Finite Group Databasebeta

← #13355494

Subgroups — #13355494

Order 1792.

1986 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90519C211yesmaximal, characteristic
2C22×D7×M16C211yesmaximal, characteristic, complemented
3C2×C7×#417C211yesmaximal, characteristic, complemented
4C2×#90004C211yesmaximal, characteristic, complemented
5C2×#89759C211yesmaximal, characteristic, complemented
6#11729739C211yesmaximal, characteristic, complemented
7#11729312C211yesmaximal, characteristic, complemented
8#11728025C212yesmaximal, complemented
9#11728024C212yesmaximal, complemented
10#11727957C212yesmaximal, complemented
11#11727956C212yesmaximal, complemented
12C22×C7×#41C2211yescharacteristic
13C23×C4×D7C2211yescharacteristic
14C22×C7×M16C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16#90519—24no—
17#90519C418yescomplemented
18C2×#6509C2211yescharacteristic
19C2×#6509C2211yescharacteristic
20C2×#6501C2211yescharacteristic
21C2×#6501C2211yescharacteristic
22C2×#6500—21no—
23C2×#6498—21no—
24C2×C4×C22⋊D7—21no—
25C2×C4×C22⋊D7—21no—
26C22×(C2×D7)⋊C4—21no—
27C2×#6489C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×#1136C2211yescharacteristic
30C2×D7×M16—24no—
31C2×D7×M16—24no—
32C2×D7×M16—24no—
33C22×#1131C2212yes—
34C22×C8×D7C2212yes—
35C7×#417—24no—
36C2×C7×#103C2212yescomplemented
37C2×C7×#102C2212yescomplemented
38#90004—24no—
39C2×#6409C2212yescomplemented
40C2×#6406C2212yescomplemented
41C2×C7⋊#95—21no—
42#89759—21no—
43#89759—21no—
44#89759C2212yes—
45#89759C2212yes—
46#89346C2212yescomplemented
47#89346C2212yescomplemented
48#89324C2212yescomplemented
49#89324C2212yescomplemented
50#20971—71nomaximal, Sylow
51C24×D7D411yescharacteristic
52C2×C7×#41—22no—
53C2×C7×#41—22no—
54C2×C7×#41—22no—
55C2×C7×#41—22no—
56C2×C7×#41—22no—
57C2×C7×#41C2×C414yes—
58C22×C7×Q8C2311yescharacteristic
59C22×C7×D4—21no—
60C22×C7×D4C2311yescharacteristic
61C23×C4×C7—21no—
62C23×C4×C7—21no—
63C23×C4×C7C2311yescharacteristic
64C22×C22⋊D7—21no—
65C22×C22⋊D7—21no—
66C23×Dic7—21no—
67C23×Dic7D411yescharacteristic
68C22×C4×D7—22no—
69C22×C4×D7—22no—
70C22×C4×D7—22no—
71C22×C4×D7—22no—
72C22×C4×D7C2×C414yes—
73C22×C4×D7D411yescharacteristic
74C22×C4×D7D411yescharacteristic
75C22×C4×D7D414yes—
76C22×C4×D7C2311yescharacteristic
77C22×C4×D7C2311yescharacteristic
78C2×C7×M16—22no—
79C2×C7×M16—22no—
80C2×C7×M16D414yescomplemented
81C22×C7×C8C2312yes—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4—21no—
85C2×C7×C4⋊C4C2312yes—
86C2×C22⋊Dic7—21no—
87C2×C22⋊Dic7—21no—
88C2×C22⋊Dic7—21no—
89#6509—22no—
90#6509—22no—
91#6509C2×C414yescomplemented
92#6509C2×C414yescomplemented
93#6501—22no—
94#6501—22no—
95#6501C2×C414yescomplemented
96#6501C2×C414yescomplemented
97#6500—28no—
98#6498—28no—
99C4×C22⋊D7—28no—
100C4×C22⋊D7—28no—
101C2×(C2×D7)⋊C4—21no—
102C2×(C2×D7)⋊C4—21no—
103C2×(C2×D7)⋊C4—22no—
