Finite Group Databasebeta

← #13360856

Subgroups — #13360856

Order 1792.

878 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89873C211yesmaximal, characteristic, complemented
2#11739791C211yesmaximal, characteristic
3C2×#89783C211yesmaximal, characteristic
4C7×#1869C211yesmaximal, characteristic
5#11729728C211yesmaximal, characteristic, complemented
6#11727703C211yesmaximal, characteristic, complemented
7#11727702C211yesmaximal, characteristic, complemented
8#11727701C211yesmaximal, characteristic, complemented
9#11727669C211yesmaximal, characteristic, complemented
10#11727667C211yesmaximal, characteristic, complemented
11#11727665C211yesmaximal, characteristic, complemented
12#11726408C211yesmaximal, characteristic, complemented
13#11726406C211yesmaximal, characteristic, complemented
14#11726368C211yesmaximal, characteristic, complemented
15#11726365C211yesmaximal, characteristic, complemented
16C23×C7×C8C2211yescharacteristic
17C2×C4×C7×D4C2211yescharacteristic
18C2×#6489C2211yescharacteristic
19C22×#1136C2211yescharacteristic
20C23×C7⋊C8C2211yescharacteristic
21C2×C7×C22⋊C8C2211yescharacteristic
22C2×C7×C22⋊C8C2211yescharacteristic
23C2×C7×C22⋊C8C2211yescharacteristic
24#89994C411yescharacteristic
25#89994C411yescharacteristic
26C4×C22⋊Dic7C2211yescharacteristic
27C4×C22⋊Dic7C2211yescharacteristic
28C4×C22⋊Dic7C2211yescharacteristic
29C2×C22⋊(C7⋊C8)C2211yescharacteristic
30C2×C22⋊(C7⋊C8)C2211yescharacteristic
31#89873—24no—
32C2×#6389C2211yescharacteristic
33C2×#6389C2211yescharacteristic
34C2×#6389C2211yescharacteristic
35C2×Dic7⋊C8C2211yescharacteristic
36C2×Dic7⋊C8C2211yescharacteristic
37C2×C8×Dic7C2211yescharacteristic
38C2×C8×Dic7C2211yescharacteristic
39C2×C8×Dic7C2211yescharacteristic
40#89783—24no—
41#89758C411yescharacteristic
42#89755C411yescharacteristic
43#89725C411yescharacteristic
44#89724C411yescharacteristic
45#89724C411yescharacteristic
46#89721C411yescharacteristic
47C4×Dic7⋊C4C2211yescharacteristic
48C4×Dic7⋊C4C2211yescharacteristic
49C2×C4⋊(C7⋊C8)C2211yescharacteristic
50C2×#6377C2211yescharacteristic
51C7×#336C2211yescharacteristic
52C7×#336C2211yescharacteristic
53#89345C2211yescharacteristic
54#89345C2211yescharacteristic
55#89345C2211yescharacteristic
56#89345C2211yescharacteristic
57#89345C2211yescharacteristic
58#89345C2211yescharacteristic
59#89345C2211yescharacteristic
60#89345C2211yescharacteristic
61#21568—71nomaximal, Sylow
62C22×C7×D4C2×C411yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C22×C7×C8—22no—
66C22×C7×C8—22no—
67C22×C7×C8—22no—
68C22×C7×C8C2311yescharacteristic
69C22×C7×C8C2311yescharacteristic
70C22×C7×C8C2311yescharacteristic
71C22×C7×C8C2311yescharacteristic
72C4×C7×D4—22no—
73C4×C7×D4—22no—
74C2×C7×C4⋊C4C2×C411yescharacteristic
75C2×C7×C22⋊C4C2×C411yescharacteristic
76C2×C7×C22⋊C4C2×C411yescharacteristic
77C2×C42×C7C2311yescharacteristic
78C2×C22⋊Dic7C2×C411yescharacteristic
79C2×C22⋊Dic7C2×C411yescharacteristic
80C2×C22⋊Dic7C2×C411yescharacteristic
