Finite Group Databasebeta

← #14218065

Subgroups — #14218065

Order 1792.

2650 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C7×2−1+4C211yesmaximal, characteristic, complemented
2C2×#90529C211yesmaximal, characteristic
3C4×#6554C211yesmaximal, characteristic, complemented
4#11741556C211yesmaximal, characteristic, complemented
5#11740016C213yesmaximal, complemented
6#11740015C211yesmaximal, characteristic, complemented
7#11740006C211yesmaximal, characteristic, complemented
8#11740003C213yesmaximal, complemented
9#11739994C213yesmaximal, complemented
10#11739992C213yesmaximal, complemented
11C4×#6514C213yesmaximal, complemented
12#11739956C211yesmaximal, characteristic, complemented
13#11739951C213yesmaximal, complemented
14C4×#6505C213yesmaximal, complemented
15C2×#89802C213yesmaximal, complemented
16C2×C7×2−1+4C2211yescharacteristic
17C2×#6554C2211yescharacteristic
18C7×#520—23no—
19C7×#520C2213yes—
20C7×#520C2211yescharacteristic
21C7×#519—21no—
22C7×#519C2213yes—
23C4×C7×#41—23no—
24C4×C7×#41C2213yes—
25C4×C7×#41C2211yescharacteristic
26C2×C4×C7×Q8—21no—
27C2×C4×C7×Q8C2213yes—
28#90529C4116yescomplemented
29#90518C2211yescharacteristic
30C2×#6514C2213yes—
31C2×#6513C2213yes—
32C2×#6511C2211yescharacteristic
33C2×#6511C2211yescharacteristic
34C22×#1144C2213yes—
35C2×#6505C2213yes—
36#90263—21no—
37C4×Q8×D7—21no—
38#90237—23no—
39C4×#1159—23no—
40#90214C2213yes—
41#90207C2213yes—
42C4×#1157C2213yes—
43C2×C4×Dic14C2213yes—
44#90005C2213yes—
45#90004C2213yes—
46#89997C2213yes—
47C2×#6409C2213yes—
48#89802C2213yes—
49#89802C2213yes—
50#89802C2216yes—
51#89802C2216yes—
52#89802C2216yes—
53C4×#1144C2216yes—
54C4×#1144C2216yes—
55#89798C2213yes—
56#89798C2213yes—
57C4×#1143C2216yes—
58#89790C2213yes—
59#89790C2213yes—
60C4×#1142C2216yes—
61#89786C2211yescharacteristic
62#89786C2213yes—
63#89776C2213yes—
64#89774C2213yes—
65#89770C2213yes—
66#89769C2213yes—
67#89769C2213yes—
68#89767C2213yes—
69C2×#6384C2213yes—
70#89738C2213yes—
71#89736C2213yes—
72C2×#6382C2213yes—
73C4×#1136C2213yes—
74C2×#6377C2213yes—
75#60175—71nomaximal, Sylow
76C7×2−1+4—24no—
77C7×2−1+4C2×C418yescomplemented
78C2×C7×#41—23no—
79C2×C7×#41C2313yes—
80C2×C7×#41C2311yescharacteristic
81C22×C7×Q8—21no—
82C22×C7×Q8C2313yes—
83#6554—24no—
84#6554C2×C418yescomplemented
85C2×Q8×D7—21no—
86C2×#1159—23no—
87C2×#1157C2313yes—
88C22×Dic14C2313yes—
89C4×C7×Q8—21no—
90C4×C7×Q8—23no—
91C4×C7×Q8—23no—
