Finite Group Databasebeta

← #13249263

Subgroups — #13249263

Order 1792.

546 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C8×#41C211yesmaximal, characteristic, complemented
2C4×#6512C211yesmaximal, characteristic
3#11729393C211yesmaximal, characteristic, complemented
4#11728537C211yesmaximal, characteristic, complemented
5C2×#89254C211yesmaximal, characteristic, complemented
6#11725550C211yesmaximal, characteristic, complemented
7#11725462C211yesmaximal, characteristic, complemented
8C4×C7×#41C2211yescharacteristic
9C2×#6512C411yescharacteristic
10C2×C4×D28C2211yescharacteristic
11C7×C8×Q8—21no—
12C7×C8×D4—21no—
13C7×C8×D4—22no—
14C7×#431—21no—
15C7×#431C2211yescharacteristic
16C2×C4×C7×C8—21no—
17C2×C4×C7×C8C2211yescharacteristic
18#90004C411yescharacteristic
19#89798—21no—
20C4×#1143—21no—
21#89786—21no—
22C4×#1141—21no—
23#89773C411yescharacteristic
24#89767C411yescharacteristic
25#89697C2211yescharacteristic
26C2×C4⋊(C7⋊C8)C2211yescharacteristic
27C4×#1136C2211yescharacteristic
28Q8⋊(C7⋊C8)—21no—
29D4⋊(C7⋊C8)—21no—
30#89263—22no—
31#89254—21no—
32#89254—21no—
33#9095—71nomaximal, Sylow
34C2×C7×#41C2×C411yescharacteristic
35C22×D28C2×C411yescharacteristic
36C22×C4×D7—21no—
37C22×C7×C8—22no—
38C22×C7×C8—21no—
39C4×C7×Q8D411yescharacteristic
40C4×C7×Q8D411yescharacteristic
41C4×C7×D4—21no—
42C4×C7×D4—21no—
43C4×C7×D4D411yescharacteristic
44C4×C7×D4D411yescharacteristic
45C7×#117—21no—
46C7×#117C2×C411yescharacteristic
47C2×C42×C7—21no—
48C2×C42×C7C2311yescharacteristic
49#6512—22no—
50#6512C814yescomplemented
51C2×#1143—21no—
52C2×#1141—21no—
53C2×(C2×D7)⋊C4—21no—
54C2×C4⋊Dic7C2×C411yescharacteristic
55C2×#1136C2×C411yescharacteristic
56C2×#1136C2×C411yescharacteristic
57C22×C7⋊C8—21no—
58C4×D28—21no—
59C4×D28—21no—
60C4×D28—21no—
61C4×D28—21no—
62C7×C4⋊C8—22no—
63C7×C4⋊C8—21no—
64C7×C22⋊C8—22no—
65C7×C22⋊C8D412yes—
66C4×C7×C8—22no—
67C4×C7×C8—21no—
68C4×C7×C8—21no—
69C4×C7×C8D411yescharacteristic
70C4×C7×C8D411yescharacteristic
71#6409—21no—
72#6406—21no—
73C22⋊(C7⋊C8)—21no—
74#6383—21no—
75#6383—21no—
76#6382—21no—
77#6381—21no—
78C4⋊(C7⋊C8)—21no—
79C4⋊(C7⋊C8)—21no—
80C4⋊(C7⋊C8)—21no—
81#6377—21no—
82C4×C7⋊C8—21no—
83C4×C7⋊C8—21no—
84C8×#41D711yescharacteristic, complemented
85C4×AGL(1,ℤ/8)—71no—
86#1477—71no—
87C2×D4⋊C8—71no—
88#1460—71no—
89#1283—71no—
90#1278—71no—
91C23×D7—21no—
92C7×#41—21no—
93C7×#41—21no—
94C7×#41C2×C812yes—
95C7×#41M1612yes—
96C2×C7×Q8C22⋊C411yescharacteristic
97C2×C7×D4—21no—
98C2×C7×D4C22⋊C411yescharacteristic
99C22×C4×C7—21no—
100C22×C4×C7—21no—