81C2×C22⋊Dic7C2×C411yescharacteristic
82C2×C22⋊Dic7C2×C411yescharacteristic
83C2×C22⋊Dic7C2×C411yescharacteristic
84C2×C22⋊Dic7C2×C411yescharacteristic
85C2×C22⋊Dic7C2×C411yescharacteristic
86#6489—22no—
87#6489—22no—
88C2×C4⋊Dic7C2×C411yescharacteristic
89C2×C4⋊Dic7C2×C411yescharacteristic
90C2×Dic7⋊C4C2×C411yescharacteristic
91C2×Dic7⋊C4C2×C411yescharacteristic
92C2×Dic7⋊C4C2×C411yescharacteristic
93C2×Dic7⋊C4C2×C411yescharacteristic
94C2×C4×Dic7C2311yescharacteristic
95C2×C4×Dic7C2311yescharacteristic
96C2×C4×Dic7C2311yescharacteristic
97C2×C4×Dic7C2311yescharacteristic
98C2×#1136—22no—
99C2×#1136—22no—
100C2×#1136D414yes—
101C22×C7⋊C8—22no—
102C22×C7⋊C8—22no—
103C22×C7⋊C8—22no—
104C22×C7⋊C8C2311yescharacteristic
105C22×C7⋊C8C2311yescharacteristic
106C22×C7⋊C8C2311yescharacteristic
107C22×C7⋊C8C2311yescharacteristic
108C7×C22⋊C8—22no—
109C7×C22⋊C8—22no—
110C7×C22⋊C8—22no—
111C7⋊#95C2×C411yescharacteristic
112C7⋊#95C2×C411yescharacteristic
113C7⋊#95C2×C411yescharacteristic
114C7⋊#95C2×C411yescharacteristic
115C7⋊#95C2×C411yescharacteristic
116C7⋊#95C2×C411yescharacteristic
117C7⋊#95C2×C411yescharacteristic
118C7⋊#95C2×C411yescharacteristic
119C7⋊#95C2×C411yescharacteristic
120C7⋊#95C2×C411yescharacteristic
121C22⋊(C7⋊C8)—22no—
122C22⋊(C7⋊C8)—22no—
123#6389—22no—
124#6389—22no—
125#6389—22no—
126Dic7⋊C8—22no—
127Dic7⋊C8—22no—
128C8×Dic7—22no—
129C8×Dic7—22no—
130C8×Dic7—22no—
131C4⋊(C7⋊C8)—22no—
132#6377—22no—
133C2×#435—71no—
134C2×#405—71no—
135#2395—71no—
136#1924—71no—
137#1923—71no—
138#1917—71no—
139#1916—71no—
140#1869D711yescharacteristic
141#1850—71no—
142#1818—71no—
143#1771—71no—
144#1770—71no—
145#1753—71no—
146#1752—71no—
147C8×C22⋊C4—71no—
148C24×C7C22×C411yescharacteristic
149C24×C7C22×C411yescharacteristic
150C2×C7×D4—22no—
151C2×C7×D4—22no—
152C2×C7×D4—41no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7C22×C411yescharacteristic
164C22×C4×C7C22×C411yescharacteristic
165C22×C4×C7C22×C411yescharacteristic
166C22×C4×C7C22×C411yescharacteristic
167C22×C4×C7C2×D412yes—
168C22×C4×C7#4112yes—
169C22×C4×C7C2411yescharacteristic
170C22×Dic7C22×C411yescharacteristic
171C22×Dic7C22×C411yescharacteristic
172C22×Dic7C22×C411yescharacteristic
173C22×Dic7C22×C411yescharacteristic
174C22×Dic7C22×C411yescharacteristic
175C22×Dic7C22×C411yescharacteristic
176C22×Dic7C22×C411yescharacteristic
177C22×Dic7C22×C411yescharacteristic
178C2×C7×C8—28no—
179C2×C7×C8—21no—
180C2×C7×C8—21no—
181C2×C7×C8—21no—
182C2×C7×C8—21no—
183C2×C7×C8—21no—
184C2×C7×C8—21no—
185C2×C7×C8—21no—
186C2×C7×C8—21no—
187C2×C7×C8—21no—
188C2×C7×C8—21no—
189C2×C7×C8#4112yes—
190C2×C7×C8#4112yes—
191C7×C4⋊C4—22no—
192C7×C22⋊C4—22no—
193C7×C22⋊C4—22no—
194C42×C7—21no—
195C42×C7—21no—
196C22⋊Dic7—22no—
197C22⋊Dic7—22no—
198C22⋊Dic7—22no—
199C22⋊Dic7—22no—
200C22⋊Dic7—22no—
201C22⋊Dic7—22no—
202C22⋊Dic7—41no—
203C22⋊Dic7—41no—
204C4⋊Dic7—22no—
205C4⋊Dic7—22no—
206Dic7⋊C4—22no—
207Dic7⋊C4—41no—
208Dic7⋊C4—41no—
209Dic7⋊C4—41no—
210C4×Dic7—21no—
