Finite Group Databasebeta

← #13365953

Subgroups — #13365953

Order 1792.

784 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2293C211yesmaximal, characteristic
2C2×#89781C211yesmaximal, characteristic
3C4×#6433C211yesmaximal, characteristic, complemented
4#11729359C211yesmaximal, characteristic
5#11727399C211yesmaximal, characteristic
6#11727399C211yesmaximal, characteristic
7#11727391C211yesmaximal, characteristic
8#11727390C211yesmaximal, characteristic
9#11727375C211yesmaximal, characteristic, complemented
10#11727374C211yesmaximal, characteristic, complemented
11#11727355C211yesmaximal, characteristic, complemented
12#11727354C211yesmaximal, characteristic, complemented
13#11727245C211yesmaximal, characteristic, complemented
14#11727222C211yesmaximal, characteristic, complemented
15#11727145C211yesmaximal, characteristic, complemented
16C2×C4×C7×D4C2211yescharacteristic
17C2×C7×#117—21no—
18C2×#6433C2211yescharacteristic
19C7×#390C2211yescharacteristic
20C7×#390C2211yescharacteristic
21C7×#389C2211yescharacteristic
22C7×#389C2211yescharacteristic
23C7×#388—21no—
24C7×#388—21no—
25C4×C7×C4⋊C4C2211yescharacteristic
26C4×C7×C22⋊C4—21no—
27C43×C7C2211yescharacteristic
28C2×#6406C2211yescharacteristic
29C2×#6406C2211yescharacteristic
30C2×#6406C2211yescharacteristic
31C2×#6406C2211yescharacteristic
32#89781C418yescomplemented
33C2×#6382C2211yescharacteristic
34C2×#6382C2211yescharacteristic
35C2×#6381C2211yescharacteristic
36C2×#6381C2211yescharacteristic
37#89708C2211yescharacteristic
38C4×C4⋊Dic7C2211yescharacteristic
39C4×C4⋊Dic7C2211yescharacteristic
40#89705—21no—
41#89705—21no—
42C4×Dic7⋊C4—21no—
43C4×Dic7⋊C4—21no—
44#89700C2211yescharacteristic
45#89700C2211yescharacteristic
46C2×C4⋊(C7⋊C8)C2211yescharacteristic
47C2×C4⋊(C7⋊C8)C2211yescharacteristic
48C2×#6377C2211yescharacteristic
49C2×#6377C2211yescharacteristic
50#89324C2211yescharacteristic
51#89324C2211yescharacteristic
52#89324C2211yescharacteristic
53#89324C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89319C2211yescharacteristic
59#89319C2211yescharacteristic
60#22120—71nomaximal, Sylow
61C22×C7×D4C2311yescharacteristic
62C23×C4×C7—21no—
63C4×C7×D4—22no—
64C4×C7×D4C2×C414yes—
65C7×#117—44no—
66C2×C7×C4⋊C4—21no—
67C2×C7×C4⋊C4—21no—
68C2×C7×C4⋊C4C2311yescharacteristic
69C2×C7×C4⋊C4C2311yescharacteristic
70C2×C7×C4⋊C4C2311yescharacteristic
71C2×C7×C22⋊C4—21no—
72C2×C7×C22⋊C4—21no—
73C2×C7×C22⋊C4—21no—
74C2×C7×C22⋊C4—21no—
75C2×C7×C22⋊C4—21no—
76C2×C42×C7—21no—
77C2×C42×C7D411yescharacteristic
78C2×C42×C7D411yescharacteristic
79C2×C42×C7D411yescharacteristic
80C2×C42×C7D411yescharacteristic
