Finite Group Databasebeta

← #13248643

Subgroups — #13248643

Order 1792.

540 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3101C211yesmaximal, characteristic
2D4×#1136C211yesmaximal, characteristic
3#11729595C211yesmaximal, characteristic, complemented
4#11729580C211yesmaximal, characteristic, complemented
5C4×#6406C211yesmaximal, characteristic
6#11725552C211yesmaximal, characteristic, complemented
7#11725545C211yesmaximal, characteristic, complemented
8C7×#533C2211yescharacteristic
9C2×C4×C7×D4C2211yescharacteristic
10C22×#1136—21no—
11C7×#483—21no—
12C7×#476C411yescharacteristic, complemented
13C7×#476C411yescharacteristic, complemented
14C7×#461C411yescharacteristic, complemented
15C7×#461C411yescharacteristic, complemented
16C7×#450—21no—
17C4×C7×SD16—21no—
18C4×C7×SD16—21no—
19C7×#431C2211yescharacteristic
20C2×#6406—21no—
21#89979—21no—
22#89784—21no—
23#89783—22no—
24D4×C7⋊C8—21no—
25C4×C4⋊Dic7C2211yescharacteristic
26#89696C2211yescharacteristic
27C4×#1136C2211yescharacteristic
28C2×C4×C7⋊C8C2211yescharacteristic
29Q8⋊(C7⋊C8)—22no—
30#89327—21no—
31#89327—21no—
32#89324—21no—
33#8989—71nomaximal, Sylow
34C22×C7×D4D411yescharacteristic
35C23×C4×C7—21no—
36C2×C7×SD16—21no—
37C2×C7×SD16—21no—
38C7×C4⋊Q8C2×C411yescharacteristic
39C7×C4⋊Q8C2×C411yescharacteristic
40C7×#125—21no—
41C7×C22⋊Q8—21no—
42C7×C22⋊Q8—21no—
43C4×C7×Q8—21no—
44C4×C7×Q8—21no—
45C4×C7×D4—21no—
46C4×C7×D4—21no—
47C4×C7×D4C2×C411yescharacteristic
48C4×C7×D4C2×C411yescharacteristic
49C4×C7×D4D411yescharacteristic
50C4×C7×D4D411yescharacteristic
51C7×#117—21no—
52C2×C7×C4⋊C4D411yescharacteristic
53C2×C7×C22⋊C4—21no—
54C2×C42×C7C2311yescharacteristic
55C2×C4⋊Dic7—21no—
56C2×C4×Dic7—21no—
57C2×#1136—22no—
58C2×#1136—21no—
59C2×#1136—42no—
60C2×#1136—42no—
61C2×#1136D411yescharacteristic
62C2×#1136D411yescharacteristic
63C22×C7⋊C8—22no—
64C22×C7⋊C8—21no—
65C7×#106—21no—
66C7×#106—21no—
67C7×C4⋊C8C2×C411yescharacteristic
68C7×C4⋊C8C2×C411yescharacteristic
69C7×#103—21no—
70C7×#103—21no—
71C7×#102—21no—
72C7×#102—21no—
73C7×C22⋊C8—21no—
74C4×C7×C8—21no—
75#6406—24no—
76C7⋊#95—21no—
77C22⋊(C7⋊C8)—22no—
78C22⋊(C7⋊C8)—22no—
79C4⋊(C7⋊C8)—21no—
80C4⋊(C7⋊C8)D412yes—
81#6377—21no—
82C4×C7⋊C8—21no—
83C4×C7⋊C8—21no—
84C4×C7⋊C8—21no—
85#3101D711yescharacteristic
86D4×M16—71no—
87#1986—71no—
88C4×#102—71no—
89#1493—71no—
90#1303—71no—
91#1278—71no—
92C24×C7—21no—
93C2×C7×Q8—21no—
94C2×C7×Q8—21no—
95C2×C7×D4—22no—
96C2×C7×D4—21no—
97C2×C7×D4—41no—
98C2×C7×D4C22⋊C411yescharacteristic
99C2×C7×D4C22⋊C411yescharacteristic
100C22×C4×C7—21no—
101C22×C4×C7—21no—
102C22×C4×C7—21no—
103C22×C4×C7—21no—
104C22×C4×C7—21no—
105C22×C4×C7—41no—
106C22×C4×C7—41no—
107C22×C4×C7—41no—
108C22×C4×C7—41no—
109C22×C4×C7C2×D411yescharacteristic
110C22×C4×C7C2×D411yescharacteristic
111C22×C4×C7#4111yescharacteristic
112C22×Dic7—41no—
113C7×SD16—42no—
114C7×SD16—42no—
115C2×C7×C8—21no—
116C2×C7×C8—21no—
117C7×C4⋊C4—21no—
118C7×C4⋊C4—21no—
119C7×C4⋊C4—21no—
120C7×C4⋊C4—21no—
121C7×C4⋊C4—21no—
122C7×C4⋊C4—41no—
123C7×C4⋊C4—41no—
124C7×C4⋊C4C22⋊C411yescharacteristic
125C7×C4⋊C4C22⋊C411yescharacteristic
126C7×C22⋊C4—21no—
127C7×C22⋊C4—21no—
128C7×C22⋊C4—21no—
129C7×C22⋊C4—21no—
130C7×C22⋊C4—41no—
131C42×C7—41no—
132C42×C7C22×C411yescharacteristic
133C42×C7C2×D411yescharacteristic
134C42×C7C2×D411yescharacteristic
135C42×C7#4111yescharacteristic
136C4⋊Dic7—22no—
137C4⋊Dic7—41no—
138C4×Dic7—41no—
139C4×Dic7—41no—
140#1136—21no—
141#1136—21no—
