Finite Group Databasebeta

← #13395116

Subgroups — #13395116

Order 1792.

828 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#432C211yesmaximal, characteristic
2#11739521C211yesmaximal, characteristic
3C4×#6487C211yesmaximal, characteristic
4C2×#89622C211yesmaximal, characteristic, complemented
5#11728239C211yesmaximal, characteristic, complemented
6#11728213C211yesmaximal, characteristic, complemented
7#11728208C211yesmaximal, characteristic, complemented
8#11727692C212yesmaximal
9#11727690C212yesmaximal
10#11727574C212yesmaximal, complemented
11#11727571C212yesmaximal, complemented
12C22×C42×C7C2211yescharacteristic
13C2×#6487—21no—
14C2×#6487C2211yescharacteristic
15C2×#6432C2211yescharacteristic
16C2×C4×Dic14C2211yescharacteristic
17C7×#432—24no—
18C2×C7×C4⋊C8C2211yescharacteristic
19C2×C7×C4⋊C8C2211yescharacteristic
20C2×C7×C22⋊C8C2212yes—
21C2×C7×#97C2212yes—
22#89984—21no—
23#89984C2212yes—
24#89984C2211yescharacteristic
25#89982—21no—
26C4×C22⋊Dic7—21no—
27C2×#6392C2212yes—
28C2×#6391C2212yes—
29C2×#6390C2212yes—
30C2×#6390C2212yes—
31#89707C2211yescharacteristic
32C4×C4⋊Dic7C2211yescharacteristic
33#89705—21no—
34C4×Dic7⋊C4—21no—
35#89701—21no—
36#89701C2211yescharacteristic
37#89700—21no—
38#89700C2211yescharacteristic
39#89700C2212yes—
40#89622—24no—
41#89346C2212yes—
42#89346C2212yes—
43#89346C2212yes—
44#89346C2212yes—
45#24711—71nomaximal, Sylow
46C23×C4×C7D411yescharacteristic
47C23×C4×C7D411yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C22×Dic14—21no—
50C22×Dic14C2311yescharacteristic
51C22×C7×C8C2312yes—
52C22×C7×C8C2312yes—
53C2×C42×C7—22no—
54C2×C42×C7—22no—
55C2×C42×C7D411yescharacteristic
56C2×C42×C7D411yescharacteristic
57C2×C42×C7C2311yescharacteristic
58C2×C42×C7C2311yescharacteristic
59C2×C22⋊Dic7—21no—
60C2×C22⋊Dic7—22no—
61C2×C22⋊Dic7—21no—
62C2×C4⋊Dic7—21no—
63C2×C4⋊Dic7—21no—
64C2×C4⋊Dic7—21no—
65C2×C4⋊Dic7C2311yescharacteristic
66C2×C4⋊Dic7C2312yes—
67C2×C4⋊Dic7C2312yes—
68C2×C4⋊Dic7C2311yescharacteristic
69C2×C4⋊Dic7C2311yescharacteristic
70#6487—22no—
71#6487—22no—
72#6487—44no—
73C2×Dic7⋊C4—21no—
74C2×Dic7⋊C4—21no—
75C2×Dic7⋊C4—22no—
76C2×Dic7⋊C4—21no—
77C2×C4×Dic7—21no—
78C2×C4×Dic7—21no—
79#6432—22no—
80#6432—22no—
81C4×Dic14—22no—
82C4×Dic14—22no—
83C7×C4⋊C8—22no—
84C7×C4⋊C8D414yes—
85C7×C22⋊C8—24no—
86C7×#97—24no—
87C7⋊#95—22no—
88C7⋊#95—22no—
89C7⋊#95—21no—
90C7⋊#95—21no—
91C7⋊#95—21no—
92C7⋊#95—21no—
93C7⋊#95—21no—
94#6392—24no—
95#6391—24no—
96#6390—24no—
97#6390—24no—
98C2×#477—71no—
99C2×#432D711yescharacteristic
100#2857—71no—
101C4×C22⋊Q8—71no—
102#2075—72no—
103#2035—72no—
104#1987—71no—
105#1948—71no—
106#1944—72no—
107#1935—72no—
108#1803—71no—
109C24×C7C2×D411yescharacteristic
110C22×C4×C7—22no—
111C22×C4×C7—22no—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7—22no—