101C22×C4×C7—21no—
102C22×C4×C7C22×C411yescharacteristic
103C22×C4×C7C2×D411yescharacteristic
104C22×C4×C7#4111yescharacteristic
105C22×Dic7—21no—
106C2×D28—21no—
107C2×D28—21no—
108C2×D28—21no—
109C2×D28—21no—
110C2×D28—21no—
111C2×D28C2×C812yescomplemented
112C2×C4×D7—41no—
113C2×C4×D7—41no—
114C2×C4×D7—81no—
115C2×C4×D7—81no—
116C2×C7×C8—21no—
117C2×C7×C8—22no—
118C2×C7×C8—21no—
119C2×C7×C8—42no—
120C2×C7×C8—44no—
121C7×C4⋊C4—21no—
122C7×C4⋊C4—21no—
123C7×C4⋊C4C22⋊C411yescharacteristic
124C7×C4⋊C4C22⋊C411yescharacteristic
125C7×C22⋊C4—21no—
126C7×C22⋊C4—21no—
127C7×C22⋊C4—21no—
128C42×C7—21no—
129C42×C7—21no—
130C42×C7—21no—
131C42×C7C2×D411yescharacteristic
132C42×C7C2×D411yescharacteristic
133C42×C7C2×D411yescharacteristic
134C42×C7#4111yescharacteristic
135#1143—24no—
136#1141—24no—
137(C2×D7)⋊C4—41no—
138(C2×D7)⋊C4—41no—
139C4⋊Dic7—21no—
140C4⋊Dic7—21no—
141#1136—21no—
142#1136—21no—
143#1136—21no—
144#1136C2×C812yescomplemented
145C2×C7⋊C8—21no—
146C2×C7⋊C8—21no—
147C2×C7⋊C8—41no—
148C2×C7⋊C8—41no—
149C2×C7⋊C8—81no—
150C2×AGL(1,ℤ/8)—71no—
151C4×#41C2×D711yescharacteristic
152C2×C4×D4—71no—
153C8×Q8—21no—
154#442—141no—
155#440—141no—
156C4×SD16—141no—
157C4×D8—141no—
158C8×D4—21no—
159C8×D4—22no—
160#431—21no—
161#431—71no—
162#431C2×D711yescharacteristic
163#428—71no—
164C2×C4⋊C8—71no—
165#418—71no—
166#417—71no—
167C4×M16—71no—
168C2×C4×C8—21no—
169C2×C4×C8C2×D711yescharacteristic
170Q8⋊C8—141no—
171D4⋊C8—141no—
172D4⋊C8—141no—
173D4⋊C8—141no—
174#323—142no—
175C23×C7—21no—
176C23×C7C4×D411yescharacteristic
177C22×D7—22no—
178C22×D7—41no—
179C22×D7—41no—
180C22×D7—81no—
181C22×D7—81no—
182C7×Q8—21no—
183C7×Q8C22⋊C812yes—
184C7×D4—22no—
185C7×D4—22no—
186C7×D4—21no—
187C7×D4C22⋊C812yes—
188C2×C4×C7—21no—
189C2×C4×C7—22no—
190C2×C4×C7—22no—
191C2×C4×C7—21no—
192C2×C4×C7—21no—
193C2×C4×C7—21no—
194C2×C4×C7—21no—
195C2×C4×C7—41no—
196C2×C4×C7—42no—
197C2×C4×C7—41no—
198C2×C4×C7—41no—
199C2×C4×C7C2×C22⋊C411yescharacteristic
200C2×C4×C7C4×D411yescharacteristic
201C2×C4×C7#12011yescharacteristic
202C2×C4×C7#12111yescharacteristic
203C2×C4×C7#12111yescharacteristic
204C2×C4×C7#12311yescharacteristic
205C2×C4×C7C22×C811yescharacteristic
206C2×C4×C7C2×M1611yescharacteristic
207C2×C4×C7#13111yescharacteristic
208C2×C4×C7#13111yescharacteristic
209C2×Dic7—41no—
210C2×Dic7—81no—
211D28—22no—
212D28—22no—
213D28—41no—
214D28—41no—
215C4×D7—82no—
216C4×D7—81no—
217C4×D7—81no—
218C7×C8—22no—
219C7×C8—42no—
220C7×C8—41no—
221C7⋊C8—22no—
222C7⋊C8—41no—
223C7⋊C8—81no—
224C7⋊C8—81no—