104C2×(C2×D7)⋊C4—22no—
105C2×(C2×D7)⋊C4—44no—
106#6489—22no—
107#6489C2×C414yes—
108C2×C4⋊Dic7—22no—
109C2×C4⋊Dic7—22no—
110C2×C4⋊Dic7—21no—
111C2×C4⋊Dic7C2312yes—
112C2×C4⋊Dic7C2311yescharacteristic
113C2×C4⋊Dic7C2311yescharacteristic
114C2×Dic7⋊C4—21no—
115C2×Dic7⋊C4—21no—
116C2×C4×Dic7—21no—
117C2×#1136—22no—
118C2×#1136—22no—
119C2×#1136D414yescomplemented
120C22×C7⋊C8C2312yes—
121D7×M16—232no—
122C2×#1131—24no—
123C2×#1131—24no—
124C2×#1131—24no—
125C2×C8×D7—24no—
126C2×C8×D7—24no—
127C2×C8×D7—24no—
128C7×#103—24no—
129C7×#102—24no—
130#6409—24no—
131#6406—24no—
132C7⋊#95—22no—
133C7⋊#95—22no—
134C23×M16—71no—
135C2×#525—71no—
136C2×#417—71no—
137C2×#417D711yescharacteristic, complemented
138C2×#380—71no—
139#1895—72no—
140#1894—72no—
141#1893—72no—
142#1892—72no—
143#1736—71no—
144#1736—71no—
145C24×C7—21no—
146C24×C7C2×D411yescharacteristic
147C23×D7—22no—
148C23×D7—22no—
149C23×D7—22no—
150C23×D7—22no—
151C23×D7—41no—
152C23×D7—41no—
153C23×D7C22⋊C414yes—
154C23×D7C2×D411yescharacteristic
155C23×D7C2×D411yescharacteristic
156C7×#41—28no—
157C7×#41—28no—
158C7×#41—44no—
159C7×#41—44no—
160C2×C7×Q8—21no—
161C2×C7×Q8—21no—
162C2×C7×Q8—21no—
163C2×C7×Q8—21no—
164C2×C7×Q8—21no—
165C2×C7×Q8C22×C412yes—
166C2×C7×D4—24no—
167C2×C7×D4—21no—
168C2×C7×D4—21no—
169C2×C7×D4—21no—
170C2×C7×D4—21no—
171C2×C7×D4—21no—
172C2×C7×D4—42no—
173C2×C7×D4—42no—
174C2×C7×D4C22×C412yes—
175C22×C4×C7—21no—
176C22×C4×C7—24no—
177C22×C4×C7—22no—
178C22×C4×C7—42no—
179C22×C4×C7—42no—
180C22×C4×C7—42no—
181C22×C4×C7—42no—
182C22×C4×C7—42no—
183C22×C4×C7C22×C412yes—
184C22×C4×C7C2×D411yescharacteristic
185C22×C4×C7C2×D412yes—
186C22×C4×C7C2×D412yes—
187C22×C4×C7C2×D412yes—
188C22×C4×C7#4112yes—
189C22×C4×C7#4112yes—
190C22×C4×C7C2411yescharacteristic
191C2×C22⋊D7—24no—
192C2×C22⋊D7—24no—
193C2×C22⋊D7—42no—
194C2×C22⋊D7—42no—
195C2×C22⋊D7—42no—
196C2×C22⋊D7—42no—
197C22×Dic7—22no—
198C22×Dic7—22no—
199C22×Dic7—21no—
200C22×Dic7—21no—
201C22×Dic7—22no—
202C22×Dic7—42no—
203C22×Dic7—42no—
204C22×Dic7—42no—
205C22×Dic7C22⋊C414yes—
206C22×Dic7C2×D411yescharacteristic
207C22×Dic7C2×D411yescharacteristic
208C2×C4×D7—28no—
209C2×C4×D7—28no—
210C2×C4×D7—28no—
211C2×C4×D7—22no—
212C2×C4×D7—22no—
213C2×C4×D7—22no—
214C2×C4×D7—22no—
215C2×C4×D7—28no—
216C2×C4×D7—21no—
217C2×C4×D7—21no—
218C2×C4×D7—21no—
219C2×C4×D7—21no—
220C2×C4×D7—21no—
221C2×C4×D7—21no—
222C2×C4×D7—21no—
223C2×C4×D7—21no—
224C2×C4×D7C22⋊C414yes—
225C2×C4×D7C22⋊C414yes—
226C2×C4×D7C22×C412yes—
227C2×C4×D7C22×C412yes—
228C2×C4×D7C2×D412yes—
229C2×C4×D7C2×D412yes—
230C7×M16—28no—
231C2×C7×C8—22no—
232C2×C7×C8—22no—
233C2×C7×C8C2×D414yes—
234C7×C4⋊C4—22no—
235C7×C4⋊C4—22no—
236C7×C4⋊C4—42no—
237C22⋊Dic7—24no—
238C22⋊Dic7—24no—
239C22⋊Dic7—24no—
240(C2×D7)⋊C4—24no—
241(C2×D7)⋊C4—24no—
242(C2×D7)⋊C4—44no—
243(C2×D7)⋊C4—44no—
244C4⋊Dic7—21no—