92C4×C7×Q8—23no—
93C4×C7×Q8—23no—
94C4×C7×Q8D411yescharacteristic
95C4×C7×Q8D411yescharacteristic
96C4×C7×Q8C2313yes—
97C4×C7×Q8C2316yes—
98C4×C7×Q8C2313yes—
99C4×C7×D4—23no—
100C4×C7×D4—23no—
101C4×C7×D4—23no—
102C4×C7×D4—26no—
103C4×C7×D4D413yes—
104C4×C7×D4D413yes—
105C4×C7×D4C2311yescharacteristic
106C4×C7×D4C2313yes—
107C7×#117—23no—
108C7×#117—26no—
109C7×#117—23no—
110C7×#117C2313yes—
111C7×#117C2313yes—
112C2×C7×C4⋊C4—23no—
113C2×C7×C4⋊C4—23no—
114C2×C7×C4⋊C4C2313yes—
115C2×C42×C7—23no—
116C2×C42×C7—23no—
117C2×C42×C7C2313yes—
118#6514C2×C4124yescomplemented
119#6513C2×C4124yescomplemented
120#6511—24no—
121#6511C2×C418yescomplemented
122Q8×Dic7—21no—
123C2×#1144C2×C4124yescomplemented
124C2×#1144C2316yes—
125C2×#1144C2313yes—
126#6505C2×C4124yescomplemented
127C2×#1143C2313yes—
128D4×Dic7—23no—
129C2×#1142C2313yes—
130C2×#1141C2311yescharacteristic
131C4×C22⋊D7—23no—
132C4×C22⋊D7—23no—
133#6489C2313yes—
134C2×C4⋊Dic7C2313yes—
135C2×Dic7⋊C4—23no—
136C2×C4×Dic7—23no—
137C2×#1136C2313yes—
138C2×#1136C2313yes—
139C22×C7⋊C8C2313yes—
140C22×C7⋊C8C2313yes—
141#6455—23no—
142D7×C4⋊C4—23no—
143#6450—23no—
144#6450—23no—
145(C22⋊D7)⋊C4—26no—
146#6440—26no—
147C4×D28C2311yescharacteristic
148C4×D28C2313yes—
149#6435—23no—
150C42×D7—23no—
151C4×Dic14—23no—
152C4×Dic14—23no—
153C4×Dic14C2313yes—
154C4×Dic14C2316yes—
155C4×Dic14C2313yes—
156#6409C2313yes—
157#6409C2316yes—
158#6409C2313yes—
159#6406C2313yes—
160#6406C2311yescharacteristic
161#6384C2316yes—
162#6384C2313yes—
163#6384C2313yes—
164#6383C2313yes—
165#6383C2311yescharacteristic
166#6382C2313yes—
167#6382C2316yes—
168#6382C2311yescharacteristic
169#6381C2313yes—
170#6381C2313yes—
171#6377C2311yescharacteristic
172#6377C2313yes—
173#6377C2313yes—
174#6377C2313yes—
175C4×C7⋊C8C2316yes—
176C2×#578—71no—
177C4×2−1+4—71no—
178C4×2−1+4D711yescharacteristic, complemented
179#2952—73no—
180#2950—73no—
181#2947—73no—
182#2947—73no—
183C4×#137—73no—
184C4×#137—73no—
185#2943—73no—
186C2×#441—73no—
187#2912—71no—
188#2898—71no—
189#2898—71no—
190#2875—71no—
191C7×#41—224no—
192C7×#41—26no—
193C7×#41C22×C4112yes—
194C7×#41C22×C414yes—
195C7×#41#4114yes—
196C2×C7×Q8—28no—
197C2×C7×Q8—23no—
198C2×C7×Q8—26no—
199C2×C7×Q8C22×C4112yes—
200C2×C7×Q8C2×D411yescharacteristic
201C2×C7×Q8C2413yes—
202C2×C7×D4—23no—
203C2×C7×D4C2×D413yes—
204C2×C7×D4C2411yescharacteristic
205C22×C4×C7—23no—
206C22×C4×C7—23no—
