Finite Group Databasebeta

← #13359485

Subgroups — #13359485

Order 1792.

1552 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×#41C211yesmaximal, characteristic, complemented
2C2×#90010C211yesmaximal, characteristic
3C2×#89798C211yesmaximal, characteristic, complemented
4C2×#89786C211yesmaximal, characteristic, complemented
5C4×#6493C211yesmaximal, characteristic, complemented
6#11729889C211yesmaximal, characteristic, complemented
7#11729387C211yesmaximal, characteristic, complemented
8#11729385C211yesmaximal, characteristic, complemented
9#11729383C211yesmaximal, characteristic, complemented
10#11729367C211yesmaximal, characteristic, complemented
11#11729363C211yesmaximal, characteristic, complemented
12#11729360C211yesmaximal, characteristic, complemented
13#11729340C211yesmaximal, characteristic, complemented
14#11729330C211yesmaximal, characteristic, complemented
15#11729283C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C4×C7×#41—24no—
18C4×C7×#41—24no—
19C2×C4×C7×Q8C2211yescharacteristic
20C2×C4×C7×Q8C2211yescharacteristic
21C2×C4×C7×D4—21no—
22C2×C4×C7×D4—21no—
23C2×C4×C7×D4C2211yescharacteristic
24C2×C4×C7×D4C2211yescharacteristic
25C2×C7×#117—21no—
26C2×C7×#117C2211yescharacteristic
27C22×C42×C7—21no—
28C22×C42×C7C2211yescharacteristic
29C22×#1143C2211yescharacteristic
30C22×#1141C2211yescharacteristic
31C2×#6493C2211yescharacteristic
32C2×C4×C22⋊D7—21no—
33C2×C4×D28C2211yescharacteristic
34#90010C418yescomplemented
35C2×#6409C2211yescharacteristic
36C2×#6409C2211yescharacteristic
37C2×#6409C2211yescharacteristic
38C2×#6406C2211yescharacteristic
39C2×#6406C2211yescharacteristic
40C2×#6406C2211yescharacteristic
41#89985—21no—
42#89984C2211yescharacteristic
43C2×C22⋊(C7⋊C8)C2211yescharacteristic
44C2×C22⋊(C7⋊C8)C2211yescharacteristic
45#89798—24no—
46#89786—24no—
47C2×#6383C2211yescharacteristic
48C2×#6383C2211yescharacteristic
49C2×#6382C2211yescharacteristic
50C2×#6381C2211yescharacteristic
51#89712—21no—
52#89711C2211yescharacteristic
53C4×(C2×D7)⋊C4—21no—
54C4×C4⋊Dic7C2211yescharacteristic
55#89700C2211yescharacteristic
56C2×#6377C2211yescharacteristic
57C2×#6377C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#89319C2211yescharacteristic
63#89319C2211yescharacteristic
64#21456—71nomaximal, Sylow
65C2×C7×#41—22no—
66C2×C7×#41—22no—
67C2×C7×#41—22no—
68C2×C7×#41—22no—
69C2×C7×#41—22no—
70C2×C7×#41C2×C414yescomplemented
71C22×C7×Q8C2311yescharacteristic
72C22×C7×D4—21no—
73C22×C7×D4C2311yescharacteristic
74C23×C4×C7—21no—
75C23×C4×C7—21no—
76C23×C4×C7—21no—
77C23×C4×C7D411yescharacteristic
78C23×C4×C7D411yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C22×C22⋊D7—21no—
81C22×D28C2311yescharacteristic
82C22×C4×D7—21no—
83C4×C7×Q8—22no—
84C4×C7×Q8—22no—
85C4×C7×Q8—22no—
86C4×C7×Q8D414yescomplemented
87C4×C7×D4—28no—
88C4×C7×D4—28no—
89C4×C7×D4—22no—
90C4×C7×D4—22no—
91C4×C7×D4—22no—
92C4×C7×D4D414yescomplemented
