Finite Group Databasebeta

← #13355697

Subgroups — #13355697

Order 1792.

1704 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#575C211yesmaximal, characteristic
2#11744328C211yesmaximal, characteristic, complemented
3C2×#90012C211yesmaximal, characteristic, complemented
4C2×#90008C211yesmaximal, characteristic, complemented
5#11741517C211yesmaximal, characteristic, complemented
6#11729855C214yesmaximal, complemented
7#11729843C214yesmaximal, complemented
8C2×#89351C211yesmaximal, characteristic, complemented
9C2×#89352C211yesmaximal, characteristic, complemented
10C22×C7×#41C2211yescharacteristic
11C22×C7×#41C2211yescharacteristic
12C7×#575—22no—
13C7×#575—22no—
14C7×#575—22no—
15C7×#575—22no—
16C2×C7×#137C412yescomplemented
17C2×C7×#137C2212yes—
18C2×C7×AGL(1,ℤ/8)C412yescomplemented
19C2×C7×AGL(1,ℤ/8)C2212yes—
20C2×C7×#135C414yescomplemented
21C22×C7×M16C2211yescharacteristic
22#90518—22no—
23#90518—22no—
24#41×Dic7—22no—
25#41×Dic7—22no—
26#90503C2212yescomplemented
27#90489—22no—
28#90489C2212yescomplemented
29C2×#6489—22no—
30C2×#6489C2211yescharacteristic
31C2×#6489C2211yescharacteristic
32C2×#6489C2211yescharacteristic
33C22×#1136C2211yescharacteristic
34#90012—22no—
35#90012C2214yes—
36#90008—22no—
37#90008C2214yes—
38C2×#6411—22no—
39#90005—22no—
40#90004—22no—
41#89997C2212yescomplemented
42C2×#6408—22no—
43#89987C2212yescomplemented
44#89352C2214yescomplemented
45#89351C2214yescomplemented
46#20998—71nomaximal, Sylow
47C2×C7×#41—21no—
48C2×C7×#41—21no—
49C2×C7×#41—21no—
50C2×C7×#41—21no—
51C2×C7×#41—21no—
52C2×C7×#41—21no—
53C2×C7×#41—21no—
54C2×C7×#41—21no—
55C2×C7×#41—21no—
56C2×C7×#41—21no—
57C2×C7×#41—21no—
58C2×C7×#41—21no—
59C2×C7×#41—21no—
60C2×C7×#41—21no—
61C2×C7×#41—21no—
62C2×C7×#41—21no—
63C2×C7×#41C2×C412yes—
64C2×C7×#41C2×C412yes—
65C2×C7×#41C2×C412yescomplemented
66C2×C7×#41D412yes—
67C2×C7×#41D412yes—
68C2×C7×#41D412yes—
69C2×C7×#41D412yes—
70C2×C7×#41C2312yes—
71C22×C7×Q8C2×C411yescharacteristic, complemented
72C22×C7×Q8C2311yescharacteristic
73C22×C7×D4—21no—
74C22×C7×D4—21no—
75C22×C7×D4C2×C411yescharacteristic, complemented
76C22×C7×D4C2311yescharacteristic
77C23×C4×C7—21no—
78C23×C4×C7—21no—
79C23×C4×C7C2311yescharacteristic
80C7×#137—24no—
81C7×#137—24no—
82C7×#137—24no—
83C7×#137—24no—
84C7×AGL(1,ℤ/8)—24no—
85C7×AGL(1,ℤ/8)—24no—
86C7×AGL(1,ℤ/8)—24no—
87C7×AGL(1,ℤ/8)—24no—
88C7×#135—28no—
89C7×#135—28no—
90C2×C7×Q16C2×C414yescomplemented
91C2×C7×SD16C2×C414yescomplemented
92C2×C7×SD16C2×C414yescomplemented
93C2×C7×D8C2×C414yescomplemented
94C2×C7×M16—21no—
95C2×C7×M16—21no—
96C2×C7×M16—21no—
97C2×C7×M16—21no—