245C4⋊Dic7—21no—
246C4⋊Dic7—22no—
247C4⋊Dic7—22no—
248C4⋊Dic7—42no—
249C4⋊Dic7C22×C412yes—
250C4⋊Dic7C22×C412yes—
251Dic7⋊C4—24no—
252Dic7⋊C4—24no—
253C4×Dic7—24no—
254#1136—28no—
255C2×C7⋊C8—22no—
256C2×C7⋊C8—22no—
257C2×C7⋊C8C2×D414yes—
258#1131—216no—
259C8×D7—216no—
260C22×#41C2×D711yescharacteristic
261C24×C4—71no—
262C22×M16—71no—
263C22×M16—72no—
264C22×M16—144no—
265C22×M16—144no—
266C22×M16—144no—
267C22×M16C2×D711yescharacteristic
268C23×C8—72no—
269#525—78no—
270#525—144no—
271C2×#123—141no—
272C2×C22⋊Q8—71no—
273C2×C22⋊Q8—71no—
274C2×#121—71no—
275C2×#121—71no—
276C2×#120—141no—
277C2×C4×D4—141no—
278C2×C4×D4—141no—
279C2×#117—71no—
280C22×C4⋊C4—71no—
281C22×C4⋊C4C2×D711yescharacteristic
282C22×C22⋊C4—141no—
283#417—24no—
284#417—144no—
285C2×#103—72no—
286C2×#103C2×D712yescomplemented
287C2×#102—72no—
288C2×#102C2×D712yescomplemented
289#380—72no—
290#380—72no—
291#380—141no—
292#380—141no—
293C2×#95—141no—
294#340—72no—
295#340—72no—
296#340—72no—
297#340—72no—
298C23×C7—21no—
299C23×C7—21no—
300C23×C7—21no—
301C23×C7—21no—
302C23×C7—22no—
303C23×C7—41no—
304C23×C7—41no—
305C23×C7—41no—
306C23×C7—41no—
307C23×C7—41no—
308C23×C7—41no—
309C23×C7C2×C22⋊C412yes—
310C23×C7#12112yes—
311C23×C7#12112yes—
312C23×C7C22×D411yescharacteristic
313C22×D7—21no—
314C22×D7—21no—
315C22×D7—21no—
316C22×D7—21no—
317C22×D7—21no—
318C22×D7—21no—
319C22×D7—21no—
320C22×D7—21no—
321C22×D7—21no—
322C22×D7—21no—
323C22×D7—28no—
324C22×D7—28no—
325C22×D7—44no—
326C22×D7—44no—
327C22×D7—44no—
328C22×D7—44no—
329C22×D7—44no—
330C22×D7C2×C22⋊C412yes—
331C22×D7C2×C22⋊C412yes—
332C22×D7AGL(1,ℤ/8)12yes—
333C22×D7#13712yes—
334C7×Q8—22no—
335C7×Q8—22no—
336C7×Q8—41no—
337C7×Q8—41no—
338C7×D4—22no—
339C7×D4—22no—
340C7×D4—48no—
341C7×D4—41no—
342C7×D4—41no—
343C2×C4×C7—22no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—48no—
347C2×C4×C7—42no—
348C2×C4×C7—42no—
349C2×C4×C7—42no—
350C2×C4×C7—84no—
351C2×C4×C7C2×C22⋊C412yes—
352C2×C4×C7C4×D414yes—
353C2×C4×C7C4×D414yes—
354C2×C4×C7#12014yes—
355C2×C4×C7#12112yes—
356C2×C4×C7#12112yes—
357C2×C4×C7#12314yes—
358C2×C4×C7C23×C411yescharacteristic
359C2×C4×C7C22×D411yescharacteristic
360C2×C4×C7C22×D411yescharacteristic
361C2×C4×C7C22×D411yescharacteristic
362C2×C4×C7C2×#4111yescharacteristic
363C2×C4×C7C2×#4111yescharacteristic
364C22⋊D7—48no—
365C22⋊D7—48no—
366C2×Dic7—21no—
367C2×Dic7—21no—
368C2×Dic7—21no—
369C2×Dic7—21no—
370C2×Dic7—28no—
371C2×Dic7—22no—
372C2×Dic7—22no—
373C2×Dic7—41no—
374C2×Dic7—41no—
375C2×Dic7—41no—
376C2×Dic7—41no—
377C2×Dic7—42no—
378C2×Dic7—42no—
379C2×Dic7—42no—
380C2×Dic7—84no—
381C2×Dic7C2×C22⋊C412yes—
382C2×Dic7C2×C22⋊C412yes—
383C4×D7—22no—
384C4×D7—22no—
385C4×D7—22no—
386C4×D7—22no—
387C4×D7—22no—
388C4×D7—22no—
389C4×D7—22no—
390C4×D7—22no—
391C4×D7—28no—
392C4×D7—28no—
393C7×C8—24no—
394C7⋊C8—24no—
395C25—71no—