93C7×#117—28no—
94C7×#117—22no—
95C7×#117—22no—
96C2×C7×C4⋊C4—21no—
97C2×C7×C4⋊C4—21no—
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C22⋊C4—21no—
101C2×C7×C22⋊C4—21no—
102C2×C7×C22⋊C4—21no—
103C2×C42×C7—28no—
104C2×C42×C7—21no—
105C2×C42×C7—21no—
106C2×C42×C7—21no—
107C2×C42×C7—22no—
108C2×C42×C7—22no—
109C2×C42×C7D411yescharacteristic
110C2×C42×C7D411yescharacteristic
111C2×C42×C7C2311yescharacteristic
112C2×C42×C7C2311yescharacteristic
113C2×C22⋊Dic7—21no—
114C2×#1143—22no—
115C2×#1143—22no—
116C2×#1143C2×C414yescomplemented
117C2×#1141—22no—
118C2×#1141—22no—
119C2×#1141C2×C414yescomplemented
120#6493—22no—
121#6493C2×C414yescomplemented
122C4×C22⋊D7—44no—
123C2×(C2×D7)⋊C4—21no—
124C2×(C2×D7)⋊C4—21no—
125C2×(C2×D7)⋊C4—21no—
126C2×(C2×D7)⋊C4—21no—
127C2×C4⋊Dic7C2311yescharacteristic
128C2×C4⋊Dic7C2311yescharacteristic
129C2×C4⋊Dic7C2311yescharacteristic
130C2×Dic7⋊C4—21no—
131C2×C4×Dic7—21no—
132C22×C7⋊C8C2311yescharacteristic
133C22×C7⋊C8C2311yescharacteristic
134C22×C7⋊C8C2311yescharacteristic
135C22×C7⋊C8C2311yescharacteristic
136C4×D28—22no—
137C4×D28—22no—
138#6409—22no—
139#6409—22no—
140#6409C2×C414yescomplemented
141#6406—22no—
142#6406—22no—
143#6406C2×C414yescomplemented
144C7⋊#95—21no—
145C7⋊#95—21no—
146C7⋊#95—21no—
147C22⋊(C7⋊C8)—22no—
148C22⋊(C7⋊C8)C2×C414yescomplemented
149#6383—22no—
150#6383—22no—
151#6382—22no—
152#6381—22no—
153#6377—22no—
154#6377—22no—
155C2×C4×#41D711yescharacteristic, complemented
156C2×#449—71no—
157C2×#442—71no—
158C2×#440—71no—
159C4×#121—71no—
160#1880—71no—
161#1879—71no—
162#1875—71no—
163#1865—71no—
164#1862—71no—
165#1854—71no—
166#1788—71no—
167#1763—71no—
168#1762—71no—
169#1749—71no—
170C24×C7—21no—
171C24×C7C2×D411yescharacteristic
172C23×D7—21no—
173C7×#41—28no—
174C7×#41—28no—
175C7×#41—28no—
176C7×#41—28no—
177C2×C7×Q8—21no—
178C2×C7×Q8—21no—
179C2×C7×Q8—21no—
180C2×C7×Q8C22×C412yes—
181C2×C7×Q8C2×D412yes—
182C2×C7×Q8#4112yes—
183C2×C7×D4—24no—
184C2×C7×D4—24no—
185C2×C7×D4—24no—
186C2×C7×D4—21no—
187C2×C7×D4—21no—
188C2×C7×D4—21no—
189C2×C7×D4C22×C412yes—
190C2×C7×D4C2×D412yes—
191C2×C7×D4#4112yes—
192C22×C4×C7—24no—
193C22×C4×C7—24no—
194C22×C4×C7—21no—
195C22×C4×C7—24no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—24no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—24no—
206C22×C4×C7—22no—
207C22×C4×C7—41no—
208C22×C4×C7—41no—
209C22×C4×C7—41no—
210C22×C4×C7—42no—
211C22×C4×C7—42no—
212C22×C4×C7—42no—
213C22×C4×C7—42no—
214C22×C4×C7C22×C412yes—
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2×D411yescharacteristic
220C22×C4×C7#4112yes—
221C22×C4×C7C2411yescharacteristic
222C2×C22⋊D7—24no—
223C2×C22⋊D7—42no—
224C2×C22⋊D7—42no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C2×D28—21no—
229C2×D28—21no—
230C2×D28—21no—
231C2×D28—21no—
232C2×D28—21no—
233C2×D28C22×C412yes—
234C2×C4×D7—42no—
235C2×C4×D7—42no—
236C2×C4×D7—42no—