81C2×C42×C7C2311yescharacteristic
82C2×C42×C7C2311yescharacteristic
83C2×C42×C7C2311yescharacteristic
84C2×C4⋊Dic7C2311yescharacteristic
85C2×C4⋊Dic7C2311yescharacteristic
86C2×C4⋊Dic7C2311yescharacteristic
87C2×C4⋊Dic7C2311yescharacteristic
88C2×Dic7⋊C4—21no—
89C2×Dic7⋊C4—21no—
90C2×Dic7⋊C4—21no—
91C2×Dic7⋊C4—21no—
92C2×C4×Dic7—21no—
93C2×C4×Dic7—21no—
94C22×C7⋊C8C2311yescharacteristic
95C22×C7⋊C8C2311yescharacteristic
96C22×C7⋊C8C2311yescharacteristic
97C22×C7⋊C8C2311yescharacteristic
98#6433—22no—
99#6433C2×C414yes—
100C7×#95—21no—
101C7×#95—21no—
102C7×#95—21no—
103#6406—41no—
104#6406—41no—
105#6406C2×C414yes—
106#6406C2×C414yes—
107C7⋊#95—21no—
108C7⋊#95—21no—
109C7⋊#95—21no—
110C7⋊#95—21no—
111C7⋊#95—21no—
112C7⋊#95—21no—
113#6382—41no—
114#6382C2×C414yes—
115#6381—41no—
116#6381C2×C414yes—
117C4⋊(C7⋊C8)—22no—
118C4⋊(C7⋊C8)C2×C414yes—
119#6377—41no—
120#6377—41no—
121C2×#478—71no—
122C4×#125—71no—
123#2293D711yescharacteristic
124#1989—71no—
125#1949—71no—
126#1944—71no—
127#1943—71no—
128#1936—71no—
129#1936—71no—
130#1926—71no—
131#1925—71no—
132#1919—71no—
133#1918—71no—
134#1804—71no—
135#1767—71no—
136C24×C7—21no—
137C2×C7×D4—21no—
138C2×C7×D4—21no—
139C2×C7×D4—21no—
140C2×C7×D4—21no—
141C2×C7×D4—21no—
142C2×C7×D4C22×C412yes—
143C22×C4×C7—21no—
144C22×C4×C7—24no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—42no—
148C22×C4×C7—42no—
149C22×C4×C7C2×D411yescharacteristic
150C22×C4×C7C2×D411yescharacteristic
151C22×C4×C7C2×D411yescharacteristic
152C22×C4×C7C2×D411yescharacteristic
153C22×C4×C7C2×D411yescharacteristic
154C22×C4×C7C2×D411yescharacteristic
155C22×C4×C7C2411yescharacteristic
156C22×Dic7—21no—
157C22×Dic7—21no—
158C22×Dic7—21no—
159C22×Dic7—21no—
160C7×C4⋊C4—21no—
161C7×C4⋊C4—21no—
162C7×C4⋊C4—21no—
163C7×C4⋊C4—21no—
164C7×C4⋊C4—21no—
165C7×C4⋊C4—42no—
166C7×C4⋊C4—42no—
167C7×C4⋊C4C22×C412yes—
168C7×C22⋊C4—24no—
169C7×C22⋊C4—42no—
170C7×C22⋊C4—42no—
171C7×C22⋊C4—42no—
172C7×C22⋊C4—42no—
173C42×C7—22no—
174C42×C7—21no—
175C42×C7—21no—
176C42×C7—21no—
177C42×C7—21no—
178C42×C7—41no—
179C42×C7—41no—
180C42×C7—41no—
181C42×C7—42no—
182C42×C7C22×C412yes—
183C42×C7#4112yes—
184C4⋊Dic7—21no—
185C4⋊Dic7—21no—
186C4⋊Dic7—21no—
187C4⋊Dic7—21no—
188C4⋊Dic7—21no—
189C4⋊Dic7—21no—
190C4⋊Dic7C22×C412yes—
191C4⋊Dic7C22×C412yes—
192Dic7⋊C4—24no—
193Dic7⋊C4—24no—
194Dic7⋊C4—42no—
195Dic7⋊C4—42no—
196C4×Dic7—42no—
197C4×Dic7—42no—
198C2×C7⋊C8—21no—
199C2×C7⋊C8—21no—
200C2×C7⋊C8—21no—
201C2×C7⋊C8—21no—
202C2×C7⋊C8—21no—
203C2×C7⋊C8—21no—
204C2×C7⋊C8—21no—
205C2×C7⋊C8—21no—
206C2×C7⋊C8—21no—
207C2×C7⋊C8—21no—
208C2×C7⋊C8C22×C412yes—