225C2×#41C4×D711yescharacteristic
226C22×D4—71no—
227C23×C4—141no—
228AGL(1,ℤ/8)—74no—
229AGL(1,ℤ/8)—142no—
230C2×SD16—141no—
231C2×D8—141no—
232C2×M16—71no—
233C2×M16—71no—
234C22×C8—22no—
235C22×C8—21no—
236C22×C8—141no—
237C4×Q8D2811yescharacteristic
238C4×Q8C22⋊D711yescharacteristic
239C4×D4—21no—
240C4×D4—21no—
241C4×D4—141no—
242C4×D4—141no—
243C4×D4—141no—
244C4×D4—141no—
245C4×D4D2811yescharacteristic
246C4×D4C22⋊D711yescharacteristic
247#117—21no—
248#117C4×D711yescharacteristic
249C2×C4⋊C4—71no—
250C2×C22⋊C4—141no—
251C2×C42—21no—
252C2×C42C22×D711yescharacteristic
253#107—141no—
254#106—141no—
255C4⋊C8—22no—
256C4⋊C8—21no—
257C4⋊C8—141no—
258C4⋊C8—141no—
259C4⋊C8—141no—
260#103—141no—
261#102—141no—
262#102—141no—
263#102—141no—
264C22⋊C8—22no—
265C22⋊C8—141no—
266C22⋊C8C22⋊D712yes—
267#97—141no—
268C4×C8—22no—
269C4×C8—21no—
270C4×C8—21no—
271C4×C8—141no—
272C4×C8—141no—
273C4×C8C22⋊D711yescharacteristic
274C4×C8C22⋊D711yescharacteristic
275C22×C7—21no—
276C22×C7—21no—
277C22×C7—22no—
278C22×C7—41no—
279C22×C7—41no—
280C22×C7#38611yescharacteristic
281C22×C7C8×D411yescharacteristic
282C22×C7#43511yescharacteristic
283C2×D7—42no—
284C2×D7—82no—
285C2×D7—81no—
286C2×D7—81no—
287C2×D7—82no—
288C4×C7—22no—
289C4×C7—21no—
290C4×C7—21no—
291C4×C7—21no—
292C4×C7—41no—
293C4×C7—41no—
294C4×C7C2×C22⋊C811yescharacteristic
295C4×C7#40811yescharacteristic
296C4×C7C8×D411yescharacteristic
297C4×C7#43511yescharacteristic
298C4×C7#47111yescharacteristic
299C4×C7#47211yescharacteristic
300Dic7—81no—
301C24—141no—
302#41—21no—
303#41—21no—
304#41C8×D712yes—
305#41#113112yes—
306C2×Q8(C2×D7)⋊C411yescharacteristic
307C2×D4—21no—
308C2×D4—72no—
309C2×D4—141no—
310C2×D4—141no—
311C2×D4—141no—
312C2×D4—141no—
313C2×D4—141no—
314C2×D4(C2×D7)⋊C411yescharacteristic
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—141no—
319C22×C4—281no—
320C22×C4—281no—
321C22×C4—561no—
322C22×C4—561no—
323C22×C4C2×C4×D711yescharacteristic
324C22×C4#115711yescharacteristic
325C22×C4C2×C22⋊D711yescharacteristic
326SD16—144no—
327D8—144no—
328M16—72no—
329M16—141no—
330M16—141no—
331M16—141no—
332C2×C8—21no—
333C2×C8—22no—
334C2×C8—21no—
335C2×C8—42no—
336C2×C8—44no—
337C2×C8—141no—
338C2×C8—141no—
339C2×C8—281no—
340C2×C8—281no—
341C2×C8—561no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—141no—
345C4⋊C4—141no—
346C4⋊C4(C2×D7)⋊C411yescharacteristic
347C4⋊C4(C2×D7)⋊C411yescharacteristic
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—281no—
352C22⋊C4—281no—
353C42—21no—
354C42—21no—
355C42—21no—