396C2×#41—22no—
397C2×#41—22no—
398C2×#41—22no—
399C2×#41—22no—
400C2×#41—22no—
401C2×#41C4×D714yes—
402C22×Q8C22×D711yescharacteristic
403C22×D4—21no—
404C22×D4—141no—
405C22×D4—141no—
406C22×D4C22×D711yescharacteristic
407C23×C4—21no—
408C23×C4—21no—
409C23×C4—71no—
410C23×C4—74no—
411C23×C4—71no—
412C23×C4—71no—
413C23×C4—74no—
414C23×C4—71no—
415C23×C4—71no—
416C23×C4—142no—
417C23×C4—142no—
418C23×C4—142no—
419C23×C4—142no—
420C23×C4—141no—
421C23×C4C22×D711yescharacteristic
422C2×M16—22no—
423C2×M16—22no—
424C2×M16—74no—
425C2×M16—144no—
426C2×M16—144no—
427C2×M16—1432no—
428C2×M16—142no—
429C2×M16—142no—
430C2×M16—144no—
431C2×M16C22⋊D714yescomplemented
432C22×C8—72no—
433C22×C8—144no—
434C22×C8—144no—
435C22×C8—144no—
436C22×C8C22×D712yes—
437#123—148no—
438C22⋊Q8—74no—
439C22⋊Q8—74no—
440C22⋊Q8—142no—
441C22⋊Q8—142no—
442#121—74no—
443#121—74no—
444#121—142no—
445#121—142no—
446#120—148no—
447C4×D4—148no—
448C4×D4—148no—
449#117—74no—
450#117—142no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—71no—
455C2×C4⋊C4—71no—
456C2×C4⋊C4—72no—
457C2×C4⋊C4—141no—
458C2×C4⋊C4—141no—
459C2×C4⋊C4—142no—
460C2×C4⋊C4—142no—
461C2×C4⋊C4—141no—
462C2×C4⋊C4C22×D712yes—
463C2×C22⋊C4—141no—
464C2×C22⋊C4—141no—
465C2×C22⋊C4—141no—
466C2×C22⋊C4—141no—
467C2×C22⋊C4—141no—
468C2×C22⋊C4—142no—
469C2×C22⋊C4—142no—
470C2×C22⋊C4—284no—
471C2×C42—141no—
472#103—24no—
473#103—144no—
474#102—24no—
475#102—144no—
476#95—142no—
477#95—142no—
478C22×C7—22no—
479C22×C7—22no—
480C22×C7—22no—
481C22×C7—22no—
482C22×C7—22no—
483C22×C7—22no—
484C22×C7—42no—
485C22×C7—42no—
486C22×C7—42no—
487C22×C7—81no—
488C22×C7—81no—
489C22×C7—81no—
490C22×C7—81no—
491C22×C7#38614yes—
492C22×C7C22×C22⋊C411yescharacteristic
493C22×C7C2×#12111yescharacteristic
494C22×C7C2×#12111yescharacteristic
495C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
496C22×C7C2×#13711yescharacteristic
497C22×C7#57511yescharacteristic
498C22×C7#57511yescharacteristic
499C2×D7—22no—
500C2×D7—22no—
501C2×D7—22no—
502C2×D7—22no—
503C2×D7—22no—
504C2×D7—22no—
505C2×D7—22no—
506C2×D7—22no—
507C2×D7—22no—
508C2×D7—416no—
509C2×D7—41no—
510C2×D7—41no—
511C2×D7—41no—
512C2×D7—41no—
513C2×D7#41714yescomplemented
514C4×C7—42no—
515C4×C7—82no—
516C4×C7#38614yes—
517C4×C7C2×C4×D411yescharacteristic
518C4×C7C2×C4×D411yescharacteristic
519C4×C7C2×#12011yescharacteristic
520C4×C7C2×#12311yescharacteristic
521Dic7—22no—
522Dic7—22no—
523Dic7—42no—
524Dic7—42no—
525Dic7—82no—
526C24—21no—
527C24—71no—
528C24—71no—
529C24—74no—
530C24—142no—
531C24—142no—
532C24—142no—
533C24—142no—
534C24—281no—
535C24—281no—
536C24D4×D711yescharacteristic
537#41—28no—
538#41—28no—
539#41—44no—
540#41—44no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8C2×C4×D712yes—
547C2×D4—24no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—144no—
556C2×D4—144no—