142#1136—21no—
143#1136—44no—
144#1136—41no—
145#1136—41no—
146#1136SD1612yescomplemented
147C2×C7⋊C8—21no—
148C2×C7⋊C8—22no—
149C2×C7⋊C8—21no—
150C2×C7⋊C8—22no—
151C2×C7⋊C8—44no—
152C2×C7⋊C8—41no—
153C2×C7⋊C8—41no—
154C22×M16—141no—
155#533C2×D711yescharacteristic
156C2×C4×D4C2×D711yescharacteristic
157#483—21no—
158#476Dic711yescharacteristic, complemented
159#476Dic711yescharacteristic, complemented
160#461Dic711yescharacteristic, complemented
161#461Dic711yescharacteristic, complemented
162#450—21no—
163C4×SD16—21no—
164C4×SD16—21no—
165#436—141no—
166#435—142no—
167C8×D4—141no—
168#431C2×D711yescharacteristic
169#423—71no—
170C2×#102—141no—
171#407—141no—
172C4×M16—71no—
173C2×C4×C8—71no—
174C4×C4⋊C4—71no—
175#340—141no—
176#339—141no—
177#339—141no—
178Q8⋊C8—142no—
179C23×C7—21no—
180C23×C7—21no—
181C23×C7—42no—
182C23×C7—41no—
183C23×C7—41no—
184C23×C7—81no—
185C23×C7#12111yescharacteristic
186C7×Q8—42no—
187C7×Q8—41no—
188C7×Q8—41no—
189C7×D4—21no—
190C7×D4—21no—
191C7×D4—21no—
192C7×D4—42no—
193C7×D4#10412yes—
194C2×C4×C7—21no—
195C2×C4×C7—21no—
196C2×C4×C7—21no—
197C2×C4×C7—21no—
198C2×C4×C7—41no—
199C2×C4×C7—41no—
200C2×C4×C7—41no—
201C2×C4×C7—41no—
202C2×C4×C7—41no—
203C2×C4×C7—41no—
204C2×C4×C7—41no—
205C2×C4×C7—41no—
206C2×C4×C7—41no—
207C2×C4×C7—41no—
208C2×C4×C7—41no—
209C2×C4×C7—41no—
210C2×C4×C7—41no—
211C2×C4×C7C2×C22⋊C411yescharacteristic
212C2×C4×C7C4×D411yescharacteristic
213C2×C4×C7C4×D411yescharacteristic
214C2×C4×C7#12011yescharacteristic
215C2×C4×C7#12111yescharacteristic
216C2×C4×C7#12311yescharacteristic
217C2×C4×C7C2×SD1611yescharacteristic
218C2×C4×C7#13511yescharacteristic
219C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
220C2×C4×C7#13711yescharacteristic
221C2×Dic7—42no—
222C2×Dic7—81no—
223C2×Dic7—81no—
224C7×C8—41no—
225C7×C8—41no—
226C7⋊C8—22no—
227C7⋊C8—42no—
228C7⋊C8—42no—
229C7⋊C8—41no—
230C22×D4C22⋊D711yescharacteristic
231C23×C4—21no—
232C2×SD16—21no—
233C2×SD16—21no—
234C2×M16—71no—
235C2×M16—71no—
236C2×M16—142no—
237C2×M16—141no—
238C2×M16—282no—
239C2×M16—282no—
240C22×C8—142no—
241C22×C8—141no—
242C4⋊Q8C2×Dic711yescharacteristic
243C4⋊Q8C2×Dic711yescharacteristic
244#125—21no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4C2×Dic711yescharacteristic
252C4×D4C2×Dic711yescharacteristic
253C4×D4C22⋊D711yescharacteristic
254C4×D4C22⋊D711yescharacteristic
255#117—21no—
256C2×C4⋊C4—141no—
257C2×C4⋊C4C22⋊D711yescharacteristic
258C2×C22⋊C4—21no—
259C2×C42—141no—
260C2×C42C22×D711yescharacteristic
261#106—21no—
262#106—21no—
263C4⋊C8—72no—
264C4⋊C8—141no—
265C4⋊C8C2×Dic711yescharacteristic
266C4⋊C8C2×Dic711yescharacteristic
267#103—21no—
268#103—21no—
269#102—21no—
270#102—21no—
271#102—144no—
272C22⋊C8—21no—
273C22⋊C8—142no—
274C22⋊C8—142no—
275#97—141no—
276C4×C8—21no—
277C4×C8—141no—
278C4×C8—141no—
279C4×C8—141no—
280#95—141no—
281C22×C7—21no—
282C22×C7—21no—
283C22×C7—22no—
284C22×C7—41no—
285C22×C7—41no—
286C22×C7—41no—
287C22×C7—41no—
288C22×C7—41no—
289C22×C7—82no—
290C22×C7—82no—
291C22×C7#38611yescharacteristic
292C22×C7#46111yescharacteristic
293C22×C7#46311yescharacteristic
294C4×C7—21no—
295C4×C7—21no—
296C4×C7—21no—
297C4×C7—41no—
298C4×C7—41no—
299C4×C7—81no—
300C4×C7—81no—
301C4×C7C2×#10411yescharacteristic
302C4×C7#42111yescharacteristic
303C4×C7C4×SD1611yescharacteristic
304C4×C7#44011yescharacteristic
305C4×C7#45011yescharacteristic
306C4×C7#45211yescharacteristic
307Dic7—82no—