115C22×C4×C7—21no—
116C22×C4×C7—21no—
117C22×C4×C7—21no—
118C22×C4×C7—21no—
119C22×C4×C7—21no—
120C22×C4×C7—21no—
121C22×C4×C7—41no—
122C22×C4×C7C2×D411yescharacteristic
123C22×C4×C7C2×D411yescharacteristic
124C22×C4×C7C2×D411yescharacteristic
125C22×C4×C7C2×D411yescharacteristic
126C22×C4×C7C2×D411yescharacteristic
127C22×C4×C7C2411yescharacteristic
128C22×Dic7—21no—
129C22×Dic7—21no—
130C22×Dic7—21no—
131C22×Dic7—21no—
132C22×Dic7—22no—
133C22×Dic7—22no—
134C2×Dic14—21no—
135C2×Dic14—21no—
136C2×Dic14—21no—
137C2×Dic14—21no—
138C2×Dic14—21no—
139C2×Dic14—42no—
140C2×Dic14—42no—
141C2×Dic14—42no—
142C2×Dic14#4112yes—
143C2×C7×C8—22no—
144C2×C7×C8—22no—
145C2×C7×C8—22no—
146C2×C7×C8—22no—
147C2×C7×C8—22no—
148C2×C7×C8C2×D414yes—
149C42×C7—22no—
150C42×C7—22no—
151C42×C7—21no—
152C42×C7—21no—
153C42×C7C2×D412yes—
154C42×C7#4112yes—
155C22⋊Dic7—24no—
156C22⋊Dic7—44no—
157C22⋊Dic7—42no—
158C4⋊Dic7—21no—
159C4⋊Dic7—21no—
160C4⋊Dic7—22no—
161C4⋊Dic7—21no—
162C4⋊Dic7—22no—
163C4⋊Dic7—22no—
164C4⋊Dic7—22no—
165C4⋊Dic7—21no—
166C4⋊Dic7—21no—
167C4⋊Dic7—42no—
168C4⋊Dic7—42no—
169C4⋊Dic7—42no—
170C4⋊Dic7#4112yes—
171Dic7⋊C4—24no—
172Dic7⋊C4—42no—
173Dic7⋊C4—44no—
174Dic7⋊C4—42no—
175C4×Dic7—42no—
176C4×Dic7—42no—
177C2×C4⋊Q8—71no—
178C2×C22⋊Q8—71no—
179C2×C22⋊Q8—141no—
180C2×C4×Q8—71no—
181C22×C42C2×D711yescharacteristic
182#477—144no—
183#432—24no—
184C2×#107—72no—
185C2×#106—72no—
186C2×C4⋊C8C2×D711yescharacteristic
187C2×C4⋊C8C2×D711yescharacteristic
188C2×#103—72no—
189C2×#103—72no—
190C2×C22⋊C8C2×D712yes—
191C2×#97C2×D712yes—
192#391—71no—
193#391—141no—
194#389—72no—
195#389—71no—
196#389—141no—
197#387—141no—
198#385—141no—
199#384—71no—
200#380—71no—
201#380—72no—
202#380—141no—
203C4×C4⋊C4—71no—
204C4×C4⋊C4—141no—
205C4×C22⋊C4—141no—
206#340—72no—
207#340—72no—
208#340—72no—
209#340—72no—
210C23×C7—21no—
211C23×C7—21no—
212C23×C7—21no—
213C23×C7—21no—
214C23×C7—21no—
215C23×C7—21no—
216C23×C7AGL(1,ℤ/8)12yes—
217C23×C7C22×D411yescharacteristic
218C2×C4×C7—21no—
219C2×C4×C7—21no—
220C2×C4×C7—21no—
221C2×C4×C7—21no—
222C2×C4×C7—21no—
223C2×C4×C7—21no—
224C2×C4×C7—21no—
225C2×C4×C7—21no—
226C2×C4×C7—21no—
227C2×C4×C7—21no—
228C2×C4×C7—21no—
229C2×C4×C7—44no—
230C2×C4×C7—41no—
231C2×C4×C7—41no—
232C2×C4×C7—41no—
233C2×C4×C7—41no—
234C2×C4×C7—44no—
235C2×C4×C7#12112yes—
236C2×C4×C7#12112yes—
237C2×C4×C7#13712yes—
238C2×C4×C7#13712yes—
239C2×C4×C7C22×D411yescharacteristic
240C2×C4×C7C2×#4111yescharacteristic
241C2×C4×C7C2×#4111yescharacteristic
242C2×C4×C7C2×#4111yescharacteristic
243C2×C4×C72−1+411yescharacteristic
244C2×C4×C72−1+411yescharacteristic
245C2×Dic7—22no—
246C2×Dic7—22no—
247C2×Dic7—41no—
248C2×Dic7—41no—
249C2×Dic7—41no—
250C2×Dic7—41no—
251C2×Dic7—41no—
252C2×Dic7—42no—