209C2×C7⋊C8C22×C412yes—
210C2×#125—71no—
211C2×C4×D4C2×D711yescharacteristic
212C2×#117—21no—
213#478—78no—
214C2×#107—71no—
215C2×#107—71no—
216C2×#106—71no—
217C2×#106—71no—
218C2×C4⋊C8—71no—
219C2×C4⋊C8—71no—
220C2×#102—71no—
221C2×#102—71no—
222C2×#102—71no—
223C2×#102—71no—
224C2×#97—71no—
225C2×#97—71no—
226#390C2×D711yescharacteristic
227#390C2×D711yescharacteristic
228#389—71no—
229#389—71no—
230#389C2×D711yescharacteristic
231#389C2×D711yescharacteristic
232#388—21no—
233#388—21no—
234#387—141no—
235#387—141no—
236#382—71no—
237C4×C4⋊C4—71no—
238C4×C4⋊C4—71no—
239C4×C4⋊C4—141no—
240C4×C4⋊C4—141no—
241C4×C4⋊C4C2×D711yescharacteristic
242C4×C22⋊C4—21no—
243C43C2×D711yescharacteristic
244#340—71no—
245#340—71no—
246#340—71no—
247#340—71no—
248#340—71no—
249#340—71no—
250#340—71no—
251#340—71no—
252#336—71no—
253#336—71no—
254C23×C7—22no—
255C23×C7—41no—
256C23×C7—41no—
257C23×C7—41no—
258C23×C7—41no—
259C23×C7—41no—
260C23×C7—41no—
261C23×C7C22×D411yescharacteristic
262C7×D4—22no—
263C7×D4—22no—
264C7×D4—41no—
265C7×D4—41no—
266C2×C4×C7—21no—
267C2×C4×C7—21no—
268C2×C4×C7—21no—
269C2×C4×C7—21no—
270C2×C4×C7—21no—
271C2×C4×C7—21no—
272C2×C4×C7—22no—
273C2×C4×C7—21no—
274C2×C4×C7—21no—
275C2×C4×C7—21no—
276C2×C4×C7—21no—
277C2×C4×C7—21no—
278C2×C4×C7—21no—
279C2×C4×C7—21no—
280C2×C4×C7—21no—
281C2×C4×C7—21no—
282C2×C4×C7—48no—
283C2×C4×C7—41no—
284C2×C4×C7—41no—
285C2×C4×C7—41no—
286C2×C4×C7—41no—
287C2×C4×C7—41no—
288C2×C4×C7—41no—
289C2×C4×C7—41no—
290C2×C4×C7—41no—
291C2×C4×C7C4×D412yes—
292C2×C4×C7C4×D412yes—
293C2×C4×C7AGL(1,ℤ/8)12yes—
294C2×C4×C7C23×C411yescharacteristic
295C2×C4×C7C2×#4111yescharacteristic
296C2×C4×C7H(5,𝔽2)11yescharacteristic
297C2×C4×C72−1+411yescharacteristic
298C2×C4×C72−1+411yescharacteristic
299C2×C4×C72−1+411yescharacteristic
300C2×Dic7—22no—
301C2×Dic7—22no—
302C2×Dic7—41no—
303C2×Dic7—41no—
304C2×Dic7—41no—
305C2×Dic7—41no—
306C2×Dic7—41no—
307C2×Dic7—41no—
308C2×Dic7—41no—
309C2×Dic7—41no—
310C2×Dic7—41no—
311C2×Dic7—41no—
312C7⋊C8—22no—
313C7⋊C8—22no—
314C7⋊C8—41no—
315C7⋊C8—41no—
316C22×D4C22×D711yescharacteristic
317C23×C4—21no—
318C22×C8—71no—
319C22×C8—71no—
320C22×C8—71no—
321C22×C8—71no—
322#125—74no—
323#125—142no—
324C4×D4—22no—
325C4×D4C4×D714yes—
326#117—44no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—71no—
330C2×C4⋊C4—71no—
331C2×C4⋊C4—71no—
332C2×C4⋊C4—71no—
333C2×C4⋊C4—141no—
334C2×C4⋊C4—141no—
335C2×C4⋊C4—141no—
336C2×C4⋊C4—141no—
337C2×C4⋊C4C22×D711yescharacteristic
338C2×C4⋊C4C22×D711yescharacteristic
339C2×C4⋊C4C22×D711yescharacteristic
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C42—21no—