207C22×C4×C7—23no—
208C22×C4×C7—21no—
209C22×C4×C7—23no—
210C22×C4×C7C2×D413yes—
211C22×C4×C7C2×D413yes—
212C22×C4×C7C2413yes—
213C2×C22⋊D7—23no—
214C22×Dic7—23no—
215C22×Dic7—23no—
216Q8×D7—28no—
217#1159—224no—
218#1157—26no—
219#1157C22×C4112yes—
220C2×D28C2411yescharacteristic
221C2×C4×D7—23no—
222C2×C4×D7—21no—
223C2×C4×D7—23no—
224C2×Dic14—23no—
225C2×Dic14—26no—
226C2×Dic14C22×C4112yes—
227C2×Dic14C2413yes—
228C7×C4⋊C4—23no—
229C7×C4⋊C4—26no—
230C7×C4⋊C4—23no—
231C7×C4⋊C4—23no—
232C7×C4⋊C4C2×D413yes—
233C7×C4⋊C4C2×D413yes—
234C7×C4⋊C4C2413yes—
235C7×C4⋊C4C2411yescharacteristic
236C7×C22⋊C4—23no—
237C7×C22⋊C4—21no—
238C7×C22⋊C4—23no—
239C7×C22⋊C4C2×D416yes—
240C42×C7—23no—
241C42×C7—23no—
242C42×C7—26no—
243C42×C7—23no—
244C42×C7C2×D413yes—
245C42×C7C2×D413yes—
246C42×C7C2411yescharacteristic
247C42×C7C2413yes—
248C22⋊Dic7—23no—
249#1144C22×C4124yes—
250#1144C22×C4112yes—
251#1143C22×C4112yes—
252#1142C22×C4112yes—
253#1141C22×C414yes—
254(C2×D7)⋊C4—21no—
255(C2×D7)⋊C4—23no—
256C4⋊Dic7—23no—
257C4⋊Dic7C2413yes—
258C4⋊Dic7C2411yescharacteristic
259Dic7⋊C4—23no—
260Dic7⋊C4—26no—
261Dic7⋊C4—23no—
262C4×Dic7—23no—
263C4×Dic7—26no—
264C4×Dic7—23no—
265C4×Dic7—23no—
266#1136—26no—
267#1136C22×C4112yes—
268C2×C7⋊C8—26no—
269C2×C7⋊C8C22×C4112yes—
270C2×C7⋊C8C2411yescharacteristic
271C2×C7⋊C8C2413yes—
272C2×C7⋊C8C2411yescharacteristic
273C2×C7⋊C8C2413yes—
274C2×2−1+4—71no—
275C2×2−1+4C2×D711yescharacteristic
276#578—716no—
277C2×#137—73no—
278C2×#137—73no—
279C2×#135—73no—
280C22×Q16—73no—
281C2×#131—71no—
282C2×#131—71no—
283#520—23no—
284#520—71no—
285#520—73no—
286#520—143no—
287#520C2×D713yes—
288#520C2×D711yescharacteristic
289#519—21no—
290#519—73no—
291#519—141no—
292#519C2×D713yes—
293C4×#41—23no—
294C4×#41—73no—
295C4×#41—143no—
296C4×#41C2×D713yes—
297C4×#41C2×D711yescharacteristic
298C2×C4×Q8—21no—
299C2×C4×Q8—73no—
300C2×C4×Q8—141no—
301C2×C4×Q8C2×D713yes—
302#442—71no—
303#442—73no—
304#441—73no—
305#441—76no—
306#441—76no—
307#441—76no—
308#441—73no—
309#440—73no—
310#440—73no—
311#440—73no—
312#440—73no—
313C4×Q16—76no—
314C4×Q16—76no—
315C4×SD16—76no—
316C4×SD16—76no—
317#428—73no—
318#428—73no—
319#427—73no—
320C2×#106—73no—
321#419—73no—
322#419—73no—
323#417—73no—
324#417—73no—
325#416—73no—
326#416—73no—
327C2×#103—73no—
328C2×#103—73no—
329#405—73no—
330#405—73no—
331C4×M16—73no—
332C2×#97—73no—
333C23×C7—21no—
334C23×C7C22×D413yes—
335C22×D7—21no—