98C2×C7×M16C2×C412yescomplemented
99C2×C7×M16C2312yes—
100C22×C7×C8C2×C412yescomplemented
101C2×C22⋊Dic7—21no—
102C2×C22⋊Dic7—24no—
103C2×C22⋊Dic7—21no—
104C2×C22⋊Dic7D412yes—
105Q8×Dic7—24no—
106Q8×Dic7—24no—
107D4×Dic7—28no—
108D4×Dic7—28no—
109D4×Dic7—24no—
110D4×Dic7—24no—
111#6489—24no—
112#6489—24no—
113#6489—21no—
114#6489—21no—
115#6489—21no—
116#6489—21no—
117#6489—24no—
118#6489—21no—
119#6489—21no—
120#6489—21no—
121#6489D412yes—
122#6489D412yes—
123#6489C2312yes—
124#6489C2312yes—
125#6489C2312yes—
126C2×C4⋊Dic7—24no—
127C2×C4⋊Dic7—21no—
128C2×C4⋊Dic7—21no—
129C2×C4⋊Dic7—21no—
130C2×C4×Dic7—24no—
131C2×C4×Dic7—21no—
132C2×C4×Dic7—21no—
133C2×C4×Dic7D412yes—
134C2×#1136—21no—
135C2×#1136—21no—
136C2×#1136—21no—
137C2×#1136—21no—
138C2×#1136—21no—
139C2×#1136C2312yes—
140C22×C7⋊C8—21no—
141#6411—28no—
142#6409—24no—
143#6408—28no—
144#6406—24no—
145C2×#575D711yescharacteristic
146#3428—71no—
147C2×#421—71no—
148#2896—71no—
149C2×#410—71no—
150#1905—74no—
151#1904—74no—
152C2×#344—71no—
153C2×H(3,ℤ/4)—71no—
154C24×C7—21no—
155C24×C7—21no—
156C24×C7C2×D411yescharacteristic
157C7×#41—22no—
158C7×#41—22no—
159C7×#41—22no—
160C7×#41—22no—
161C7×#41—22no—
162C7×#41—22no—
163C7×#41—22no—
164C7×#41—22no—
165C7×#41—22no—
166C7×#41—22no—
167C7×#41—22no—
168C7×#41—22no—
169C7×#41—22no—
170C7×#41—22no—
171C7×#41—22no—
172C7×#41—22no—
173C7×#41—22no—
174C7×#41—22no—
175C7×#41—22no—
176C7×#41—22no—
177C7×#41—41no—
178C7×#41—41no—
179C7×#41—41no—
180C7×#41—41no—
181C7×#41—41no—
182C7×#41—41no—
183C7×#41—41no—
184C7×#41—41no—
185C7×#41C22⋊C414yes—
186C7×#41C22⋊C414yes—
187C7×#41C22⋊C414yes—
188C7×#41C22⋊C414yes—
189C2×C7×Q8—21no—
190C2×C7×Q8—21no—
191C2×C7×Q8—21no—
192C2×C7×Q8—21no—
193C2×C7×Q8—21no—
194C2×C7×Q8—21no—
195C2×C7×Q8—21no—
196C2×C7×Q8—21no—
197C2×C7×Q8C22×C412yes—
198C2×C7×Q8C22×C412yes—
199C2×C7×Q8C2×D412yes—
200C2×C7×Q8C2×D412yes—
201C2×C7×D4—22no—
202C2×C7×D4—22no—
203C2×C7×D4—22no—
204C2×C7×D4—22no—
205C2×C7×D4—22no—
206C2×C7×D4—22no—
207C2×C7×D4—22no—
208C2×C7×D4—22no—
209C2×C7×D4—21no—
210C2×C7×D4—21no—
211C2×C7×D4—21no—
212C2×C7×D4—21no—
213C2×C7×D4—21no—
214C2×C7×D4—21no—
215C2×C7×D4—21no—
216C2×C7×D4—21no—
217C2×C7×D4—41no—
218C2×C7×D4—41no—
219C2×C7×D4—41no—
220C2×C7×D4—41no—
221C2×C7×D4C22×C412yes—
222C2×C7×D4C22×C412yes—
223C2×C7×D4C2×D412yes—
224C2×C7×D4C2×D412yes—
225C22×C4×C7—21no—
226C22×C4×C7—22no—
227C22×C4×C7—22no—
228C22×C4×C7—22no—
229C22×C4×C7—22no—
230C22×C4×C7—22no—
231C22×C4×C7—22no—
232C22×C4×C7—21no—
233C22×C4×C7—22no—
234C22×C4×C7—22no—
235C22×C4×C7—41no—
236C22×C4×C7—41no—
237C22×C4×C7—41no—
238C22×C4×C7—41no—
239C22×C4×C7C22×C411yescharacteristic