356C42C2×D2811yescharacteristic
357C42#115711yescharacteristic
358C42C2×C22⋊D711yescharacteristic
359C42C2×C22⋊D711yescharacteristic
360C2×C7—21no—
361C2×C7—21no—
362C2×C7—42no—
363C2×C7#186911yescharacteristic
364C2×C7#190611yescharacteristic
365C2×C7#190711yescharacteristic
366D7—82no—
367C23—21no—
368C23—142no—
369C23—281no—
370C23—281no—
371C23—561no—
372C23—561no—
373C23C4×C22⋊D711yescharacteristic
374Q8—21no—
375Q8(C2×D7)⋊C812yes—
376D4—22no—
377D4—22no—
378D4—21no—
379D4—142no—
380D4—142no—
381D4—281no—
382D4—281no—
383D4(C2×D7)⋊C812yes—
384C2×C4—21no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—281no—
396C2×C4—562no—
397C2×C4—561no—
398C2×C4—561no—
399C2×C4—561no—
400C2×C4C2×C8×D711yescharacteristic
401C2×C4C2×#113111yescharacteristic
402C2×C4#646411yescharacteristic
403C2×C4#646411yescharacteristic
404C2×C4C2×(C2×D7)⋊C411yescharacteristic
405C2×C4C4×C22⋊D711yescharacteristic
406C2×C4#649211yescharacteristic
407C2×C4#649311yescharacteristic
408C2×C4#649311yescharacteristic
409C2×C4#651611yescharacteristic
410C8—22no—
411C8—42no—
412C8—41no—
413C8—142no—
414C8—281no—
415C8—561no—
416C8—561no—
417C7#909511yescharacteristic, complemented, Sylow
418C22—21no—
419C22—21no—
420C22—22no—
421C22—41no—
422C22—41no—
423C22—282no—
424C22—562no—
425C22—562no—
426C22—561no—
427C22—561no—
428C22C8×C22⋊D711yescharacteristic
429C22#8988311yescharacteristic
430C22#8998511yescharacteristic
431C4—22no—
432C4—21no—
433C4—21no—
434C4—21no—
435C4—41no—
436C4—41no—
437C4—561no—
438C4C2×(C2×D7)⋊C811yescharacteristic
439C4C8×C22⋊D711yescharacteristic
440C4#8988211yescharacteristic
441C4#8988311yescharacteristic
442C4#8991311yescharacteristic
443C4#8991411yescharacteristic
444C2—21no—
445C2—21no—
446C2—42no—
447C2—562no—
448C2#1172939911yescharacteristic
449C2#1172972911yescharacteristic
450C2#1172977211yescharacteristic
subgroupG/H
centerC2×C4#6493
commutatorC2×C4×C7C22×C8
FrattiniC2×C42C22×D7
FittingC7×C8×#41C2
socleC22×C7#386
prime radicalC2×#6512C4
cosocleC2×C42×C7C23
hypercenterC8×#41D7
hypocenterC7#9095
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
1. C7×C8×#41C2semidirect
3. #11729393C2semidirect
4. #11728537C2semidirect
5. C2×#89254C2semidirect
6. #11725550C2semidirect
7. #11725462C2semidirect
50. #6512C8semidirect
84. C8×#41D7semidirect
111. C2×D28C2×C8semidirect
144. #1136C2×C8semidirect
417. C7#9095semidirect

Maximal subgroups

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

subgroupindex
C7×C8×#412
C4×#65122
#117293932
#117285372
C2×#892542
#117255502
#117254622
#90957