253C2×Dic7—42no—
254C2×Dic7—41no—
255C2×Dic7—42no—
256C2×Dic7—42no—
257C2×Dic7—41no—
258C2×Dic7—41no—
259C2×Dic7—41no—
260C2×Dic7—42no—
261C2×Dic7—41no—
262C2×Dic7—42no—
263Dic14—22no—
264Dic14—22no—
265Dic14—41no—
266Dic14—41no—
267Dic14—84no—
268C7×C8—24no—
269C7×C8—42no—
270C22×Q8—71no—
271C22×Q8—141no—
272C23×C4D2811yescharacteristic
273C23×C4D2811yescharacteristic
274C23×C4C22×D711yescharacteristic
275C22×C8C22×D712yes—
276C22×C8C22×D712yes—
277C4⋊Q8—142no—
278C4⋊Q8—142no—
279C22⋊Q8—142no—
280C22⋊Q8—142no—
281C22⋊Q8—284no—
282C4×Q8—142no—
283C4×Q8—142no—
284C2×C4⋊C4—71no—
285C2×C4⋊C4—71no—
286C2×C4⋊C4—72no—
287C2×C4⋊C4—71no—
288C2×C4⋊C4—72no—
289C2×C4⋊C4—141no—
290C2×C4⋊C4—141no—
291C2×C4⋊C4—142no—
292C2×C4⋊C4—141no—
293C2×C4⋊C4—141no—
294C2×C4⋊C4—141no—
295C2×C4⋊C4—141no—
296C2×C22⋊C4—141no—
297C2×C22⋊C4—142no—
298C2×C22⋊C4—141no—
299C2×C42—22no—
300C2×C42—22no—
301C2×C42—141no—
302C2×C42—141no—
303C2×C42D2811yescharacteristic
304C2×C42D2811yescharacteristic
305C2×C42C22×D711yescharacteristic
306C2×C42C22×D711yescharacteristic
307#107—144no—
308#106—144no—
309C4⋊C8—22no—
310C4⋊C8C22⋊D714yes—
311#103—144no—
312#103—144no—
313C22⋊C8—24no—
314#97—24no—
315#95—141no—
316#95—141no—
317#95—141no—
318#95—141no—
319#95—141no—
320#95—142no—
321#95—142no—
322C22×C7—22no—
323C22×C7—22no—
324C22×C7—22no—
325C22×C7—41no—
326C22×C7—41no—
327C22×C7—41no—
328C22×C7—41no—
329C22×C7C2×#12111yescharacteristic
330C22×C7#52511yescharacteristic
331C22×C7#53611yescharacteristic
332C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C7C2×#13711yescharacteristic
334C22×C7C2×#13711yescharacteristic
335C22×C7#57511yescharacteristic
336C4×C7—22no—
337C4×C7—41no—
338C4×C7—41no—
339C4×C7—41no—
340C4×C7#47014yes—
341C4×C7#54711yescharacteristic
342C4×C7#54811yescharacteristic
343C4×C7#55211yescharacteristic
344C4×C7#55611yescharacteristic
345Dic7—42no—
346Dic7—42no—
347Dic7—82no—
348Dic7—81no—
349Dic7—82no—
350Dic7—81no—
351C24C2×D2811yescharacteristic
352C2×Q8—72no—
353C2×Q8—141no—
354C2×Q8—141no—
355C2×Q8—141no—
356C2×Q8—141no—
357C2×Q8—141no—
358C2×Q8—282no—
359C2×Q8—282no—
360C2×Q8—282no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—41no—
373C22×C4—141no—
374C22×C4—141no—
375C22×C4—141no—
376C22×C4—141no—
377C22×C4—142no—
378C22×C4—142no—
379C22×C4C2×D2811yescharacteristic
380C22×C4C2×D2811yescharacteristic
381C22×C4C2×D2811yescharacteristic
382C22×C4C2×D2811yescharacteristic
383C22×C4C2×D2811yescharacteristic
384C22×C4C23×D711yescharacteristic
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8C2×C22⋊D714yes—
391C4⋊C4—72no—
392C4⋊C4—144no—
393C4⋊C4—141no—
394C4⋊C4—141no—
395C4⋊C4—142no—
396C4⋊C4—142no—
397C4⋊C4—142no—
398C4⋊C4—141no—
399C4⋊C4—141no—
400C4⋊C4—142no—
401C4⋊C4—141no—
402C4⋊C4—282no—
403C4⋊C4—284no—
404C4⋊C4—282no—