240C22×C4×C7C22×C411yescharacteristic
241C22×C4×C7C2×D411yescharacteristic
242C22×C4×C7C2×D411yescharacteristic
243C22×C4×C7C2×D411yescharacteristic
244C22×C4×C7C2×D411yescharacteristic
245C22×C4×C7C2×D411yescharacteristic
246C22×C4×C7C2×D411yescharacteristic
247C22×C4×C7C2×D411yescharacteristic
248C22×C4×C7#4111yescharacteristic
249C22×C4×C7#4111yescharacteristic
250C22×C4×C7#4111yescharacteristic
251C22×C4×C7#4111yescharacteristic
252C22×C4×C7C2411yescharacteristic
253C22×Dic7—28no—
254C22×Dic7—22no—
255C22×Dic7—22no—
256C22×Dic7—41no—
257C7×Q16—28no—
258C7×SD16—28no—
259C7×SD16—28no—
260C7×D8—28no—
261C7×M16—22no—
262C7×M16—22no—
263C7×M16—22no—
264C7×M16—22no—
265C2×C7×C8—22no—
266C2×C7×C8—22no—
267C2×C7×C8C22×C414yes—
268C22⋊Dic7—28no—
269C22⋊Dic7—22no—
270C22⋊Dic7—22no—
271C22⋊Dic7—22no—
272C22⋊Dic7—22no—
273C22⋊Dic7—41no—
274C22⋊Dic7C2×D414yes—
275C4⋊Dic7—28no—
276C4⋊Dic7—22no—
277C4⋊Dic7—22no—
278C4⋊Dic7—22no—
279C4⋊Dic7—22no—
280C4⋊Dic7—22no—
281C4⋊Dic7—41no—
282C4×Dic7—28no—
283C4×Dic7—22no—
284C4×Dic7—22no—
285C4×Dic7—22no—
286C4×Dic7—22no—
287C4×Dic7—41no—
288C4×Dic7C2×D414yes—
289#1136—22no—
290#1136—22no—
291#1136—41no—
292#1136—41no—
293C2×C7⋊C8—22no—
294C2×C7⋊C8—41no—
295C2×C7⋊C8—41no—
296C22×#41C2×D711yescharacteristic
297C22×#41C2×D711yescharacteristic
298#575—22no—
299#575—22no—
300#575—22no—
301#575—22no—
302C2×#137Dic712yescomplemented
303C2×#137C2×D712yes—
304C2×AGL(1,ℤ/8)Dic712yescomplemented
305C2×AGL(1,ℤ/8)C2×D712yes—
306C2×#135Dic714yescomplemented
307C22×M16—71no—
308C22×M16C2×D711yescharacteristic
309#520—142no—
310#520—142no—
311#519—72no—
312#518—72no—
313#518—142no—
314C4×#41—142no—
315C4×#41—142no—
316C2×#117—71no—
317C2×#117—71no—
318C2×#117—71no—
319C2×#117—142no—
320#421—74no—
321#421—142no—
322C2×#104—142no—
323#419—72no—
324#418—72no—
325#417—142no—
326#416—142no—
327#410—74no—
328#410—142no—
329C2×#99—142no—
330#344—74no—
331H(3,ℤ/4)—74no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7—22no—
336C23×C7—41no—
337C23×C7—41no—
338C23×C7—81no—
339C23×C7—82no—
340C23×C7—82no—
341C23×C7C4×D411yescharacteristic
342C23×C7C4×D411yescharacteristic
343C23×C7#12011yescharacteristic
344C23×C7#12011yescharacteristic
345C23×C7#12111yescharacteristic
346C23×C7#12111yescharacteristic
347C23×C7C22×D411yescharacteristic
348C7×Q8—22no—
349C7×Q8—22no—
350C7×Q8—22no—
351C7×Q8—22no—
352C7×Q8—22no—
353C7×Q8—41no—
354C7×Q8—41no—
355C7×Q8C2×C22⋊C414yes—
356C7×D4—24no—
357C7×D4—24no—
358C7×D4—24no—
359C7×D4—24no—
360C7×D4—22no—
361C7×D4—22no—
362C7×D4—22no—
363C7×D4—22no—
364C7×D4—22no—
365C7×D4—42no—
366C7×D4—42no—
367C7×D4—42no—
