Finite Group Databasebeta

← #13410233

Subgroups — #13410233

Order 1792.

1314 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#547C211yesmaximal, characteristic
2C2×#89853C211yesmaximal, characteristic, complemented
3#11739829C211yesmaximal, characteristic, complemented
4C2×#89780C211yesmaximal, characteristic, complemented
5#11729889C214yesmaximal, complemented
6#11729532C211yesmaximal, characteristic, complemented
7#11729448C214yesmaximal, complemented
8#11729368C211yesmaximal, characteristic, complemented
9C4×#6406C211yesmaximal, characteristic, complemented
10C22×C7×#41C2212yes—
11C7×#547—24no—
12C7×#547—24no—
13C2×C7×C4⋊Q8C2211yescharacteristic
14C2×C7×#123—22no—
15C2×C7×C22⋊Q8C2212yes—
16C2×C7×#121—21no—
17C2×C4×C7×D4C2211yescharacteristic
18C2×C4×C7×D4C2211yescharacteristic
19C22×C7×C4⋊C4—21no—
20C2×#6432C2211yescharacteristic
21C2×#6409C2214yes—
22C2×#6409C2214yes—
23#89993—21no—
24C2×#6406C2212yes—
25C2×#6406C2212yes—
26#89984C2214yes—
27C2×C22⋊(C7⋊C8)C2214yes—
28#89853—24no—
29#89780—24no—
30#89749—21no—
31C2×#6382C2212yes—
32#89719—22no—
33C4×C4⋊Dic7C2211yescharacteristic
34C2×C4⋊(C7⋊C8)C2211yescharacteristic
35C2×C4×C7⋊C8C2211yescharacteristic
36#89324C2212yes—
37#25886—71nomaximal, Sylow
38C2×C7×#41—24no—
39C2×C7×#41—24no—
40C2×C7×#41—28no—
41C2×C7×#41—44no—
42C22×C7×Q8C2312yes—
43C22×C7×D4—22no—
44C22×C7×D4D411yescharacteristic
45C22×C7×D4C2311yescharacteristic
46C23×C4×C7—22no—
47C23×C4×C7—21no—
48C23×C4×C7C2312yes—
49C22×Dic14—21no—
50C7×C4⋊Q8—22no—
51C7×C4⋊Q8D414yes—
52C7×#123—216no—
53C7×C22⋊Q8—24no—
54C7×C22⋊Q8—24no—
55C7×#121—28no—
56C4×C7×D4—22no—
57C4×C7×D4—22no—
58C4×C7×D4—22no—
59C4×C7×D4D414yes—
60C2×C7×C4⋊C4—28no—
61C2×C7×C4⋊C4—21no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—21no—
64C2×C7×C4⋊C4D411yescharacteristic
65C2×C7×C4⋊C4C2311yescharacteristic
66C2×C7×C22⋊C4—22no—
67C2×C7×C22⋊C4—21no—
68C2×C7×C22⋊C4D412yes—
69C2×C42×C7C2311yescharacteristic
70C2×C22⋊Dic7—24no—
71C2×C4⋊Dic7—21no—
72C2×C4⋊Dic7C2312yes—
73C2×C4⋊Dic7C2312yes—
74C2×C4×Dic7—21no—
75C22×C7⋊C8C2312yes—
76C22×C7⋊C8C2312yes—
77#6432—22no—
78#6432—22no—
79#6409—28no—
80#6409—44no—
81#6406—24no—
82#6406—24no—
83C7⋊#95—21no—
84C7⋊#95—24no—
85C22⋊(C7⋊C8)—44no—
86#6382—24no—
87C4⋊(C7⋊C8)—22no—
88C4×C7⋊C8—22no—
89C2×#547D711yescharacteristic
90C2×#487—71no—
91C2×#476—71no—
92#2563—71no—
93#2035—74no—
94#1981—71no—
95#1954—71no—
96#1788—74no—
97C4×#102—71no—
98C24×C7—21no—
99C24×C7C2×D412yes—
100C7×#41—416no—
101C7×#41—48no—
102C7×#41—48no—
103C2×C7×Q8—22no—
104C2×C7×Q8—24no—
105C2×C7×Q8—24no—
106C2×C7×Q8C2×D414yes—
107C2×C7×D4—28no—
108C2×C7×D4—22no—
109C2×C7×D4—22no—
110C2×C7×D4—22no—
111C2×C7×D4—21no—
112C2×C7×D4—22no—
113C2×C7×D4—48no—
114C2×C7×D4C2×D412yes—
115C2×C7×D4#4114yes—
116C22×C4×C7—28no—
117C22×C4×C7—21no—
118C22×C4×C7—22no—
119C22×C4×C7—24no—
120C22×C4×C7—22no—
121C22×C4×C7—22no—
122C22×C4×C7—24no—
123C22×C4×C7—24no—
124C22×C4×C7—48no—
125C22×C4×C7—42no—
126C22×C4×C7—42no—
127C22×C4×C7C2×D412yes—
128C22×C4×C7C2×D411yescharacteristic
129C22×C4×C7C2×D411yescharacteristic
130C22×C4×C7C2411yescharacteristic
131C22×Dic7—22no—
132C22×Dic7—22no—
133C2×Dic14—42no—
134C2×Dic14—82no—
135C7×C4⋊C4—28no—
136C7×C4⋊C4—22no—
137C7×C4⋊C4—24no—
