
205C23×C4C22×D711yescharacteristic
206C22×C8—21no—
207C22×C8—141no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211C22⋊Q8—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—72no—
214C2×C4⋊C4—142no—
215C2×C4⋊C4—144no—
216C2×C4⋊C4—282no—
217C2×C4⋊C4—282no—
218C2×C4⋊C4C4×D711yescharacteristic
219C2×C22⋊C4—21no—
220C2×C22⋊C4—141no—
221C2×C42—72no—
222C2×C42—72no—
223C2×C42—141no—
224C2×C42—141no—
225C2×C42—141no—
226C2×C42—141no—
227C22⋊C8—21no—
228C22⋊C8—21no—
229C22⋊C8—141no—
230C22⋊C8—141no—
231#95—21no—
232#95—72no—
233#95—142no—
234#95—142no—
235#95—142no—
236#95—144no—
237#95—141no—
238#95—141no—
239#95C22⋊D712yes—
240C22×C7—21no—
241C22×C7—21no—
242C22×C7—21no—
243C22×C7—21no—
244C22×C7—22no—
245C22×C7—22no—
246C22×C7—22no—
247C22×C7—22no—
248C22×C7#38611yescharacteristic
249C22×C7#41012yes—
250C22×C7C2×#10311yescharacteristic
251C22×C7#41711yescharacteristic
252C22×C7#42112yes—
253C22×C7#45011yescharacteristic
254C22×C7#45111yescharacteristic
255C22×C7#48311yescharacteristic
256C22×C7#48411yescharacteristic
257C4×C7—21no—
258C4×C7—21no—
259C4×C7—21no—
260C4×C7—21no—
261C4×C7—82no—
262C4×C7—81no—
263C4×C7—81no—
264Dic7—24no—
265Dic7—42no—
266Dic7—82no—
267Dic7—82no—
268C24D4×D711yescharacteristic
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—42no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—72no—
281C22×C4—72no—
282C22×C4—72no—
283C22×C4—72no—
284C22×C4—141no—
285C22×C4—141no—
286C22×C4—141no—
287C22×C4—141no—
288C22×C4—141no—
289C22×C4—141no—
290C22×C4—142no—
291C22×C4—142no—
292C22×C4—282no—
293C22×C4—282no—
294C22×C4—282no—
295C22×C4—281no—
296C22×C4—281no—
297C22×C4C2×C4×D711yescharacteristic
298C22×C4#115711yescharacteristic
299C22×C4D4×D711yescharacteristic
300C22×C4D4×D711yescharacteristic
301C22×C4#115911yescharacteristic
302C22×C4C2×C22⋊D711yescharacteristic
303C2×C8—42no—
304C2×C8—41no—
305C2×C8—282no—
306C2×C8—281no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—282no—
312C4⋊C4—284no—
313C4⋊C4—288no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—281no—
317C22⋊C4—281no—
318C42—142no—
319C42—142no—
320C42—142no—
321C42—142no—
322C2×C7—21no—
323C2×C7—21no—
324C2×C7—21no—
325C2×C7—21no—
326C2×C7#151212yes—
327C2×C7#151812yes—
328C2×C7#187211yescharacteristic
329C2×C7#189711yescharacteristic
330C2×C7#189911yescharacteristic
331C23—22no—
332C23—22no—
333C23D7×C22⋊C411yescharacteristic
334C23#644611yescharacteristic
335C23D7×SD1611yescharacteristic
336C23#647711yescharacteristic
337C23D7×Q1611yescharacteristic
338C23#648111yescharacteristic
339C23#650011yescharacteristic
340Q8—81no—
341Q8—81no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—74no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4—142no—
359C2×C4—142no—
360C2×C4—142no—
361C2×C4—142no—
362C2×C4—142no—
363C2×C4—142no—
364C2×C4—142no—
365C2×C4—142no—
366C2×C4—142no—
367C2×C4—282no—
368C2×C4—282no—
369C2×C4—282no—
370C2×C4—282no—
371C2×C4—282no—
372C2×C4—282no—
373C2×C4—282no—
374C2×C4—282no—
375C2×C4—562no—
376C2×C4—562no—
377C2×C4(C22⋊D7)⋊C411yescharacteristic
378C2×C4#644711yescharacteristic
379C2×C4C4×C22⋊D711yescharacteristic
380C2×C4#650111yescharacteristic
381C8—81no—
382C8—561no—
383C7#915211yescharacteristic, complemented, Sylow
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22#8951212yes—
393C22D7×#10311yescharacteristic
394C22#8957511yescharacteristic
395C22#8957711yescharacteristic
396C22#8958111yescharacteristic
397C22#8959312yes—
398C22#8972811yescharacteristic
399C22#8994111yescharacteristic
400C22#8995811yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—82no—
406C4—81no—
407C4—81no—
408C4—144no—
409C4—282no—
410C4—562no—
411C4—562no—
412C2—21no—
413C2—21no—
414C2—21no—
415C2—21no—
416C2#1172606612yes—
417C2#1172606812yes—
418C2#1172778311yescharacteristic
419C2#1172802211yescharacteristic
420C2#1172813711yescharacteristic
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#9152
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
13. #90002C4semidirect
19. #89745C4semidirect
383. C7#9152semidirect

Maximal subgroups

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

subgroupindex
#117402552
C2×#894222
C2×C7×#3282
C2×#893332
#117276642
#117254812
#117254182
#91527