211C4×Dic7—21no—
212C4×Dic7—21no—
213C4×Dic7—21no—
214C4×Dic7—21no—
215C4×Dic7—21no—
216C4×Dic7—21no—
217C4×Dic7—21no—
218#1136—28no—
219C2×C7⋊C8—21no—
220C2×C7⋊C8—21no—
221C2×C7⋊C8—21no—
222C2×C7⋊C8—21no—
223C2×C7⋊C8—21no—
224C2×C7⋊C8—21no—
225C2×C7⋊C8—21no—
226C2×C7⋊C8—21no—
227C2×C7⋊C8—44no—
228C2×C7⋊C8C2×D412yes—
229C2×C7⋊C8C2×D412yes—
230C2×C7⋊C8#4112yes—
231C2×C7⋊C8#4112yes—
232C22×M16—71no—
233C23×C8—71no—
234C23×C8C2×D711yescharacteristic
235C2×C4×D4C2×D711yescharacteristic
236C2×#117—71no—
237#435—144no—
238C2×C4⋊C8—71no—
239C2×C4⋊C8—71no—
240C2×C4⋊C8—71no—
241C2×C22⋊C8—71no—
242C2×C22⋊C8—71no—
243C2×C22⋊C8C2×D711yescharacteristic
244C2×C22⋊C8C2×D711yescharacteristic
245C2×C22⋊C8C2×D711yescharacteristic
246#405—144no—
247C2×#97—71no—
248C2×#97—71no—
249C2×#97—71no—
250C2×#97—71no—
251C2×C4×C8—71no—
252C2×C4×C8—71no—
253C2×C4×C8—71no—
254#400—71no—
255#399—71no—
256#398—71no—
257#397—71no—
258#397—71no—
259#397—71no—
260#394—71no—
261#394—71no—
262C4×C4⋊C4—71no—
263C4×C4⋊C4—71no—
264C4×C22⋊C4—71no—
265C4×C22⋊C4—71no—
266C4×C22⋊C4—71no—
267#336—71no—
268#336—71no—
269#336—71no—
270#336—71no—
271#336—71no—
272#336—71no—
273#336—71no—
274#336—71no—
275#336C2×D711yescharacteristic
276#336C2×D711yescharacteristic
277C23×C7—21no—
278C23×C7—21no—
279C23×C7—21no—
280C23×C7—21no—
281C23×C7—21no—
282C23×C7—21no—
283C23×C7—21no—
284C23×C7—21no—
285C23×C7—21no—
286C23×C7—21no—
287C23×C7—21no—
288C23×C7—21no—
289C23×C7C4×D412yes—
290C23×C7#13112yes—
291C23×C7C23×C411yescharacteristic
292C7×D4—44no—
293C2×C4×C7—21no—
294C2×C4×C7—21no—
295C2×C4×C7—22no—
296C2×C4×C7—22no—
297C2×C4×C7—22no—
298C2×C4×C7—22no—
299C2×C4×C7—21no—
300C2×C4×C7—21no—
301C2×C4×C7—21no—
302C2×C4×C7—21no—
303C2×C4×C7—21no—
304C2×C4×C7—21no—
305C2×C4×C7—21no—
306C2×C4×C7—21no—
307C2×C4×C7—21no—
308C2×C4×C7—41no—
309C2×C4×C7—41no—
310C2×C4×C7—41no—
311C2×C4×C7—41no—
312C2×C4×C7C4×D412yes—
313C2×C4×C7C22×D411yescharacteristic
314C2×C4×C7C2×#4111yescharacteristic
315C2×C4×C7C2×#4111yescharacteristic
316C2×C4×C7C2×#4111yescharacteristic
317C2×C4×C7C2×#4111yescharacteristic
318C2×C4×C7C2×#4111yescharacteristic
319C2×Dic7—21no—
320C2×Dic7—21no—
321C2×Dic7—21no—
322C2×Dic7—21no—
323C2×Dic7—21no—
324C2×Dic7—21no—
325C2×Dic7—21no—
326C2×Dic7—21no—
327C2×Dic7—21no—
328C2×Dic7—21no—
329C2×Dic7—21no—
330C2×Dic7—21no—
331C2×Dic7—21no—
332C2×Dic7—21no—
333C2×Dic7—21no—
334C2×Dic7—21no—
335C2×Dic7—21no—
336C2×Dic7—21no—
337C2×Dic7—21no—
338C2×Dic7—21no—
339C2×Dic7—21no—
340C2×Dic7—21no—
341C2×Dic7—21no—
342C2×Dic7#13112yes—
343C7×C8—22no—
344C7×C8—22no—
345C7×C8—41no—
346C7×C8—41no—
347C7⋊C8—22no—
348C7⋊C8—41no—
349C7⋊C8—41no—
350C7⋊C8#12314yes—
351C22×D4C4×D711yescharacteristic
352C23×C4C22×D711yescharacteristic
353C23×C4C22×D711yescharacteristic
354C2×M16—74no—
355C2×M16—142no—
356C2×M16—142no—
357C22×C8—22no—
358C22×C8—22no—
359C22×C8—22no—
360C22×C8—71no—
361C22×C8—71no—
362C22×C8—71no—
363C22×C8—71no—
364C22×C8—142no—
365C22×C8—142no—
366C22×C8—142no—
