Finite Group Databasebeta

← #13403914

Subgroups — #13403914

Order 1792.

958 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#476C211yesmaximal, characteristic, complemented
2#11740705C211yesmaximal, characteristic, complemented
3#11739862C211yesmaximal, characteristic
4C2×#89606C211yesmaximal, characteristic, complemented
5#11729541C211yesmaximal, characteristic, complemented
6C4×#6406C211yesmaximal, characteristic, complemented
7#11728337C212yesmaximal, complemented
8#11728331C212yesmaximal, complemented
9#11728208C211yesmaximal, characteristic, complemented
10#11727956C212yesmaximal, complemented
11#11727930C212yesmaximal, complemented
12C2×C7×C4⋊Q8C2211yescharacteristic
13C2×C4×C7×D4C2211yescharacteristic
14C2×#6501C2212yes—
15C2×#6493—21no—
16C22×C8×D7C2212yes—
17C2×C4×D28C2211yescharacteristic
18C7×#476—24no—
19C2×C7×#106C2212yes—
20C2×C7×C4⋊C8C2211yescharacteristic
21C2×C7×#102C2212yes—
22#90003—22no—
23C2×#6406C2211yescharacteristic
24C2×#6406C2211yescharacteristic
25#89984—21no—
26C2×(C2×D7)⋊C8C2212yes—
27C2×#6391C2212yes—
28#89760—21no—
29#89759C2212yes—
30#89759C2212yes—
31#89759C2212yes—
32#89749—21no—
33#89733—22no—
34#89707C2211yescharacteristic
35C4×C4⋊Dic7C2211yescharacteristic
36C2×C4×C7⋊C8C2211yescharacteristic
37#89606—24no—
38#89346C2212yes—
39#89324C2212yes—
40#89324C2212yes—
41#89324C2211yescharacteristic
42#89324C2211yescharacteristic
43#25339—71nomaximal, Sylow
44C22×C7×Q8—21no—
45C22×C7×D4C2311yescharacteristic
46C23×C4×C7—21no—
47C22×C22⋊D7—22no—
48C22×D28D411yescharacteristic
49C22×C4×D7C2312yes—
50C22×C7×C8C2312yes—
51C7×C4⋊Q8—22no—
52C7×C4⋊Q8—22no—
53C4×C7×D4—22no—
54C4×C7×D4—22no—
55C2×C7×C4⋊C4—21no—
56C2×C7×C4⋊C4C2311yescharacteristic
57C2×C7×C4⋊C4C2312yes—
58C2×C7×C22⋊C4—21no—
59C2×C42×C7C2311yescharacteristic
60C2×C22⋊Dic7—22no—
61#6501—24no—
62#6501—42no—
63#6493—44no—
64C2×(C2×D7)⋊C4—22no—
65C2×(C2×D7)⋊C4—22no—
66C2×(C2×D7)⋊C4—22no—
67C2×(C2×D7)⋊C4D412yes—
68C2×C4⋊Dic7—21no—
69C2×C4⋊Dic7—21no—
70C2×C4⋊Dic7D411yescharacteristic
71C2×C4⋊Dic7C2311yescharacteristic
72C2×C4⋊Dic7C2312yes—
73C2×C4⋊Dic7C2311yescharacteristic
74C2×C4×Dic7—21no—
75C22×C7⋊C8C2311yescharacteristic
76C22×C7⋊C8C2311yescharacteristic
77C2×C8×D7—24no—
78C2×C8×D7—24no—
79C2×C8×D7—42no—
80C4×D28—22no—
81C4×D28—22no—
82C7×#106—24no—
83C7×C4⋊C8D414yescomplemented
84C7×#102—24no—
85#6406—22no—
86#6406—22no—
87C7⋊#95—21no—
88C7⋊#95—22no—
89C7⋊#95—22no—
90C7⋊#95—22no—
91(C2×D7)⋊C8—24no—
92#6391—42no—
93C4×C7⋊C8—22no—
94C2×#476D711yescharacteristic, complemented
95C2×C8×D4—71no—
96#2563—71no—
97#2537—71no—
98#2077—72no—
99#2034—72no—
100#1990—71no—
101#1948—71no—
102#1893—72no—
103#1807—72no—
104C4×#102—71no—
105C24×C7—21no—
106C23×D7C2×D412yes—
107C2×C7×Q8—42no—
108C2×C7×Q8—81no—
109C2×C7×Q8—81no—
110C2×C7×D4—21no—
111C2×C7×D4—21no—
112C2×C7×D4—21no—