138C7×C4⋊C4—24no—
139C7×C4⋊C4—21no—
140C7×C4⋊C4C2×D412yes—
141C7×C22⋊C4—28no—
142C7×C22⋊C4—24no—
143C7×C22⋊C4—24no—
144C42×C7C2×D412yes—
145C42×C7C2×D412yes—
146C22⋊Dic7—84no—
147C4⋊Dic7—22no—
148C4⋊Dic7—22no—
149C4⋊Dic7—22no—
150C4⋊Dic7—22no—
151C4⋊Dic7—42no—
152C4×Dic7—42no—
153C2×C7⋊C8—22no—
154C2×C7⋊C8—22no—
155C2×C7⋊C8—22no—
156C2×C7⋊C8—22no—
157C2×C7⋊C8—24no—
158C22×#41C2×D712yes—
159#547—24no—
160#547—24no—
161C2×C4⋊Q8—71no—
162C2×C4⋊Q8C2×D711yescharacteristic
163C2×#123—22no—
164C2×C22⋊Q8C2×D712yes—
165C2×#121—21no—
166C2×C4×D4C2×D711yescharacteristic
167C2×C4×D4C2×D711yescharacteristic
168C22×C4⋊C4—21no—
169#487—144no—
170#476—144no—
171C2×#106—72no—
172C2×C4⋊C8—71no—
173C2×#103—74no—
174C2×#103—74no—
175C2×#102—72no—
176C2×#102—72no—
177C2×C22⋊C8—74no—
178C2×C4×C8—71no—
179#393—142no—
180#390—141no—
181#382—141no—
182#380—74no—
183C4×C4⋊C4—71no—
184#340—72no—
185C23×C7—22no—
186C23×C7—24no—
187C23×C7—22no—
188C23×C7—24no—
189C23×C7—22no—
190C23×C7—22no—
191C23×C7—24no—
192C23×C7—41no—
193C23×C7—41no—
194C23×C7—42no—
195C23×C7C22×D411yescharacteristic
196C7×Q8—28no—
197C7×Q8—42no—
198C7×Q8—42no—
199C7×D4—22no—
200C7×D4—24no—
201C7×D4—416no—
202C7×D4—44no—
203C7×D4#12414yes—
204C2×C4×C7—22no—
205C2×C4×C7—22no—
206C2×C4×C7—22no—
207C2×C4×C7—24no—
208C2×C4×C7—24no—
209C2×C4×C7—416no—
210C2×C4×C7—44no—
211C2×C4×C7—41no—
212C2×C4×C7—41no—
213C2×C4×C7—42no—
214C2×C4×C7—42no—
215C2×C4×C7—44no—
216C2×C4×C7—48no—
217C2×C4×C7#12012yes—
218C2×C4×C7#12012yes—
219C2×C4×C7#13512yes—
220C2×C4×C7#13712yes—
221C2×C4×C7C22×D411yescharacteristic
222C2×C4×C7C22×D411yescharacteristic
223C2×C4×C7C2×#4112yes—
224C2×C4×C7H(5,𝔽2)12yes—
225C2×Dic7—42no—
226C2×Dic7—42no—
227C2×Dic7—42no—
228C2×Dic7—42no—
229C2×Dic7—44no—
230Dic14—84no—
231C7⋊C8—42no—
232C7⋊C8—42no—
233C2×#41—24no—
234C2×#41—24no—
235C2×#41—28no—
236C2×#41—44no—
237C22×Q8—141no—
238C22×Q8C22×D712yes—
239C22×D4—22no—
240C22×D4C22⋊D711yescharacteristic
241C22×D4C22×D711yescharacteristic
242C23×C4—21no—
243C23×C4—22no—
244C23×C4C22×D712yes—
245C22×C8—72no—
246C22×C8—72no—
247C4⋊Q8—22no—
248C4⋊Q8—142no—
249C4⋊Q8—142no—
250C4⋊Q8C22⋊D714yes—
251#123—216no—
252C22⋊Q8—24no—
253C22⋊Q8—24no—
254#121—28no—
255C4×D4—22no—
256C4×D4—22no—
257C4×D4—22no—
258C4×D4C22⋊D714yes—
259C2×C4⋊C4—28no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—72no—
264C2×C4⋊C4—72no—
265C2×C4⋊C4—141no—
266C2×C4⋊C4C22⋊D711yescharacteristic
267C2×C4⋊C4C22×D711yescharacteristic
268C2×C22⋊C4—22no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—144no—
271C2×C22⋊C4C22⋊D712yes—
272C2×C42—141no—
273C2×C42C22×D711yescharacteristic
274#106—144no—
275C4⋊C8—142no—
276#103—148no—
277#103—284no—
278#102—144no—
279#102—144no—
280C22⋊C8—284no—
281C4×C8—142no—
282#95—141no—
283#95—144no—
284C22×C7—24no—
285C22×C7—44no—
286C22×C7—42no—
287C22×C7—42no—
288C22×C7—44no—
289C22×C7—44no—
290C22×C7—42no—
291C22×C7—42no—
292C22×C7—42no—
293C22×C7—44no—
294C22×C7C2×#12011yescharacteristic
295C22×C7#54612yes—
296C22×C7C2×#13511yescharacteristic
297C22×C7C2×#13711yescharacteristic
298C22×C7#57712yes—
299C4×C7—22no—
300C4×C7—42no—
301C4×C7—44no—
302C4×C7—42no—
303C4×C7#45214yes—
304C4×C7C2×#12411yescharacteristic
305C4×C7#53511yescharacteristic
306C4×C7#54612yes—