336C7×Q8—212no—
337C7×Q8—23no—
338C7×Q8C4×D414yes—
339C7×Q8C23×C416yes—
340C7×D4—212no—
341C7×D4—21no—
342C7×D4C4×D4112yes—
343C7×D4C23×C412yes—
344C2×C4×C7—212no—
345C2×C4×C7—23no—
346C2×C4×C7—212no—
347C2×C4×C7—21no—
348C2×C4×C7—23no—
349C2×C4×C7—43no—
350C2×C4×C7—43no—
351C2×C4×C7—42no—
352C2×C4×C7—83no—
353C2×C4×C7—83no—
354C2×C4×C7C23×C416yes—
355C2×C4×C7C22×D411yescharacteristic
356C2×C4×C7C22×D413yes—
357C2×C4×C7C22×D413yes—
358C2×C4×C7C22×D411yescharacteristic
359C2×C4×C7C22×D413yes—
360C2×C4×C7C2×#4116yes—
361C2×C4×C7C2511yescharacteristic
362C22⋊D7—212no—
363C2×Dic7—212no—
364C2×Dic7—23no—
365C2×Dic7—21no—
366C2×Dic7—23no—
367C2×Dic7—83no—
368D28—21no—
369D28C23×C412yes—
370C4×D7—212no—
371C4×D7—42no—
372C4×D7—83no—
373Dic14—212no—
374Dic14—23no—
375Dic14C23×C416yes—
376C7⋊C8—21no—
377C7⋊C8—23no—
378C7⋊C8C23×C412yes—
379C7⋊C8C23×C416yes—
3802−1+4—24no—
3812−1+4—78no—
3822−1+4—144no—
3832−1+4C4×D718yescomplemented
384C2×#41—23no—
385C2×#41—73no—
386C2×#41—143no—
387C2×#41C22×D713yes—
388C2×#41C22×D711yescharacteristic
389C22×Q8—21no—
390C22×Q8—73no—
391C22×Q8—141no—
392C22×Q8C22×D713yes—
393#137—724no—
394#137—724no—
395#135—724no—
396C2×Q16—724no—
397C2×Q16—73no—
398C2×Q16—76no—
399C2×SD16—73no—
400C2×SD16—73no—
401C2×D8—71no—
402#131—78no—
403#131—144no—
404C2×M16—73no—
405C2×M16—73no—
406C22×C8—73no—
407C22×C8—73no—
408C4×Q8—21no—
409C4×Q8—23no—
410C4×Q8—23no—
411C4×Q8—23no—
412C4×Q8—23no—
413C4×Q8—73no—
414C4×Q8—76no—
415C4×Q8—73no—
416C4×Q8—141no—
417C4×Q8—143no—
418C4×Q8—143no—
419C4×Q8—143no—
420C4×Q8—143no—
421C4×Q8C22⋊D711yescharacteristic
422C4×Q8C22⋊D711yescharacteristic
423C4×Q8C22×D713yes—
424C4×Q8C22×D716yes—
425C4×Q8C22×D713yes—
426C4×D4—23no—
427C4×D4—23no—
428C4×D4—23no—
429C4×D4—26no—
430C4×D4—71no—
431C4×D4—73no—
432C4×D4—143no—
433C4×D4—143no—
434C4×D4—143no—
435C4×D4—146no—
436C4×D4C22⋊D713yes—
437C4×D4C22⋊D713yes—
438C4×D4C22×D711yescharacteristic
439C4×D4C22×D713yes—
440#117—23no—
441#117—26no—
442#117—23no—
443#117—73no—
444#117—143no—
445#117—146no—
446#117—143no—
447#117C22×D713yes—
448#117C22×D713yes—
449C2×C4⋊C4—23no—
450C2×C4⋊C4—23no—
451C2×C4⋊C4—73no—
452C2×C4⋊C4—143no—
453C2×C4⋊C4—143no—
454C2×C4⋊C4C22×D713yes—
455C2×C42—23no—
456C2×C42—23no—
457C2×C42—143no—
458C2×C42—143no—
459C2×C42C22×D713yes—
460#107—73no—
461#107—73no—
462#106—73no—
463#106—76no—
464#106—71no—
465#103—73no—
466#103—76no—
467#103—73no—
468#103—73no—