346C2×C42—141no—
347C2×C42—141no—
348C2×C42C22⋊D711yescharacteristic
349C2×C42C22⋊D711yescharacteristic
350C2×C42C22⋊D711yescharacteristic
351C2×C42C22⋊D711yescharacteristic
352C2×C42C22×D711yescharacteristic
353C2×C42C22×D711yescharacteristic
354C2×C42C22×D711yescharacteristic
355#107—74no—
356#107—281no—
357#106—74no—
358#106—281no—
359C4⋊C8—74no—
360C4⋊C8—142no—
361#102—74no—
362#102—74no—
363#102—281no—
364#102—281no—
365#97—281no—
366#97—281no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—141no—
371#95—141no—
372#95—141no—
373#95—141no—
374#95—141no—
375#95—141no—
376C22×C7—42no—
377C22×C7—42no—
378C22×C7—42no—
379C22×C7—81no—
380C22×C7—81no—
381C22×C7—81no—
382C22×C7—81no—
383C22×C7C2×C4×D411yescharacteristic
384C22×C7#53611yescharacteristic
385C22×C7#53711yescharacteristic
386C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
387C22×C7#57511yescharacteristic
388C22×C7#57511yescharacteristic
389C22×C7#57511yescharacteristic
390C4×C7—22no—
391C4×C7—22no—
392C4×C7—22no—
393C4×C7—42no—
394C4×C7—41no—
395C4×C7—41no—
396C4×C7—41no—
397C4×C7—81no—
398C4×C7—81no—
399C4×C7#51911yescharacteristic
400C4×C7#52011yescharacteristic
401C4×C7#54111yescharacteristic
402C4×C7#54211yescharacteristic
403Dic7—42no—
404Dic7—42no—
405Dic7—81no—
406Dic7—81no—
407C24—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4C2×C4×D712yes—
414C22×C4—21no—
415C22×C4—24no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—141no—
421C22×C4—141no—
422C22×C4—141no—
423C22×C4—141no—
424C22×C4C2×C22⋊D711yescharacteristic
425C22×C4C2×C22⋊D711yescharacteristic
426C22×C4C2×C22⋊D711yescharacteristic
427C22×C4C2×C22⋊D711yescharacteristic
428C22×C4C2×C22⋊D711yescharacteristic
429C22×C4C2×C22⋊D711yescharacteristic
430C22×C4C23×D711yescharacteristic
431C2×C8—72no—
432C2×C8—72no—
433C2×C8—141no—
434C2×C8—141no—
435C2×C8—141no—
436C2×C8—141no—
437C2×C8—141no—
438C2×C8—141no—
439C2×C8—141no—
440C2×C8—141no—
441C2×C8—141no—
442C2×C8—141no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—42no—
449C4⋊C4—42no—
450C4⋊C4—72no—
451C4⋊C4—72no—
452C4⋊C4—144no—
453C4⋊C4—144no—
454C4⋊C4—141no—
455C4⋊C4—141no—
456C4⋊C4—141no—
457C4⋊C4—141no—
458C4⋊C4—141no—
459C4⋊C4—141no—
460C4⋊C4—282no—
461C4⋊C4—282no—
462C4⋊C4C2×C4×D712yes—
463C22⋊C4—24no—
464C22⋊C4—42no—
465C22⋊C4—42no—
466C22⋊C4—42no—
467C22⋊C4—42no—
468C42—22no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—41no—
474C42—41no—
475C42—41no—
476C42—42no—
477C42—282no—
478C42—282no—
479C42C2×C4×D712yes—
480C42#115712yes—
481C2×C7—82no—
482C2×C7#232311yescharacteristic
483C2×C7#294311yescharacteristic
484C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