557C2×D4—282no—
558C2×D4—282no—
559C2×D4—282no—
560C2×D4—282no—
561C2×D4C2×C4×D712yes—
562C22×C4—21no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—74no—
571C22×C4—71no—
572C22×C4—71no—
573C22×C4—74no—
574C22×C4—74no—
575C22×C4—72no—
576C22×C4—72no—
577C22×C4—72no—
578C22×C4—72no—
579C22×C4—142no—
580C22×C4—142no—
581C22×C4—148no—
582C22×C4—148no—
583C22×C4—142no—
584C22×C4—142no—
585C22×C4—148no—
586C22×C4—148no—
587C22×C4—142no—
588C22×C4—142no—
589C22×C4—141no—
590C22×C4—141no—
591C22×C4—141no—
592C22×C4—141no—
593C22×C4—141no—
594C22×C4—141no—
595C22×C4—141no—
596C22×C4—141no—
597C22×C4—141no—
598C22×C4—141no—
599C22×C4—142no—
600C22×C4—282no—
601C22×C4—282no—
602C22×C4—282no—
603C22×C4C2×C4×D712yes—
604C22×C4#115712yes—
605C22×C4D4×D711yescharacteristic
606C22×C4D4×D712yes—
607C22×C4D4×D712yes—
608C22×C4#115912yes—
609C22×C4C2×C22⋊D712yes—
610C22×C4C23×D711yescharacteristic
611M16—28no—
612M16—1416no—
613M16—148no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—74no—
617C2×C8—1416no—
618C2×C8—142no—
619C2×C8—142no—
620C2×C8C2×C22⋊D714yes—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—42no—
624C4⋊C4—72no—
625C4⋊C4—72no—
626C4⋊C4—144no—
627C4⋊C4—144no—
628C4⋊C4—141no—
629C4⋊C4—141no—
630C4⋊C4—142no—
631C4⋊C4—142no—
632C4⋊C4—282no—
633C22⋊C4—144no—
634C22⋊C4—144no—
635C22⋊C4—144no—
636C22⋊C4—144no—
637C22⋊C4—144no—
638C22⋊C4—284no—
639C22⋊C4—284no—
640C42—144no—
641C2×C7—24no—
642C2×C7—82no—
643C2×C7C2×#38611yescharacteristic
644C2×C7C2×#41711yescharacteristic
645C2×C7#289611yescharacteristic
646C2×C7#305511yescharacteristic
647C2×C7#305511yescharacteristic
648C2×C7#305611yescharacteristic
649C2×C7#305611yescharacteristic
650D7—24no—
651D7—42no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—22no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—72no—
664C23—72no—
665C23—72no—
666C23—72no—
667C23—148no—
668C23—141no—
669C23—141no—
670C23—141no—
671C23—141no—
672C23—141no—
673C23—141no—
674C23—141no—
675C23—141no—
676C23—141no—
677C23—141no—
678C23—148no—
679C23—284no—
680C23—284no—
681C23—284no—
682C23—284no—
683C23—284no—
684C23D7×C22⋊C412yes—
685C23#644712yes—
686C23#650112yes—
687C23C2×D4×D711yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—41no—
691Q8—41no—
692D4—22no—
693D4—22no—
694D4—48no—
695D4—41no—
696D4—41no—
697D4—288no—
698D4—288no—
699C2×C4—22no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—48no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—72no—
707C2×C4—72no—
708C2×C4—84no—
709C2×C4—141no—
710C2×C4—141no—
711C2×C4—141no—
712C2×C4—141no—
713C2×C4—148no—
714C2×C4—142no—
715C2×C4—142no—
716C2×C4—142no—
717C2×C4—142no—
718C2×C4—142no—
719C2×C4—142no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—148no—
723C2×C4—148no—
724C2×C4—142no—
725C2×C4—142no—
726C2×C4—281no—
727C2×C4—281no—
728C2×C4—281no—
729C2×C4—281no—