405C4⋊C4—282no—
406C4⋊C4—282no—
407C4⋊C4—282no—
408C22⋊C4—144no—
409C22⋊C4—282no—
410C22⋊C4—284no—
411C42—22no—
412C42—22no—
413C42—21no—
414C42—21no—
415C42—282no—
416C42—282no—
417C42#115712yes—
418C42C2×C22⋊D712yes—
419C2×C7—42no—
420C2×C7#241511yescharacteristic
421C2×C7C2×#47011yescharacteristic
422C2×C7#305511yescharacteristic
423C2×C7#311211yescharacteristic
424C2×C7#311611yescharacteristic
425C2×C7#323711yescharacteristic
426C2×C7#323811yescharacteristic
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23#647112yes—
434C23C22×D2811yescharacteristic
435Q8—142no—
436Q8—142no—
437Q8—281no—
438Q8—281no—
439Q8—564no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—44no—
452C2×C4—44no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—142no—
458C2×C4—142no—
459C2×C4—281no—
460C2×C4—281no—
461C2×C4—281no—
462C2×C4—281no—
463C2×C4—282no—
464C2×C4—282no—
465C2×C4—281no—
466C2×C4—281no—
467C2×C4—281no—
468C2×C4—282no—
469C2×C4—281no—
470C2×C4—282no—
471C2×C4—282no—
472C2×C4—281no—
473C2×C4—281no—
474C2×C4—282no—
475C2×C4#647212yes—
476C2×C4#647212yes—
477C2×C4#649312yes—
478C2×C4#649312yes—
479C2×C4C2×#115711yescharacteristic
480C2×C4D7×#4111yescharacteristic
481C2×C4D7×#4111yescharacteristic
482C2×C4#655411yescharacteristic
483C2×C4#655411yescharacteristic
484C2×C4C22×C22⋊D711yescharacteristic
485C8—24no—
486C8—42no—
487C7#2471111yescharacteristic, complemented, Sylow
488C22—22no—
489C22—22no—
490C22—22no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22#9021511yescharacteristic
496C22#9021711yescharacteristic
497C22C2×#647111yescharacteristic
498C22C2×#647211yescharacteristic
499C22C2×#647211yescharacteristic
500C22#9043911yescharacteristic
501C22C2×#649311yescharacteristic
502C4—22no—
503C4—41no—
504C4—41no—
505C4—41no—
506C4—282no—
507C4—282no—
508C4—562no—
509C4—561no—
510C4—561no—
511C4—562no—
512C4#8990914yes—
513C4#9022011yescharacteristic
514C4#9022411yescharacteristic
515C4#9051511yescharacteristic
516C4#9052211yescharacteristic
517C2—42no—
518C2#1173676611yescharacteristic
519C2#1173676711yescharacteristic
520C2#1173679311yescharacteristic
521C2#1173680011yescharacteristic
522C2#1173972211yescharacteristic
523C2#1174121711yescharacteristic
524C2C2×#8990911yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#432C2
socleC23×C7C22×D4
prime radicalC24×C7C2×D4
hypercenterC2×#432D7
hypocenterC7#24711
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
4. C2×#89622C2semidirect
5. #11728239C2semidirect
6. #11728213C2semidirect
7. #11728208C2semidirect
10. #11727574C2semidirect
11. #11727571C2semidirect
487. C7#24711semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4322
#117395212
C4×#64872
C2×#896222
#117282392
#117282132
#117282082
#117276922
#117276902
#117275742
#117275712
#247117