485C2×C7#323411yescharacteristic
486C2×C7#324011yescharacteristic
487C2×C7#325111yescharacteristic
488C2×C7#325611yescharacteristic
489C23—22no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23C22×C22⋊D711yescharacteristic
497D4—22no—
498D4—22no—
499D4—41no—
500D4—41no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—48no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—142no—
527C2×C4—142no—
528C2×C4—281no—
529C2×C4—281no—
530C2×C4—281no—
531C2×C4—281no—
532C2×C4—281no—
533C2×C4—281no—
534C2×C4—281no—
535C2×C4—281no—
536C2×C4—281no—
537C2×C4—281no—
538C2×C4C4×C22⋊D712yes—
539C2×C4C4×C22⋊D712yes—
540C2×C4#649512yes—
541C2×C4C22×C4×D711yescharacteristic
542C2×C4C2×#115711yescharacteristic
543C2×C4#655311yescharacteristic
544C2×C4#655411yescharacteristic
545C2×C4#655411yescharacteristic
546C2×C4#655411yescharacteristic
547C8—142no—
548C8—142no—
549C8—281no—
550C8—281no—
551C7#2212011yescharacteristic, complemented, Sylow
552C22—42no—
553C22—42no—
554C22—42no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22C2×C4×C22⋊D711yescharacteristic
560C22C2×#649511yescharacteristic
561C22#9051311yescharacteristic
562C22#9051311yescharacteristic
563C22#9051311yescharacteristic
564C22#9051611yescharacteristic
565C22#9052411yescharacteristic
566C4—22no—
567C4—22no—
568C4—22no—
569C4—41no—
570C4—42no—
571C4—41no—
572C4—41no—
573C4—81no—
574C4—81no—
575C4—282no—
576C4—282no—
577C4—561no—
578C4—561no—
579C4#9020711yescharacteristic
580C4#9020911yescharacteristic
581C4#9021411yescharacteristic
582C4#9022511yescharacteristic
583C2—82no—
584C2#1173968011yescharacteristic
585C2C4×#649511yescharacteristic
586C2#1173995111yescharacteristic
587C2#1174057011yescharacteristic
588C2#1174059611yescharacteristic
589C2#1174071811yescharacteristic
590C2#1174075711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2293C2
socleC23×C7C22×D4
prime radicalC22×C7×D4C23
cosocleC22×C4×C7C24
hypercenter#2293D7
hypocenterC7#22120
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C43 ◁ #2293

Complements

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

NH ≅ G/Ntype
3. C4×#6433C2semidirect
9. #11727375C2semidirect
10. #11727374C2semidirect
11. #11727355C2semidirect
12. #11727354C2semidirect
13. #11727245C2semidirect
14. #11727222C2semidirect
15. #11727145C2semidirect
32. #89781C4semidirect
551. C7#22120semidirect

Maximal subgroups

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

subgroupindex
C7×#22932
C2×#897812
C4×#64332
#117293592
#117273992
#117273912
#117273902
#117273752
#117273742
#117273552
#117273542
#117272452
#117272222
#117271452
#221207