469#103—76no—
470#103—73no—
471#102—71no—
472#102—73no—
473#102—71no—
474#102—73no—
475#97—71no—
476#97—73no—
477#97—73no—
478#97—73no—
479C4×C8—76no—
480C22×C7—23no—
481C22×C7—23no—
482C22×C7—22no—
483C22×C7—41no—
484C22×C7—41no—
485C22×C7C2×C4×D416yes—
486C22×C7C23×D411yescharacteristic
487C2×D7—22no—
488C2×D7—41no—
489C2×D7—41no—
490C4×C7—21no—
491C4×C7—23no—
492C4×C7—21no—
493C4×C7—23no—
494C4×C7—26no—
495C4×C7—41no—
496C4×C7—43no—
497C4×C7C2×C4×D416yes—
498C4×C7C24×C411yescharacteristic
499C4×C7C22×#4111yescharacteristic
500Dic7—26no—
501Dic7—41no—
502Dic7—43no—
503#41—224no—
504#41—26no—
505#41—712no—
506#41—1424no—
507#41—146no—
508#41C2×C4×D7112yes—
509#41C2×C4×D714yes—
510#41#115714yes—
511C2×Q8—28no—
512C2×Q8—26no—
513C2×Q8—23no—
514C2×Q8—712no—
515C2×Q8—73no—
516C2×Q8—148no—
517C2×Q8—146no—
518C2×Q8—143no—
519C2×Q8C2×C4×D7112yes—
520C2×Q8C2×C22⋊D711yescharacteristic
521C2×Q8C23×D713yes—
522C2×D4—23no—
523C2×D4—71no—
524C2×D4—143no—
525C2×D4C2×C22⋊D713yes—
526C2×D4C23×D711yescharacteristic
527C22×C4—23no—
528C22×C4—23no—
529C22×C4—23no—
530C22×C4—21no—
531C22×C4—23no—
532C22×C4—143no—
533C22×C4—143no—
534C22×C4—143no—
535C22×C4—141no—
536C22×C4—143no—
537C22×C4C2×C22⋊D713yes—
538C22×C4C2×C22⋊D713yes—
539C22×C4C23×D713yes—
540Q16—712no—
541Q16—724no—
542SD16—712no—
543SD16—712no—
544D8—74no—
545M16—712no—
546M16—146no—
547C2×C8—712no—
548C2×C8—73no—
549C2×C8—71no—
550C2×C8—73no—
551C2×C8—71no—
552C2×C8—146no—
553C4⋊C4—26no—
554C4⋊C4—23no—
555C4⋊C4—23no—
556C4⋊C4—23no—
557C4⋊C4—73no—
558C4⋊C4—71no—
559C4⋊C4—143no—
560C4⋊C4—146no—
561C4⋊C4—143no—
562C4⋊C4—143no—
563C4⋊C4C2×C22⋊D713yes—
564C4⋊C4C2×C22⋊D713yes—
565C4⋊C4C23×D713yes—
566C4⋊C4C23×D711yescharacteristic
567C22⋊C4—23no—
568C22⋊C4—21no—
569C22⋊C4—23no—
570C22⋊C4—143no—
571C22⋊C4—141no—
572C22⋊C4—143no—
573C22⋊C4C2×C22⋊D716yes—
574C42—23no—
575C42—23no—
576C42—26no—
577C42—23no—
578C42—143no—
579C42—143no—
580C42—143no—
581C42—146no—
582C42C2×C22⋊D713yes—
583C42C2×C22⋊D713yes—
584C42C23×D713yes—
585C42C23×D711yescharacteristic
586C2×C7—26no—
587C2×C7—42no—
588C2×C7C22×C4×D411yescharacteristic
589C2×C7#358611yescharacteristic
590C2×C7#358611yescharacteristic
591D7—42no—
592C23—21no—
593C23—141no—
594C23C22×C22⋊D713yes—
595Q8—212no—
596Q8—23no—
597Q8—76no—
598Q8—1412no—
599Q8—143no—
600Q8C4×C22⋊D714yes—
601Q8C22×C4×D716yes—
602D4—212no—
603D4—21no—
604D4—72no—
605D4—1412no—
606D4—141no—