113C2×C7×D4—21no—
114C2×C7×D4—21no—
115C2×C7×D4#4112yes—
116C22×C4×C7—21no—
117C22×C4×C7—22no—
118C22×C4×C7—42no—
119C22×C4×C7—42no—
120C22×C4×C7—42no—
121C22×C4×C7C2×D411yescharacteristic
122C22×C4×C7C2×D411yescharacteristic
123C22×C4×C7C2411yescharacteristic
124C2×C22⋊D7—44no—
125C2×C22⋊D7—44no—
126C2×C22⋊D7—82no—
127C22×Dic7—21no—
128C22×Dic7—21no—
129C22×Dic7—22no—
130C22×Dic7C2×D412yes—
131C2×D28—22no—
132C2×D28—22no—
133C2×D28SD1614yes—
134C2×C4×D7—22no—
135C2×C4×D7—22no—
136C2×C4×D7—22no—
137C2×C4×D7—22no—
138C2×C4×D7—22no—
139C2×C4×D7—22no—
140C2×C7×C8—22no—
141C2×C7×C8—22no—
142C2×C7×C8C2×D414yes—
143C7×C4⋊C4—22no—
144C7×C4⋊C4—21no—
145C7×C4⋊C4—21no—
146C7×C4⋊C4—22no—
147C7×C4⋊C4—42no—
148C7×C22⋊C4—42no—
149C42×C7C2×D412yes—
150C42×C7#4112yes—
151C22⋊Dic7—44no—
152(C2×D7)⋊C4—24no—
153(C2×D7)⋊C4—44no—
154(C2×D7)⋊C4—82no—
155(C2×D7)⋊C4—82no—
156C4⋊Dic7—22no—
157C4⋊Dic7—21no—
158C4⋊Dic7—21no—
159C4⋊Dic7—22no—
160C4⋊Dic7—22no—
161C4⋊Dic7—21no—
162C4⋊Dic7—21no—
163C4⋊Dic7—42no—
164C4⋊Dic7—81no—
165C4×Dic7—42no—
166C2×C7⋊C8—21no—
167C2×C7⋊C8—21no—
168C2×C7⋊C8—21no—
169C2×C7⋊C8—21no—
170C2×C7⋊C8—21no—
171C2×C7⋊C8#4112yes—
172C8×D7—48no—
173C23×C8—72no—
174C2×C4⋊Q8C2×D711yescharacteristic
175C2×#121—72no—
176C2×#121—141no—
177C2×C4×D4—71no—
178C2×C4×D4C2×D711yescharacteristic
179#476—24no—
180C8×D4—144no—
181C2×#106—72no—
182C2×#106C2×D712yes—
183C2×C4⋊C8C2×D711yescharacteristic
184C2×#102—71no—
185C2×#102—71no—
186C2×#102C2×D712yes—
187C2×C22⋊C8—72no—
188C2×C4×C8—71no—
189#394—142no—
190#393—142no—
191#390—141no—
192#384—71no—
193#382—141no—
194#380—72no—
195#380—72no—
196#380—72no—
197#380—141no—
198C4×C4⋊C4—71no—
199#340—72no—
200#340—71no—
201#340—72no—
202#340—71no—
203#340—72no—
204C23×C7—22no—
205C23×C7—41no—
206C23×C7—41no—
207C23×C7—41no—
208C23×C7—41no—
209C23×C7—41no—
210C23×C7—41no—
211C23×C7C22×D411yescharacteristic
212C22×D7—22no—
213C22×D7—22no—
214C22×D7—22no—
215C22×D7—22no—
216C22×D7—22no—
217C22×D7—22no—
218C22×D7C2×SD1614yes—
219C7×Q8—84no—
220C7×D4—22no—
221C7×D4—22no—
222C7×D4—41no—
223C7×D4—41no—
224C2×C4×C7—21no—
225C2×C4×C7—21no—
226C2×C4×C7—41no—
227C2×C4×C7—42no—
228C2×C4×C7—41no—
229C2×C4×C7—41no—
230C2×C4×C7—42no—
231C2×C4×C7—42no—
232C2×C4×C7—84no—
233C2×C4×C7#12112yes—
234C2×C4×C7#12112yes—
235C2×C4×C7C2×SD1612yes—
236C2×C4×C7#13512yes—
237C2×C4×C7C22×D411yescharacteristic
238C2×C4×C7C2×#4111yescharacteristic
239C2×C4×C7C2×#4111yescharacteristic
240C2×C4×C7C2×#4111yescharacteristic
241C2×C4×C7H(5,𝔽2)11yescharacteristic
242C2×C4×C72−1+411yescharacteristic
243C22⋊D7—88no—
244C2×Dic7—22no—
245C2×Dic7—22no—
246C2×Dic7—22no—
247C2×Dic7—42no—
248C2×Dic7—41no—
249C2×Dic7—41no—
250C2×Dic7—42no—
251C2×Dic7—41no—
252C2×Dic7—41no—
253C2×Dic7—42no—
254C2×Dic7—41no—
255C2×Dic7—41no—
256D28—28no—
257C4×D7—42no—
258C4×D7—42no—
259C4×D7—42no—
260C4×D7—42no—