237C7×C4⋊C4—24no—
238C7×C4⋊C4—24no—
239C7×C4⋊C4—21no—
240C7×C4⋊C4—21no—
241C7×C4⋊C4C2×D412yes—
242C7×C4⋊C4C2×D412yes—
243C7×C22⋊C4—24no—
244C7×C22⋊C4—24no—
245C7×C22⋊C4—24no—
246C42×C7—24no—
247C42×C7—24no—
248C42×C7—22no—
249C42×C7—24no—
250C42×C7—22no—
251C42×C7—21no—
252C42×C7—21no—
253C42×C7C2×D412yes—
254C42×C7C2×D412yes—
255C22⋊Dic7—42no—
256#1143—28no—
257#1141—28no—
258(C2×D7)⋊C4—24no—
259(C2×D7)⋊C4—42no—
260(C2×D7)⋊C4—42no—
261(C2×D7)⋊C4—42no—
262C4⋊Dic7—21no—
263C4⋊Dic7—21no—
264C4⋊Dic7—21no—
265C4⋊Dic7—21no—
266C4⋊Dic7—21no—
267C4⋊Dic7C22×C412yes—
268Dic7⋊C4—42no—
269C4×Dic7—42no—
270C2×C7⋊C8—21no—
271C2×C7⋊C8—21no—
272C2×C7⋊C8—21no—
273C2×C7⋊C8—21no—
274C2×C7⋊C8—21no—
275C2×C7⋊C8—21no—
276C2×C7⋊C8—21no—
277C2×C7⋊C8—21no—
278C2×C7⋊C8—21no—
279C2×C7⋊C8—21no—
280C2×C7⋊C8C22×C412yes—
281C2×C7⋊C8C22×C412yes—
282C22×#41C2×D711yescharacteristic
283C22×SD16—71no—
284C22×D8—71no—
285C2×#121—71no—
286C4×#41—24no—
287C4×#41—24no—
288C2×C4×Q8C2×D711yescharacteristic
289C2×C4×Q8C2×D711yescharacteristic
290C2×C4×D4—21no—
291C2×C4×D4—21no—
292C2×C4×D4—71no—
293C2×C4×D4—141no—
294C2×C4×D4C2×D711yescharacteristic
295C2×C4×D4C2×D711yescharacteristic
296C2×#117—21no—
297C2×#117C2×D711yescharacteristic
298C22×C42—21no—
299C22×C42C2×D711yescharacteristic
300#449—78no—
301#442—144no—
302#440—144no—
303C2×#107—71no—
304C2×#106—71no—
305C2×#103—71no—
306C2×#103—71no—
307C2×#103—71no—
308C2×#102—71no—
309C2×#102—71no—
310C2×#102—71no—
311C2×#102—71no—
312C2×#102—71no—
313C2×C22⋊C8—71no—
314C2×C22⋊C8—71no—
315C2×#97—71no—
316C2×#97—71no—
317#390—71no—
318#389—71no—
319#388—141no—
320#386—141no—
321#380—71no—
322C4×C4⋊C4—71no—
323C4×C22⋊C4—141no—
324#340—71no—
325#340—71no—
326#340—71no—
327#340—71no—
328#336—71no—
329#336—71no—
330C23×C7—22no—
331C23×C7—21no—
332C23×C7—22no—
333C23×C7—21no—
334C23×C7—22no—
335C23×C7—21no—
336C23×C7—21no—
337C23×C7—21no—
338C23×C7—21no—
339C23×C7—41no—
340C23×C7—41no—
341C23×C7—41no—
342C23×C7—41no—
343C23×C7C4×D412yes—
344C23×C7C22×D411yescharacteristic
345C22×D7—22no—
346C22×D7—41no—
347C22×D7—41no—
348C22×D7—41no—
349C22×D7—41no—
350C22×D7—41no—
351C22×D7—41no—
352C7×Q8—22no—
353C7×Q8—22no—
354C7×Q8—22no—
355C7×Q8C4×D414yescomplemented
356C7×D4—216no—
357C7×D4—22no—
358C7×D4—22no—
359C7×D4—22no—
360C7×D4C4×D414yescomplemented
361C2×C4×C7—216no—
362C2×C4×C7—22no—
363C2×C4×C7—21no—
364C2×C4×C7—21no—
365C2×C4×C7—22no—
366C2×C4×C7—21no—
367C2×C4×C7—22no—
368C2×C4×C7—21no—
369C2×C4×C7—21no—
370C2×C4×C7—21no—
371C2×C4×C7—21no—
372C2×C4×C7—21no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—21no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—21no—
381C2×C4×C7—21no—
382C2×C4×C7—44no—
383C2×C4×C7—44no—
384C2×C4×C7—48no—
385C2×C4×C7—48no—
386C2×C4×C7—41no—
387C2×C4×C7—41no—
388C2×C4×C7—41no—
389C2×C4×C7—41no—
390C2×C4×C7C4×D412yes—
391C2×C4×C7#12012yes—
392C2×C4×C7#12012yes—
393C2×C4×C7AGL(1,ℤ/8)12yes—