368C7×D4—42no—
369C7×D4—41no—
370C7×D4—41no—
371C7×D4C2×C22⋊C414yes—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—24no—
376C2×C4×C7—24no—
377C2×C4×C7—24no—
378C2×C4×C7—24no—
379C2×C4×C7—22no—
380C2×C4×C7—41no—
381C2×C4×C7—41no—
382C2×C4×C7—42no—
383C2×C4×C7—42no—
384C2×C4×C7—42no—
385C2×C4×C7—42no—
386C2×C4×C7C2×C22⋊C411yescharacteristic
387C2×C4×C7C2×C22⋊C411yescharacteristic
388C2×C4×C7C2×C22⋊C411yescharacteristic
389C2×C4×C7C2×C22⋊C411yescharacteristic
390C2×C4×C7C4×D411yescharacteristic
391C2×C4×C7C4×D411yescharacteristic
392C2×C4×C7C4×D411yescharacteristic
393C2×C4×C7C4×D411yescharacteristic
394C2×C4×C7C4×D411yescharacteristic
395C2×C4×C7C4×D411yescharacteristic
396C2×C4×C7#12011yescharacteristic
397C2×C4×C7#12011yescharacteristic
398C2×C4×C7#12111yescharacteristic
399C2×C4×C7#12111yescharacteristic
400C2×C4×C7#12111yescharacteristic
401C2×C4×C7#12111yescharacteristic
402C2×C4×C7#12111yescharacteristic
403C2×C4×C7#12111yescharacteristic
404C2×C4×C7#12311yescharacteristic
405C2×C4×C7#12311yescharacteristic
406C2×C4×C7#12311yescharacteristic
407C2×C4×C7#12311yescharacteristic
408C2×C4×C7C23×C411yescharacteristic
409C2×C4×C7C22×D411yescharacteristic
410C2×C4×C7C22×D411yescharacteristic
411C2×C4×C7C22×D411yescharacteristic
412C2×C4×C7C2×#4111yescharacteristic
413C2×C4×C7C2×#4111yescharacteristic
414C2×Dic7—24no—
415C2×Dic7—24no—
416C2×Dic7—42no—
417C2×Dic7—82no—
418C2×Dic7—82no—
419C2×Dic7—88no—
420C2×Dic7—82no—
421C7×C8—24no—
422C7⋊C8—42no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41—21no—
426C2×#41—21no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—21no—
435C2×#41—21no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41—21no—
439C2×#41C2×Dic712yes—
440C2×#41C2×Dic712yes—
441C2×#41C2×Dic712yescomplemented
442C2×#41C22⋊D712yes—
443C2×#41C22⋊D712yes—
444C2×#41C22⋊D712yes—
445C2×#41C22⋊D712yes—
446C2×#41C22×D712yes—
447C22×Q8C2×Dic711yescharacteristic, complemented
448C22×Q8C22×D711yescharacteristic
449C22×D4—21no—
450C22×D4—21no—
451C22×D4C2×Dic711yescharacteristic, complemented
452C22×D4C22×D711yescharacteristic
453C23×C4—21no—
454C23×C4—21no—
455C23×C4C22×D711yescharacteristic
456#137—24no—
457#137—24no—
458#137—24no—
459#137—24no—
460AGL(1,ℤ/8)—24no—
461AGL(1,ℤ/8)—24no—
462AGL(1,ℤ/8)—24no—
463AGL(1,ℤ/8)—24no—
464#135—28no—
465#135—28no—
466C2×Q16C2×Dic714yescomplemented
467C2×SD16C2×Dic714yescomplemented
468C2×SD16C2×Dic714yescomplemented
469C2×D8C2×Dic714yescomplemented
470C2×M16—21no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—21no—
474C2×M16—72no—
475C2×M16—141no—
476C2×M16—141no—
477C2×M16—141no—
478C2×M16—141no—