307Dic7—82no—
308Dic7—82no—
309C24—21no—
310C24C2×C22⋊D712yes—
311#41—416no—
312#41—48no—
313#41—48no—
314C2×Q8—22no—
315C2×Q8—24no—
316C2×Q8—24no—
317C2×Q8—282no—
318C2×Q8—562no—
319C2×Q8C2×C22⋊D714yes—
320C2×D4—28no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—21no—
326C2×D4—48no—
327C2×D4#115914yes—
328C2×D4C2×C22⋊D712yes—
329C22×C4—28no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—24no—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—48no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—142no—
341C22×C4—142no—
342C22×C4C2×C22⋊D712yes—
343C22×C4C2×C22⋊D711yescharacteristic
344C22×C4C2×C22⋊D711yescharacteristic
345C22×C4C23×D711yescharacteristic
346C2×C8—142no—
347C2×C8—142no—
348C2×C8—144no—
349C2×C8—142no—
350C2×C8—142no—
351C4⋊C4—28no—
352C4⋊C4—22no—
353C4⋊C4—24no—
354C4⋊C4—24no—
355C4⋊C4—21no—
356C4⋊C4—142no—
357C4⋊C4—142no—
358C4⋊C4—142no—
359C4⋊C4—142no—
360C4⋊C4—282no—
361C4⋊C4C2×C22⋊D712yes—
362C22⋊C4—28no—
363C22⋊C4—24no—
364C22⋊C4—24no—
365C22⋊C4—564no—
366C42—282no—
367C42C2×C22⋊D712yes—
368C42C2×C22⋊D712yes—
369C2×C7—44no—
370C2×C7—82no—
371C2×C7#243511yescharacteristic
372C2×C7C2×#45211yescharacteristic
373C2×C7#301011yescharacteristic
374C2×C7#330312yes—
375C2×C7#333112yes—
376C23—24no—
377C23—22no—
378C23—24no—
379C23—22no—
380C23—22no—
381C23—24no—
382C23—22no—
383C23—41no—
384C23—41no—
385C23—42no—
386C23C22×C22⋊D711yescharacteristic
387Q8—28no—
388Q8—42no—
389Q8—42no—
390Q8—564no—
391D4—22no—
392D4—24no—
393D4—416no—
394D4—44no—
395D4#649914yes—
396C2×C4—22no—
397C2×C4—24no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—416no—
402C2×C4—44no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—44no—
408C2×C4—48no—
409C2×C4—282no—
410C2×C4—282no—
411C2×C4—282no—
412C2×C4—284no—
413C2×C4—282no—
414C2×C4#651312yes—
415C2×C4#651412yes—
416C2×C4#651612yes—
417C2×C4#651612yes—
418C2×C4C2×#115912yes—
419C2×C4#654812yes—
420C2×C4C22×C22⋊D711yescharacteristic
421C2×C4C22×C22⋊D711yescharacteristic
422C8—282no—
423C8—282no—
424C7#2588611yescharacteristic, complemented, Sylow
425C22—24no—
426C22—44no—
427C22—44no—
428C22—42no—
429C22—42no—
430C22—44no—
431C22—44no—
432C22—42no—
433C22—42no—
434C22—42no—
435C22#9049712yes—
436C22C2×#651311yescharacteristic
437C22C2×#651411yescharacteristic
438C22#9052812yes—
439C22C2×#651611yescharacteristic
440C4—22no—
441C4—42no—
442C4—44no—
443C4—42no—
444C4—562no—
445C4—562no—
446C4#9001114yes—
447C4C2×#649911yescharacteristic
448C4#9049611yescharacteristic
449C4#9049712yes—
450C2—44no—
451C2—82no—
452C2#1174095612yes—
453C2#1174096012yes—
454C2#1174149511yescharacteristic
455C2C2×#9001111yescharacteristic
456C2#1174155811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
Fitting, prime radicalC2×C7×#547C2
socleC23×C7C22×D4
hypercenterC2×#547D7
hypocenterC7#25886
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
2. C2×#89853C2semidirect
3. #11739829C2semidirect
4. C2×#89780C2semidirect
5. #11729889C2semidirect
6. #11729532C2semidirect
7. #11729448C2semidirect
8. #11729368C2semidirect
9. C4×#6406C2semidirect
424. C7#25886semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5472
C2×#898532
#117398292
C2×#897802
#117298892
#117295322
#117294482
#117293682
C4×#64062
#258867