367C22×C8C22×D711yescharacteristic
368C22×C8C22×D711yescharacteristic
369C22×C8C22×D711yescharacteristic
370C22×C8C22×D711yescharacteristic
371C4×D4—22no—
372C4×D4—22no—
373#117—142no—
374#117—142no—
375C2×C4⋊C4—71no—
376C2×C4⋊C4—71no—
377C2×C4⋊C4—71no—
378C2×C4⋊C4—71no—
379C2×C4⋊C4—71no—
380C2×C4⋊C4—71no—
381C2×C4⋊C4C4×D711yescharacteristic
382C2×C22⋊C4—71no—
383C2×C22⋊C4—71no—
384C2×C22⋊C4—71no—
385C2×C22⋊C4—71no—
386C2×C22⋊C4—71no—
387C2×C22⋊C4—71no—
388C2×C22⋊C4—71no—
389C2×C22⋊C4—71no—
390C2×C22⋊C4C4×D711yescharacteristic
391C2×C22⋊C4C4×D711yescharacteristic
392C2×C42—71no—
393C2×C42—71no—
394C2×C42—71no—
395C2×C42—71no—
396C2×C42C22×D711yescharacteristic
397C4⋊C8—142no—
398C4⋊C8—142no—
399C4⋊C8—142no—
400C22⋊C8—22no—
401C22⋊C8—22no—
402C22⋊C8—22no—
403C22⋊C8—142no—
404C22⋊C8—142no—
405#97—142no—
406#97—142no—
407#97—142no—
408#97—142no—
409C4×C8—142no—
410C4×C8—142no—
411C4×C8—142no—
412#95—71no—
413#95—71no—
414#95—71no—
415#95—71no—
416#95—71no—
417#95—71no—
418#95—71no—
419#95—71no—
420#95—71no—
421#95—71no—
422C22×C7—22no—
423C22×C7—22no—
424C22×C7—22no—
425C22×C7—22no—
426C22×C7—22no—
427C22×C7—22no—
428C22×C7—41no—
429C22×C7—41no—
430C22×C7—41no—
431C22×C7—41no—
432C22×C7—41no—
433C22×C7—41no—
434C22×C7—41no—
435C22×C7—41no—
436C22×C7C2×C4×D411yescharacteristic
437C22×C7C4×#4111yescharacteristic
438C22×C7C4×#4111yescharacteristic
439C22×C7C2×#13111yescharacteristic
440C22×C7C2×#13111yescharacteristic
441C22×C7#56811yescharacteristic
442C22×C7#56811yescharacteristic
443C4×C7—22no—
444C4×C7—41no—
445C4×C7—41no—
446C4×C7—41no—
447C4×C7C2×#12311yescharacteristic
448C4×C7#52511yescharacteristic
449C4×C7#52911yescharacteristic
450C4×C7#52911yescharacteristic
451Dic7—22no—
452Dic7—41no—
453Dic7—41no—
454Dic7—41no—
455Dic7—41no—
456Dic7—41no—
457Dic7—41no—
458Dic7—41no—
459C24C2×C4×D711yescharacteristic
460C24C2×C4×D711yescharacteristic
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—41no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—71no—
475C22×C4—71no—
476C22×C4—71no—
477C22×C4—71no—
478C22×C4—71no—
479C22×C4—71no—
480C22×C4—71no—
481C22×C4—71no—
482C22×C4C2×C4×D711yescharacteristic
483C22×C4C2×C4×D711yescharacteristic
484C22×C4C2×C4×D711yescharacteristic
485C22×C4C2×C4×D711yescharacteristic
486C22×C4D4×D712yes—
487C22×C4#115912yes—
488C22×C4C23×D711yescharacteristic
489M16—148no—
490C2×C8—28no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—72no—
502C2×C8—72no—
503C2×C8—72no—
504C2×C8—72no—
505C2×C8—141no—
506C2×C8—141no—
507C2×C8—141no—
508C2×C8—141no—
509C2×C8—141no—
510C2×C8—141no—
511C2×C8—141no—
512C2×C8—141no—
513C2×C8—284no—
514C2×C8#115912yes—
515C2×C8#115912yes—
516C4⋊C4—22no—
517C4⋊C4—142no—
518C4⋊C4—142no—
519C4⋊C4—142no—
520C4⋊C4—281no—
521C4⋊C4—281no—
522C4⋊C4—281no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—142no—
526C22⋊C4—142no—
527C22⋊C4—142no—
528C22⋊C4—142no—
529C22⋊C4—142no—
530C22⋊C4—142no—
531C22⋊C4—281no—
532C22⋊C4—281no—
533C42—21no—
534C42—21no—
535C42—141no—