479C2×M16—141no—
480C2×M16C2×Dic712yescomplemented
481C2×M16C22×D712yes—
482C22×C8—141no—
483C22×C8C2×Dic712yescomplemented
484C4×Q8—144no—
485C4×Q8—144no—
486C4×D4—144no—
487C4×D4—148no—
488C4×D4—148no—
489C4×D4—144no—
490#117—72no—
491#117—72no—
492#117—72no—
493#117—72no—
494#117—72no—
495#117—144no—
496#117—144no—
497#117—144no—
498#117—141no—
499#117—141no—
500#117—141no—
501#117—141no—
502#117—141no—
503#117—141no—
504#117—141no—
505C2×C4⋊C4—144no—
506C2×C4⋊C4—141no—
507C2×C4⋊C4—141no—
508C2×C4⋊C4—141no—
509C2×C22⋊C4—72no—
510C2×C22⋊C4—144no—
511C2×C22⋊C4—141no—
512C2×C22⋊C4—141no—
513C2×C42—72no—
514C2×C42—144no—
515C2×C42—141no—
516C2×C42—141no—
517#104—148no—
518#103—144no—
519#102—144no—
520#99—148no—
521C22×C7—24no—
522C22×C7—41no—
523C22×C7—41no—
524C22×C7—41no—
525C22×C7—41no—
526C22×C7—41no—
527C22×C7—41no—
528C22×C7—41no—
529C22×C7—44no—
530C22×C7—42no—
531C22×C7—82no—
532C22×C7—82no—
533C22×C7—82no—
534C22×C7—82no—
535C22×C7—82no—
536C22×C7#38611yescharacteristic
537C22×C7#38611yescharacteristic
538C22×C7#38611yescharacteristic
539C22×C7#38611yescharacteristic
540C22×C7C2×C4×D411yescharacteristic
541C22×C7C2×#12011yescharacteristic
542C22×C7C2×#12111yescharacteristic
543C4×C7—24no—
544C4×C7—42no—
545C4×C7#38611yescharacteristic
546C4×C7#38611yescharacteristic
547C4×C7#38611yescharacteristic
548C4×C7#38611yescharacteristic
549C4×C7C22×C22⋊C411yescharacteristic
550C4×C7C2×C4×D411yescharacteristic
551C4×C7C2×#12111yescharacteristic
552C4×C7C2×#12311yescharacteristic
553Dic7—44no—
554Dic7—44no—
555Dic7—82no—
556C24—21no—
557C24—21no—
558C24D4×D711yescharacteristic
559#41—22no—
560#41—22no—
561#41—22no—
562#41—22no—
563#41—22no—
564#41—22no—
565#41—22no—
566#41—22no—
567#41—22no—
568#41—22no—
569#41—22no—
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—22no—
577#41—22no—
578#41—22no—
579#41—41no—
580#41—41no—
581#41—41no—
582#41—41no—
583#41—41no—
584#41—41no—
585#41—41no—
586#41—41no—
587#41C22⋊Dic714yes—
588#41C22⋊Dic714yes—
589#41C22⋊Dic714yes—
590#41C22⋊Dic714yes—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8C22×Dic712yes—
600C2×Q8C22×Dic712yes—
601C2×Q8C2×C22⋊D712yes—
602C2×Q8C2×C22⋊D712yes—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4C22×Dic712yes—
624C2×D4C22×Dic712yes—
625C2×D4C2×C22⋊D712yes—
626C2×D4C2×C22⋊D712yes—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—148no—
642C22×C4—142no—
643C22×C4—142no—
644C22×C4—281no—
645C22×C4D4×D711yescharacteristic
646C22×C4D4×D711yescharacteristic
647C22×C4D4×D711yescharacteristic
648C22×C4#115911yescharacteristic
649C22×C4#115911yescharacteristic
650C22×C4#115911yescharacteristic