394C2×C4×C7C23×C411yescharacteristic
395C2×C4×C7C22×D411yescharacteristic
396C2×C4×C7C22×D411yescharacteristic
397C2×C4×C7C2×#4111yescharacteristic
398C2×C4×C7C2×#4111yescharacteristic
399C2×C4×C7C2×#4111yescharacteristic
400C22⋊D7—48no—
401C2×Dic7—22no—
402C2×Dic7—41no—
403C2×Dic7—41no—
404C2×Dic7—41no—
405C2×Dic7—41no—
406C2×Dic7—41no—
407C2×Dic7—41no—
408C2×Dic7—41no—
409C2×Dic7—41no—
410D28—22no—
411D28—22no—
412D28—41no—
413D28—41no—
414C4×D7—84no—
415C7⋊C8—22no—
416C7⋊C8—22no—
417C7⋊C8—41no—
418C7⋊C8—41no—
419C2×#41—22no—
420C2×#41—22no—
421C2×#41—22no—
422C2×#41—22no—
423C2×#41—22no—
424C2×#41C4×D714yescomplemented
425C22×Q8C22×D711yescharacteristic
426C22×D4—21no—
427C22×D4—71no—
428C22×D4—141no—
429C22×D4C22×D711yescharacteristic
430C23×C4—21no—
431C23×C4—21no—
432C23×C4—21no—
433C23×C4—141no—
434C23×C4C22⋊D711yescharacteristic
435C23×C4C22⋊D711yescharacteristic
436C23×C4C22×D711yescharacteristic
437C2×SD16—74no—
438C2×SD16—142no—
439C2×SD16—142no—
440C2×D8—74no—
441C2×D8—142no—
442C2×D8—142no—
443C22×C8—71no—
444C22×C8—71no—
445C22×C8—71no—
446C22×C8—71no—
447#121—74no—
448#121—142no—
449C4×Q8—22no—
450C4×Q8—22no—
451C4×Q8—22no—
452C4×Q8C22⋊D714yescomplemented
453C4×D4—28no—
454C4×D4—28no—
455C4×D4—22no—
456C4×D4—22no—
457C4×D4—22no—
458C4×D4—142no—
459C4×D4—142no—
460C4×D4—284no—
461C4×D4C22⋊D714yescomplemented
462#117—28no—
463#117—22no—
464#117—22no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—71no—
468C2×C4⋊C4—71no—
469C2×C4⋊C4—71no—
470C2×C4⋊C4—141no—
471C2×C4⋊C4C22×D711yescharacteristic
472C2×C4⋊C4C22×D711yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—141no—
477C2×C22⋊C4—141no—
478C2×C22⋊C4—141no—
479C2×C22⋊C4—141no—
480C2×C22⋊C4—141no—
481C2×C42—28no—
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42—22no—
486C2×C42—22no—
487C2×C42—141no—
488C2×C42C22⋊D711yescharacteristic
489C2×C42C22⋊D711yescharacteristic
490C2×C42C22×D711yescharacteristic
491C2×C42C22×D711yescharacteristic
492#107—142no—
493#106—142no—
494#103—74no—
495#103—142no—
496#103—142no—
497#102—74no—
498#102—142no—
499#102—142no—
500#102—142no—
501#102—142no—
502C22⋊C8—74no—
503C22⋊C8—142no—
504#97—142no—
505#97—142no—
506#95—141no—
507#95—141no—
508#95—141no—
509C22×C7—22no—
510C22×C7—22no—
511C22×C7—22no—
512C22×C7—24no—
513C22×C7—41no—
514C22×C7—42no—
515C22×C7—41no—
516C22×C7—42no—
517C22×C7—42no—
518C22×C7—42no—
519C22×C7—41no—
520C22×C7—42no—
521C22×C7—41no—
522C22×C7—42no—
523C22×C7C2×C4×D411yescharacteristic
524C22×C7C2×#12011yescharacteristic
525C22×C7#52511yescharacteristic
526C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
527C22×C7#57511yescharacteristic
528C22×C7#57511yescharacteristic
529C22×C7#57511yescharacteristic
530C2×D7—42no—
531C2×D7—42no—
532C2×D7—42no—
533C2×D7—81no—
534C2×D7—81no—
535C2×D7—81no—
536C2×D7—81no—
537C4×C7—22no—
538C4×C7—22no—
539C4×C7—22no—
540C4×C7—22no—
541C4×C7—24no—
542C4×C7—41no—
543C4×C7—42no—