536C42—141no—
537C42—141no—
538C42—141no—
539C42—141no—
540C42—141no—
541C42—141no—
542C42—141no—
543C2×C7—42no—
544C2×C7—42no—
545C2×C7C4×#12311yescharacteristic
546C2×C7#293311yescharacteristic
547C2×C7#293511yescharacteristic
548C2×C7#296611yescharacteristic
549C2×C7#296711yescharacteristic
550C2×C7#296811yescharacteristic
551C2×C7#296811yescharacteristic
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23(C22⋊D7)⋊C412yes—
565C23#646412yes—
566C23C22×C4×D711yescharacteristic
567D4—44no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—72no—
588C2×C4—141no—
589C2×C4—141no—
590C2×C4—141no—
591C2×C4—141no—
592C2×C4—141no—
593C2×C4—141no—
594C2×C4—141no—
595C2×C4—141no—
596C2×C4—141no—
597C2×C4—141no—
598C2×C4—141no—
599C2×C4—141no—
600C2×C4—141no—
601C2×C4—141no—
602C2×C4—141no—
603C2×C4—141no—
604C2×C4—141no—
605C2×C4—141no—
606C2×C4—141no—
607C2×C4—141no—
608C2×C4—141no—
609C2×C4—141no—
610C2×C4—141no—
611C2×C4(C22⋊D7)⋊C412yes—
612C2×C4C2×D4×D711yescharacteristic
613C2×C4C2×#115911yescharacteristic
614C2×C4C2×#115911yescharacteristic
615C2×C4C2×#115911yescharacteristic
616C2×C4D7×#4111yescharacteristic
617C2×C4D7×#4111yescharacteristic
618C8—22no—
619C8—22no—
620C8—41no—
621C8—41no—
622C8—74no—
623C8—142no—
624C8—281no—
625C8—281no—
626C7#2156811yescharacteristic, complemented, Sylow
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22C2×(C22⋊D7)⋊C411yescharacteristic
642C22C4×#115911yescharacteristic
643C22C4×#115911yescharacteristic
644C22C2×#646411yescharacteristic
645C22#9043611yescharacteristic
646C22D7×#13111yescharacteristic
647C22#9044111yescharacteristic
648C4—22no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—142no—
653C4—281no—
654C4—281no—
655C4—281no—
656C4—281no—
657C4—281no—
658C4—281no—
659C4—281no—
660C4#9027711yescharacteristic
661C4#9029111yescharacteristic
662C4#9029111yescharacteristic
663C4D7×#12311yescharacteristic
664C2—42no—
665C2—42no—
666C2#1173210611yescharacteristic
667C2#1173604111yescharacteristic
668C2#1173610511yescharacteristic
669C2#1173684511yescharacteristic
670C2#1173684711yescharacteristic
671C2#1173690111yescharacteristic
672C2#1173690311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D7
commutator, socleC23×C7C23×C4
FittingC7×#1869C2
prime radicalC22×C7×D4C2×C4
cosocleC22×C4×C7C24
hypercenter#1869D7
hypocenterC7#21568
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
1. C2×#89873C2semidirect
5. #11729728C2semidirect
6. #11727703C2semidirect
7. #11727702C2semidirect
8. #11727701C2semidirect
9. #11727669C2semidirect
10. #11727667C2semidirect
11. #11727665C2semidirect
12. #11726408C2semidirect
13. #11726406C2semidirect
14. #11726368C2semidirect
15. #11726365C2semidirect
626. C7#21568semidirect

Maximal subgroups

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

subgroupindex
C2×#898732
#117397912
C2×#897832
C7×#18692
#117297282
#117277032
#117277022
#117277012
#117276692
#117276672
#117276652
#117264082
#117264062
#117263682
#117263652
#215687