651C22×C4#115911yescharacteristic
652C22×C4C22×Dic711yescharacteristic
653C22×C4C22×Dic711yescharacteristic
654C22×C4C2×C22⋊D711yescharacteristic
655C22×C4C2×C22⋊D711yescharacteristic
656C22×C4C2×C22⋊D711yescharacteristic
657C22×C4C2×C22⋊D711yescharacteristic
658C22×C4C23×D711yescharacteristic
659Q16—28no—
660SD16—28no—
661SD16—28no—
662D8—28no—
663M16—22no—
664M16—22no—
665M16—22no—
666M16—22no—
667M16—142no—
668M16—142no—
669M16—281no—
670M16—281no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—142no—
674C2×C8—281no—
675C2×C8—281no—
676C2×C8C22×Dic714yes—
677C4⋊C4—148no—
678C4⋊C4—142no—
679C4⋊C4—142no—
680C4⋊C4—142no—
681C4⋊C4—142no—
682C4⋊C4—142no—
683C4⋊C4—281no—
684C22⋊C4—74no—
685C22⋊C4—148no—
686C22⋊C4—142no—
687C22⋊C4—142no—
688C22⋊C4—142no—
689C22⋊C4—142no—
690C22⋊C4—281no—
691C42—74no—
692C42—148no—
693C42—142no—
694C42—142no—
695C42—142no—
696C42—142no—
697C42—281no—
698C2×C7—21no—
699C2×C7—21no—
700C2×C7—21no—
701C2×C7—21no—
702C2×C7—21no—
703C2×C7—21no—
704C2×C7—21no—
705C2×C7—44no—
706C2×C7—82no—
707C2×C7C2×#38611yescharacteristic
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—41no—
713C23—41no—
714C23—81no—
715C23—82no—
716C23—82no—
717C23D4×Dic711yescharacteristic
718C23D4×Dic711yescharacteristic
719C23#650011yescharacteristic
720C23#650011yescharacteristic
721C23#650211yescharacteristic
722C23#650211yescharacteristic
723C23C2×D4×D711yescharacteristic
724Q8—22no—
725Q8—22no—
726Q8—22no—
727Q8—22no—
728Q8—22no—
729Q8—41no—
730Q8—41no—
731Q8C2×C22⋊Dic714yes—
732D4—24no—
733D4—24no—
734D4—24no—
735D4—24no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—42no—
742D4—42no—
743D4—42no—
744D4—42no—
745D4—41no—
746D4—41no—
747D4C2×C22⋊Dic714yes—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—144no—
763C2×C4—144no—
764C2×C4—282no—
765C2×C4—562no—
766C2×C4—562no—
767C2×C4—568no—
768C2×C4—562no—
769C2×C4D4×Dic711yescharacteristic
770C2×C4D4×Dic711yescharacteristic
771C2×C4D4×Dic711yescharacteristic
772C2×C4D4×Dic711yescharacteristic
773C2×C4D4×Dic711yescharacteristic
774C2×C4D4×Dic711yescharacteristic
775C2×C4#649811yescharacteristic
776C2×C4#649811yescharacteristic
777C2×C4#649811yescharacteristic
778C2×C4#649811yescharacteristic
779C2×C4#650011yescharacteristic
780C2×C4#650011yescharacteristic
781C2×C4#650211yescharacteristic
782C2×C4#650211yescharacteristic
783C2×C4#650211yescharacteristic
784C2×C4#650211yescharacteristic
785C2×C4#650211yescharacteristic
786C2×C4#650211yescharacteristic
787C2×C4C2×C22⋊Dic711yescharacteristic
788C2×C4C2×C22⋊Dic711yescharacteristic
789C2×C4C2×C22⋊Dic711yescharacteristic
790C2×C4C2×C22⋊Dic711yescharacteristic