544C4×C7—42no—
545C4×C7C2×C4×D411yescharacteristic
546C4×C7C2×C4×D411yescharacteristic
547C4×C7#52511yescharacteristic
548C4×C7#52511yescharacteristic
549Dic7—42no—
550Dic7—81no—
551Dic7—81no—
552C24—21no—
553C24—141no—
554C24C2×C22⋊D711yescharacteristic
555#41—28no—
556#41—28no—
557#41—28no—
558#41—28no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8C2×C4×D712yes—
563C2×Q8#115712yes—
564C2×Q8C2×C22⋊D712yes—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—72no—
572C2×D4—144no—
573C2×D4—141no—
574C2×D4—141no—
575C2×D4—141no—
576C2×D4—141no—
577C2×D4—141no—
578C2×D4—282no—
579C2×D4—282no—
580C2×D4C2×C4×D712yes—
581C2×D4#115712yes—
582C2×D4C2×C22⋊D712yes—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—24no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—24no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—141no—
606C22×C4—141no—
607C22×C4—141no—
608C22×C4—282no—
609C22×C4—282no—
610C22×C4—282no—
611C22×C4C2×C4×D712yes—
612C22×C4#115712yes—
613C22×C4C2×C22⋊D711yescharacteristic
614C22×C4C2×C22⋊D711yescharacteristic
615C22×C4C2×C22⋊D711yescharacteristic
616C22×C4C2×C22⋊D711yescharacteristic
617C22×C4C2×C22⋊D711yescharacteristic
618C22×C4C23×D711yescharacteristic
619SD16—148no—
620D8—148no—
621C2×C8—72no—
622C2×C8—72no—
623C2×C8—141no—
624C2×C8—141no—
625C2×C8—141no—
626C2×C8—141no—
627C2×C8—141no—
628C2×C8—141no—
629C2×C8—141no—
630C2×C8—141no—
631C2×C8—141no—
632C2×C8—141no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—72no—
638C4⋊C4—141no—
639C4⋊C4—141no—
640C4⋊C4—141no—
641C4⋊C4—141no—
642C4⋊C4—141no—
643C4⋊C4—282no—
644C4⋊C4C2×C22⋊D712yes—
645C4⋊C4C2×C22⋊D712yes—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—144no—
650C22⋊C4—282no—
651C22⋊C4—282no—
652C22⋊C4—282no—
653C22⋊C4—282no—
654C42—24no—
655C42—24no—
656C42—22no—
657C42—24no—
658C42—22no—
659C42—21no—
660C42—21no—
661C42—282no—
662C42C2×C22⋊D712yes—
663C42C2×C22⋊D712yes—
664C2×C7—42no—
665C2×C7—44no—
666C2×C7C4×#12011yescharacteristic
667C2×C7#294311yescharacteristic
668C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
669C2×C7#300511yescharacteristic
670C2×C7#300611yescharacteristic
671C2×C7#311111yescharacteristic
672C2×C7#311511yescharacteristic
673D7—82no—
674C23—22no—
675C23—21no—
676C23—22no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—22no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—142no—
688C23—281no—
689C23—281no—
690C23—281no—
691C23—281no—
692C23—281no—
693C23—281no—
694C23C4×C22⋊D712yes—
695C23C22×C22⋊D711yescharacteristic
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8C4×C22⋊D714yescomplemented
700D4—216no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—142no—
705D4—142no—
706D4—288no—
707D4—281no—
708D4—281no—
709D4C4×C22⋊D714yescomplemented
710C2×C4—216no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—48no—
734C2×C4—48no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—142no—