261C7×C8—24no—
262C7⋊C8—22no—
263C7⋊C8—41no—
264C22×Q8—21no—
265C22×D4—71no—
266C22×D4—142no—
267C22×D4C22×D711yescharacteristic
268C23×C4—21no—
269C23×C4—72no—
270C22×C8—71no—
271C22×C8—71no—
272C22×C8—144no—
273C22×C8—144no—
274C22×C8—282no—
275C22×C8C22×D712yes—
276C4⋊Q8—22no—
277C4⋊Q8—22no—
278#121—144no—
279#121—282no—
280#121—284no—
281C4×D4—22no—
282C4×D4—22no—
283C4×D4—142no—
284C4×D4—142no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—71no—
287C2×C4⋊C4—72no—
288C2×C4⋊C4—71no—
289C2×C4⋊C4—71no—
290C2×C4⋊C4—141no—
291C2×C4⋊C4—141no—
292C2×C4⋊C4C22×D711yescharacteristic
293C2×C4⋊C4C22×D712yes—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—72no—
296C2×C22⋊C4—142no—
297C2×C22⋊C4—142no—
298C2×C22⋊C4—142no—
299C2×C22⋊C4—142no—
300C2×C42—141no—
301C2×C42C22×D711yescharacteristic
302#106—24no—
303#106—282no—
304C4⋊C8C22⋊D714yescomplemented
305#102—24no—
306#102—142no—
307#102—142no—
308C22⋊C8—144no—
309C4×C8—142no—
310#95—142no—
311#95—142no—
312#95—142no—
313#95—141no—
314C22×C7—42no—
315C22×C7—42no—
316C22×C7—42no—
317C22×C7—81no—
318C22×C7—81no—
319C22×C7—81no—
320C22×C7—81no—
321C22×C7C2×#12111yescharacteristic
322C22×C7#54611yescharacteristic
323C22×C7#54711yescharacteristic
324C22×C7C22×SD1611yescharacteristic
325C22×C7C2×#13511yescharacteristic
326C22×C7#57611yescharacteristic
327C22×C7#57711yescharacteristic
328C2×D7—24no—
329C2×D7—24no—
330C2×D7—24no—
331C2×D7—42no—
332C2×D7—42no—
333C2×D7—42no—
334C2×D7—42no—
335C4×C7—22no—
336C4×C7—81no—
337C4×C7—82no—
338C4×C7#46514yes—
339C4×C7#52911yescharacteristic
340C4×C7#54211yescharacteristic
341C4×C7#54611yescharacteristic
342C4×C7#54811yescharacteristic
343Dic7—42no—
344Dic7—81no—
345Dic7—82no—
346Dic7—81no—
347C24—21no—
348C24—72no—
349C2×Q8—42no—
350C2×Q8—81no—
351C2×Q8—81no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—74no—
358C2×D4—142no—
359C2×D4—142no—
360C2×D4—284no—
361C2×D4—284no—
362C2×D4—562no—
363C2×D4#116112yes—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—72no—
370C22×C4—142no—
371C22×C4—142no—
372C22×C4—142no—
373C22×C4—142no—
374C22×C4—142no—
375C22×C4—142no—
376C22×C4—141no—
377C22×C4—141no—
378C22×C4—142no—
379C22×C4D4×D711yescharacteristic
380C22×C4D4×D711yescharacteristic
381C22×C4C23×D711yescharacteristic
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—72no—
385C2×C8—141no—
386C2×C8—141no—
387C2×C8—141no—
388C2×C8—141no—
389C2×C8—141no—
390C2×C8—288no—
391C2×C8C2×C22⋊D714yes—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—42no—
397C4⋊C4—142no—
398C4⋊C4—141no—
399C4⋊C4—142no—
400C4⋊C4—141no—
401C4⋊C4—141no—
402C4⋊C4—141no—
403C4⋊C4—142no—
404C4⋊C4—282no—
405C4⋊C4—561no—
406C22⋊C4—42no—
407C22⋊C4—144no—
408C22⋊C4—284no—
409C22⋊C4—284no—
410C22⋊C4—562no—
411C22⋊C4—562no—
412C42—282no—
413C42#115912yes—
414C42C2×C22⋊D712yes—
415C2×C7—82no—