730C2×C4—282no—
731C2×C4—282no—
732C2×C4—282no—
733C2×C4—564no—
734C2×C4D7×C22⋊C412yes—
735C2×C4(C22⋊D7)⋊C414yes—
736C2×C4#644614yes—
737C2×C4#644712yes—
738C2×C4C4×C22⋊D714yes—
739C2×C4#650014yes—
740C2×C4#650112yes—
741C2×C4C22×C4×D711yescharacteristic
742C2×C4C2×#115711yescharacteristic
743C2×C4C2×D4×D711yescharacteristic
744C2×C4C2×D4×D711yescharacteristic
745C2×C4C2×#115911yescharacteristic
746C2×C4C22×C22⋊D711yescharacteristic
747C8—24no—
748C8—144no—
749C7#2097111yescharacteristic, complemented, Sylow
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—74no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—142no—
765C22—142no—
766C22—142no—
767C22—142no—
768C22—142no—
769C22—142no—
770C22—142no—
771C22—142no—
772C22—142no—
773C22—2816no—
774C22—281no—
775C22—281no—
776C22—281no—
777C22—281no—
778C22#8972814yes—
779C22C2×D7×C22⋊C411yescharacteristic
780C22C2×#644711yescharacteristic
781C22D7×AGL(1,ℤ/8)11yescharacteristic
782C22#9046411yescharacteristic
783C22D7×#13711yescharacteristic
784C22#9046811yescharacteristic
785C22C2×#650111yescharacteristic
786C4—42no—
787C4—82no—
788C4—142no—
789C4—142no—
790C4—282no—
791C4—282no—
792C4—562no—
793C4#8972814yes—
794C4C2×(C22⋊D7)⋊C411yescharacteristic
795C4C2×#644611yescharacteristic
796C4C2×C4×C22⋊D711yescharacteristic
797C4C2×#650011yescharacteristic
798C2—24no—
799C2—82no—
800C2—144no—
801C2—282no—
802C2D7×#41711yescharacteristic
803C2#1173632611yescharacteristic
804C2#1173633311yescharacteristic
805C2#1173633411yescharacteristic
806C2C2×#8972811yescharacteristic
807C2#1174139511yescharacteristic
808C2#1174143011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#417C2
socleC23×C7C22×D4
prime radicalC2×#90519C2
cosocleC22×C4×C7C24
hypercenterC2×#417D7
hypocenterC7#20971
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C22×D7×M16C2semidirect
3. C2×C7×#417C2semidirect
4. C2×#90004C2semidirect
5. C2×#89759C2semidirect
6. #11729739C2semidirect
7. #11729312C2semidirect
8. #11728025C2semidirect
9. #11728024C2semidirect
10. #11727957C2semidirect
11. #11727956C2semidirect
17. #90519C4semidirect
36. C2×C7×#103C22semidirect
37. C2×C7×#102C22semidirect
39. C2×#6409C22semidirect
40. C2×#6406C22semidirect
46. #89346C22semidirect
47. #89346C22semidirect
48. #89324C22semidirect
49. #89324C22semidirect
80. C2×C7×M16D4semidirect
91. #6509C2×C4semidirect
92. #6509C2×C4semidirect
95. #6501C2×C4semidirect
96. #6501C2×C4semidirect
119. C2×#1136D4semidirect
137. C2×#417D7semidirect
286. C2×#103C2×D7semidirect
288. C2×#102C2×D7semidirect
431. C2×M16C22⋊D7semidirect
513. C2×D7#417semidirect
749. C7#20971semidirect

Maximal subgroups

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

subgroupindex
C2×#905192
C22×D7×M162
C2×C7×#4172
C2×#900042
C2×#897592
#117297392
#117293122
#117280252
#117280242
#117279572
#117279562
#209717