740C2×C4—281no—
741C2×C4—281no—
742C2×C4—281no—
743C2×C4—281no—
744C2×C4—281no—
745C2×C4—281no—
746C2×C4—281no—
747C2×C4—281no—
748C2×C4—564no—
749C2×C4C4×C22⋊D712yes—
750C2×C4#651212yes—
751C2×C4#651612yes—
752C2×C4#651612yes—
753C2×C4C22×C4×D711yescharacteristic
754C2×C4C2×#115711yescharacteristic
755C2×C4C2×#115711yescharacteristic
756C2×C4C2×#115711yescharacteristic
757C2×C4C22×C22⋊D711yescharacteristic
758C2×C4C22×C22⋊D711yescharacteristic
759C8—142no—
760C8—142no—
761C8—281no—
762C8—281no—
763C7#2145611yescharacteristic, complemented, Sylow
764C22—22no—
765C22—24no—
766C22—22no—
767C22—22no—
768C22—42no—
769C22—42no—
770C22—41no—
771C22—42no—
772C22—41no—
773C22—42no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—282no—
779C22—282no—
780C22—282no—
781C22—561no—
782C22—561no—
783C22—561no—
784C22—561no—
785C22C2×C4×C22⋊D711yescharacteristic
786C22#9048211yescharacteristic
787C22C2×#651211yescharacteristic
788C22#9051311yescharacteristic
789C22#9051311yescharacteristic
790C22#9051311yescharacteristic
791C22C2×#651611yescharacteristic
792C4—22no—
793C4—24no—
794C4—22no—
795C4—22no—
796C4—22no—
797C4—41no—
798C4—42no—
799C4—42no—
800C4—282no—
801C4—561no—
802C4—561no—
803C4C2×C4×C22⋊D711yescharacteristic
804C4C2×C4×C22⋊D711yescharacteristic
805C4#9048211yescharacteristic
806C4#9048211yescharacteristic
807C2—42no—
808C2—44no—
809C2—562no—
810C2#1173995111yescharacteristic
811C2C4×#651211yescharacteristic
812C2#1173997511yescharacteristic
813C2#1173997611yescharacteristic
814C2C4×#651611yescharacteristic
815C2#1174152611yescharacteristic
816C2#1174152711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C4×C7×#41C2
socleC23×C7C22×D4
prime radicalC2×#90010C2
cosocleC22×C4×C7C24
hypercenterC2×C4×#41D7
hypocenterC7#21456
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×C4×C7×#41C2semidirect
3. C2×#89798C2semidirect
4. C2×#89786C2semidirect
5. C4×#6493C2semidirect
6. #11729889C2semidirect
7. #11729387C2semidirect
8. #11729385C2semidirect
9. #11729383C2semidirect
10. #11729367C2semidirect
11. #11729363C2semidirect
12. #11729360C2semidirect
13. #11729340C2semidirect
14. #11729330C2semidirect
15. #11729283C2semidirect
34. #90010C4semidirect
70. C2×C7×#41C2×C4semidirect
86. C4×C7×Q8D4semidirect
92. C4×C7×D4D4semidirect
116. C2×#1143C2×C4semidirect
119. C2×#1141C2×C4semidirect
121. #6493C2×C4semidirect
140. #6409C2×C4semidirect
143. #6406C2×C4semidirect
148. C22⋊(C7⋊C8)C2×C4semidirect
155. C2×C4×#41D7semidirect
355. C7×Q8C4×D4semidirect
360. C7×D4C4×D4semidirect
424. C2×#41C4×D7semidirect
452. C4×Q8C22⋊D7semidirect
461. C4×D4C22⋊D7semidirect
699. Q8C4×C22⋊D7semidirect
709. D4C4×C22⋊D7semidirect
763. C7#21456semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C7×#412
C2×#900102
C2×#897982
C2×#897862
C4×#64932
#117298892
#117293872
#117293852
#117293832
#117293672
#117293632
#117293602
#117293402
#117293302
#117292832
#214567