416C2×C7#242711yescharacteristic
417C2×C7C2×#46511yescharacteristic
418C2×C7#306211yescharacteristic
419C2×C7#329511yescharacteristic
420C2×C7#330311yescharacteristic
421C2×C7#333511yescharacteristic
422C2×C7#334111yescharacteristic
423D7—44no—
424C23—22no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—74no—
432C23—142no—
433C23—142no—
434C23—142no—
435C23—142no—
436C23—142no—
437C23—142no—
438C23C2×D4×D711yescharacteristic
439Q8—84no—
440D4—22no—
441D4—22no—
442D4—41no—
443D4—41no—
444D4—148no—
445D4—568no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—84no—
455C2×C4—142no—
456C2×C4—142no—
457C2×C4—142no—
458C2×C4—282no—
459C2×C4—282no—
460C2×C4—282no—
461C2×C4—282no—
462C2×C4—282no—
463C2×C4—281no—
464C2×C4—281no—
465C2×C4—281no—
466C2×C4—282no—
467C2×C4—281no—
468C2×C4—282no—
469C2×C4—281no—
470C2×C4—281no—
471C2×C4D7×SD1612yes—
472C2×C4#647912yes—
473C2×C4#650112yes—
474C2×C4#650112yes—
475C2×C4C2×#115911yescharacteristic
476C2×C4C2×#116111yescharacteristic
477C2×C4#655111yescharacteristic
478C2×C4D7×#4111yescharacteristic
479C2×C4#655311yescharacteristic
480C2×C4C22×C22⋊D711yescharacteristic
481C8—24no—
482C8—142no—
483C8—281no—
484C7#2533911yescharacteristic, complemented, Sylow
485C22—42no—
486C22—42no—
487C22—42no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22—144no—
493C22—144no—
494C22—144no—
495C22—282no—
496C22—282no—
497C22—282no—
498C22—282no—
499C22#9032111yescharacteristic
500C22#9032211yescharacteristic
501C22C2×D7×SD1611yescharacteristic
502C22C2×#647911yescharacteristic
503C22#9046511yescharacteristic
504C22#9046611yescharacteristic
505C22C2×#650111yescharacteristic
506C4—22no—
507C4—81no—
508C4—82no—
509C4—282no—
510C4—562no—
511C4—561no—
512C4—561no—
513C4#8994314yes—
514C4#9031511yescharacteristic
515C4#9033411yescharacteristic
516C4#9050811yescharacteristic
517C4#9052011yescharacteristic
518C2—82no—
519C2—284no—
520C2#1173852011yescharacteristic
521C2#1173852111yescharacteristic
522C2#1173852611yescharacteristic
523C2#1173852711yescharacteristic
524C2#1174020111yescharacteristic
525C2C2×#8994311yescharacteristic
526C2#1174139611yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#476C2
socleC23×C7C22×D4
prime radical#11739862C2
hypercenterC2×#476D7
hypocenterC7#25339
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×C7×#476C2semidirect
2. #11740705C2semidirect
4. C2×#89606C2semidirect
5. #11729541C2semidirect
6. C4×#6406C2semidirect
7. #11728337C2semidirect
8. #11728331C2semidirect
9. #11728208C2semidirect
10. #11727956C2semidirect
11. #11727930C2semidirect
83. C7×C4⋊C8D4semidirect
94. C2×#476D7semidirect
304. C4⋊C8C22⋊D7semidirect
484. C7#25339semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4762
#117407052
#117398622
C2×#896062
#117295412
C4×#64062
#117283372
#117283312
#117282082
#117279562
#117279302
#253397