791C2×C4C2×D4×D711yescharacteristic
792C2×C4C2×#115911yescharacteristic
793C2×C4C2×#115911yescharacteristic
794C2×C4C23×Dic711yescharacteristic
795C2×C4C22×C22⋊D711yescharacteristic
796C2×C4C22×C22⋊D711yescharacteristic
797C8—24no—
798C8—282no—
799C7#2099811yescharacteristic, complemented, Sylow
800C22—24no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—44no—
809C22—42no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22—82no—
815C22#8999211yescharacteristic
816C22#8999211yescharacteristic
817C22#8999211yescharacteristic
818C22#8999211yescharacteristic
819C22C2×D4×Dic711yescharacteristic
820C22C2×#650011yescharacteristic
821C22C2×#650211yescharacteristic
822C4—24no—
823C4—42no—
824C4—284no—
825C4—284no—
826C4—562no—
827C4#8999211yescharacteristic
828C4#8999211yescharacteristic
829C4#8999211yescharacteristic
830C4#8999211yescharacteristic
831C4C2×D4×Dic711yescharacteristic
832C4C2×#649811yescharacteristic
833C4C2×#650211yescharacteristic
834C4C22×C22⋊Dic711yescharacteristic
835C2—21no—
836C2—21no—
837C2—21no—
838C2—21no—
839C2—21no—
840C2—21no—
841C2—21no—
842C2—44no—
843C2—82no—
844C2C2×#8999211yescharacteristic
subgroupG/H
centerC4#89992
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
Fitting, prime radicalC2×C7×#575C2
socleC2×C7C2×#386
cosocleC22×C4×C7C24
hypercenterC2×#575D7
hypocenterC7#20998
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
2. #11744328C2semidirect
3. C2×#90012C2semidirect
4. C2×#90008C2semidirect
5. #11741517C2semidirect
6. #11729855C2semidirect
7. #11729843C2semidirect
8. C2×#89351C2semidirect
9. C2×#89352C2semidirect
16. C2×C7×#137C4semidirect
18. C2×C7×AGL(1,ℤ/8)C4semidirect
20. C2×C7×#135C4semidirect
26. #90503C22semidirect
28. #90489C22semidirect
41. #89997C22semidirect
43. #89987C22semidirect
44. #89352C22semidirect
45. #89351C22semidirect
65. C2×C7×#41C2×C4semidirect
71. C22×C7×Q8C2×C4semidirect
75. C22×C7×D4C2×C4semidirect
90. C2×C7×Q16C2×C4semidirect
91. C2×C7×SD16C2×C4semidirect
92. C2×C7×SD16C2×C4semidirect
93. C2×C7×D8C2×C4semidirect
98. C2×C7×M16C2×C4semidirect
100. C22×C7×C8C2×C4semidirect
302. C2×#137Dic7semidirect
304. C2×AGL(1,ℤ/8)Dic7semidirect
306. C2×#135Dic7semidirect
441. C2×#41C2×Dic7semidirect
447. C22×Q8C2×Dic7semidirect
451. C22×D4C2×Dic7semidirect
466. C2×Q16C2×Dic7semidirect
467. C2×SD16C2×Dic7semidirect
468. C2×SD16C2×Dic7semidirect
469. C2×D8C2×Dic7semidirect
480. C2×M16C2×Dic7semidirect
483. C22×C8C2×Dic7semidirect
799. C7#20998semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5752
#117443282
C2×#900122
C2×#900082
#117415172
#117298552
#117298432
C2×#893512
C2×#893522
#209987