308C24—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×D4—22no—
312C2×D4—21no—
313C2×D4—41no—
314C2×D4C22⋊Dic711yescharacteristic
315C2×D4C22⋊Dic711yescharacteristic
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—281no—
326C22×C4D4×D711yescharacteristic
327C22×C4#115911yescharacteristic
328C22×C4C2×C22⋊D711yescharacteristic
329SD16—42no—
330SD16—42no—
331M16—72no—
332M16—141no—
333M16—141no—
334M16—141no—
335M16—284no—
336M16—281no—
337M16—281no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—141no—
341C2×C8—142no—
342C2×C8—141no—
343C2×C8—142no—
344C2×C8—284no—
345C2×C8—281no—
346C2×C8—281no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—142no—
355C4⋊C4—281no—
356C4⋊C4C22⋊Dic711yescharacteristic
357C4⋊C4C22⋊Dic711yescharacteristic
358C22⋊C4—21no—
359C22⋊C4—21no—
360C22⋊C4—21no—
361C22⋊C4—21no—
362C22⋊C4—41no—
363C42—41no—
364C42—281no—
365C42—281no—
366C42D4×D711yescharacteristic
367C42#115911yescharacteristic
368C42C22×Dic711yescharacteristic
369C42C2×C22⋊D711yescharacteristic
370C2×C7—21no—
371C2×C7—21no—
372C2×C7—42no—
373C2×C7—81no—
374C2×C7#187111yescharacteristic
375C2×C7#187711yescharacteristic
376C2×C7#188111yescharacteristic
377C23—21no—
378C23—21no—
379C23—42no—
380C23—41no—
381C23—41no—
382C23—81no—
383C23#650211yescharacteristic
384Q8—42no—
385Q8—41no—
386Q8—41no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—42no—
391D4#641112yes—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—282no—
410C2×C4—561no—
411C2×C4—561no—
412C2×C4D7×SD1611yescharacteristic
413C2×C4#647711yescharacteristic
414C2×C4#647811yescharacteristic
415C2×C4#647911yescharacteristic
416C2×C4D4×Dic711yescharacteristic
417C2×C4D4×Dic711yescharacteristic
418C2×C4#649811yescharacteristic
419C2×C4#650011yescharacteristic
420C2×C4#650211yescharacteristic
421C2×C4C2×C22⋊Dic711yescharacteristic
422C8—41no—
423C8—41no—
424C8—142no—
425C8—282no—
426C8—282no—
427C8—281no—
428C7#898911yescharacteristic, complemented, Sylow
429C22—21no—
430C22—21no—
431C22—22no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—82no—
438C22—82no—
439C22#8993411yescharacteristic
440C22#8993711yescharacteristic
441C22#8999211yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—41no—
446C4—41no—
447C4—81no—
448C4—81no—
449C4—562no—
450C4SD16×Dic711yescharacteristic
451C4#8993611yescharacteristic
452C4#8994111yescharacteristic
453C4#8994511yescharacteristic
454C4C2×#641111yescharacteristic
455C4#9000811yescharacteristic
456C2—21no—
457C2—21no—
458C2—42no—
459C2—81no—
460C2#1172946711yescharacteristic
461C2#1172980111yescharacteristic
462C2#1172987011yescharacteristic
subgroupG/H
centerC2×C4#6500
commutatorC42×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#3101C2
socleC22×C7#386
prime radicalC22×C7×D4D4
cosocleC2×C42×C7C23
hypercenter#3101D7
hypocenterC7#8989
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3101

Complements

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

NH ≅ G/Ntype
3. #11729595C2semidirect
4. #11729580C2semidirect
6. #11725552C2semidirect
7. #11725545C2semidirect
12. C7×#476C4semidirect
13. C7×#476C4semidirect
14. C7×#461C4semidirect
15. C7×#461C4semidirect
146. #1136SD16semidirect
158. #476Dic7semidirect
159. #476Dic7semidirect
160. #461Dic7semidirect
161. #461Dic7semidirect
428. C7#8989semidirect

Maximal subgroups

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

subgroupindex
C7×#31012
D4×#11362
#117295952
#117295802
C4×#64062
#117255522
#117255452
#89897