607D4C4×C22⋊D7112yes—
608D4C22×C4×D712yes—
609C2×C4—212no—
610C2×C4—23no—
611C2×C4—212no—
612C2×C4—21no—
613C2×C4—23no—
614C2×C4—43no—
615C2×C4—43no—
616C2×C4—42no—
617C2×C4—83no—
618C2×C4—83no—
619C2×C4—1412no—
620C2×C4—143no—
621C2×C4—1412no—
622C2×C4—141no—
623C2×C4—143no—
624C2×C4—282no—
625C2×C4—563no—
626C2×C4—563no—
627C2×C4C22×C4×D716yes—
628C2×C4C2×#115716yes—
629C2×C4C22×C22⋊D711yescharacteristic
630C2×C4C22×C22⋊D713yes—
631C2×C4C22×C22⋊D713yes—
632C2×C4C22×C22⋊D711yescharacteristic
633C2×C4C22×C22⋊D713yes—
634C2×C4C24×D711yescharacteristic
635C8—72no—
636C8—76no—
637C8—141no—
638C8—143no—
639C7#6017511yescharacteristic, complemented, Sylow
640C22—23no—
641C22—23no—
642C22—22no—
643C22—41no—
644C22—41no—
645C22—142no—
646C22—281no—
647C22—281no—
648C22C2×C4×C22⋊D716yes—
649C22C23×C22⋊D711yescharacteristic
650C4—26no—
651C4—21no—
652C4—23no—
653C4—21no—
654C4—23no—
655C4—41no—
656C4—43no—
657C4—146no—
658C4—283no—
659C4—281no—
660C4C2×C4×C22⋊D716yes—
661C4C23×C4×D711yescharacteristic
662C4C22×#115711yescharacteristic
663C2—26no—
664C2—42no—
665C2—282no—
666C2C22×C4×C22⋊D711yescharacteristic
667C2#1174435511yescharacteristic
668C2#1174436711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D7
commutatorC4×C7C24×C4
FrattiniC2×C4C24×D7
FittingC4×C7×2−1+4C2
socleC22×C7C23×D4
prime radicalC2×#90529C2
cosocleC2×C4×C7C25
hypercenterC4×2−1+4D7
hypocenterC7#60175
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C4×#41 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. C4×C7×2−1+4C2semidirect
3. C4×#6554C2semidirect
4. #11741556C2semidirect
5. #11740016C2semidirect
6. #11740015C2semidirect
7. #11740006C2semidirect
8. #11740003C2semidirect
9. #11739994C2semidirect
10. #11739992C2semidirect
11. C4×#6514C2semidirect
12. #11739956C2semidirect
13. #11739951C2semidirect
14. C4×#6505C2semidirect
15. C2×#89802C2semidirect
28. #90529C4semidirect
77. C7×2−1+4C2×C4semidirect
84. #6554C2×C4semidirect
118. #6514C2×C4semidirect
119. #6513C2×C4semidirect
121. #6511C2×C4semidirect
123. C2×#1144C2×C4semidirect
126. #6505C2×C4semidirect
178. C4×2−1+4D7semidirect
383. 2−1+4C4×D7semidirect
639. C7#60175semidirect

Maximal subgroups

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

subgroupindex
C4×C7×2−1+42
C2×#905292
C4×#65542
#117415562
#117400162
#117400152
#117400062
#117400032
#117399942
#117399922
C4×#65142
#117399562
#117399512
C4×#65052
C2×#898022
#601757